THE LIBRARY OF EMIL KUICHLING, C. E. ROCHESTER. NEW YORK THE GIFT OF SARAH L. KUICHLING 1919 QC 21 no*"'*"""'™""'''"'''"''^ ^'SmSm^*^''*^ °" physics, experime 3 1924 005 019 249 The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/cletails/cu31924005019249 TAmiL'E ©ir SlPIE^l'SA. Pii The absorption Spectra 9&/10.are those respectively of Nitrous Acid and Chlorophyl •^AftnA^T. Lint. ELEMENTARY TREATISE ON PHYSICS EXPERIMENTAL AND APPLIED FOR THE USE OF COI,I,EGKS AND SCHOOI^S TRANSLATED FROM GANOT'S ELEMENTS DE PHYSIQUE [with the Authors sanction) BY E. ATKINSON, Ph.D., F.C.S. LATE PROFESSOR OF EXPERIMENTAL SCIENCE IN THE STAFF COLLEGE SIXTEENTH EDITION (1902) EDITED BY A. W. REINOLD, M.A., F.R.S. PROFESSOR OF PHYSICS IN THE ROYAL NAVAL COLLEGE, GREENWICH lUUSTRATED by 9 COLOURED PI, where g' denotes the number 32-1724, or the value of ^ at lat. 45°. Experience teaches that in all cases where a force is exerted there must be two bodies, between which the force acts. Newton's third law of motion asserts that the mutual action of the two bodies is always ecjual and oppositely directed. The attraction of the earth for in pounds of matter is nig, where r is the acceleration of the body. The attraction of the ;« pounds for the earth is yif where M is the mass of the earth in pounds, and / is the acceleration with which it moves towards m. According to the third law of motion M/= mg. If in is a small body, like a few thousand pounds, then, since the mass of the earth is very large, the acceleration of the earth will be inappreciable. —34] Forces acting along the same Line 21 If in and M were equal, / and g would be equal. Remembering that the acceleration is the change per second in the velocity, if the two bodies move towards each other for t seconds, the initial velocities being Vj and V„, and the final velocities Vy and ?',, the above expression becomes M^", - M V, _ 7nv„ — otVj t ' t As / divides out of this equation, it will follow that the two bodies which mutually attract each other will suffer equal changes of momenta in the same time. If the two bodies start from rest at the same instant, so that Vj and Vj are zero, then ■or they will have equal momenta at the same instant. The momenta of a freely suspended rifle and of a bullet fired from it will be equal so long as the ball is in the barrel. If the rifle is supported, the supporting body must be included with the rifle in the value M. 33. Representation of forces. — Draw any straight line AB (fig. 8) and fix on any point O in it. We may suppose a force to act on the point O, .along the line AB, either towards A or B : then O . __„ is called the point of application of the force, AB its line of action ; if it acts towards A, its direction is O A, if towards B, its direction is OB. It is rarely necessary to make the distinc- ,tion between the line of action and direction of a force ; it being very convenient to make the convention that the statement — a force acts on a point O along the line OA — means that it acts from O to A. Let us suppose the force which acts on O along OA to contain P units of force : from O towards A measure ON, containing P units of length, the line ON is said to represent the force. The analogy between the line and the force is very complete ; the line ON is drawn from O in a given direction •OA, and contains a given number of units P, just as the force acts on O in .the direction OA, and contains a given number of units P. It is scarcely necessary to add, that if an equal force were to act on O in the opposite .direction, it would be said to act in the direction OB, and would be repre- sented by OM, equal in magnitude to ON. When we are considering several forces acting along the same line we may indicate their directions by the positive and negative signs. Thus the forces mentioned above would be denoted by the symbols + P and — P respectively. 34. Forces acting along the same line. — If forces act on the point O in the direction OA equal to P and Q units respectively, they are equivalent to .a single force R containing as many units as P and Q together — that is, R = P + Q. If the sign + in the above ecjuation denote algebraical addition, the equation will continue true whether one or both the forces act along OA or OB. It is plain that the same rule can be extended to any number of forces, and if several forces have the same line of action, they are equivalent to one force ■containing the same number of units as their algebraical sum. Thus, if 22 On Matter, Force, and Motion [34- foi-ces of 3 and 4 units act on O in the direction OA, and a force of 8 in the direction OB, they are equi\-alent to a single force containing R units given by the equation R = 3 + 4-8= -i; that is, R is a force containing one unit acting along OB. This force R is called their resultant. If the forces are in equilibrium, R is equal to zero. In this case the forces have equal tendency to move the point O in oppo- site directions. 35. Resultant and components.— In the last article we saw that a single force R could be found equivalent to several others ; this is by no means peculiar to the case in which all the forces have the same line of action ; in fact, when a material point, A (fig. 9), remains in equili- brium under the action of several forces, S, P, Q, it does so because any one of the forces, as S, is capable of neutralising the combined efifects of all the others. If the force S, therefore, had its direction reversed, so as to act along AR, the prolongation of AS, it would produce the same effect as the system of forces P, Q. Now, a force whose effect is equivalent to the combined effects of several other forces is called their resultant, and with respect to this resultant, the other forces are termed components. When the forces P, Q act on a point, they can only have one resultant ; but any single force can be resolved into components in an indefinite number of ways. If a point move from rest, under the action of any number of forces, it will begm to move in the direction of their resultant. 36. Parallelogram of forces. — When two forces act on a point their resultant is found by the following theorem, known as the principle of the parallelogram of forces : — If two forces act on a point, and if lines be drawn from that point representing the forces in magnitude and direction, a?id a parallelogram be constructed on these lines as sides, their resultant will be represented in magnitude and direction by that diagonal which passes through the point. Thus let P and Q (fig. 10) be two forces acting on the point A along AP and AQ respectively, and let AB and AC be taken containing the same number of units of length that P and Q contain units of force ; let the parallelogram ABDC be completed, and the diagonal AD drawn ; then the theorem states that the resultant, R, of P and Q is represented by AD ; that is to say, P and Q together are equal to a single force R acting along the line AD, and containing as many units of force as AD contains units of length. Proofs of this theorem are given in treatises on Mechanics ; we will here give an account of a direct experimental verification of its truth ; but before doing so we must premise an account of a very simple experiment. Let A (fig. 11) be a small pulley, and let it turn on a smooth, hard, and thin axle, with little or no friction ; let W be a weight tied to the end of a fine thread which passes over the pulley ; let a spring CD be attached by one end to the end C of the thread and by the end D to another piece of -36] Parallelogram of Forces thread, the other end of which is fastened to a fixed point B ; a scale CE can be fastened by one end to the point C and pass inside the spring so that the elongation of the spring can be measured. Now it will be found on trial that with a given weight W the elongation of the spring will be the same whatever the angle contained between the parts of the string WA and BA. Fig. lo Fig. II Also it would be found that if the whole were suspended from a fixed point, instead of passing over the pulley, the weight would in this case stretch the string to the same extent as before. This experiment shows that when care is taken to diminish to the utmost the friction of the axle of the pulley, and the imperfect flexibility of the thread, the weight of W is transmitted with- out sensible diminution to B, and exerts on that point a pull or force along the line BA virtually equal to W. This being premised, an experimental proof, or illustration of the paral- lelogram of forces, may be made as follows : — Suppose H and K (fig. 12) to be two pulleys with axles made as smooth and fine as possible ; let P and Q be two weights suspended from fine and flexible threads which, after passing over H and K, are fastened at A to a third thread AL, from which hangs a weight R ; let the three weights come to rest in the positions shown in the figure. Now the point A is acted on by three forces in equilibrium — viz. P from A to H, Q from A to K, and R from A to L ; consequently any one of them must be equal and opposite to the resultant of the other two. Now if we sup- pose the apparatus to be arranged immediately in front of a large slate, we can draw lines upon it coinciding with AH, AK, and AL. If now we measure off along AH the part AB containing as many inches as P contains pounds, and along AK the part AC containing as many inches as Q contains pounds, and complete the parallelo- gram ABDC, it will be found that the diagonal AD is in the same line as AL, and contains as many inches as R weighs pounds. Consequently, the resultant of P and Q is represented by AD. Of course, any other units of length and force might have been employed. Now it will be found that when P, Q, and R are changed in any way whatever, consistent with equilibrium, the same con- struction can be made— the point A will have different positions in the different cases ; but when equilibrium is established, and the parallelogram 24 On Matter, Fotre, and Motion [36- Fig- 13 ABDC is constructed, it will be found that AD is vertical, and contains as many units of length as R contains units of force, and consequently it repre- sents a force equal and opposite to R — that is, it represents the resultant of P and Q. 37. Resultant of any number of forces acting in one plane on a point.— Let the forces P, Q, R, S (fig. 13) act on the point A, and let them be represented by the lines AB, AC, AD, AE, as shown in the figure. First, complete the parallelo- gram ABFC and join AF ; this line represents the resultant of P and Q. Secondly, complete the parallelogram AFGD and join AG ; this line re- presents the resultant of P, Q, R. Thirdly, com- plete the parallelogram ACHE and join AH ; this line represents the resultant of P, Q, R, S. It is manifest that the construction can be extended to any number of forces. A little consideration will show that the line AH might be determined by the following construction : — Through B draw BF parallel to, equal to, and towards the same part as AC ; through F draw FG parallel to, equal to, and towards the same part as AD ; through G draw GH parallel to, equal to, and towards the same part as AE ; join AH, then AH represents the required resultant. 38. Triangle of forces. — If the resultant of the forces is zero, they have no joint tendency to move the point, and consequently are in equilibrium. The case of three forces acting on a point is of such importance that we may give a brief statement of it. Let P, Q, R (fig. 14) be three forces in equilibrium on the point O. From any point B draw BC parallel to and towards the same part as OP, from C draw CA parallel to and towards the same part as OQ, and take CA such that P : Q : : BC : CA ; then on joining AB, the third force R must act along OR parallel to and towards the same part as AB, and must be proportional in magnitude to AB. This construction is frequently called the Triangle of Forces. It is evident that while the sides of the triangle are severally proportional to P, Q, R, the angles A, B, C are supplementary to QOR, ROP, POQ re- spectively ; consequently, every trigonometrical relation existing between the sides and angles of ABC will equally exist between the forces P, Q, R, and the sup- plements of the angles between their directions. Thus in the triangle ABC it is known that the sides are proportional to the sines of the opposite angles ; now, since the sines of the angles are equal to the sines of their supplements, -we at once conclude that when three forces are in equilibrium, each is firopor- tional to the sine of the angle between the directions of the other two. 39. Moments of forces. — Let P (fig. 15) denote any force acting from B to P, take A any point, let fall AN a perpendicular from A on BP. The product of the number of units of force in P, and the number of units of length in AN, is called the moment of P with respect to A. Since the force P can be represented by a straight line, the moment of P can be represented Fig. 14 -40] Composition and Resolution of Parallel Forces 25 by an area. In fact, if BC is the line representing P, the moment is properly represented by twice the area of the triangle ABC. The perpendicular AN is sometimes called the arm of the force. Now if a watch were placed with its face upwards on the paper, the force P would cause the arm AN to turn round A in the contrary direction to the hands of the watch. Under these circumstances, it is usual to con- sider the moment of P with respect to the point A to be positive. If P acted from C to B, it would turn NA in the same direction as the hands of the watch, and now its moment is reckoned negative. It is a simple geometrical consequence of the paral- lelogram of forces (36) that the moment of the resultant equals the sum of the moments of the component forces, regard being had to the signs of the moments. If the point about which the moments are measured be taken in the direc- tion of the resultant, its moment with respect to that point will be zero ; and consequently the sum of the moments with respect to such point will be zero. 40. Composition and resolution of parallel forces. — The case of the equilibrium of three parallel forces is merely a particular case of the equili- brium of three forces acting on a point. In fact, let P and Q be two forces whose directions pass through the points A and B, and intersect in O, fig. 16 ; let them be balanced by a third force R whose direction produced intersects the line AB in C. Now suppose the point O to move along AO, gradually receding from A, the magnitude and direction of R will continually change, and also the point C will continually change its position, but will always lie between A and B. In the limit P and Q become parallel forces acting towards the same part, balanced by a parallel force R acting towards the contrary part through a point X between A and B. The question is : — First, in this limiting case, what is the value of R ; secondly, what is the position of X ? Now with regard to the first point it is plain that if a triangle abc be drawn as m art. 38, the angles a and b in the limit will vanish, and c will become 180°, consequently ab ultimately equals ac-\-cb ; or R = Ph-Q. With regard to the second point, it follows from the last article (39) that the moments of P and Q about C are always equal, whence AX : XB : : Q : P, a proportion which determines the position of X. Hence the following rules for the composition of any ''^ p;^ ^g two parallel forces, viz. — I. When two parallel forces P and Q act towards the same part, at rigidly connected points A and B, their resultant is a parallel force acting towards the same part, equal to their sum, and its direction divides the line AB into two parts AC and CB inversely proportional to the forces P and Q. II. When two parallel forces P and Q, of which P is the greater, act towards contrary parts at rigidly connected points A and B, their R 26 On Matter, Force, and Motion [40- i-esultant is a parallel force acting towards the same part as P, equal to the excess of P over Q, and its direction divides BA produced in a point C such that CA and CB are inversely proportional to P and Q. In each of the above cases if we were to apply R at the point C, in opposite directions to those shown in the figure, it would plainly (by the above theorem) balance P and Q, and therefore when it acts as shown in figs. 17 and 18 it is the resultant of P and Q in those cases respectively. It will, of course, follow that the force R acting at C can be resolved into P and Q acting at A and B respectively. If the second of the above theorems be examined, it will be found that no force R exists equivalent to P and Q when these forces are equal. Two such forces constitute a couple, which may be defined to be two equal parallel forces acting towards contrary parts ; they possess the remarkable property that they are incapable of being balanced by any single force whatsoever. Thus, when a couple is applied to a body, a motion of rotation is pro- duced, not a motion of translation. A compass needle when deflected from the magnetic meridian is acted on by a couple due to the earth's magnetism. Q / Fig. 17 Fig. 18 The needle has no tendency to move away from its place. A couple is re- quired to twist a wire, turn a capstan, &c. In the case of more than two parallel forces the resultant of any two can be found, then of that and a third, and so on to any number ; it can be shown that however great the number of forces they will either be in equili- brium or will reduce to a single resultant or to a couple. 41. Centre of parallel forces. — On referring to figs. 17 and 18, it will be remarked that if we conceive the points A and B to be fixed, and the directions AP and BQ of the forces P and Q to be turned round A and B, so as to continue parallel and to make any angle with their original directions, then the direction of their resultant will continue to pass through C ; that point is therefore called the centre of the parallel forces F and Q. It appears from investigation that whenever a system of parallel forces reduces to a single resultant, those 'forces will have a centre ; that is to say, if we conceive each of the forces to act at a fixed point, there will be a point through which the direction of their resultant will pass when the directions of the forces are turned through any equal angles round their points of application in such a manner as to retain the parallelism of their directions. -43] The Lever 27 The most familiar example of a centre of parallel forces is the case in which the forces are the weights of the parts of a body ; in this case the forces all acting towards the same part will have a resultant, viz. their sum •, and their centre is called the centre of gravity o{ the body. 42. Equality of action and reaction. — We will proceed to e.Kemplify some of the principles now laid down by investigating the conditions of equilibrium of bodies in a few simple cases ; but before doing so we refer again to the law stated in art. 32, which holds good whenever a mutual action is called into play between two bodies. Reaction is always equal and contrary to action : that is to say, the mutual actions of two bodies on each other are always forces equal in amount and opposite in direction, and this is equally true when the bodies are in motion and when they are at rest. A very instructive example of this law has already been given (36), in which the action on the spring CD (fig. 11) is the weight W transmitted by the spring to C, and balanced by the reaction of the ground transmitted from B to D. In these circumstances the spring is said to be stretched by a force W. If the spring were removed, and the thread were continuous from A to B, it is clear that any part of it is stretched by two equal forces, viz. an action and reaction, each equal to W, and the thread is said to sustain a tension W. When a projectile is fired from a gun, the action is the momen- tum of the projectile, the reaction is the recoil of the gun — its momentum in the opposite direction, and Newton's third law states the equality of the two^ momenta. When a horse draws a barge with uniform velocity along a canal, the pull on the rope is the same in whichever direction we regard it ; that is, the force with which the horse pulls the barge is equal to that with which the barge pulls the horse. If the former were greater there would be ac- celeration, and the barge would approach the horse. Were the horse to do no work, the barge would speedily be brought to rest by friction, resistance of air and water, &c. The work spent by the horse overcomes this tendency and maintains the tension of the rope constant. It is the roughness, and consequent friction, of the ground which enables the horse to do this work. 43. The lever is a name given to any bar, straight or curved, AB (fig. 19)^ resting on a fixed point or edge c called the fulcrum. The forces acting on the lever are the weight or resistance Q, the power P, and the reaction of the fulcrum. Since these are in equilibrium, the re- sultant P and Q must act through c, for otherwise they could not be balanced by the reaction. Draw cb at right angles to QB and ca to PA produced ; then, ob- serving that P X ca; and <^y.cb are the moments of P and Q with respect to c, and that they have contraiy signs, we have (by 39) P X iTfl: = Q X Ci^ ; an equation commonly expressed by the rule, that in the lever the power is to the weight in the inverse ratio of their artns. On Matter, Force, and Motion [43- 28 Levers are divided into three kinds, according to the position of the fulcrum with respect to the points of apphcation of the power and the weight. In a lever of the first kind the fulcrum is between the power and resistance, as in fg. 1 9, and as in a poker and in the common steelyard; a pair of scissors and a carpenter's pincers are double levers of this kind. In a lever of the second kind ■Cn^ resistance is between the power and the fulcrum, as in a wheelbarrow, or a pair of nutcrackers, or a door ; in a lever of the third kind the power is between the fulcrum and the resistance, as in a pair of tongs or the treadle of a lathe. 44. Pulleys.— The pulley is a hard circular disc of wood or of metal, iii the edge of which is a groove, and which can turn freely on an axis in the centre. Pulleys are either fixed, as in fig. 20, where the stirrup or fork is rigidly connected with some immovable body, and where the axis rotates in the stirrup ; or it may be movable, as in fig. 21, where the axis is fixed to the fork, and it passes through a hole in the centre of the disc. The rope which passes round the pulley in fig. 20 supports a weight at one end ; while at the other a pull is applied to hold this weight in equilibrium. We may look upon the power and the resistance as acting a1 the circumference of the circle ; hence as the radii a re equal, if we fft consider the pulley as a lever, the two arms are Fig. 20 Fig. 21 equal, and equilibrium will prevail when the power and the resistance are equal. The fixed pulley affords thus no mechanical advantage, but is simply convenient in changing the direction of the application of a force. In the case of the movable pulley one end of the rope is suspended to a fixed point in a beam, and the weight is attached to the hook on which the pujley acts. The tension of the rope is evei-ywhere the same ; one portion -45] The Wheel and Axle 29 of the weight is supported by the fixed part and the other by the power, and these are equal to each other, and are together equal to the weight, including the pulley itself; hence in this case P = |Q. If several pulleys are joined together on a common axis in a special sheath, which is fixed, and a rope passes round all those, and also round a similar but movable combination of pulleys, such an arrangement, which is represented in fig. 22, is called a block and tackle. If we consider the condition of the rope it will be found to have every- tvhere the same tension ; the weight Q which is attached to the hook common to the whole system is supported by the six portions of the rope : hence each of these portions will sustain one-sixth of the weight ; the force which is applied at the free end of the rope which passes over the upper pulley, and which determines the tension, will have the same value ; that is to say, it will support one-sixth of the weight. The relation between power and weight in a block and tackle is expressed by the equation P = ^, in which P is the power, Q the weight, and n the n number of cords by which the weight is supported. 45. The wheel and axle. — The older form of this machine, fig. 23, is that of an axle, to which is rigidly fixed, concentric with it, a wheel of larger diameter. The power is applied tangentially on the wheel, and the resistance tangentially to the axle, as, for instance, in the treadmill and waterwheel. Sometimes, as in the case of the capstan, the power is applied to spokes fixed in the axle, which represent semi-diameters of the wheel ; in other cases, as in the windlass, the handle is rigidly fixed to the axis. In all its modifications we may regard the wheel and axle as an applica- tion of the lever, the arms of which are the radii of the wheel and axle respectively ; and in all cases equilibrium exists where the power is to the weight or resistance as the radius of the axle is to the radius of the wheel. Thus in fig. 23, P : Q = ai^ : ac, or P x ai;= Q x ab. Frequent applications of wheels of difl^erent diameters are met with in which the motion of one wheel is transmitted to another, either by means of teeth fitting in each other on the circumference of the wheels, as in fig. 24, or by means of bands passing over the two wheels. In fig. 24, which represents the essential parts of a crab winch, in order to raise the weight Q a power p must be applied at the circumference of f the wheel such that jii = Q =-, in which r and R are the radii of the axle b and of the toothed wheel a respectively. The rotation of the wheel a is effected by means of the smaller wheel c or crab, the teeth of which fit in those of a. But if this wheel c is to exert at its circumference a power /, the power P which is applied at the end of On Matter, Force, and Motion [45- the handle must be P = ^,p, in which r' is the radius of c, R' the length of R a lever at the end of which P acts, and consequently RR' ^ The radius of the wheel cis to that of the wheel a as their respective circum- ferences ; and, as the teeth of each are of the same size, the circumferences will be as the number of teeth. Trains of wheelwork are used, not only in raising great weights by the exertion of a small power, as in screwjacks, cranes, ci-ab winches, &c., but also in clock and watch works, and in cases in which changes in velocity or in power, or even in direction, are required. Numerous examples will be met with in the various apparatus described in this work. 46. Inclined plane. — The properties and laws of the inclined plane may be conveniently demonstrated by means of the apparatus represented in fig. 25. RS represents the sec- tion of a smooth piece of hard wood hinged at R ; by means of a screw it can be clamped at any angle x against the arc- shaped support, by which at the same time the angle can be measured ; a is a cylindrical roller, to the axis of which is attached a string passing over a pulley to a scale-pan P. It is thus easy to ascertain by direct experiments what '''^' ^5 weights must be placed in the pan P in order to balance a roller of any given weight with the plane fixed at a given angle of inclination. The line RS represents the length, ST the height, and RT the base of the inclined plane. In ascertaining the theoretical conditions of equilibrium we have a useful application of the parallelogram of forces. Let the line ab, fig. 25, repre- sent the force which the weight W of the cylinder exerts acting vertically downwards ; this may be decomposed into two others ; one ad,- acting at right angles against the plane, and representing the pressure which the weight exerts against the plane, and which is counterbalanced by the reaction of the plane ; the other, ac, represents the component which tends to move the weight down the plane, and this component has to be held in equilibrium by the weight P, equal to it, and acting in the opposite direction. It can be readily shown that the triangle abc is similar to the triangle SRT, and that the sides ac and ab are in the some proportion as the sidei ST and SR. But the line ac represents the power, and the line ab the weight ; hence ST: SR = P: W: Fig. 26 -46] Inclined Plane 31 that is, on an inclined plane, equilibrium obtains when the power is to the lueight as the height of the inclined plane to its length. ST Since the ratio - — is the sine of the angle x, we may also state the prin- ciple thus P = W sin X. The component da or be, which represents the actual pressure against the plane, is equal to W cos x ; that is the pressure against the plane is to the weight as the base is to the length of the inclined plane. In the above case it has been considered that the power acts parallel to the inclined plane. It may be applied so as to act horizontally. It will then be seen from fig. 26 that the weight W may be decomposed into two forces, one of which, ab, acts at right angles to the plane, and the other, ac, parallel to the base. It is this latter which is to be kept in equilibrium by the power. From the similarity of the two triangles acb and STR, ac : (5(r= ST : TR ; but be is equal to W, and ac is equal to P ; hence the power which must be applied at b to- hold the weight W in equilibrium is as the height of the inclined plane is to the base or as the tangent of the angle of inclination x ; that is, P = W tan x. The pressure upon the plane in this case may be easily shown to be ab = cos X that is R = where R is the pressure upon the plane. This is some- cos X times called the relative weight on the plane. If the force P which is to counterbalance W is not parallel to the plane, but forms an angle, E, with it, this force can be decomposed into one which is parallel to it, and one which is at right angles. Of these only the first is operative, and is equal to P cos E. In most cases of the use of the inclined plane, such as in moving carriages and waggons along roads, in raising casks into waggons or warehouses, the power is applied parallel to the inclined plane. An instance of a case in which a force acts parallel to the basQ is met with in the screw. Owing to the unevenness of the surfaces in actual use, and the conse- quent ^zV/z<7« when one body moves over another, the laws of equilibrium and of motion on an inclined plane undergo modification. Friction must be looked upon as a hindrance to be continually overcome, and must be deducted from the force required to keep a body from falling down an in- chned plane, or must be added to it in the case in which a body is to be moved up the plane. (See art. 50.) Thus if we place on the plane a block of some material, by gradually increasing the inclination it will begin to move at a certain angle, which will depend on the nature of the material ; this angle is the limiting angle of resistance, and its tangent is the coefficient of friction for that material. 32 On Matter, Force, and Motion [46 This may serve as a rough illustration of a mode of determining this coeffi- cient. 47. The wedge.— The ordinaiy form of the wedge is that of a three- sided prism of iron or steel, one of whose angles is very acute. Its most frequent use is in splitting stone, timber, &c. Fig. 27 represents in section the application of the wedge to this purpose. The side ab is the back, the vertex of the angle acb which the two faces air and be make with each other represents the edge, and the faces ac and ^cthe sides of the wedge. The power P is usually applied at right angles to the back ; and we may look upon the cohesion be- tween the fibres of the wood as representing the resistance to be overcome ; as corresponding to what in other machines is the weight. Suppose this to act at right angles to the two faces of the wedge, and to be represented by lines fe and ge ; complete the parallelogram gef, then the diagonal he will represent the resultant of the reaction of the fibres tending to force the wedge out ; the force which must be applied to hold this wedge in equilibrium must therefore be equal to eh. Now efh is similar to the triangle acb, therefore ab : ac = eh : ef\ but these lines represent the pressure applied at the back of the wedge, and the pressure on the face ac, hence if P repre- sent the former and Q the latter, there is equilibrium when V : <:i = ab : ac, that is, when the power is to the resistance in the same ratio as the back of the wedge bears to one of the sides. The relation between power and re- sistance is more favourable the sharper the edge, that is, the smaller the angle which the sides make with each other. The action of all sharp cutting instruments, such as chisels, knives, scissors, &c., depends on the principle of the wedge. It is also applied when very heavy weights are to be raised through a short distance, as in launching ships, and in bracing columns and walls to the vertical. 48. The screw. — Let us suppose a piece of paper in the shape of a right-angled triangle aee' to be applied with its vertical side ac'e' against a Fig. 28 cylinder, and parallel to the axis, and to be wrapped round the cylinder ; the hypotenuse «ill describe a screw line or helix on the surface of the cylinder (fig. 28) ; the points abcde «-ill occupy the positions respectively ab'c'd'e'. -49] Friction 3 3 If the dimensions be so chosen that the base of the triangle, he', is equal to the circumference of the cylinder, then the hypotenuse abc 'becomes an inclined plane traced on the surface of the cylinder ; the distance ac' being the height of the plane. An ordinai-y screw consists of an elevation on a solid cylinder ; this elevation may be either square, as in fig. 29, or acute ; and such screws are called square or sharp screws accordingly. AVhen a corresponding groove is cut in the hollow cylinder or nut of the same diameter as the bolt, this gives rise to an internal or companion screw or nut, fig. 30. The vertical distance between any two p; threads of a screw measured parallel to the axis is called tlie pitch, and the angle ace' or aee' is called the inclination of the screw. In practice, a raised screw is used with its companion in such a manner that the elevations of the one fit into, and coincide with, the depressions of the other. The screw is a modification of the inclined plane, and the condi- tions of equilibrium are those which obtain in the case of the plane. The resistance R, which is either a weight to be raised, or a pressure to be exerted, acts in the direction of the vertical, and the power acts parallel to the base ; hence we have V :'^ = h : b, and the length of the base is the circumference of the cylinder ; whence P : R = // : i-nr ; r being the radius of the cylinder, and h the pitch of the screw. The power is usually applied to the screw by means of a lever, as in the bookbinder's press, the copying press, &c., and the principle of the screw may be stated to be generally that the power of the screw is to the resistance in the same ratio as that of the pitch of the screw to the circumference of the circle through which the power acts. 49. Friction. — In the cases of the actions of machines which have hitherto been described, the resistances which are offered to motion have not been at all considered. The surfaces of bodies in contact are never perfectly smooth ; even the smoothest present inequalities which can be detected neither by the touch nor by ordinary sight ; hence when one body moves over the surface of another, the elevations of one sink into the depressions of the other, like the teeth of wheels, and thereby offer a certain resistance to motion ; this is what is called /r/rf20«. It must be regarded as a force which continually acts in opposition to actual or possible motion. Friction is of two kinds : sliding, as when one body glides over another ; this is least when the two surfaces in contact remain the same, as in the motion of an axle in its bearing ; and rolling friction, which occurs when one body rolls over another, as in the case of an ordinary wheel. The latter is less than the former, for by the rolling the inequalities of one body are raised over those of the other. As rolling friction is considerably less than sliding friction, it is a great saving of power to convert the latter into the former ; as is done in the case of the casters of chairs and other furniture, and also in that of friction wheels. This, however, is not always the case ; thus a sledge experiences less friction on snow than a carriage, for in this case the wheels sink and friction on the sides results. On the other hand, it is sometimes D 34 On Matter, Force, and Motion [49- useful to change rolling into sliding friction, as when drags are placed on carriage wheels. . Friction is directly proportional to the pressure of the two surfaces against each other. The ratio of the force which must act merely to over- come friction to the pressure is called the coefficient of friction. Friction is independent of the extent of the surfaces in contact if the pres- sure is the same. Thus, suppose a board with a surface of a square deci- metre resting on another board to be loaded with a weight of a kilogramme. If this load be distributed over a similar board of two square decimetres' surface, the total friction will be the same, while the friction per square centimetre is one-half, for the pressure on each square centimetre is one-half of what it was before. So, too, a rectangular stone experiences the same friction whether it is laid on the narrow or on the broad side. Friction is diminished by polishing and by smearing, but is increased by heat. It is greater as a body passes from the state of rest to that of motion than during motion, but seems independent of the velocity. The coefficient of friction depends on the nature of the substances in contact ; similar bodies experience in general greater friction than dissimilar ones, for with the former the in- equalities fit more into one another ; thus for oak upon oak it is o'4l8 when the fibres are parallel, and o'293 when they cross ; for beech upon beech it is 0-36. Greasy substances, which are not absorbed by the body, diminish friction, but increase it if they are absorbed. Thus moisture and oil increase, while tallow, soap, and graphite diminish, the friction of wooden surfaces. In the sliding friction of cast iron upon bronze the coefficient was found to be 0-25 without grease ; with oil it was 0-17, fat cii, soap 0-03, and with a mixture of fat and graphite 0'oo2. The coefficient of rolling friction for cast- iron wheels on iron rails as in railways is about 0-004 \ for ordinary wheels on an ordinary road it is 0-04, hence a horse can draw ten times as great a load on rails as on an ordinary road, and this is indeed a main use of rail and tram ways. The coefficient of steel upon smooth ice has been determined by a skater holding in his hand a spring balance (87) attached to a cord by which he was drawn along by a second skater. At starting the spiral showed a pull of 5 to 6 kilos, but during the motion this varied between i and 2 kilos. As the weight of the skater was 62 kilos, the coefficient of friction during the motion was ^ to ,,%, or r6 to 3-2 per cent. Without friction on the ground, neither man nor animals, neither ordinary carriages nor railway carriages, could move. Friction is necessary for the transmission of power from one wheel to another by means of bands or ropes ; and without friction we could hold nothing in the hands. 50. Resistance to motion in a fluid medium. — A body in moving through any medium, such as air or water, experiences a certain resistance ; for the moving body sets in motion those parts of the medium with which it is in contact, whereby it loses an equivalent amount of its own motion. This resistance increases with the surface of the moving body ; thus a soap-bubble or a snow-flake falls more slowly than does a drop of water of the same weight. It also increases with the density of the medium ; in rarefied air, therefore, it is less than in air under the ordinary pressure ;, and in this again it is less than in water. The influence of this resistance may be illustrated by means of the -61] Uniformly Accelerated Rectilinear Motion 35 Fig- 31 apparatus represented in fig. 31, which consists of two vanes, ww, fixed to a horizontal axis, xx, to which is also attached a bobbin s. The rotation of the vanes is effected by means of the faUing of a weight attached to the string coiled round the bobbin. The vanes can be adjusted either at right angles or parallel to the axis. In the former position the vanes rotate rapidly when the weight is allowed to act; in the latter, however, where they press with their entire surface against the air, the resistance greatly lessens the rapidity of rotation. The resistance increases with the velocity of the moving body, and for moderate velocities is propor- tional to the square ; for, supposing the velocity of a body made twice as great, it must displace twice as much matter, and must also impart to the displaced particles twice the velocity. For high velocities the resistance in a medium increases in a more rapid ratio than that of the square, for some of the medium is carried along with the moving body, and this, by its friction against the other portions of the medium, causes a loss of velocity. It is this resistance which so greatly increases the difficulty and cost of attaining very high speeds in steam-vessels, to which must be added the pro- duction of waves on the. surface, and of eddy currents. Use is made, on the other hand, of this resistance in parachutes (fig. 186) and in the windvanes for diminishing the velocity of falling bodies (fig. 63), the principle of which is illustrated by the apparatus, fig. 31. Light bodies fall more slowly in air than heavy ones of the same surface for the moving force is smaller com- pared with the resistance. The resistance to a falling body may ultimately equal its weight ; it then moves uniformly forward with the velocity which it has acquired. Thus, a raindrop faUing from a height of 3,000 feet should, when near the ground, have a velocity of nearly 440 feet, or that of a musket-shot ; owing, however, to the resistance of the air, its actual velocity is probably not more than 30 feet in a second. On railways the resistance of the air is appreciable ; with a carriage exposing a surface of 22 square feet, it amounts to 16 or 17 pounds when the speed of the train is 16 feet a second, or 1 1 miles an hour. By observing the rate of diminution in the number of oscillations of a horizontal disc suspended by a thread when immersed in water, Meyer determined the frictional or internal resistance of water, and found that at 10° it was equal to 001567 gramme on a square centimetre ; and for air it was about -^ as much. 51. Uniformly accelerated rectilinear motion. — Let us suppose a body containing m units of mass to move from rest under the action of a force of F units ; the body will move in the line of action of the force, and will acquire in each second an additional velocity/ given by the equation Y = mf; D 2 ^ 36 On Matter, Force, and Motion [51- consequently, if v is its velocity at the end of / seconds, we have v=ft. (i) To determine the space it will describe in t seconds, we may reason as follows :— The velocity at the time t being fi, that at a time i + T, where t is a small interval of time, will he/{i + T). If the body moved uniformly during the time t with the former velocity, it would describe a space j equal to/fr; if with the latter velocity, a space s^ equal to/(/ + r)T. Conse- quently, s^: s :: t + T : t ; therefore, when r is indefinitely small, the limiting values of s and j, are equal. Now, since the body's velocity is continually increasing during the , time T, the space actually described is greater than J and less than s^ But since the, limiting values of s and j, are equal, the limiting value of the space described is the same as that of j or j[. In other words, if we suppose the whole time of the body's motion to be divided into any number of equal parts, if we determine the -^ — f — f} — IT c velocity of the body at the beginning of each Pig. 32 of these parts, and if we ascertain the spaces described on the supposition that the body moves uniformly during each portion of time, the limiting value of the sum of these spaces will be the space actually described by the body. Draw a line AC (fig. 32), and at A construct an angle CAB, whose tangent equals /; divide AC into any number of equal parts in D, E, F,...and draw PD, QE, RF,...BC at right angles to AC ; then since PD = AD x/ QE = AE y.f, RF = AF X / BC = AC x / &c., PD will represent the velocity of the body at the end of the time represented by AD, and similarly QE, RF,...BC, will re- present the velocity at the end of thetimes AE, AF,...AC. Complete the rect- angles "Qe, EyJ Yg... These rectangles represent the space described by the body, on the above supposition, during the second, third, fourth,. ..portions of the time. Consequently, the space actually described during the time AC is the limit of the sum of the rectangles ; the limit being continually approached as the number of parts into which AC is divided is continually increased. But this limit i^ the area of the triangle ABC ; that is JAC x CB or JAC X AC x_/. Therefore, if AC represents the time t during which the body describes a space s, we have s = \ft\ (2) Since this equation can be written 2/jr=/V« we find, on comparison with equation (i), that 7/» = 2>. (3) To illustrate these equations, let us suppose the accelerative effect of the force to be 6 ; that is to'say that, in virtue of the action of the force, the body ■acquires in each successive second an additional velocity of 6 feet per second ; and let it be asked what, on the supposition of the body moving from rest, -52] Motion on an Inclined Plane 37 will be the velocity acquired, and the space described, at the end of 12 seconds ; equations I and 2 enable us to answer that at that instant it will be moving at the rate of 72 feet per second, and will have described 432 feet. The following important result follows from equation (2). At the end of the first, second, third, fourth, &c., second of the motion, the body will have described \f, ^fx. 4, ^/x g, ^/x 16, &c., feet ; and consequently during the first, second, third, fourth, &c., second of the motion will have described ^f, \f^ 3; i/>* 5i if^ 7> ^'^■j f^s'j namely spaces in arithmetical progression. The results of the above article can be stated in the form of laws which apply to the condition of a body moving from a state of rest under the action of a constant force ; — I. The velocities are proportional to the times dtiring which the motion has lasted. II. The spaces described are proportional to the squares of the times em- ployed in their description. III. The spaces described are proportional to the Squares of the velocities acquired during their description. IV. The spaces described in equal successive periods of time increase by u constant quantity. Instead of supposing the body to begin to move from a state of rest, we may suppose it to have an initial velocity V, in the direction of the force. In this case equations i, 2, and 3 can be easily shown to take the following forms, respectively : — z/ = V+//, s = Mt-^\ff^, v'' = V^ + -2fs. If the body move in a direction opposite to that of the force, /must be reckoned negative. The most important exemplification of the laws stated in the present article is in the case of a body falling freely in vacuo. Here the force causing the acceleration is that of gravity, and the acceleration produced is denoted by the letter g : it has already been stated (32) that the numerical value of g is 32-1912 at London, when the unit of time is a second and the unit of length a foot. Adopting the metre as unit of length, the value of^at London is 9-8117. 52. Motion on an inclined plane. — Referring to (46), suppose the force P not to act ; then the mass M of the roller is acted on by an unbalanced force M^sin;ir, in the direction SR ; consequently the acceleration down the plane is g sin x, and the motion becomes a particular case of that discussed in the last article. If it begins to move from rest, it will at the end of t seconds acquire a velocity v given by the equation v=gt sin X, and will describe a length s of the plane given by the equation Also, if V is the velocity acquired while describing s feet of the plane, T/' = igs sin X. 38 On Matter, Force, and Motion [52- Hence (fig. 25), if a body slides down the plane from S to R, the velocity which it acquires at R is equal Xo \f ^g. RS sin R or v^ 2^ . ST ; that is to say, the velocity which the body has at R does not depend on the angle x, but only on the perpendicular height ST. The same would be true if for RS we substituted any smooth curve ; and hence we may state generally that when a body moves along any smooth line under the action of gravity, the change of velocity it experiences in moving from one point to another is that due to the vertical height of the former point above the latter. 53. Motion of projectiles. — The equations given in the above article apply to the case of a body thrown vertically upwards or downwards with a certain initial velocity. We will now consider the case of a heavy body thrown in a horizontal direction. Let a, fig. 33, be such a body thrown with an initial velocity of z/ feet in a second, and let the line ab represent the space described in any interval ; then at the end of the 2nd, 3rd, 4th . . . equal interval, the body, in virtue of its inertia, will have reached the points c, d, e, &c. But during all this time the body is under the influence of gravity, which, if it alone acted, would cause the body to fall through the distances repre- sented on the vertical line ; these are determined by the successive values of igf, which is the formula for the space described by a freely falling body (52). The effect of the combination of the two motions is that at the end of the first interval, &c., the body will be at b', at the end of the second interval at c', of the third at d', Sac, the spaces bh' cc' dd' . . . being propor- tional to the squares of ab, ac, ad, respectively, and the line joining these points represents the path of the body. By taking the intervals of time sufficiently small we get a regularly curved line of the form known as the parabo'a. In order to demonstrate motion with horizontal and inclined direction the appa- ratus represented in fig. 34 may be made use of It consists of a bottle from which a steady stream of water issues through an india rubber tube terminating in a jet. This can be discharged in front of a slate or blackboard on which the path of the curve in each case can be chalked. If the direction in which the body is thrown makes an angle of a with the horizon (fig- 35)1 then after t seconds it would have travelled a distance ab = vt, where v is the original velocity ; during this time, however, it will have fallen through a distance be = ^gf^ ; the height which it will have actually reached is =bd-bc = vt sin a-^'' ; and the hori- zontal distance will be ad=ab cos a^vt cos «. The rattge of the body, or the greatest distance through which it is thrown, will be reached when the height is again = o ; that is, when vt sin a - Igi'^ = o, from which / = ^^ ^'" ° g ' Introducing this value of/ into the equation for the distance, d, we have Fig. 33 -64] Composition of Velocities 2V' Sin a cos a which by a trigonometrical transformation = — 39 w' sin 2a The greatest height is attained in half the time of flight, or when t='^?^—, g from which we get , _ z/' sin' a It follows from the formula that the height is greatest when sin u is greatest, which is the case when it = go ', or when the body is thrown vertically upwards ; the range is greatest where sin 2a is a maximum, that is, when 2a = 90° or a = 45°. In these formulas it has been assumed that the air offers no resistance. This is, however, far from the case, and in practice, par- ticularly if the velocity of projection is very great, the path differs from that of a parabola. Fig. 35 approximately represents the path, allowing for the resistance of the air. The divergence from the true theoretical path is affected by the fact that in the modern rifled arms the projectiles are not spherical in shape ; and also because, along with their j'j»'iU.i'Mi8i;' fi*_^ Fig. 34 Fig- 35 motion of translation, they have, in consequence of the rifling, a rotatory motion above their axis. 54. Composition of velocities. — The principle for the composition of velocities is the same as that for the composition of forces : this follows evi- dently from the fact that forces are measured by the momentum they com- municate, and are therefore to one another in the same ratio as the velocities they communicate to the same body. Thus (fig. 10, art. 36), if the point has 40 On Matter, Force, and Motion [54- at anyl instant a velocity AB in the direction AP, and there is communicated to it a velocity AC in the direction AQ, it will move in the direction AR with a velocity represented by AD. And, conversely, the velocity of a body re- presented by AD can be resolved into two component velocities AB and AC. This suggests the method of determining the motion of a body when acted on by a forcejin a direction transverse to the direction of its velocity ; namely, suppose the time to be divided into a great number of intervals, and suppose the velocity actually communicated by the force to be communicated at once ; then by the composition of velocities we can determine the motion during each interval, and therefore during the whole time ; the actual motion is the limit to which the motion, thus determined, approaches when the number of intervals is increased. 55. Motion in a circle. Centrifugal force.^ — When a body is once in motion, unless it be acted upon by some force, it will move uniformly forward in a straight line with unchanged velocity (29). If, therefore, a body moves uniformly in any other path than a straight line — in a circle, for instance — this must be because some force is constantly at work which continuously deviates it from this straight line. We have already seen an example of this in the case of the motion of projectiles (53), and will now consider it in the case of central motion or motion in a circle, of which we have an example in the motion of the celestial bodies, or in the motion of a sling. In the latter case, if the string is cut, the stone, ceasing to be acted upon by the tension of the string, will move in a straight line with the velocity which it already possesses — that is, in the direction of the tangent to the curve at the point where the stone was when the string was cut. The tension of the string, the effect of which is to pull the stone towards the centre of the circle and to cause the stone to move in its circular path, is called the centripetal or central force ; the reaction of the stone upon the string, which is equal and opposite to this force, is called the centri- fugal force. The amount of the forces may be arrived at as follows : — Let us suppose a body moving in a circle with given uniform velocity to be at the point a (fig. 36) ; then, had it not been acted on by a force in the direction ac, it would, in a small succeeding interval of time /, have continued to move in the direction of the tangent at a, and have passed through a distance which we will represent by ab. In consequence, however, of this force, it has not followed this direction, but has arrived at the point d on the curve ; hence the force has made it traverse the distance bd=ae in this interval. If/be the acceleration with which the body is drawn towards the centre ae = \ft'', and Uadhe very small, it may be taken as equal to ad or vi, where v is the velocity of the moving body. Now if an is the diameter of the circle, the triangle adn is inscribed in a Fig. 36 -56] Motion of a Simple Pendulum 41 semicircle and is right-angled, whence ad'^ = aex. an = ae x ir. Substituting their values for ad and ae in this equation, we find that v^f- = ^ft"^ x ir, from which/" = — , hence F = mf = — ; that is, in order that a body with a certain velocity may move in a circle, it must be drawn to the centre by a force which is directly as the square of the velocity with which the body moves, and inversely as the radius of the circle. To keep the body of mass m in a circle, an attraction towards the centre is needed, which is constantly equal to , and this attraction is also constantly neutralised by the centri- fugal force. The above expression may be put in a form which is sometimes more convenient. If T be the time in seconds required to traverse the circum- ference inr with the velocity ■y, then v^ = ^L,- ■ from which F = - J^_ . If a rigid body rotates about -a fixed axis, all parts of the body describe circles of various diameters. The velocity of the motion of individual particles increases with the distance from the axis of rotation. By angular velocity is understood the velocity of a point at unit distance from the axis of rotation. If this is denoted by m, the velocity w of a point at a distance from the axis is tor, from which m = _ = 1 and F = mraP-. r T The existence of centrifugal force may be demonstrated by means of numerous instructive experiments, such as the centrifugal railway. If a small can of water hung by the handle to a string be rapidly rotated in a vertical circle, no water will fall out, for, at a suitable velocity, the liquid will press against the bottom of the vessel with a force at right angles to the circle and greater than its own weight. Centrifugal force has been used in chemical laboratories to separate crystals from the mother-liquors, and also to promote the deposition of fine precipitates which under ordinary circumstances settle very slowly ; it is also applied industrially in sugar factories to purify sugar from symp, in dyeworks to dry yarn and cloth rapidly, and in laundries. 56. Motion of a simple pendulum. — ^By a simple pendulum is meant a heavy particle suspended by a fine weightless thread from a fixed point, about which it oscillates without friction. We; cannot realise such a pendulum but we can approximate to it foi experimental purposes by using a small leaden bullet attached to a fine wire — the friction at the point of suspension being reduced to a minimum. Let the bullet be drawn aside to the point A (fig. 37), and let go so that it may oscillate in a vertical plane. We proceed to consider the velocity of the bullet and the force acting, upon it at different parts of its path. We notice first that the motion is symmetrical about the vertical. Starting from rest at A the bullet moves with gradually increasing velocity to C, then slows down until it comes to rest at B. Then it returns through ^ to A, passing through the same series of changes in the opposite direction. Suppose the bullet to be at P, descending the curve. The forces acting upon it are its weight, mg., acting vertically downwards, and the tension of the string T acting along PO. The resultant is a force, F, at 42 On Matter, Force, and Motion [56- right angles to the string, and is the resolved part of the weight acting tangentially to the circle. If F denotes this resolved part, F = mg sin 6. But since the sine of an angle when the angle is small is directly proportional to the arc which it subtends, it follows that the force acting on the bullet is proportional to its displacement from the vertical. As the bullet oscillates, the resultant of the forces acting upon it is a maximum at A and B, and is zero at C. The velocity of the bullet may easily be deter- mined. Complete the circleABC(seefig. 38), join P to D, and draw the horizontal lines AMB, PNP'. Then since the velocity acquired in falling from A to P is that due to MN, the vertical height of A above P, we shall have, if v denote the velocity of the bullet, v^ = 2g. MN. But, by a well-known property of the circle, a^ = 2/xMC and j-'^ = 2/NC, where a and s are the chords CA and CP respectively, and /= OC. mq Fig. 37 Fig. 38 3'-j^ = 2/MN, and^/» =fK -.^). Now, V has equal values for a given value of s whether positive or negative, and for any value of j there are two values of v, one positive and one negative. That is to say, since CP' = CP, the bullet will have the same velocity at P' that it has at P, and atj any pomt it will have the same velocity whether it is going up the curve or down the curve. Of course it is included in this statement that if the bullet begins to move from A it will just ascend to B on the other side of C, such that A and B are on the same horizontal line. The velocity is a maximum when j = o, i.e. at C, its value there being "V ^^a Vf The energy of the bullet (64) is the same at all parts of its path. At A and B it is entirely potential ; at C it is entirely kinetic. At other points it is partly potential and partly kinetic. The cause of motion is gravity. The pendulum would not oscillate but for the attraction between the earth and the bullet. If this were the only agency in operation the oscillations would go on with undiminished amplitude for ever. But the friction at the point of support and that of the air are constantly acting to oppose the motion, and so the bullet passing the point C from A does not quite mount up as high as B ; thus the bullet is gradually brought to rest. The period oi the pendulum is the time of a complete vibration, i.e. the -57] Simple Harmonic Motion 43 It IS proved The aniplihcde oi the time required for the bob to pass from A to E and back again. in works on dynamics that the period T = 27rA /-. oscillation is the distance CA or CB, i.e. the greatest distance of the oscillating point from its mean position. A seconds pendulum is one which moves from A to B or from B to A in one second. Theperiod of a seconds pendulum is two seconds. The period of oscillation is independent of the amplitude provided the latter be small, not' exceeding five degrees. This property is spoken of as the isochronism of the pendulum, and the oscillations are said to be isochronous. We see from the above that the period or time of oscillation of a pendulum is directly proportional to the square root of its length and inversely proportional to the acceleration of gravity. As an example of the use of the formula we may take the following : — It has been found that 39-13983 inches is the length of a seconds pendulum at Greenwich ; the formula at once leads to an accurate determination of the acceleration of gravity at Greenwich ; for, using feet and seconds as our units, we have t = l, ^=3-26165, and tt stands for the known number 3"I4I59 ; therefore the formula gives us ^= (3-141 59)'^x 3-26165 = 32-1912. This is the value employed in (32). Other examples will be met with in the Appendix. 57. Simple harmonic motion. Circle of reference. — If the pendulum be long and the arc of vibration small, the bullet, regarded as a particle, moves to and fro in a straight line. Let AB be the straight line. The velocity of the particle is zero at A and B, and a maximum, viz. aA /C at C ; or since T, the period, = 27r */-, the maximum velocity is -—-, where g the distance, AC, or amplitude of vibration. On BA describe a circle. A particle moving- round the circle with a certain uniform velo- city will make a complete circuit in the time (T) which the oscillating particle requires to go from A to B and back again. This velocity is clearly -—-, since lira is the circumference of the circle, and it is not difficult to prove that the velocity at any point, P, in the circular path resolved parallel to AB, is equal to the velocity of the oscillating particle when it has reached M, the foot of the perpendicular drawn from P on AB. Thus the revolving and the oscillating particles, if they start together, are throughout the period in such relative positions as P to M, Q to N, &c. The motion in AB is called simple harnionic motion, and in regard to it the circle ADBD' is called the circle of reference. Simple harmonic motion is characterised by the condition that the acceleration is proportional to the displacement of the vibrating particle from its mean position. 44 On Matter, Force, and Motion [57- The i>hase of vibration is the distance of the moving point, measured either in angle or in time-from some definite point on its path, say from A. T For instance, if the angle ACP is 30°, the phase of P or M is 30°, or — ' T since the time required to go from A to P is -. A and B are m opposite phases, and C is a quarter of a period, or 90°, before A or behind B. 58. Composition of two simple harmonic motions at right angles to each other.— We will first take the case in which the periods and also the ampli- tudes are equal to each other. Let ADB be the circle of reference, and let'each quadrant be divided into four equal parts. If T be the period of a particle oscillating in AB, its T T X positions, supposing it to start from A, will be in the times —^ 2—, 3-^, &c., Pv Ai Ai ^c. respectively, If another particle start at D and have simple harmonic motion along DD', and the period be the same for the two rect- angular motions, it is clear that the particles at the same moment will have the same velocity — they will meet at C, and when one reaches B the other will reach D', and so on. The two particles are in the same phase. If we suppose a single point to have simultaneously two simple harmonic motions in rectangular directions, the path traced out by the point will de- pend upon the difference of phase in the two directions. If the phases are the same the resultant path will be a straight line equally inclined to the two component directions. For suppose the particle to be at C and to move T ■ sirnultaneously towards A and towards D, it is clear that m the tune ^ it T will be at r^, having traversed the line C^j, in the time 2 -- it will be at Pj, and so on. In the period T it will trace the Hne r^s^ twice over ; in other words, it will have simple harmonic motion along s^^ its amplitude being C^a and its period T. If the two simple harmonic motions, instead of being in the same phase, differ in phase by a half period (or by 1 80°), the result of compounding them will again be a straight line, but it will be at right angles to r^s^. Suppose that the vibrating particle, considered as moving along AB, is at A (fig. 41), and, considered as moving along DD' is at q^, descending. T T Its actual position is X ; after an interval — it will be at P, after 2_ atAi 10 16 and so on ; and it is easy to see that the path traced out will be the ellipse shown in the figure. The difference of phase is one-eighth of a period, or one of the vibrations is . 45° behind the other. If the phase difference -58] Composition of Harmonic Motions 45 a quarter period, the ellipse will coincide with the circle of / y^ ^ ■^ i / y>. \ t / / 1i / \ J c A|S / VI' 1 \\ / / i^ ^ ^ /^ _ D' Fig. 41 IS 90", or reference. These results may be illustrated by a pendulum consisting of a bullet attached to a long string. Set the pendulum in vibration in a definite plane, and as the bullet passes its mean position give it a blow in a direction at right angles to that in which it is moving. p The blow must be of such strength as will give the bullet a velocity equal to that which it has, but in a direction at right angles to the latter. The pendulum will now vibrate in a plane equally in- clined to the two rectangular directions, g and it will be seen that its amplitude is greater than before. If the experiment be repeated in such a way that the blow (of the same force as before) be given to the bullet at the end, instead of in the middle, of its swing, the bullet will acquire a circular motion, and we shall have what is called a conical ■bendulum, since the string of the pendulum traces out a cone. In this case the motions in rectangular directions differ in phase by a quarter period. We may make the difference in phase anything we like by suitably choosing the point in the path of the vibrating pendulum at which the rectangular blow is delivered. If the amplitudes of the vibrat- ing points are not equal, the re- sulting curve will be an ellipse ; it will be a straight line if the phase difference is -, and in 2 every other case an ellipse. This may be easily verified by trial, either geometrically, or experi- mentally by the pendulum as above. The geometrical con- struction in this case, as in others in which the periodic times are different, is best effected by the use of two circles of reference. We proceed to give an example of the use of two such circles. Let XfY, XVY' (fig. 42) be the circles of reference of two rectangular simple harmonic motions, one along XY, the other along X'Y', and let the periods be as 3 : 2 ; that is, the oscillating point moves through ^th of the circumference of XfY while it is moving through ^th of the circumference of X'^Y'. Divide the circum- ferences of the circles respectively into 1 2 and 8 parts, and draw horizontal and vertical lines through the points of division, as in the figure. The form of Fig. 42 46 On Matter, Force, and Motion [58- the curve obtained by compounding the vibrations will depend upon the difference of phase. We will suppose that the point a in the one circle corre- sponds to X' in the other, b top, c to g, &c. Then marking the intersections of the corresponding vertical and horizontal lines we get the points I, 2, 3, &c. By joining these points the curve shown is obtained. In chapter vi. of Book V. we shall see how beautifully these curves may be illustrated by means of tuning forks provided with mirrors at the ends of their prongs. We may, however, by various me- chanical contrivances obtain very close approximations to the theoretical figures. Tisley's Compound Pendulum apparatus or Harmonograph is one of the best of these. It consists of two pendulums (fig. 43; with adjustable sliding weights vibrating about knife edges in planes at right angles to each other. Light rods connect their upper ends to a vertical pencil or pen. If either pendulum is at rest -and the other is set in vibration, the pencil traces a nearly straight line. If both Fig- 43 Fig.. pendulums are vibrating the pencil point traces a curve which is the result of compounding the curves produced by the separate vibrations. The relative -59] Composition of Simple Harmonic with Uniform Motion 47 periods are varied by altering the positions of the sliding weights. Very beautiful figures may be obtained in this way. An example is given in fig. 44. The pendulums are adjusted so hat their periods are as 2 : 3 ; owing to the gradual diminution of the amplitudes of vibration, the point of the pen does not go over the same line a second time, but traces out a new curve in each period until it is stopped. 59. Composition of simple harmonic motion with uniform motion in a direc- ti6n at right angles to it. — Let a point be moving in simple harmonic motion along DCD' (fig. 45), and suppose the line DCD' to move at right angles to Fig. 4S itself with uniform velocity such that the distance XY is traversed in the periodic time T. Draw the circle of reference and divide the period and the circumference of the circle into any convenient number of equal parts, say iz. Divide XY also into 12 equal parts. Let the time be reckoned from the moment the oscillating point is moving upwards through C. Then in a time T — the oscillating point is at M, the corresponding point on the circle of re- 12 ference being P, the revolving radius CP having swept out at an angle of 30° ; '" 2 — , the point is at N and the angle swept out is 60°. 12 T T In 3 — or — , the 12 4 angle is 90° and so on ; thus we may conveniently divide the distance XY into 360°. Through M, N, D, &c., draw lines parallel to XY, and at the points 30, 60, 90, &c., erect perpendiculars equal respectively to CM, CN, CD, &c., and join the ends of the lines so drawn. The curve so obtained is called a sine curve, because any ordinate to the curve — e.g. that at 30, which is equal to CM — is proportional to the sine of the angle PCA or 30°. The equation of the curve \%y = a sin 6, where a is the amplitude, _)/ any ordinate of the curve, and 6 the distance from X. Since 6 = -^ x t, = nt, where T is the period and t the line measured from X, we have / = a sin jit. A sine curve thus represents graphically simple harmonic motion, and we see from it at a glance the displacement corresponding to any phase of the motion. Two or more harmonic vibrations in the same straight line, of any periods or amplitudes, may be compounded by the aid of their sine curves. All that is necessary for this purpose is to draw the curves corresponding to the separate vibrations with the necessary phase differences, and draw ordinates from point to point equal to the algebraic sum of the ordinates of the separate curves, above or below the mean line as the sum is positive or 48 On Matter, Force, and Motion [59- negative. By joining together the extremities we obtain the resultant curve. The actual form of this curve will depend upon the differences of phase at any particular epoch. 60. Work : meaning of the term. — It has been pointed out (22, 29) that a moving body has no power of itself to change either the direction or the speed of its motion, and that, if any such change takes place, it is a proof that the body is acted upon by some external force. But although change of motion thus always implies the action of force, forces are often exerted with- out causing any change in the motion of the bodies on which they act. For instance, when a ship is sailing at a uniform speed, the force exerted on it by the wind causes no change in its motion, but simply prevents such a change being produced by the resistance of the water ; or, when a railway-train is running with uniform velocity, the force of the engine does not change, but only maintains its motion in opposition to the forces, such as friction and the resistance of the air, which tend to destroy it. These two classes of cases — namely, first, those in which forces cause a change of motion ; and, secondly, those in which they prevent, wholly or in part, such a change being produced by other forces — include all the effects to which the action of forces can give rise. When acting in either of these ways, a force is said to do work : an expression which is used scientifically in a sense somewhat more precise, but closely accordant with that in which it is used in common language. A little reflection will make it evident that, in all cases in which we are accustomed to speak of work being done — whether by men, horse-power, or steam-power, and however various the pro- ducts may be in different cases — ^the physical part of the process consists solely in producing or changing motion, or in keeping up motion in opposition to resistance, or in a combination of these actions. The reader will easily convince himself of this by calling to mind what the definite actions are which constitute the work done by (say) a navvy, a joiner, a mechanic, a weaver ; that done by a horse, whether employed in drawing a vehicle or in turning a gin ; or that of a steam-engine, whether it be used to draw a railway-train or to drive machinery. In all cases the work done is reducible, from a mechanical point of view, to the elements that have been mentioned, althougn it may be performed on different materials, with different tools, and with different degrees of skill. It is, moreover, easy to see that any possible change or motion may be represented as a gain by the moving body of an additional (positive or negative) velocity either in the direction of its previous motion, or at right angles to it; but a body which gains velocity is (30) said to be accelerated. Hence, what has been said above may be summed up as follows: — When a force produces acceleration, or when it maintains motion unchanged in opposition to resistance, it is said to do WORK. 61. Measure of work.— In considering how work is to be measured, or how the relation between different quantities of work is to be expressed numerically, we have, in accordance with the above, to consider, first, work of acceleration ; and, secondly, work against resistance. But in order to make the evaluation of the two kinds of work consistent, we must bear in mind that one and the same exertion of force will result in work of either kind according to the conditions under which it takes place : thus, the force -61] Measure of Work 49 of gravity acting on a weight let fall from the hand causes it to move with a continually accelerated velocity until it strikes the ground ; but if the same weight, instead of being allowed to fall freely through the air, be hung to a cord passing round a cylinder by means of which various degrees of friction can be applied to hinder its descent, it can be made to fall with a very small and practically uniform velocity. Hence, speaking broadly, it may be said that, in the former case, the work done by gravity upon the weight is work of acceleration only, while in the latter case it is work against resistance (friction) only. But it is very important to note that an essential condition, without which a force, however great, cannot do work either of one kind or the other, is that the thing acted on by it shall move while the force continues to act. This is obvious, for if no motion takes place it clearly cannot be either accelerated or maintained against resistance. The motion of the body on which a force acts being thus necessarily involved in our notion of work being done by the force, it naturally follows that, in estimating how much work is done, we should consider how much — that is to say, how far — the body moves while the force acts upon it. This agrees with the mode of estimating quantities of work in common life, as will be evident if we consider a very simple case — for instance, that of a labourer employed to carry bricks up to a scaffold : in such a case a double number of bricks carried would represent a double quantity of work done, but so also would a double height of the scaffold, for whatever amount of work is done in raising a certain number to a height of twenty feet, the same amount must be done again to raise them another twenty feet, or the amount of work done in raising the bricks forty feet is twice as great as that done when they are raised only twenty feet. It is also to be noted that no direct reference to time enters into the conception of a quantity of work : if we want to know how much work a labourer has done, we do not ask how long he has been at work, but what he has done — for instance, how many bricks he has carried, and to what height ; and our estimate of the total amount of work is the same whether the man has spent hours or days in doing it. The foregoing relations between force and work may be put into definite mathematical language as follows : — ^If the point of application of a force moves in a straight line, and if the part of the force resolved along this line acts in the direction of the motion, the product of that component and the length of the line is the work done by the force. If the component acts in the opposite direction to the motion, the component may be considered as a resistance, and the product is work done against the resistance. Thus, in (46), if we suppose a to move up the plane from R to S, the work done by P is P X RS : the work done against the resistance W is W sin ;ir x RS. It will be observed that if the forces are in equilibrium during the motion, so that the velocity of a is uniform, P equals W sin x, and consequently the work done by the power equals that done against the resistance. Also, since RS sin X equals ST, the work done against the resistance equals W x ST. In other words, to raise W from R to S requires the same amount of work as to raise it from T to S. If, however, the forces are not in equilibrium, the motion of a will not be uniform, but accelerated ; the work done upon it will nevertheless still be E 50 On Matter, Force, and Motion [61- represented by the product of the resultant force resolved along the direction of motion into the distance through which it moves. In order to ascertain the relation between the amount of work done and the change produced by it in the velocity of the moving mass, we must recall one or two elementary mechanical principles. Let F be the resultant force resolved along the direction of motion, and S the distance through which its point of application moves : then, according to what has been said, the work done by the force = FS. Further, it has been pointed out (31) that a constant force is measured by the momentum produced by it in a unit of time : hence, if T be the time during which the force acts, V the velocity of the mass M at the beginning of this period, and Vj the velocity at the end, the momentum produced during the time T is M Vj - M V, and consequently the momentum produced in a unit of time, or, in other words, the measure of the force, is P_ M(V,-V) T The distance S through which the mass M moves while its velocity changes from the value V to the value V, is the same as if it had moved during the whole period T with a velocity equal to the average value of the varying velocity which it actually possesses. But a constant force acting upon a constant mass causes its velocity to change at a uniform rate ; hence, in the present case, the average velocity is simply the arithmetical mean of the actual and final velocities : S = ^(V, + V)T. Combining this with the last equation, we get as the expression for the work done by the force F : FS = 4M(Vi2-V=); or, in words, when a constant force acts on a mass so as to change its velocity, the work done by the force is equal to half the product of the mass into the change of the square of the velocity. 62. Unit of work. Power. — For strictly scientific purposes a unit of work is taken to be the work done by a unit of force when its point of appli- cation moves through the unit distance in the direction of its action ; but, as a convenient and sufficiently accurate standard for practical purposes, the quantity of work which is done in lifting i pound through the height of I foot is commonly adopted as the unit, and this quantity of work is spoken of as one ' foot-pound.' It is, however, important to observe that the foot-pound is not perfectly invariable, since the weight of a pound, and therefore the work done in lifting it through a given height, differs at different places, being a little greater near the Poles than near the Equator. On the metric system the kilogrammetre is the unit ; it is the work done when a weight of a kilogramme is raised through a height of a metre. This is equal to 7-23 foot-pounds, and one foot-pound = -1383 of a kilogrammetre. In estimating the usefulness of any motor it becomes necessary to know the time required by it for doing a given amount of work. The amount of work per second is the power of the motor. The unit of power is the -63] Systems of Units 51 power required to do a unit of work in a unit of time. For measuring the power of engines the unit used is the horse-power, which represents a rate of work of 33,000 foot-pounds per minute. It is to be observed that in every case the unit is of the same denomina- tion as the thing or quantity measured. The unit of length must be a length ; the unit of value must be a definite quantity of some valuable commodity. The numbers, to determine which is one of the objects of physical research, are to be considered as abstract numbers, representing how many times the unit is taken. 63. Systems of units. — The units of mass, length, and time are said to he funda?nental units, as all other units, such as those of area, velocity, acceleration, power, &c., are referred to them. These latter units are there- fore called derived units. The magnitudes of the fundamental units are, however, arbitrary. A large class of writers use the centimetre, gramme, and second, and this system is usually called the C.G.S. system; others use the foot, pound, and second. It thus becomes important to have a systematic method of reducing measurements from one system of units to another. Let L, M, T represent respectively the magnitude or dimensions of the centimetre, the gramme, and the second, and L', M', T' represent the dimensions of the foot, the pound, and the minute. Then, if a wire is found to be / cm. or /' ft. in length, its length may be represented either by /L or /'L', and hence /L = /'L', or, /= --/'. L' The ratio — is the length of a foot in centmietres, and has been found by direct comparison to be 30-4797. Hence any measurement, /' in feet, is converted into centimetres by multiplying /' by this number. In a similar manner, if ?« and ot' represent the number of units of mass in a piece of matter in the two systems, M' , m = -—m , M where the unit ratio is the number of grammes in a pound, or 453'59. For converting a volume ij' into the equivalent v, For Density, ^ = D, m yi _m' M' /» ■ L?"" /'3 ■ 173' M' D = -- M (y°-- Here the ratio — , is said to be a measure of the magnitude or dimensions L^ E 2 $2 On Matter, Force, and Motion [68 of the unit of density, in terms of the dimensions of the fundamental units of mass and length. If a substance is said to have a unit density, then if M were the gramme and L' the cubic centimetre, the density of the substance would be that of water. If, however, M were the kilogramme and L' the cubic centimetre, the density would be a thousand times that of water. If, again, L' represent a cubic decimetre, and M a kilogramme, the density would again be that of water. It appears, then, that the magnitude of the unit of density is directly proportional to the magnitude of the unit of mass, and inversely as the magnitude of the unit of volume or the cube of the unit of length. As unit density is the density of a unit mass occupying unit volume, it is clear that — - measures the dimensions of the unit of density. Similar explanations apply in the succeeding cases. For Velocity, v = ^. / L_/' L' ? ■ T f T" V T L T ■ T ratio — , T' second i minute 60' T If the units of time were the same, the unit factor =,-, = i and the velocity in centimetres would be L' , where v' is the velocity in feet per second. For Motnentu7n, mv= --, For Acceleration, a = - = '^, ml ML _ m'l' M'L' i ' T t' T' 71111 M M L'T L T' r • m'v' I ~t'-' I L /' V i' •j".- ~ t-^' T^.' = LYTX LVT7 where a' is the acceleration in feet per minute. ?;il For Force, F = wza = ' , ;«/ ML^otV M'L' p. M' L', ^ = M L'/TV L \r') -64] Energy S3 In the C.G.S. system the unit offeree is called the Dyne. mP For Work, W = 71-- mP MU m'l"^ M'L'- M \L T'/ In the C.G.S. system the unit of work is called the Erg. 71 mP Rate of Work, or Power, P = — = , -S'©'©"- If work is expressed in foot-pounds or kilogramme-metres, the unit of force being the weight of a pound or kilogramme, then to convert a certain number of foot-pounds into kilogramme-metres we have w/. WL = 'zc/7'W'L'. Work (kgr.-m.) = ( ^. • ^ ) work, foot-pounds, where ^'=P21^d^. W kilogr. L' foot „..,„. a _ =o-304i5, L metre the unit factor being thus 0-1383. Similarly, to convert foot-pounds perminute into kilogr. -metres per second, Vw L t) ' where the conversion factor becomes 0-00230. The units commonly used for measuring the power of engines are the horse-power, which is 33,000 times as great as the unit in which P' of the last equation was measured, and the force de cheval, which is 75 times as great as the unit in which P was measured. Hence, if P' is to be in horse- power, and P m force de cheval, the equation will become T, •?3,ooo -nt P = 0"002SO X -i^ P 75 = 1-0139 P', and hence one British horse-power= roiy) force de cheval. These examples will be sufficient to indicate the method of converting measurements from one system of units to any other, and the treatment of other derived units may be deferred until they are needed. 64. Energy. — The fact that any agent is capable of doing work is usually expressed by saying that it possesses energy, and the quantity of energy it 54 On Matter, Force, and Motion [64- possesses is measured by the amount of work it can do. For example, in the case of the inclined plane above referred to, the energy of the force P is P X RS ; and if this force acts under the conditions last supposed, by the time its own energy is exhausted (in consequence of its point of apphcation having arrived at S, the limit of the range through which it is supposed able to act), it has conferred upon the mass M a quantity of energy equal to that which has been expended ; for, in the first place, M has been raised through a vertical height equal to ST, and could by falling again through the same height do an amount of work represented by W x ST ; and in the second place M can do work by virtue of the velocity that has been imparted to it, and can continue moving in opposition to any given resistance R through a distance J, such that R.j = ^Mt/2. The energy possessed by the mass M in consequence of its having been raised from the ground is commonly distinguished as energy of posiiion or potential energy, and is measured by the product of the force tending to cause motion into the distance through which the point of application of the force is capable of being displaced in the direction in which the force acts. The energy possessed by a body in consequence of its velocity is commonly dis- tinguished as energy of motion, or kinetic energy : it is measured by half the product of the moving mass into the square of its velocity. 65. Varieties of energ'y. — On considering tlie definition of work given above, it will be seen that a force is said to do work when it produces any change in the condition of bodies ; for the only changes which, according to the definition of force given previously (29), a force is capable of producing, are changes in the state of rest or motion of bodies, and changes of their place in opposition to resistances tending to prevent motion or to produce motion in an opposite direction. There are, however, many other kinds of physical changes which can be produced under appropriate conditions, and the recent progress of investigation has shown that the conditions under which changes of all kinds occur are so far analogous to those required for the production of work by mechanical forces that the term work has come to be used in a more extended sense than formerly, and is now often used to signify the production of any sort of physical change. Thus work is said to be done when a body at a low temperature is raised to a higher temperature, just as much as when a weight is raised from a lower to a higher level ; or, again, work is done when an electric, magnetic, or chemical change is produced. This extension of the meaning of the term work involves a similar extension of the meaning of energy, which in this wider sense may be defined as the capacity for producing physical change. As examples of energy in this more general sense, the following may be mentioned : — (a) The energy possessed by gunpowder in virtue of the mutual chemical affinities of its constituents, whereby it is capable of doing work by generating heat or by acting on a cannon-ball so as to change its state of rest into one of rapid motion ; {b) the energy of a charged Leyden jar, which, according to the way in which the jar is discharged, can give rise to changes of temperature, to changes of chemical composition, to mechanical changes, -66] Transformation of Energy 55 or to changes of magnetic or electric condition ; {c) the energy of a red-hot ball, which, amongst other effects it is capable of producing, can raise the temperature and increase the volume of bodies colder than itself, or can change ice into water or water into steam ; the energy of the stretched string of a bow : here work has been consumed in stretching the string ; when it is released the work reappears in the velocity imparted to the arrow. 66. Transformation of energy. — It has been found by experiment that, when one kind of energy disappears or is expended, energy of some other kind is produced, and that, under proper conditions, the disappearance of any one of the known kinds of energy can be made to give rise to a greater or less amount of any other kind. One of the simplest illustrations that can be given of this transformation of energy is afforded by the oscillations of a pendulum. When the pendulum is at rest in its lowest position it does not possess any energy, for it has no power of setting either itself or other bodies in motion, or of producing in them any kind of change. In order to set the pendulum oscillating, work must be done upon it, and it thereafter possesses an amount of energy corresponding to the work that has been expended. When it has reached either end of its path, the pendulum is for an instant at rest ; but it possesses energy by virtue of its position, and can do an amount of work while falling to its lowest position, which is represented by the product of its weight into the vertical height through which its centre of gravity de- scends. When at the middle of its path, the pendulum is passing through its position of equilibrium, and has no power of doing work by falling lower ; but it now possesses energy by virtue of the velocity which it has gained, and this energy is able to carry it up on the second side of its lowest position to a height equal to that from which it has descended on the first side. By the time it reaches this position the pendulum has lost all its velocity, but it has regained the power of falling ; this, in its turn, is lost as the pendulum returns again to its lowest position, but at the same time it regains its pre- vious velocity. Thus, during every quarter of an oscillation the energy of the pendulum changes from potential energy of position into actual energy or energy of motion, or vice versd. A more complex case of the transformation of energy is afforded by a thermo-electric pile, the terminals of which are connected by a conducting wire : the application of energy in the form of heat to one face of the pile gives rise to an electric current in the wire, which, in its turn, reproduces heat, or by proper arrangements can be made to produce chemical, magnetic, or mechanical effects, such as those described below in the chapters on Electricity. It has also been found that the transformations of energy always take place according to fixed proportions. For instance, when coal or any other combustible is burned, its chemical energy, or power of combining with oxygen, vanishes, and heat or thermal energy is produced, and the quantity of heat produced by the combustion of a given amount of coal is fixed and invariable. If the combustion takes place under the boiler of a steam-engine, mechanical work can be obtained by the expenditure of part of the heat pro- duced, and here again the quantitative relation between the heat expended and the work gained in place of it is perfectly constant. 56 On Matter, Force, and Motion [67- 67. Conservation of energy. — Another result of great importance, which has been arrived at by experiment, is that the total amount of energy possessed by any system of bodies is unaltered by any transformations arising from the action of one part of the system upon another, and can only be increased or diminished by effects produced on the system by external agents. In this statement it is of course understood that in reckoning the sum of the energy of various kinds which the system may possess, those amounts of the different forms of energy which are mutually convertible into each other are taken as being numerically equal ; or, what comes virtually to the same thing, the total energy of the system is supposed to be reduced — either ac- tually, or by calculation from the known ratio of transformation of the various forms of energy — to energy of some one kind ; then the statement is equivalent to this : that the total energy of any one form to which the energy of a given system of bodies is reducible is unalterable so long as the system is not acted on from without. Practically it is always possible, in one way or another, to convert the whole of the energy possessed by any body or system of bodies into heat, but it cannot be all converted without loss into any other form of energy ; hence the principle stated at the beginning of this article can be enunciated in the closest conformity with the direct results of experiment by saying that, so long as any system of bodies is not acted on from without, the total quantity of heat that can be obtained from it is unalterable by any changes which may go on within the system itself. For instance, a quantity of air compressed into the reservoir of an air-gun possesses energy which is represented partly by the heat which gives to it its actual temperature above the absolute zero (337), and partly by the work which the air can do in expand- ing. This latter portion can be converted into heat in various ways, as, for example, by allowing the air to escape through a system of capillary tubes so fine that the air issues from them without any sensible velocity ; if, how- ever, the expanding air be employed to propel a bullet from the gun, it produces considerably less heat than in the case previously supposed, the deficiency being represented for a time by the energy of the moving bullet, but reappearing in the form of heat in the friction of the bullet against the air, and, when the motion of the bullet is destroyed, by striking against an inelastic obstacle at the same level as the gun. But whatever the mode and however numerous the intermediate steps by which the energy of the com- pressed air is converted into heat, the total quantity of heat finally obtainable from it is the same. -68] Universal Attraction: its Laws S7 BOOK II GRAVITATION AND MOLECULAR ATTRACTION CHAPTER I GRAVITY. CENTRE OF GRAVITY. THE BALANCE 68. Universal attraction : its laws. — Universal attraction is a force in virtue of which the material particles of all bodies tend incessantly to approach each other ; it is an action, however, which all bodies, at rest or in motion, exert upon one another, no matter how great or how small the space between them may be, or whether this space be occupied or un- occupied by other matter. A vague hypothesis of the tendency of the matter of the earth and stars to a common centre was adopted even by Democritus and Epicurus. Kepler assumed the existence of a mutual attraction between the sun, the earth, and the other planets. Bacon, Galileo, and Hooke also recognised the existence of universal attraction. But Newton was the first who estabhshed the law, and the universality of gravitation. After Newton's time the attraction of matter by matter was experimentally established by Cavendish. This eminent English physicist succeeded, by means of a delicate torsion balance (89), in rendering visible the attraction between a large leaden and a small copper ball. The attraction between any two bodies is the resultant of the attractions of each molecule of the one upon every molecule of the other according to the law of Newton, which may be thus expressed : the attraction between two material particles is directly proportional to the product of their masses and inversely proportional to the square of their distances asunder. To illustrate this, we may take the case of two spheres, which, owing to their symmetry, attract each other just as if their masses were concentrated in their centres. If without other alteration the mass of one sphere were doubled, tripled, &c., the attraction between them would be doubled, tripled, &c. If, however, the mass of one sphere being doubled, that of the other were increased three times, the distance between their centres remaining the same, the attraction would be increased six times. Lastly, if, without alter- mg their masses, the distance between their centres were increased from i to 2, 3, 4 . . . units, the attraction would be diminished to the 4th, 9th, 5 8 Gravitation and Molecular Attraction [68- 1 6th ... . part of its former intensity. Thus, F = G . —-, where m, m' are the masses of the spheres, r the distance between their centres, F the force between them, and G the Newtonian constant of gravitation. Cavendish measured F with known vahies of m, m\ and r, and so determined G. Cavendish's experiment has been repeated by Cornu, Boys, and others. The value of G, according to the most recent experiments, is 6-6579 x 10-" in C.G.S. units. 69. Terrestrial gravitation. — The tendency of any body to fall towards the earth is due to the mutual attraction of that body and the earth, or to terrestrial gravitation, and is, in fact, merely a particular case of universal attraction. At any point of the earth's surface, the direction of gravity — that is, the line which a falling body describes — is called the vertical line. The vertical lines drawn at different points of the earth's surface converge very nearly to the earth's centre. For points situated on the same meridian the angle con- tained between the vertical lines equals the difference between the latitudes of those points. The directions of the earth's attraction upon neighbouring bodies, or upon different molecules of one and the same body, must therefore be considered as parallel, for the two vertical lines form the sides of a triangle whose vertex is near the earth's centre, about 4,000 miles distant, and whose base is the small distance between the molecules under consideration. A plane or line is said to be horizontal when it is perpendicular to the vertical line. The vertical line at any point of the globe is generally determined by the plumb-line (fig. 46), which consists of a weight attached to the end of a string. It is evident that the weight cannot be in equilibrium unless the direction of the earth's attraction upon it passes through the point of support, and therefore co- incides with that of the string. The horizontal plane is also determined with gi'eat ease, since it coincides, as will be afterwards shown, with the level surface of every liquid when in a state of equili- brium. When the mean figure of the earth has been approxi- mately determined, it becomes possible to compare the direction of the plumb-line at any place with that of the normal to the mean figure at that place. When any differ- ence in these directions can be detected, it constitutes a deviation of the plumb-line, and is due to the attraction of ■* some great mass of matter in the neighbourhood, such as a mountain. Thus, in the case of the mountain of Schiehallion, in Perthshire, It was found by Dr. Maskelyne that the angle between the directions of two plumb-lines, one at a station to the north, and the other to the south, of the mountain was greater by n-6" than the angle between the normals of the mean surface of the earth at those points ; in other words, each plumb- line was deflected by about 6" towards the mountain. By calculating the volume and mass of the mountain, it was inferred from this observation 9 -70] Centre of Gravity : its Experimental Determination 59 that the mean density of the mountain was to that of the earth in the ratio of 5 : 9, and that the mean density of the earth is about five times that of water. The mean density of the earth is calculated from Cavendish's experiment as follows : — In the formula F = G ^^ , let 7?/ = i gramme, and ot = the mass of the earth, concentrated at its centre, r = 4ooo miles = 6-4 x 10" cm. ; then F=^dynes, and^= G — _, whence m is determined, and hence the mean density, which is the mass of the earth divided by its volume. If G be taken = 6-6579 x io~*, the mean density = 5'527. 70. Centre of gravity : its experimental determination. — Into what- ever position a body may be turned with respect to the earth, there is a certain point invariably situated with respect to the body, through which the resultant of the attracting forces between the earth and its several mole- cules always passes. This point is called the centre of gravity ; it may be within or without the body, according to the form of the latter ; its existence, however, is easily established by the following considerations : let m 711' m" m'". . . . (fig. 47) be molecules of any body. The earth's attraction upon these molecules will constitute a system of parallel forces, having a common vertical direction, whose resultant will be found by seeking first the resultant of the forces which act on any two molecules, m and m', then that of this resultant and a third force acting on m", and so on until we arrive at the final resultant W, representing the weight of the body and applied at a certain point G. If the body be now turned into the position shown in fig. 48, the molecules in m' m". . . . will continue to be acted on by the same forces as before, the resultant of the forces on m and w?' will pass through the same point in the line mm', the following resultant will again pass through the same point o' in om'\ and so on up to the final resultant P, which will still pass through the same point G, which is the centre of gravity. To find the centre of gravity of a body is a purely geometrical problem ; in many cases, however, it can be at once determined. For instance, the centre of gravity of a right line or fine straight wire of uniform density is the point which bisects its length ; in the circle and sphere it coincides with the geometrical centre ; in cylindrical bars it is the middle point of the axis. The centre of gravity of a plane triangle is in the line which joins any vertex 6o Gravitation and Molecular Attraction [70- with the middle of the opposite side, and at a distance from the vertex equal to two-thirds of this line : in a cone or pyramid it is in the line which joins the vertex with the centre of gravity of the base, and at a distance from the vertex equal to three-fourths of this line. These rules, it must be remembered, presuppose that the several bodies are of uniform density. In order to determine experimentally the centre of gravity of a body, it is suspended by a string in two different positions, as shown in figs. 49 and 50 ; the point where the directions AB and CD of the string in the two experiments intersect each other is the centre of gravity required. For, the resultant of the earth's attraction being a vertical force applied at the centre of gravity, the body can only be in equilibrium when the point lies vertically under the point of suspension ; that is, in the prolongation of the suspended string. But the centre of gravity, being in AB as well as in CD, must coincide with the point of intersec- tion of these two lines. The centre of gravity of a thin piece of cardboard of irregular shape, for instance, may be found by balancing it in two positions on a knife-edge ; the centre of gravity will then He in the inter- section of the two lines. 71. Equilibrium of heavy bodies. — Since the action of gravity upon a body reduces itself to a single vertical force applied at the centre of gravity and directed to- wards the earth's centre, equili- brium will be established only when this resultant is balanced by the resultant of other forces and resistances acting on the body at the fixed point through which it passes. When only one point of the body is fixed, it will be in equilibrium if the vertical line through its centre of gravity passes through the fixed point. If more than one point is supported, the body will be in equilibrium if a vertical line, through the centre of gravity, passes through a point within the polygon formed by joining the points of support. The Leaning Tower of Pisa continues to stand because the vertical line drawn through its centre of gravity passes within its base. It is easier to stand on our feet than on stilts, because in the latter case the smallest motion is sufficient to cause the vertical line through the centre of gravity of our bodies to pass outside the supporting base, which is here reduced to a mere line joining the feet of the stilts. A man carrying a load on his back must lean forward ; if he carries it in the left hand he must incline the upper part of his body to the right, for otherwise the centre of gravity of the body and of the load would fall outside the line joining the feet, and he would fall. Again, it is impossible to stand on one leg if we keep one side of the foot and head close to a vertical wall, because the latter prevents Fig. 49 Fig. 50 -73] The Balance 6i us from throwing the body's centre of gravity vertically above the supporting base. 72. Different states of equilibrium. — Although a body supported by a fixed point is in equilibrium whenever its centre of gravity is in the vertical line through that point, the fact that the centre of gravity tends incessantly to occupy the lowest possible position leads us to distinguish between three states of equilibrium — stable, unstable, 7teutraL A body is said to be in stable equilibrium if it tends to return to its first position after the equilibrium has been slightly disturbed. Every body is in this state when its position is such that the slightest alteration of the same elevates its centre of gravity ; for the centre of gravity will descend again when permitted, and after a few oscillations the body will return to its original position. The pendulum of a clock continually oscillates about its position of stable equilibrium, and an ^^'g on a level table is in this state when its long axis is horizontal. We have another illustration in the toy represented in the adjoining fig. 51. A small figure cut in ivory is made to stand on one foot at the top of a pedestal by being loaded with two leaden balls, a, b, placed sufficiently low to throw the centre of gravity g of the whole compound body below the foot of the figure. After being disturbed, the little figure oscillates like a pendulum, having its point of suspension at the toe, and its centre of gravity at a lower point, g. A body is said to be in unstable eguilibtium when, after the slightest dis- turbance, it tends to depart still more from its original position. A body is in this state when its centre of gravity is vertically above the point of support, or higher than it would be in any adjacent position of the body. An egg standing on its end, or a stick balanced upright on the finger, is in this state. Lastly, if in any adjacent position a body still remains in equilibrium, its state of equilibrium is said to be neutral. In this case an alteration in the position of the body neither raises nor lowers its centre of gravity. A perfect sphere resting on a horizontal plane is in this state. Fig. 52 represents three cones, A, B, C, placed respectively in ^'s- 5= stable, unstable, and neutral equilibrium upon 4 horizontal plane. The letter g in each shows the position of the centre of gravity. 73. The balance. — The balance is an instrument for determining the relative weights or masses of bodies. There are many varieties. The ordinary balance (fig. 53) consists of a lever of the first kind, called Fig. SI 62 Gravitation and Molecular Attraction [73- the biam, AB, with its fulcrum in the middle ; at the extremities of he beam are suspended two scale-pans, C and D, one intended to receive the object to be weighed, and the other the counterpoise. The fulcrum consists of a steel prism, n, commonly called a knife-edge, which passes through the beam, and rests with its sharp edge, or axis of suspension, upon two supports ; these are formed of agate, in order to diminish the friction. A needle or pointer is fixed to the beam, and oscillates with it in front of a graduated arc : when the beam is perfectly horizontal the needle points to the zero of the graduated arc (fig. 57). Since two equal forces in a lever of the first kind cannot be in equi- librium unless their leverages are equal (40), the length of the arms nk. and «B ought to remain equal during the process of weighing. To secure this the scale-pans are suspended from hooks, whose curved parts have sharp wiamiiiiiMiiiiiiiwiwiiiiiiim iBmapiiiiiiiiii F'g. 53 edges, and rest on similar edges at the ends of the beam. In this manner the scale-pans are in effect supported on mere points, which remain unmoved during the oscillations of the beam. This mode of suspension is represented in fig. 53. 74. Conditions to be satisfied by a balance.— A good balance ought to satisfy the following conditions : — i. The two arms of the beam ought to be precisely equal ; otherwise, according to the principle of the lever, unequal weights will be required to produce equilibrium. To test whether the arms of the beam are equal, weights are placed in the two scale-pans, until the beam becomes horizontal ; the contents of the pans being then interchanged, the beam will remain horizontal if its arms are equal, but if not, it will descend on the side of the longer arm. 75] Delicacy of the Balance 63 ii. The balance ought to be in equilibrium when the scale-pans are empty, for otherwise unequal weights must be placed in the pans in order to produce equilibrium. It must be borne in mind, however, that the arms are not necessarily equal, even if the beam remains horizontal when the scale -pans are empty ; for this result might also be produced by giving to the longer arm the lighter scale. iii. The beam being horizontal, its centre of gravity ought to be in the same vertical plane with the edge ofthefulctum, and a little below the latter, for otherwise the beam would not be in stable equilibrium (72). The effect of changing the position of the centre of gravity may be shown by means of a beam (fig. 54), whose fulcrum, being the nut of a screw, a, can be raised or lowered by turning the screw head, b. Fir- 54 When the fulcrum is at the top of the groove c, in which it slides, the centre of gravity of the beam is below its edge, and the latter oscillates freely about a position of stable equilibrium. By gradually lowering the fulcrum its edge may be made to pass through the centre of gravity of the beam when the latter is in neutral equilibrium ; that is to say, it no longer oscillates, but remains in equilibrium in all positions. When the fulcrum is lowered still more, the centre of gravity passes above its edge, the beam is in a state of unstable equilibrium, and is overturned by the least displacement. 75. Delicacy of the balance. — A balance is said to be delicate or sensible when a very small difference between the weights in-the scale-pans causes a perceptible deflection of the pointer. Let A and B (figs. 55 and 56) be the points from which the scale-pans are suspended, and C the axis of suspension of the beam. A, B, and C are Fis- 55 Fig. 56 assumed to be in the same straight line, according to the usual arrangement. Suppose weights P and Q to be in the pans, suspended from A and B re- spectively, and let G be the centre of gravity of the beam ; then the beam will come to rest in the position shown in the figure, where the line DCN is 64 Gravitation and Molecular Attraction [76- vertical, and ECG is the direction of the pointer. According to the above statement, the greater the angle ECD for a given difference between P and Q, the greater is the sensibility of the balance. Draw GN at right angles to CG. Let W = the weight of the beam, 2a = the length of the beam, and CG = ^, then from the properties of the lever(43) it follows that, measuring moments with respect to C, the moment of P equals the sum of the moments of Q and W, a condition which at once leads to the relation -Q)AC = WxGN; (P- or, since GN = /« tan 5, where 6 = tane the angle DCE, (P-Q)g AW ■ From this we learn that for a given value of P — Q {e.g: i milligramme), tan 6, and therefore 0, is greater as a is greater, and A and W less. Hence the means of rendering a balance delicate are — i. To make the arms of the balajice long. ii. To make the weight of the beam as small as is consistent with its rigidity. iii. To bring the centre of gravity of the beam a very little below the point of support. If the arms of the balance were long there would be a tendency for the beam to bend when the pans are loaded ; consequently, a is usually not rig. 57 more than about 1 5 cm., and sensitiveness is secured by making W, or /z, or both, small. The weight of the beam is reduced as far as possible, without diminishing its rigidity, by portions of it being rut away (fig. 57). The posi- -77] Method of Double Weighing 65 tion of the centre of gravity of the beam and pointer is controlled by the circular nut, C, which works on a screw immediately over the pointer : by raising the nut we may make h as small as we please, and so increase the sensitiveness. The sensitiveness of a balance is expressed by the angle of deflection of the beam when the weights in the pans differ by a milligramme. 76. Physical and chemical balances. — Fig. 57 represents one of the accurate balances ordinarily used for chemical analysis. Its sensitiveness is such that when charged with a kilogramme (1,000 grms.) in each scale an excess of a tenth of a milligramme (x^h^TS of^^ g'^'^-) '" either scale produces a very perceptible deflection of the index. In order to protect the balance from air currents, dust, and moisture, it is always, even during a weighing, surrounded by a glass case, whose front slides up and down, to enable the operator to introduce the object to be weighed and the balancing weights. Where extreme accuracy is desired the case is constructed so that the space may be exhausted, and the weighing made in vacuo. In order to preserve the edge of the fulcrum as much as possible, the whole beam, BB, with its fulcrum K, can be raised from the support on which the latter rests by simply turning the button O outside the case. 77. Method of double' weighing. — Even if a balance be not perfectly accurate, the true weight of a body may still be determined by its means. To do so, the body to be weighed is placed in one scale, and shot or sand poured into the other until equi- librium is produced ; the body is then replaced by known weights until equilibrium is re-established. The sum of these weights will necessarily be equal to the weight of the body, for, acting under precisely the same circumstances, both have produced pre- cisely the same effect. The exact weight of a body may also be deter- mined by placing it successively in the two pans of a balance, and then deducing its true weight. For having placed in one pan the body to be weighed, whose true weight is x, and in the other the weight p, required to balance it, let u. and b be the arms of levers corresponding to x and p. Then from the principle of the lever (43) we have ax^pb. Similarly, if p^ is the weight when the body is placed in the other pan, then bx = ap^. Hence abx"^ = abpp^, from which x = Vppi- This method was invented by Pfere Amiot, but is ordinarily known as Borda's Method. lip and /, do not differ much from each other, \/pPi = l{p+Pi)y for example, if a body weigh 43-479 grammes in one pan and 43'47i in the other, its true weight is 43-475. Fig. 58 66 Gravitation and Molecular Attraction [77- Jolly made use of a very sensible balance to determine the constant of gravity. The balance (fig. 58) was placed in a room in the tower of the University of Munich, and to each of the scale-pans was attached, by a wire 21 metres in length, a second scale-pan. A mass of mercury of 5 kilo- grammes contained in a glass vessel was first counterpoised in the upper scale-pan ; it was then moved to the lower one, and it was found necessary to add 3 1 "683 mgr. to the upper pan in order to counterbalance the increase in attractiveness due to the greater force in the lower pan. Taking the radius of the earth at Munich at 6,365,722 metres, the number calculated from the formula in (84) is 33 mgr. ; a sufficiently close result when the difficulties of the experiments are taken into account. A large lead sphere was then placed immediately below the mass in the lower pan, and produced a measurable attraction. From the attraction thus produced by the known mass of the lead it was possible to deduce the mass and the mean density of the earth (69, 70) ; the number obtained was 5-69. Similar experiments made by Professor Poynting have led to the number S'5. -78] Laws of Falling Bodies 67 CHAPTER II LAWS OF FALLING BODIES. INTENSITY OF TERRESTRIAL GRAVITY. THE PENDULUM 78. Laws of fallings bodies. — Since a body falls to the ground in consequence of the earth's attraction on each of its molecules, it follows that, everything else being the same, all bodies, great and small, light and heavy, ought to fall with equal rapidity, and a lump of sand without cohesion should during its fall retain its original form as perfectly as if it were compact stone. The fact that a stone falls more rapidly than a feather is due solely to the unequal resistances opposed by the air to the descent of these bodies ; in a vacuum all bodies fall with equal rapidity. To demonstrate this by ex- periment a glass tube about two yards long (fig. 59) may be taken, having one of its ends completely closed, and a brass cock fixed to the other. After bodies of diffei'ent weights and densities (pieces of lead, paper, feathers, &c.) have been introduced into the tube, the air is withdrawn from it by an air- pump, and the cock closed. If the tube be now suddenly reversed, all the bodies will fall equally quickly. On introducing a little air and again in- verting the tube, the lighter bodies become slightly retarded, and this retardation increases with the quantity of air introduced. The resistance opposed by the air to falling bodies is especially remarkable in the case of liquids. The Staubbach in Switzerland is a good illustration ; an immense mass of water is seen falling over a high precipice, but before reaching the bottom it is shattered by the air into the finest mist. In a vacuum, however, liquids fall like solids without separation of their molecules. The water-hammer (fig. 60) illustrates this : the instrument consists of a thick glass tube about a foot long, half filled with water, the air having been expelled by ebullition previous to closing one extremity with the blow- pipe. When such a tube is suddenly inverted, the water falls in one undivided mass against the Fig. 59 F 2 68 Gravitation and Molecular Attraction [78- other extremity of the tube, and produces a sharp dry sound, resembling that which accompanies the shock of two solid bodies. From Newton's law (68) it follows that when a body falls to the earth the force of attraction which causes it to s do so increases as the body approaches the earth. Unless the height from which '' ■> d>^ the body falls, however, be very great, this increase will be altogether inappreci- able, and the force in question may be considered as constant and continuous. If the resistance of the air were removed, therefore, the motion of all bodies falling to the earth would be uniformly accele- rated, and would obey the laws already explained (52). 79. Atwood's machine. — Several in- struments have been invented for illus- trating and experimentally verifying the laws of falling bodies. Galileo, who dis- covered these laws in the early part of the seventeenth century, illustrated them by means of bodies falling down inclined planes. The great object of all such in- struments is to diminish the rapidity of the fall of bodies without altering the character of their motion, for by this means their motion may not only be better observed, but it will be less modified by the resistance of the air (50) The most convenient instrument of this kind is that invented by Atwood at the end of the nineteenth century, and represented in fig. 61. It consists of a stout pillar of wood, about 2 J yards high, at the top of which is a brass pulley, whose axle rests and turns upon four other wheels, called friction •wheels, inasmuch as they serve to diminish friction. Two equal weights, M and M', are attached to the extremities of a fine silk thread, which passes round the pulley ; a timepiece, H, fixed to the pillar, is regulated by a seconds pendulum, P, in the usual way ; that is to say, the oscillations of the pendulum are communicated to an escapement, whose two teeth, as seen in the figure, fit into those of the ratchet wheel. The axle of this wheel gives motion to the seconds hand of the dial, and also to an eccentric behind the dial, as shown at E by a separate figure. This eccentric plays against the extremity of a lever, D, which it pushes until the latter no longer supports the small plate i ; and thus the weight M, which at first rested on this plate, is suddenly exposed to the free action of gravity. The eccentric is so con- structed that the little plate z falls precisely when the hand of the dial points to zero. The weights, M and M', being equal, hold each other in equilibrium ; the weight M, however, is made to descend slowly by putting a small bar or overweight m upon it ; and, to measure the spaces which it describes, the rod Fig. 60 -79] Atwood's Machine or scale Q is divided into feet and inches, commencing from the To complete the instrument there are a number of plates, A, A', C, a number of rings, B, B', which may be fixed by screws at any part of the scale. The plates arrest the descending weight M, the rings only arrest the bar or overweight in, which was the cause of motion, so that after passing through a ring the weight M, in consequence of its inertia, will move on uniformly with the velocity it had acquired on reaching the ring. The several parts of the apparatus being described, a few words will suffice to explain the method of experimenting. Let the hand of the dial be placed behind the zero point, ■the lever D adjusted to support the plate z', on which the weight M with its overweight m rests, and the pendulum put in motion. As soon as the hand of the dial points to zero, the plate i will fall, the weights M and in will descend, and by a little attention and a few trials it will be easy to place a plate A so that M may reach it exactly as the dial indi- cates the expiration of one second. To make a second ex- periment let the weights M and in, the plate i, and the lever D be placed as at first ; remove the plate A, and in its place put a ring, B, so as to arrest the overweight ;« just when the weight M would have reached A ; on putting the pendulum in motion again it will be easy, after a few trials, to put a plate, C, so that the weight M may fall upon it precisely when the hands of the dial point to two seconds. Since the overweight in in this 69 plate i. C, and Fig. 61 experiment was arrested by the ring B at the expiration of one second, the space BC was described by M in one second purely in virtue of its own 70 Gravitation and Molecular Attraction [79- inertia, and consequently (32), BC will indicate the velocity of the falling mass at the expiration of one second. Proceeding in the same manner as before, let a third experiment be made in order to ascertain the point B' at which the weights M and;« arrive after the lapse of two seconds, and putting a ring at B', ascertain by a fourth experiment the point C at which M arrives alone, three seconds after the descent commenced ; B'C will then express the velocity acquired after a descent of two seconds. In a similar manner, by a fifth and sixth experiment, we may detei'mine the space OB" described in three seconds, and the velo- city B"C" acquired during those three seconds, and so on ; we shall find that B'C is twice and B"C" three times as great as BC — in other words, that the velocities BC, B'C, B"C" increase in the same proportion as the times, (i, 2, 3, ... . seconds) employed in their acquirement. By the defi- nition (51), therefore, the motion is uniformly accelerated. The same ex- periments will also serve to verify and illustrate the four laws of uniformly accelerated motion as enunciated in 51. For example, the spaces OB, OB', OB", . . . described from a state of rest in i, 2, 3, seconds, will be found to be proportional to the numbers i, 4, g . . . ; that is to say, to the squares of those numbers of seconds, as stated in the third law. Lastly, if the overweight ni be changed, the acceleration or velocity BC acquired per second will also be changed, and we may easily verify the assertion (30) that force is proportional to the product of the mass moved, into the acceleration produced in a given time. For instance, assuming the pulley to be so light that its inertia can be neglected, then if m weighed half an ounce, and M and M' each 1 5f ounces, the acceleration BC would be found to be six inches ; whilst if m weighed one ounce, and M and M' each 63J ounces, the acceleration BC would be found to be three inches. Now in these cases the forces producing motion, that is the overweights, are in the ratio of i : 2 ; while the products of the masses and the accelerations are in the ratio of (J + 15J+ ijf) x 6 to (i -1-63^ + 63^) x 3 ; that is, they are also in the ratio i : 2. Now the same result is obtained in whatever way the magnitudes of m, M, and M' are varied, and consequently in all cases the ratio of the forces producing motion equals the ratio of the momenta generated. To determine the value of^we may make use of the formula of article 30, viz. F = Myj where F is the force acting upon a mass M, and/ is the resulting acceleration. When the weight of m (i.e. mg) puts the mass ;« -^ M -h M' in motion, let the acceleration be/"; then mg= {m -I- M + M')/; whence g is determined. If /= 3 inches, the unit of time being one second, ;« = J oz., and M = M'=I5| ; 5.^= (i + 1 51 + I Si) -J, and ^= 32. 80. Morin's apparatus. — The principle of this apparatus, the original idea of which is due to General Poncelet, is to make the falling body trace its own path. Fig. 62 gives a view of the whole apparatus, and fig. 63 gives the details. The apparatus consists of a wooden framework, about 7 feet high, which holds in a vertical position a very light wooden cylinder, M, which can turn freely about its axis. This cylinder is coated with paper divided into squares by equidistant horizontal and vertical lines. The latter -80] Morin's Apparatus 71 measure the path traversed by the body falling along the cylinder, while the horizontal lines are intended to divide the duration of the fall into equal parts. The falling body is a mass of iron, P, provided with a pencil, which is pressed against the paper by a small spring. The iron is guided in its fall by two light iron wires which pass through guide-holes on the two sides. The top of this mass is provided with a tipper which catches against the end Fig. 63 Fig. 62 of a bent lever, AC. This being pulled by the string K attached at A, the weight falls. If the cylinder M were fixed, the pencil would trace a straight line on it ; but if the cylinder moves uniformly, the pencil traces the line mn, from which the law of the fall may be deduced. The cylinder is rotated by means of a weight, Q, suspended to a cord which passes round the axle G. At one end of this is a toothed wheel e 72 Gravitation and Molecular Attraction [80- which turns two endless screws, a and b, one of which is connected to the axis of the cyhnder, and the other to the two vanes x and x' (fig. 63). At the other end is a ratchet wheel, in which fits the end of a lever, B ; by pulling at a cord fixed to the other end of B, the wheel is liberated, the weight Q descends, and the whole system begins to turn. The motion is at first accelerated, but as the air offers a resistance to the vanes (50), which increases as the rotation becomes more rapid, the resistance finally equals the acceleration which gravity tends to impart. From this time the motion becomes uniform. This is the case when the weight Q has traversed about three- quarters of its course ; at this moment the weight P is detached by pulling the cord K, and the pencil then traces the curve mn. If, by means of this curve, we examine the double motion of the pencil on the small squares which divide the paper, we see that for displacements i, 2, 3 .... in a horizontal direction, the displacements are i, 4, 9 .... in a vertical direction. This shows that the paths traversed in the direction of the fall are directly as the squares of the lines in the direction of the rotation, which verifies the second law of falling bodies. From the relation which exists between the two dimensions of the curve nin, it is concluded that this curve is s. parabola (53). 81. The length of the compound pendulum. — The formula deduced in article 56, and the conclusions which follow there- from, refer to the case of the simple or mathematical pendulum ; that is, to a single heavy point suspended by a thread without weight. Such a pendulum has only an imaginary existence, and any pendulum which does not realise these conditions is called a compound or physical pendulum. The laws for the time of vibration of a compound pendulum vibrating about an axis (axis of suspension) are the same as those for a simple pendulum, though it will be necessary to define accurately what is meant by the length of such a pendulum. A compound pendulum being formed of a heavy rod terminated by a greatei or less mass, it follows that the several material points of the whole system will strive to perform their oscillations in different times, their distances from the axis of suspension being different, and the more distant points requiring a longer time to complete an oscillation. From this, and from the fact that being points of the same body they must all oscillate together, it follows that the motion of the points near the axis of suspension will be Fig. 64 retarded, whilst that of the more distant points will be accelerated, and between the two extremities there will necessarily be a series of points whose motion will be neither accelerated nor retarded, but which will oscillate precisely as if they were perfectly free and unconnected with the other points of the system. These points, being equidistant from the axis of suspension, constitute a parallel axis known as Xhs^axis of. oscillation; and it is to the distance between these two axes that the term length of the compound pendulum is applied : we may say, therefore, that the length of a compound pendulum is that of the si?nple pendulum which would describe its oscillations in the sajne time. -81] The Length of the Compound Pendulum n Huyghens, the celebrated Dutch physicist, discovered that the axes of suspension and oscillation are mutually convertible ; that is to say, the time of oscillation will remain unaltered when the pendulum is suspended from its axis of oscillation. This enables us to determine experimentally the length of the compound pendulum. For this purpose the reversible pendulum devised by Bohnenberger and Kater may be used. One form of this (fig. 64) is a rod with the knife-edges a and b turned towards each other. W and V are sHding masses the relative positions of which may be varied. By a series of trials a position can be found such that the number of oscillations of the pendulum in a given time is the same whether it oscillates about the axis a or the axis b. This being so, the distance ab represents the length / of a simple pendulum which has the same period. From the value of /, thus obtained, it is easy to determine the length of the seconds pendulum. The length of the seconds pendulum— that is to say, of the pendulum which makes half a complete oscillation (to orixo motion) in a second — varies, of course, with the force of gravity. The following table gives its value at the sea-level at various places as determined by observation. The accelerative effect of gravity at these places (56) is obtained in feet and metres, by multi- plying the length of the seconds pendulum, expressed in feet and metres respectively, by the square of 3'i4i5g or 9"8696. Length of Seconds Acceleration of Gravity in Latitude Pendulum in inches Foot-second Metre-second units units Hammerfest . 7o°-4o'N. 39-1948 32-2364 9-8258 Aberdeen 57-9 39-1550 32-2066 9-8164 Konigsberg 54-42 39-1507 32-2002 9-8142 Manchester 53-29 39-1466 32-1968 9-8134 Dublin . 53-21 39-1461 32-1963 9-8132 Berlin 52-30 39-1439 32-1945 9-8124 Greenwich 51-29 39-1398 32-1912 9-8115 Paris 48-50 39-1285 32-1819 9-8039 Rome 41-54 39-1145 32-1703 9-8053 New York 40-43 39-1012 32-1594 9-8019 • Washington . 38-54 39-0968 32-1558 9-8006 Madras . 13-4 39-0268 32-0982 9-7836 Ascension 7-56 39-0242 32-0961 9-7817 St. Thomas 0-25 39-0207 32-0932 9-7826 Cape of Good Hope 33-55 s. 39-0780 32-1404 9-7962 Consequently, ^ or the space described in the first second of its motion by a body falling in vacuo from a state of rest (51) is 16-0466 feet or 4-891 metres at St. Thomas, 1 6*0956 „ „ 4-905 „ at London, and 16-1182 „ „ 4'9I3 „ at Hammerfest. In all calculations, which are merely used for the sake of illustration, we may take 32 feet, or 9*8 metres, as the acceleration due to gravity. The metre (22) and the length of the seconds pendulum differ, at Greenwich, by less than a quarter of an inch. 74 Gravitation and Molecular Attraction [81- From observations with the pendulum, after applying the necessary corrections, and taking into account the effect of rotation (84), the form of the earth can be deduced. 82. Verification of the laws of the pendulum.— In order to verify the laws of the simple pendulum (56) we are compelled to employ a pendulum which, though not strictly simple, is made to differ as little as possible from the simple pendulum. It consists of a small sphere of a very dense substance, such as lead or platinum, suspended from a fixed point by means of a very fine metal wire. A pendulum thus formed oscillates almost like a simple pendulum, whose length is equal to the distance of the centre of the sphere from the point of suspension. In order to verify the isochronism of small oscillations, it is merely neces- sary to count the number of oscillations made in equal times, as the ampli- tudes of these oscillations diminish from 3 degrees to a fraction of a degree ; this number is found to be constant. That the time of vibration is proportional to the square root of the length is verified by causing pendulums, whose lengths are as the numbers i, 4, 9, .... to oscillate simultaneously. The corresponding numbers of oscillations in a given time are then found to be proportional to the fractions i, |, -J-, &c., . . which shows that the times of oscillation in- crease as the numbers i, 2, 3, . . . . &c. By taking several pendulums of exactly equal length, B, C, D (fig. 65), but with spheres of different substances — lead, copper, ivory — it is found that, neglecting the resistance of the air, these pendulums oscillate in equal times, thereby showing that the accelerative effect of gravity on all bodies is the same at the same place. By means of an arrangement resembling the above, Newton verified the fact that the masses of bodies are determined by the balance ; which, it will be remarked, lies at the foundation of the measure of force. For it will be seen on com- paring 56 and 57 with 51 that the law of the periodic time is obtained on the supposition that the force of gravity on all bodies is repre- sented by M.g, in which M is determined by the balance. In order to verify this, he had two equal cylindrical wooden boxes made ; one he filled with wood, and as nearly as possible in the centre of oscillation of the other he placed an equal weight of gold. He then suspended the boxes by threads eleven feet long, so that they formed pendulum? exactly equal so far as weight, figure, and resistance of the air were concerned. Their oscilla- tions were performed in exactly the same time. The same results were obtained when other substances were used, such as silver, lead, glass, sand, salt, wood, water, corn. Now all these bodies had equal weights, and, being- contained in the same boxes, they experienced the same resistance by the Fig. 65 -83] Application of the Pendulum to Clocks 7S air, and if the inference that therefore they had equal masses had been erroneous, by as Httle as the one-thousandth part of the whole, the experi- ment would have detected it. 83. Application of the pendulum to clocks. — The regulation of the motion of clocks is effected by means of pendulums, that of watches by balance- springs. Pendulums were first applied to this purpose by Huyghens in 1658, and in the same year Hooke applied a spiral spring to the balance of a watch. The manner of employing the pendulum is shown in fig. 66. The pendulum rod passing between the prongs of a fork, a, communicates its motion to a rod, b, which oscillates on a horizontal axis, o. To this axis is fixed a piece, mn, called an escapement or crutch, terminated by two pro- jections ox pallets, which work alternately with the teeth of the escapement luheel R. This wheel being acted on by the weight tends to move con- tinuously, let us say, in the direction indicated by the arrow-head. Now, if the pendulum is at rest, the wheel is held at rest by the pallet ni, and with it the whole of the clockwork and the weight. If, how- ever, the pendulum moves and takes the position shown by the dotted line, m is raised, the wheel escapes from the confinement in which it was held by the pallet, the weight descends, and causes the wheel to turn until its motion is arrested by the other pallet n ; which, in consequence of the motion of the pendulum, will be brought into contact with another tooth of the escapement wheel. In this manner the descent of the weight is alternately permitted and arrested — or, in a word, regulated — by the pendulum. By means of a proper train of wheelwork the motion of the escape- ment is communicated to the hands of the clock ; and consequently their motion, also, is regulated by the pendulum. In watches the watch-spring plays the part of the weight in clocks. The pendulum has also been used for measuring great velocities. A large wooden box filled with sand and weighing from 3 to 5 tons is coated with iron ; against this arrangement, which is known as a ballistic pendulum, a shot is fired, and the deflection thereby produced is observed. From the laws of the impact of inelastic bodies, and from those of the pendulum, the velocity of the ball may be calculated from the amount of this deflection. The gun may also be fastened to a pendulum arrangement ; and, when fired, the reaction causes an angular deflection, from which the initial velocity of the shot can be deduced. An interesting application of the pendulum is to the metronome, which consists of a short rod with a fixed bob ; on the rod and above the axis is a sliding weight. By raising this the rate of the pendulum is lengthened ; by lowering it accelerated ; and thus even with a short pendulum the beats can be made pretty long. Maelzel connected this with a clockwork arrange- ment so that the beats are quite audible. Fig. 66 76 Gravitation and Molecular Attraction [84- 84. Causes which modify the intensity of terrestrial gravitation. — The intensity of the force of gravity — that is, the value of ^ — is not the same in all parts of the earth. It is modified by several causes, of which the form of the earth and its rotation are the most important. i. The attraction which the earth exerts upon a body at its surface is the sum of the partial attractions which each part of the earth exerts upon that body, and the resultant of all these attractions may be considered to act from a single point — the centre ; that is, the whole mass of the earth may be supposed to be concentrated at its centre. Hence, if the earth were a perfect sphere, a given body would be equally attracted at any part of the earth's surface. The attraction would, however, vary with the height above the surface. For small alterations of level the differences would be inappreciable ; but for greater heights and in accurate measurements observations of the value of ^ must be reduced to the sea-level. The attraction of gravitation being inversely as the square of the distance from the centre (68), we shall have ^'^ -— • where g is the value of the acceleration of gravity at ' = R'^ ■ (R + hf' ^ s> 1 the sea-level, g^ its value at any height h, and R is the radius of the earth. From this, seeing that h is very small compared with R, and that therefore its square may- be neglected in comparison with R^, we get by simple algebraical transformation^' = -- — ~-^ = =. .? (Rh-/0 K + 2k But even at the sea-level the force of gravity varies in different places in consequence of the form of the earth. The earth is not a true sphere, but an ellipsoid, the major axis of which is 12,754,796 metres, and the minor 12,712,160 metres. The distance, therefore, from the centre being greater at the Equator than at the Poles, and the attraction on a body bemg inversely as the square of these distances, calculation shows that, due to this cause, the attraction is 5,^5 greater at the Poles than at the Equator. This is what would be true if, other things being the same, the earth were at rest. ii. In consequence of the earth's rotation, the force of gravity is further modified. If we imagine a body relatively at rest on the Equator, it really shares the earth's rotation, and describes, in the course of one day, a circle, whose centre and radius are the centre and radius of the earth. Now, since a body in motion tends by reason of its inertia to move in a straight line, it follows that to make it move in a circle, a force must be employed at each instant to deflect it from the tangent (55). Conse- quently, a certain portion of the earth's attraction must be employed in keeping the above body on the surface of the earth, and only the remainder is sensible as L weight. It appears from calculation that at the Equator the 3j^th part of the earth's attraction on any body is thus employed, so that the magnitude of g at the Equator is less by the ,J^th part of what it would be _ were the earth at rest. iii. As the body goes nearer the Poles the force of ^'^•^' gravity is less and less diminished by the effect of centrifugal force. For in any given latitude it will describe a circle coin- ciding with the parallel of latitude in which it is placed ; but as the radii of -84] Terrestrial Gravitation "jy these circles diminish, so does the centrifugal force up to the Pole, where the radius is null. Further, on the Equator the centrifugal force is directly- opposed to gravitation : in any other latitude only a component of the whole force is thus employed. This is seen in fig. 67, in which PP' represents the axis of rotation of the earth, and EE' the Equator. At any given point E on the Equator the centrifugal force is directed along CE, and acts wholly in diminishing the intensity of gravitation ; but on any other point, a, nearer the Pole, the centrifugal force acting in a right line ab at right angles to the axis PP', while gravity acts along aC, gravity is no longer diminished by the whole of the centrifugal force, but only by its component ad^ which is less the nearer a is to the Pole. The combined effect of these two causes — the flattening of the earth at the Poles, and the centrifugal force — is to make the attraction of gravitation at the Equator less by about the yj^nd part of its value at the Poles. 78 Gravitation and Molecular Attraction [85- CHAPTER III PROPERTIES PECULIAR TO SOLIDS 85. Various special properties. — After having described the principal properties common to solids, liquids, and gases, we shall discuss the proper- ties peculiar to solids. They are elasticity, tenacity, ductility, and hardness. With regard to elasticity we must distinguish between elasticity of volume, longitudinal elasticity, and torsional elasticity or simple rigidity. When force is applied to a solid body the shape or the volume of the latter is changed. The force per unit area which produces this change is called the applied stress, and the change itself is spoken of as a strain. Thus stress produces strain. If the displacements of the molecules of a body due to the action of stress are small, the strains produced are proportional to the stresses producing them, and hence the ratio !_£5i! is constant and is called ^ '^ ' strain the coefficient of elasticity of the body, this coefficient being greatest in those cases where a small displacement requires a very large force to produce it. Thus, steel and glass are highly elastic bodies because in them the appli- cation of even a large force will produce only a small change of shape or volume. For by force of elasticity is understood the force with which the displaced particles tend to revert to their original position, and this force is equivalent to that which has brought about the change. Considered from this point of view, gases have the least force of elasticity ; that of liquids is considerably greater, and is, indeed, greater than that of many solids. Thus the force of elasticity of mercury is greater than that of india rubber, glass, wood, and stone. It is, however, less than that of the other metals, with the exception of lead. This mode of defining elasticity differs somewhat from ordinary ideas according to which bodies, 'such as india rubber, are considered highly elastic which undergo considerable change of form on the application of a small force. A body is perfectly elastic when any given stress produces no permanent set, restitution being always complete. It is imperfectly elastic when it does retain permanently such a set. Within the limits of elasticity all bodies may be regarded as perfectly elastic. 86. Volume elasticity. — Elasticity of volume is the only kind of elasticity a liquid or a gas possesses, for hquids and gases have no definite shape. A soUd may by the application of stress have not only its volume but also its shape altered. The volume elasticity of a body is measured, as we have said, by the ratio stress/strain. The stress is the force per unit area uniformly applied to the body to compress it ; the strain is the resulting compression, -87] Longitudinal Elasticity 79 that is, the ratio of the change of volume to the original volume. If the original volume V be reduced to V-w when the stress upon it is increased by an amount^, the strain is w/V, and Coefficient of volume elasticity = c =-c_ = k. V V V The dimensions (63) of p are those of a force divided by an areaj i.e. -=j-/L^ or M/LT*. Since the strain is the ratio of a volume to a volume, its dimensions are zero. Thus the dimensions of k, the coefficient of volume elasticity, are the same as those of a pressure. The reciprocal of k is called the coefficient of compressibility or simply the compressibility of the body. In the following table the volume-elasticities of some sohds are given, and of a few liquids for comparison. The units are C.G.S. Substance /&=:volume elasticity =compressibility Wrought iron 14-56 X 10" •069 X IQ-^' Cast iron . 9-64 X 10" ■103 X IO-" Steel . 18-4 X 10" •054 X IQ-" Glass . ... 4-0 X lO'l •250 X IQ-" Copper i6-8 X 10" ■060 X IO-" Water •22 X 10" 4-55 X IO-" Mercury . 2-6o X 10" •38 X IO-" Alcohol •14 X 10" 7-14 X IO-" 87. Longitudinal elasticity. — If a wire is clamped securely at its upper end, and a weight is attached to its lower end, the wire becomes longer, and, provided the Umits of elasticity are not overstepped, the elongation is directly proportional to the stretching force ; and for wires of the same material but of different diameters, the elongation is inversely proportional to the cross section, the stretching force being constant. These results have been esta- blished by experiment with apparatus such as that represented in fig. 68. At the lower end of the wire AB there is a scale-pan, and on the wire two points A and B are marked, the distance between which is measured by means of the cathetometef . The cathetometer consists of a strong upright brass support, K, with a scale divided into millimetres, which can be adjusted in an exactly vertical position by means of levelling screws and the plumb-line. A small telescope, exactly at right angles to the scale, can be moved up and down, and is provided with a vernier which measures fiftieths of a millimetre. By adjusting the telescope successively on the two points A and B, as represented in the figure, the distance between these points is obtained on the graduated scale. By measuring AB before and after the load has been increased by an amount W, the elongation is obtained. By experiments of this kind it has been ascertained that — The alteration in length within the limits of elasticity is in proportion to 8o Gravitation and Molecular Attraction [87- the length and to the load acting on the body, and is inversely as the cross section. Let r be the radius of the wire, / its length, and e the elongation produced by the application of a load W. The stress, or force per unit of cross section of the wire, is W^/n-r*, and since the length / is stretched by an amount e, the strain is e\l. Thus by the definition, 1 ^ Coefficient of longitudinal I _ ^^^ _ w^/ elasticity, or Young's Modulus \^~ ~~ '^j^e We see from this expression that if the wire have unit cross section (jrr''= i) and be stretched to double its length (« = /), /x = W. In other words, we may define Young's Modulus as the stretching force which must be applied to a wire of unit cross section to double its length. This cannot be directly observed, for no substance has elastic limits so wide as to undergo stretching to double its length without permanent set ; /x, however, may be calculated from any accurate observations by means of the above formula. In the following table the values of /i are given in C.G.S. units : — Sub.stance Longitudinal Elasticity=^ Substance Wrought iron Steel . Platinum Copper Slate Zinc Brass . Crown glass 21-2 X 10" ig-2 X 10" 17-4 X 10" 1275 X 10" 11-25 X 10" 8-g X 10" 87 X 10" 8-1 X 10" Rock salt Marble Lead . Pine Oak . Whalebone Ice Sandstone Longitudinal Elasticity =/x 431 X 10" 2-35 X l&^ 1-84 X lo'l 1-13 X 10" •94 X 10" 71 X 10" ■66 X lo^i ■64 X 10" As an example, suppose" we wish to determine the length of copper wire I sq. mm. in cross section which would be stretched 2 mm. by a weight of 10 kilogr. Here W^= 10 x 1000 x 981 dynes, e=-2 cm., nr^ = -oi sq. cm., and 116 = 1275 X 10" ; hence, from the formula, „ io*xq8i X / J , 1275 X 10" = ^ , and/ = 259-5 cm. •01 X -2 The limit of elasticity is given by the smallest force necessary to produce appreciable permanent elongation in a wire of unit cross section. Longitudinal stretching is accompanied by a lateral contraction, and the ratio of the contraction to the stretching is known as Poisson's coefficient. Let S be the section of the wire, and s the diminution of section due to stretching ; then the contraction = - . Also, if L be the original, and / the Increase of, length, — = the stretching. Poisson's ratio = The -=the stretching. Poisson's ratio =-/-/ = _. L * S'l S/ numerator of this fraction is the change of volume due to contraction, the length being constant, and the denominator is the change of volume due to -87] Longitudinal Elasticity 8i stretching, the section being constant. This ratio was taken by Poisson to be o'25, but later experiments have found it to vary from o to 0-5 ; it is about 0-25 for glass, and nearly 0-5 for india rubber. When a wire is stretched by a load to within the limit of elasticity, some time often elapses before the full effect is produced, and conversely when the load is removed the wire does not at once wholly resume its original condition, but a small portion of the deformation remains, and it only reverts to its initial state after the lapse of some time. This phenomenon, first observed by Weber, which is met with in most elastic changes of form, is called the elastic after-action or effect, or the elastic fatigue. This phenomenon is probably due to the fact that the mole- 'cules of bodies are not spherical, but are variously ex- tended in diffe- rent directions, and in elastic de- formation are not only displaced in reference to each other, but are also twisted. This may be illustrated by the following experi- ment. A piece of india rubber tube is closed by a glass plug at the bottom, while the open end is passed over a piece of glass tube. Coloured liquid is then poured in so that it stands at a certain height in this tube. If then a weight is sus- pended to the F- fia F' 6 lower end of the '^' india rubber tube, the liquid at once sinks to a considerable distance and afterwards very slowly a little further. On removing the weight it rises again, but not immediately to the old height. This it only reaches after some time. Both calculation and experiment show that when bodies are lengthened by traction their volume increases. When weights are placed on a bar, the amount by which it is shortened, or the coefficient of contraction, is equal to the elongation which it would experience if the same weights were suspended to it, and is represented by the above numbers. G 82 Gravitation and Molecular Attraction [87- The influence of temperature on the elasticity of iron, copper, and brass was investigated by Kohlrausch and.Loomis. They found that the altera- tion in the coefficient of elasticity by heat is the same as that which heat produces in the coefficient of expansion and in the refractive power ; it is also much the same as the change in the permanent magnetism, and in the specific heat, while it is less than the alteration in the conductivity for elec- tricity. As an application of elasticity may be mentioned Jolly's spring balance. This consists of a long steel wire, ab (fig. 69), wound in the form of a spiral, which is suspended in front of an accurately graduated scale. To the lower end of the spiral two scale-pans, c and d, are hung by a thread, the lower one, d, dipping in a small vessel of water on an adjustable support. The instrument is graduated empirically by observing what displacement of the mark m is produced by putting a known weight in the scale-pan c. Knowing then once for all the constant of the instrument, it is easy to determine the weight of a body by reading the displacement which it produces along the scale. 88. Determination of Young's modulus by flexure. — A solid, when cut into a roid or thin plate, and fixed at one end, after having been more or less bent, strives to return to its original position when left to itself This property is known as the elasticity of flexure., and is very marked in steel india rubber, wood, and paper. If a rectangular bar AB be clamped at one end and loaded at the other end by a weight W (fig. 70), a flexure will pro- duced which may be ob- served by the catheto- meter. The elasticity in- volved here is of the same kind as that investigated above, viz. longitudinal elasticity, the coefficient of which is Young's modulus ; for, as the bar is bent, its upper parts are elongated while the lower parts are compressed. If the amount of this flexure Fig. 70 is denoted by X, Young's modulus is given by the formula _^yNgl'k where W is the load, / the length of the bar, b its breadth, h its depth or thickness, and k a constant, which depends on the manner in which the rod is supported, the three principal cases being represented in fig. 71 ; a is that in which the rod is supported at one end, as in fig. 70 ; in /3 the rod rests on knife-edges, with both ends free ; while in y both ends are rigid ; if one and the same bar be fastened in these different ways, the values of X are respectively i, ijt> ek -89] Elasticity of Torsion. Simple Rigidity 83 It will thus be seen that if for a given load the depression is not to be greater with a long beam than with a short one, the height must increase in the same ratio as the length. The elasticity of flexure is applied in a vast variety of instances — for example, in bows, watch-springs, carriage-springs ; in spring balances it is used to determine weights, in dynamometers to determine the force of agents in prime movers ; and, as a property of wool, hair, and feathers, it is applied to domestic uses in cushions and mattresses. • Whatever be the kind of elasticity, there is, as has been already said (85), a limit to it — that is, there is a molecular displacement beyond which bodies are broken, or at any rate do not regain their primitive form. This limit is affected by various causes. The elasticity of many metals is increased by hardening, whether by cold, by means of thp draw-plate, by rolhng, or by hammering. Some substances, such as steel, cast iron, and glass, become both harder and more elastic by tempering (93). Elasticity, on the other hand, is diminished by annealing, which consists in raising the body to a temperature lower than that necessary for tempering, and allowing it to cool slowly. By this means the elasticity of springs may be regulated at pleasure. Glass, when it is heated, undergoes a true tempering in being rapidly cooled, and hence, in order to lessen the fragility of glass objects, they are reheated in a furnace, and are carefully allowed to cool slowly, so that the particles have time to assume their most stable position (93). 89. Elasticity of torsion. Simple rigidity. — ^The laws of the torsion of wires were determined by Coulomb, by means of an apparatus called the torsion balance (fig. 72). It consists essentially of a metal wire, clamped at one end in a support. A, and holding at the other a metal sphere, B, to which is affixed a light index. Immediately below this there is a graduated •circle, CD. If the sphere is rotated through a certain angle indicated by the position of the index on the scale, which is the angle of torsion, the twisting couple necessary to produce this effect is called the moment of torsion. When, after this deflection, the sphere is left to itself, the reaction of torsion produces its effect, the wire untwists itself, and the sphere rotates about its vertical axis with increasing rapidity until it reaches its position of equilibrium. It does not, however, rest there : in virtue of its inertia it passes this position, and the wire undergoes a torsion in the opposite direc- tion. The equilibrium being destroyed, the wire tends to untwist itself, the 5ame alterations are again produced, and the needle does not rest at zero of the scale until after a certain number of oscillations about this point have been completed. Such an arrangement is sometimes called a torsion j)endulwn. By means of this apparatus Coulomb found that when the amplitude of G 2 84 Gravitation and Molecular Attraction [89- oscillations are represented by the oscillations is within certain limits, the the following laws : I. The oscillations are very nearly isochronous. II. For the same wire, the angle of torsion is proportional to the vioment of torsion. III. With the same moment of torsion, and with wires of the same diameter, the angles of torsion are proportional to the length of the wires. IV. The same moment of torsion being applied to wires of the same length, the angles of torsion are inversely proportional to the fourth powers of the diameters. Wertheim examined the elasticity of torsion in the case of stout rods by means of a different apparatus, and found that it is also subject to these laws. He further found that, all dimensions being the same, different substances undergo different degrees of torsion for the same force, and each substance has its own coefficient of torsion, which is usually denoted by n. The value of this co- efficient is about J that of the longitudinal modulus of felasticity. The laws of torsion may be enunciated in the 2/F formula m = — ^ ; in which a is the angle of tor- nr* sion, F the moment of the force of torsion — i.e. the applied deflecting couple — / the length of the wire, r its radius, and n the torsion-coefficient or simple rigidity. As the angle of torsion is inversely proportional to the fourth power of the radius, rods of some thickness require very great force to produce even small twists. With very small diameters, such as those of a cocoon or glass thread, the proportionality between the angle of torsion and the twisting couple holds even for several complete turns. We may here mention a very ingenious method of obtaining veiy fine threads of glass, aiid even of quartz and other minerals, which has been de- vised by Professor Boys. It consists in attaching a stout thread of the sub- stance in question to a small arrow of straw, melting the end so as to form a small drop. When the arrow is shot from a small crossbow, the drop remains behind in virtue of its inertia (ig), and a thread practically uniform but of excessive tenuity is spun out from it and carried along with the arrow. In this way glass threads go feet in length and TTsViyth of an inch in diameter have been produced. By the same method, melting quartz with the oxy- hydrogen blowpipe, threads of this substance have been produced which are not more than o-ooooi inch in diameter. Such threads are of great value in torsion experiments, for, while they possess great tenacity, they are almost destitute of the property of elastic fatigue (87). go. Tenacity. — Tenacity is the resistance which a body opposes to the total separation of its parts. According to the manner in which the external force acts, we may have various kinds of tenacity : tenacity in the ordinaiy -90] Tenacity 85 sense, or resistance to traction ; relative tenacity, or resistance to fracture ; reactive tenacity, or resistance to crushing ; sheering tenacity, or resistance to displacement of particles in a lateral direction ; and torsional tenacity, or resistance to twisting. Ordinary tenacity is determined in different bodies by forming them into cylindrical or prismatic wires, and ascertaining the weight necessary to break them. Mere increase in length does not influence the breaking weight, for the weight acts in the direction of the length, and stretches all parts as if it had been directly applied to them. Tenacity is directly proportional to the breaking weight, and inversely proportional to the area of a tratisverse section of the wire. Tenacity diminishes with the duration of the traction. A small force continuously applied for a long time will often break a wire, which would not at once be broken by a larger weight. Not only does tenacity vary with different substances, but it also varies with the form of the body. Thus, with the same sectional area, a cylinder has greater tenacity than a prism. The quantity of matter being the same, a hollow cylinder has greater tenacity than a solid one ; and the tenacity of this hollow cylinder is greatest when the external radius is to the internal one in the ratio of 1 1 to 5. The shape has also the same influence on the resistance to crushing as it has on the resistance to traction. A hollow cylinder with the same mass, and the same weight, offers a greater resistance than a solid cylinder. Thus it is that the bones of animals, the feathers of birds, the stems of corn and other plants, offer greater resistance than if they were solid, the mass remaining the same. Tenacity, like elasticity, is not the same in all directions in bodies. In wood, for example, both the tenacity and the elasticity are greater in the direc- tion of the fibres than in a transverse one. And this difference obtains in general in all bodies the texture of which is not uniform. Wires by being worked acquire greater tenacity on the surface, and have therefore a higher coefficient than even somewhat thicker rods of the same material ; and, according to some physicists, solids have a surface tension analogous to that of liquids (133). A strand of wires is stronger than a rod whose section is equal to the sum of the sections of the wires. Wertheim found the following numbers representing the weight in kilo- g'rammes for the limit of elasticity, and for the tenacity of wires, i mm. in diameter. Lead . Tin Silver Copper Platinum C drawn . \ annealed Limit of Elasticity. Kilogrammes 0-25 Tenacity. Kilogrammes 2-07 0-20 I -So j' drawn . \ annealed • 0-45 0'20 2-45 1-70 / drawn . 1 annealed 11-25 29-00 ■ 275 16-02 / drawn . 1 annealed I2-00 . 3-0O 40-30 30-54 / drawn . \ annealed . 26-00 34-IO 14-50 23-50 Limit of Elasticity. Kilogrammes Tenacity Kilogrammes f drawn . . 32-50 6i-io \ annealed 5-00 46-88 /drawn . \ annealed . 42-50 . 15-00 70-00 40-00 / drawn . \ annealed 55-60 80-00 5-00 65-75 86 Gravitation and Molecular Attraction [90- Iron . Steel. Cast Steel . The table shows that of all metals cast steel has the greatest tenacity. Yet it is exceeded by fibres of unspun silk, a thread of which i square milli- metre in section can carry a load of 500 kilogrammes. Single fibres of cotton can support a weight of 100 to 300 grammes ; that is, millions of times their own weight. The tenacity of glass is greatly affected by its chemical com- position, varying from 3-5 to 11 -9 kilogrammes per square millimetre. In this table the bodies are supposed to be at the ordinary temperature. At higher temperatures the tenacity rapidly decreases. Seguin made some experiments on this point with iron and copper, and obtained the following values for the tenacity, in kilogrammes, of millimetre wire at different tem- peratures : — Iron . . at 10°, 60 ; at 370°, 54 ; at 500°, 37 Copper . . „ 21 ; „ 7-7 ; „ o On the other hand, the tenacity is greatly increased at low temperatures : thus Dewar found that at — 182° C. the breaking stress of iron is twice as great as at the normal temperature, and other metals and alloys are all increased by one-third to one-half the normal amount. 91. Ductility. — Ductility is the property in virtue of which a great num- ber of bodies change their forms by the action of traction or pressure. With certain bodies, such as clay, wax, &c., the application of a very little force is sutficient to produce a change ; with others, such as the resins and glass, the aid of heat is needed ; while with the metals more powerful agents must be used, such as percussion, the draw-plate, or the rolling-mill. Malleability is that modification of ductility which is exhibited by ham- mering. The most malleable metal is gold, which has been beaten into leaves about the ^^ dVircth of an inch thick. The most ductile metal is platinum. Wollaston obtained a wire of it 0-00003 of an inch in diameter. This he effected by covering with silver a platinum wire o-oi of an inch in diameter, so as to obtain a cylinder 0-2 inch in diameter only, the axis of which was of platinum. This was then drawn out in the form of wire as fine as possible : the two metals were equally extended. When this wire was afterwards boiled with dilute nitric acid the silver was dissolved, and the platinum wire left intact. The wire was so fine that a mile of it would have weighed only 1-25 of a grain. The glass threads drawn by Professor Boys' method (89) are so fine, being under the -^hsTsCa. of an inch, that a mile would not weigh more than one-third of a grain. Such threads of quartz have a tenacity approaching that of steel wire. 92. Hardness. — Hardness is the resistance which bodies offer to being scratched or worn by others. It is only a relative property, for a body which I. Talc 5- 2. Rock Salt 6. 3. Calcspar 7- 4. Fluorspar -93] Temper 87 is hard in reference |to one body may be soft in reference to others. The relative hardness of two bodies is ascertained by trying which of them will scratch the other. Diamond is the hardest of all bodies, for it scratches all, and is not scratched by any. The hardness of a body is expressed by referring it to a scale of hardness : that usually adopted is — Apatite 8. Topaz Felspar 9. Corundum Quartz 10. Diamond Thus, the hardness of a body which would scratch felspar, but would be scratched by quartz, would be expressed by the number 6'5. Huegenay determined the weight necessary to force a steel point to a depth of 10 mm., and found the order of the metals in increasing hardness as follows : lead, tin, aluminium, gold, silver, platinum, zinc, copper, iron, steel. The pure metals are softer than their alloys. Hence it is that, for jewel- lery and coinage, gold and silver are alloyed with copper to increase their hardness. The hardness of a body has no relation to its resistance to compression. Glass and diamond are much harder than wood, but the latter offers far greater resistance to the blow of a hammer. Hard bodies are often used for polishing powders ; for example, emery, pumice, and tripoli. Diamond, being the hardest of all bodies, can only be ground by means of its own powder. A body which moves with great velocity can cut into bodies which are harder than itself. Thus a disc of wrought iron rotating with a velocity of 1 1 metres in a second was cut by a steel graver ; while when it rotated with a velocity of 20 metres, the edge of the disc could cut the graver, and with a velocity of 50 to 100 metres it could even cut into agate and quartz. A brittle body is one in which the connection between the parts is destroyed by the application of a small force. Arsenic, bismuth, and heated zinc are examples of brittle metals ; they are easily reduced to powder. Brittleness or fragility depends on the fact that bodies possessing it do not allow the molecules to be displaced in reference to each other, but rather the molecules become detached. 93. Temper. — By sudden cooling after they have been raised to a high temperature, many bodies, more especially steel, become hard and brittle. By reheating and cooling slowly, a process which is called annealing, hard and brittle steel may be converted into a soft, flexible material, and in general, by varying the limits of temperature within which the change takes place, almost any degree of elasticity and flexibility may be given to it. This opera- tion is called tempering. All cutting instruments are made of tempered steel. There are, however, some few bodies upon which tempering produces quite a contrary effect. An alloy of one part of tin and four parts of copper, called tantam metal, is ductile and malleable when rapidly cooled, but hard and brittle as elass when cooled slowly. Manganese steel, an alloy of manganese and iron containing about 13 per cent, of manganese, becomes more ductile when raised to a high temperature and quenched in cold water. When annealed in the ordinary way it is hard and brittle. 88 On Liquids [94- BOOK III ON LIQUIDS CHAPTER I HYDROSTATICS 94. Province of hydrostatics. — The science of hydrostatics treats of the conditions of the equilibrium of liquids, and of the pressures they exert, whether within their own mass or on the sides of the vessels in which they are contained. 95. General characters of liquids. — It has been already seen (4) that liquids are bodies whose molecules are displaced by the slightest force. Their fluidity, however, is not perfect ; their particles always adhere slightly to each other, and when a thread of liquid moves, it attempts to drag the adjacent stationary particles with it, and conversely is held back by them. This property is called viscosity (147), and bodies which possess this property in a high degree are said to be viscous. Gases also possess fluidity, but in a higher degree than liquids. The distinction between the two forms of matter is that liquids are only slightly compressible and are comparatively inexpansible, while gases are eminently compressible and expand spontaneously. The fluidity of liquids is seen in the readiness with which they take all sorts of shapes. Their compressibility is established by the following experi- ment. 96. Compressibility of liquids. — From the experiment of the Florentine Academicians (13), liquids were for a longtime regarded as being completely incompressible. Since then researches have been made on this subject by various physicists, which have shown that liquids are really compressible. The apparatus used for measuring the compressibility of liquids has been named the piezometer (Tru'fca, 1 compress ; \>.tT\>ov, measure). That shown in fig. 73 consists of a strong glass cylinder with very thick sides, and an internal diameter of about 3^ inches. The base of the cylinder is firmly cemented into a wooden foot, and on its upper part is fitted a metal cylin- der closed by a cap which can be unscrewed. In this cap there is a funnel, R, for introducing water into the cylinder, and a small barrel hermetically closed by a piston, which is moved by a screw, P. -96] Compressibility of Liquids 89 In the inside of the apparatus there is a glass vessel, A, containing the liquid to be compressed. The upper part of this vessel terminates in a capillary tube, which dips under mercury, O. This tube has been previously divided into parts of equal capacity, and it has been determined \\(m many of these parts the vessel A contains. The latter is ascertained by finding the weight, P, of the mercury which the reservoir A contains, and the weight, p, of the mercury contained in a certain number of divisions, «, of the capillary tube. If N be the number of divisions of the small tube contained in the whole reservoir, we have - = -, from which n p the value of N is obtained. There is further a manometer. This is a glass 'tube, B, contain- ing air, closed at one end, the other end of which dips under mercury. When there is no pressure on the water in the cylinder, the tube B is completely full of air ; but when the water within the cylinder is compressed by means of the screw P, the pressure is transmitted to the mercury, which rises in the tube, compressing the air which it contains. A graduated scale fixed on the side of the tube shows the reduction of volume, and this reduction of volume indicates the pressure exerted on the liquid in the cylin- der, as will be seen later (184). In making the experiment, the vessel A is filled with the liquid to be compressed, and the ^ end dipped under the mercury. By means of I the funnel R the cylinder is entirely filled with water. The screw P being then turned, the Fig. 73 piston moves downwards, and the pressure exerted upon the water is transmitted to the mercury and the air ; in conse- quence of which the mercury rises in the tube B, and also in the capillary tube. The ascent of mercury in the capillary tube shows that the liquid in the vessel A has diminished in volume, and gives the amount of its com- pression, for the capacity of the whole vessel A in terms of the graduated divisions on the capillary tube has been previously determined. In his first experiments, Oersted assumed that the capacity of the vessel A remained the same, its sides being compressed both internally and ex- ternally by the liquid. But this capacity diminishes in consequence of the external and internal pressures. CoUadon and Sturm made some experi- ments allowing for this change of capacity, and found that for a pressure equal to that of the atmosphere, mercury experiences a compression of 0-000003 part of its original volume, water a compression of 0-00005, ^"d ether a com- pression of 0-000133 part of its original bulk. The compressibility of sea- water is only about 0-000044 : it is not materially denser even at great depths ; thus at the depth of a mile its density would be only about x4?t the greater. Amagat has investigated the compressibility of liquids within very wide go On Liquids [96- limits of pressure and temperature. Fig. 74 represents an apparatus by which he worked from 0° to 50° and up to pi-essures exceeding 3,000 atmospheres. The glass cyUnder in Oersted's experi- ment is replaced by-one of steel, G G' G', 18 cm. in diameter and 120 cm. long. It is surrounded by a jacket, HH, which can either be filled with ice, or through which a current of water of uniform temperature can be passed. The liquid is contained in a glass piezometer, the bottom of which dips in a cup of mercuiy, the whole being placed in the mercuiy in the cylinder GG'G'. When pressure is applied the mercury rises in the stem, and touches successively a series of fine platinum wires fused in the stem and connected with an insulated wire which passes from the apparatus through F ; the arrange- ment is such that when the liquid is U HI I ' compressed the mercury rising comes in W H It " contact with the wire and completes a galvanic circuit (Book X), the existence of which is shown by a galvanometer. The pressure is produced at first by a pump which injects water through the tap E ; beyond a certain pressure this is closed, and the pressure continued by the arrange- ment screwed in the top of the apparatus. In this a steel cylinder P, driven by a screw V, worked by a lever T, pushes before it a leather collar C shown on the side. The pressure was measured by means of a manometer let in at the side on the same level as the pieces E and F, which could not be shown in the figure. The results which Amagat attained by this apparatus show that the co- efficient of compressibility of liquids diminishes as the pressure increases ; this diminution is more marked the higher the temperature, but the rate of diminution is less at higher pressures. The coefficient of the compressibility, except in the case of water, increases with the temperature ; the increase is more rapid the higher the temperature, and is less so as the pressures are higher. All the results are corrected for the compressibility of glass, which was found to be 0-05222 per atmosphere ; particular attention was paid to the determination of the coefficient for mercury, which was found to loe cOsSg. Whatever be the pressure to which a liquid has been subjected, experi- ment shows that as soon as the pressure is removed the liquid regains its original volume, from which it is concluded that liquids are perfectly elastic. 97. Equality of pressures. Pascal's law.— By considering hquids as perfectly fluid, and assuming them to be uninfluenced by the action of gravity, the following law has been established. It is often called PascaVs law, for it was first enunciated by him. Fig. 74 -97] Equality of Pressures. Pascal's Law 91 Pressure exerted anywhere upon a viass of liquid is transmitted undi- minished in all directions, and acts with the same force on all equal surfaces, and in a direction at right angles to those surfaces. To get a clearer idea of the truth of this principle, let us conceive a vessel of any given form in the sides of which are placed various cylindrjcal aper- tures, all of the same size, and closed by movable pistons. Let us, further, imagine this vessel to be filled with liquid and unaffected by the action of gravity ; the pistons will, obviously, have no tendency to move. If now a weight of P pounds be placed upon the piston A (fig. 75), which has a surface a, it will be pressed inwards, and the pressure will be transmitted to the internal faces of each of the pistons B, C, D, and E, which will each be forced outwards by a pressure P, their surfaces being equal to that of the first piston. Since each of the pistons undergoes a pressure, P, equal to that on A, let us suppose two of the pistons united so as to constitute a surface na ; it will have to support a pressure 2P. Similarly, if the piston were equal to 3a, it would experience a pressure of 3P ; and if its area were 100 or 1,000 times that of a, it would sustain a pressure of 100 or 1,000 times P. In other Fig. 75 Fig. 76 words, the pressure on any part of the internal walls of the vessel would be proportional to the surface. The principle of the equality of pressure is assumed as a consequence of the constitution of fluids. By the following experiment it can be shown that pressure is transmitted in all directions, although it cannot be shown that it is equally transmitted. A cylinder provided with a piston is fitted into a hollow sphere (fig. 76), in which small cylindrical jets are placed perpen- dicular to the sides. The sphere and the cylinder being both filled with water, when the piston is moved the liquid spouts forth from all the orifices, and not merely from that which is opposite to the piston. The reason why a satisfactory quantitative experimental demonstration of the principle of the equality of pressure cannot be given is, that the influence of the weight of the liquid and of the friction of the pistons cannot be altogether eliminated. Yet an approximate verification may be effected by the experiment represented in fig. 77. Two cylinders of different diameters are joined by a tube and filled with water. On the surface of the liquid are two pistons, P and/, supposed to be without weight, which hermetically close the cylinders, but move without friction. Let the area of the large piston, P, be, for 92 On Liquids [97- mstance, thirty times that of the smaller one, /. That being assumed, let a weight, say of two pounds, be placed upon the small piston ; this pressure will be transmitted to the water and to the large piston, and as this pres- sure amounts to two pounds on each portion of its surface equal to that of the small piston^ the large piston must be exposed to an upward pressure thirty times as much, or of sixty pounds. If now this weight be placed upon the large piston, both will remain in equilibrium ; but, if the weight is '^' '' • greater or less, this is no longer the case. If S and s are the areas of the large and small piston respectively, and P and/ the corresponding loads, then -■-- ; whence P = <—. If instead of being weightless the piston p weighs (say) one pound and the piston P ten pounds, it will be necessary to put a weight of fifty pounds on P to balance one pound put on p. It is important to observe that in speaking of the transmission of pres- sures to the sides of the containing vessel, these pressures must always be supposed to be perpendicular to the sides ; for any oblique pressure may be decomposed into two others, one at right angles to the side, and the other acting parallel with the side ; but, as the latter has no action on the side, the perpendicular pressure is the only one to be considered. PRESSURE PRODUCED IN LIQUIDS BY GRAVITY 98. Vertical downward pressure : its laws.— Any given liquid being in a state of rest in a vessel, if we suppose it to be divided into horizontal layers of the same density, it is evident that each layer supports the weight of those above it. Gravity, therefore, produces internal pressures in the mass of a liquid, which vary at different points. These pressures are sub- mitted to the following general laws : — I. The pressure in each layer is proportional to the depth. I I. With different liquids and the same depth, the pressure is proportional to the density of the liquid. III. The pressure is the same at all points of the same horizontal layer. The first two laws are self-evident ; the third necessarily follows from the first and from Pascal's principle. Meyer has found, by direct experiments, that pressure is transmitted through liquids contained in tubes, with the same velocity as that with which sound travels in the same circumstances. 99. Vertical upward pressure. — The pressure which the upper layers of a liquid exert on the lower layers causes them to exert an equal reaction in an upward direction, a necessary consequence of the principle of trans- mission of pressure in all directions. This upward pressure is termed the buoyancy of liquids ; it is very sensible when the hand is plunged into a liquid, more especially one of great density, like mercury. Fig. 78 -100] Pressure is Independent of the Shape of the Vessel 93 The following experiment (fig. 78) serves to exhibit the upward pressure of liquids. A large open glass tube, A, one end of which is ground, is fitted with a ground-glass disc, O, or, still better, with a thin card or piece of mica, the weight of which may be neglected. To the disc is fitted a string, C, by which it can be held against the bottom of the tube. The whole is then immersed in water, and now the disc does not fall, although no longer held by the string ; it is consequently kept in its position by the upward pressure of the water. If water be now slowly poured into the tube, the disc will only sink when the height of the water inside the tube is equal to the height outside. It follows thence that the upward pressure on the disc is equal to the pressure of a column of water, the base of which is the internal section of the tube A, and the height the distance from the disc to the upper surface of the liquid. Hence the upward pressure of liquids at any point is governed by the same laws as the downward pressure. 100. Pressure is independent of the shape of the vessel. — The pressure exerted by a liquid, in virtue of its weight, on any portion of the liquid, or on the sides of the vessel in which it is contained, depends on the depth and density of the liquid, but is indepen- dent of the shape of the vessel and of the quantity of the liquid. This principle, which follows from the law of the equality of pressure, may be experimentally demonstrated by many forms of apparatus. The following is the one most frequently used, and is due to Haldat. It con- sists of a bent tube, ABC (fig. 79), at one end of which, A, is fitted a stopcock, in which can be screwed two vessels, M and P, of the same height, but different in shape and Fig. 79 capacity, the first being conical, and the other nearly cylindrical. Mercury is poured into the tube ABC, until its level nearly reaches A. The vessel M is then screwed on and filled with water. The pressure of the water acting on the mercury causes it to rise in the tube C, and its height 94 On Liquids [100- may be marked by means of a little collar, a, which slides up and down the tube. The level of the water in M is also marked by means of the movable rod o. When this is done, M is emptied by means of the stop- cock, unscrewed, and replaced by P. When water is now poured in this, the mercury, which had resumed its original level in the tube ABC, again rises in C, and when the water in P has the same height as it had in M, which is indicated by the rod o, the mercury will have risen to the height it had before, which is marked by the collar a. Hence the pressure on the mercury in both cases is the same. This pressure is therefore independent of the shape of the vessels, and, consequently, also of the quantity of liquid. The base of the vessel is obviously the same in both cases ; it is the surface of the mercury in the interior of the tube A. Another mode of demonstrating this principle is by means of an appa- ratus devised by Masson. In this (fig. 80) the pressure of the water con- tained in the vessel M is not exerted upon the column of mercury, as in that of Haldat, but on a small disc or stop, a, which closes a tubulure, c, on which is screwed the vessel M. The disc is now fixed to the tubulure, but is sustained by a thread attached to the end of a scale-beam. At the other end is a pan, in which weights can be placed until they counter- balance the pressure exerted by the water on the stop. The vessel M being emptied is unscrewed, and replaced by the narrow tube P. This being filled to the same height as the large vessel, which is observed by means of the mark 0, it will be observed that to keep the disc in its place just the same weight must be placed in the pan as before ; which leads, therefore, to the same conclusion as does Haldat's experiment. The same result is obtained if, instead of the straight tube P, the oblique tube Q be screwed to the tubulure. From a consideration of these principles it will be readily seen that a -102] Hydrostatic Paradox 95 very small quantity of water can produce considerable pressures. Let us imagine any vessel — a cask, for example — filled with water, and with a long narrow vertical tube tightly fitted into the side. If water is poured into the tube, there will be a pressure on the bottom of the cask equal to the weight of a column of water whose base is the bottom itself, and whose height is that of the water in the tube. The pressure may be made as great as we please ; by means of a narrow thread of water forty feet high Pascal succeeded in bursting a very solidly constructed cask. The toy known as the hydrostatic bellows depends on the same principle, and we shall meet with a most important appHcation of it in the hydraulic press (107). From the principle just laid down, the pressures produced at the bottom of the sea may be calculated. It will be presently demonstrated that the pressure of the atmosphere is equal to that of a column of sea-water about 33 feet high. At sea the lead has frequently descended to a depth of 13,000 feet ; at the bottom of some seas, therefore, there must be a pressure of 400 atmospheres. loi. Pressure on the sides of vessels. — Since the pressure caused by gravity in the mass of a liquid is transnjitted in every direction, according to the general law of the transmission of fluid pressure, it follows that at every point of the side of any vessel a pressure is exerted, at right angles to the side, which we wiU suppose to be plane. The resultant of all these pressures is the total force on the sides. But since these pressures increase in proportion to the depth, and also in proportion to the horizontal extent of the side of the vessel, their resultant can only be obtained by calculation, which shows that the total pressure on any given portion of the side is equal to the weight of a column of liquid which has this portion of the side for its base, and whose height is the vertical distance from the centre of gravity of the portion to the surface of the liquid. If the side of a vessel is a curved surface, the same rule gives the pressure of the surface. The point in the side assumed to be plane, at which the resultant of all the pressures (that is, the total force) is applied, is called the centre of pressure, and is always below the centre of gravity of the side. For if the pressures exerted at different parts of the plane side were equal, the point of applica- tion of their resultant, the centre of pressure, would obviously coincide with the centre of gravity of the side. But since the pressure increases with the depth, the centre of pressure is necessarily below the centre of gravity. This point is determined by calculation, which leads to the following results : — i. With a rectangular plate whose upper edge is level with the water, the centre of pressure is at two-thirds of the line which joins the middle of the horizontal sides measured from the top. ii. With a triangular plate whose base is horizontal, and coincident with the level of the water, the centre of pressure is at the middle of the line which joins the vertex of the triangle with the middle of the base. iii. With a triangular plate whose vertex is level with the water, the centre of pressure is in the line joining the vertex and the middle of the horizontal base, and at three-fourths of the distance of the latter from the vertex. 102. Hydrostatic paradox. — We have already seen that the pressure on the bottom of a vessel depends neither on the form of the vessel nor on the 96 On Liquids [102- quantity bottom. of the liquid, but simply on the height of the liquid above the But the pressure thus exerted must not be confounded with the pressure which the vessel itself exerts on the body which supports it. The latter is always equal to the combined weight of the liquid and the vessel in which it is contained, while the former may be either smaller or greater than this weight, according to the form of the vessel. This fact is often termed the hydrostatic paradox, because at first sight it appears paradoxical. CD (fig. 8i) is a vessel composed of two cylin- drical parts of unequal diameters, and filled with water to a. From what has been said before, the bottom of the vessel CD supports the same pressure as if its diameter were everywhere the same as that of its lower part ; and it would at first sight seem that the scale MN of the balance, in which the vessel CD is placed, ought to show the same weight as if there had been placed in it a cylindrical vessel having the same height of water, and having the diameter of the part D. But the pressure exerted on the bottom of the vessel is not all transmitted to the scale MN ; for the upward pressure upon the surface no oi the vessel is precisely equal to the weight of the extra quantity of water which a cylindrical vessel would contain, and balances an equal portion of the downward pressure on m. Conse- quently the pressure on the plate MN is simply equal to the weight of the vessel CD and of the water which it contains. Fig. 8i CONDITIONS OF THE EQUILIBRIUM OF LIQUIDS 103. Equilibrium of a liquid in a single vessel. — In order that a liquid may remain at x'est in a vessel of any given form, it must satisfy the two following conditions : — I. Its surface must be everywhere perpendicular to the resultant of the forces which act on the molecules of the liquid. II. Every molecule of the mass of the liquid must be subject in every direction to equal and contrary forces. The second condition is self-evident ; for if, in two opposite directions, the forces exerted on any given molecule were not equal and contrary, the molecule would be moved in the direction of the greater force and there would be no equilibrium. Thus the second condition follows from the principle of the equahty of pressures, and from the reaction which all pressure causes on the mass of liquids. To prove the first condition, let us suppose that mp is the resultant of all the forces acting upon any molecule m on the surface (fig. 82), and that this surface is inclined in reference to the force mp. The latter can consequently be decomposed into two forces, mq and mf; the one perpendicular to the surface of the liquid, and the other to the direction mp. Now the first force Fig. 82 -105] Equilibrium of Superposed Liquids 97 Fig. 83 mg would be destroyed by the resistance of the liquid, while the second would move the molecule in the direction mf, which shows that the equili- brium is impossible. If gravity be the force acting on the liquid, the direction mp is vertical ; hence, if the liquid is contained in a basin or vessel of small extent, the sur- face ought to be plane and horizontal (69), because then the direction of gravity is the same in every point. But the case is different with hquid sur- faces of greater extent like that of the ocean. The surface will be perpendi- cular to the direction of gravity ; but as this changes from one point to another, and always tends towards a point near the centre of the earth, it follows that the direction of the surface of the ocean will change also, and assume a nearly spherical form. 104. Eqmlibrium of the same liquid in several communicating' vessels. — When several vessels of any given form communicate with each other, there will be equilibrium when the liquid in each vessel satisfies the two preceding conditions (103), and further, when the surfaces of the liquids in all the vessels are in the same horizontal plane. In the vessels ABCD (fig. 83), which communicate with each other, let us consider any transverse section of the tube inn ; the liquid can only remain in equilibrium as long as the pressures which this section supports from m in the direction of «, and from n in the direction of wz, are equal and opposite. Now it has been already proved that these pressures are respec- tively equal to the weight of a column of water, whose base is the supposed section, and whose height is the distance from the centre of gravity of this section t6 the surface of the liquid. If we conceive, then, a horizontal plane, ;««, drawn through the centre of gravity of this section, it will be seen that there will only be equilibrium as long as the height of the liquid above this plane is the same in each vessel, which demonstrates the principle enunciated. 105. Equilibrium of superposed liquids. — In order that there may be equilibrium when several different liquids are superposed in the same vessel, each of them must satisfy the conditions necessary for a single liquid (103) ; and further, there will be stable eguilibtium only when the liquids are arranged in the order of tlieir decreasing densities from the bottom upwards. The last condition may be experimentally demonstrated by means of a long narrow bottle containing mercury, water saturated with potassium carbonate, alcohol coloured red, and petroleum. When the bottle is shaken the liquids mix, but when it is allowed to rest they separate ; the mercury sinks to the bottom, then comes the water, then the alcohol, and then the H 98 On Liquids [105- r~ m^^: ^ petroleum. This is the order of the decreasing densities of the bodies. The water is saturated with potassium carbonate to prevent its mixing with the alcohol. This separation of the liquids is due to the same cause as that which ■enables solid bodies to float on the surface of a liquid of greater density than their own. On this account, also, fresh water at the mouths of rivers floats for a long time on the denser salt water of the sea ; and for the same reason cream, which is lighter than milk, rises to the surface. io6. Equilibrium of two different liquids in communicating vessels. — When two liquids of different densities, which do not mix, are contained in two communicating vessels, they will be in equilibrium when, in addition to the pre- ceding principles, they are subject to the following condition : that the heights above the horizontal surface of contact of two columns of liquid in equilibrimn are in the inverse ratio of their densities. To show this experimentally, mercury is poured into a bent glass tube, mn, fixed against an upright wooden support (fig. 84) and then water is poured into one of the legs, AB. The column of water, AB, press- ing on the mercury at B, lowers its level in the leg AB, and raises it in the other by a j quantity, CD ; so that if, when equilibrium is established, we imagine a horizontal plane, BC, to pass through B, the column of water in AB will balance the column of mercury, CD. If the heights of these two columns are then measured, it will be found that the height of the column of water is about 13 J times that of the column of mercury. We shall presently see that the density of mercury is about 13J times that of water, from which it follows that the heights are inversely as the densities. It may be added that the equilibrium cannot exist unless there is a sufficient quantity of the heavier liquid for part of it to remain in both legs of the tube. The preceding principle may be deduced by a very simple calculation. Let d and d' be the densities of water and mercury, and h and h' their re- spective heights, and let g be the acceleration due to gravity. The pressure on B will be proportional to the density of the liquid, to its height, and to g; on the whole, therefore, to the product dhg. Similarly, the pressure at C will be proportional to d'h'g. But in order to produce equilibrium, dhgmas'i'h^ equal to d'h'g, or dh = d'h'. This is nothing more than an algebraical expression of the above principle ; for since the two products must always be equal, d' must be as many times greater than d as h' is less than h. In this manner the density of a liquid may be determined. Suppose one of the branches contained water and the other oil, and their heights above their common surface were, respectively, 15 inches for the oil and \CJ!E«I Fig. 84 -107] Hydraulic Press 99 14 inches for the water. The density of water being taken as unity, and that of oil being called x, we shall have 15 X x= 14 X I ; whence x= -3 =o"933. APPLICATIONS OF THE PRECEDING HYDROSTATIC PRINCIPLES 107. Hydraulic press. — The law of the equal transmission of iluid pressure has received a most important application in the hydraulic press, a machine by which enormous pressures may be produced. Its principle is due to Pascal, but it was first constructed by Bramah in 1796. It consists of a cylinder, B, with very strong thick sides (fig. 85), in which there is a cast-iron ram, P, working water-tight in the collar of the Fig. 8s cylinder. On the ram P there is a cast-iron plate on which the substance to be pressed is placed. Four strong columns serve to support and fix a second plate, Q. By means of a leaden pipe, K, the cylinder B, which is filled with water, communicates with a small force-pump. A, which works by means of a lever, M. When the piston of this pump, /, ascends, water rises in the tube a, at the end of which there is a rose, to prevent the entrance of foreign matters. When the piston / descends, it drives the water into the cylinder by the tube K. lOO On Liquids [107- Fig. 86 represents a section, on a larger scale, of the system of valves- necessary in working the apparatus. The valve c, below the piston /, opens. when the piston rises, and closes when it: descends. The valve below h, during this descent, is opened by the pressure of the water which passes by the pipe K. The valve i is a safety-valve, held by a weight which acts on it by means of a lever. By weight- ing the latter to a greater or less extent the pressure can be regulated, for as soon as there is an upward pressure greater than that due to the weight upon it, it opens and water escapes. A screw, r, serves to relieve the pressure, for when it is opened it affords a passage for the efflux of the water in the cylinder B. A most important part is the leather collar, n, the invention of which by Bramah removed the difficulties which h^d been experienced in making the large ram work water-tight when submitted to great pressures. It consists of a circular piece of stout leather (fig. 87), saturated with oil so as to> be impervious to water, in the centre of which a circular hole is cut. This piece is bent so that a section of it represents a reversed (J, and is Fig. 87 fitted into a groove, n, made in the neck of the cylinder. The collar, being concave downwards, fits the more tightly as the pressure increases against the ram P on one side and the neck of the cylinder on the other, and quite prevents any escape of water. The pressure which can be obtained by this press depends on the relation of the diameter of the piston P to that of the piston/. If the former has a transverse section fifty or a hundred times as large as the latter, the upward pressure on the large piston will be fifty or a hundred times that exerted upon the snail one. By means of the lever M an additional advantage is obtained. If the distance from the fulcrum to the point where the force is applied is five times the distance from the fulcrum to the piston /, the pressure on/ will be five times the force applied. Thus, if a man acts on M with a force of sixty pounds, the force transmitted by the piston p will be 300 pounds, and the force which tends to raise the piston P will be 30,000 pounds, supposing the section of P is a hundred times that of/. The hydraulic press is used in cases in which great pressures are re- quired. It is used in pressing cloth and paper, in extracting the juice of beet- root, in compressing hay and cotton, in expressing oil from seeds, and in bending iron plates ; it also serves to test the strength of cannon, of steam -108] The Water-Level lOI boilers, and of chain cables. The parts composing the tubular bridge which ;spans the Menai Straits were raised by means of an hydraulic press. The ■cylinder of this machine, the largest which has ever been constructed, was nine feet long and twenty-two inches in internal diameter ; it was capable ■of raising a weight of two thousand tons. The principle of the hydraulic press is advantageously employed in cases in which great power is only required at intervals, such as in opening dock gates, working cranes, in lifts in hotels, warehouses, and the like. It has ■even been used in working stage machinei-y. In these cases an hydraulic accu- mulator is used. The piston P is loaded with very great weights, and water is continually forced into the cylinder B by powerful pumps. From the bottom of this cylinder a tube conducts water to any place where the power is to be applied, and the flow of even small quantities of water which is under high pressure can perform a great amount of work. Suppose, for instance, that the area of the piston P is four square feet, and that it has a load of loo tons ; this represents a pressure of over 370 pounds ■on the square inch, or more than 25 atmospheres. When the large piston sinks through one-seventeenth of an inch, about a pint of water will flow out, .and this represents a work of about 1,100 foot-pounds. In London hydraulic power is supplied by water delivered under a pressure of 700 pounds per square inch (165). 108. The water-level. — The water-level is an application of the con- •ditions of equilibrium in communicating vessels. It consists of a metal tube i)ent at both ends, in which are fitted glass tubes, D and E (fig. 88). It is placed on a tripod, and water poured in until it rises in both legs. When the Fig. ( liquid is at rest, the level of the water in both tubes is the same ; that is they are both in the same horizontal plane. This instrument is used in levelling, or ascertaining how much one point is higher than another. If, for example, it is desired to find the difterence 'between the-heights of B and A, a levelling-staff' is fixed on the latter place. This staff consists of a rule formed of two sliding pieces of wood, and sup- porting a piece of tin plate, M, at the centre of which there is a mark. This staff being held vertically at A, an observer looks at it through the level :along the surfaces D and E, and directs the holder to raise or lower the slide Fig. 90 102 On Liquids [108— until the mark is in the prolongation of the line DE. The height AM is then measured, and, subtracting it from the height of the level, the height of the point A above B is obtained. 109. The spirit-level. — The spirit-level is both more delicate and more accurate than the water-level. It consists of a glass tube, AB (fig. 89), very slightly curved ; that is, ^'^' ^' the tube, instead of being a true cylinder as it seems to be, is in fact slightly curved in such a manner that its axis is an arc of a circle of very large radius. It is filled with spirit with the exception of a bubble of air, which tends to occupy the high- est part. The tube is placed in a brass case, CD (fig. go), which is so arranged that when it is in a perfectly horizontal position the bubble of air is exactly between the two points marked in the case. To take levels with this apparatus, it is fixed on a telescope, which can be placed in a horizontal position. no. Artesian -wells. — All natural collections of water exemplify the tendency of water to find its level. Thus a group of lakes, such as the great lakes of North America, may be regarded as a number of vessels in communication, and consequently the water tends to maintain the same level in all. This, too, is the case with a source of a river and the sea, and, as the latter is on the lower level, the river continually flows down to the sea along its bed, which is, in fact, the means of communication between the two. Perhaps the most striking instance of this class of natural phenomena is that of artesian wells. These wells derive their name from the province of Artois, where it has long been customary to dig them, and whence their use in other places was derived. It seems, however, that at a very remote period wells of the same kind were dug in China and Egypt. The strata composing the earth's crust are of two kinds : the on^ permeable to water, such as sand, gravel, &c. ; the other impermeable, such as clay. Let us suppose, then, a geographical basin of greater or less extent, in which the two impermeable layers AB, CD (fig. 91), enclose between them a per- meable layer, KK. The rain-water falling on that part of this layer which comes to the surface, and which is called the outcrop, will filter through it, and, following the natural fall of the ground, will collect in the hollow of the basin, whence it cannot escape owing to the impermeable strata above and below it. If, now, a vertical hole, 1, be sunk down to the water-bearing stratum, the water striving to regain its level will spout out to a height which depends on the difference between the levels of the outcrop and of the point at which the perforation is made. The waters which feed artesian wells often come from a distance of -Ill] Pressure on a Body immersed in a Liquid 103 60 or 70 miles. The depth varies in different places. The well at Crenelle is 1,800 feet deep ; it gives 656 gallons of water in a minute, and is one of the deepest and most abundant which have been made. The temperature Fig. 91 of the water is 27° C. It follows from the law of the increase of tempera- ture with the increasing depth below the surface, that, if this well were 210 feet deeper, the water would have all the year round a temperature of 32° C. ; that is, the ordinary temperature of warm baths. BODIES IMMERSED IN LIQUIDS III. Pressure on a body immersed in a liquid. — When a solid is immersed in a liquid, every portion of its ■ surface is submitted to a perpendicular pressure which increases with the depth. If we imagine all these pressures decomposed into horizontal and vertical pressures, the first set are in equilibrium. The vertical pressures are obviously unequal, and will tend to move the body upwards. Let us imagine a cube immersed in a mass of water (fig. 92), and that four of its edges are vertical. The pressures upon the four vertical faces being clearly in equilibrium, we need only consider the pressures exerted on the horizontal faces A and B. The first is pressed downwards by a column of water whose base is the face A, and whose height is AD ; the lower face B is pressed upwards by the weight of a column of water whose base is the face itself, and whose height is BD (99). The cube, therefore, is urged upwards by a force equal to the difference between these two forces, which latter is manifestly equal to the weight of a column of water having the same base and the same height as this cube. Consequently, this upward ^orce is equal to the weight of the volume of water displaced by the im- mersed body. We shall readily see from the following reasoning that every body immersed in a liquid is pressed upwards by a force equal to the weight of the displaced liquid. In a liquid at rest let us suppose a portion of it of any given shape, regular or irregular, to become solidified, with'out either increase or decrease of volume. The liquid thus solidified will remain at 104 On Liquids [Ill- rest, and therefore must be acted upon by a force equal to its weight, and acting vertically upwards] through its centre of gravity ; for otherwise motion would ensue. If in the place of the solidified water we imagine a solid of another substance of exactly the same volume and shape, it will necessarily receive the same pressures from the surrounding liquid as the solidified portion did ; hence, like the latter, it will sustain a force acting vertically up- wards through the centre of gravity of the dis- placed liquid, and equal to the weight of the dis- placed liquid. If, as almost invariably happens, the liquid is of uniform density, the centre of gravity of the displaced liquid means the centre of gravity of the immersed part of the body sup- posed to be of uniform density. This distinction is sometimes of importance : for example, if a '^' '^ sphere is composed of a hemisphere of iron and another of wood, its centre of gravity would not coincide with its geo- metrical centre, but, if it were placed under water, the centre of gravity of the displaced water would be at the geometrical centre — that is, would have the same position as the centre of gravity of the sphere if of uniform density. 112. Principle of Archimedes. — The preceding principles prove that every body immersed in a liquid is submitted to the action of two forces : gravity, which tends to lower it, and the buoyancy of the liquid, which tends to raise it with a force equal to the weight of the liquid displaced. The weight of the body is either totally or partially balanced by its buoyancy, so that a body immersed in a liquid loses a part of its weight equal to the weight of the displaced liquid. This principle, which is the basis of the theory of immersed and fioating bodies, is called the principle of Archimedes, after the discoverer. It may be shown experimentally by means of the hydrostatic balance (fig. 93). This is an ordinary balance, each pan of which is provided with a hook ; the beam can be raised by means of a toothed rack, which is worked by a little pinion C. A catch, D, holds the rack when it has been raised. The beam being raised, a hollow brass cylinder. A, is suspended from one of the pans, and below this a solid cylinder, B, whose volume is exactly equal to the capacity of the first cylinder ; lastly, an equipoise is placed in the other pan. If now the hollow cylinder A be filled with water, the equilibrium is disturbed ; but if at the same time the beam is lowered so that the solid cylinder B be- comes immersed in a vessel of water placed beneath it, the equihbrium will be restored. By being immersed in water the cylinder B loses a portion of its weight equal to that of the water in the cylinder A. Now, as the capacity of the cylinder A is exactly equal to the volume of the cylinder B, the prin- ciple which has been before laid down is proved. 113. Determination of the volume of a body. — The principle of Archimedes furnishes a method for obtaining the volume of a body of any shape, provided it is not soluble in water. The body is suspended by a fine" thread to the hydrostatic balance, and is weighed first in the air, and then in distilled water at 4° C. The loss of weight is the weight of the displaced -114] Equilibrium of Floating Bodies 105 water, from which the volume of the displaced water is readily calculated. But this volume is manifestly that of the body itself Suppose, for example, 155 grammes is the loss of weight. This is consequently the weight of the I Fig- 93 displaced water. Now it is known that a gramme is the weight of a cubic centimetre of water at 4° ; consequently, the volume of the body immersed is 155 cubic centimetres. 114. Equilibrium of floating bodies. — A body when floating is acted on by two forces — namely, its weight, which acts vertically downwards through its centre of gravity, and the resultant of the fluid pressures, which (ill) acts vertically upwards through the centre of gravity of the fluid displaced ; but if the body is at rest these two forces must be equal and act in opposite directions ; whence follow the conditions of equilibrium, namely — i. The floating body must displace a volume of liquid whose weight equals that of the body. ii. The centre of gravity of the floating body must be in the same vertical line with that of the fluid displaced. Thus in fig. 94, if C is the centre of gravity of the body, and G that of the displaced fluid, the line G C must be vertical, since when it is so the io6 On Liquids [114- Fig- 94 Fig. 95 weight of the body and the fluid pressure will act in opposite direction along the same line, and will be in equilibrium if equal. It is convenient, with reference to the subject of the present article, to speak of the line C G produced, as the axis of the body. Next, let it be inquired whether the equilibrium be stable or unstable. Suppose the body to be turned through a small angle (fig. 95), so that the axis takes a position / inclined to the vertical. The centre of gravity of the displaced fluid will no longer be G, but some other point, G'. And since the fluid pressure acts vertically upwards through G', its direction will cut the axis in some point M', which will gene- rally have different positions according as the inclination of the axis to the vertical is greater or smaller. If the angle is indefinitely small, M' will have a definite position, M, which always admits of determination, and is called the metacentre. If we suppose M to be above C, an inspection of fig. g6 will show that when the body has received an indefinitely small displacement, the weight of the body acting at C, and the resultant of the fluid pressures acting through M, tend to bring the body back to its original position ; that is, in this case, the equilibrium is stable (72). If, on the contrary, M is below C, the forces tend to cause the axis to deviate farther from the vertical, and the equilibrium is unstable. Hence the rule — iii. The equilibrium of a floating body is stable or unstable according as the metacentre is above or below the centre of gravity. The determination of the metacentre can rarely be effected except by means of a somewhat difficult mathematical process. When, however, the form of the immersed part of a body is spherical, it can be readily determined ; for since the fluid pressure at each point converges to the centre, and continues to do so when the body is slightly dis- placed, their resultant must in all cases pass through the centre, which is therefore the meta- centre. To illustrate this : let a spherical body float on the surface of a liquid (fig. 97) ; then its centre of gravity and the metacentre both coin- ciding with the geometrical centre, C, its equilibrium is neutral (72). Now suppose a small heavy body to be fastened at P, the summit of the vertical diameter. The centre of gravity will now be at some point, G, above C. Consequently, the equilibrium is unstable, and the sphere, left to itself, will instantly turn over and will rest when P is the lower end of a vertical diameter. On investigating the position of the metacentre of a cylinder, it is found Fig. 97 -117] Swimming 107 that, where the ratio of the radius to the height is greater than a certain quantity, the position of stable equilibrium is that in which the axis is vertical ; but if it be less than that quantity, the equilibrium is stable when the axis is horizontal. For this reason the stump of a tree floats lengthwise, but a thin disc of wood floats flat on the water. Hence, also, if it is required to make a cylinder of moderate length float with its axis vertical, it is necessary to load it at the lower end.. In-this way its centre of gravity is brought below the metacentre. The determination of the metacentre and of the centre of gravity is of great importance in the loading of vessels, for on their relative positions the stability depends. 115. Cartesian diver. — The different effects of suspension, immersion, and floating are reproduced by means of a well- known hydrostatic toy, the Cartesian diver (fig. 98). It consists of a glass cylinder nearly full of water, on the top of which a brass cap, provided with a piston, is hermetically fitted. In the liquid there is a little porcelain figure attached to a hollow glass ball, a, which contains air and water, and floats on the surface. In the lower part of this ball there is a little hole by which water can enter or escape, according as the air in the interior is more or less compressed. The quantity of water in the globe is such that very little more is required to make the figure sink. If the piston is slightly lowered the air is compressed, and this pressure is transmitted to the water of the vessel and the air in the bulb. The compression of the air allows a small quantity of water to penetrate into the bulb, which therefore becomes heavier and sinks. If the pressure is re- lieved, the air in the bulb expands, expels the excess of water which had entered it, and the apparatus, being now lighter, rises to the surface. The appara- tus may be simplified by replacing the brass cap and piston by a cover of sheet india rubber, which is tightly tied over the mouth ; when this is pressed by the hand the same effects are produced. 116. Swimming-bladder of fishes. — Most fishes have an air-bladder below the spine, which is called the swimmmg-bladder. The fish can com- press or dilate this at pleasure by means of a muscular effort, and produce the same effects as those just described — that is, it can either rise or sink in water. 117. Swimming. — The human body is lighter, on the whole, than an equal volume of water, the average ratio being as o'934 : i ; it consequently floats Qn the surface, and still better in sea-water, which is heavier than fresh water. The difficulty in swimming consists, not so much in floating, as in keeping the head above water, so as to breathe freely. In man the head is heavier than the lower parts, and consequently tends to sink, and hence swimming is an art which requires to be learned. With quadrupeds, on the Fig. 98 io8 On Liquids [117- contrary, the head, being less heavy than the posterior parts of the body, remains above water without any effort, and these animals therefore swim naturally. SPECIFIC GRAVITY — HYDROMETERS ii8. Determination of specific gravities. — It has been already ex- plained (27) that the specific gravity of a body, whetner solid or liquid, is the number which expresses the relation of the weight of a given volume of this body to the weight of the same volume of distilled water at a temperature of 4°. In order, therefore, to calculate the specific gravity of a body, it is sufficient to determine its weight and that of an equal volume of water, and then to divide the first weight by the second : the quotient is the specific gravity of the body. Three methods are commonly used in determining the specific gravities of solids and liquids. These are — ist, the method of the hydrostatic balance ; 2nd, that of the hydrometer ; and 3rd, the specific gravity flask. All three, however, depend on the same principle — that of first ascertaining the weight of a body, and then the weight of an equal volume of water. We shall apply these methods to the determination of the specific gravity, first, of solids, and then of liquids. 119. Specific gravity of solids. — i. Hydrostatic balance. — To obtain the specific gravity of a solid by the hydrostatic balance (fig. 93), the body is first weighed in the air, and is then suspended to the hook of the balance and weighed in water (fig. 99). The loss of weight which it experiences is, according to Archi- medes' principle, the weight of its own volume of water ; consequently, dividing the weight in air by the loss of weight in water, the quotient is the specific gravity required. If P is the weight of the body in air, P' ts weight in water, and D its specific gravity, P — P' being the weight of the displaced water, we have D = - — — . It may be observed that, though the weighing is performed in air, yet, strictly speaking, the quantity required is the weight of the body in vacuo ; and when great accuracy is required, it is necessary to apply to the observed weights a correction for the weights of the unequal volumes of air displaced by the substance, and by the weights in the other scale-pan. The water in which bodies are weighed is supposed to be distilled water at the standard temperature. ii. Nicholson's hydrometer. — The apparatus consists of a hollow metal cylinder, B (fig. 100), to which is fixed a cone, C, loaded with lead. The object of the latter is to bring the centre of gravity below the metacentre, so that the cylinder may float with its axis vertical. At the top is a stem terminated by a pan, in which is placed the substance whose specific gravity is to be determined. On the stem a standard point, o, is marked. Fig. 99 -120] Specific Gravity Bottle. Pyknometer 109 Fig. The apparatus stands partly out of the water, and the first step is to ascertain the weight which must be placed in the pan in order to make the hydrometer sink to the standard point o. Let this weight be 125 grains, and let sulphur be the sub- stance whose specific gravity is to be determined. The weights are removed from the pan, and re- placed by a piece of sulphur which weighs less than 125 grains, and weights added till the hydro- meter is again depressed to the point o. If, for instance, it has been necessary to add 55 grains, the weight of the sulphur is evidently the differ- ence between 125 and 55 grains; that is, 70 grains. Having thus determined the weight of the sulphur in air, it is only necessary to ascertain the weight of an equal volume of water. To do this, the piece of sulphur is placed in the lower pan, C, at »z, as re- presented in the figure. The whole weight is not changed ; nevertheless, the hydrometer no longer sinks to the standard ; the sulphur, by immersion, has lost a part of its weight equal to that of the water displaced. Weights are added to the upper pan until the hydrometer sinks again to the stan- dard. This weight, 34-4 grains, for example, re- presents the weight of the volume of water displaced ; that is, of the volume of water equal to the volume of the sulphur. It is only necessary, therefore, to divide 70 grains, the weight in air, by 34-4 grains, and the quotient, 2-03, is the specific gravity. If the body in question is lighter than water, it tends to rise to the surface, and will not remain on the lower pan C. To obviate this, a small movable cage of fine wire is adjusted so as to prevent the ascent of the body. The experiment is in other respects the same. 120. Specific gravity bottle. Pyknometer. — When the specific gravity of a substance in a state of powder is required, it can be found most conve- niently by means of the pyknometer, or specific gravity bottle. This instru- ment is a bottle, in the neck of which is fitted a thermometer. A, an enlarge- ment on the stem being carefully ground for this purpose (fig. loi). In the 'side is a narrow stem widened at the top and provided with a stopper, as shown in the figure. On this tube is a mark, m, and the thermometer stopper having been inserted, the bottle is filled with water exactly to this mark at each weighing. The bottle may conveniently have dimensions such that when the thermometer stopper is inserted and the liquid filled to the mark ?«, it represents a definite volume. This is done by filling the bottle when wholly under water, and putting in the stopper while it is im- mersed. The bottle and the tube are then completely filled, and the quantity of water in excess is removed by blotting-paper. To find the specific gravity, proceed as follows : Having weighed the powder, place it in one of the scale-pans, and with it the bottle filled exactly to m, and carefully dried. Then balance it by placing small shot, or sand, in the other pan. Next, remove the bottle and pour the powder into it, and, as before, fill it up no On Liquids [lao- with water to the mark m. On replacing the bottle in the scale-pan it will no longer balance the shot, since the powder has displaced a volume of water equal to its own volume. Place weights in the scale-pan along with the bottle until they balance the shot. These weights give the weight of the water displaced. Then the weight of the powder and the weight of an equal bulk] of water being known, the specific gravity of the powder is determined as before. The thermometer gives the temperature at which the determination is made, and thus renders it easy to make a correction (123). It is important in this determination to remove the layer of air which adheres to the powder, and unduly increases the quantity of water expelled. This is effected by placing the bottle under the receiver of an air-pump and working the pump. Under the reduced pressure the air adhering to the powder expands, comes to the surface, and ig thus got rid of. The same result is obtained by boiling the water in which the powder is placed. 121. Specific gravity of bodies soluble in water. — If the body whose specific gravity is to be determined by any of these methods is soluble in water, the determination is made in some liquid in which it is not soluble, such as oil of turpentine or naphtha, the specific gravity of which is known or is separately determined. The specific gravity is obtained by multiplying the number obtained in the experiment by the specific gravity of the liquid used for the determination. Suppose, for example, a determination of the specific gravity of potassium has been made in naphtha. For equal volumes, P represents the weight of the potassium, P' that of the naphtha, and P" that of water; consequently, P P' P" Fig. 101 -, will be the specific gravity of the substance in reference to naphtha, and 77 the specific gravity of the naphtha in reference to water. The product of these two fractions - ^,- is the specific gravity of the substance compared with water. A specific gravity bottle of a more simple kind is shown in fig. 104. Porous substances, whose specific gravities are required, are varnished before being immersed in water, which renders them impervious to moisture without altering their volume. -122] Specific Gravity of Liquids III 'lecific gravity of solids at zero as compared with distilled water at 4° C. Platinum, rolled . . 22-069 Rock crystal . 2-653 cast ■ 20-337 St. Gobin glass 2-488 Gold, stamped 19-362 China porcelain . . 2-380 Gold, cast . 19-258 Sfevres porcelain . 2-140 Lead, cast 11-352 Native sulphur • 2-043 Silver, cast . ■ IO-474 Common salt . 2-220 Bismuth, cast 9-822 Ivory • 1-917 Copper, drawn wire . 8-878 Anthracite . 1-800 „ cast . . 8-788 Magnesia 1-740 Bronze coinage . 8-660 Boxwood ■ 1-330 German silver • 8-432 Compact coal 1-329 Brass . 8-383 Amber . . 1-078 Steel, not hammered 7-816 Sodium . . 0-970 Iron, bar • 7788 Iceat o°C. 0-930 „ cast . 7-207 Parafifin . . 0-874 Tin, cast . 7-291 Potassium 0-865 Zinc, cast 6-861 Beech . 0-852 Antimony, cast . 6-712 Oak 0-845 Iodine . 4-950 Elm 0-800 Heavy spar . • 4-430 Yellow pine . . 0-657 Faraday's glass . 4-360 Lithium 0-585 Diamond 3-531 to 3-501 Common poplar . 0-389 Fhnt glass . 3-329 Cork 0-240 Statuary marble . 2-837 Snow ■ 0-183 Aluminium . . 2-680 Pith - 0-055 In this table the different woods are supposed to be in the ordinary air- dried condition. 122. Specific gravity of liquids. — i. Method of the hydrostatic balance. — From the pan of the hydrostatic balance a body is suspended, on which the liquid whose specific gravity is to be determined exerts no chemical action ; for example, a ball of platinum. This is then successively weighed in air, in distilled water, and in the liquid. The loss of weight of the body in these two liquids is noted. They represent respectively the weights of equal volumes of water and of the given liquid, and consequently it is only necessary to divide the second of them by the first to obtain the required specific gravity. Let P be the weight of the platinum ball in air, P' its weight in water, P" its weight in the given liquid, and let D be the specific gravity sought. The weight of the water displaced by the platinum is P — P', and that of the P — P" second liquid is P — P ', from which we get D = ^ — ~^. ii. Fahrenheit's hydrometer. — This instrument (fig. 102) resembles Nichol- son's hydrometer, but it is made of glass, so as to be used in all liquids. At its lower extremity, instead of a pan, it is loaded with a small bulb containing mercury. There is a standard mark on the stem. The weight of the instrument is first accurately determined in air ; it is 112 On Liquids [122- Fig. I02 Fig. 103 then placed in water, and weights added to the scale-pan until the mark on the stem is level with the water. It follows, from the first principle of the equilibrium of floating bodies, that the weight of the hydrometer, together with the weight in the scale-pan, is equal to the weight of the volume of the displaced water. In the same manner the weight of an equal volume of the given liquid is determined, and the specific gravity is found by dividing the latter weight by the former. Neither Fahrenheit's nor Nicholson's hydro- meter gives such accurate results as the hydro- static balance or the specific gravity bottle. iii. Specific gravity bottle.^— Ont form of this has been already described (130). In deter- mining the specific gravity of a liquid, a bottle of special construction is used ; it consists of a cylindrical reservoir, b (fig. 103), to which is fused a capillary tube, c, and to this again a wider tube, a, closed with a stopper. The bottle is first weighed empty, and then full of water to the mark c on the capillary stem, and afterwards of the given liquid. If the weight of the bottle be subtracted from the two weights thus obtained, the result represents the weights of equal volumes of the liquid and of water, from which the specific gravity is obtained by division. Another common form of specific gravity bottle is shown in fig. 104. It consists of a bottle of about 25 c.c. capacity fitted with a well ground-in solid glass stopper perforated by a fine capillary tube. The bottle is completely filled with liquid" and the stopper inserted. The excess of liquid escapes by the capillary channel in the stopper, and is re- moved by blotting-paper. iv. Specific gravity bulbs. — -The specific gravity of a liquid is often determined for technical and even scientific purposes by means oi specific gravity bulbs ; these are small hollow glass bulbs (fig. 105), which are prepared in series, loaded and adjusted so that they exactly float in a liquid of a definite specific gravity. When carefully prepared they are capable of giving results of considerable accuracy. Solutions of certain metallic salts of high specific gravity have been used for the mechanical separation of individual minerals of certain rocks. Such minerals will float or sink according as their specific gravities are lower or higher than that of a given solution. A saturated solution of the double iodide of barium and mercury, the specific gravity of which is 3-58, has been used for this purpose. A saturated solution of cadmium boro- tungstate has the specific gravity 3-3. An application of this principle consists in taking a liquid such as methylene iodide (sp. gr. 3-3) on -which a mineral will float, and then adding to it benzole until the mineral just remains suspended. Its specific gravity Fig. los -125] Beaum^'s Hydrometer II' is then that of the hquid mixture, which is determined by a pyknoraeter (120). 123. On the observation of temperature in ascertaining specific gravities. As the volume of a body increases with the temperature, and as this increase varies with different substances, the specific gravity of any given body is not exactl)' the same at different temperatures ; and, consequently, a certain fixed temperature is chosen for these determinations. That of water, for example, has been made at 4° C, for at this point it has the greatest density. The specific gravities of other bodies are assumed to be taken at zero ; but, as this is not always possible, certain corrections must be made which we shall consider in the Book on Heat. I Specific gravities of liquids at zero, compared with that of ■water at 4° C. as unity Mercury • 13-598 Urine . I -020 Methylene iodide • 3-342 Distilled water at 4° C. I -coo Bromine 2-960 „ at 0° C. - 0-999 Ethylic iodide ■ 1-946 Claret 0-994 Sulphuric acid . 1-841 Olive oil 0-915 Chloroform . • 1-525 Liquid oxygen . . 0-899 Nitric acid . I -420 Oil of turpentine 0-870 Bisulphide of carbc m . 1-293 Oil of lemon . 0-852 Glycerine I -260 Petroleum . 0-836 Hydrochloric acid . I -240 Liquid carbonic acid . 0-830 Blood . I -060 Absolute alcohol - 0-793 Milk . I -029 Ether 0-713 Sea-«ater 1-026 Pentane . . 0-626 124. Hydrometers of variable immersion. — The hydrometers of Nicholson and Fahrenheit are called hydrometers of constant immer- sion bid variable weight, because they are always immersed to the same extent, but cany different weights. There are also hydrometers of variable immersion, but of constant weight. 125. Beaume's hydrometer. — This, which was the first of these instruments, may serve as a type of them. It consists of a glass tube (fig. 106) loaded at the bottom with mercury, and with a bulb blown in the middle. The stem, the external diameter of which is as regular as possible, is hollow, and the scale is marked upon it. The graduation of the instrument differs according as the liquid for which it is to be used is heavier or lighter than water. In the first case, it is so constructed that it sinks in water nearly to the top of the stem, to a point A, which is marked zero. A solution of 15 parts of salt in 85 parts of water is made, and the instrument immersed in it. It sinks to a certain point on the stem B, which is marked 15 ; the distance between A and B is divided into 15 equal parts, and the graduation continued to the bottom of the stem, the gradu.ation is on a piece of paper inside the stem. Sometimes 114 On Liquids [125- The hydrometer thus graduated only serves for liquids of a greater specific gravity than water, such as acids and saline solutions. For liquids lighter than water a different plan must be adopted. Beaum^ took for zero the point to which the apparatus sank in a solution of lo parts of salt in 90 of water, and for 10 he took the level in distilled water. This distance he divided into 10 parts, and continued the division to the top of the scale. TwaddelVs hydrometer is in common use in England for testing liquids denser than water. It is graduated in such a manner that the reading or number of degrees multiplied by 5 and added to 1000 gives the specific gravity with reference to water at 1000. Thus 10° Twaddell represents the specific gravity 1050, and 90° represents 1450. The graduation of these hydrometers is entirely conventional, and they give neither the densities of the liquids nor the quantities dissolved. But they are very useful in making mixtures or solutions in given proportions and in evaporating acids, alkaline liquids, solutions of salts, worts, syrups, and the like to a proper degree of concentration, the results they give being sufficiently exact in the majority of cases. 126. Gay-Lussac's alcoholometer. — This instrument is used to determine the strength of spirituous liquors ; that is, the proportion of pure alcohol which they contain. It differs from Beaume's hydrometer in the graduation. The alcoholometer is so constructed that, when placed in pure distilled water, the bottom of its stem is level with the water, and this point is zero. It is next placed in absolute alcohol, which marks 100°, and then successively in mixtures of alcohol and water containing 10, 20, 30, &c., per cent. The divisions thus obtained are not exactly equal, but their difference is not great, and they are subdivided into ten divisions, each of which marks one per cent, of absolute alcohol in a liquid. Thus a brandy in which the alcoholometer stood at 48° would contain 48 per cent, of absolute alcohol, and the rest would be water. All these determinations are made at 15° C, and for that temperature only are the indications correct. For, other things being the same, if the temperature rises the liquid expands, and the alcoholometer will sink, and the contrary if the temperature fall. To obviate this error, Gay-Lussac constructed a table which for each per- centage of alcohol gives the reading of the instrument for each degree of temperature from 0° up to 30°. When the exact analysis of an alcoholic mixture is to be made, the temperature of the liquid is first determined, and then the point to which the alcoholometer sinks in it. The number in the table corre- sponding to these data indicates the percentage of alcohol. From its giving the percentage of alcohol, this is often called the centesimal alcoholometer. 127. Direct reading hydrometer. — The most commonly used form of constant weight hydrometer is similar in appear- ance to Fahrenheit's and is shown in fig. 107. It consists of a narrow glass stem attached to a cylindrical bulb weighted by a smaller bulb filled with shot or mercury so as to float in a vertical position. The stem is graduated in such a way that when the in- strument is immersed in a liquid, the graduation, which is on a level with the 1000 1100 IZOO Fig. 107 -129] Densimeter 115 surface of the liquid, gives the specific gravity directly. The instrument shown in the figure is intended for a liquid whose specific gravity lies be- tween \-o and 1-2. When placed in distilled water it sinks to the mark 1000. If the graduation 11 17 is level with the surface when the instrument floats in (say) dilute acid, the specific gravity of the acid is I'liy. These hydro- meters are supplied in sets of 5, giving a range of specific gravities from 7 to 1-9. 128. Salimeters. — Salimeiers, or instruments for indicating the percentage of a salt contained in a solution, are made on the principle of the centesimal alcoholometer. They are graduated by immersing them in pure water, which gives the zero, and then in solutions containing different percentages of the salt, and marking on the scale the corresponding points. These in- struments are open to the objection that every salt requires a special instru- ment. Thus one graduated for common salt would give false indications in a solution of nitre. Lactometers are similar instruments, and are based on the fact that the average density of a good natural quality of milk is i -029. Hence if water is added to milk, it will indicate a lower specific gravity. But a common plan of adulteration is to remove cream from the milk, by which its specific gravity is increased, and then add water so as to reproduce the original density ; the lactometer will not reveal a fraud of this kind. Urino- meters are frequently used in medicine to test the variations in the density of urine which accompany and characterise certain forms of disease. 129. Densimeter. — Rousseau's densimeter (fig. 108) is of great use in many scientific investigations, in determining the specific gravity of a small quan- tity of a liquid. It has the same form as Beaume's hydrometer, but there is a small tube AC at the top of the stem, in which is placed the substance to be de- teiTnined. A liiark. A, on the side of the tube indicates a measure of a cubic centimetre. The instrument is so constructed that when AC is empty it sinks in distilled water to a point, B, just at the bottom of the stem. It is then filled with distilled water to the height measured on the tube AC, which indicates a cubic centimetre, and the point to which it now sinks is marked 20. The interval between o and 20 is divided into 20 equal parts, and this graduation is continued to the top of the scale. As this is of uniform bore, each division corresponds to ^ gramme, or 0-05. To obtain the density of any liquid — bile for ex- ample — the tube is filled with it up to the mark A ; if the densimeter sinks to 20 divisions, its weight is 0-05 X 20'5 = I -025 ; that is to say, with equal volumes, the weight of water being i, that of bile is i'025. The specific gravity of bile is therefore i'025. Fig. 108 ii6 On Liquids [130- CHAPTER II CAPILLARITY, ENDOSMOSE, DIFFUSION, AND ABSORPTION 130. Capillary phenomena. — When solid bodies are placed in contact with liquids, phenomena are produced which are classed under the general head of capillary phenomena, because they are best seen in tubes whose diameters are so small as to be comparable with that of a hair. These phe- nomena are treated of in Physics under the head of capillarity or capillary attraction ; the latter expression is also applied to the force which produces the phenomena. When a body is placed in a liquid which wets it — for e.Kample, a glass rod in water — the liquid, as if not subject to the action of gravitation, is raised upwards against the sides of the solid, and its surface, instead of being hori- zontal, becomes shghtly concave (fig. 109). If, on the contrary, the solid is one which is not moistened by the liquid, as glass by mercury, the liquid is depressed against the sides of the solid, and assumes a convex shape, as represented in fig. 1 10. The surface of the liquid exhibits the same concavity rig. 109 Fig. or convexity against the sides of a vessel in which it is contained, accord- ing as the sides are or are not moistened by the liquid. These phenomena are much more marked when a tube of small diameter is placed in a liquid. And according as the tubes are or are not moistened by the liquid an ascent or a depression of the liquid is produced which is greater in proportion as the diameter is less (figs, iii and 112). When the tubes are moistened by the liquid, its surface assumes the form of a concave hemispherical segment, called the concave meniscus (fig. 112); when the tubes are not moistened, there is a convex meniscus (fig. III). 131. Laws of the ascent and depression of liquids in capillary tubes. — The most im'portant law in reference to capillarity is known as Juriris law. It is : For the same liquid and the same temperature, the mean height of the -131] Capillary Phenomena "7 ascent in a capillary tube is inversely as the diameter of the tube. Thus, if water rises to a height of 30 mm. in a tube i mm. in diameter, it will only rise to a height of 15 mm. in a tube 2 mm. in diameter, but to a height of 300 mm. in a tube o-i mm. in diameter. This law has been verified with tubes whose diameters ranged from 5 mm. to 0-07 mm. It presupposes that the liquid has previously moistened the tube. The mean height is the height of a cylinder with a circular base which has exactly the same volume as the liquid column raised. If h is this height and ir the diameter of the tube, Jurin's law may be expressed by the ^^"^'*°" rh = const. For various liquids, and the same temperature, the mean heights raised in capillary tubes of the same diameter vary with the nature of the liquid. Of all liquids water rises the highest ; thus in a glass tube 1-29 mm. in diameter, the heights of water, alcohol, and turpentine are respectively 23'i6, 9-18, and 9-85 mm. For the same liquid, and the same temperature, the mean heights are independent of the form of the capillary tube. That is to say, the shape of the tube above or below the meniscus has no effect on the phenomenon. The columns raised would be of very unequal weights, but of equal heights, h, in the tubes represented in fig. 1 1 3, all of which have the same diameter when the liquid stops. The value of r in the formula rh = const is the radius of the tube in the region of the meniscus. X= Fig. 113 Provided the liquid moistens the tube, neither its thickness nor its nature has any influence on the height to which the liquid rises. Thus water rises to the same height in tubes of different kinds of glass, and of rock crystal, provided the diameters are the same. The height to which a given liquid rises in a capdllary tube diminishes as the temperature increases. Thus in a capillary tube in which water stood at a height of 307 mm. at 0°, it stood at 28"5 mm. at 35°, and at 26 mm. at 80° This diminution of height is considerably greater than is accounted for by the diminished density of the water ; for, while this is about 0-00045 fo"^ each degree between 0° and 100°, the mean diminution of the height is 0'00i82, or about four times as much. At the same time that the height becomes less the meniscus is flattened, so that above a certain temperature, which varies with different liquids, the capillary surface becomes flat and horizontal, and its level is that of the external liquid. Working in closed vessels, Wolff found this temperature to be 191° for ether and 500° for water. In regard to the depression of liquids in tubes which they do not moisten, Jurin's law has not been found to hold with the same accuracy. The reason for this is probably to be found in the following circumstances : — When a liquid moistens a capillary tube, a very thin layer of liquid is formed' Ii8 On Liquids [131- against the sides, and remains adherent even when the liquid sinks in tlie tube. The ascent of the column of liquid takes place then, as it were, inside a central tube, with which it is physically and chemically identical. The ascent of the liquid is thus an act of cohesion. It is therefore easy to understand why the nature of the sides of the capillary tube should be without influence on the height of the ascent, which only depends on the diameter. With liquids, on the contrary, which do not moisten the sides of the tube, the capillaty action takes place between the sides and the liquid. The nature and structure of the sides are never quite homogeneous, and there is always, moreover, a layer of air on the inside, which is not dissolved by the liquid. These two causes undoubtedly exert a disturbing influence on the law of Jurin. The law of Jurin may be illustrated and verified for glass capillary tubes and liquids which wet them by the arrangement shown in fig. 114. The diameters of the tubes are measured by introducing a thread of mercury into them and ascertaining the weight of a given length. If P is Fig IJ4 the weight in grammes ot a length / centimetres of mercury whose specific gravity at the temperature of the experiment is D, P = tt^^/D, whence r is determined in centimetres. The height to which the liquid rises in the capillary tube is read off by the cathetometer (87). The capillary tube is fixed to a cross piece of wood, which is placed on the edges of a glass vessel, ee, half filled with the liquid. In order that the liquid may properly moisten the tube it is sucked up by means of an india rubber tube beyond the height at which it finally stands. The cathetometer telescope is then raised to the level // of the lowest point of the meniscus. The pointed screw b is then turned until its point just grazes the liquid, and the position of the point is read off. The difference of these -133] Tension of the Free Surface of Liquids 119 A C^ B N — —^■^., = ^^^= ^H 1 Fig. 115 two readings gives the desired height. Determining thus the radii and capillary heights of different glass tubes, we may verify the constancy of the product rh. 132. Ascent and depression between parallel or inclined surfaces. — When two bodies of any given shape are dipped in water, analogous phe- nomena are produced, provided the bodies are sufficiently near. If, for example, two parallel glass plates are immersed in water at a very small distance from each other, water will rise between the two plates in the inverse ratio of the distance which separates them. The height of the ascent for any given distance is half what it would be in a tube whose diameter is equal to the dis- tance between the plates. If the parallel plates are immersed in mer- cury, a corresponding depression is produced, subject to the same laws. If two glass plates, AB and AC, with their planes vertical and inclined to each other at a small angle, as represented in fig. 1 1 5, have their ends dipped into a liquid which wets them, the liquid will rise between them. The elevation will be greatest at the line of contact of the plates, and from hence gradually less, the surface taking the form of an equilateral hyperbola. A similar curve is obtained by dipping the inclined plates into mercury, the depression increasing towards the line of contact of the two plates. The best way of seeing this phenomenon is to use a prismatic glass cell of \fery small angle. 133. Tension of the free surface of liquids.— The great mobility which s characteristic of the liquid state undergoes an alteration in the neighbour- hood of the free surface of a liquid, or that which is bounded by a gas or by a vacuum. This surface has greater cohesion than any other. For consider any particle, a, at the sur- face (fig. 1 16), and let the sphere represent the range through which the mole- cular attraction is exerted, the radius of which is called the radius of mole- cular action (3). The at- tractive forces of the adja- cent particles, which are exerted in all directions, may be resolved into horizontal and vertical components ; the attractions of the former will compensate each other. But the attractions represented by the molecules within the hemisphere, beneath the surface, are not so compensated, and consequently the latter will e.xercise a considerable pull towards the interior. Consider, again, a particle, b, so much below the surface that the greater part of the sphere comes into operation. If a plane, afe, be drawn as much Fig. n6 I20 On Liquids [133- below b as the surface is above b, the attractive forces from the molecules within ghed will neutralise each other. But the segment rf«/" remains uncom- pensated, and exerts a pull similar to, though weaker than, that which acts on the molecule a. The molecules finally is surrounded uniformly by its adjacent ones, and their resultant action is zero. The effect of these actions is to lessen the mobility of particles at or very near the surface, while those in the interior are quite mobile ; the sur: face, as it were, is stretched by an elastic skin, the result being the same as if the surface layer exerted a pressure on the interior. An imaginary line drawn in the surface of a liquid may be supposed to be kept in equilibrium by equal and opposite forces, acting in the surface at right angles to the line. The magnitude of this force per unit of length of the line is called the surface tension of the liquid. The effect of surface tension is to reduce the area of the liquid surface to a minimum. If T represent the surface tension of a liquid, Ta will be the force acting perpen- dicularly to a line of length a in the surface, and thus we see that to stretch a rectangle whose sides are a and b, into another whose sides are a and b -h b\ an amount of work equal to Ta x b' or Tab' is required. Thus T is numerically equal to the work which must be done upon a liquid surface to stretch its area by the unit amount. Similarly, when the surface is diminished, some molecules pass into the interior, and work is done by the liquid, its amount being numerically equal to T when the diminution in area is I sq. cm. The existence of this surface tension may be illustrated by several inter- esting experiments. In that of Dupre (fig. 117), a quadrangular flat vessel, A ABCD, is used, of which one side, I." P i CD, is movable about a hinge. By means of a string this side is pressed against a wedge, and the vessel is filled with water. On Ijurning the string the side CD ' reverts to its original position, CD. Now hydrostatic pressure would keep CD pressed against the wedge, but the surface tension, tending as it does to reduce the surface-area, overcomes the hydrostatic pressure and restores CD to the vertical position. The area by which the surface is reduced, multiplied by the surface tension, measures the work done. This work would be numerically equal to the surface tension if the diminution in area were i sq., cm. Similarly the work done in stretching a liquid surface until it is increased by i sq. cm. is equal to the surface tension. Another experiment, due to van der Mensbrugghe, is made by means of a wire frame (fig. 118), which is immersed in solution of soap, such as is used for blowing soap bubbles. On removal this carries a thin film with it. A loop of fine silk thread moistened with Fig. 117 Fig. 118 -134] Consequences of Surface Tension. Capillary Pressure I2i the liquid in question is carefully placed on the film, and assumes any shape (fig. ii8 a). By means of a hot wire, the film is broken inside the loop, and the silk thread is then seen to stretch and assume a circular form (fig. 1 18 V). Before the film inside the loop was broken, the surface tension acted equally on both sides of the thread, but after its rupture the tension on the outer side of the thread was unbalanced, and, being equal in all directions, drew the thread into the circular form, rendering the remaining liquid surface as small as possible. 134. Consequences of surface tension. Capillary pressure. — The exist- ence of a real force or tension acting in the surface of a liquid and tending to reduce the area of the free surface to a minimum may thus be regarded as proved experimentally. Surface tension gives rise to a pressure acting at right angles to the free surface, distinct altogether from | | o aTTb hydrostatic pressure. The magnitude of this capillary pressure depends partly upon the surface tension and partly upon the curvature of the surface. It is ex- pressed by the formula of Laplp.ce ^'^'i- •'? > = ^(R-li) A\'here T is the surface tension,, R, R, the principal radii of curvature of the liquid surface at the point considered. If the, surface is spherical, R, = R2 and^= 2T/R. The capillary pressure is always directed towards the concave side of the surface. Hence for a spherical soap bubble, the internal radius OA (fig. 119) is R, and its thickness AB = rf, the pressure due to the outer layer is 2T/(R + ^), and to the inner layer 2T/R : thus the total pressure, directed inwards, is 2T/R + 2T/(R + d) or 4T/R, since rfmay be neglected in comparison with R. This is well illustrated by blowing a soap bubble on a glass tube. So long as the other end of the tube is closed, the bubble remains, the elastic force of the enclosed air counterbalancing the capillary pressure ; but when the tube is opened, the pressure due to the surface tension being unbalanced, the bubble gradually contracts and finally disappears. As a direct consequence of the pressure due to surface tension may be cited the motion of the liquid in a horizontal tapering tube. If a drop of water be placed in a conical glass tube whose angle is small and axis horizontal, it will have a concave meniscus at each end (fig. 120) ; therefore the capillary pressure at each end will be directed outwards. But since the _ pressure is inversely proportional to the radius of curvature, there will be a resultant pressure towards the fine end of the tube, and the liquid therefore will move in this direc- tion. But if the drop be of mercury, it will have a convex meniscus at each end (fig. 121), and will move towards the wider part of the tube. The force causing motion depends upon the difference of the curvatures of the liquid free surfaces, and may be considerable, as is shown by placing vertically a wide glass tube, the lower end of which is drawn out into a very fine capillary termination, and introducing mercury at the other end. A mercury Fig. 120 122 On Liquids [134- a. column I metre long may thus be easily supported, its downward hydro- static pressure being balanced by the upward capillary pressure at the surface of the mercury in the fine part of the tube. If water be gently poured into a glass tube similar to that shown in fig. 122 a, we shall find that, supposing all parts of the tube to have been previously wetted, when the water stands at any point a in the larger tube it will be at a higher point a' in the smaller, both free surfaces being concave upwards. When more water is poured in, the level in the fine tube rises, reaches the top, and remains there until overtaken by the liquid in the wide tube. During this time no liquid has escaped, but the curvature has gradu- ally diminished in the fine tube, so that when the same level is attained the liquid surface is plane (fig. 122 b). The effect of adding still more water is to convert the plane into a convex surface, and the direction of the capil- lary pressure is down- wards. Thus water may be poured into the larger tube until its level is con- siderably above the top of the fine tube, without any escape of liquid (fig. 1221;). Insects can often move on the surface of water without sinking. This phenomenon is caused by the fact that, as their feet are not wetted by the water, a depression is produced, and the elastic reaction of the surface layer keeps them up in spite of their weight. Similarly, a sewing-needle, gently placed on water, does not sink, because its surface, being covered with an oily layer, does not become wetted. The pressure of the needle brings about a concavity, the surface tension of which acts in opposition to the weight of the needle. But if washed in alcohol or in potash, the metal is wetted and at once sinks to the bottom. Among the phenomena due to surface tension may be mentioned the well- known one of the ' tears of wine.' The surface tension of water in contact with air is greater than that of any other liquid except mercury. It is nearly three times as great as that of alcohol. When a wine-glass is half filled with a strong wine, the wine rises up against the sides like any other liquid ; but the alcohol evaporates rapidly from the surface, the consequence of which is that the liquid layer becomes more and more watery. Near the surface of the liquid the strength of the liquid layer is kept up by diffusion; but higher up, owing to the increased surface tension of the more aqueous wine, it creeps up the sides and draws with it some of the stronger alcoholic liquid below, the increasing weight of which ultimately causes it to break and run down in drops. If a thin layer of water be spread on a plate, and a drop of ether be placed upon it, the water retreats from the drop. Here, instead of the surface tension between water and air, we have that between water and ether, which -136] Contact of Liquids and Solids. Angle of Contact 123 is smaller ; the effect is much the same as if there were a tightly stretched India rubber skin, and a portion of it were softened or made thinner. 135. Contact of liquids and solids. Angle of contact. — It has been seen that the particles in and close to the surface of a liquid, A, are subject to molecular forces different from those experienced by particles in the interior, and that surface tension is a consequence of this difference. The effect of placing more of the same liquid, B, on the surface of A would be to destroy the surface tension, since the surface is destroyed. The tangential action of the added liquid B on the surface layer of A is equal to — T, where T is the surface tension. If, instead of adding more of the same liquid, we place in contact with A another body, B, either liquid or solid, the tangential action of B upon A will similarly be a certain force, — T', and the tension in the surface of contact will become T — T'. ^Thus in contact with another liquid, or a solid, B, the surface tension in A is T — T'. Suppose the body B to be a solid, e.g. a glass tube, and first let the liquid be one which does not wet glass, as mercury. Let Tj be the surface ten- sion between glass and mercury. Ac- cording to the nature of the substances in contact, Tj may be positive or nega- tive ; with glass and mercury it is positive. Consider a molecule at B (fig. 123) ; since its weight may be Fig. 123 neglected in comparison with the molecular forces which act upon it, this molecule is solicited by two forces only, T acting tangential to the liquid, and Tj along the tube. For equi- librium, Tj must be equal to the resolved part of T upwards, or Tj = — T cos 6, 6 being the angle DBC of the wedge of liquid formed by the tangent BD, .-.cos ^= -T,/T. Fig. 124 Since T is always positive, d is obtuse when Tj is positive, and (fig. 1 24) acute when Tj is negative. The latter condition holds when the liquid wets the tube. With glass and water under proper conditions 6 is very small and may be taken =0 without sensible error. With regard to the angle of contact when there is no wetting, theory indicates that it should be constant for the same liquid and the same solid ; and experiments made by Gay-Lussac seemed to con- firm the theory, at least where mercury and glass are con- , ; cemed. More recent and pre- cise experiments by Quincke have thrown doubt on the accuracy of Gay-Lussac's conclusions. Quincke determined by an optical method the angle of contact of different drops of mercury placed on the same plate of glass. In addition, by measuring three ordinates of the surface, viz. a, the maximum ordinate (fig. 125) i, the 'hi Fig. 125 124 On Liquids [135- ordinate of the exti'eme point of contact, and c, the ordinate at the edge of the drop, he was enabled to determine the form of the surface. Quincke found that there is a continuous change in the form of drops, very rapid when the drop is first placed on the glass, then slower, but without having ceased even at the end of several days, and further that there is a continuous change in the magnitude of the angle of contact. It follows from this that, for a drop of mercury resting on a glass plate, capillary equilibrium is never complete or stable. Numerous observations (by Bravais and by Quincke) have shown that the same statement is true with regard to columns of mercury, rising or falling, in glass tubes, although here friction may establish an apparent equilibrium, which however is but momentary. The angle of contact is not then constant for the same sohd and liquid. Thus for mercury and glass it varies, without apparent reason, between 135° and 142°. The variation is much greater when there is an apparent cause, such as the interposition of a very thin layer of a foreign substance between the liquid and the solid in contact. 136. Various capillary phenomena. — The attractions and repulsions observed between bodies floating on the surface of liquids find their expla- nation in the concave or convex curvature which the liquid assumes in contact with the solid. The following are some of them. When two floating balls both moistened by the liquid — for example, cork upon water — are so near that the liquid surface between them is not level, an attraction takes place. The same effect is produced when neither of the balls is moistened, as is the case with balls of wax on water. Lastly, if one of the balls is moistened and the other not, as a ball of cork and a ball of wax in water, they repel each other if the curved surfaces of the liquid in their respective neighbourhoods intersect. A drop of mercury on a table has a shape which is the more nearly spherical the smaller the drop. The smaller the mass of a liquid the greater is the surface in comparison with the weight ; the less, therefore, is the action of gravity in comparison with that of the surface tension ; hence the smaller the globule the nearer it is to a perfect sphere ; if the quantity of mercury is much greater, the globule then flattens, but always remains convex at its edge. The spherical or quasi-spherical form is due to the action of surface tension, which constrains the liquid to present the least possible surface ; and the surface of a sphere is less than that of any other figure having the same volume. A liquid immersed in another, with which it does not mix, of exactly the same specific gravity, such as olive oil in a mixture of alcohol and water, assumes the spherical form (fig. 4). To this cause also is due the spherical form acquired by small masses of liquid which fall through great heights, such as raindrops, and molten lead in the manufacture of small shot. , When a capillary tube is immersed in a liquid which moistens it, and is then carefully removed, the column of liquid in the tube is seen to be twice as long as while the tube was immersed in the liquid. This arises from the fact that a drop adheres to the lower extremity of the tube and forms a convex meniscus, which concurs with that of the upper meniscus to form a longer column since the pressure atthe convex surface will drive the liquid up the tube. It is from capillarity that oil ascends in the wicks of lamps, that water -137] Determination of Surface Tension I2S rises in woods, sponge, bibulous paper, sugar, sand, and in all bodies \\ liich possess pores of a perceptible size. In the cells of plants the sap rises with great force, for here we have to do with vessels whose diameter is less than O'oi mm. Efflorescence of salts is also due to capillarity ; a solution rising against the side of a vessel, the water evaporates, and the salt forms on the side a means of furthering still more the ascent of a liciuid. Capillarity is, moreover, the cause of the following phenomenon : — When a porous sub- stance, such as gypsum, or chalk, or even earth, is placed in a porous vessel of unbaked porcelain, and the whole is dipped in water, the water penetrates into the pores, and the air is driven inwards, with such force that it is under four or five times its usual pressure and density. Jamin has proved this by cementing a manometer into blocks of chalk, gypsum, &c., and he has made it probable that a pressure of this kind, exerted upon the roots, promotes the ascent of sap in plants. Capillarity is thus one of the most widely diffused and important natural phenomena 137. Determination of surface tension or the constant of capillarity. — This determination may be effected in various ways, of which the simplest and perhaps the most accurate is that of the measuring the ascent of a liquid in capillary tubes. Suppose the radius of the tube to be r, p the density of the liquid, 6 its angle of contact, T the tension of the surface film, and /; the mean height to which it is elevated. Then the vertical component of the whole tension round the edge of the film is iirrT cos 6. But this supports the weight ■nr-hgp of liquid which fills a mean length h of the tube. Equat- ing these quantities, we readily obtain T = hrjig\i cos 6. When 6 is greater than 90°, h is negative, and the liquid is depressed, tube is determined by introducing a thread of mercury ascertaining the weight of a given length ; h is measured by a cathetometer (131), and p and g are known. Hence T is determined if 6 can be found by a separate process. In the case of water in glass 6 = 0, and cos 6=1, so that the above relation gives T directly. The principle of another method of determining this constant is represented in fig. 126. The parallel limbs of a thin iron wire DABC are con- nected by a cross wire DC with two loops. If DC is brought near AB and some soap solution added, a thin film of liquid forms when CD is left to itself By gradually adding weights, P, a point is reached at which the total weight of CD and P just counter- balances the tension of the liquid film ; when the weight P is removed the film contracts, while if the weight is sufficiently increased the film breaks. If P, in this experiment, represents the total weight in grammes, and DC = ^ cm., the surface tension in grammes-weight per linear centimetre is P ■lb The radius of the into the tube and T = seeing that the surface tension acts on both sides of the film. 126 On Liquids [137- When two fluids are in contact the surface tension between them depends on the nature of the fluids ; in the case of water, for instance, it differs accord- ing as this is bounded by air or by oil. The surface tension between two liquids I and 2 we denote by T,j. The following table (mainly from Quincke) gives the value of the surface tension for a few cases in grammes-weight per centimetre. Mercury — Air 0-5S Mercury — Olive oil ■ 0-342 Water — „ . 0-075 Olive oil —Water 0-021 Olive oil — „ . 0-038 Turpentine — „ 0-012 Chloroform — „ 0-031 Turpentine — „ 0-030 Alcohol — „ . 0-026 Ether — „ . . 0-018 Fig. 127 If there are several surfaces of separation, the formation of that with the smallest tension is promoted. Thus if a drop of olive oil is placed on water (fig. 127), as represented by 3, then at the edge of the drop the three fluids, air, water, and oil, coincide, and three surface tensions act which are proportional to T,,, T23, Tjo. Now from the table Tj2 = -075, T13 = -038, and T23 = -021 ; therefore Tj, > Tj3 + T,3, and the two forces T,, and Tjj cannot counterbalance the force Tj^, and the oil spreads until the whole surface is covered with a thin layer of oil. Although oil is spread over water by the pull Tj2, it is usual to say that oil spreads itself on water. That surface tension is only exhibited at the boundary of two liquids is well seen by an experiment of Professor Boys : — If a camel's-hair brush is dry the hairs are separately visible, and to make them come to a point they must be wetted ; this adherence is not due to moisture, for if the pencil is wholly immersed in water the separate hairs are as visible as when the pencil is dry. 138. Formation of drops in a capillary orifice. — When a liquid is contained in a vessel terminating in a narrow capillary opening, such as a dropping tube, a certain excess of pressure is required to make the liquid flow out. If this pressure is limited, the lower meniscus has an invariable shape, and the drop does not increase. But as the pressure increases the drop gradually expands like a small elastic bag, the tension of which is less in the degree in which the surface increases, and when the drop is so large that its weight exceeds the normal component of the surface tension, it contracts at the upper part, and finally breaks across a circum- ference o'o' , which is nearly equal to that of the orifice o o. Tate has found ih^t the weights of drops formed with different capillary tubes are for the same liquid proportional to the diameters of the orifice. n) Fig. 128 -139] Osmose 127 The weights of the drops are independent of the substance of the tube, provided it is moistened ; they diminish with rise of temperature. When a small but very hot flame is directed against the point of a fine metal wire, such as gold or platinum, the metal is melted and falls in drops, the weight P of which is found to be very uniform. P is the greatest weight which the melted mass can support, and is equal to T-irrT, where T is the constant of capillarity and ir the diameter of the wire. Quincke has applied this method of determining the constant in cases where other methods are not applicable, such as in the case of the noble metals, salts, selenium, phosphorus, &c. 139. Osmose. — Other phenomena are observed when two different liquids miscible with each other are separated by a porous diaphragm. This may be best illustrated by means of the apparatus represented in fig. 1 29, in which a vessel, b, open at the bottom, is tied round with a bladder. In the neck a long narrow tube, a a, is fitted. This A-essel is filled with solution of copper sulphate, so that it stands at a certain height, r, in the tube, and is then placed in a larger vessel containing pure water, at the level n n. If the temperature remains stationary, it will be seen that after some time the liquid in the tube a a, which was originally at the level r, has risen, while the level of n n has become somewhat lower ; it will also be seen that the outer liquid has acquired a faint bluish tinge. This process continues for some time until the liquid has attained a certain height. It thus appears that there is an interchange of the two liquids, but the quantity of water which passes into the sulphate of copper is greater than that of the solution which passes out. If the experiment be reversed — that is, if water is contained in b, and copper sulphate in the outer vessel — the phenomena are reversed ; that is, the level in r sinks, while that in 71 n rises. Dutrochet, who first investigated these phenomena, applied the term exosmose to the current which passes from the denser liquid to the less dense, and endosmose to the opposite current, and the apparatus itself he called an endosmometer. The phenomena are now known as those of diosmose or osmose. For the occurrence of osmose the membrane must be permeable to at least one of the liquids, and the liquids must be different, but capable of mixing, such as alcohol and water ; there is none, for instance, between water and oil. Osmose may occur between two liquids of the same kind, but of different densities, such as solutions of acids or salts of different strengths ; , ; , here the current is from the weaker towards the stronger solution, and this is general, osmose usually taking place towards the denser liquid. Alcohol and ether form an exception ; although they are specifi- cally lighter than water, they behave in this respect like liquids which are denser. 128 On Liquids [139- If a tulje filled with water is closed at both ends by a bladder (fig. 130), and one end is placed in a vessel of water, the other being in contact with the air, the water gradually evaporates through the bladder ; it is, however, as rapidly replaced, so that, in consequence of evaporation, water moves through the tube towards the outer end. Hence osmose plays a part in the motion. The evaporation from the skin of animals brings about a motion of liquids from the interior towards the e\-aporating surface. In like manner, the passage of water to the rootlets of plants, as well as the ascent of sap :.to the highest points of the trees, is favoured by evaporation from branchlets, leaves, flowers, and fruit. The well-known fact that dilute alcohol kept in a porous \'essel becomes concentrated depends on osmose. If a mixture of alcohol and water be kept for some time in a bladder, the volume diminishes, but the alcohol becomes Fig. 130 much more concentrated. The reason doubtless is that the bladder absorbs water more readily than alcohol, and accordingly water evaporates on the surface, and thus brings about a concentration of the residue. Dutrochet's method is not adapted for quantitative measurements, for it does not take into account the hydrostatic pressure produced by the column. Jolly examined the endosmose of various liquids by determining the weights of the bodies diffused. He called the endosmoHc equivalent of a substance the number which expresses how many parts by weight of water pass through the bladder in exchange for one part by weight of the substance. The fol- lowing are some of the endosmotic equivalents which he determined : — Sulphuric acid 0-4 Copper sulphate 9-S Alcohol . 4-2 Magnesium sulphate 117 Sodium chloride 4-3 Caustic potash 215-0 Sugar 7-1 He also found that the endosmotic equivalent increases with the temperature, and that the ciuantities of substances which pass in equal times through the bladder are proportional to the strengths of the solutions. Porous diaphragms differ very greatly in the facility with which they permit osmose ; of all substances, goldbeater's skin is the best, being twice as good as vegetables, and sixty or seventy times as good as porous earthen- ware, which, however, is necessary in some cases, for organic membranes are apt to decompose. Pfeffer has constructed what he calls semipermeable j?iembranes, by immersing a porous cell, such as is used for voltaic cells, in solution of copper sulphate, and then in one of ferrocyanide of potassium. By double decomposition, a coherent layer of ferrocyanide of copper is found, which is permeable to the molecules of water, but not to those of sugar, for instance. If a solution of sugar be exposed to pressure in such a vessel, pure water filters through ; the membrane acts as a molecular sieve. The whole phenomena and laws of osmose have, in recent times, acquired great importance from the theoretical considerations of Van 't Hoff on the nature of solutions, of which we may indicate the general results. -140] Diffusion of Liquids 129 If a one-per-cent. solution of sugar be placed in the vessel in such an arrangement as that represented by b in fig. 129, when the semi-permeable diaphragm is of ferrocyanide of copper, since the diaphragm is permeable to water but not to sugar, the quantity of liquid in b increases and rises in the tube to a height of 53-5 cm. ; when the pressure due to the water is the same on both sides the diaphragm, this height is a measure of the osmotic pressure due to the sugar. Dealing with dilute solutions, it is found that this pressure is proportional to the concentration ; thus, with solutions of I, 2, 4, and 6 per cent, respectively, the correspondmg osmotic pressures are 53'5, ioi-6, 2o8'2, and 307-5, respectively. We shall afterwards see (294) that we conceive a mass of gas as made up of a \ery large number of molecules moving in all directions with extreme velocity, and that the pressure of a gas is due to the impacts of these molecules against the sides of the containing vessel. Now in what are called ideal solutions — those, that is to say, in which the dimensions of the molecules (3) of the body dis- solved may be disregarded in compaiison with the space in which they are contained — Van 't Hoff considers that the molecules of the body dis- solved are animated by just such a motion as they possess in the case of gases. If the pressure on a given volume of gas be gradually increased its volume will be diminished, and it is found that to reduce it to one-half, the temperature remaining constant, the original pressure must be doubled. For a given mass of gas, the product of pressure and volume is constant ; this is what is kno\vn as Boyle's law (181). Osmotic pressure in liquids is exactly analogous to the pressure of gases ; if we double the number of molecules in a given volume of liquid, we double the pressure, just as we can force two volumes of gas into the space occupied by one if we double the pressure. This analogy between osmotic and gaseous pressure is not a fanciful one, but holds good in details so far as it has been tried. It can be shown, for nistance, that the osmotic pressure of sugar in solution is the same as would be exerted by the same weight of sugar if it existed in the state of gas in the same space as that occupied by the solution. Gases, as will afterwards be shown, expand by a certain definite propor- tion of their volume when heated, the pressure remaining constant ; or, if the volume be kept constant, the increase of pressure is proportional to the increase of temperature. This is also found to hold with the osmotic pres- sure ; it increases in direct proportion to the temperature. 140. Diffusion of liquids. — If oil be poured on water, no tendency tO' intermix is observed, and even if the two liquids be violently agitated together, two separate layers are formed on allowing them to stand. With alcohol and water the case is different ; if alcohol, which is specifically lighter, be carefully poured upon water, so as to form two distinct layers,, it will be seen that the heavier water rises in opposition to gravity into the lighter alcohol, which, in turn, passes into the denser liquid below ; the- liquids gradually intermix, in spite of the difference of the specific gravities ; they diffuse into one another. This point may be illustrated by the experiment represented in fig. 131. A tall jar contains water coloured by solution of blue litmus ; by means of a funnel some dilute sulphuric acid is carefully poured in, so as to form a K I30 On Liquids [140- layer at the bottom ; the colour of the solution is changed into red, pro- gressing upwards, and after forty-eight hours the change is complete — a result of the action of the acid, and a proof, therefore, that it has diffused throughout the entire mass. <■ The laws of this diffusion, in which no porous diaphragm is used, were completely investigated by Graham. The method by which his latest experiments were made was the following : — A small wide-necked bottle, A {fig. 132), filled with the liquid whose rate of diffusion was to be examined, was closed by a thin glass disc and placed in a larger vessel, B, in which water was poured to a height of about an inch above the top of the bottle. The disc was carefully removed, and then after a given time successive layers were carefully drawn off by means of a siphon or pipette, and their contents examined. ^ \ Fig. 131 Fig. 132 The general results of these investigations may be thus stated : — i. When solutions of the same substance, but of different strengths, are taken, the quantities diffused in equal times are proportional to the strengths of the solutions. ii. In the case of solutions containing equal weights of different substances, the quantities diffused vary with the nature of the substances. Saline sub- stances may be divided into a number of equidiffusive groups, the rates of •diffusion of each group being connected with the others by a simple numerical relation. iii. The quantity diffused varies with the temperature. Thus, taking the rate of diffusion of hydrochloric acid at 15° C. as unity, at 49° C. it is 2-18. iv. If two substances which do not combine be mixed in solution, they ■may be partially separated by diffusion, the more diffusive one passing out most rapidly. In some cases chemical decomposition even may be effected by diffusion. Thus, potassium bisulphate is decomposed into free sulphuric acid and neutral sulphate. V. If liquids be dilute, a substance will diffuse into water containing another substance dissolved, as it would into pure water ; but the rate is materially reduced if a portion of the same diffusing substance be already present. —140] Diffusion of Liquids The following table gives the approximate times of equal diffusion :— Magnesium sulphate . yo 49-0 . 98-0 131 Hydrochloric acid Sodium chloride Sugar 2-3 >-o Albumen Caramel It will be seen from the above table that the difference between the rates of diffusion is very great. Thus magnesium sulphate, one of the least •diffusible saline substances, diffuses 7 times as rapidly as albumen and 14 times as rapidly as caramel. These last substances, like hydrated silicic acid, starch, dextrine, gum, &c., constitute a class of substances which are characterised by their incapacity for taking the crystalline form, and by the mucilaginous character of their hydrates. Considering gelatine as the type of this class, Graham called them colloids -(xoXXa, glue), in contradistinction to the far more easily diffusible crystalloid substances. Colloids are for the most part bodies of high molecular weight, and it is probably the larger size of their molecules which hinders their passing through minute apertures. Graham devised a method of separating bodies based on their unequal -diffusibility, which he called dialysis. His dialyser (fig. 133) consists of a Fig. 133 Fig. ring of gutta-percha, over which is stretched while wet a sheet of parchment paper, forming thus a vessel about two inches high and ten inches in dia- meter, the bottom of which is of parchment paper. After pouring in the mixed solution to be dialysed, the whole is floated on a vessel containing a very large quantity of water (fig. 134). In the course of one or two days a more or less complete separation will have been effected. Thus a solution •of arsenious acid mixed with various kinds of food readily diffuses out. The process has received important applications to laboratory and pharmaceutical purposes. K 2 132 On Liquids [141- CHAPTER III HVDRODYNAMICS 141. Hydrodynamics. — The science which treats of the motion of liquids is called hydrodynamics ; and the application of the principles of this science to conducting and raising water in pipes and to the use of water as a motive power is known by the name of hydraulics. 142. Velocity of efflux. Torricelli's theorem. — Let us imagine an aper- ture made in the bottom of any vessel, and consider the case of a particle of liquid on the surface, without reference to those which are beneath. If this particle fell freely, it would have a velocity on reaching the orifice equal to that of any other body falling through the distance between the level of the liquid and the orifice. This, from the laws of falling bodies, is -J'l.gh, in which g is the acceleration due to gravity, and h the height. If the liquid be maintained at the same level, for instance, by a stream of water running into the vessel, sufficient to replace what has escaped, the particles will follow one another with the same velocity, and will issue in the form of a stream. Since pressure is transmitted equally in all directions, a liquid would issue from an orifice in the side with the same velocity, provided the- depth were the same. The law of the velocity of efflux was discovered by Torricelli. It may be- stated as follows : — The velocity of efflux is the velocity which a freely falling body would have on reaching the orifice after having started from a state of rest at the surface. It is expressed by the formula v= 'J2gh. It follows directly from this law that the velocity of efflux depends on the depth of the orifice below the surface, and not on the nature of the liquid. Through orifices of equal size and of the same depth, water and mercury would issue with the same velocity ; for although the density of the latter liquid is greater, the weight of the column, and consequently the pressure, are greater too. It follows further that the velocities of efflux are directly proportional to the square roots of the depth of the orifices. Water could issue from an orifice 100 inches below the surface with ten times the velocity with which it would issue from one an inch below the surface. The quantities of water which issue from orifices of different areas are very nearly proportional to the size of the orifice, provided the level remains- constant. 143. Direction of the jet from lateral orifices. — From the principle of the equal transmission of pressure, water issues from an orifice in the side of a \essel- with the same velocity as from an aperture in the bottom of a vessel at the same depth. Each particle of a jet issuing from the side of a. -145] Quantity of Efflux. Vena contracta 133 vessel begins to move horizontally with the velocity above mentioned, but it is at once drawn downward by the force of gravity in the same manner as a bullet fired from a gun, with its barrel horizontal. It is well known that the bullet describes a parabola (53) with a vertical axis, the vertex being the muzzle of the gun. Now, since each particle of jet moves in the same curve, the jet itself takes the para- bolic form. In every parabola there is a ■certain point called the focus, and the distance from the vertex to the focus fixes the magnitude of a para- bola in much the same manner as the distance from the centre to the circumference fixes the magnitude of a circle. Now it can easily be proved that the focus is as much below as the surface of the water is above the orifice. Accordingly, if water issues through orifices which are small in comparison with the dimensions of the vessel, the jets from orifices at diflferent depths below the surface take different forms, as shown in fig. 135. If these are traced on paper held behind the jet, then, knowing the horizontal and vertical distances of any point of the jet from the orifice, it is easy to demonstrate that the jet forms a parabola. 144. Height of the jet. — If a jet issuing from an orifice in a vertical direction has the same velocity as a body would have which fell from the surface of the liquid to that orifice, the jet ought to rise to the level of the liquid. It does not, however, reach this ; for the particles which fall hinder it. But by inclining the jet at a small angle with the vertical it reaches about ^ of the theoretical height, the difference being due to friction and to the resistance of the air. By experiments of this nature the truth of Torricelli's law has been demonstrated. 145. Quantity of efflux. Vena contracta. — If we suppose the sides of a vessel containing water to be thin, and the orifice to be a small circle whose area is A, we might think that the quantity of water, E, discharged in a second would be given by the expression A \/2gh, since each particle has, on the average, a velocity equal to s/igh, and particles issue from each point of the orifice. But this is by no means the case. This may be explained by reference to fig. 136, in which AB represents an orifice in the bottom of a vessel — what is true in this case being equally true of an orifice in the side of the vessel. Every particle above AB endeavours to pass out of the vessel, and in so doing exetts ] a pressure on those near it. Those that issue neai A and B 1 ■exert pressures in the directions MM and NN ; those near Fig. 136 the centre of the orifice in the direction RQ, those in the intermediate parts in the directions PQP. In consequence, the water within the space PQP is unable to escape, and that which does escape, instead of assuming a cylindric^al form, at first contracts, and takes the form yfBi, B. \tr J I 134 On Liquids [145- of a truncated cone. It is found that the escaping jet continvies to contract until at a distance from the orifice about equal to the diameter of the orifice. This part of the jet is called the ve?ia contracta. It is found that the area of its smallest section is about | or 0-625 of that of the orifice. Accord- ingly, the true value of the efflux per second is given approximately by the formula E = o-62A'v/2^/i, or the actual value of E is about 0'62 of its theoretical value. 146. Influence of tubes on the quantity of efflux. — The result given in the last article has reference to an aperture in a thin wall. If a cylindrical or conical efflux tube is fitted to the aperture, the amount of the efflux is considerably increased, and in some cases falls but little short of its theoretical \'alue. A short cylindrical ajutage, whose length is from two to three times its dia- meter, has been found to increase the efflux per second to about o-%iK\/2gh. In this case the water on entering the ajutage forms a contracted vein (fig. 137), just as it would do on issuing freely into the air ; but afterwards it expands, and, in consequence of the adhesion of the water to the interior sur- face of the tube, has, on leaving the ajutage, a section greater than that of the contracted vein. The contraction of the jet within the ajutage causes a par- tial vacuum. If an aperture is made in the ajutage, near the point of greatest contraction, and is fitted with a vertical tube, the other end of which dips into water (fig. 137), it is found that water rises in the vertical tube, thereby proving the formation of a partial vacuum. If the ajutage has the form of a conical frus- tum whose larger end is at the aperture, the efflux-rate may be raised to o-t)2Pi.^2gh, pro- vided the dimensions are properly chosen. If the smaller end of a frustum of a cone of suitable dimensions be fitted to the orifice, the efflux may be still further increased, and fall very litde short of the theoretical amount. When the ajutage has more than a certain length, a considerable diminution takes place in the amount of the efflux ; for example, if its length is 48 times its diameter, the efflux is reduced to o-biK's/zgh. This arises from the fact that, when water passes along cylindrical tubes, the resistance increases with the length of the tube ; for a thin layer of liquid is attracted to the walls by adhesion, and the internal flowing liquid rubs against this. The resistance which gives rise to this result is called hydraulic friction ; it is independent of the material of the tube, provided it be not roughened ; but depends chiefly on the viscosity of the liquid ; for instance, ice-cold water experiences a greater resistance than lukewarm water. According to Prony, the mean velocity v of water in a cast-iron pipe of the length /, and the diameter d, under the pressure/, is in metres Fig. 137 = 26-8 ^/'l y a piece of buckskin, ce, which is firmly tied at ir to a contraction in the tube, and at e to a brass tubulure in the cover of the cistern. This mode of closing prevents the mercury from escaping when the barometer is inverted, while the pores of the leather transmit the atmospheric pressure. The bottom of the cylinder b is cemented on a boxwood cylinder, zz, on a contraction in which, zz, is firmly tied the buckskin, mn^ which forms the base of the cistern. On this skin is fast- ened a wooden button, x, which rests against the end of a screw, C. According as this is turned in one direc- tion or the other the skin mn is raised or lowered, and with it the mercury. In using this barometer the mercury is first made exactly level with the point a, which is effected by turning the screw C either in one direction or the other. The graduation of the scale is counted from this point a, and thus the distance of the top of the column of mercury from a gives the height of the barometer. The bottom of the cistern is surrounded by a brass case, which is fastened to the cover M by screws, /', k, k. We have already seen (163) the importance of ha\ing the barometer quite vertical, which is effected by the following plan, known as Cardan's suspension. The metal case containing the barometer is fixed in a copper sheath X by two screws, a and b (fig. 156). This is provided with two axles (only one of which, o, is seen in the figure), which turn freely in two holes in a ring, Y. Fig. 155 -169] Gay-Lussac's Siphon Barometer 153 In a direction at right angles to that of the axles, oo, the ring has also two similar axles, /// and n, resting on a support, Z. By means of this double suspension the barometer can oscillate freely about the axes mn and oo, in two directions at right angles to each other. But as care is taken that the point at which these axes cross corresponds to the tube itself, the centre of gravity of the system, which must always be lower than the axis of sus- pension, is below the point of intersection, and the barometer is thus perfectly vertical. X]. Fig. 158 Fig. 159 Fig. 160 Fig. i6r Fig. 157 169. Gay-Lussac's siphon barometer. — The siphon barometer is a bent glass tube, one of the branches of which is much longer than the other. The longer branch, which is closed at the top, is filled with mercury as in the cistern barometer ; while the shorter branch, which is open, serves as a cistern. The difference between the two levels is the height of the barometer. Fig. 157 represents the siphon barometer as modified by Gay-Lussac. 154 On Gases [169- In order to render it more available for travelling, by preventing the entrance of air, he joined the two branches by a capillary tube (fig. 158) ; when the instrument is inverted (fig. 159) the tube always remains full in virtue of its capillarity, and air cannot penetrate into the longer branch. A sudden shock, however, might separate the mercury and admit some air. To avoid this, Bunten introduced an ingenious modification into the apparatus. The longer branch is drawn out to a fine point, and is joined to a tube, B, of the form represented in fig. 160. This arrangement forms an air-trap ; for if air passes through the capillary tube it cannot penetrate the drawn- out extremity of the longer branch, but lodges in the upper part of the enlargement B. In this position it does not affect the observations, since the vacuum is always at the upper part of the tube ; it is, moreover, easily removed. In ; the siphon barometer the shorter branch is, closed, but there is a capillary aperture in the side i, through which the atmospheric pressure is transniitted. The barometric height is determined by means of two scales, which have a common zero at O, towards the middle of the longer branch, and are gra- duated, in contrary directions, the one from O to E, and the other from O to B, either on the tube itself, or on brass rules fixed parallel to the tube. Two sHding verniers, m and r, indicate tenths of a millimetre. The total height of the barometer, AB, is the sum of the distances from O to A and from O to B. Fig. 161 represents a very convenient mode of arranging the open end of a siphon barometer for transport. The quantity of mercury is so arranged that when the Torricellian space is quite filled with mercury, by inclining the tube the enlargement is just filled to d. This is closed by a carefully fitted cork, fixed on the end of a glass tube, do, about a millimetre in diameter, which allows for the expansion of mercury by heat. When the barometer is to be used, the cork and tube are raised. In marine barometers, in order to prevent violent oscillations of the mercury and the possible breaking of the tube by the impact of the mercury on the upper end, the tube is contracted at one part so as to have a capillary diameter. The friction in this fine part is so great that ten or fifteen minutes elapse, when the tube is inclined, before the mercury creeps up to the end of it. These barometers are also provided, as are all standard barometers, with air-traps. 170. Precautions in reference to barometers. — In the construction of barometers mercury is chosen in preference to any other liquid, since, being the densest of all liquids, it stands at the least height. When the mercury barometer stands at 30 inches, the water barometer would stand at about 34 feet (166). It also deserves preference because it does not moisten the glass. It is necessary that the mercury be pure and free from oxide, other- wise it adheres to the glass and tarnishes it. Moreover, if it is impure, its density is changed, and the height of the barometer is too great. Mercury is purified, before being used for barometers, by treatment with dilute nitric acid, and by distillation. The space at the top of the tube (figs. 152 and \.t)^\ which is called the TorruelHa7i vacuum, must be quite free from air and from aqueous vapour, -173] Variations in the Height of the Barometer 155 for otherwise either would depress the mercurial column by its elastic force. To obtain this result, a small quantity of pure mercury is placed in the tube and boiled for some time. It is then allowed to cool, and a further quantity, previously warmed, added, which is boiled, and so on, until the tube is quite full ; in this manner the moisture and the air which adhere to the sides of the tube (195) pass off with the mercurial vapour. A barometer tube should not be too narrow, for otherwise the mercury is moved with difficulty ; and before a reading is taken, the barometer should be tapped so as to get rid of the adhesion to the glass. A barometer is free from air and moisture if, when it is inclined, the mercury strikes with a sharp metallic sound against the top of the tube. If there is air or moisture in it, the sound is deadened. 171. Correction for capillarity. — In cistern barometers there is always a certain depression of the mercurial column due to capillarity. The cor- rection to be made for this depression depends upon the diameter of the tube, and may be neglected when the diameter exceeds '8 inch. For a tube a quarter of an inch in diameter, the correction to be applied (i.e. added to the observed height) is approximately '017 inch. In the siphon barometer the two tubes are of the same diameter, so that the error caused by the depression in the one tube very nearly corrects that caused by the depression in the other. As, however, the meniscus in the one tube is formed by a column of mercury with an ascending motion, while that in the other is formed by a column \\ ith a descending motion, and as further the mercury in one tube is clean while in the other it is exposed to the air and becomes dusty and oxidised, the correction cannot be quite exact. 172. Correction for temperature. — In all observations with barometers, whatever be their construction, a correction must be made for temperature. Mercury contracts and expands with change of temperature, hence its density changes, and consequently the barometric height for a given pressure is inversely as the density of the mercury, so that for different atmospheric pressures the mercurial column might have the same height. Accordingly, in each observation the height observed must be reduced to a standard temperature. The choice of this is quite arbitrary, but that of melting ice is always adopted in practice. It will be seen in the book on Heat how this correction is made. 173. Variations in the heig^ht of the barometer. — When the barometer is observed for several days, its height, corrected for temperature, is found to vary in the same place, not only from one day to another, but also during the same day. The extent of these variations — that is, the difference between the greatest and the least height — is different in different places. It increases from the equator towards the poles. Except under extraordinary circumstances, the greatest variations do not exceed six millimetres under the equator, 30 under the tropic of Cancer, 40 in France, and 60 at 25 degrees from the pole. The greatest variations are observed in winter. The mean daily height is the height obtained by dividing the sum of 24 successive hourly observations by 24. In our latitudes the barometric height at noon corresponds to the mean daily height. The mean monthly height 156 On Gases [173- is obtained by adding together the mean daily heights for a month and dividing by 30. The mean yearly height is similarly obtained. Under the equator the mean annual height at the level of the sea is 0758m., or 29-84 inches. It increases from the equator, and between the latitudes 30° and 40° it attains a maximum of 0763m., or 30-04 inches. In lower latitudes it decreases, and in Paris it does not exceed o-7568m. The general mean at the level of the sea is o-76im., or 29-96 inches. The mean monthly height is greater in winter than in summer, in conse- quence of the cooler atmosphere. Two kinds of variations are observed in the barometer : i st, the acci- dental variations, which present no regularity ; they depend on the seasons, the direction of the winds, and the geographical position, and are common in our climates ; 2nd, the daily variations, which are produced periodically at certain hours of the day. At the equator, and between the tropics, no accidental variations are observed ; but the daily variations take place with such regularity that a barometer may serve to a certain extent as a clock. The barometer sinks from midday till towards four o'clock ; it then rises, and reaches its maximum at about ten o'clock in the evening. It then again sinks, and reaches a second minimum towards four o'clock in the morning, and a second maxi- mum at ten o'clock. In the temperate zones there are also daily variations, but they are detected with difficulty, since they occur in conjunction with accidental variations. The hours of the maxima and minima appear to be the same in all climates, whatever be the latitude ; they merely vary a little with the seasons. 174. Causes of barometric variations. — It is observed that the course of the barometer is generally in the opposite direction to that of the thermo- meter ; that is, that when the temperature rises the barometer falls, and vice versd ; which indicates that the barometric variations at any given place are produced by the expansion or contraction of the air, and therefore by its change in density. If the temperature were the same throughout the whole extent of the atmosphere, no currents would be produced, and at the same height atmospheric pressure would be everywhere the same. But when any portion of the atmosphere becomes warmer than the neighbouring parts its specific gravity is diminished, and it rises and passes away through the upper regions of the air, whence it follows that the pressure is diminished and the barometer falls. If any portion of the atmosphere retains its temperature, while the neighbouring parts become cooler, the same effect is produced ; for in this case, too, the density of the first-mentioned portion is less than that of the others. Hence, also, it usually happens that an extraordinary fall of the barometer at one place is counterbalanced by an extraordinary rise at another place^ The daily variations appear to result from the expansions and contractions which are periodically pro- duced in the atmosphere by the heat of the sun during the rotation of the earth. 175. Relation of barometric variations to the state of the weather. — It has been observed that, in our climate, the barometer in fine weather is generally above 30 inches, and is below this point when there is rain, snow, wind, or storm ; and also, that for any given number of days at which the -176] Wheel Barometer 157 barometer stands at 30 inches there are as many fine as rainy days. From this coincidence between the height of the barometer and the state of the weather, the following indications have been marked on the barometer, counting by thirds of an inch above and below 30 inches : — Height State of the weather 3 1 inches . Very dry. 3of „ . Settled weather. 30^ „ Fine weather. 30 ,, . . Variable. 29I „ . . . Rain or wind. 29|- „ . . Much rain. 29 „ Tempest. In using the barometer as an indicator of the state of the weather, we must not forget that it really only serves to measure the pressure of the atmo- sphere, and that it only rises or falls as the pressure increases or diminishes ; and although a change of weather frequently coincides with a change in the pressure, they are not necessarily connected. This coincidence arises from meteorological conditions peculiar to our climate, and does not occur every- where. That a fall in the barometer usually precedes rain in our latitudes is caused by the position of Europe. The prevailing winds here are the south- west and north-east. The former, coming to us from the equatorial regions, are warmer and lighter. They often, therefore, blow for hours or even days in the higher regions of the atmosphere before manifesting themselves on the surface of the earth. The air is therefore lighter, and the pressure lower. Hence a fall of the barometer is a probable indication of the south- west winds, which gradually extend downwards, and, reaching us, after having traversed large tracts of water, are charged with moisture, and bring us rain. The north-east wind blows simultaneously above and below, but the hindrances to the motion of the current on the earth, by hills, forests, and houses, cause the upper current to be somewhat in advance of the lower ones, though not so much so as the south-west wind. The air is therefore somewhat heavier even before we perceive the north-east, and a rise in the barometer affords a forecast of the occurrence of this wind, which, as it reaches us after having passed over the immense tracts of dry land in Central and Northern Europe, is mostly dry and fine. When the barometer rises or sinks slowly, that is, for two or three days, towards fine weather or towards rain, it has been found from a great number of observations that the indications are then extremely probable. Sudden variations in either direction indicate bad weather or wind. 176. Wheel barometer. — The wheel barometer, which was invented by Hooke, is a siphon barometer, and is especially intended to indicate good and bad weather (fig. 162). In the shorter leg of the siphon there is a float which rises and falls with the mercury. A string attached to this float passes round a pulley, and at the other end there is a weight somewhat lighter than the float. A needle fixed to the pulley moves round a gra- duated circle, on which is marked stormy, rain, set fair, &c. When the 158 On Gases [176- pressure varies the float sinks or rises, and moves the needle round to the corresponding points on the scale. The barometers ordinarily met with in houses, which are called weather- glasses, are of this kind. They are, however, of little use, for two reasons. The first is, that they are neither very delicate nor very accurate in their indications. The second, which applies equally to all barometers, is that those commonly in use in this country are made in London, and the indications, if they are of any value, are only so for a place of the same level above the sea as London. Thus a baro- meter standing at a certain height in London would indicate a certain state of weather, but if removed to Shooter's Hill it would stand half an inch lower, and would indicate a different state of weather. As the pressure differs with the level and with geographical conditions, it is necessary to take these into account if exact data are wanted. 177. Fixed barometer. — For accurate observations Regnault used a barometer the height of which he measured by means of a cathetometer (87). The cistern (fig. 163) is of cast iron ; against the frame on which it is supported a screw is fitted, which is pointed at both ends, and the length of which has been determined, once for all, by the cathetometer. To measure the barometric height. Fig. 162 Fig. 163 the screw is turned until its point grazes the surface of the mercury in the bath, which is the case when the point and its image are in contact. The distance then from the top of the point to the level of the mercury in the tube b is measured by the cathetometer, and this, together with the length of the screw, gives the barometric height with great accuracy. This barometer has, moreover, the advantage that, as a tube an inch in diameter may be used, the influence of capillarity becomes inappreciable. Its construction, moreover, is very simple ; it has no scale, and any errors in reading the barometric height are those which are incidental to the cathetometer. Un- fortunately, the latter instrument requires great accuracy in its construction, and is expensive. 178. Glycerine barometer.— Jordan constructed a barometer in which the -179] Determination of Heights by the Barometer 159 liquid used is pure glycerine. This has the specific gravity r26, and there- fore the length of the column of liquid is rather more than ten times that of mercury ; hence small alterations in the atmospheric pressure produce con- siderable changes in the height of the liquid. The tube consists of ordinary composition gas-tubing about | of an inch in diameter and 28 feet or so in length ; the lower end is open and dips in the cistern, which may be placed in a cellar ; the top is sealed to a closed glass tube an inch in diameter, in which the fluctuations of the column are observed. This may be arranged in an upper story, and the tubing, being easily bent, lends itself to any adjustment which the locality requires. The vapour of glycerine has very low pressure at ordinary temperatures, and the change of pressure with ordinary changes of atmospheric tempera- ture is insignificant. On the other hand, it readily attracts moisture from the air, whereby the density, and therewith the height, of the liquid column vary. This is prevented by covering the liquid in the cistern with a layer of parafiSnoil. The ' Philosophical Magazine,' vol. xxx. Fourth series, page 349, contains a detailed account of a method of constructing a water barometer. 179. Determination of heights by the barometer. — Since the atmo- spheric pressure decreases as we ascend, it is obvious that the barometer will keep on falling as it is taken to a greater and greater height. On this depends a method of determining the difference between the heights of two stations, such as the base and summit of a mountain. The method may be explained as follows : — According" to Boyle's law (181), if the temperature of an enclosed por- tion of air is constant, its volume ^^'ill vary inversely as the pressure ; that is to say, if we double the pressure we shall halve the volume. But if we halve the volume we manifestly double the quantity of air in each cubic inch — that is to say, we double the density of the air ; and so on in any proportion. Consequently the law is equivalent to this : — That for a constant temperature tlic density of air is proportional to the pressure which it sustains. Now suppose A and B (fig. 164) to represent two stations, and "^ that it is required to determine the vertical height of B above A, it being borne in mind that A and B are not necessarily in the same vertical line. Take P, any point in AB, and Q, a point at a small distance above P, and consider a small rectangular volume of air between P and Q, its height being PQ, and its horizontal area I square inch. This volume is in equilibrium because its weight, acting downwards, is equal to the difference of pressure on its upper and lower faces acting upwards. We can write down an equation Fig- 164 representing this equality, and, by the Integral Calculus, sum up the various differences of pressure due to differences of height of all points between A and B. We thus arrive at the following expression : — /&^X = logp =Iog jj^, where X is the vertical distance between A and B, P and Pj the pressures, and H and H, the barometric heights at A and B, g the acceleration of P i6o On Gases [179- gravity which is different at different parts of the earth, and k a constant depending on the relation between the density of air and its temperature and pressure. Putting in the proper vahies for these symbols we arrive, after certain reductions, at the formula X (in feet) = 60346 (i + 0-00256 cos 2(^) i i + 2Ljt_iAlog,(, , which is Laplace's barometric formula. In using it we must remember that T and Tj are temperatures on the Centigrade thermometer at the lower and upper stations, and that H and Hj are the heights of the barometer reduced to 0° C, and ^ is the latitude. For heights not exceeding 2,000 feet we may, without much error, use the formula X (in feet) = 52500 { i + ^F-*'^'!') x ^--^1. \ 1000 / H + Hj 180. Ruhlmann's observations. — The results obtained for the difference in height of places by using the above formula often differ from the true heights, as measured trigonometrically, to an extent which cannot be ascribed to errors in observation. The numbers thus found for the height of places are influenced by the time of day, and also by the season of year, at which they are made. Ruhlmann has investigated the cause of this discrepancy by a series of direct barometric and thermometric observations made at two different stations in Saxony, and also by a comparison of the continuous series of observations made at Geneva and on the St. Bernard. Ruhlmann thus ascertained that the cause of the discrepancy is to be found in the fact that the mean of the temperatures indicated by the thermo- meter at the two stations is not an accurate measure of the actual mean temperature of the column of air between the two stations — a condition which is assumed in the above formula. The variations in the temperature of the column of air are not of the same extent as those indicated by the thermo- meter, nor do they follow them so rapidly ; they drag after them, as it were. If the mean monthly temperatures at the two fixed stations are introduced into the formula, they give in winter heights which are somewhat too low, and in summer such as are too high. The results obtained by introducing the mean yearly temperature of the two stations are very near the true ones. This influence of temperature is most perceptible in individual observa- tion of low heights. Thus, using the observed temperatures in the barometric formula, the error in height of the Uetliberg above Zurich (about 1,700 feet) was found to be -^ of the total, while the height of the St. Bernard above Geneva was found within yjj- of the true height. The reason why the thermometers do not indicate the true temperature of the air is undoubtedly that they are too much influenced by radiation from the earth and surrounding bodies. The earth is highly absorbent, and becomes rapidly heated under the influence of the sun's rays, and becomes as rapidly cooled at night ; the air, as a very diathermanous body, is but little heated by the sun's rays, and on the contrary is little cooled by radia- tion during the night. -181] Boyle's Law i6i CHAPTER II MEASUREMENT OF THE ELASTIC FORCE OF GASES i8i. Boyle's law. — The law of the compressibility of gases was dis- covered by Boyle in 1662, and afterwards independently by JMariotte in 1679. It is in England commonly called ' Boyle's Law,' and, on the Continent, ' Mariotte's Law.' It is as follows : — The temperature remaining the same, the volume of a given quantity of gas is inversely as the pressure which it bears. This law may be verified by means of an apparatus devised by Boyle (fig. 165). It consists of a long glass tube fixed to a vertical support ; it is open at the upper part, and the other end, which is bent into a short vertical leg, is closed. On the shorter leg there is a scale which indicates equal capacities ; the scale against the long leg gives the heights. The zero of both scales is in the same horizontal line. A small quantity of mercury is poured into the tube, so that its level in both branches is at zero, which is effected without much difficulty after a few trials (fig. 165). The air in the short leg is thus under the ordinary atmo- spheric pressure, which is exerted through the open tube. Mercury is then poured into the longer tube until the volume of the air in the smaller tube is reduced to one-half ; that is, until it is reduced from 10 to 5, as shown in fig. 166. If the height of the mercurial column, CA, be measured, it will be found exactly equal to the height of the barometer at the time of the experi- ment. The pressure of the column CA is therefore equal to an atmosphere, and therefore the air in CB is subjected to a pressure of two atmospheres. Accordingly, by doubling the pressure, the volume of the gas has been diminished to one-half If mercury be poured into the longer branch until the volume of the air is reduced to one-third, it will be found that the distance between the level of the two tubes is equal to twice the barometric height. The pressure is now 3 atmospheres, while the volume is reduced to one-third. Dulong and Petit verified the law for air up to 27 atmospheres, by means of an apparatus analogous to that which has been described. The law also holds good in the case of pressures of less than one atmo- sphere. To estabhsh this, mercury is poured into a graduated tube until it is about two-thirds full, the rest being air. It is then inverted in a deep trough M containing mercury (fig. 167), and lowered until the levels of the mercury inside and outside the tube are the same, and the volume AB noted. The tube is then raised, as represented in the figure, until the volume of air AC is double that of -AB (fig. 168). The height of the mercury in the tube M l62 On Gases [181- above the mercury in the trough CD is then found to be exactly half the height of the barometric column. The air whose volume is now doubled is only under the pressure of half an atmosphere ; for its pressure is equal to atmospheric pressure minus that due to the column CD. If the tube be further raised until AC is three times AB, CD will be found to be equal to two-thirds of the height of the barometer, i.e. the pressure which AC bears is now one-third of an atmosphere. Accordingly the volume is inversely as the pressure. Fig.' 165 Fig. 166 Fig. 167 Fig. 168 In general, if V be the original volume of a gas under the pressure P, and V the volume of the same gas under another pressure P', we have the ratio V: V' = P': P or VP = V'P'. This may be expressed by saying that, the temperature of a given mass of gas being constant, the product of pressure and volume is constant ; that is, P V = const. In the e-xperiment with Boyle's tube, as the mass of air remains the -182] Boyle's Laiv 163 same, its density must obviously increase as its volume diminishes, and vice versa. The law may thus be enunciated : — ' For the same temperature the density of a gas is proportional to its pressure! Hence, as water is 773 times as heavy as air, under a pressure of 773 atmospheres air would be as dense as water, supposing the law to hold good for so high a pressure. 182. Boyle's law is only approximately true. — Until within the last few years Boyle's law was supposed to be absolutely true for all gases at all pressures, but Despretz obtained results incom- patible with the law. He took two graduated glass tubes of the same length, and filled one with air and the other with the gas to be examined. These tubes were placed in the same mercury trough, and the whole apparatus immersed in a strong glass cylinder filled with water. By means of a piston moved by a screw which worked in a cap at the top of a cylin- der, the liquid could be subjected to an increasing pressure, and it could be seen whether the com- pression of the two gases was the same or not. The apparatus resembled that used for examining' the compressibility of liquids (fig. 73). In this manner Despretz found that car- bonic acid, sulphuretted hydrogen, ammonia, and cyanogen are more com- pressible than air : hydro- gen, which has the same compressibility as air up to 15 atmospheres, is then less compressible. From these experiments it was concluded that the law of Boyle was not general. In some experiments on the elastic force of vapours, Dulong and Aragfo had occasion to test the accuracy of Boyle's law. The method adopted was exactly that of Boyle, but the apparatus had gigantic dimensions. The gas to be compressed was contained in a strong glass tube, GE (fig. i6g), about six feet long and closed at the top, G. The pressure was produced by a column of mercury, which could be increased to a height of ■ M 2 Fig. 169 1 64 On Gases [182- 65 feet, contained in a long vertical tube, KL, formed of a number of tubes firmly joined by good screws, so as to be perfectly tight. The tubes KL and GF were hermetically fixed in a horizontal iron pipe, DE, which formed part of a mercurial reservoir, A. On the top of this reservoir there was a force-pump, BC, by which mercury could be forced into the apparatus. At the commencement of the experiment the volume of the air in the tube GF (fig. 169) was observed, and the initial pressure determined, by adding to the pressure of the atmosphere the height of the mercury in K above its level in H. If the level of the mercury in the air tube had been above the level in KL, it would have been necessary to subtract the difference. By means of the pump, water was injected into A. The mercury, being then pressed by the water, rOse in the tube GF, where it compressed the air, and in the tube KL, where it rose freely. It was only then necessary to measure the volume of the air in GF ; the height of mercury in KL above the level in GF, together with the pressure of the atmosphere, was the total pressure to which the gas was exposed. These were all the elements necessary for comparing different volumes and the corresponding tempera- tures. The tube GF was kept cold during the experiment by a stream of cold water. The long tube was attached to a long mast by means of staples. The individual tubes were supported at the junction by cords, which passed round pulleys, R and R', and were kept stretched by small buckets, P, con- taining shot. In this manner each of the thirteen tubes having been sepa- rately counterpoised, the whole column was perfectly free notwithstanding its weight. Dulong and Arago experimented with pressures up to 27 atmospheres, and observed that the volume of air always diminished a little more than is required by Boyle's law. But as these differences were very small, thej' attributed them to errors of observation, and concluded that the law was perfectly exact, at any rate up to 27 atmospheres. The experiments of Regnault (1847) on the same subject were dis- tinguished by the extreme care and attention to small sources of error with which they were carried out. The apparatus used was similar to that already described, but the tube containing the gas under examination, instead of being closed at the top as in the experiments of his predecessors, was connected with a reservoir of the gas and with a force-pump. E.xperi- ments were conducted in such a way that the pressure was obser^ ed when the gas filled the tube and also when the volume was reduced by compression to about half If PV are the pressure and volume of the. gas when filling the tube, and PjVi the corresponding values for the half tube, PV = PiV„ PV PV supposing Boyle's law to hold. \i—— >i, or -— = i -i- e, the gas is more PV PV compressible than Boyle's law requires. If p-^rr- < ij or — -=-- = I - e, the gas is less compressible than it would be in accordance with the law. The following table gives the results of a series of experiments made on air, nitrogen, carbonic acid, and hydrogen : — -182] Boyle's Law i6s Air Nitrogen Carbonic Acid Hydrogen P. mm. 738-72 2112-53 4140-82 9336-41 P.V„ P.V, Po PoVo P.V. P. P.V„ PiV. Po mm. 2211-18 5845'i8 I 9176'so PoVo PiV, 1-001414 1-002765 I "003253 1-006366 mm. 753-46 10981-42 1-000988 1-002952 1-004768 I -006456 mm. 764-03 3486-is 4879-77 9619-97 1-007597 T -028698 1-045625 1-155865 0-99S584 0-996121 0-992933 Regnault's conclusions were — 1. That no gas rigorously obeys Boyle's law. The divergence is small for small pressures, but increases with the pressure. 2. That e is positive for all the gases experimented on except hydrogen. Hydrogen then is less compressible, all the other gases more compressible, than Boyle's law requires. 3. The divergence from the law is greater for the easily liquefiable gases, such as carbonic acid, sulphurous acid, ammonia, and cyanogen, than for the gases called in Regnault's time /^i>7«a«««^ gases, viz. oxygen, nitrogen, methane, nitric oxide, and carbon monoxide. Thus to reduce air to ^V of ''^ original volume, a pressure of 1 9-7 1 99 atmo- spheres was required instead of 20 ; and while carbonic acid only required 16-705, hydrogen required 20-269 atmospheres. Very much higher pressures have been employed in similar experiments by Natterer and by Andrews. Natterer's experiments showed that air, oxygen, nitrogen, and carbonic oxide are for moderate pressures more compressible and for high pressures less compressible than in accordance with Boyle's law. Andrews's experiments will be described later (373). Cailletet used a special apparatus by which the pressure could be raised to 600 atmospheres. Amagat made a remarkable series of experiments by a method based on Boyle's experiment. The pressure could be applied directly by means of mercury in a steel tube about 1,300 feet in length, arranged in the shaft of a deep coalpit, and suitably connected at the bottom with a carefully calibrated glass compression tube. In this way pressures of as much as 500 atmospheres could be applied ; the temperatures were kept constant by sur- rounding the compression tube by a jacket through which water circulated. The general result of these experiments is exhibited by the curves in fig. 170, which are plotted with pressures as abscissae and the products PV as ordinates. Were Boyle's law true for these gases, the curves wovild be straight lines parallel to the axis of pressures. The curves show that PV diminishes at first for all the gases examined (except hydrogen). The deviation from Boyle's law reaches a maximum, different for different gases, and then diminishes ; further, that at a certain pressure (which for atmospheric air is 175 atmospheres, or a little over one ton weight per square inch) each gas accurately obeys Boyle's law. From this point the deviation from the law is in the same direction as that exhibited by hydrogen, and appears to increase indefinitely with the pressure. The newly discovered gas helium behaves under ordinary pressures like hydrogen, i.e. it is not so compressible as Boyle's law requires. 1 66 On Gases [182- Experiments have been made as to the vahdity of Boyle's law for pres- sures much lower than one atmosphere, but the variations observed arc within the errors of observation. Fig. 170 183. Van der Waals' formula. — Under high pressures gases do not, as we have seen, follow Boyle's law with strictness. In order to account for these discrepancies Van der Waals has introduced a modification into the formula W = const. (i8i) which is based on the following considerations. Suppose the molecules of the gas attract each other, and that the attraction is greater the neai'er the molecules are together. When the volume of the gas is diminished by the application of external pressure, the mean distance between molecule and molecule diminishes, and the mutual attraction consequently increases. .Thus the molecules are drawn together not only by the externally applied pressure, but by that due to their mutual attraction, and the diminution of volume is such that the actual pressure to which the gas is subjected may be regarded as equal to P +p, where P is the applied pressure and p that due to attraction. This additional pressure p will be proportional to the number of attracting particles and hence to the square of the density, or inversely proportional to the square of the volume. Suppose,, however, that the force between the gaseous particles is one of repulsion instead of attraction. For a given reduction of volume (the temperature being always considered constant) the real pressure of the gas is less than that applied by the pressure due to molecular repulsion. Thus in any case the pressure of the gas may be written P + —^, a being positive or negative -184] Manometers i6y according as the molecular force is attractive or repulsive. Further, Boyle's formula assumes that the particles of a gas are mere points, so that with indefinitely increased pressure the volume would become indefinitely small. But the molecules of a gas must have some magnitude, and all that pressure can do is diminish the spaces between them and ultimately bring them mto contact, beyond which point the volume could not be reduced. Thus, the volume of the gas which is capable of being reduced by pressure is not V but V — b, where b is the molecular volume or some multiple of it. The formula of Boyle's law, as thus modified by Van der Waals, becomes (v+^^yY-b) = const. In the case of gases — oxygen, nitrogen, &c. — in which there is molecular attraction, a is positive, and (neglecting b for the moment) increase, of pressure will produce a greater diminution of volume than corresponds to Boyle's' law. But the effect of b (neglecting - ,, for the moment) will be, for a given pressure, to produce a smaller diminution than corresponds to Boyle's law. Thus the two effects oppose each other. With hydrogen and helium, on the other hand, for which a is negative, the two effects are additive and the gases are less compressible than Boyle's law requires. To go back to air, oxygen, &c., we see that at low pressures the product PV is less than that required by Boyle's law, and the influence of a preponderates ; but as the pressure con- tinuously increases, this influence diminishes in comparison with that of b, and the product now increases, and at high pressures the gases behave as does hydrogen at low pressures. Between these a maximum compressibility is seen, which varies with different gases according to the values of a and b in each case. , . ; Van der Waals deduced from the experimental results obtained by Regnault for the comparison of various gases and for their expansion by heat, values for a and b for the respective gases, which when introduced into the formula satisfactorily represent the numbers obtained by experiment. Thus for b in the case of hydrogen he obtained the number 0-00069 ; this is confirmed by Budde, who obtained o'ooo7 by an entirely different method. 184. Manometers. — Manometers are instruments for measuring the pressure of gases or vapours. In all such irt- struments the unit chosen is the pressure of one atmosphere, or 30 inches of mercury at th« standard temperature, which,' as we have seen, is nearly 1 5 pounds to the square inch. The open-air manometer consists of a bent glass tube BD (fig. 171 \ fastened to the bottom of a reservoir AC, of the same material containing mercury, which is connected with the closed recipient containini' the gas or vapour the pressure of which is to be measured. The whole is fixed on a long plank kept in a vertical position. — SI — Fig. 171 i68 On Gases [184- \ f-'. ? ^ i 3 In graduating this manometer, C is left open, and the number i marked at the level of the mercurj', for this represents one atmosphere. From this point the numbers 2, 3, 4, 5, 6, are marked at each 30 inches, indicating so many atmospheres, since a column of mercury |i* 30 inches represents a pressure of one atmosphere. In the (-8 graduation, allowance is made for the depression of the mercury at A as it rises in the tube. The intervals from 1 to 2, and from 2 to 3, &c., are divided into tenths. C being then placed in connection with a boiler, for example, the mercury rises in the tube BD to a height which measures the pressure of the vapour. In the figure the manometer marks 2 atmospheres, which represents a height of 30 inches or 76 cm. plus the atmospheric pressure exerted at the top of the colurrin through the aperture D. This manometer is' only used where the pressures do not exceed 5 to 6 atmospheres. Beyond this, the length of tube necessary makes it very inconvenient, and the following apparatus is commonly used. 185. Manometer with compressed air. — The manometer •with compressed air is founded on Boyle's law : one form is represented in fig. 172, which may be screwed into a boiler or steam-pipe where pressure is to be measured. The pres- sure is transmitted through the opening a into the closed space b. In this is an iron vessel containing mercury, in which dips the open end of the manometer tube, which is screwed air-tight in the tubulure. In the graduation of this manometer, the quantity of air contained in the tube is such that when the aperture a com- municates freely with the atmosphere, the level of the mercury is the same in the tube and in the tubulure. Consequently, at this level, the number i is marked on the scale to which the tube is affixed. As the pressure acting tjirough the tubulure a increases, the mercury rises in the tube, until its pressure, added to that of the compressed air, is equal to the external pressure. It would consequently be incorrect to mark two atmospheres in the middle of the tube ; for, since the volume of the air is reduced to one-half, its pressure is equal to two atmospheres, and, together with the weight of the mercury raised in the tube, is therefore more than two atmospheres. The position of the number is at such a height that the elastic force of the compressed air, together with the weight of the column of mercury in the tube, is equal to two atmospheres. The exact position of the numbers 2, 3, 4, &c. on the manometer scale can only be determined by calculation. ■^* '73 186. Volumenometer. — An interesting application of Boyle's law is met with in the volumenometer, which is used in determinations of the specific gravity of solids which cannot be brought into contact with water or other liquids. A simple form consists of a glass tube -N Fig. 172 -188] Aneroid Barometer i6g with a cylinder, G, at the top (fig. 173), the edges of which are carefully ground, and which can be closed hermetically by means of a ground-glass plate D. The top being open, the tube is depressed until the level of the mercury inside and outside is at the mark Z. The apparatus is then closed airtight by the plate, and is raised until the mercury stands at a height, /i, above the level Q, in the bath. The original volume of the enclosed air V, which was under the pressure of the atmosphere, is now increased to V + z/, since the pressure has diminished by the height of the column of mercury A Calling the height of the barometer at the time of observation 6, we shall have V : N + v = b — h : b. Placing now in the cylinder a body K, whose volume x is unknown, the same operations are repeated ; the tube is raised until the mercury again stands at the same mark as before, but its height above the bath is now different ; a second reading, hy, is obtained and we have (y-x) : i:S!-x) + v^b-h^ : b. Combining and reducing, we get ;ir=(V + 7/) (i — ^ ). The volume V + z/ is constant, and is determined numerically, once for all, by making the experi- ment with a substance of known volume, such as a glass bulb. This apparatus is also known as the stereometer. It is of great value in determining the geometrical or true density of gunpowder ; this averages from I '67 to I '84, and is thus materially different from its apparent density, or the weight of a given volume compared « ith that of an equal volume of water, which is from 0-89 to 0-94. 187. Regnault's barometric manometer. — For measuring pressures of less than one atmosphere, Regnault devised the following arrangement, which is^ modification of his fixed barometer (fig. 163). In the barometer cistern dips a second tube, a, of the same diameter, open at both ends, and provided at the top with a three-way cock, one aperture of which is connected with an air-pump and the other with the space to be exhausted. The further the exhaustion is carried the higher the mercury rises in the tube a. The differences of level in the tubes b and a give the pressures. Hence, by measuring the height, ab, by means of the cathetometer, the pressure in the space that is being exhausted is accurately given. This apparatus is also called a differential barometer or a barometer gauge. ■ 188. Aneroid barometer. — This instrument derives its name from the circumstance that no liquid is used in its construction (a, without ; vripos, moist). Fig. 174 represents one of the forms of this instrument ; it consists of a cylindrical metal box, partially exhausted of air, the top of which is made of thin corrugated metal, so elastic that it readily yields to alterations in the pressure of the atmosphere. When the pressure increases, the top is pressed inwards ; when, on the contrary, it decreases, the elasticity of the lid, aided by a spring, tends to move it in the opposite direction. These motions are transmitted by delicate multiplying levers to an index which moves on a scale. The instrument is graduated empirically by comparing its indications, under different pressures, with those of an ordinary mercury barometer. The aneroid has the advantage of being portable, and can be constructed I/O On Gases [188- of such delicacy as to indicate the difference in pressure between the height of an ordinary table and the ground. It is hence much used in determining heights in mountain ascents. But it is somewhat liable to get out of order, Fig. 174 especially when it has been subjected to great sudden variations of pressure ; and its indications must from time to time be controlled by comparison with those of a standard barometer. 189. Laws of the mixture of g'ases. — If a communication is opened between two closed vessels containing gases, they at once begiq to mix, whatever be their density, and in a longer or shorter time the mixture is complete, and will continue so unless chemical action is set up, each gas filling the whole available volume. The laws which govern the mixture of gases may be thus stated : — I. The mixture takes place rapidly and is hoTnogeneous ; that is, each portion of the mixture contains the two gases in the same proportio7i. II. If the gases severally and the mixture have the same temperature, and if the gases severally and the mixture occupy the same volume, then the pressure exerted by the mixture will equal the sum of pressicres exerted by the gases severally. From the second law a very convenient formula can be easily deduced. Let Wj, fj, 7/3 . . be the volumes of several gases under pressure of /], /o, p^ . . . respectively. Suppose these gases when mixed to have a volume V, under a pressure P, the temperatures being the same. By Boyle's law we know that v^ will occupy a volume V under a pressure p\, provided that V/' = v^p^ ; similarly, V/'., = v„p.^ and so on. But from the above law therefore VP - v^pi + v.^p., + v^p^ + -190-] Absorption of Gases by Liquids 171 It obviously follows that if the pressures are all the same, the volume of the mixture equals the sum of the separate volumes. The first law was shown experimentally by BerthoUet, by means of an apparatus represented in fig. 175. It consists of two glass globes provided with stopcocks, which can be screwed one on the other. The upper globe was filled with hydi'ogen, and the lower one with carbonic acid, which has 22 times the density of hydro- gen, the pressure being the same in each. The globes, having been fixed together, were placed in the cellars of the Paris Observa- tory and the stopcocks then opened, the globe containing hydrogen being uppermost. After some time BerthoUet found that the pressure had not changed, and that, in spite of the difference in density, the two gases had become uniformly mixed in the tAvo globes. Experi- ments made in the same manner with other gases gave the same results, and it was found that the diflfusion was more rapid in proportion as the difference between the densities was greater. The second law may be demonstrated by passing into a graduated tube, over' mercury, known volumes of gas at known pressures. The pressure and volume of the whole mixture are then measured, and found to be in accordance with the law. Gaseous mixtures follow Boyle's law, like simple gases, as has been proved for air (181), which is a mixture of nitrogen and oxygen. 190. Absorption of gases by liquids. — Water and many liquids possess the property of absorbing gases. Under the same conditions of pressure and temperature a liquid does not absorb equal volumes of different gases. At the temperature 0° C. and pressure 760 mm., one volume of water dissolves the following volumes of gas : — Nitrogen 0-020 Sulphuretted hydrogen 4-37 Oxygen . 0-041 Sulphurous acid . 7979 Carbonic acid 179 Ammonia 1046-63 From the very great condensation observed, it may be inferred that the gases in solution are in the liquid state. Gases are more soluble in alcohol than in water' ; thus at 0° C. alcohol dissolves 4-33 volumes of carbonic acid gas. The whole subject of gas absorption has been investigated by Bunsen. The general rules are the following : — I. For the same gas, the same liquid, and the same temperature, the ■weight of gas absorbed is proportional to the pressure. This may also be expressed by saying that at all pressures the volume dissolved is the same ; or that the density of the gas absorbed is in constant relation with that of the external gas which is not absorbed. Accordingly, when the pressure diminishes, the quantity of dissolved 172 On Gases [190- gas decreases. If a solution of gas be placed under the receiver of an air- pump and the pressure be diminished, the gas obeys its expansive force, and escapes with effervescence. II. The quantity of gas absorbed decreases with increase of the tempera- ture ; 'that is to say, when the elastic force of the gas is greater. Thus at 15° water absorbs only i-oo of carbonic acid. III. The quantity of gas which a liquid can dissolve is independent of the nature and of the quantity of other gases which it may already hold in solution. This absorption of gases may be determined by the absorptiometer represented in fig. I7'6, which consists of a graduated measuring tube. A, connected by an India rubber tube with a tube of equal diameter, B. The absorption vessel, C, is connected with A by means of a thin flexible capillary lead tube ; a and b are three-way stop- cocks, and c an ordinary one. The vessel C is fitted with air-free liquid, and A with the gas, which by means of the two three-way stopcocks is easily effected. The tube B is raised or lowered until the level of the mercury is the same as in A, and the volume of gas is read off. A is now put in connection with C, and, the stopcock c having been opened, B is raised so that a determinate \-olume of liquid runs out. An equal volume of the gas then passes into C, and the absorption proceeds, C being constantly shaken. In order to work at constant tempera- ture, A and C may be surrounded by water. In every gaseous mixture each gas exercises the same pressure as it would if its volume occu- pied the whole space ; and the total pressure is equal to the sum of the individual pressures. When a liquid is in contact with a gaseous mixture, it absorbs a certain part of each gas, but less than it would if the whole space were occupied solely by that gas. The quantity of each gas dissolved is proportional to the pressure which the unabsorbed gas exercises alone. For instance, oxygen forms only about J the quantity of air ; and water under ordinary conditions absorbs exactly the same quantity of oxygen as it would if the atmosphere were entirely formed of this gas under a pressure equal to J that of the atmosphere. 191. Diffusion of gases. — Phenomena analogous to those of osmose (138) are seen in a high degree in the case of gases. When two different gases are separated by a porous diaphragm, an interchange takes place between them, and ultimately the composition of the gas on both sides of the dia- phragm is the same ; but the rapidity with which different gases diffuse into each other under these circumstances varies considerably. There is, however, an essential difference between the phenomena of osmose and those of diffusion ; for while the inequality in the currents in the former case is due to the different attraction of the material of the diaphi'agm for the con- stituents, in the diffusion of gases the nature of this material has no influence ; Fig. 176 -191] Diffusion of Gases 173 from the smallness of the pores the actions are molecular, and not molar, and the rate of interchange depends only on the size of the molecules, that is, on the specific gravities of the gases. The laws of the diffusion of gases were investigated by Graham. Numerous experiments illustrate them, some of the most interesting of which are the following : — A glass cylinder closed at one end is filled with carbonic acid gas, its open end tied over with a bladder, and the whole placed under a jar of hydrogen. Diffusion takes place between them through the porous dia- phragm, and after the lapse of a certain time hydrogen has passed through the bladder into the cylindrical vessel in much greater quantity than the carbonic acid which has passed out, so that the bladder becomes very much distended outwards (fig. 177). If the cylinder be filled with hydrogen and the bell-jar with carbonic acid, the reverse phenomenon will be produced — the bladder will be pressed inwards (fig. 178). A tube about 12 inches long, closed at one end by a plug of dry plaster of Paris, is filled with dry hydrogen, and its open end then immersed in a fi ■\ •> i {• Fig- 177 Fig. 178 Fig. 179 mercury bath. Diffusion of the hydrogen towards the air takes place so rapidly that a partial vacuum is produced, and mercury rises in the tube to a height of several inches (fig. 1 79). If several such tubes are filled with different gases, and allowed to diffuse into the air in a similar manner, in the same time, different quantities of the various gases will diffuse, and Graham found that the law regulating these diffusions is that the quantity of a gas which passes through a porous diaphragm in a given tune is inversely as the square root of the density of the gas. Thus, if two vessels of equal capacity, containing oxygen and hydrogen, be separated by a porous plug, diffusion takes place ; and after the lapse of some time, for every one part of oxygen which has passed into the hydrogen, four parts of hydrogen have passed into the oxygen. Now, the density of hydrogen being i, that of oxygen is 16 ; hence the rapidity of diffusion is inversely as the square roots of these numbers. It is four times as great in the one which has j^ the density of the other. Let the stem of an ordinary tobacco pipe be cemented, so that its ends project, in an outer glass tube, which can be connected with an air-pump and thus exhausted. On allowing then a slow current of air to enter one 174 On Gases [191- end of the pipe, its nitrogen diffuses more rapidly on its way through the porous pipe than the heavier oxygen, so that the gas which emerges at the other end of the porous pipe, and which can be collected, is richer in oxygen, and by repeating the operation on the gas which has passed through, the proportion of oxygen is so much increased that the gas can rehght ^a semi-extinguished taper. To this process, in which one gas can be separated from another by diffusion, the term atmolysis is given. Fig. 1 80 is an excellent illustration of the action of diffusion. A porous pot, A, such as is used for voltaic cells, is fi.xed by means of a cork to the glass tube, which contains water up to the bulb, C, the upper part containing air. When a beaker containing hydrogen, B, is placed over the pot, the diffusion of the hydrogen into it is so rapid that the water is at once driven down and jets out. When the beaker is removed, the gas inside the pot, being richer in hydrogen, now diffuses out with great rapidity, and the water rises in the tube much higher than its original level. 192. Effusion of gases. — A gas can only flow from on^'space to another space occupied by the same' gas when the pressure in the one is greater thSn in the other. Effusion is the term applied to the phenomenon of the passage of gaSeS into vacuum, through a minute aperture not much more or less than 0-013 millimetre in diarrieter, in a thin plate of metal or of glass ; for in a tube we are dealing with masses of gases, and friction comes into play, and in a larger aperture the particles would strike against one another, and form eddies and whirlpools. The velocity of the efflux is measured by the formula -u = i^Jigh, in which h represents the pressure under which the gas flows, expressed in terms of the height of a column of the gas which would exert the same pressure as that of the effluent gas. Thus for air under the ordinary pressure flowing into a vacuum' the pressure is equivalent to a column of mercury 76 centimetres high ; and as mercury is approximately 10,500 times as dense as air, the equivalent column of air will be 76 x 10,500 cm. = 7,980 metres. Hence the velocity of efflux of air into vacuum is = y'2 x g'8 x 7980 = 395 '5 metres per second. This velocity into vacuum only holds, however, for the first moment, for the space contains a continually increasing quantity of air, so that the velocity becomes con^ tinually smaller, and is null when the pressure on each side is the same. If h and h' are the pressures of the gas on the two sides of the aperture, measured as before, the velocity of efflux at that moment is 1"= s/'2.g {h — h') Since the height of a column of gas corresponding to a given pressure is inversely as the density of the gas, it follows that the velocities of efflux of -193] Transpiration of Gases I7S various gases must be inversely as the square roots of their densities. A simple inversion of this statement is that the densities of two gases are inversely as the squares of their velocities of effusion. On this law Bunsen has based an interesting method of determining the densities of gases and vapours, which is of great service where only small quantities of the sub- stances are available. The gas in question is contained (fig. i8i) in a glass tube A, closed at the top with a stopper, S, in the neck, B. In a little enlargement here a thin platinum plate V is fixed, in which is a fine capillary aperture. The tube is depressed in a deep mercury trough, CC, until the top r of a glass float D is level with the mercury. The stopper S having been removed, the gas issues through the capillary aperture, and the time is noted which elapses until a mark / in the float is level with the mercury. Working in this way with different gases, Bunsen found that the ratios of the times of effusion are directly as the square roots of the densities, which is another form of the above statement. By this method it may often be ascertained whether a gas is a mixture or not. Thus marsh gas (CH ,) has the same specific gravity (0-554) as a mixture in equal volumes of dimethyl (CjH^, sp. gr. I '039) and hydrogen (sp. gr. 0-069), ^nd would furnish the same results on chemical analysis. But if the composition of the gas which had been subjected to effusion were examined in the two cases, it would be found that the residual marsh gas would retain the same composition, while that of the mixture would be different, for a relatively larger volume of the specificalh' lighter hydrogen would have passed out. 193. Transpiration of g^ases. — If gases issue through long, fine capillary tubes into a vacuum, the phenomenon is called transpiration ; arid the rate of efflux, or the velocity of transpiration, is not the same as the rate of diffusion, either through a single aperture or through a series of fine capillary tubes, as in a porous diaphragm. This property of gases may be investigated by means of an apparatus analogous to that represented in fig. 139, and consisting essentially of an arrangement by which gas under known pressure is allowed to flow through a capillary tube of known length and diameter. The volume which flows out in a given time, or the rate of transpiration, is represented by a formula which is identical with Poiseuille's formula for liquids (146), namely, ■nif-py^ %r,l 176 On Gases [193- where/ is the pressure of the gas on entering, and p^ that on leaving the capillary tube ; r is the diameter, and / the length of the tube, and rj is the coefficient of internal friction or viscosity of the gas. This method is a simple one for determining the value of ij, as all the other magnitudes in this formula are capable of direct accurate measurement. This is a most important physical constant, as it occurs in many formulae by which molecular magnitudes are determined, such as the length of the mean free path of gases (296), the number of impacts in a second, and even the dimensions of the molecules themselves. Expressed in C. G. S. units, the value of J/ for air is o-03l8. . 194. Absorption of gases by solids.^The surfaces of all solid bodies exert an attraction on the molecules of gases with which they are in contact of such a nature that they become covered with a more or less thick layer of condensed gas. When a porous body, such as a piece of charcoal, which in con- sequence of its pores presents an immensely increased surface in proportion to its size, is placed in a vessel of ammonia gas over mercury (fig. 182), the great diminu- tion of volume which ensues indicates that considerable quantities of gas are absorbed. Now, although there is no absorption such as arises from chemical combination between the solid and the gas (as with phosphorus and oxygen), still the quan- tity of gas absorbed is not entirely dependent on the physical conditions of the solid body ; it is influenced in some measure by the chemical nature both of the solid and the gas. Boxwood charcoal has very great absorptive power. The following table gives the volumes of gas, under standard conditions of tempera- absorbed by one volume of boxwood charcoal and of 'in ' p W Fig. 182 ture and pressure, meerschaum respectively : Charcoal Meerschaum Ammonia 90 15 Hydrochloric acid .... 8S Sulphurous acid 65 — Sulphuretted hydrogen . 55 II Carbonic acid 35 5 '3 Carbonic oxide 9-4 1-2 Oxygen ... 9-2 1-5 Nitrogen 7-4 1-6 Hydrogen 175 0-5 ibsorption of gases is in general grea Ltest in the case of tl lose which most easily liquefied. Cocoa-nut charcoal is even more highly absorbent ; it absorbs 171 of ammonia, 73 of carbonic acid, and 108 of cyanogen at the ordinary pressure ; the amount of absorption increases with the pressure. The absorptive power of pine charcoal is about half as much as that of boxwood. The charcoal made from cork wood, which is \'ery porous, is not absorbent ; -195] Occlusion of Gases 177 neither is graphite. Platinum, in the finely divided form known as platintiin sponge, is said to absorb 250 times its volume of oxygen gas. Many other porous substances, such as gypsum, silk, &c., are also highly absorbent. If a coin is laid on a plate of glass or metal, after some time, when the plate is breathed on, an image of the coin appears. If a figure is traced on a glass plate with the finger, nothing appears until the plate is breathed on, when the figure is at once seen. Indeed, the traces of an engraving which has long lain on a glass plate may be produced in. this way. These phenomena are known as Mosefs images, for they were first inves- tigated by Moser, although he explained them erroneously. The correct explanation was given by Waidele, who ascribed them to alterations in the layer of gas, vapour, and fine dust which is condensed on the surface of all solids. If this layer is removed by wiping, on afterwards breathing against the surface more vapour is condensed on the marks in question, which then present a different appearance from the rest. If a die or a stamp is laid on a freshly polished metal plate, one therefore which has been deprived of its atmosphere, the layer of vapour from the coin will diffuse on to the metal plate, which thereby becomes altered ; so that when this is breathed on an impression is seen. Conversely, if a coin is polished and placed on an ordinary glass plate, it will partially remove the layer of gas from the parts in contact, so that on breathing on the plate the image is visible^ Ordinary glass kept in moist air becomes covered with a layer of water, which can be weighed. This is due to an action of the alkali in glass which attracts moisture, and is absent in glass free from alkali ; it can be consider- ably diminished by boiling with water, by which the alkali on the surface is removed. In addition to this layer, which appears rather to be chemically than physically attracted, there is a temporary one which escapes in a vacuum at the ordinary temperature. These considerations will be seen to be of great importance when we come to consider the use of glass supports for electric apparatus. 195. Occlusion of gases. — ^Graham found that at a high temperature platinum and iron allow hydrogen to traverse them even more readily than does india rubber in the cold. Thus, while a square metre of India rubber 0-014 millimetre in thickness allowed 129 cubic centimetres of hydrogen at 20° to traverse it in a minute, a platinum tube v\ millimetre in thickness and of the same surface allowed 489 cubic centimetres to traverse it at a bright red heat. This is probably connected with the property which some metals, though destitute of physical pores, possess of absorbing gases either on their surface or in their mass, and to which Graham has applied the term occlusion. It is best observed by allowing the heated metal to cool in contact with the gas. The gas which is then absorbed cannot be extracted by the airi pump, but is disengaged on heating. In this way Graham found that platinum occluded four times its volume of hydrogen ; iron wire 0-44 its volume of hydrogen, and 4-15 volumes of carbonic oxide ; silver, reduced from the oxide, absorbed about seven volumes of oxygen, and nearly one volume of hydrogen when heated to dull redness in these gases. This pro- perty is most remarkable in palladium, which absorbs hydrogen not only in cooling after being heated, but also in the cold. When, for instance, a N 178 On Gases [195- palladium electrode is used in the decomposition of water, one volume of the metal can absorb 980 times its volume of the gas. This gas is again driven out on being heated, in which respect there is a resemblance to the solution of gases in liquids. By the occlusion of hydrogen the volume of palladium is increased by 0-09827 of its original amount, from which it follows that the hydrogen, which under ordinary circumstances has a density of O'oooo89546 that of water, has here a density nearly 9,868 times as great, or about 0-88 that of water. Hence the hydrogen must be in the liquid or .even solid state ; it probably forms thus an alloy with palladium, like a true metal — a view of this gas which is strongly supported by independent chemical considerations. The physical properties, too, in so far as they have been examined, support this view of its being an alloy. The phenomenon of occlusion may be illustrated by the followii-.;^' experi- ment (fig. 183). A platinum wire, be, is stretched between supports on a glass plate ; one end of a palladium wire, fg, is also fixed, the other end being attached to the short arm of a light lever movable about o, the long arm of which is loaded with a weight (not repre- sented in the figure) to keep the wire tight. The platinum wire is connected with the positive pole a, and the palladium with the negative pole d, of a voltaic battery, and the apparatus is partially immersed in acidulated water ; the water is thereby decomposed into its constituent gases ; oxygen is liberated in bubbles from the platinum wire, but there is no visible dis- engagement at the palladium. The latter becomes longer, however, as is seen by the motion of the lever. If the current is reversed, the wire again contracts and the lever resumes its original position. Fig. 183 -196] Archimedes' Principle applied to Gases 179 CHAPTER III PRESSURE ON BODIES IN AIR. BALLOONS 196. Archimedes' principle applied to gases. — The pressure exerted by gases on bodies immersed in tliem is exerted equally in all directions, as has been shown by the experiment with the Magdeburg hemispheres ( i6i). It therefore follows that all which has been said about the equilibrium of bodies in liquids applies to bodies in air ; they lose apparently a part of their weight equal to that of the air which they displace. The loss of weight in air is demon- strated by means of the baroscope, which consists of a scalebeam, at one end of which a small leaden weight is supported, and at the other there is a hollow copper sphere (fig. 184). In the air they exactly balance each other ; but when they are placed under the receiver of an air-pump, and a vacuCim is produced, the sphere sinks, thereby showing that in reality it is heavier than the smaller leaden weight. Before the air is exhausted each body is buoyed up by the weight of the air which it displaces. But as the sphere is much the larger of the two, its weight undergoes most apparent diminution, and thus, though in reality the heavier body, it is balanced by the small leaden weight. It may be proved by means of the same apparatus that this loss is equal to the weight of the displaced air. Suppose the volume of the sphere is 10 cubic inches. The weight of this volume of air is 3'i grains. If now this weight be added to the leaden weight, it will overbalance the sphere in air, but will exactly balance it in vacuo. The principle of Archimedes is true for bodies in air ; all that has been said about bodies immersed in liquids applies to them ; that is, that when a body is heavier than air it will sink, owing to the excess of its weight over the buoyancy. If it is as heavy as air, its weight will exactly counterbalance the buoyancy, and the body will float in the atmosphere. If the body is lighter than air, the buoyancy of the air will prevail and the body will rise N 2 Fig. 184 i8o On Gases [196- in the atmosphere until it reaches a layer of the same density as its own. The force causing ascent is equal to the excess of the buoyancy over the weight of the body. This is the reason why smoke, vapours, clouds, and air- balloons rise in the air. It will be understood that by buoyancy is meant the iveight of the medium displaced whatever that medium may be. AIR-BALLOONS 197. Air-balloons. — Air-balloons are hollow spheres made of some light impermeable material, which, when filled with heated air, with hydrogen gas, or with coal gas, rise in the air by virtue of their relative lightness. They were invented by the brothers Montgolfier of Annonay, and the first experiment was made at that place in June 1783. Their balloon was a sphere of forty yards in circumference, and weighed 500 pounds. At the lower part there was an aperture, and a sort of boat was suspended, in which fire was lighted to heat the internal air. The balloon rose to a height of 2,200 yards, and then descended without any accident. Charles, a professor of physics in Paris, substituted hydrogen for hot air. He himself ascended in a balloon of this kind in December 1783. The use of hot-air balloons was entirely given up in consequence of the serious accidents to which they were liable. Since then the art of ballooning has been greatly extended, and many ascents have been made. That which Gay-Lussac made in 1804 was the most remarkable for the facts with which it has enriched science, and for the height which he attained — 23,000 feet above the sea-level. At this height the barometer sank to 12-6 inches, and the thermometer, which was 31° C. on the ground, was 9 degrees below zero. In these high regions the dryness was such on the day of Gay-Lussads ascent, that hygrometric substances, such as paper, parchment .&c., became dried and crumpled as if they had been placed near the fire. The respira- tion and circulation of the blood were accelerated in consequence of the great rarefaction of the air. Gay-Lussac's pulse made 120 pulsations in a minute instead of 66, the normal number. At this great height the sky had a very dark blue tint, and an absolute silence prevailed. One of the most remarkable ascents was made by Mr. Glaisher and Mr. Coxwell, in a large balloon belonging to the latter. This was filled with 90,000 cubic feet of coal gas (sp. gr. 0-37 to 0-33) ; the weight of the load was 600 pounds. The ascent took place at I P.iNl. on September 5, 1861 ; at 1.28 they had reached a height of 15,750 feet, and in eleven minutes after a height of 21,000 feet, the temperature being -10-4°; at 1.50 they were at 26,200 feet, with the thermometer at -15-2° At 1.52 the height attained was 29,000 feet, and the temperature- 16° C. At this height the rarefaction of the air was so great, and the cold so intense, that Mr. Glaisher fainted and could no longer observe. According to an approximate estimation, the lowest barometric height they attained was 7 inches, which would correspond to an elevation of from 36,000 to 37,000 feet. 198. Construction and management of balloons. — A balloon (fig. 185) is made of long bands of silk sewed together and covered with India rubber varnish, which renders it airtight. At the top there is a safety-valve closed -198] Construction and Management of Balloons i8i by a spring, which'the aeronaut can open at pleasure by means of a cord. A light wickerwork boat is suspended by means of cords to a network which entirely covers the balloon. A balloon of the ordinary dimensions, which'can carry three persons, is about 1 6 yards high, 12 yards in diameter, and its volume, when it is quite full, is about 680 cubic yards. The balloon itself weighs 200 pounds ; the accessories, such as the rope and boat, 100 pounds. The balloon is filled either with hy- drogen or with coal gas. Although the latter is heavier than the former, it is generally preferred, because it is cheaper and more easily obtained. It is passed into the balloon from the gas reservoir by means of a flexible tube. It is im- portant not to fill the balloon quite full, for the atmospheric pressure dimi- nishes as it rises, and the gas inside, expanding in consequence of its elastic force, tends to burst it. It is suffi- cient for the ascent if the weight of the displaced air exceeds that of the balloon by 8 or 10 pounds. And this force remains constant so long as the balloon is not quite distended by the dilatation of the air in the interior. If the atmospheric pressure, for example, has diminished to one-half, the gas in the balloon, according to Boyle's law, has doubled its volume. The volume of the air displaced is therefore twice as great ; but since its density has become only one-half, the weight, and consequently the upward buoyancy, are the same. When once the balloon is completely dilated, if it continues to rise, the force of the ascent decreases, for the volume of the displaced air remains the same, but its density diminishes, and a time arrives at which the buoyancy is equal to the weight of the balloon. The balloon can now only take a horizontal direction, carried by the currents of air which prevail in the atmosphere. The aeronaut |knows by the barometer whether he is ascending or descending, and by the same means he determines the height which he has reached. A long flag fixed to the boat would indicate, by the position it takes either above or below, whether the balloon is descending or ascending. When the aeronaut wishes to descend, he opens the valve at the top of the balloon by means of the cord, which allows gas to escape, and the Fig. 18s I 82 On Gases [198- v / balloon sinks. If he wants to descend more slowly, or to rise again, he empties out bags of sand, of which there is an ample supply in the car. The descent is facilitated by means of a grappling-iron fixed to the boat. When once this is fixed to any obstacle, the balloon is lowered by pulling the cord. The only practical applications which air-balloons have hitherto had have been in military reconnoitring. At the battle of Fleurus, in 1794, a captive balloon — that is, one held by a rope — was used, in which there was an observer who reported the movements of the enemy by means of signals. At the battle of Solferino the movements and dispositions of the Austrian troops were watched from a captive balloon ; and in the war in America balloons were frequently used, while their importance during the siege of Paris will not have been forgotten. In the war in South Africa frequent use was made of captive balloons. It has been proposed to use captive balloons for observations on the changes of temperature in the air, &c. Air-balloons can only be truly useful when they can be guided, and as yet all attempts made with this view have completely failed. There is no other course at present than to rise in the air until there is a current which has more or less the desired direction. Unfortunately, the currents in the higher regions of the atmosphere are variable and irregular. 199. Parachute. — The ob- ject of the parachute is to allow the aeronaut to leave the bal- loon, by giving him the means of lessening the rapidity of his descent. It consists of a large circular piece of cloth (fig. 186), about i6feet in diameter, which by the resistance of the air spreads out like a gigantic umbrella. In the centre there is an aperture through which the air compressed by the rapidity of the descent makes its escape ; for otherwise oscillations might be produced, which, when communicated to the boat, would be dangerous. In fig. 185 there is a parachute attached to the network of the balloon by means of a cord which passes round a pulley, and is fixed at the other end to the boat. When the cord is cut the parachute sinks, at first very rapidly, but more slowly as it becomes distended, as represented in fig. 186. 200. Calculation of the weight which a balloon can raise. — To calculate the weight which can be raised by a balloon of given dimensions, let us Fig. 186 -BOOj Calculation of Weight a Balloon can raise 183 suppose it perfectly spherical, and premise that the formulas which express the volume and the superficies in terms of the radius are V = ^^, S = 47rR^ 3 The radius R being measured in feet, let p be, in pounds, the weight of a square foot of the material of which the balloon is constructed ; let P be the weight of the car and the accessories, a the weight in pounds of a cubic foot of air at zero, and under the pressure 076m., and a' the weight of the same volume, under the same conditions, of the gas with which the balloon is inflated (157). Then the total weight of the envelope in pounds will be 47rR''/ ; that of the gas will be 4£^ ; and that of the displaced air 4^i^. 3 3 If X be the weight which the balloon can support, we have 3 3 Whence X = 4!!^ (a -a')- 47rR^/ - P. 3 But, as we have before seen (198), the weight must be less by 8 or 10 pounds than that given by this equation, in order that the balloon may rise. 1 84 On Gases [201- CHAPTER IV I APPARATUS WHICH DEPEND ON THE PROPERTIES OF AIR 20I. Air-pump. — The air-pump is an instrument by Avhicli a vacuum can be i produced in a given space, or rather by which air can be greatly rarefied, for aniabsolute vacuum cannot be produced by its means. It was invented Fig. 187 by Otto von Guericke in 1650, a few years after the invention ot the baro- meter. The air-pump, as now usually constructed, may be described as follows. Fig. 187 represents a general view, fig. 188 a section, and figs. 189-194 various parts ; the letters in all the figures having everywhere the same meaning. -201] Air-pump 185 The base VGL is of stout metal, and is firmly fixed on a table. At one end two glass cylinders or barrels are firmly cemented, and the two pistons P and P', tightly packed with leather washers, work airtight in them. To these pistons are attached racks H,K, ^g M and by means . of a handle MN, work- ing about a pinion X, the pistons P and P' are moved alternately up and down. On the plate V is fitted a thick glass plate with a ver)' true surface. In its centre is a screw tubulure, «, fixed into a conduit, nc, which connects the receiver and the barrels. Fig. 189 gives a vertical section of one of the pistons On a larger scale. It consists of two brass discs, A and B, the latter of Fig. ii which is provided with a brass tube in which is a screw, D ; this presses together a number of leather washers very slightly larger than the disc. The leather is thoroughly soaked with oil, and slides airtight in the barrels, but with slight friction. D is pierced by a channel which connects it with the outer air. In the centre of the disc B is a hole, i, closed by a metal valve, Z, which is shod with cork, and by means of a rod, extent, the atmospheric pressure on the top of P will be very great, but it will Fig. igo be very nearly balanced by the atmospheric pressure on the top of the other piston Consequently, the experimenter will have to overcome only the difference of the two pressures. This is the reason why two barrels are employed, a plan first adopted by Hawksbee. 202. Air-pump gauge. — When the pump has been worked some time, the pressure in the receiver is indicated by the difference of level of the rpercury in the two legs of a glass tube bent hke a siphon, one of which is opened, and the other closed like a barometer. This little apparatus, which is called the gauge, is fixed to an upright scale and placed under a small bell-jar, E, which communicates with the receiver R by a stopcock, T, inserted in the tube leading from the orifice G to the cylinders (fig. 188). Before the exhaustion begins, the pressure of the air in E exceeds the -202] Air-pump Gauge iZ-j weight of the column of mercurj' which is in the closed branch and which consequently remains full. But as the pump is worked the pressure soon diminishes, and is unable to support the weight of the mercury, which sinks and tends to stand at the same level in both legs. If an absolute vacuum could be produced, they would be exactly on the same level, for there would be no pressure either on the one side or the other. But with the very best machines of this type the level is always about a thirtieth of an inch higher in the closed branch, which indicates that the pressure of the air in the receiver has been reduced to the ^J^ part of an atmosphere. Theoretically an absolute vacuum is impossible ; for since the volume of each cylinder is, say, ^5 that of the receiver, only ^ of the air in the receiver is extracted at each stroke of the piston, and consequently it is im- possible to exhaust all the air which it contains. The theoretical degree of exhaustion after a given number of strokes is easily calculated as follows : — Let a denote the volume of the receiver, including in that term the pipe ; b the volume of the cylinder between the highest and lowest positions of the piston ; and assume, for the sake of distinctness, that there is only one cylinder : then the air which occupied a before the piston is lifted occupies a-\-b after it is lifted ; and consequently if d^ is the density at the end of the first stroke, and d the original density, we must ha-ic d^ = d . If d.^ is the density at the end of the second stroke, we have d.,^d,---^=di-^\; a + b \a^ b) consequently, after n strokes, d„ = d ( ) \a + b/ If there are two equal cylinders, the same formula holds ; but in this case, in counting n, upstrokes and downstrokes equally reckon as one. If P„ be the pressure of the rarefied air after n strokes of the pump, and P the original (atmospheric) pressure, the above formula gives, since the pressure is directly proportional to the density when the volume and tem- perature are constant, P„.p( «y \a + b/ It is obvious that the exhaustion is never complete, since rf„ or P^ can be zero only when « is infinite. However, no very great number of strokes is re- quired to render the exhaustion virtually complete, even if a is several times greater than ^ Thus if a = lo^ a hundred strokes will reduce the density from dto o-ooooyd ; that is, if the initial pressure is 30 inches, the pressure at the end of 100 strokes is 0-021 of an inch. Practically, however, a limit is placed on the rarefaction that can be pro- duced by any given air-pump ; for, as we have seen, the air becomes ulti- mately so rarefied that, when the pistons are at the bottom of the cylinder, its elastic force cannot overcome the pressure in the valves on the inside of the piston ; they therefore do not open, and there is no further action of the pump. 1 88 On Gases [202- The space between the piston and the bottom of the barrel is called the clearance. The efficiency of the pump depends upon its being' made as small as possible. 203. Double-exhaustion stopcock. — By means of this device the ex- haustion of the air can be carried to a very high degree. Fig. 190 gives a horizontal section of the stopcock Q, which by means of a central channel and two lateral ones forms a communication with the receiver and the barrels. When the working" ceases, that is, when Z no longer rises, a quarter- turn is given to Q (fig. 192). The connections are now altered, as is seen from the horizontal sections in figs. 191 and 192, and the vertical sections in figs. 193 and 194. Figs. 191 and 193 refer to the state of things before, and figs. 192 and 194 after Q is turned. The new channels correspond now with Fig. 192 Fig. 193 Fig. 194 those of the base, and the right barrel is alone connected with the receiver by the channel nmc, while the left is connected by an oblique channel in the stopcock with a central aperture o, in the base of the right barrel. The right piston as it rises exhausts air from the receiver ; but when it sinks the exhausted air is drawn into the left barrel by the apertures o and d, this latter being always open, for the corresponding conical valve, s, is raised. When the right piston rises that of the left sinks ; but the air below does not return to the right barrel, for the orifice is now closed by the conical valve. As the right cylinder contintres to exhaust the air in the receiver, and to force it into the left cylinder, the air accumulates here, and ultimately acquires sufficient pressure to raise the valve of the piston P', which was impossible before the stopcock was turned, for it is only when -204] Bianchi's Air-pump 189 the valves in the piston no longer open that a quarter of a turn is given to the stopcock. In this way a rarefaction of half a millimetre has been attained. 204. Bianchi's air-pump. — Bianchi invented an air-pump which has several advantages. It is made entirely of iron, and it has only one cylinder, which oscillates on a horizontal axis fixed at its base, as seen in fig 195. A horizontal shaft, with heavy fly-wheel V, works in a frame, and is turned Fig. 195 by a handle, M. A crank, m, which is joined to the top of the piston rod, is fixed to the same shaft, and consequently at every revolution of the wheel the cylinder makes two oscillations. In some cases, as in that shown in the figure, the crank and the fly-wheel are on parallel axes connected by a pair of cog-wheels. The modification in the action produced by this arrangement is as follows : — If the [cog-wheel igo On Gases [204- on the former axis has twice as many teeth as that on the latter axis, the force which raises the piston is doubled : an advantage which is counter- balanced by the inconvenience that now the piston will make one oscillation for one revolution of the fly-wheel. The machine is double-acting ; that is, the piston PP (fig. 196) produces a vacuum, both in ascending and descending. This is effected by the fol- lowing arrangements : — In the piston there is a valve, b, opening upwards as in the ordinary machine. The piston-rod AA is hollow, and in the inside there is a copper tube, X, by which the air escapes through the valve b. At the top of the cylinder there is a second valve, a, opening up- wards. An iron rod, D, works with gentle friction in the piston, and terminates at its ends in two conical valves, J and s' , which fit into the openings of the tube B leading to the receiver. Let us suppose the piston de- scends. The valve s' is then closed, and, the valve s being open, the air of the receiver passes into the space above the piston, while the air in the space below the piston under- goes compression, and, -raising the valve, escapes by the tube X, which communicates with the atmosphere. When the piston ascends, the ex- haustion takes place through s', and the valve j being closed, the com- pressed air escapes by the valve a. The machine has a stopcock for double exhaustion, similar to that already described (203). It is also oiled in an ingenious manner. A cup, E, round the rod is filled with oil, which passes into the annular space between the rod AA and the tube X ; it passes then into a tube 00 in the piston, and, forced by the atmospheric pressure, is uniformly distributed on the surface of the piston. The apparatus, being of iron, may be made of much greater dimensions than the ordinary air-pump. A vacuum can also be produced with it in far less time and in apparatus of greater size than usual. 205. Fleuss or Geryk pump. — The Fleuss pump is a mechanical pump by which a vacuum of i mm. of mercury can rapidly be obtained. A section of the pump is shown in fig. 197. AB is a cylinder in which a piston P, carried by a piston-rod C, moves up and down. Near the middle of the Fig. 196 -206] Sprengel's Air-pump 191 cylinder is a partition with a central opening a, through which C passes, and J is a collar with a disc T attached, through which the piston-rod can slide airtight, and which serves as a valve. Due to the action of a strong spring, SS, the valve J keeps the aperture a ordi- narily closed ; but as the piston rises to the top of its stroke, its shoulder slightly raises J, and expels into the upper compartment any air which may have been carried up by the piston. EE is an annular space sur- rounding the lower compartment, communi- cating by G with the vessel to be exhausted, by H with the bottom of the cylinder, and by F with the lower compartment. D is a disc-valve in the piston closing an aperture, b, in the lower part of the piston, while c is an opening in the upper part. K is an open- ing communicating with the external air in the case of a single-barrel pump, and with the lower compartment of the second barrel, if the pump has two barrels, by a tube similar to G. The effective action of the pump depends upon a copious use of a special non-volatile oil which floods the lower parts of each com- partment and seals all the joints and valves. It is a single-acting pump. In the position of the piston shown in the figure, the receiver communicates with B by the tube G. As the piston rises F is closed, the air in B is com- pressed, and escapes through the oil into the upper compartment in consequence of the valve J being slightly raised by the shoulder on the piston. When the piston descends the pressure of air below it raises the valve D, so that the pressures above and below '''S' '*' the piston are equalised or nearly so. P has now reached the bottom, and the action is repeated. Thus at each double (down and up) stroke the volume of air contained in B is expelled. The merit of the pump consists in the absence of clearance at a. All the air in B is expelled at each upstroke — its place being taken by oil. 206. Sprengel's air-pump. — Sprengel has devised a form of air-pump which depends on the principle of converting the space to be exhausted into a Torricellian vacuum. If an aperture be made in the top of a barometer tube, the mercury sinks and draws in air ; if the experiment be so arranged as to allow air to enter along with mercury, and if the supply of air be limited while that of mercury is unlimited, the air will be carried away and a vacuum produced. The fol- lowing is the simplest form of the apparatus in which this action is realised. In fig. 198, cd is a glass tube longer than a barometer, open at both ends, 192 On Gases [206- and connected by means of india rubber tubing with a funnel, A, filled with mercury and supported by a stand. Mercury is allowed to fall in this tube at a rate regulated by a clamp at c ; the lower end of the tube cd fits in the flask B, which has a spout at the side a little higher than the lower end of cd ; the upper part has a branch at .r, to which the vessel R to be ex- hausted can be tightly fixed. When the clamp at c is opened, the first por- tions of mercury which run out close the tube and prevent air from entering below. As the mercury is allowed to run down the exhaustion begins, and the whole length of the tube from x to d is filled with alternate cylinders of air and mercury moving downwards. Air and mercury escape through the spout of the flask B, which is above the basin H, where the mercury is collected. It is poured back from time to time into the funnel A, to be repassed through the tube until the exhaustion is complete. As this point is approached, the enclosed air be- tween the mercury cylinders is seen to diminish, until the lower part of cd forms a continuous column of mercury about 30 inches high. Towards this stage of the process the falling mercury produces a noise like that of a water- hammer when shaken ; the operation is completed when the column of mercury encloses no air, and a drop of mercury falls on the top of the column without enclosing the slightest air-bubble. The height of the column then represents the height of the column of mercury in the barometer ; in other words, it is a barometer whose Torricellian vacuum is the receiver R. Modifications of this apparatus have been used with great success in experiments in which a very complete exhaustion is required, as in the pre- paration of Geissler's tubes and in incandescent electric lamps. It may be advantageously combined with a mechanical air-pump such as the Fleuss, which first removes the greater part of the air, the exhaustion being then completed as above. The most perfect vacua are obtained by absorbing the residual gas, after the exhaustion has been pushed as far as possible, either mechanically or by some substance with which it combines chemically. Thus Dewar has produced a vacuum the pressure in which he estimates at ^J^- of a milli- metre, by heating charcoal to redness, in a vessel from which air had been Fig. 198 B -207] BunserCs Sprengel Pump 193 exhausted by the Sprengel pump, and then allowing it to cool. Finkener filled a vessel with oxygen, then exhausted as far as possible, and finally heated to redness some copper contained in the vessel. This absorbed the minute quantity of gas left, with the formation of cupric oxide. In some of his experiments Crookes obtained by chemical means a vacuum of jj^J^y^j of a millimetre. This represents a pressure of one-twentieth of a millionth of an atmosphere (micro-atmosphere). In these highly rarefied gases the pressure is so low that it is very difficult to measure minute differences. For such cases McLeod has devised a very valuable gauge, the principle of which is to con- dense a measured volume of the highly rarefied gas to a much smaller volume, and then to measure its pressure under the new conditions. McLeod's gauge is illustrated in fig. 199. BG is a vertical tube connected above with the vessel which is being exhausted, and dipping into a bottle, F, containing mercury. The latter is connected by a tube, E, with a Bunsen's pump (207), so that the pressure in the space above the mercury in F can be reduced. ACK is a tube the upper part of which, AC, is capillary and graduated, the volume of the whole tube and of the capillary part for each division being care- fully determined. This tube fits airtight into the opening of a lateral projection, D, from the tube BG, the junction being sealed by mercury in the cup L. The upper part of BG is of the same tubing as AC, to avoid errors from capillarity, and is also graduated. To determine the pressure of the rarefied air, we proceed as follows : — Turn the stopcock E and admit air into F ; the mercury at G rises, reaches K, and shuts off in ACD a known volume V of air at a pressure P (mm.) which is to be deter- mined. The mercury still rising compresses this air, and reaches a point A, while in the long tube it stands (say) at B, h mm. above A. The volume v above A is known ; the pressure on the mercury at B is P, for it has not been sensibly altered by rise of the mercury from G to B. Hence by Boyle's law VP = v {^ -v h), whence P is determined. Care must be taken to maintain the temperature constant. 207. Bunsen's Sprengel pump. — This is a con- Fig. 199 venient arrangement for producing a very con- siderable exliaustion in cases where a good supply of water isSavailable, as in laboratories. A composition tube, a (fig. 200), connected with'^the service-pipe of a water-supply, is joined by means of an india rubber-tube to a glass tube, cdf, to which is attached at / a leaden tube about 10 to 12 yards long. The tube sr is connected with the space to be exhausted. 0, 194 On Gases [207- The water enters by a, and in falling down the tube carries with it air from the space to be exhausted. The supply of water, and therewith the Fig. 200 rate of exhaustion, can be regulated by the stopcock b ; the bent tube pq, which contains mercury, measures the pressure which may be reduced to 10 to 15 millimetres. 208. Aspirating action of currents of air. — When a jet of liquid or of a gas passes through air, it carries the surrounding air along with it, fresh air rushes in to supply its place, comes also in contact with the jet, and is in like manner carried away. Thus, then, there is a continual rarefaction of the air round the jet, in consequence of which it exerts an aspiratory action. This phenomenon may be well illus- trated by means of an apparatus repre- sented in fig. 201, the analogy of which to the experiment described (145) will be at once evident. It consists of a wide glass tube, in the two ends of which are fitted two small tubes, nd and B ; in the bottom is a manometer tube containing a coloured liquid. On blowing through the narrow tube the liquid at o is seen to rise. If, on the contrary, the wide tube is blown into, a depression is produced at o. Fig. 201 -208] Aspirating Action of Currents of Air I9S Fig. 202 To this class of phenomena belongs the following experiment, which is a simple modification of one originally described by Clement and Ddsormes. A tube is fixed in a metal disc (fig. 202), its end being flush with the surface. A light disc is held at a little distance by means of three metal studs. Holding the tube vertically with the discs downwards, and blowing into it, the movable disc is seen to rise until it comes in contact with the upper one. The current of air spreads out from the centre of the plate towards the circumference, and in doing so is rarefied ; in consequence of this lessened pressure in the space, the lower disc is lifted by the external pressure against the upper one, where it remains as long as the blow- ing continues. The simplest plan of making this experiment was devised by Faraday. Holding one hand horizontal, the palm downwards and the fingers closed, the space between the index and middle fingers is blown through. If a piece of light paper, of 2 or 3 square inches, is held against the aperture, it does not fall as long as the blowing continues. The old water-bellows, still used in mountainous places where there is a continuous fall, is a further application of the principle. Water falling from a reservoir down a narrow tube divides and carries air along with it ; and, if there are apertures in the sides through which air can enter, this also is carried along, and becomes accumulated in a reservoir placed below, from which by means of a lateral tube it can be directed into the hearth of a forge. This may be illustrated by the simple apparatus represented in fig. 203, the construction of which from glass tubes and corks will be readily intelligible. It may be remarked that the outer tube is at h represented in section, and that the parts of the tubes ofd and h outside the cork are relatively much longer horizont- ally and vertically than is here represented. If the vertical tube/i:^ is fitted to a vessel, of boiling water, as soon as steam issues through 0, it not only raises water from a vessel in which the bottom of the tube h dips, but drives it through the aperture 0. And if a bent tube, with a narrow opening like o, be fitted at n, and directed upwards, a continuous jet of water is produced, often reaching to the ceiling. This apparatus serves well to illustrate the principle of Giffard's injector, an extremely ingenious and important apparatus by which steam-boilers are kept supplied with water. The principle is also applied in a series of machines for moving and O 2 196 On Gases [208- lifting liquids, and even solids such as corn ; in pumping, in blowers, exhausters, aiv-pumps, &c. An interesting application is that of the well- known spray producer ; this principle has further been utilised by Sprengel in supplying water to sulphuric acid chambers. By the locomotive steam-pipe a jet of steam entering the chimney of the locomotive carries the air away, so that fresh air must arrive through the fire, and thus the draught is kept up. 209. Morren's mercury pump. — Figs. 204 and 205 represent a mercury air-pump, constructed by Alvergniat. It consists of two reservoirs, A Fig. 204 Fig. 205 and B, connected by a barometer tube, T, and a long India rubber tube, C. The reservoir B and the tube T are fixed to a vertical support ; A, which is movable and open, can be alternately raised and lowered through a~dis- tance of nearly 4 feet. This is effected by means of a long wire rope, which is fixed at one end to the reservoir A, and passes over two pulleys, a and b, the latter of which is turned by a handle. Above the reservoir Bjis-a three- -210] Condensing Pump 197 way cock, n ; to this is attached a tube, d, for exhaustion, and on the left is an ordinary stopcock, /«, which communicates with a reservoir of mercury, v, and with the air. The exhausting tube d is not in direct com- munication with the receiver to be exhausted ; it is first connected with a reservoir, o, partially filled with sulphuric acid, and designed to dry the gases \\hich enter the apparatus. An india rubber tube, r, makes communication with the receiver which is to be exhausted. On the reservoir ; closing then the stopcock m, and lower- ing the reservoir A (fig. 205), the mercury sinks in the reservoir B and in the tube T, until the difference of levels in the two tubes is equal to the baro- metric height, and there is a vacuum in the reservoir B. Turning now the stopcock n, as shown in fig. X, the gas from the space to be exhausted passes into the barometer chamber B by the tubes c and rf, and the level again sinks in the tube T. The stopcocks are now replaced in the first position (fig. Z), and the reservoir A is again lifted, the excess of pressure of mercury in the india rubber tube expels, through the Stopcocks n and m, the gas which had passed into the chamber B, and, if a few droplets of mercury are carried along with it, they are collected in the vessel i/. The process is repeated until the mercury is virtually at the same level in both legs of the gauge. Like Sprengel's pump, this is very slow in its working, and, like it, is best employed in completing the exhaustion of a space which has already been partially rarefied ; for a vacuum of jij of a milli- metre may be obtained by its means. 210. Condensing pump. — The con- densing pump is an apparatus for com- pressing air or any other gas. The form usually adopted is the following :— In a cylinder, A, of small diameter (fig. 207), there is a solid piston, the rod of which is moved by the hand. The cylinder is provided with a screw which fits into the receiver K. Fig. 206 shows the arrange- ment of the valves, which are so con- structed that the lateral valve o opens into the cylinder A, and the dower valve j downwards towards the receiver. When the piston descends the valve o closes and the air in the cylinder A is forced through the valve s into the receiver. When the piston ascends, .f closes and o opens, and permits the entrance of fresh air, which in turn Fig. 207 198 On Gases [210- becomes compressed by the descent of the piston, and so on. This apparatus is useful for charging hquids with gases. For this purpose the stopcock B is connected with a reservoir of the gas by means of the tube D. The pump exhausts this gas, and forces it into the vessel K, in which the liquid is contained. Artificial gaseous waters are made by means of analogous apparatus. Suppose air is being compressed into K. If a and b denote the volumes of the receiver and cylinder respectively, P atmospheric pressure, and Pj, Pj, . . . Pn the pressures of the compressed air after I, 2 ... » strokes of the piston, we see that after one downward stroke the volume a + b at pressure P is compressed into a at pressure Pj ; .*. 7 {a + b) = V^a. As the piston rises the cylinder is refilled with air at atmospheric pressure. At the end of the second stroke, P (a + 2b) = V./i ; and after n strokes, P (a + nb) = Vj^a, assuming constancy of temperature. The applications of condensed air are both numerous and important. In a certain sense condensed air plays the part of a metal spring in which energy is stored, and from which it can be drawn and utilised by CKpanding the air at a given moment and at a given point in the most favourable condition for its being applied. In some cases the expansion is sudden and intermittent, as in the air-gun, the pneumatic post, or in atmospheric brakes ; and in some cases slow, gradual, and continuous, as in boring machines. One of the most important applications is that to the larger boring machines used in 'tunnelling through the Alps and elsewhere. There, where steam power would be objectionable owing to the steam produced, com- pressed air is of great service, for it not only supplies the power, but it helps to ventilate the underground spaces. The principal parts of such machines, which were first employed on a large scale in the Mont Cenis tunnel, are as follows : — A sheaf of borers or iron rods with punches on the ends are mounted on a framework. Each of these borers is susceptible of three simultaneous motions : one backward and forward producing repeated shocks against the rock ; a second analogous to that of a gimlet ; while a third moves the whole framework backwards and forwards. This triple motion is effected by a machine like a steam-engine, but driven by compressed air ; the first motion by a piston, the action of which is regulated by a slide valve (476) ; the other two motions are effected by means of a separate machine. The air is under a pressure of five atmo- spheres the compression being effected by special machines worked by water power. The air, by which all this is effected, on expanding helps to cool and venylate the mine. Tbs pneumatic post is of great service in London and other large towns in forwarding the actual written telegraphic messages from the several receiving stations to a central telegraph station. The messages are placed in a carrier, which is a gutta-percha cylinder 7 inches long by 2 inches in diameter, closed at one end ; it is covered with felt, and there is a welt of that material at one end ; the felt projects at the other, so that it can be folded down and held in position by an india rubber band, so as to keep the contents in their place. -211] Uses of the Atr-pump 199 Such carriers move airtight in carefully turned leaden tubes polished internally and protected by being incased in iron tubes. The propulsion is effected either by pressure or by exhaustion ; and by suitable valves the tubes can be placed in connection with compressed or rarefied air, so that the carriers may either be shot in one direction by compressed air, or drawn in the other by rarefied air. The compression and rarefaction are produced by means of powerful steam-engines to a pressure of about 10 pounds, or a vacuum of 8 pounds to the square inch. By this means a speed of nearly a mile in a minute may be obtained in tubes not more than a mile in length. Other applications of compressed air are in the small pumps used by plumbers for testing and for clearing gas-pipes, in ventilating mines, in supplying air to blast furnaces, in the atmospheric brakes used in railway trains, as motive power in torpedoes, and so forth. Compressed air has long been used in Paris for the synchronised work- ing of clocks, and this has led to its successful application on a large scale for the transmission of power from a central station for working small motors. It is distributed in tubes a foot in diameter under a pressure of 6 atmospheres, and in this way it is possible to work small air motors at a distance of four miles from the source of power with an efficiency of 50 per cent. 211. Uses of the air-pump. — A great many experiments with the air-pump have been already described. Such are the mer- curial rain (13), the fall of bodies in vacuo (78), the bladder (154), the bursting of a bladder (160), the Magdeburg hemispheres (161), and the baroscope (196). The fountain in vacuo (fig. 208) is an experiment made with the air-pump, and shows the elastic force of the air. It con- sists of a glass vessel. A, provided at the bottom with a stopcock and a tubulure which projects into the interior. This apparatus having been screwed to the air-pump is ex- hausted, and, the stopcock being closed, is placed in a vessel of water, R. When the stopcock is opened, atmospheric pressure acting upon the water in the vessel forces the water through the tube in a jet, as shown in the drawing. Fig. 209 represents an experiment illus- trating the effect of atmospheric pressure on the human body. A glass vessel, open at both ends, being placed on the plate of the machine, the upper end of the cylinder is closed by the hand, and the pump set in action. The hand is then forced down by the difference between the pressure outside and inside, and can only be taken away by a great effort. And as the elasticity of the fluids contained in the blood-vessels and Fig, 208 nil 200 On Gases [211- other organs is not counterbalanced by the pressure of the atmosphere; the palm of the hand swells, and blood tends to escape from the pores. By means of the air-pump it may be shown that air, by reason of the oxygen it contains, is necessary for the support of combustion and of life. For if we place a lighted taper under the receiver, and begin to exhaust the air, the flame becomes weaker as rarefaction proceeds and is finally ex- tinguished. Similarly, an animal faints and dies if a vacuum is formed in a receiver under which it is placed. Mammalia and birds soon die in vacuo. Fish and reptiles support the loss of air for a much longer time. Insects can live several days in vacuo. Substances liable to ferment may be kept in vacuo for a long time without alteration, as they are not in contact with oxygen, which is necessary for fermentation. Food kept in airtight cases, from which the air had been exhausted, has been found as fresh after years as on the first day. 213. Hero's fountain. — Hero's fountain, which derives its name from its inventor. Hero, who lived at Alexandria, 120 B.C., depends on the elasticity of the air. It consists of a brass dish, D (fig. 210), and of two glass globes, M and N. The dish com- municates with the lower part of the globe N by a long tube, . B ; and another tube, A, connects the two globes. A third tube passes through the dish D to the lower part of the globe M. This tube having been taken out, the globe M is partially filled with water ; the tube is then replaced and water is poured into the dish. The water flows through the tube B into the lower globe, and expels the air, which is forced into the upper globe ; the air, thus compressed, acts upon the water, and makes it jet out as represented in the figure. If it were not for the resist- ance of the atmosphere and friction, the liquid would rise to a height above the water in the dish equal to the difference of the level in the two globes. 213. Intermittent fountain. — The intcT- mittent fountain consists of a stoppered glass globe (C, fig. 211), provided with two or three lateral tubes with fine nozzles, D. -214] The Siphon 201 A glass tube open at both ends reaches at one end to the upper part of the globe C ; the other end terminates just above a little aperture in the dish B, which supports the whole apparatus. The water with which the globe C is nearly two-thirds filled runs out by the tubes D, as shown in the figure, the interna pressure at D being equal to the atmo- spheric pressure together with the weight of the column of water CD, while the external pressure at that point is only that of the atmosphere. These conditions pre- vail so long as the lower end of the glass tube is open, that is, so long as air can enter C and keep the air in C at the same density as the external air ; but the apparatus is arranged so that the orifice in the dish B does not allow so much water to flow out as it re- ceives from the tubes D, in consequence of which the level gradually rises in the dish, and closes the lower end of the glass tube. As the external air cannot now enter the globe C, the air becomes rare- fied in proportion as the flow continues, until the pressure of the column of water CD, together with that of the air con- tained in the globe, is equal to this external pressure at D ; the flow conse- quently stops. But as water continues to flow out of the dish B, the tubes D become open again, air enters, and the flow recommences, and so on, as long as there is water in the globe C. 214. The siphon. — The siphon is a bent tube open at both ends, and with unequal legs (fig. 212). It is used in transferring liquids in the following man- ner : — The siphon is filled with some liquid, and, the two ends being closed, the shorter leg is dipped in the liquid, as represented in fig. 2:2 ; or, the shorter leg having been dipped in the liquid, the air is exhausted by applying the mouth at B. The air in the tube is thus rarefied, and the liquid in C rises and fills the tube in consequence of the atmospheric pres- sure. It will then run out through the siphon as long as the shorter end dips in the liquid. °' To explain this flow of water from the siphon, let us suppose the siphon filled and the short leg immersed in the liquid ; also suppose W temporarily Fig. >PMP' 202 On Gases [214- closed. Then, considering the pressure at the point M in the tube in so far as it is influenced by the Hquid in the tube MC, we see that this pressure is equal to the atmospheric pressure minus the pressure due to DC, or H— /;, if H represent the height of the water barometer. This, if it acted alone, would cause the liquid at M to move in the direction DA. But the pressure at M, considered as influenced by the liquid in the tube MB, is equal to atmospheric pressure minus the pressure due to the column AB or H—A', and this acts from A to D. Now H -^>H-^', if h' >h. Thus water will flow from the vessel if AB is greater than DC. If AB = DC, there will be no flow ; and if AB is less than DC, the liquid will flow in the opposite direction. It follows from the explanation of the siphon that it would not work in vacuo, nor if the height CD were greater than that of a column of liquid which counterbalances the atmospheric pressure. 215. The intermittent siphon. — In the intermittent siphon the flow is not continuous. It is arranged in a vessel, so that the shorter leg is near the bottom of the vessel, while the longer leg passes through it (fig. 213). Being fed by a constant supply of water, the level gradually rises both in the vessel and in the tube to the top of the siphon, which it fills, and water begins to flow out. But the apparatus is arranged so that the flow of the siphon is more rapid than that of the tube which supplies the vessel, and consequently the level sinks in the vessel until the shorter branch no longer dips in the liquid ; the siphon is then empty, and the flow ceases. But as the vessel is continually fed from the same source the level again rises, and the same series of phenomena is reproduced. The theory of the intermittent siphon explains the natural intermittent springs which are found in many countries, and of which there is an excel- lent example near Giggleswick in Yorkshire. Many of these springs furnish water for several days or months, and then, after stopping for a certain interval, again recommence. In others the flow stops and recommences several times in an hour. These phenomena are explained by assuming that there are subterranean fountains, which are more or less slowly filled by springs, and which are then emptied by fissures so occurring in the ground as to form an intermittent siphon. 216. Different kinds of pumps. — Pumps are machines which serve to raise water either by suction, by pressure, or by both effects combined ; they are consequently divided into suction or lift pumps, force-pumps, and suction a,nd forcing pumps. The various parts entering into the construction of a pump are the barrel, the piston, the valves, and the pipes. The barrel is a cylinder of metal or of wood, in which is Ihe piston. The latter is a metal or wooden cylinder wrapped with tow, and working with gentle friction the whole length of the barrel. The valves are discs of metal or leather, which alternately close the Fig. 213 -217] Suction-pump 203 apertures which connect the barrel with the pipes. The most usual valves are the clack valve (fig. 214) and the conical valve (fig. Z15). The former is a metal disc fixed to a hinge on the edge of the orifice to be closed. In order more effectu- ally to close it, the lower part of the disc is covered with thick leather. Sometimes the valve consists merely of a leather disc, of larger dia- IP^J ■ i; Fig. 214 Fig. 215 Its flexibility meter than the orifice, nailed on the edge of the orifice, enables it to act as a hinge. The conical valve consists of a metal cone fitting in an aperture of the same shape. Below this is an iron hoop, through which passes a bolt- head fixed to the valve. The object of this is to limit the play of the valve when it is raised by the water, and to prevent its removal. 217. Suction-pump. — Fig. 216 re- presents a model of a suction-pump such as is used in lectures, but which has essentially the same arrangement as the pumps in common use. It consists, 1st, of a glass cylinder, B, at the bottom of which is a valve, S, opening upwards ; 2nd, of a suction- tube, A, which dips into the reservoir from which water is to be raised ; 3rd, of a piston, which is moved up and down by a rod worked by a handle, P. The piston is perforated by a hole ; the upper aperture is closed by a valve, O, opening upwards. When the piston rises from the bottom of the cylinder B, a vacuum is produced below, and the valve O is kept closed by the atmospheric pres- sure, while the air in the pipe A, in consequence of its elasticity, raises the valve S, and partially passes into the cylinder. The air being thus rarefied, water rises in the pipe until the pres- sure of the liquid column, together with the pressure of the rarefied air which remains in the tube, counter- balances the pressure of the atmosphere on the water of the reservoir. When the piston descends, the valve S closes by its own weight, and pre- vents the return of the air from the cylinder into the tube A. The air com- pressed by the piston opens the valve O, and escapes into the atmosphere by the pipe C. With a second stroke of the piston the same series of phenomena Fig. 216 204 On Gases [217- is produced, and after a few strokes the water reaches the cyhiider. The effect is now somewhat modified ; during the descent of the piston the valve S closes, and the water raises the valve O, and passes above the piston by which it is lifted into the upper reservoir D. There is now no more air in the pump, and the water forced by the atmospheric pressure rises with the piston. It is essential for the action of the pump that the valve S should be less than 34 feet above the level of the water in which the tube A dips, for we have seen (163) that a column of water of this height is equal to the pressure of the atmosphere. In practice the height of the tube A does not exceed 26 to 28 feet ; for although the atmospheric pressure can support a higher column, the vacuum produced in the barrel is not perfect, owing to the fact that the piston does not fit exactly on the bottom of the barrel. But when the water has passed the piston, it is the force applied to the latter , which raises it, and the height to which it can be brought depends on the power which works the piston. 218. Suction- and force-pump.- — The action of this pump, a model of which is represented in fig. 217, depends both on exhaustion and on pres- sure. At the base of the barrel, where it is con- nected with the tube A, there is a valve, S, which opens upwards. Another valve, O, opening in the same direction, closes the aperture of a conduit, which passes from a hole, o, near the valve S, into a vessel, M, which is called the air-chamber. From this chamber there is another tube, D, up which the water is forced. At each ascent of the piston B, which is solid, the water rises through the tube A into the barrel. When the piston sinks the valve S closes, and the water is forced through the valve O into the reser- voir M, and thence into the tube D. The height to which it can be raised in this tube depends solely on the motive force which works the pump. If the tube D were a prolongation of the tube Jac, the flow would be intermittent ; it would take place when the piston descended, and would Fig, 217 -220] Fire-engine 205 cease as soon as it ascended. But between these tubes there is an interval, which, by means of the air in the reservoir M, ensures a continuous flow. The water forced into the reservoir M divides into t«o parts, one of which, rising in D, presses on the water in the reservoir by its weight ; while the other, in virtue of this pressure, rises in the reservoir above the lower orifice of the tube D, compressing the air above. Consequently, when the piston ascends, and no longer forces the water into M, the air of the reser- voir expands, and raises the liquid in the tube D, until the piston again descends, so that the jet is continuous. 219. Load which the piston supports. — In the suction-pump, when once the water fills the pipe, and the barrel, as far as the spout, the effort necessary to raise the piston is equal to the weight of a column of water the base of which is this piston, and the height the vertical dista7ice in the spout from the level of the water in the reservoir ; that is, the height to which the water is raised. For if H is the atmospheric pressure, h the height of the water above the piston, and h' the height of the column which fills the suction-tube A (fig. 217), and the lower part of the barrel, the pressure above the piston is obviously H +^, and that below is H — /;', since the weight of the column h' tends to counterbalance the atmospheric pressure. But as the pressure H— ,4' tends to raise the piston, the effective resistance is equal to the excess of H + ^ over H — A' ; that is to say, to h + h'. In the suction- and force-pump it is readily seen that the pressure which the piston supports is also equal to the weight of a column of water the base of which is the section of the piston, and the height that to which the water is raised Fig. 218 220. Fire-engine. — The ^r«-««^/«£ is a force-pump in which a steady jet is obtained by the aid of an air-chamber, and also by two pumps working 2o6 On Gases [220- alternately (fig. 218). The two pumps in and n, worked by the same lever, PQ, are immersed in a tank, which is kept filled with water as long as the pump works. From the arrangement of the valves it will be seen that when one pump, n, draws water from the tank, the other, m, forces it into the air- chamber, R ; whence, by an orifice, Z, it passes into the delivery tube, by which it can be sent in any direction. Without the air-chamber the jet would be intermittent. But as the velocity of the water on entering the reservoir is less than on emerging, the level of the water rises above the orifice Z, compressing the air which fills the reservoir. Hence, whenever the piston stops, the air thus compressed, reacting on the liquid, forces it out during its momentary stoppage, and thus keeps up a constant flow. -223] Cause of Sound 207 BOOK V ON SOUND CHAPTER I PRODUCTION, PROPAGATION, AND REFLKCTION OF SOUND 221. Province of acoustics. — The study of sounds and that of the vibra- tions of elastic bodies form the province of the science of sounds, or acoustics. Music considers sounds witli reference to tlie pleasurable feeling they are calculated to excite. Acoustics is concerned with the questions of the pro- duction, transmission, and comparison of sounds ; to which may be added the physiological question of the perception of sounds. 222. Sound and noise. — Souitd is the peculiar sensation excited in the organ of hearing by the vibratory motion of bodies, when this motion is transmitted to the ear through an elastic medium. Sounds are distinguished from noises. Sound properly so called, or musical sound, is that which produces a continuous sensation, the musical value of which can be estimated ; while noise is either a sound of too short a duration to be determined, like the report of a cannon ; or else it is a confused mixture of many discordant sounds, like the rolling of thunder or the noise of the waves. Nevertheless, the difference between sound and noise is by no means precise ; Savart showed that there are relations of height in the case of noise, as well as in that of sound ; and there are said to be certain ears sufficiently well organised to determine the musical value of the sound produced by a carriage rolling on the pavement. 223. Cause of sound. — When a tuning-fork is bowed it emits a sound. A body capable of emitting a sound is called a sonorous body. In the case of the tuning-fork we know that the prongs are in motion by their blurred appear- ance, if the amplitude be large, or, if the motion is too small to be detected by the eye, by placing the finger-nail close to the prong, when the motion will be felt. Generally, when a body emits sound the parts of it are in vibratory motion. It is not enough that the molecules are in motion. Mere molecular motion does not constitute sound. The molecules of a body are always in motion, and on the energy of this motion the temperature of 2o8 On Sound [223- the body depends. The molecular motion may be increased or diminished without the consequent emission of sound. In order that sound may be produced the body must vibrate as a whole. As understood in England and Germany, a vibration comprises a motion to andiro ; in France, on the contrary, a vibration means a movement to or fro. The French vibrations are with us semi-vibrations ; an oscillation or vibration is the movement of the vibrating particle in only one direction ; a double or complete vibration comprises the oscillation both backwards and forwards. Vibrations of sounding bodies are very readily observed. If a light powder is sprinkled on a body which is in the act of yielding a musical sound, a rapid motion is imparted to the powder, which renders visible the vibrations of the body ; and, in the same manner, if a stretched cord is smartly pulled and let go, its vibrations are apparent to the eye. A bell-jar is held horizontally in one hand (fig. 219), and made Fig. 219 to vibrate by being struck with the other ; if then a piece of metal is placed in it, it is rapidly raised by the vibrations of the side ; touching the cell-jar with the hand, the sound ceases, and with it the motion of the metal. 224. Sounds not propagfated in vacuo. — The vibrations of elastic bodies can only produce the sensation of sound in us by the intervention of a medium interposed between the ear and the sonorous body and vibrating with it. This medium is usually the air ; but all gases, vapours, liquids, and solids also transmit sounds. The following experiment shows that the presence of a ponderable medium is neces- sary for the propagation of sound. A small metal bell, which is continually struck by a small hammer by means of clockwork, or else an ordinary musical box, is placed under the receiver of an air-pump (fig. 220). So long as the receiver is full of air at the ordi- nary pressure the sound is transmitted ; but in proportion as the air is exhausted the sound becomes feebler, and cannot be heard in a vacuum. To ensure the success of the experiment, the bellwork or the musical box must be placed on wadding or on a block of vul- canised rubber ; for otherwise the vibrations would be transmitted to the air through the plate of the pump. 225. Sound is propagated in all elastic bodies. — If, in the above experi- ment, any vapour or gas be admitted after the vacuum has been made, Fi-. 22. -226] Propagation of Sound in Air 209 the sound of the bell will be heard, showing that sound is propagated in this- medium as in air. Sound is also propagated in liquids. When two stones are struck against each other under water, the shock is distinctly heard ; and a diver at the bottom of the water can hear the sound of voices on the bank. The sound is, however, enfeebled, as a considerable portion is reflected at the boundarj- of the two media. When a tuning-fork is struck, not too violently, the sound is scarcely audible at the distance of a few feet from the fork. But if a prong of the fork while still vibrating touches the surface of water in a tumbler which rests on the table, the sound becomes distinct, proving that the vibrations of the fork are transmitted through the water to the glass and the table. If the tumbler rests on the sounding-box belonging to-the fork (251) the effect is. more striking. The conductibility of solids is such that the faint scratching of a pen or the ticking of a watch at one end of a long horizontal wooden rod is heard much more distinctly when the ear is directly applied against the other end of the rod than when it is at the same distance in the air. Sound may even reach the ear through solids alone without passing through the air ; for if the ears be closed, and the rod be put between the teeth, the ticking is distinctly heard. The earth conducts sound so well that at night, when the ear is applied to the ground, the stepping of horses, or any other noise at a great distance, is heard. 226. Waves in an elastic medium. Transverse and longitudinal vibra- tions. Propagation of sound in air. — When a disturbance is made at any point of a medium, such as a gas or liquid or the luminiferous ether, the particles of the medium are set in vibration, and the vibrations are passed on to the neighbouring particles, so that waves are formed which travel with a uniform velocity depending upon the medium, and by these the disturbance- is propagated to considerable distances from its point of origin. The waves are due to the vibrations of the particles of the medium ; the vibrations may be- along the line in which the disturbance is travelling (as when sound is trans- mitted through solids, liquids, and gases), or at right angles to it (as in the case of light and radiant heat), or it may partake of both motions at the- same time (water-waves). Consider the case of transverse vibrations. Imagine a row of equidistant particles of a medium at rest, and suppose that when one of them is set ini vibration at right angles to the row the disturbance is passed on from particle to particle, each in turn going through the same motions as its- predecessors. Let the motion be simple harmonic (57). If T represents the periodic time, and if each particle starts from its mean position, T/12, after T T T Its next preceding, the state of thmgs after metrvals _^ -, -, T, is shown in O J 2 fig. 221 {a to e). Thus the vibrations of the particles, each passing m succession throtfgb the same phases as the others, give rise to waves, each consisting of are elevation and depression, or crest and furrow. The length of a wave is the distance from crest to crest or from furrow to furrow, or between any twoi points in the same phase. p 2IO On Sound [226- An illustration of wave-formation is obtained by observing what occurs when a small stone is dropped into smooth water. A depression is caused at the point of incidence, surrounded immediately by a circular ridge of water higher than the level of the smooth water. As this elevated portion sinks by its weight, it causes the water in front of it to rise, and thus the appearance is presented of a ridge followed by a trough travelling outwards from the point of disturbance. The ridge and trough constitute a wave, and this wave ' Time h o fa 1 6 ) ) m -J- • e • ^* (d ]) i • • • * T • " • • ■ (e ) • • • • Fig 221 is followed by a succession of others. The wave-form travels along the surface of the water ; the particles of water merely move up and down, they do not move away from their mean positions. Their motion is not purely transversal, but is partly longitudinal, so that the particles of water on the surface move in circular paths. Next, consider sound-waves in air. Sound is transmitted through air by waves which are due to the vibrations of air particles. But in the case of sound the vibrations of the air particles are in the direction of propagation, they are longitudinal. Consequently, in place of elevations and depression a sound-wave is composed of two portions, in one of which the air-pressure is greater, and in the other less, than normal. ^ Let AB be a line of equidistant air particles at rest, and let each particle when disturbed perform simple harmonic motion. If the vibrations were transverse a wave-form would be produced as shown in fig. 222 (a), the particles A, C, and B being at rest. If the vibrations take place along the line AB, then, in order to find the resulting configuration, we must displace the particles by an amount equal to the ordinate of the corresponding point in curve (a), towards A for the elevation and from A for the depression (fig. 222, b). In ng. 223 the top line shows a row of equidistant particles at rest. At the time zero these particles are supposed to be in the positions shown, and the -226] Propagation of Sound in Air 211 rows below represent the relative positions of the particles after times T/12,, 2T/12, &c., T being the periodic time. The figure clearly shows the progres- sion in time of a compression, and also of a rarefaction from the left towards the right. i • • • c B (a.) i ^ • c • • • B (b) Fig. 222 The variations in local pressure as a sound-wave passes through air may be illustrated by considering a particular case. Let MN (fig. 224) be a ' A TM • • • • • • • • • • • • • • • • • • • • • ' 2 • • « . • • > • • • • • • * T/,2 • • ' • • • • • • • • T/,z • • • • • • • • • • • 6 • • • • • • • • • • • • T/>2 ,' • • • • • ' • • • • • • 4 • • ' • • • • 10 TM . • • • • • « • ' a • .,, • • • • • • • \ • • ■ a TM • • • • • • & • • • Fig. 223 tube filled with air at a constant pressure and temperature, and let P be|a piston oscillating rapidly from A to a. When the piston starts from A, H'" . H" H' TI CI .\ M 1 1 i N Fig. 224 it compresses the air in front ot it, and the compression increases until P reaches the position halfway between A and a, when it is a maximum, after which it diminishes as P reaches a. Suppose that as the piston moves from p 2 212 On Sound [226- A to a, the disturbance of the air in the tube travels to H. Thus in aH the pressure of the air is greater than normal, the compression being greatest at the centre. When the piston returns in the direction aA, the pressure behind it is diminished and the diminution of pressure is a maximum when P is halfway back. This reduction of pressure or rarefaction travels along the tube in the same way and at the same rate as the compression, so that when the piston has reached A, the point from which it started, the compres- sion has advanced to the position HH', and its place has been taken by the rarefied portion. Thus after one complete oscillation of the piston the beginning of the air disturbance is at H' and the end at a. The whole length aH' is a wave or undulation. It consists of two equal parts in one of which the air is more compressed and in the other is more rarefied than in the undisturbed tube. When the piston has made another complete oscillation, the wave aH' will have advanced by a distance equal to itself, and its place will have been taken by another wave, and so on. The velocity with which the disturbance travels is the velocity of sound in the air of the tube. If X denote the length of a wave, and n be the number of oscillations of the piston per second, nK is equal to the total distance travelled by the beginning of the distance in one second. If this distance is v, then the velocity of sound = v = rik. It is an easy transition from the explanation of the motion of sound- waves in a cylinder to that of their motion in an unenclosed medium. It is simply necessary to apply in all directions to each molecule of the vibrating body what has been said about a piston movable in a tube. A series of spherical waves alternately condensed and rarefied is produced around each centre of disturbance. As these waves are contained within two concentrical spherical surfaces, whose radii gradually increase while the length of the undulation remains the same, their mass increases with the distance from the centre of disturbance, so that the amplitude of the vibration of the mole- cules gradually lessens, and the intensity of the sound, which depends upon the square of the amplitude, diminishes. It is these spherical waves, consisting of portions alternately condensed and expanded, which in being propagated transmit sound. If many points are disturbed at the same time, a system of waves is produced around each point. But all these waves . are transmitted one through the other without modifying either their lengths or their velocities. When two waves meet each other the effect will be an augmentation or diminution of sound accord- ing to the relative phases in which the waves meet. If the surface of still water is disturbed at two or more points, the coexistence of waves becomes sensible to the eye. 227. Causes which influence the intensity of sound. — Many causes modify the force or the intensity of sound. These are the distance of the sounding body, the amplitude of the vibrations, the density of the air at the place where the sound is produced, the direction of the currents of air, and, lastly, the neighbourhood of other sounding bodies. i. The intensity of sound is inversely as the square of the distance of the sounding body from the ear. This law has been deduced by calculation, assuming the sound to radiate from a point, but it may be also demon- strated experimentally. Let us suppose several sounds of equal intensity— -228] Influence of Tubes on the Transmission of Sound 213 for instance, bells of the same kind, struck by hammers of the same weight falHng from equal heights. If four of these bells are placed at a distance of 20 yards from the ear, and one at a distance of 10 yards, it is found that the single bell produces a sound of the same intensity as the four bells struck simultaneously. Consequently, for double the distance the intensity of the sound is only one-fourth. A method of comparing the intensities of different sounds will be described afterwards (291). The distance at which sounds can be heard depends on their intensity. The report of a volcano at St. Vincent was heard at Demerara, 300 miles off, and the firing at Waterloo was heard at Dover. ii. The intensity of sound increases with the amplitude of the vibrations of the sonorous body. The connection between the intensity of the sound and the amplitude of the vibrations is readily observed by means of vibrating strings (267). For, if the strings are somewhat- long, the oscillations are per- ceptible to the eye, and it is seen that the sound is feebler in proportion as the amplitude of the oscillations decreases. The intensity varies as the square of the amplitude of oscillation. iii. The intensity of sound depends on the density of the air in the place in which it is produced. As we have already seen (224), when an alarum actuated by clockwork is placed under the bell-jar of an air-pump, the sound becomes weaker in proportion as the air is rarefied. In hydrogen, which is about ^ the density of air, sounds are much feebler, although the pressure is the same. In carbonic acid on the con- trary, whose density is i'529, sounds are more intense. On high mountains, where the air is much rarefied, it is necessary to speak with some effort in order to be heard, and the discharge of a gun produces only a feeble sound. The ticking of a watch is heard in water at a distance of 23 feet, in oil of l6j, in alcohol of 13, and in air of only 10 feet. iv. The intensity of sound is modified by the motion of the atmosphere and the direction of the wind. In calm weather sound is always better propagated than when there is wind ; in the latter case, for an equal distance, sound is more intense in the direction of the wind than in the contrary direction. V. Lastly, sound is strengthened by the neighbourhood of a sonorous body. A string made to vibrate in free air has but a very feeble sound ; but when it vibrates above a sounding-box, as in the case of the violin, guitar, or violon- cello, its sound is much stronger. This arises from the fact that the box and the air which it contains vibrate in unison with the string. Hence the use of sounding-boxes in stringed instruments. Attempts have been made to get a measure of the loudness of sound which should serve as a standard, by allowing leaden bullets to fall from various heights on an iron plate of some size. It appears that within certain limits the loudness is nearly proportional to the square root of the height from which the bullet falls, and not to the height itself It thus appears that only a portion of the energy of the falling body is expended in producing vibrations of the plate. 228. Influence of tubes on the transmission of sound. — The law that the intensity of sound decreases in proportion to the square of the distance does not apply to the case of tubes, especially if they are straight andpcylindrical. 214 On Sound [228- The sound-waves in that case are not propagated in the form of increasing concentric spheres, and sound can be transmitted to a great distance with- out any perceptible alteration. Biot found that in one of the Paris water- pipes, 1040 yards long, the voice lost so little of its intensity that a con- versation could be kept up at the ends of a tube in a very low tone. The weakening of sound becomes, however, perceptible in tubes of large diameter, or where the sides are rough. This property of transmitting sounds was first used in England for speaking tubes. They consist of india rubber or metal tubes, smooth inside and as free as possible from bends, passing from one room to another. If a person speaks at one end of the tube, he is distinctly heard by a person with his ear at the other end. From Biot's experiments it is evident that a communication might be made between two towns by means of speaking tubes. The velocity of sound is 1 125 feet in a second at i6-6° C, so that a distance of 50 miles, would be traversed in four minutes. 229. Regnault's experiments. — Theoretically, a sound should be propa- gated in a straight cylindrical tube with a constant intensity. Regnault found, however, that in these circumstances the intensity of sound gradually diminishes with the distance, and that the distance at which it ceases to be audible is nearly proportional to the diameter of the tube. He reproduced sound-waves of equal strength by means of a small pistol charged with a gramme of powder, and fired at the open ends of tubes of various diameters ; and he then ascertained the distance at which the sound could no longer be heard, or at which it ceased to act on what he calls a sensitive membrane. This was a very flexible membrane which could be fixed across the tube at various distances, and was provided with a small metal disc in its centre. When the membrane begins to vibrate, this disc struck against a metallic contact, and thereby closed a voltaic circuit, which traced on a chronograph the exact moment at which the membrane received the sound-wave. Experimenting in this manner, Regnault found that the report of a pistol charged as stated is no longer audible at a distance of 1 1 59 metres in a tube of . . . o-i 08m. diameter 3810 „ „ . . o-30om. „ 9540 „ „ . I -loom. These numbers represent the limit of distance at which the sound-wave is- no longer heard, but it still acts on the membrane at the distances of 4156, 11,430, and 19,851 metres respectively. According to Regnault the principal cause of this diminution of intensity is the loss of energy against the sides of the tube ; he found also that sounds of high pitch are propagated in tubes less easily than those of low pitch ; a bass voice would be heard at a greater distance than a treble voice. 230. Velocity of sound in air. — Since the propagation of sound-waves is gradual, sound requires a certain time for its transmission from one place to another, as is seen in numerous phenomena. For example, the sound of thunder is only heard some time after the flash of lightning has been seen, although both the sound and the light are produced simultaneously ; and in -230] Velocity of Sound in Air 215 like manner we see a mason at a distance in the act of striking a stone, or a man felling a tree, before we hear the sound. The velocity of sound in air has often been the subject of experimental research. One of the most accurate of the direct measurements was made by Moll and Van Beck in 1823. Two hills, near Amsterdam, Kooltjesberg and Zevenboomen, were chosen as stations : their distance from each other as determined trigonometrically was 57,971 feet, or nearly eleven miles. Cannon were fired at stated intervals simultaneously at each station, and the time which elapsed between seeing the flash and hearing the sound was noted by chronometers. This time could be taken as that which the sound required to travel between the two stations ; for it will be subsequently seen that light takes an inappreciable time to traverse the above distance. In- troducing corrections for tfie temperature and hygrometric state, and elimi- nating the influence of the wind, Moll and Van Beck's results as recalculated by Schroder van der Kolk gave 109278 as the velocity of sound in feet per second in dry air at 0° C. The velocity of sound at 0° may be taken at 1093 feet, or 333 metres per second. It increases with increase of temperature, and may be calcu- lated for a temperature f from the formula %!= 1093^(1 -H 0-003665/), where 1093 is the velocity in feet per second at o'' C, and 0-003665 the coefficient of expansion of air. This amounts to an increase of nearly 2 feet for every degree Centigrade. Kendall, in a North Pole expedition, found that the velocity of sound at a temperature of —40'' was 314 metres or 1030-4 feet. Stone's determinations, made at the Cape of Good Hope with very great care, gave 1090-57 feet, or 332-4 metres, as the velocity of sound at 0°. Greely determined the velocity of sound in metres per second in air between - 10° and —45° to be ^ = 333 + o"6 A where / is the temperature Centigrade. For the same temperature it is inde- pendent of the density of the air, and consequently of the pressure. It is the same forthe same temperature with all sounds, whether they be strong or weak, deep or acute. Biot found, in his experiments on the conductivity of sound in tubes, that when a well-known air was played on a flute at one end of a tube 1,040 yards long, it was heard without alteration at the other end, from which he concluded that the velocity of different sounds is the same. For the same reason the tune played by a band is heard at a great distance without alteration, except in loudness, which could not be the case if sounds differ- ing in pitch and intensity travelled with different velocities. This cannot, however, be admitted as universally true. Earnshaw, as the result of a mathematical investigation of the laws of the propagation of sound, concluded that the velocity of a sound depends on its strength ; and, accordingly, that a violent sound ought to be propagated with greater velocity than a gentler one. This conclusion is confirmed by an observation made by Captain Parry on his Arctic expedition. During artillery practice it was found, by persons stationed at a considerable distance from the guns, that the report of the cannon was heard before the command to fire given 2i6 On Sound [230- by the officer. And, more recently, Mallet made a series of experiments on the velocity with which sound is propagated in rocks, by observing the times ■which elapsed before blastings, made at Holyhead, were heard at a distance. He found that the larger the charge of gunpowder, and therefore the louder the report, the more rapid was the transmission. With a charge of 2000 pounds of gunpowder the velocity was 967 feet per second, while with a •charge of 12,000 it was 1210 feet per second. Jacques made a series of experiments by firing different weights of powder from a cannon, and determining the velocity of the report at different ■distances from the gun by means of an electrical arrangement. He thus found that, close to the gun, the velocity is least, and that it increases to a certain maximum which is considerably greater than the average velocity. The velocity is also greater with the heavier charge. Thus with a charge of li pound the velocity was 1187, and with a charge of J pound it was 1032 at a distance of from 30 to 50 feet ; while at a distance of 70 to 80 it was 1267 and 1120 ; and at 90 to 100 feet it was 1262 and 11 14 respectively. Threlfall experimented with the explosion of charges in water at Port Jackson, Australia. The calculated velocity was 1 500 metres per second ; the observed velocity rose from 1752 metres per second with 9 ounces of gun- cotton to 2013 metres per second with 64 ounces. Bravais and Martins found, in 1844, that sound travelled with the same velocity from the base to the summit of the Faulhorn as from the summit to the base. A laboratory method of determining the velocity of sounds consists in using a metronome (83) which is beating slowly, and is approached to a wall until a position is found at which the echo of one beat coincides with the sound of another heard directly. The distance from the wall is then half the distance which sound traverses in the interval between two beats of the metronome. 231. Calculation of the velocity of sound in gases. — From theoretical considerations Newton gave a rule for calculating the velocity of sound in gases, which may be represented by the formula '■'\l-d-' in which v represents the velocity of the sound, e the elasticity of the gas, and d its density. This formula expresses that the velocity of the propagation of sound in gases is directly as the square root of the elasticity of the gas, and inversely as the square root of its density. It is easy to prove that, if Boyle's law is applicable — that is, if the changes of volume take place without change of temperature — the elasticity of a gas is equal to its pressure. It follows that the velocity of sound is the same under any pressure ; for although the elasticity increases with increased pressure, according to Boyle's law, the density increases in the some ratio. At Quito, where the mean barometric height is only 2r8 inches, the velocity is the same as at the sea-level provided the temperature is the same. If h be the height of the barometer, 8 the density of mercury, and ^ the acceleration due to gravity, the pressure P =gih ; further, if d be the density -232] Velocity of Sound in Various Gases 2 1 7 of the gas at t° C. and 4, the density at 0° C, d^ = d{\ +at), where a is the coefficient of expansion of the gas (332). Thus Newton's formula becomes Substituting in this formula the values in centimetres and grammes, j'= 981, S= 13,596, ^ = 76, 4) = °'OOi293, the pressure is 1-0135x10" dynes, or i'oi35 megadynes, per square centimetre, and the value of v is 27,995 centimetres per second = 279-95 metres per second, which is about one- sixth less than the experimental result. The reason for this discrepancy was given by Laplace, who pointed out that when sound-waves are travelHng through air the heat which is produced by the increase of pressure in the compressed part of any wave does not rapidly escape into the surrounding air. Similarly the cold due to the diminution of pressure in the rarefied portion of the wave is not at once compensated by the ingress of heat from the surrounding space. Consequently the temperature in the two parts of any wave cannot be regarded as constant, and therefore Boyle's law does not hold. Although the average tempera- ture of the air is unaltered, its elasticity is increased and is no longer measured by the pressure P. It may be shown that the elasticity is greater than the isothermal elasticity P in the proportion in which the specific heat of the gas at constant pressure is greater than the specific heat at constant volume. If these specific heats are denoted by c, c' respectively, the elasticity = P— = Py, and the expression for the velocity of sound in the gas is ^=VrV5'=Vf (--)>• The value of -y for air is 1-41, and if the value of the velocity obtained above, viz. 279-95 metres, be multiphed by v'i-4i or 1-1875, the product is 332-55, which agrees with the experimental value. Knowing the velocity of sound, we can calculate approximately the dis- tance at which it is produced. Light travels with such velocity that the flash or the smoke accompanying the report of a gun may be considered to be seen simultaneously with the occurrence of the explosion. Counting then the number of seconds which elapse between seeing the flash and hearing the sound, and multiplying this number by 1 125, supposing the temperature to be 16° C, we get the distance in feet at which the gun is discharged. In the same way the distance of thunder may be estimated. 232. Velocity of sound in various gases. — The velocity of sound in air and other gases may be determined by making use of the principle of resonance in air pipes. The method is described in article 276. Since in gases which differ in density, but are subjected to the same pressure, the velocity of sound varies inversely as the square root of the density, knowing the velocity of sound in air, we may calculate it for other gases ; thus in hydrogen it will be /_^3 4,68 feet. n/o-o688 2i8 On Sound [232- Velocities calculated in this way cannot be universally accurate, for the coefficient - or y differs somewhat in different gases. And when pipes were sounded with different gases, and the number of vibrations of the notes multiplied with twice the length of the pipe, numbers were obtained which differed for those calculated by the above formula. When, however, the proper value of y for each gas was introduced into the calculation, the theo- retical results agreed very well with the observed ones. By the above method the following values have been obtained : — Velocity of sound at o° C. in Chlorine 677 feet in u second Carbonic acid 856 „ Oxygen . . 1040 „ Air . . . 1093 Carbonic oxide . . i io5 „ Hydrogen ... . . 4163 „ 233. Doppler's principle. — When a sounding body approaches the ear, the note perceived is somewhat higher than the true one ; but if the source of sound recedes from the ear, the note perceived is lower. The truth of this, which is known as Doppler' s principle, will be apparent from the follow- ing considerations : — When the source of sound and the ear are relatively at rest, the ear receives n waves in a second ; but if the ear approaches the sound, or the sound approaches the ear, it receives more ; just as a ship meets more waves when it ploughs through them than if it is at rest. Conversely, the ear receives a smaller number when it recedes from the source of sound. The effect in the first case is as if the sounding body emitted more vibrations in a second than it really does, and in the second case fewer. Hence in the first case the note appears higher ; in the second case lower. If the distance which the ear traverses in a second towards the source of sound (supposed to be stationary) is f feet, and the wave-length of the particular note is X feet, then - waves are passed in a second ; this is equal A to — , forX= , where v is the velocity of sound (226). Hence the ear c n receives not only the n original waves, but also — in addition. Therefore V the number of waves per second which enter the ear is , ns , .r , n =n+ — =n (1+—) V v for an ear which approaches the sound ; and by similar reasoning it is , ns , s. n =n = n (i ) V V for an ear receding from the sound. To test Doppler's theory Buys Ballot stationed trumpeters on the Utrecht -234] Velocity of Sound in Liquids 219 jailway and also upon locomotives, and had the height of the approaching or receding notes compared with stationary ones by musicians. He thus found both the principle and the formula fully confirmed. Similar conclu- sive experiments were made by Scott Russell on English railways. The observation may often be made as one fast train passes another in which the engine is sounding its whistle. Suppose each train to be running at 30 miles an hour, the relative velocity is 60 miles an hour, or 88 feet per second. If we . , ' / 88 \ „ / w \ . n" 151 ,.,, take t/ = 1120, « = « ( I + \. n =n \\ - ) . . -, =^i-= vi"]. \ 1120/ \ 1 120/! n 129 Hence the note of the whistle is flattened, as the trains pass each other, by nearly a minor third (247). It must be noted that the pitch of the whistle changes only at the moment the locomotive passes. It is constant as the train approaches, and constant again, but lower in pitch, as the train recedes. Doppler's principle may also be established by direct laboratory ex- periments. RoUmann fixed a long rod on a turning table, at the end of which was a large glass bulb with a slit in it, which sounded like a humming-top when a tangential current of air was blown against the slit. The uniform and sufficiently rapid rotation of the sphere developed such a current, and produced a steady note, the pitch of which was higher or lower in each rotation according as the bulb came nearer, or receded from, the observer. The principle may also be illustrated by means of a tuning-fork with wide branches, and producing a very high note of 2046 vibrations. When this is ■loudly sounded, and, being held in front of a smooth wall, is moved towards it with a velocity of a metre in a second, the direct note and that reflected from the wall undergo opposite changes, so that an observer may distinctly hear beats (263). 234. Velocity of sound in liquids. — The velocity of sound in water was experimentally determined in 1827 by Colladon and Sturm. They moored two boats at a known distance apart in the Lake of Geneva. The first supported a bell immersed in water, and a bent lever provided at one end with a hammer which struck the bell, and at the other with a lighted wick, so arranged that it ignited some powder the moment the hammer struck the bell. To the second boat was affixed an ear-trumpet, the bell of which was in water, while the mouth was applied to the ear of the observer, so that he could measure the time between the flash of lig'ht and the arrival of sound by the water. By this method the velocity was found to be 4708 feet in a second at the temperature 8'i°, or four times as great as in air. The velocity of sound, which is different in different liquids, can be cal- culated by a formula, identical with that given above (231) as applicable to gases — that is, v = a/ -j. In this formula, e is the volume elasticity of the liquid — that is, the ratio of pressure applied to the compression produced — and d its density. The compression per unit of volume due to the applica- tion of a pressure of one atmosphere is called, the compressibility of the liquid. The numbers given in the following table were computed from 220 On Sound [234- the above formula. As in the case of gases, the velocity varies with the tem- perature, vi^hich is therefore appended in each case. River water (Seine) Artificial sea water Mercury Solution of common sal Absolute alcohol , Turpentine , , Ether . 13° C. = 4714 feet in a second 3° = 5013 J5 20 = 4761 J7 lO = 4866 )) i8 = 5132 11 23 = 3854 11 24 = 3976 11 24 = 3801 11 It will be seen how close is the agreement between the two values for the velocity of sound in water, the only case in which they have been directly compared. There is considerable uncertainty about the values for other liquids, owing to the doubt as to the values for their compressi- bility. 235. Velocity of sound in solids. — As a general rule, the elasticity of solids, as compared with the density, is greater than that of liquids, and consequently the propagation of sound is more rapid. The difference is well seen in an experiment by Biot, who found that when a bell was struck by a hammer, at one end of an iron tube 3120 feet long, two sounds were distinctly heard at the other end. The first of these was transmitted by the tube itself with a velocity, x ; and the second by the enclosed air with a known velocity, a. The interval between the sounds was 2-5 seconds. The value of Jtr obtained from the equation 3I20_3I20^ shows that the velocity of sound in the tube is nearly nine times as great as that in air. Biot's experiment is an interesting one, though no great value can be attached to the result, as the pipe was not continuous, but formed a series of jointed tubes. That the report of the firing of cannon is heard at far greater distances than peals of thunder is doubtless owing to the fact that the sound in the former case is mainly transmitted through the earth. To this class of phenomena belongs the fact that if the ear is held against a rock in which a blasting is being made at a distance, two distinct reports are heard — one transmitted through the rock to the ear, and the other trans- mitted through the air. The propagation of sound in soUds is also well illustrated by the fact that in laying telegraph wires the filing at any particular part can be heard at distances of miles by placing one end of the wire in the ear. The toy telephone also is based on this fact. The velocity of sound in wires has also been determined theoretically, by Wertheim and others, by the formula v= a/^ in which /i is the longi- -236] Reflection of Sound 221 tudinal elasticity (Young's modulus) of the material (87), while d is the density. This may be illustrated from a determination by Wertheim of the velocity of sound in a specimen of annealed steel wire, the density j of which was 7-631 and longitudinal elasticity 2r4 x 10" (87). The formula gives V = A / — ^: = "5294x10° — ^^ = 5294 metres per sec. = 17,370 ft. per sec. The following table gives the velocity in various bodies, expressed in feet per second, mostly from the experimental determinations of Wertheim and of Stefan : — India rubber 100 to 200 Copper . 12194 Tallow ii8o Oak 12622 Wax . 2394 Cedar . 13120 Paraffin 4250 Elm • 13516 Lead . 4653 Ash 15314 Membranes . 2300 to 6560 Fir • 15316 Gold . 7021 Walnut 15744 Paper . . 5250 to 8860 Glass . . 16057 Silver . 8806 Steel wire . • 16336 Pine . . 10900 Wrought iron and steel 16498 The numbers for India rubber are of the same order of magnitude as those for the propagation of a nervous impulse, and suggest that such an impulse is transmitted by longitudinal vibrations (283) like those of sound. In the case of wood these velocities are in the directions of the fibres, and are considerably greater than across the rings or along the rings ; thus with fir the velocities are 4382 and 2572 for these directions respectively. From a recent determination of the elasticity of ice, Trowbridge and Macrae deduced the velocity of sound in it to be 9,600 feet per second, or about nine times that of air. Mallet investigated the velocity of the transmission of sound in various rocks, and found that it is as follows : — Wet sand 825 feet in a second Contorted, stratified quartz and slate rock . io88 Discontinuous granite .... 1306 „ Solid granite . . 1664 „ A direct .experimental method of determining the velocity of sound in solids, gases, and vapours will be described subsequently (279). If a medium through which sound passes is heterogeneous, the waves of sound are reflected on the diflFerent surfaces, and the sound becomes rapidly enfeebled. Thus a soft earth conducts sound badly, while a hard ground which forms 'a compact mass conducts it well. So also we hear badly through air-spaces which are filled with porous materials, such as shavings,, sawdust, cinders, and the like. 236. Reflection of sound.— So long as sound-waves diverging from a point 222 On Sound [236- are not obstructed in their motion they are propagated in the form of concen- tric spheres ; but when they meet with an obstacle they follow the general law of elastic bodies ; that is, they return upon themselves, forming new concentric waves, which seem to emanate from a second centre on the other side of the obstacle. This phenomenon constitutes the reflection of sound. Fig. 225 represents a series of incident waves reflected from an obstacle, PQ. Taking for example, the incident wave MCDN, emitted from the centre A, the corresponding reflected wave is represented by the arc CKD of a circle whose centre a is as far behind the obstacle PQ as A is before it. If any point, C, of the reflecting surface be joined to the centre of sound, and if the perpendicular CH be let fall on the surface of this body, the angle ACH is called the angle of incidence, and the angle BCH, formed by the prolongation oi aC, is the angle of reflection. The reflection of sound is subject to the two following laws : — I. The a/igle of reflection is equal to the angle of incidence. II. The incident sonorous ray and the reflected ray are in the same plane perpendicular to the reflecting surface. From these laws it follows that the wave, which in the figure is propa- gated in the direction AC, takes the direction CB after reflection, so that an observer placed at B hears a second sound, which appears to come from C, besides the sound proceeding from the point A. The laws of the reflection of sound are the same as those for light and radiant heat, and may be demonstrated by similar experiments. One of the simplest of these is made with conjugate mirrors (see chapter on Radiant Heat) ; if in the focus of one of these] mirrors] a "watch is fixed, the ear placed in the focus of the second mirror hears the ticking very distinctly even when the mirrors are at a distance of 12 or 13 yards. The mirrors should be large, so that the head may obstruct the sound waves as little as possible. With smaller mirrors the bell of an ear trumpet is held at the focus, and the tube end is placed in the ear, which is held on one side of the mirror. -237] Echoes and Resonances 223 In like manner, the explosion of fulminating' mercury in the focus of one mirror causes that of iodide of nitrogen placed in that of the other. 237. Echoes and resonances. — An echo is the repetition of a sound in the air, caused by its reflection from some obstacle. A very sharp quick sound can produce an echo when the reflecting surface is 55 feet distant; but for articulate sounds at least double that distance is necessary, for it may be easily shown that no one can pronounce or hear distinctly more than five syllables in a second. Now, as the velocity of sound at ordinary temperatures maybe taken at 1 125 feet in a second, in a fifth of that time sound would travel 225 feet. If the reflecting surface is II2'5 feet distant, in going and returning sound would travel through 225 feet. The time which elapses between the articulated and the reflected sound would, therefore, be a fifth of a second, the two sounds would not interfere, and the reflected sound would be distinctly heard. A person speaking with a loud voice in front of a reflector, at a distance of II2'5 feet, can only distinguish the last reflected syllable : such an echo is said to be monosyllabic. If the reflector were at a distance of two or three times 112-5 feet, the echo would be disyllabic, trisyllabic, and so on. When the distance of the reflecting surface is less than II2'5 feet, the direct and the reflected sound are confounded. They cannot be heard separately, but the sound is strengthened. This is what is often called resonance, and is frequently observed in large rooms. Bare walls, and par- ticularly woodwork, are very resonant ; they reflect the sound and add to it the effect of their own vibrations, so that the sound is prolonged and enforced. In a large meeting- room this may considerably aid a speaker's voice ; too great resonance, however, hinders the distinct perception of the words. Tapestry and hangings, on the contrary, which are bad reflectors, deaden the sound. To control or eliminate the effects of resonance is a difficult problem in the acoustics of the building art. Multiple echoes are those which repeat the same sound several times ; this is the case when two opposite surfaces (for example, two parallel walls) successively reflect sound. There are echoes which repeat the same sound 20 or 30 times. An echo in the chiteau of Simonetta, in Italy, repeats a sound 30 times. At Woodstock there is one which repeats from 1 7 to 20 syllables. As the laws of reflection of sound are the same as those of light and heat, curved surfaces produce acoustic foci like the luminous and calorific foci produced by concave reflectors. If a person standing under the arch of a bridge speaks with his face turned towards one of the piers, the sound is reproduced near the other pier with such distinctness that a conversation can be kept up in a low tone, which is not heard by anyone standing in the intermediate spaces. There is a square room with an elliptical ceiling on the ground floor of the Conservatoire des Arts et Metiers in Paris which presents this phenomenon in a remarkable degree to persons standing in the two foci of the ellipse. Whispering galleries are formed of smooth walls having a continuous curved form. The mouth of the speaker is presented at one point, and the ear of the hearer at another and distant point. In this case the sound is successively reflected from one point to the other until it reaches the ear. 224 On Sound [237- In the whispering gallery of St. Paul's the faintest sound is thus conveyed from one side to the other of the dome, but it is not heard at any intermediate points. Placing himself close to the upper wall of the Colosseum, a circular building 130 feet in diameter, Wheatstone found a word to be repeated a great many times. A single exclamation sounded like a peal of laughter, while the tearing of a piece of paper resembled the patter of hail. It is not merely by solid surfaces, such as walls, rocks, ships' sails, &c., that sound is reflected. It is also reflected by clouds, and it has even been shown by direct experiment that a sound in passing from a gas of one density into another is reflected at the surface of separation as it would be against a solid surface. Now, different parts of the earth's surface are unequally heated by the sun, owing to the shades of trees, evaporation of water, and other causes, so that in the atmosphere there are numerous ascending and descending currents of air of different density. Whenever a sound-wave passes from a medium of one density into another it undergoes partial reflec- tion, which, though not strong enough to form an echo, distinctly weakens the direct sound. This is doubtless the reason, as Humboldt remarked, why sound travels further at night than at daytime, even in the South American forests, where the animals, which are silent by day, fill the atmosphere at night with thousands of confused sounds. To this may be added that at night and in repose, when other senses are at rest, that of hearing becomes more acute. This is the case with persons who have become blind. It has generally been considered that fog in the atmosphere is a great deadener of sound ; it being a mixture of air and globules of water, at each of the innumerable surfaces of contact a portion of the vibration is lost. The evidence as to the influence of this property is conflicting ; Tyndall's researches show that a white fog, or snow, or hail, is not an important obstacle to the transmission of sound, but that aqueous vapour is. Expe- riments made on a large scale, in order to ascertain the best form of fog signals, gave remarkable results. On some days, which optically were quite clear, certain sounds could not be heard at a distance far inferior to that at which they could be heard even during a thick haze. Tyndall ascribed this result to the presence in the atmosphere of aqueous vapour, which forms in the air innumerable striae that do not interfere with its optical clearness, but render it acoustically turbid, the sound being reflected by this invisible vapour just as light is by the visible cloud. These conclusions, first drawn from observations, have been verified by laboratory experiments. Tyndall showed that a medium consisting of alternate layers of light and heavy gas, such as coal gas and carbonic acid, deadens sound, and also that a medium consisting of alternate strata of heated and ordinary air exerts a similar influence. The same is the case with an atmosphere containing the vapours of volatile liquids. So long as the continuity of air is preserved, sound has great power of passing through the interstices of solids ; thus it will pass through twelve folds of a dry silk handkerchief, but is stopped by a single layer if it is wetted. 238. Refraction of sound. — It will be found afterwards that refraction is the change of direction which hght and heat experience on passing from one medium to another. It has been shown by Hajech that the laws of the -338] Refraction of Sound 225 refraction of sound are the same as those for Hght and heat : he used tubes filled with various gases and liquids, and closed by membranes ; the mem- ■farane at one end was at right angles to the axis of the tube, while the other made an angle with it. When these tubes were placed in an aperture in the wall between two rooms, a sound produced in front of the tube in one room, that of a tuning-fork for instance, was heard in directions in the other varying with the inclination of the second membrane, and with the nature of the sub- stance with which the tube was filled. Accurate measurements showed that the law held that the sines of the angles of incidence and refraction are in a constant ratio, and that this ratio is equal to that of the velocity of sound in the two media. Thus the velocity of sound in water is not very different from that in hydrogen, and they produce deviations which are nearly equal. Sondhauss confirmed the analogy of the refraction of sound-waves to those of light and heat. He constructed lenses of gas by cutting equal segments out of a large collodion balloon, and fastening them on the two sides of a sheet-iron ring a foot in diameter, so as to form a double convex lens about 4 inches thick in the ■centre (fig. 226). This was j ,,.-,-;.'-'--'-' n^Hnan ^---- fiUed with carbonic acid, and A.§'^::-_--- HiHilSr ---»-• -U a watch. A, was placed in the '"--'." direction of the axis ; the point was then sought on the other side of the lens at which the sound was most distinctly Tieard. It was found that when the ear was removed from the axis the sound was scarcely perceptible, but that Fig. 226 at a certain point B on the axial line it was very distinctly heard. Consequently, the sound-waves in passing from the lens had converged towards the axis ; their direction had been changed ; in other words, they had been refracted. The refraction of sound may be easily demonstrated by means of one of the very thin India rubber balloons used as children's toys, inflated by carbonic acid. If, however, the balloon be filled with hydrogen, no focus is detected ; it acts like a concave lens, and the divergence of the rays is increased, instead of their being converged to the ear. A direct proof of the refraction of sound is given by the experiments of Schellbach and Bohm. The source of sound was a film of collodion stretched across a ring ab (fig. 227), which was put in vibration by electric sparks at a. A disc of paper, p, sprinkled with fine charcoal powder, was suspended in the vessel BB'. When this vessel contained air, rings of dust were formed, the centre of which was at / in the direction of the propaga- tion of the sound. But if the vessel was filled with carbonic acid the centre of the rings was found to be at/', showing that the sound had been refracted towards the perpendicular on passing from air into the denser medium ; and' Q ' 226 On Sound [238- measurements showed that the position of the point/' was in accordance with the law of refraction for hght. Experiments suitably modified showed that, when hydrogen was substituted for carbonic acid, the sound was bent away from the pei'pen- dicular. It has long been known that sound is propa- gated in a direction against that of the wind with less velocity than with the wind. This is probably due to a refraction of sound on a large scale. The velocity of wind along the gi'ound is always con- siderably less than at a greater height ; thus, the velocity at a height of 8 feet has been observed to be double what it is at a height of i foot above the ground. Hence a wave-front (fig. 225), origin- ally vertical, becomes tilted upwards, with the lower part forward ; and, as the direction of the wave-motion is at right angles to the front of the wave, the effect of the coalescence of a number of these rays, thus directed upwards, is to produce an increase of the sound in the higher regions. The rays which travel with the wind will, for similar reasons, be refracted downwards, and thus the sound be better heard. 239. Speaking trumpet. Ear trumpet. — These instruments depend on the reflection of sound in tubes. The speaking trumpet, as its name implies, is used to render the voice audible at great distances, more especially on board ship. It consists of a slightly conical tin or brass tube (fig. 228), very much wider at one end (which Fig. 227 Fig. 228 is called the bell), and provided with a mouthpiece at the other. Speaking trumpets are sometimes as much as 7 feet in length, the bell being i foot in diameter. The larger the dimensions of this instrument the greater is the distance at which the voice is heard. Its action is usually ascribed to the successive reflections of sound-waves from the sides of the tube, by which the waves tend more and more to pass in a direction parallel to the axis of the instrument. It has, however, been objected to this explanation that the sounds emitted by the speaking trumpet are not stronger solely in the direction of the axis, but in all directions ; that the bell would not tend to produce parallelism in the sound-wave, whereas it certainly exerts consider- able influence in strengthening the sound. According to Hassenfratz, the bell acts by causing a large mass of air to be set in consonant vibration before it begins to be diffused. This is probably also the reason why sound travels best in the chief direction of the sounding body ; thus the report of a cannon. -240] Stethoscope 227; the sound of a wind instrument in the Hne of the tube, the voice of the direction of the mouth, &c. The ear trumpet is used by persons who are hard of hearing. It is essentially an inverted speaking trumpet, and consists of a conical metallic tube, one of whose ends, terminating in a bell, receives the sound, while the other end is introduced into the ear. This instrument is the reverse of the speaking trumpet. The bell serves as a mouthpiece ; that is, it receives the sound coming from the mouth of the person who speaks. These sounds are transmitted by a series of reflections to the interior of the trumpet, so that the waves, which would become greatly diffused, are concentrated on the ear, and produce a far greater effect than divergent waves would have done. 240. Stethoscope. — One of the most useful applications of acoustical principles is the stethoscope. Figs. 229 and 230 represent an improved form of Fig. 229 Fig, 230 this instrument devised by Konig. Two sheets of india rubber, c and a, are fixed to the circular edge of a hollow metal hemisphere ; the edge is provided with a stopcock, so that the sheets can be inflated, and then present the appearance of a double convex lens, as represented in section in fig. 229. To a tubulure on the hemisphere is fixed an india rubber tube terminated by horn or ivory, b, which is placed in the ear (fig. 230). When the membrane c of the stetho- scope is applied to the chest of a sick person, the beating of the heart and the sounds of respiration are transmitted to the air in the chamber a, and thence to the ear by means of the flexible tube. If several tubes are fixed to the instrument, as many observers may simultaneously auscultate the same patient. A recent application — that to the water stethoscope — has been found of great ser- vice. It consists of a steel rod about three feet in length, with an enlargement at each end ; one of these is so shaped that Fig. 231 it fits against a water-pipe, while the other is apphed to the ear. The taps having been turned off, a skilled observer can detect the slight sound due to any flow of water, which, in the circum- stances, must be due to leakage. Q2 228 On Sound [240- The audiphone, invented by Mr. Rhodes, of Chicago, is of considerable service to people hard of hearing ; in its most simple form (fig. 231) it con- sists of a thin rectangular piece of fine cardboard, the square end of which is held in one hand while the opposite and convex edge is pressed against the teeth of the upper jaw so that it is slightly bent : it receives the sounds which are produced in the air, and transmits them to the auditory nerves through the bones of the head. -242] 229 CHAPTER II MEASUREMENT OF THE NUMBER OF VIBRATIONS 241. Savart's apparatus. — Savart's toothed wheel, so called from the name of its inventor, is an apparatus by which the absolute number of vibra- tions corresponding to a givetf note can be determined. It consists of a solid oak frame in which are two' wheels, A and B (fig. 232)j the larger wheel, A, is connected with the toothed wheel by means of a strap and a multiplying wheel, thereby causing the toothed wheel to revolve with great velocity ; a card, E, is fixed on the frame, and, in revolving, the toothed wheel strikes against it and causes it to vibrate. The card, being struck by each tooth, make as many vibrations as there are teeth. At the side of the apparatus is an indicator, H, which gives the number of revolutions of the wheel, and consequently the number of vibrations in a given time. Fig. 232 When the wheel is moved slowly, the separate shocks against the card are distinctly heard ; but if the velocity is gradually increased, the sound becomes higher and higher. Having obtained the sound whose number of vibrations is to be determined, the revolution of the wheel is continued with the same velocity for a certain number of seconds. The number of turns of the toothed wheel B is then read off on the indicator, and this multiphed by the number of teeth in the wheel gives the total number of vibrations. Dividing this by the corresponding number of seconds, the quotient gives the number of vibrations per second for the given sound. 242. Siren. — The siren is an apparatus which, like Savart's wheel, is used to measure the number of vibrations of a body in a given time. The name was given to it by its inventor, Cagniard Latour, because it yields sounds under water. 230 On Sound [242- It is made entirely of brass. Fig. 233 represents it fixed on the table of a bellows, by which a continuous current of air can be sent through it. Figs. 234 and 235 show the internal details. The lower part consists of a cylin- drical box, O, closed by a fixed plate, B. On this plate a vertical rod, T, rests, to which is fixed a disc. A, moving with the rod. In the plate B there are equidistant circular holes, and in the disc A an equal number of holes of the same size, and at the same distance from the centre as those of the plate. These holes are not perpendicular to the disc ; they are all inclined to the same extent in the same direction in the plate, and are inclined to the same extent in the opposite direction in the disc, so that when they are opposite each other they have the appearance represented in inn, fig. 234. Conse- quently, when a current of air from the bellows reaches the hole m, it strikes obliquely against the sides of the hole n, and makes the disc A rotate in the direction «A. Fig. 233 Fig- 235 For the sake of simplicity, let us first suppose that in the movable disc A there are eighteen holes, and in the fixed plate B only one, which faces one of the upper holes. The wind from the bellows striking against the sides of the latter, the movable disc begins to rotate, and the space between two of its consecutive holes closes the hole in the lower plate. But as the disc continues to turn from its acquired velocity, two holes are again opposite each other, a new impulse is produced, and so on. During a complete revolution of the disc the lower hole is eighteen times open and eighteen times closed. A series of puffs and stoppages is thus produced, which makes the air vibrate, and ultimately produces a sound when the successive impulses are sufficiently rapid. If the fixed plate, like the moving disc, had eighteen holes, each hole would separately produce the same effect as a separate one, the sound would be eighteen times as intense, but the number of vibrations would not be increased. -243] Bellows 231 In order to know the number of vibrations corresponding to the sound produced, it is necessary to know the number of revolutions of the disc A in a second. For this purpose an endless screw on the rod T transmits the motion to a wheel, a, with 100 teeth. On this wheel, which moves by one tooth for every turn of the disc, there is a catch, P, which at each complete revolution moves one tooth of a second wheel, b (fig. 235). On the axis of these wheels there are two needles, which move round dials represented in fig- 233. One of these indices gives the number of turns of the disc A, the other the number of hundreds of turns. By means of two screws, D and C, the wheel a can be uncoupled from the endless screw. Since the pitch of the sound rises in proportion to the velocity of the disc A, the wind is forced until the desired note is produced. The same current is kept up for a certain time — two minutes, for example — and the number of turns read off. This number, multiphed by 18 and divided by 120, gives the number of vibrations in a second. For the same velocity of rotation the siren gives the same sound in air as in water ; the same is the case with all gases ; and it appears, therefore, that any given sound depends on the number of vibrations produced, and not on the nature of the sounding body. The buzzing and humming noise of certain insects is not vocal, but is produced by very rapid flapping of the wings against the air or the body. The siren has been ingeniously applied to count the rate per second of the vibrations thus produced, which is effected by bringing" it into unison with the sound. It has in this way been found that the wings of a gnat flap at the rate of 1,500 times in a second. If a report is pro- duced in a space with two parallel walls at no great dis- tance apart, the sound is re- flected from one to the other, and reaches the ear at regular and frequent intervals ; that is, the repetition of the echo acts as a note. A modification of the siren known as Brown's stemn- horn, in which high-pressure steam is employed instead of compressed air, is used as a fog-signal. Its shrill and penetrating note is better adapted than an ordinary fog-horn, or even cannon, for being heard over the noise of breakers. Fig. 236 243. Bellows. — In acoustics a bellows is an apparatus by which wind instruments, such as the siren andjorgan-pipes, are worked. Between the 232 On Sound [243- four legs of a table there is a pair of bellows, S (fig. 236), which is worked by means of a pedal, P. D is a reservoir of flexible leather, in which is stored the air forced in by the bellows. If this reservoir is pressed by means of •weights; on a rod, T, moved by the hand, the air is driven through a pipe, E, into a chest, C, fixed on the table. In this chest there are small holes closed by leather valves, which can be opened by pressing on keys in front of the box. The siren or sounding pipe is placed in one of these holes. 244. Limit of perceptible sounds.— Previous to Savart's researches, physicists assumed that the ear could not perceive a sound when the number of vibrations was below 16 for deep sounds, or above 9,0013 for acute sounds. But he showed that these limits were too close, and that the faculty of per- ceiving sounds depends rather on their intensity than on their pitch ; so that when extremely acute sounds are not heard it arises from the fact that they have not been produced with sufficient intensity to affect the organ of heai-ing. By increasing the diameter of the toothed wheel, and consequently the amplitude and intensity of the vibrations, Savart pushed the upper limit of audibility to 24,000 vibrations in a second. For deep sounds he substituted for the toothed wheel an iron bar about two feet long, which revolved on a horizontaljaxis between two thin wooden plates, about o-o8 of an inch from the bar. As often as the bar passed a grave sound was produced, due to the displacement of the air. As the motion was accelerated the sound became continuous, very grave, and deafening. By this means Savart found that, with 7 to 8 vibrations in a second, the ear perceived a distinct but veiy deep sound. Despretz, however, who investigated the same subject, disputed Savart's results as to the limits of deep sounds, and considers that no sound is audible that is made by less than i6 vibrations per second. Von Helmholtz held that the perception of a sound begins at 30 vibrations, and only has a definite musical value when the number is more than 40. Below 30 the impression of a number of sepa- rate beats is produced. On the other hand, acute sounds are audible up to those corresponding to 38,000 vibrations in a second. Such sounds, how. ever, are far from pleasurable : they affect the ear as if it had been pricked with a pin or needle. The discordant results obtained by these and other observers for the limit of audibility of higher notes are no doubt due to the circumstance that different observers have different capacities for the perception of sounds. Preyer has investigated this subject by means of experimental methods of greater precision than any that have hitherto been applied for this purpose. The minimum limit for the normal ear he found to lie between 16 and 24 single vibrations in a second ; the maximum limit reached 41,000 ; but many persons with average powers of hearing were found to be absolutely deaf to notes of 16,000, 12,000, or even fewer vibrations. It appears that the limit of audibility for any particular ear is increased with the strength of the sound. Paucher examined this by sounding a powerful siren by steam ; he found that with steam of \ an atmosphere pres- sure the upper limit was at 48,000 vibrations, with i^ atmosphere it was 60,000, while with steam of 2^ atmospheres it had not been attained with 72,000 vibrations. -246] Duliamel's Graphic Method 233 245. Duharael's graphic method. — When the siren or Savart's wheel is used to determine the exact number of vibrations corresponding to a given note, it is necessary to bring the sounds which they produce into unison with the given note, and this cannot be done exactly unless the experi- menter has a practised ear. Duhamel's graphic method is very simple and exact, and free from this difficulty. It consists in fixing a fine point to the body emitting the note, and causing it to trace the vibrations on a properly prepared surface. The apparatus consists of a wood or metal cylinder, A (fig. 237), fixed to a vertical axis, O, and turned by a handle. The lower part of the axis is a screw working in a fixed nut, so that according as the handle is turned from left to right, or from right to left, the cylinder is raised or depressed. Round Fig. 237 the cylinder is rolled a sheet of paper covered with an inadhesive film of lampblack. On this film the vibrations register themselves. This is effected as follows. Suppose the body emitting the note to be a steel rod. It is held firmly at one end, and carries at the other a fine point which grazes the sur- faces of the cylinder. If the rod is made to vibrate and the cyhnder is at rest, the point would describe a short line ; but if the cylinder is turned, the point produces an undulating line, containing as many undulations as the point has made vibrations. Consequently, the number of vibrations can be counted. It remains only to determine the time in which the vibrations were made. There are several ways of doing this. The simplest is to compare the curve traced by the vibrating rod with that traced by a tuning-fork (251), which gives a known number of vibrations per second — for example, 500. 234 On Sound [245- The prong of the fork is furnished with a point, which is placed in contact with the lampblack. The fork and the rod are then set vibrating together, and each produces its own undulating trace. When the paper is unrolled, it is easy, by counting the number of vibrations each has made in the same distance, to determine the number of vibrations made per second by the elastic rod. Suppose, for instance, that the tuning-fork made 150 vibrations, while the rod made 165 vibrations. Now we already know that the tuning- fork makes one vibration in the -^^-^ part of a second, and therefore 1 50 vibrations in Jf § of a second. But in the same time the rod makes 165 vibrations ; therefore, it makes one vibration in the 2 — — of a second, 500 X 165 and hence it makes per second ? — ^ — ? , or ; ?o vibrations. 150 -247] Musical Intervals 235 CHAPTER III THE PHYSICAL THEORY OF MUSIC 246. Properties of musical notes.^ — A simple musical note results from continuous rapid isochronous vibrations, provided the number of the vibra- tions falls vifithin the very wide limits mentioned in the last chapter (244). Musical notes are in most cases compound. The distinction between a simple and a compound musical note will be explained later in the chapter. The tone yielded by a tuning-fork furnished with a proper resonance-box is simple ; that yielded by a wide-stopped organ pipe, or by a flute, is nearly simple ; that yielded by a musical string is compound. Musical notes have three leading qualities, namely, pitch, intensity or loudness, and tim.bre or quality. i. The pitc/i of a musical note is determined by the number of vibrations per second yielded by the body producing the, note. It may be called the vibration-frequency. ii. The intensity of the note depends on the extent of the vibrations. It is greater when the|extent is greater, and less when it is less.| It is, in fact, proportional to the square of the extent, or amplitude (56) of the vibrations which produce the note. iii. The timbre or quality is that peculiar property of note which distin- guishes a note when sounded on one instrument from the same note when sounded on another, and which by some is called the colour. Thus when the C of the treble stave is sounded on a violin and on a flute, the two notes will have the same pitch or vibration-frequency ; and they may have the same intensity, and yet the two notes will have very distinct qualities ; that is, their timbre is different. The cause of the peculiar timbre of notes will be con- sidered later in the chapter. 247. Musical intervals. — Let us suppose that a musical note, which for the sake of future reference we will denote by the letter C, is produced by m vibrations per second ; and let us further suppose that any other musical note, X, is produced by n vibrations per second, n being greater than tn ; then the interval from the note C to the note X is the ratio n : m, the interval between two notes being obtained hy division, not hy subtraction. Although two or more notes may be separately musical, it by no means follows that when sounded together they produce a pleasant sensation. On the con- trary, unless they are concordant, the result is harsh, and usually unpleasing. We have, therefore, to inquire what notes are fit to be sounded together. Now, when musical notes are compared, it is found that if they are separated by an interval of 2 : i, 4 : j i, &c. they so closely resemble one another that they may for most purposes of music be considered as|the same note Thus 236 On Sound [247- suppose c to stand for a musical note produced by 2/« vibrations per second, then C and c so closely resemble each other as to be called in music by the same name. The interval from C to c is called an octave, and c is said to be an octave above C, and conversely C an octave below c. If we now consider musical sounds that do not differ by an octave, it is found that if we take three notes, X, Y, and Z, resulting respectively from/, q, and r vibrations per second, these three notes when sounded together will be con- cordant if the ratio oi p : q : r equals 4:5:6. Three such notes form an harmonic triad, and if sounded with a fourth note, which is the octave of X, constitute what is called in music a major chord. Any of the notes of a chord may be altered by one or more octaves without changing its distinc- tive character ; for instance, C, E, G, and c are a chord, and C, c, e, g form the same chord. If, however, the ratio p : q : r equals 10 : 12 : 15, the three sounds are slightly dissonant, but not so much so as to disqualify them for producing a pleasing sensation. When these three notes and the octave to the lower are sounded together, they constitute what in music is called a minor chord. 248. The musical scale. — The series of sounds which connects a given note C with its octave c is called the diatonic scale or gamut. The notes composing it are indicated by the letters C, D, E, F, G, A, B. The scale is then continued by taking the octaves of these notes, namely, c, d, e,f,g, a, b, and again the octaves of these last, and so on. The notes are also known by names, viz. do or ut, re, mi, fa, sol, la, si, do. The relations existing between the notes are these : — C, E, G form a major triad, G, B, d form a major triad, and F, A, c form a major triad. C, G, and F have, for this reason, special names, being called respectively the tonic, dominant, and subdominant, and the three triads the tonic, dominant and subdominant triads or chords respectively. Consequently, the numerical relations between the notes of the scale will be given by the three proportions— C : E : G G : B : rf F : A : c 4:5:6 4:5:6 4:5:6 Hence, if m denotes the vibration-frequency corresponding to the note C, the frequency corresponding to the remaining notes will be given by the following table : — do re mi fa sol la sz do C D E F G A B c m %m f?« \m Im ^m ^m -zm The intervals between the successive notes being respectively — • C to D D to E E to F F to G G to A A to B B to f f V if I V f if It will be observed here that there are three kinds of intervals, |, y, and ^ ; of these the first two are called a tone, the last a semitone, because it is about half as great as the interval of a tone. The two tones, however, are not identical, but differ by an interval of |J, which is called a comma. Two —250] On Musical Temperament 237 notes which differ by a comma can be readily distinguished by a trained ear. The interval between the tonic and any note is denominated by the position of the latter note in the scale ; thus the interval from C to G is a fifth. The scale we have now considered is called the major scale, as being formed of major triads. If the minor triad were substituted for the major, a scale would be formed that could be strictly called a minor scale. As scales are usually written, however, the ascending scale is so formed that the tonic bears a minor triad, the dominant and subdominant bear major triads, while in the descending scale they all bear minor triads. Practically, in musical composition, the dominant triad is always major. If the ratios given above are examined, it will be found that in the major scale the interval from C to E equals f , while in the minor scale it equals f . The former interval is called a major third, the latter a minor third. Hence the major third exceeds the minor third by an interval of Jf. This interval is called a semitone, though very different from the interval above called by that name. 249. On semitones and on scales with different keynotes. — It will be seen from the last article that the term ' semitone ' does not denote a constant interval, being in one case equivalent to ff and in another to f |. It is found convenient for the purposes of music to introduce notes intermediate to the seven notes of the gamut ; this is done by raising or lowering these notes by an interval of |f . When a note (say C) is increased by this interval, it is said to be sharpened, and is denoted by the symbol Cj, called ' C sharp ; ' that is, Clt -=-C = |f. When it is lowered by the same interval, it is said to \>^ flattened, and is represented thus — Bb, called 'B flat;' that is, B-=-Bb = ff. If the effect of this be examined, it will be found that the number of notes in the scale from C up to c has been increased from seven to twenty-one notes, all of which can be easily distinguished by the ear. Thus, reckoning C to equal i, we have — C C8 Db D DS Eb E &c. I If H f H « I &c. Hitherto we have made the note C the tonic or keynote. Any other of the twenty-one distinct notes above mentioned, e.g. G, or F, or Cs , &c., may be made the keynote, and a scale of notes constructed with reference to it. This will be found to give rise in each case to a series of notes, some of which are identical with those contained in the series of which C is the keynote, but most of them different. And of course the same would be true for the minor scale as well as for the major scale, and indeed for other scales which may be constructed by means of the fundamental triads. 250. On musical temperament. — The number of notes that arise from the construction of the scales described in the last article is so great as to prove quite unmanageable in the practice of music ; and particularly for music designed for instruments with fixed notes, such as the pianoforte or harp. Accordingly it becomes practically important to reduce the nurnber of notes, which is done by slightly altering their just proportions. This process is ealled te7nperament, and the scale is called the tempered scale. By tempering the notes, however, more or less dissonance is introduced, and accordingly several different systems of temperament have been devised for rendering 238 On Sound [250- this dissonance as slight as possible. The system usually adopted is called the system of equal temperament. It consists in retaining the octaves pure, and in substituting between C and c eleven notes at equal intervals, each interval being, of course, the twelfth root of 2, or i "05946. By this means the distinction between the semitones is abolished, so that, for example, Qf and D b become the same note. The scale of twelve notes thus formed is called the chromatic scale. It follows, of course, that major triads become slightly dissonant. Thus, in the diatonic scale, if we reckon C to be I, E is denoted by 1-25000, and G by 1-50000. On the system of equal tempera- ment, if C is denoted by i, E is denoted by 1-25992 and G by 1-49831. If individual intervals are] made pure while the errors are distributed over the others, such a system is called that of unequal temperatnent. Of this class is Kirnberger's, in which nine of the tones are pure. Although the system of equal temperament has the advantage of afford- ing the greatest variety of tones with as small a number of notes as possible^ yet it has the drawback that no chord of an equally tempered instrument, such as the piano, is perfectly pure. And as musical education mostly has its basis on the piano, even singers and instrumentalists usually give equally tempered intervals. Only in the case of string quartet players, who have freed themselves from school rules, and in that of vocal quartet singers, who sing frequently without accompaniment, does the natura pure temperament assert itself, and thus produce the highest musical effect. 251. The number of vibrations producing; each note. The tuning-fork. — Hitherto we have denoted ;the number of vibrations corresponding to the note C by m, and have not assigned any numerical value to|that symbol. In the theory of music it is frequently assumed that the middle C corresponds to 256 double vibrations in a second. This is the note which, on a pianoforte of seven octaves, is produced by the white key on the left of the two black keys close to the centre of the keyboard. This number is con- venient as being continually divisible by two, and is therefore frequently used in numerical illustrations. It is, however, arbitrary. An instrument is in tune provided the intervals between the notes are correct, when c is yielded by any number of vibrations per second not differing much from 256. Moreover, two instru- ments are in tune with each other if, being separately in tune, they have any one note, for instance C, yielded by the same number of vibra- tions. Consequently, if two instruments have one note in common, they can then be brought into tune jointly by having their remaining notes separately adjusted with reference to the fundamental note. A tuning-fork is an instrument yielding a con- stant sound, and is used as a standard for tuning musical instruments. It consists of an elastic steel rod, bent as represented in fig. 238. It is made Fig. 23S -262] Musical Notation. Musical Range 239 to vibrate either by drawing a bow across the ends, or by striking one of the legs against a small hammer covered with leather, or by rapidly sepa- rating the two prongs by means of a steel rod as shown in the figure. The vibration produces a note which is always the same for the same tuning-fork. The note is strengthened by fixing the tuning-fork on a box open at one end called a sounding or resonance box, adjusted so as to strengthen the special note of the tuning-fork. The vibrations of the air in the box produce the same note as the fork itself ; the vibrations of the tuning-fork, being com- municated to the column of air in the box, set it in vibration, and thus a note of considerable intensity is obtained. The standard tuning-fork in any country represents its accepted concert pitch. It has been remarked for some years that not only has the pitch of the tuning-fork been getting higher in the large theatres of Europe, but also that it is not the same in London, Paris, Berlin, Vienna, Milan, &c. This is a source of great inconvenience both to composers and singers, and a com- mission was appointed in 1859 to establish in France a tuning-fork of uniform pitch, and to prepare a standard which would serve as an invariable type. In accordance with the recommendations of that body, a normal tuning fork was established, which is compulsory on all musical establishments in France, and a standard has been deposited in the Conservatory of Music in Paris. It performs 437'5 double vibrations per second, and gives the stan- dard note a or la, or the a in the treble stave (252). Consequently, with reference to this standard, the middle c or do would result from 262-5 double vibrations per second. In England, a committee, appointed by the Society of Arts, recommended that a standard tuning-fork should be one constructed to yield 528 double vibrations in a second, and that this should represent c' in the treble stave. This number has the advantage of being divisible by 2 down to 33, and is in fact the same as the normal tuning-fork adopted in Stuttgart in 1834, which makes 440 vibrations in the second, and, like the French one, corresponds to a in the same stave. In exact determinations of pitch the temperature must be taken into account. Heat acts on the tuning-fork by expanding it, and also by diminishing the elasticity of the metal. Both effects concur in lowering the pitch. Thus Konig found that a tuning-fork which made 5 1 2 vibrations at 20° C. varied by 0'0572 for each degree Centigrade. Stone and McLeod found the number 0-055. An international conference at Vienna in 1885 adopted a tuning-fork of polished mild cast-steel with prismatic prongs, making 435 vibrations in a second at 15° C, as the standard a note. This corresponds to 261 vibra- tions per second for the middle c. 252. Musical notation. Musical range. — It is convenient to have some means of at once naming any particular note in the whole range of musical sounds other than by stating its number of vibrations. Perhaps a conve- nient practice is to call the octave, of which the C is produced by a four- foot organ open pipe, by the capital letters C, D, E, F, G, A, B ; the next higher octave by the corresponding small letters, c, d, e, f, g, a, b ; and to designate the octaves higher than this by the index placed over the letter thus, c' , d', e',f',g', a', b' , and the higher series in a similar manner. The 240 On Sound [252- same principle may be applied to the notes below C ; thus the octave below C is C,, and the next lower one C,,. Hence we have the series C„ C,Cc r' c" r'" c'\ In musical writing the notes are expressed by signs which indicate the length of time during which the note is to be played or sung, and are written on a series of lines called a stave. Thus stands for the octave in the treble clef, of which the top note is the standard c' and the bottom is the middle c. When the five lines are insufficient they are continued above and below the stave by what are called ledger lines. In order to avoid confusion, a bass clef is used for the lower notes ; and it may be remarked that ^ ~ j — ^ and @ ' = stand for the same note {251), which is the middle c. The deepest note of orchestral instruments is the E^, of the double bass, which makes 4I5 vibrations, taking the keynote as making 440 vibrations in a second. Some organs and pianofortes go as low as C„ with 33 vibra- tions in a second, some grand pianos even as low as A,,, with 27^ vibrations. But the musical character of all these notes below E,^ is imperfect, for we are near the limit at which it is possible for the ear to combine the separate vibrations to a musical note (244). These notes can only be used musically with their next higher octave, to which they impart a certain character of depth and richness. In the other direction, pianofortes go to a'" with 3,520 or even c" with 4,224 vibrations in a second. The highest note of the orchestra is probably the d" of the piccolo flute, which makes 4,752 vibrations. Although the ear can distinguish sounds which are still higher, they have no longer a pleasurable character. And while the notes which are distinguishable by the ear range between 16 and 38,000 vibrations, or 11 octaves, those which are musically available range from about 40 to 4,000 vibrations, or within 7 octaves. 253. Amplitude of oscillation. — The amplitude of oscillation which is required for the production of audible sounds is very small. Lord Rayleigh determined it in the case of the waves due to a pipe giving the note /", which could be heard at a distance of 820 metres. He calculated that the amplitude of the oscillation of these waves could not be greater than o-o6 of a millimetre. Topler and Boltzmann were able to observe the sound of a stopped pipe making 181 vibrations, at a distance at which the amplitude of the vibrations could only be 0-0,4 cm., or about ^ the wave-length of green light. 254. On compound musical tones and harmonics. — When any given note (say C) is sounded on most musical instruments, not that note alone is produced, but a series of other notes, of small and varying intensity. If C, which may be called the primary note, is denoted by. unity, the —256] Consonance and Resonance 241 -whole series is given by the numbers i, 2, 3, 4, 5, 6, 7, &c. ; in other words, first the primary C is sounded, then its octave becomes audible, then the fifth to that octave, then the second octave, then the third, fifth, -and a note between the sixth and seventh to the second octave, and so on. These secondary notes are called the harmonics of the primary note. Though feeble in comparison with the primary note, they may, with a little practice, iDe heard when the primary note is produced on most musical instruments ; when, for instance, one of the lower notes is sounded on the pianoforte. 255. Consonance and resonance. — A singular property of bodies in a state of vibration is that of setting in vibration bodies at rest. Thus, if two tuning-forks, tuned so as to give accurately the same note, be at some distance from each other, and one of them be sounded, the other will be set in vibration and emit the same note. But, if one of the forks be put slightly ■out of tune with the other, by attaching a piece of wax to one prong, for instance, then the excitation of either one will have no effect on the other. It is remarkable that the successive action of a series of small mechanical impulses should, as in this case, be able to set a relatively very heavy body — such as a tuning-fork — in vibration ; but for this there are many purely mechanical analogies. Thus, if a series of pulls be exerted in regular inter- vals on the rope of a large church bell, the superposition of these small motions will ultimately set the bell swinging. A regiment of soldiers marching in step over an iron bridge at Angers set it in such powerful oscilla- tion as to endanger its stability. In like manner, the position of a ship in the trough of the sea is very dangerous when the period of vibration of the waves coincides with that of its own vibration. This phenomenon, that a body in a state of vibration has the power of causing an independent body at rest to vibrate in the same period, is called ■consonance. If a metal wire freely suspended in the air be tightly stretched and then be set in vibration, the note which it emits will be feeble, seeing that from its small surface it can set in vibration only small masses of air. So, too, a tuning-fork when sounded gives but a feeble note ; but if its stem be held •on a table the note becomes far louder. The reinforcement of a sound by attaching the sounding body to a large ■dry, elastic wooden plate, called a sound-board, or to a wooden box enclosing a mass of air, is called resonance ; the vibrations of the sounding body are transmitted to the sound-board, which, being set in vibration, communicates its motion to large masses of air. Although the terms consonance and resonance are sometimes used indis- <;riminately, there are distinctions between them. Consonance is the excitation of an independent body to vibrate in unison with the sounding body ; it begins later than the sounding body, and con- tinues after it has become silent. Resonance begins and ends with the sound ■of the exciting body. A sound-board strengthens and imparts a general sonority to a complex series of notes. The more a body diverges from the form of a plate and approaches that of a rod, the more is its resonance limited to strengthening one or two notes. In resonance, however, there is a certain amount of tuning. For the loud and deep notes of the 'cello a large resonance-box is used, and a smaller R 242 On Sound [255- one for the higher notes of the \ioUn. Small enclosed \ olumes of air also strengthen one note in preference. 256. Von Helmholtz's analysis of sound. — For the purpose of experiment- ally proving the presence of the harmonics as distinct tones, von Helmholtz devised an instrument which he called a resonance-globe. The use of this apparatus may be illustrated by the following experiment, which is analogous in principle with that described in article 276 : — If an empty glass cylinder be taken, and a vibrating tuning-fork be held over the mouth of the vessel, the air will not be set in vibration unless it be of a certain definite length ; such, indeed, that the wave-length of the fundamental note corresponds to the wave-length of the note produced by the tuning-fork. Now, by pouring in water we can regulate the length of the column of air, and by trial can hit off the exact length ; when this is attained the note of the tuning-fork will be heard to be powerfully reinforced (276). A resonance-globe (fig. 239) is a glass or brass globe tuned to a particular note, furnished with two openings, one of which, a, is turned towards the origin of the sound, and the other, b, by means of an india rubber tube, is applied to the ear. If the note proper to the resonance-globe exists among the harmonics of the compound note|that Fig. 239 Fig. 240 is sounded, it is strengthened by the globe, and thereby rendered distinctly audible. Further, other things being the same, the note proper to a given globe depends on the diameter of the globe and that of the uncovered open- ing. Consequently, by means of a series of such globes, the whole series of harmonics in a given compound tone can be rendered distinctly audible, and their existence put beyond a doubt. Konig, the eminent acoustical-instrument makei", has made an important modification in the resonance-globe, to which he has given the form repre- sented in fig. 240. The resonator is cylindrical, and the end which receives the sound can be drawn out, so that the volume may be ncreased at pleasure. As the sound thereby becomes deeper, the same resonator may- be tuned to a variety of notes. On the tubulure fits an india rubber tube by which] the vibrations may be transmitted in any direction. 257. Konig's apparatus for the analysis of sound. — As the successive application to the ear of various resonators is both slow and tedious, Konig devised a remarkable apparatus in which a series of resonators act on mano- metric flames (290) ; the sounds thus, as it were, become \'isible, and may be shown to a large auditory. It consists of an iron frame (fig. 241), on which are fixedjin two parallel lines fourteen resonators tuned so as to give the notes from F to c" — that is -257] Kt-fiig's Apparatus for the Analysis of Sound 243 to say three octaves and a half ; or notes ot which the highest give the lower harmonics of the primary. On the right is a chamber, C, which is supplied with coal gas by the India rubber tube D, and on which are placed eight gas-jets, each provided with a manometric capsule (290). Each jet is con- nected with the chamber C by a special india rubber tube, while behind the apparatus a second tube connects the same jet to one of the resonators. On the right of the jets is a system of rotating mirrors identical with that described in article 290 Fig. 241 These details being understood, suppose the largest resonator on the right tuned to resound with the note i, and seven others with the harmonics of this note. Let the sound i be produced in part of this apparatus ; if it is simple, the lower resonator alone answers, and the corresponding flame is- alone dentated ; but if the fundamental note is accompanied by one or more of its harmonics, the corresponding resonators speak at the same time, which is recognised by the dentation of their flames ; and thus the constituents of each sound may be detected. R 2 244 On Sound [2S8- 258. Synthesis of sounds. — -Not only did von Helmholtz succeed in decomposing sounds into their constituents ; he also verified the result of his analysis by performing the reverse operation, the synthesis ; that is, he reproduced a given sound by combining the individual sounds of which his resonators had shown that it was composed. The apparatus which he used for this purpose consists of eleven tuning-forks, the first of which yields the fundamental note of 256 vibrations, or C, nine others its harmonics, while the eleventh serves as make and break to cause the tuning-forks to vibrate by means of electro-magnets. Each tuning-fork has a special electro-magnet, and moreover a resonator, which strengthens it. All these tuning-forks and their accessories are arranged in parallel lines of five (fig. 242), the first comprising the fundamental note and its uneven harmonics, 3, 5, 7, and 9 ; the second the even harmonics, 2, 4, 6, 8, and Fig. 242 io|; beyond, there is the tuning-fork break, K, arranged horizontally. One ■of its prongs is provided with a platinum point which grazes the surface of mercury contained in a small cup, the bottom of which is connected by a copper wire with an electro-magnet placed in front of the fork. The apparatus being thus arranged, a wire from a voltaic battery is con- nected with the binding-screw, c, and this with the electro-magnet, E ; which in turn is connected with those of the nine following tuning-forks, and then with the fork, K, itself. So long as the latter does not vibrate the current does not pass, for the platinum point does not dip in the mercury cup which is connected with the other pole of the battery. But when the fork is made to vibrate by means of a bow, the current passes. Owing to their elasticity, the limbs of the tuning-fork soon revert to their original position, the point is no longer in the mercury, the current is broken, and so on at each double vibration of the fork. The intermittence of the current being -259] Results of von Helmholtz's Researches 245 transmitted to all the other electro-magnets, they are alternately active and inactive. Hence they communicate to all the forks by their attraction the same number of vibrations. This is the case with the fork i, which is tuned in unison with the fork break ; but the fork 3, being tuned to make three times as many vibrations, makes three vibrations at each break of the current ; that is to say, the electro-magnet only attracts it at every third vibration ; in like manner, fork 5 only receives a fresh impulse every five vibrations, and so on. The following is the working of the apparatus :— The resonator of each tuning-fork may be closed by a disc, O (fig. 243), so that the sound made by it is scarcely perceptible when the disc is lowered. Each disc is fixed to the end of a bent lever, the shorter arm of which is worked by a cord, a, which is connected with one of the keys of a keyboard placed in front of the apparatus (fig. 242). When a key is depressed, the cord moves the lever, which raises the clapper, and the resonator then acts by strengthening its fork. Hence by depress- ing a special key we may add to the fundamental sounds any of the ninu primary harmonics, and thus reproduce the sounds, the composition of which has been determined by analysis. For example, by depressing all the keys at once we obtain the sound of an open pipe in unisons with the deepest tuning-fork. By depressing the key of the fundamental note and those of its uneven harmonics, we obtain the sound of a closed pipe. 259. Results of von Helmholtz's researches. — By both his analytical and synthetical investigations into sounds of the most varied kinds — those from various musical instruments, the human voice, and even noises — ^von Helmholtz fully succeeded in explaining the different timbre or quality of sounds. It is due to the different intensities of the harmonics which accom- pany the primary tones of these sounds. The leading results of these researches into the colour (246) of sounds may be thus stated : — i. Simple sounds, as those produced by a tuning-fork with a resonance- box, and by wide covered pipes, are soft and agreeable, without any rough- ness, but weak, and in the deeper notes dull. ii. Musical sounds accompanied by a series of harmonics, say up to the sixth, in moderate strength, are full and rich. In comparison with simple tones they are grander and more sonorous. Such are the sounds of open organ-pipes, of the pianoforte, &c. iii. If only the uneven harmonics are present, as in the case of narrow stopped pipes, of pianoforte strings struck in the middle, &c., the sound Fig. 243 246 On Sound [269- becomes indistinct ; and, when a greater number of harmonics is audible, the sound acquires a nasal character. iv. If the harmonics beyond the sixth and seventh are very distinct the sound becomes sharp and rough. If less strong, the harmonics are not prejudicial to the musical usefulness of the notes. On the contrary, they are useful as imparting character and expression to the music. Of this kind are most stringed instruments, and most pipes furnished with tongues, &c. Sounds in which harmonics are particularly strong acquire thereby a pecu- liarly penetrating character ; such are those yielded by brass instruments. 260. Production of vocal sounds. — The trachea or windpipe is a tube which terminates at one end in the lungs, and at the other in the larynx, which is the true organ of vocal sound. Fig. 244 represents a horizontal section of this organ. It consists of a number of cartilaginous structures, bb, which are connected by various muscles, by which great variety and control in the motions are attainable. These muscles are connected with, and move, two elastic mem- branes or bands with broad bases fixed to the larynx, and with sharp edges, cc ; these are called the vocal cords. According to the pressure of the muscles, these cords are more or less tightly stretched, and the space between them, the vocal slit, is narrower or wider accordingly. In ordinary breathing, o air passes through the triangular aperture Fig. 244 o ; but when in singing this is closed, the vocal cords are stretched and are put in vibration by the current of air, and produce tones which are higher the more tightly the cords are stretched and the narrower is the vocal slit. These changes can be effected with surprising rapidity, so that in this respect the human voice far exceeds anything that can be made artificially. The notes produced by men are deeper than those of women or boys, because in them the larynx is longer and the vocal cords larger and thicker ; hence, though equally elastic, they vibrate less swiftly. The vocal cords are 18 millimetres long in men, and 12 millimetres long in women. Chest notes are due to the fact that the whole membrane vibrates, while the fal- setto is produced by a vibration of the extreme edges only. The ordinary compass of the individual voice is within two octaves, though this is exceeded by some celebrated singers. Catalani, for instance, is said to have had a range of 3 J octaves. The wave-length of the sounds emitted by a man's voice in ordinary con- versation is from 8 feet to 12 feet, and that of a woman's voice is from 2 feet to 4 feet. The vowel sounds can be produced in any pitch, and the difference in them arises from the fact that to form a given vowel sound one or more characteristic notes, which are always the same, must be added. These change with the syllable pronounced, but depend neither on the height of the note nor on the person who emits them. The form and cavity of the mouth can be greatly modified by the extent -261] Perception of Sounds. The Ear 247 to which it is opened, by the altered position of the tongue, and so forth. It thus forms a resonator which can be quickly and completely controlled. When the mouth is adjusted so as to produce the broad A, as m father, it has then a sort of funnel shape, with the wide part outward ; for O, as in more, the effect is like that of a bottle with a wide neck ; and for U, as in poor, it is that of a similar bottle with a narrow neck. For the other vowels, such as A, E, and I, the effect is as if the bottle were prolonged by a tube, formed by contracting the tongue against the palate. If now, while the mouth is adjusted for the position in which it could utter the vowel U, different vibrating tuning-forks are successively held in front of it, only that emitting the note f will be found to be reinforced by the enclosed column of air vibrating in unison with it. This is accordingly the characteristic note of that vowel ; in like manner, b' is the note for O, a,nd b" that for A. The other vowel sounds, such as I, have a higher and lower characteristic note ; thus those of A, as in day, are d and a'" , of I,/andrf''. In most cases, however, the deeper notes have but little influence. 261. Perception of sounds. The ear. — The organ of hearing in man consists of several structures ; there is first the outer ear (fig. 245) by which .the sound is collected and transmitted through the auditory passage, a, to the drum or tympanum, t. This is a delicate tightly stretched membrane or skin which separates the outer ear from the middle ■ear or tympanic cavity, -which is a cavity in the temporal bone in which are several small bones whose dimensions are considerably exaggerated in the figure. One of these, the hammer, d, is attached at one end to the drum, and at the other is jointed to the anvil, e ; the latter is connected by means of the stirrup bone,f, to the oval window, an aperture closed by a fine membrane, which separates the tympanic cavity from the labyrinth. The tympanic cavity is also connected by the Eustachian tube, b, with the ■cavity of the mouth, so that the air in it is always under the same pressure. The labyrinth is a complicated structure filled with fluid ; it is entirely of bone, with the exception of the oval window already mentioned and the round window, 0. The labyrinth consists of three parts : the vestibule, which is closed by the oval window ; the three semicircular canals, k ; and the spiral-shaped cochlea, or snail shell, s. This is separated throughout its entire length by a division partly of bony projection and partly of membrane ; the upper part of this division is connected with the vestibule, and therefore with the oval window, while the lower part is connected with the round *.T *»-»- Fig. 245 248 On Sound [261- window. In the labyrinthine fluid of this part the termination of the auditory nerve is spread, the other end leading to the brain. The membranous part of this diaphragm is lined with about 3,000- extremely minute fibres, which are the terminations of the acoustic nerve, n. Each of these, which are called Cortfs fibres, seems to be tuned for a particular note as if it were a small resonator. Thus when the vibrations of any particular note reach these fibres, through the intervention of the stirrup bone and the fluid of the labyrinth, one fibre or set of fibres only vibrates in unison with this note, and is deaf for all others. Hence each simple note causes only one fibre to vibrate, while compound notes cause several ; just as when we sing with a piano only the ftindamental note and its harmonics vibrate. Thus, however complex external sounds may be, these microscopic fibres can analyse them and reveal the constituents of which they are formed. 262. Interference of sound. — If two waves of sound of the same length proceed in the same direction, and if they coincide in their phases and the amplitudes of vibration are the same, they strengthen each other ; if,, however, their phases di^er by half a wave-length they neutralise each other,, and silence is the result. This is called the interference of sound. It may be illustrated by a number of experiments, of which that repre- sented in fig. 246 is one of the simplest and most convenient. Two glass tubes, abac and nedf axe. connected at one end by a short india rubber tube ad, while at the other end they are connected by a long india rubber tube, cqf. The end o is held in one ear, the other ear being closed, and a tuning-fork is sounded in front of the long free tube,. nrs. If the length of the india rubber tube cgf be half the wave-length of the note produced by the fork, the sounds will reach the ear in completely opposite phases ; they will accordingly neutralise each other and no sound will be heard. But if this india rubber tube is closed by pinching it, the note is at once heard. If the tuning-fork gives the note c', the note it produces makes 528 vibrations in a second, and the length of the tube should be 34 centimetres. 263. Beats. — If the notes are of the same kind and slightly different in pitch — for instance, if they are produced by two tuning-forks not quite in tune — they alternately weaken and strengthen each other ; they are said to (5^5% or about /g of a second. 290. Konig's inanometric flames. — Konig's method consists in trans- mitting the motion of the waves which form a sound to gas flames, which, by their pulsations, indicate the nature of the sounds. For this purpose a Fig. 286 metal capsule, represented in section at A, fig. 286, is divided mto two com- partments by a thin membrane of india rubber ; on the right of the figure is a gas jet, and below it a tube conveying coal gas ; on the left is a tubu- lure, to which may be attached an india rubber tube. The other end of this 278 On Sound [290- may be placed at the node of an organ pipe (276), or it terminates in a- mouthpiece in front of which a given note may be sung : this is the arrange- ment represented in fig. 286. Fig. 287 When the sound-waves enter the capsule by the mouthpiece and the tube, the membrane yielding to the condensation and rarefaction of the waves, the coal gas in the compartment on the right is alternately contracted and expanded, and hence are produced alternations in the length of the Fig. 289 Fig. 290 flame, which are, however, scarcely perceptible when the flame is observed directly. But to render them distinct they are received on a mirror with four] faces, M, which may be turned by two cog-wheels and a handle. As -291] Determination of the Intensity of Sounds 279 iong?as, the flame burns steadily, there appears in the mirror, when turned, a continuous band of hgfht. But, if the capsule is connected with a sounding- tube yielding the fundamental note, the image of the flame takes the form represented in fig. 287, and that of fig. 288- if the sound yields the octave. If the two sounds reach the capsule simultaneously, the flame has the appear- ance of fig. 289 ; in that case, however, the tube leading to the capsule must be connected by a T-pipe with two sounding-tubes, one giving the funda- mental note, and the other the octave. If one gives the fundamental note and the other the third, the flame has the appearance of fig. 290. Fig. zgi Fig. 292 If the vowel E be sung m front of the mouthpiece first upon c, and then upon c', the mirror gives the flames represented in figs. 291 and 292. 291. Determination of the intensity of sounds. — Meyer has devised a plan by which the intensities of two sounds of the same pitch may be directly compared. The two sounds are separated from each other by a medium impervious to sound, and in front of each of them is a resonance globe (256) accurately tuned to the sound. Each of these resonance globes is attached by means of india rubber tubes of equal length to the two ends of a U-tube, in the middle of the bend of which is a third tube provided with a manometric capsule. If the resonance globes are each at the same distance from the sounding bodies, and if the note of only one of them is produced, the flame vibrates. If both sounds are produced, and they are of the same intensity, and in the same phase, they interfere completely in the tube, so that the flame of the manometric capsule is quite stationary, and appears in the turning mirror as a straight luminous band. If, however, the sounds are not of the same intensity, the nterference will be incomplete, and the luminous band will be jagged at the edge. The distance of one of the sounds from the resonance globes is altered until the flame is stationary. The intensities of the two sounds are then directly as the squares of their distances from the resonators. 28o On Sound [292- 292. Acoustic attraction and repulsion. — ft was observed by Guyot, and afterwards independently by Guthrie and by Schellbaph, that a sounding body, one in a state of vibration therefore, exercises an action on a body in its neighbourhood which is sometimes one of attraction and sometimes of repul- sion. The vibrations of an elastic medium attract bodies which are specifi- cally heavier than itself, and repel those which are specifically lighter. Thus a balloon of goldbeatei-'s skin filled with carbonic acid is attracted towards the opening of a resonance-box on whjch is a vibrating tuning-forjc ; while a similar balloon filled with hydrogen and tied down by a thread is repelled. This result always follows, even when the hydrogen balloon is made heavier than air by loading it with wax. A light piece of cardboard suspended and held near a tuning-fork moves towards it when the fork is made to vibrate. If the tuning-fork is suspended and is then made to vibrate, it moves towards the card if the latter is fixed. Two suspended tuning-forks in a state of vibration move towards each other. The flame of a candle placed near the end of a sounding tuning- fork is repelled if held near it ; if held underneath, it flattens out to a disc. A gas flame near the end of the tuning-fork divides into two arms. Guthrie found that, when one prong of a tuning-fork is enclosed in a tube drawn out to a capillary portion dipping into a liquid, and is set in vibration by bowing the free prong, the air around the enclosed prong is expanded, and he theilce con- cluded that the approach, above described, of a suspended body to the sounding-fork is due to^ the diminution of the pressure of the air between the fork and the body below that on the other side of the body. A cylindrical resonator of stiff drawing-paper is fastened to a strip of wood, which is provided with a glass cap and counterpoise, and thus can be made to turn on a needle-point. If the open end of the sounding-box of a tuning-fork vibrating' in unison with the resonator is brought near this, it is repelled even at a distance of some inches. When a small mill with four arms (fig. 293), each provided with a small resonator, is placed near Fig- 293 the open end of the sounding-box, the repulsion is so strong as to produce a uniform rotation. These phenomena do not seem to be due to the aspirating action of currents of air, nor are they caused by any heating effect ; and it must be confessed that the phenomena require further elucidation ; they are of special interest as furnishing a possible clue to the solution of the problem of attraction in general. 293. Phonograph. Graphophone. — In the year 1877 Edison devised the apparatus known as the phonograph for recording and reproducing sound, which was equally remarkable for the simplicity of its construction and for the striking character of the results which it produced. This instrument in its original form is illustrated in fig. 294, and it con- sisted generally of a cylinder C, mounted on a horizontal axis AA' which could -293] Edison's Phonograph 281 be rotated beneath a mouthpiece E, by means of a winch-handle M, the speed of rotation being controlled by a fly-wheel attached to one end of the spindle AA'. Upon the cylindrical surface of C was cut a helical groove, and one end of the spindle A' was formed into a screw, the pitch of which was equal to that of the groove upon the cylinder. This screw worked in a corre- spondingly screwed bearing, so that, on turning the handle, the cyhnder not only rotated upon its axis, but also travelled from end to end in a direc- tion parallel to its axis. Fig. 295 Fig. 294 The mouthpiece was closed with a diaphragm ormembraneJP (fig. [295) to the centre of which was attached, by means of an India rubber tube, a small style S, directed towards the cylinder, and caused to vibrate longitudinally by the vibratory action of the diaphragm P, and the position of the mouth- piece was so adjusted that the point of the style was always directed to the centre of the helical groove in the cylinder. On this grooved cylinder was stretched a sheet of tinfoil which bridged over the grooves, being supported by the ridges and the position of the mouth- piece, and its distance from the cylinder was adjusted by the handle m, which could be fixed in its place by the set screw v. Their position and distance were so adjusted that when the apparatus was at rest the point of the style was within the groove and a little lower than the top of the ridge. If, while the cylinder was being rotated, sounds or words were uttered into the mouthpiece, the diaphragm attached thereto was set into vibration and caused the style to indent on the foil a groove of varying depth, the bottom of which was a mechanical record of the vibration of the diaphragm, and therefore of the sounds by which those vibrations were set up, and as tinfoil is a very imperfectly elastic material it is able to retain a record so made. When this record was passed again beneath the style the varying inden- tations on the foil caused the style to vibrate as it did when it produced the indentations, and the diaphragm was similarly set into vibration, and repro- duced the sound by which it was in the first instance set into vibration. In this way sound could be reproduced so as to be audible to a large audience ; the articulation was distinct though feeble ; it reproduced the voice of a person who spoke into it, but with a nasal intonation. Speech could thus lae stored up on a sheet of tinfoil and kept for an indefinite period, and the sound could be reproduced more than once from the same record, but after a second reproduction the clearness was greatly diminished. 282 On Sound [293- If the velocity of rotation were greater than before, the pitch.'of the sound was raised ; and if the speed were not uniform, then, in the case of a song, the reproduction was incorrect. In order to produce a uniform velocity the instrument may, with advantage, be driven by clockwork. There was a great difference in the distinctness with which the various con- sonants and vowels were reproduced ; the most distinct were words containing the vowels A, O, and U, and the consonants /, k, and r ; the s and similar consonants, on the contrary, were seldom distinct. If the phonograph be rotated in the reverse direction, the sounds of which the words are made up retain their character, but are produced in the reverse order. The impressions on the tinfoil appear at first sight as a series of successive points or dots, but when examined under a microscope they are seen to have a distinct form of their own. When a cast is taken by means of fusible metal and a longitudinal section made, the outline closely resembles the jagged edge of a Konig's flame. Mr. Edison stated that as many as 40,000 words can be registered on the foil on a space not exceeding lolsquare inches. The phonograph has been used with great advantage by Jenkins and King for the analysis of vocal sounds, for which purpose it is better suited than Konig's flames. The graphophone, invented by Mr. Sumner Tainter, in conjunction with Professor Graham Bell and Dr. Chichester Bell, consists essentially of three parts : the recorder, the cylinder on which the record is made, and the reproducer. Fig. 296 The record is made on a hollow cylinder C (fig. 296) of cardboard, bb, coated with a composition of wax and paraffin ; it is mounted horizontally, and is rotated by means of a treadle underneath the table, which supports the whole apparatus. Between the treadle and the cylinder is interposed a very ingenious governor, R, by which the speed of rotation of the cylinder may be regulated to perfect uniformity, the force required for this rotation being veiy small. On a bar parallel to and in front of the cylinder is clamped the recorder, -293] Edison's Phonograph 283 which consists of an exceedingly minute cutting point, or rather chisel, fixed to a mica diaphragm. This diaphragm is at the end of a flexible tube pro- vided with a mouthpiece. If this be spoken into, the diaphragm vibrates with a to-and-fro motion, and if at the same time the cylinder rotate at a uniform speed the style cuts or carves out a groove in the surface of the wax, forming a very irregular outline which is the exact reproduction of the sound-wave. Therein lies the difference between the graphophone and the phonograph, for in the latter the record is produced by a process of indentation, while in the former the record of the sound-waves is engraved in a waxy material. The grooves are so excessively minute that their variations in depth cannot lae recognised by the naked eye ; they are not more than the x^o °^ ^^ ''^'-'^ in diameter, and there are 160 to the inch. The reproducer (fig. 297) consists of a light ebonite tube SM, at one end of which is the enlargement M containing the diaphragm, which, like that of the recorder, is of mica, but is somewhat smaller. The diaphragm is connected tjy means of a fine waxed silk thread^^, with a fine steel point or hook a, which rocks on a pivot at the end of the tube. There is an arrangement by which this reproducer can be clamped in front of the recorder, so that when the Fig. 297 cylinder is rotated the reproducer travels at a proportionate speed, allow- ing the small point to rest in the groove forming the sound record, along which it rides and vibrates ; and these vibrations are transmitted to the mica diaphragm, and, being communicated to the ear by the tube /, faith- fully reproduce the sound. Notwithstanding what appears the very yield- ing character of the wax, the sounds, and even elaborate pieces of music, are reproduced with great fidelity. The phonograph of the present day is a more perfect instrument than that of 1877 or the graphophone. As in the latter instrument, the record is made on a cylindrical surface of wax, but instead of a paper backing, it is a rigid hollow cylinder of wax, which is fitted into a slightly conical rotating mandril. The diaphragm of both recorder and reproducer is of glass, and one of the great improvements devised by Mr. Augustus Stroh is the substitution of sapphire styles for those of steel in the recorder and receiving apparatus. The modern instrument is further driven by an electric motor, which is quite silent, and by a very perfect governor ; the speed of the rotation is almost absolutely uniform. 284 On Heat [294- BOOK VI ON HEAT CHAPTER I PRELIMINARY IDEAS. THERMOMETERS 294. Heat. Hypothesis as to its nature. — In ordinary language the term heat is used not only to express a particular sensation, but also to describe that particular state or condition of matter which produces this sensation. Besides producing this sensation, heat acts variously upon bodies ; it melts ice, boils water,| makes metals red-hot, produces electric currents, decom- poses compound bodies, and so torth. Two theories as to the cause of heat have been propounded : these are, the theory of emission, and the theory of undulation. On the first theory, heat is a subtle imponderable fluid, which surrounds the molecules of bodies, and can pass from one body to another. The heat atmospheres, which thus surround the molecules, exert a repelling influence on each other, in consequence of which heat acts in opposition to the force of cohesion. The entrance of this substance into our bodies produces the sensation of warmth, its egress the sensation of cold. On the second hypothesis the heat of a body is caused by an extremely rapid oscillating or vibratory motion of its molecules ; and the hottest bodies are those in which the vibrations are most rapid and have the greatest amplitude. At any given time the whole of the molecules of a body possess energy of motion, which is the heat they contain. To increase their tempera- ture is to increase this energy ; to lower their temperature is to decrease their energy. Hence, on this view, heat is not a substance but a condition of matter, and a condition which can be transferred from one body to another. When a heated body is placed in contact with a cooler one, the former cedes more molecular motion than it receives ; but the loss of the former is the equivalent of the gain of the latter. It is also assumed that there is an imponderable elastic ether, which pervades all matter and infinite space. A hot body sets this ether in rapid vibration, and the vibrations being communicated to material objects set their particles in more rapid vibration ; that is, increase their temperature. Here we have an analogy with sound ; a sounding body is in a state of —294] Heat. Hypothesis as to its Nature 285 vibration, and its vibrations are transmitted by atmospheric air to the audi- tory apparatus in vj^hichis produced the sensation of sound. This hypothesis as to the nature of heat is now admitted by the most ■distinguished physicists. It affords a better explanation of all the phenomena •of heat than any other theory, and it reveals an intimate connection between heat and light. It will be subsequently seen that by the friction of bodies against each other an indefinite quantity of heat is produced. Experiment has shown that there is an exact equivalence between the energy of the motion thus destroyed and the heat produced. These and many other facts are utterly inexplicable on the assumption that heat is a substance, and not a form of energy. In what follows, however, the phenomena of heat will be considered, as far as possible, independently of either hypothesis ; but we shall subsequently return to the reason for the adoption of the latter hypothesis. Assuming that the heat of bodies is due to the motion of their particles, i.e. to their internal kinetic energj', we may admit the following explanation as to the nature of this motion in the various forms of matter : — In solids the molecules of even the most rigid bodies have a kind of yibratory motion about certain fixed positions. This motion is probably very complex ; the constituents of the molecule may oscillate about each other, this motion being in addition to the oscillation of the molecule as a whole ; and this latter again may be a to-and-fro motion, or it may be a rotatory motion about the centre. In cases in which external forces, such as violent shocks, a.ct upon the body, the molecules may permanently acquire fresh positions. In the liquid state the molecules have no fixed positions. They can rotate about their centres of gravity, and the centre of gravity itself may move. But the motion due to collisions, compared with the mutual attrac- tion of the molecules, is not sufficient to separate the molecules from each other. A molecule no longer adheres to particular adjacent ones ; but it does not spontaneously leave them except to come into the same relation to fresh ■ones as to its previous adjacent ones. Thus in a liquid there is a vibratory, rotatory, and progressive motion of the molecules. In the gaseous state the molecules are almost entirely without action upon each other ; they neither attract nor repel each other. They fly forward in straight lines according to the ordinary laws of motion, until they impinge against other molecules or against a fixed envelope which they cannot pene- trate, and then fly off in another direction, with, in the main, their original velocity. If the molecules were in space, where no external force could act upon them, they would fly apart, and disappear in infinity. But if contained in any vessel, the molecules continually impinge in all directions against the sides, and thus arises the pressure which a gas exerts on its vessel. The perfection of the gaseous state, or what may be regarded as an ideal gas, implies that the space actually occupied by the molecules of the gas is infinitely small compared with the entire volume of the gas ; that the time occupied by the impact of a molecule either against another molecule, or against the sides of the vessel, is infinitely small in comparison with the interval between any two impacts ; and that the influence of molecular attraction is infinitely small. When these conditions are not fulfilled the gas partakes more or less of the nature of a liquid, .and exhibits certain 286 On Heat [294- deviations from Boyle's law (i8i). This is the case with all gases ; to a very slight extent with the less easily condensable gases, but to a far greater extent with vapours and the more condensable gases, especially near their points of liquefaction. These are now explained by the modification which Van der Waals has introduced into the equation for gases (183). 295. Dynamical theory of gases. — We have seen that in the gaseous condition the particles are assumed to fly about in right lines in all possible directions. A rough illustration of this condition of matter is afforded by imagining- the case of a number of bees enclosed in a box. Let us suppose a cubical vessel to be filled with air under standard con- ditions of temperature and pressure. Let the length of the sides be a. We will for the present suppose that each particle moves freely in the space without striking against another particle. All possible motions may be con- ceived to be resolved into motions in three directions which are parallel to the faces of the cube. Conceive any single particle of mass, m ; it will strike against one face with such a velocity, u, as not only to annul its own motion, but to cause it to rebound in the opposite direction with the same velocity ; hence the measure of the force with which it strikes against the side will be 2.mu. Now, by their rapid succession and their uniform distribution, the total action of these separate impacts is to produce a pressure against the sides of the vessel which is the elastic force of the gas ; and, to measure the pressure on the side, we must multiply the force of each individual impact by the total number of such impacts. Since the length of the side is a, if there are n molecules in the unit of space, there will be na' in the volume of the cube, of which will be moving in a direction parallel to each one of the sides. To get the number of impacts on one face, we must remember that they succeed each other, after the interval of time required for a particle to fly to the opposite side and back again. Hence, u being the velocity, the number of impacts which each particle makes in the unit of time, asecond, will be — , and the number 2a of all such which strike against one side will be ina^— =ina'u. 2a Now, since each one exerts a pressure represented by 2>m<, we shall have for the total pressure p on the surface a'^ pcP = \c^nmu-, and therefore the pressure on the unit of surface will be p — \ntnii". Again, if N is the number of molecules in the volume i/, N = nv, and therefore N p-\ -mti^ ; that is, pv = JN;«m'. V But, for any given mass of gas at constant temperature, N, m, and u are constant quantities, and the product pv must therefore also be constant : this, however, is only, one form of expressing Boyle's law (181). -296] Molecular Velocity 287 We may put the above expression in the form pv = f N — , so that for equal vohimes of two different gases under the same conditions of tempera- ture and pressure, fN = fN' ' ' . The latter part of the expression represents the energy of the gas in each case. But under the conditions stated these are equal ; accordingly we have N = N', that is to say that equal volumes of two different gases under the same conditions of temperature and pressure contain the same number of molecules. This, which is known as Avogadro's law, was deduced by him from other considerations, and forms one of the most important bases of theoretical chemistry. 296. Molecular velocity. — In the formula p = Inmu', nm represents the mass in unit volume which we may designate as the density, p, of the gas, and which can be directly measured ; and, since the pressure p is also capable of direct measurement, we can calculate the third magnitude u in absolute measure. The pressure ^ on a gas is equal to the action of gravity on a column of mercury of given height, h ; so that, if S is the density of mercury= I3"596, and g the acceleration of gravity, p = hgh and P Now, if a be the specific gravity of the gas as compared with air, which is lighter than water, a x 773'3 = tr, or p = — ?— 773"3 7733 2 _ 3 X 1 3-596 X 076 X 9-8 1 1 5 X 773-3 u , which gives u = 1-i ; that is, that for atmospheric air the mean velocity of Vo- the particles is 485 metres in a second. For other gases we have, expressed in the same units, O = 461, N = 492, H = 1844. It follows from the above equation that u : u^ = \J (f^ : s/ (T ; that is, that the moleculm velocities are inversely as the square roots of the densities or the molecular weights. This is confirmed by experiments on diflfusion (191). In a gas the velocities of the particles are unequal ; since, even supposing that tney were all originally the same, it is not difficult to see that they would soon alter. For imagine a particle to be moving parallel to one side and to be struck centrically by another moving at right angles to the direction of its motion ; the particle struck would proceed on its new path with increased velocity, while the striking particle would rebound in a different direction with a smaller velocity. Notwithstanding the accidental character of the velocity of any individual particle in such a mass of gas as we have been considering, there will, at any one given time, be a certain average distribution of velocities. Now, from considerations based on the theory of probabilities. Maxwell inferred that 288 On Heat [296- some velocities will be more probable than others — that there will, indeed, be one velocity which is more probable than any other. This is called the most probable velocity. The mean velocity of the particle, as deduced above, IS not this, nor is it the same as the arithmetical mean of all the velocities ; it may be defined to be that velocity which, if all the molecules possessed it, would give rise to the same mean energy of the molecular impacts against the side as that which actually exists. This mean velocity is about ^5 greater than the arithmetical mean velocity, and is | that of the most probable single velocity. Theoretical as well as experimental observations render it possible to determine with great probability the length of the path which one molecule of a gas traverses before it encounters another, which is known as the free Jiath. This is not a constant number in one and the same gas ; that is, the paths which the molecules travel between two impacts are not equal, and the average of these is known as the mean free path. The length of this depends on the number of molecules in unit volume of a gas, being inversely as the density ; for it is obvious that as the density increases the number of molecules increases also, and therewith the path which one molecule travels before it meets another will be so much the smaller. The mean free path in different gases will be shorter the larger are the molecules. In nitrogen measured under standard conditions it has been determined to be 98-6/i/i (micromillimetres), in hydrogen 185 '5, and in carbonic acid 68^/i. The frequency of the impacts has also been determined ; in the case of hydrogen this is 9,480 millions, and of nitrogen and air 8,000 millions per second. It has been urged against the kinetic theory of gases that with its enormous molecular velocity the diffusion of a gas with another ought to take place instantaneously, and be at once perceived in the case of those with strong odours ; this, as we know, is not the case ; the velocity is the rate between successive impacts, and billions of such impacts must take place before a molecule passes to any great distance. The magnitudes of the molecules themselves have been calculated by several observers from different methods based on various physical pheno- mena (3). Loschmidt found, for instance, that the diameter of the molecule of hydrogen was 4-1 /i^, oxygen 07 /li/i, and nitrogen o-8 }i.\i.. The results of other estimates, made by various methods, agree remarkably with these 297. General effects of heat. — -The general effects of heat upon bodies may be classed under three heads. One portion is expended in raising the temperature of a body ; that is, in increasing the kinetic energy of its molecules. A second portion of the heat communicated to a body may be spent in altering the relative positions of the atoms within the molecule These two effects are classed as internal work. The third portion is spent in increasing the volume, and so doing work against external pressure. The heat or work required for this is called the external work. 298. Expansion.' — -Nearly all bodies expand when heated. As a general rule, gases are the most expansible, then liquids, and lastly solids. In solids which have definite figures, we can consider the expansion either in one dimension, the linear expansion ; |in two dimensions, the superficial expansion ; or in three dimensions, the cubical expansion or the ■expansion of volume, although one of these never takes place without the -298] Expansion other. As liquids and gases have no definite figures, tlie expansions of volume have in them alone to be considered. To show the linear expansion of solids, the apparatus represented in fig. 298 may be used. A metal rod, A, is fixed at one end by a screw, B, Fig. 298 while the other end presses against the short arm of an index, K, which moves on a scale. Below the rod there is a sort of cylindrical- lamp in which alcohol is burned. The needle K is at the first at zero point, but as the rod becomes heated it expands, and moves the needle along the scale. The cubical expansion of solids is shown by a Gravesandis ring. This consists of a brass ball, a (fig. 299), which at the ordinary temperature passes Fig. 299 Fig. 301 Fig, 300 freely through a ring, wz, almost of the same diameter. But when the ball has been heated, it expands, and no longer passes through the ring. In order to show the expansion of liquids, a large glass bulb provided with a capillary stem is used (fig. 300). If the bulb and a part] of the stem contain some coloured liquid, the liquid rapidly rises in the stem when heat U 290 On Heat [298- is applied, and the expansion thus observed is far greater than in the case of solids. The same apparatus may be used for showing the expansion of gases. The bulb being filled with air, a small thread of mercury is introduced into the capillary tube to serve as index (fig. 301). When the globe is even slightly heated, for instance, by approaching the hand, the expansion is so great that the index is driven to the end of the tube, and is finally expelled. It is thus seen that gases are highly expansible. In these different experiments the bodies contract on cooling, and when they have attained their former temperature they resume their original volume. Certain metals, however, especially zinc, form an exception to this rule, as do also some kinds of glass. MEASUREMENT OF TEMPERATURE. THERMOMETRY 299. Temperature. — The temperature or kotness of a body may be •defined, independently of any hypothesis as to the nature of heat, as being a quality of the body depending on the greater or less extent to which it tends to impart sensible heat to other bodies. The temperature of a body must not be confounded with the quantity of keat it possesses : a body may have a high temperature and yet have a veiy small quantity of heat, and, conversely, a low temperature and yet possess a large amount of heat. If a cup of water be taken from a bucketful, both will have the same temperature, yet the quantities of heat they possess will be different. This subject of the quantity of heat will be afterwards more fully explained in the chapter on Specific Heat. 300. Thermometers. — Thermometers are instruments for measuring temperature. Owing to the imperfections of our senses, we are unable to measure temperatures by the sensation of heat or cold which they produce in us, and hence recourse must be had to the physical actions of heat on bodies. These actions are of various kinds, but the expansion of bodies has been selected as the easiest to observe. Heat also produces electric phenomena in bodies ; and on these the most delicate methods of observing temperatures have been based, as we shall see in a subsequent ■chapter. Liquids are best suited for the construction of thermometers — the expan- sion of solids being too small, and that of gases complicated by variations of pressure. Mercury and alcohol are the only liquids used — the former "because it boils at a moderately high temperature, and the latter because it requires an extremely low temperature for its solidification. The mercury thermometer is the most extensively used. It consists of a capillary glass tube, at the end of which is blown the bulb, a cylindrical or spherical reservoir. Both the bulb and a part of the stem are filled with mercury, and the expansion is measured by a scale graduated either on the stem itself or on a frame to which the stem is attached. Besides the manufacture of the bulb, the construction of the thermometer comprises three operations : the calibration of the tube, to test the unifor- mity of its bore ; the introduction of the mercury into the reservoir ; and the graduation. -303] Determination of the Fixed Points ,291 301. Division of the tube into parts of equal capacity. Calibration. — As the indications of the thermometer are only correct when the divisions of the scale correspond to equal expansions of the mercury in the reservoir, the scale must be graduated, so as to indicate parts of equal capacity in the tube. I the tube were of the same diameter throughout, it would only be neces- sary to divide it into equal lengths. But as the diameter of glass tubes is usually greater at one end than another, parts of equal capacity in the tube are represented by vmequal lengths of the scale. In order, therefore, to select a tube ofuniforra bore, the tube \% calibrated ; for this purpose, a thread of mercury about an inch long is introduced into the capillary tube, and moved to different positions in the tube, care being taken to keep it at the same temperature. If the thread is of the same length in every part of the tube, the capacity is everywhere the same ; but if the thread occupies different lengths in different parts, the tube is rejected, and another one sought. 302. Filling the thermometer. — In order to fill the thermometer with mercury, a small funnel, C (fig. 302), is blown on the top, and is filled with mercury ; the tube is then slightly inclined, and the air in the bulb expanded by heating it with a spirit lamp. The expanded air partially escapes by the funnel, and, on cooling, the air which re- mains contracts, and a portion of the mercury passes into the bulb, D. The bulb is then again warmed, and allowed to cool, a fresh quantity of mercury enters, and so on, until the bulb and part of the tube are full of mercury. The mercury is then heated to boiling ; the mercury vapour in escaping carries with it the air and moisture which remain in the tube. The tube, being full of the expanded mercury and of mercury vapour, is hermetically sealed at one end. When the ther- mometer is cold, the mercury ought to fill the bulb and a portion of the stem. 303. Determination of the fixed points and graduation of the thermo- meter.— Experiment has shown that ice constantly melts at the same tem- perature, whatever be the source of heat, and that distilled water under the same pressure and in a given vessel always boils at the same temperature. These two temperatures therefore, that of melting ice, and that of water boiling under a pressure of 76 cm. of mercury, may be taken as fixed points of reference for the thermometer stem. To obtain the lower fixed point snow or pounded ice is placed in a vessel (fig. 303). The bulb and a part of the stem of the thermometer are immersed in this for about a quarter of an hour, and a mark made at the level of the mercury, which represents the point required. The second fixed point is determined by means of an apparatus of which fig. 304 represents a vertical section. A central tube, B, open at both u 2 Fig. 302 292 On Heat [303- ends, is fixed on a cylindrical vessel containing water ; a second tube, C, concentric with the first, and surrounding it, is fixed on the same vessel, A. In this second cylinder, which is closed at both ends, there are three tubulures, a, r, r'. A cork, in which is the thermometer, fits in a. To r', a glass tube, containing mercury,|is attached, which serves as a mano- meter for measuring the pressure of the vapour in the apparatus ; r is an escape tube for the vapour and condensed water. Fig. 303 Fig. 304 The apparatus is heated over a flame till the water boils ; the vapour produced in A rises in the tube B, and, passing through the outside tube, escapes by r. The thermometer being thus surrounded with vapour, the mercury expands, and when the top of the mercurial column has become stationary, the point at which it stops is marked. This is the point sought for. The object of the outer case, C, is to avoid the cooling of the inner tube by its contact with the air. The determination of the point loo (see next article) would seem to require that the height of the barometer during the experiment should be 760 millimetres, for, when the barometric height is greater or less than this quantity, water boils either above or below 100 degrees. But the point 100 may always be exactly obtained by making a suitable correction. For every 27 millimetres difiference in height of the barometer there is a differ- ence in the boiling point of i degree. If, for example, the height of the barometer is 778 — that is, 18 millimetres, or two-thirds of 27, above 760 — -304] Construction of the Scale 293 water would boil at 100 degrees and two-thirds. Consequently loof would have to be marked at the point at which the mercury stops. Gay- Lussac observed that water boils at a somewhat higher temperature in a glass than in a metal vessel ; and as the boiling point is raised by any salts which are dissolved, it has been assumed that it was necessary to use a metal vessel and distilled water in fixing the boiling point. Rudberg showed, however, that these latter precautions are superfluous. The nature of the vessel and salts dissolved in ordinary water affect the temperature of boil- ing water, but not that of the vapour which is formed. That is to say, that if the temperature of boiling water from any of the above causes is higher than 100 degrees, the temperature of the vapour does not exceed 100, provided the pressure is not more than 760 millimetres. Consequently, the higher point may be determined in a vessel of any material, when the thermometer is quite surrounded by vapour, and does not dip in the water. Even with distilled water the bulb of the thermometer must not dip in the liquid ; for, strictly speaking, it is only the upper layer that really has the temperature of 100 degrees, since the temperature increases from layer to layer towards the bottom, in consequence of the increased pressure. 304. Construction of the scale. — Just as the foot-rule which is adopted as the unit of comparison for length is divided into a number of equal divisions called inches for the purpose of pro- viding a smaller unit of comparison, so likewise the unit of comparison of temperatures, the range from the melting point to the boiling point, must be divided into a number of parts of equal capacity called degrees. On the Continent, and more especially in France, this space is divided into 100 parts, the lower fixed point being marked o and the upper 100, and this division is called the Centigrade or Celsius scale ; Celsius, its inventor, died in 1742. The Centigrade thermometer is almost exclusively adopted in foreign scientific works, and, as its use is gradually extending in this country, it has been and will be adopted in this book. The degrees are designated by a small cipher placed a little above on the right of the number which marks the temperature, and to indicate temperatures below zero the minus sign is placed before them. Thus, —15 signifies 1 5 degrees below zero. In accurate thermometers the scale is marked on the stem itself (fig. 305). It cannot be displaced, and its length remains fixed, as glass has very little expansibility. The graduation is effected by covering the stem with a thin layer of wax, and then marking the divisions of the scale, as well as the corresponding numbers, with a steel point. The thermometer is then exposed for about ten minutes to the vapours of hydrofluoric acid, which attacks the glass where the wax has been removed. The stem is thus permanently etched. Besides the Centigrade scale two others are frequently used — Fahrenheifs scale and Rdaumufs scale. In Reaumur's scale the fixed points are the same as on the Centigrade Fig. 30s 294 On Heat [304- scale, but the distance between them is divided into 80 degrees, instead of into 100. That is to say, 80 degrees Reaumur are equal to 100 degrees Centigrade ; i degree Rdaumur is equal to ^"jp or f of a degree Centi- grade, and I degree Centigrade equals f-^ or | degree Reaumur. Con- sequently, to convert any number of R&umur's degrees into Centigrade degrees (20, for example), it is merely necessary to multiply them by J (which gives 25). Similarly, Centigrade degrees are converted into Reaumur by multiplying them by |. The thermometric scale invented by Fahrenheit in 1714 is still much used in England, and also in Holland and North America. The higher fixed point is, like that of the other scales, the temperature of boiling water ; but the null point of zero is the temperature obtained by* mixing equal weights of sal-ammoniac and snow, and the interval between the two points is divided into 212 degrees. The zero was selected because the temperature was the lowest then known, and was thought to represent absolute cold. When Fahrenheit's thermometer is placed in melting ice it stands at 32 degrees, and therefore 100 degrees on the Centigrade scale are equal to 180 degrees on the Fahrenheit scale, and thus i degree Centigrade is equal to f of a degree Fahrenheit, and, conversely, i degree Fahrenheit is equal to- f of a degree Centigrade. Since the distance on the thermometer stem between boiling point and freezing point is divided into 180, 100, and 80 equal parts respectively on the Fahrenheit, Centigrade, and Reaumur scales, it is clear that 9 degrees Fahrenheit = 5 degrees Centigrade = 4 degrees Reaumur. Hence, since on the two latter scales the graduations begin from the freezing point and on the Fahrenheit scale from a point 32 degrees below the freezing point, if F, C,. and R represent the same temperature on the different scales, F-32 _C_R 9 5~ 4' 305. Displacement of zero. — Thermometers, even when constructed with the greatest care, are subject to a source of error which must be taken into account ; this is, that in course of time the zero tends to rise, the dis- placement sometimes extending to as much as 2 degrees ; so that when the thermometer is immersed in melting ice the mercury no longer sinks to zero. This is generally attributed to a diminution of the volume of the bulb and also of the stem, occasioned by the pressure of the atmosphere. It is usua with very accurate thermometers to fill them two or three years before they are graduated. Joule once observed that even after twenty-five years a delicate thermometer indicated a displacement of zero. Besides this slow displacement, there are often variations in the position of the zero, when the thermometer has been exposed to temperatures above 60°, caused by the fact that the bulb and stem do not immediately contract on cooling to their original volume ; these differences are greater the thicker-the glass sides, and hence it is necessary from time to time to verify the position of zero when a thermometer is used for delicate determinations. Regnault noticed that some mercury thermometers, which agree at 0° and at 100°, differ between these points, and he ascribed this to the unequal expansion of different kinds of glass. -308] Conditions of Delicacy of a Thermometer 295 According to Pfaundler the difference due to this cause is scarcely o'2 of a degree between 0° and 100°, while at 350° it may be as much as 10 degrees. 306. Limits to the employment of mercury thermometers. — Of all thermometers in which liquids are used, the one with mercury is the most useful, because this liquid is easily obtained pure and expands very regularly between — 36° and 100° ; that is, proportionally to the rise of temperature. It also has the advantage of having a very low specific heat. But for temperatures below — 36° C. the alcohol thermometer must be used, since mercury solidifies at —39° C. Above 100 degrees the coefficient of expan- sion increases, and the indications of the mercury thermometer are only approximately correct, the error rising sometimes to several degrees. Mercury thermometers cannot be used for temperatures above 350°, for this is the boiling point of mercury. For veiy accurate measurements the air thermometer is used (336). 307. Alcohol thermometer. — The alcohol thermometer diflfers from the mercury thermometer in being filled with coloured alcohol, and in having a tube of larger calibre. The method of filling an alcohol thermometer is similar to that already described for mercury thermometers. When the bulb and tube have been filled to the requisite height, the end of the tube is sealed by the blowpipe, but no attempt is made to get rid of the air in the tube. On the contrary, it is an advantage to have air in the tube at somewhat greater than atmospheric pressure, as the alcohol column is thus prevented from breaking up into short cylinders separated by vapour. Alcohol thermo- meters, after 0° C. has been obtained by melting ice, are usually graduated by placing them in baths at different temperatures together with a standard mercury thermometer, and marking on the alcohol thermometer the tem- perature indicated by the mercuiy thermometer. In this manner the alcohol thermometer is made comparable with the mercury one ; that is to say, it indicates the same temperatures under the same conditions. The alcohol thermometer is especially used for low temperatures, as alcohol only freezes at -130° C. 308. Conditions of delicacy of a thermometer. — A thermometer may be delicate in two ways : — i. When it indicates very small changes of tem- perature. 2. When it quickly assumes the temperature of the surrounding medium. The first kind of delicacy is attained by having a very narrow capillary tube and a very large bulb ; the expansion of the mercury on the stem is then limited to a small number of degrees, from 10 to 20 or 20 to 30 for instance, so that each degree occupies a great length on the stem, and can be subdivided into very small fractions. The second kind of delicacy is obtained by making the bulb very small, for then it rapidly assumes the temperature of the liquid in which it is placed. A good mercury thermometer should answer to the following tests : — When its bulb and stem, to the top of the column of mercury, are immersed in melting ice, the top of the mercury should exactly indicate 0° C. ; and when suspended with its bulb and scale immersed in the steam of water boiling in a metal vessel (as in fig. 304), the barometer standing at 760 mm., the mercury should be stationary at 100° C. The value of the degrees should be uniform ; to ascertain this a little cylinder of mercury may be 296 On Heat [308- Fig. 306 detached from the column by a shght jerk, and on inchning the tube it may be made to pass from one portion of the bore to another. If the scale be properly graduated and the tube be of uniform bore, the column will occupy an equal number of degrees in all parts of the tube. 309. Differential thermometer. — Sir John Leslie constructed a thermo- meter for showing the difference of temperature of two neighbouring places, from which it has received the name of the differential thermo- meter. A modified form of it is that de- vised by Matthiessen (fig. 306), which has the advantage of being available for indicating the temperature of liquids. It consists of a bent glass tube, each end of which is bent twice, and terminates in a bulb ; the bulbs being pendent can be readily immersed in two different liquids. The bend contains some coloured liquid, and in a tube which connects the two limbs is a stop- cock, by which the liquid in each limb is easily brought to the same level. The whole is supported by a frame. When one of the bulbs is at a higher temperature than the other, the liquid in the stem is depressed and rises in the other stem. The instrument is now only used as a thennoscope ; that is, to indicate a difference of temperature between the two bulbs, and not to measure its amount. 310. Breguet's metallic thermometer. Breguet invented a thermometer of con- siderable delicacy, which depends on the unequal expansion of metals. It consists of three strips, of platinum, gold, and silver, which are passed through a roll- ing mill so as to form a very thin metallic ribbon. This is then coiled in a spiral form, as seen in fig. 307, and, one end being fixed to a support, a ^^' """^ light needle is fixed to the other, which is free to move round a graduated scale. Silver, which is the most expansible of the metals, forms the inner face of the spiral, and platinum the outer. When the temperature rises, the silver expands more than the gold or platinum, the spiral unwinds itself, and the needle moves from left to right of the above figure. The contrary -311] Maximum and Minimum Thermometers 297 effect is produced when the temperature sinks. The gold is placed between thelother two metals because its expansibility is intermediate between that of the silver and that of the platinum. Were these two metals employed alone, their rapid unequal expansion might cause a fracture. Breguet's thermometer is empirically graduated in Centigrade degrees, by comparing its indications with those of a standard mercury thermometer. Several forms of pocket thermometers depend on this principle, which is also applied in some registering thermometers. Fig. 308 311. Maximum and minimum thermometers. — It is necessary, in meteoro- logical obsei-vations, to know the highest temperature of the day and the lowest temperature of the night. Ordinary thermometers could only give these indications by a continuous observation, which would be impracticable. Several instru- ments have accordingly been invented for this purpose, the simplest of which is Rutherford's. On a rectangular piece of plate-glass (fig. 308) two thermometers are fixed, whose stems are bent horizontally. The upper one is a mercury, and the lower an alcohol thermometer. In the maximum thermometer-^there is a small piece of iron wire or hard wood moving freely in the tube, and serving as an index. The thermometer being placed horizontally, the mercury pushes the index before it when the temperature rises. But when the temperature falls and the mercury contracts, the index retains that position in the tube to which it has been moved, for there is no adhesion between the iron and the mercury. In this way the index registers the - highest temperature which has been attained. In the minimum thermometer alcohol is the liquid employed ; the index is a small piece of glass, shaped like a dumb-bell, which is placed in the liquid. When the temperature falls the convex side of the liquid meniscus carries the index with it ; when the temperature rises the liquid passes by the index without disturbing it ; the position of the index gives therefore the lowest temperature which has been reached. Sixis thermometer (fig. 309) is not only a maximum and minimum, but gives a double reading and therefore corrects itself It consists of a U-shaped glass tube which is bent round at one extremity and terminates in a long cylindrical bulb, B. At the other end of the U tube is a conical bulb, C. The bend of the tube from a \.o b contains mercury. Fig. 309 298 On Heat [311- Fig. 310 Alcohol occupies the bulb B and extends as far as to the top of the mercury b \ above a, again, is alcohol which occupies a portion of the bulb C. The rest of C contains air and alcohol vapour. The liquid — alcohol, mercury, alcohol — is thus continuous from the surface in C to the other end of the system. When the temperature rises, the alcohol in B expands and pushes the mercury down at b and up at a, and the mercury in its turn drives the alcohol towards the bulb C, in which the air is compressed and the alcohol vapour partially condensed. When the temperature falls, the alcohol in B contracts, but in consequence of the pressure exerted by the air in C, no break occurs in the liquid column, the mercury at b following the receding alcohol. In the alcohol columns, above a and b, are indexes consisting either of iron wire, or of fine glass tubing in which an iron wire is sealed ; and to each index a short piece of horsehair is fastened (fig. 310). When the temperature rises the index a is pushed up, and remains in position owing to the friction of the horse- hair. Similarly, when the temperature falls the index 3 is pushed forward and marks the minimum temperature. The setting of the indexes is effected by a magnet. In NegretWs maximum thermometer the tube near the bulb is nearly throttled, the result of which is, that although during a rise of temperature the mercury is continuous from the bulb to the end of the column, as soon as the mercury begins to contract by reason of fall of temperature, the mercury column is broken at the con- striction. Thus, a thread of mercury is left in the tube and indicates the highest temperature reached. This thread contracts to a small extent as the temperature falls, but the chief contraction takes place in the bulb. The clinical thermometer (fig. 311) — used by physicians for determining the temperature of the body — is generally constructed on the Negretti principle. It is graduated from 90° F. to 1 10°, the normal temperature of the healthy body being 98-4°. To be reset the instru- ment must be held in the hand and sharply jerked. The momentum of the mercury can thus be made to overcome the friction at the constriction, and continuity is re- established between the mercury in the tube and that in the bulb. 312. Pyrometers.— The name ^^OT^^iferj is given to instruments for measuring temperatures so high that mercurial thermometers could not be used. The older contrivances for this purpose — ^Wedgwood's, Daniell's (which in principle resembled the apparatus in fig. 298), Brongniart's, &c. — have gone entirely out of use. None S8-4. Fig. 311 of them give an exact measure of temperature. The arrangements now used -•313] Different Remarkable Temperatures agg- for the purpose are based either on the expansion of gases and vapours, on the specific heat of solids, or on the electric properties of bodies, and will be subsequently described. 313. Different remarkable temperatures. — The following table gives some of the most remarkable points of temperature. It may be observed that it is easier to produce veiy high than very low temperatures. Liquid nitrogen boils . — 194° C. Liquid oxygen boils — 183 Greatest natural cold recorded in Arctic expeditions — 587 Mercury freezes ... .... — 39-9 Mixture of snow and salt . . about — 20 Ice melts . . o Greatest density of water . . . . + 4 Mean temperature of London . 9-9 Temperature of the blood 36-9 Water boils ..... 100 Highest temperature of a Turkish bath 125 Mercury boils . . . 357 Sulphur boils ... . . 444 Red heat (just visible) about 500 Silver melts . . . 954 Zinc boils . . . 960 Cast iron melts . about 1 200 Platinum melts . -1775 Iridium melts . , 1950 300 On Heat [314- CHAPTER II EXPANSION OF SOLIDS 314. Linear, superficial, and cubical expansion. Coefficients of expan- sion. — It has been already explained that in solid bodies the expansion may be considered either in one or two or three dimensions — linear, superficial, ■or cubical. The coefficient of linear expansion is the increase of the unit of length ■of a body when its temperature rises from zero to 1 degree C. ; the coefficient vf superficial expansion is the increase of the unit surface when heated from zero to I degree, and the coefficient of cubical expansion is the increase of the unit of volume under the same circumstances. These coefficients vary with different bodies, but for the same body the coefficient of cubical expansion is three ti^nes that of the linear expansion, as is seen from the following considerations : — Suppose a cube the length of whose side is i at zero. Let k be the elongation of this side in passing from zero to I degree, its length at i degree will be \^■k, and the volume of the cube, which was i at zero, will be (i +^)^ or i +3^ + 3^^ + ,4^ But as the elongation k is always a very small fraction (see table, art. 318), its square, /&", and still more its cube, li^, are so small that they may be neglected, and the value at I degree becomes very nearly i + 3/fe. Consequently, the increase of volume is 3A, or the coefficient of cubical expansion is thrice the coefficient of linear expansion. In the same manner it may be shown that the coefficient of superficial ■expansion is double the coefficient of linear expansion. 315. Measurement of the coefficient of linear expansion. Lavoisier and Laplace's method. — ^The apparatus used by Lavoisier and Laplace for determining the coefficients of linear expansion (fig. 312) consists of a brass r" Fig. 312 trough, placed on a furnace between four stone supports. On the two sup- ports on the right hand there is a horizontal axis, at the end of which is a telescope ; on the middle of this axis, and at right angles to it, is fixed a -316] Roy and Ramsden's Method 301 glass rod, turning with it, as does also the telescope. The other two supports^ are joined by a cross-piece of iron, to which another glass rod is fixed, also- at right angles. The trough, which contains oil or water, is heated by a furnace not represented in the figure, and the bar whose expansion is to be determined is placed in it. Fig. 313 represents a section of the apparatus ; G is the telescope, KH the bar, whose ends press against the two glass rods F and D. As the rod' F is fixed, the bar can only expand in the direction KH, and in order to eliminate the effects of friction it rests on two glass rollers. Lastly, the telescope has a cross-wire in the eyepiece, which, when the telescope moves,, indicates the depression by the corresponding number of divisions on a vertical scale, AB, at a distance of 220 yards. The trough is first filled with ice, and the bar being at zero, the division on the scale AB, corresponding to the wire of the telescope, is read off. The ice having been removed, the trough is filled with oil or water, which is heated to a given temperature. The bar then expands, and when its tem- perature, as indicated by thermometers in the bath, has become stationary,, the division of the scale, seen through the telescope, is read off. Fig- 313 From these data the elongation of the bar is determined ; for since it has- become longer by a quantity, CH, and the optical axis of the telescope has become inclined in the direction GB, the two triangles, GHC and ABG, are similar, for they have the sides at right angles each to each, so that HC AB GH A preliminary measurement showed -r-^.to be y^j-. Conse- quently, T-Jj, whence HC = AB that is, the total elongation of the- GH AG' HC AB '**' 744' bar is obtained by dividing the length on the scale traversed by the cross- wire by 744. Dividing this elongation by the length of the bar, and then by the temperature of the bath, the quotient is the dilatation for the unit of length and for a single degree — in other words, the mean coefficient of linear expansion between 0° and 100°. 316. Roy and Ramsden's method. — Lavoisier and Laplace's method is founded on an artifice which is frequently adopted in physical determinations, and which consists in amplifying by a known amount dimensions which, in themselves, are too small to be easily measured. Unfortunately, this plan is often more fallacious than profitable, for it is first necessary to determine the ratio of the motion measured to that on which it depends. In the pre- sent case, it is necessary to know the lengths of the arms of the lever in the apparatus. But this preliminary operation may introduce errors of such importance as partially to counterbalance the advantage of great delicacy. 302 On Heat [316- The following method, devised by Ramsden and used by General Roy in 1787, depends on another principle. It measures the elongations directly, •and without amplifying them ; but it measures them by means of a micro- meter arrangement, which indicates very small displacements. The apparatus (fig. 314) consists of three parallel metal troughs about •6 feet long. In the middle one there is a bar of the material whose expansion 5s to be determined, and in the two others are cast-iron bars of exactly the same length as this bar. Rods are fixed vertically on both ends of these three bars. On the rods in the troughs A and B there are rings with cross- wires like those of a telescope. On the rods in the trough C are small telescopes, also provided with cross-wires. The troughs being filled with ice, and all three bars at zero, the points of intersection of the wires in the rings and of the wires in the telescope are all in a line at each end of the bar. The temperature in the middle trough is then raised to 100° C. by means of spirit lamps placed beneath the trough ; the bar expands, but as it is in contact with the end of the screw, a, fixed on the side, all the elongation takes place in the direction nm, and, as the cross- wire n remains in position, the cross-wire m is moved towards B by a quantity equal to the elongation. But since the screw a is attached to the bar, by turning it slowly from right to left, the bar is moved in the direction mn, and the cross-wire m regains its original position. The distance through which m has been moved is equal to the elongation of the bar, and this is deduced from the number of turns of the screw a, when the thread of the screw is once known. Thus the total expansion of the bar is obtained, which, divided by the temperature of the bath, and this quotient by the length of the bar at zero, gives the coefficient of linear expansion. -317] Coefficients of Linear Expansion 303 317. Coefficients of linear expansion. — By one or the other method the following results have been obtained :■ — Mean coefficients of linear expansion for 1° between 0° and 100° C. Diamond . Pine . Graphite Marble White glass Platinum Untempered steel Cast iron . Sandstone . Wrought iron Tempered steel Gold . Copper Bronze Brass . o-oooooii8o Silver . . o'ooooigo97 0-000006080 Tin. O'oooo2i730 0-000007860 Aluminium . 0-000023130 0-000008490 Lead . . 0-000028575 0-000008613 ^i"c . . 0-000029417 0-000008842 Sodium chloride 0-000040390 0-000010788 Sal ammoniac 0-000063000 0-000011250 Ice . . . 0-000064000 0-0000 1 1740 Sulphur . . 0-000064130 0-000012204 Sodium . 0-000072000 0-000012395 Ebonite( 1 7° to 35°) 0-000080600 0-000014660 Potassium . 0-000083000 0-000017 1 82 Paraffin . . 0-000278540 0-000018167 Gutta-percha . 0-000598000 0-000018782 In accordance with what has been said about the linear expansion (314), the coefficients of cubical expansion of solids are obtained by multiplying those of linear expansion by 3, and conversely those of linear expansion may be deduced from the cubical if we divide by 3. The coefficients of expansion of the metals vary with their physical con- dition, being different for the same metal according as it has been cast or hammered and rolled, hardened or annealed. As a general rule, operations which increase the density increase also the rate of expansion. But even for substances in apparently the same condition, different observers have found very unequal amounts of expansion ; this may arise in the case of compound substances, such as glass, brass, or steel, from a want of uni- formity in chemical composition, and in simple bodies from slight differences of physical state. The expansion of amorphous solids, and of those which crystallise in the regular system, is the same in all directions, unless they are subject to a strain in some particular direction. A fragment of such a substance varies in bulk when its temperature is changed, but retains the same shape. Crystals not belonging to the regular system when heated exhibit an unequal expan- sion in the direction of their different axes, in consequence of which the magnitude of their angles, and therefore their form, are altered. In the dimetric system the expansion is the same .n the direction of the two equal axes, but different in the third. In crystals belonging to the hexagonal system the expansion is the same in the direction of the three secondary axes, but different from that along the principal axis. In the trimetric system it is different in all three directions. To the general law that all solid bodies expand by heat there is an im- portant exception in the case of iodide of silver, which contracts somewhat when heated. Between —60'^ and 4- 142° C. it has a negative coefficient of expansion, the value of which is 0-00000139 fo'f 1° C. 304 On Heat [317- Fizeau determined the expansion of a great number of crystallised bodies by an optical method. He placed thin plates of the substance on a glass plate and let yellow light pass through them. He thus obtained alternately yellow and dark Newton's rings {q.v.). On rise of temperature, the plate of the substance expanded, the thin layer of air became thinner, and the posi- tion of the rings was altered. From the alteration in their position the amount of the expansion could be deduced. Among the results he has obtained is the curious one that certain crystallised bodies, such as diamond, emerald, and cuprous oxide, contract on being cooled to a certain tempera- ture, but as the cooling is continued below this temperature they expand. They have thus a temperature of maximum density, as is the case with water (331). In the case of emerald and cuprous oxide this temperature is at — 4-2°, in the case of diamond at — 42-3°. 318. The coefficients of sKpansion increase with the temperature. — ■ According to Matthiessen, who determined the expansion of some metals and alloys by weighing them in water at different temperatures, the coefficients of expansion are not quite regular between 0° and 100°. Some of his results are given below, the letters Lo, Lt denoting the lengths of a bar of the metal at 0° and t° respectively. Zinc . . . Lt= Lo (i +0-00002741 /+O-OO0OOOO235 /^) Lead . . . Lt= Lo (i +O'oooo27i6 / + o'oooooooo74 Z'') Silver . Lt = Lo (i +0-00001809 / + 0-0000000135 /'') Copper Lt = Lo (i + 0-00001408 t + 0-0000000264 f') Gold . . . Lt = Lo (i +000001358 / + 0-000000OII2 /^) Matthiessen further found that the coefficients of expansion of an alloy are very nearly equal to the mean of the coeflficients of expansion of the volumes of the metals composing it. 319. Formulae relative to the expansion of solids. — Let 4 be the length of a bar at zero, /t its length at the temperature t° C, and ,3 its coefficient of linear expansion. The elongation corresponding to / is ^ times /3 or ^t for unit length, or 3/4 for /o units. The length of the bar which is 4 at zero is /„ + ?tl^ at /, con- sequently /. = /o + /3/4 = 4(i+/34 This formula gives the relation between the four magnitudes 4, 4, &■, A and it is clear that if any three of these are given we can determine the fourth. The formulae for cubical expansion are entirely analogous to the preceding.. The following are examples of the application of these formute r — (i.) A metal bar has a length /' at t'° ; what will be its length / aX i°? From the above formula we first get the length of the given bar at zero, which is r > by means of the same formula we pass from zero to i'° in. multiplying by i + af, which gives for the desired length , /Xi+W (ii.) The density of a body being rfat zero, required its density if at ^°.. -320] Applications 305 If I be the \olume of the body at zero, and D its coefficient of cubical expansion, the \olume at t will be I + D/ ; and as the density of a body is in inverse ratio of the volume which the body assumes in expanding, we get the inverse proportion, rf' : rf= I : I + D/ '^' - ' ■ a- /I' - '^ 1 ~ i + D/ ' ' - r+ D? ■ Consequently, when a body is heated from o to /°, its density, and therefore its weight for an equal volume, are inversely as the expression i + "Qt. 320. Applications of the expansion of solids. — In the arts we meet with numerous examples of the influence of expansion, (i.) The bars of furnaces must not be fitted tightly at their extremities, but must, at least, be free at one end, otherwise in expanding they would split the masonry, (ii.) In making railways a small space is left between the successive rails, for, if they touched, the force of expansion would cause them to curve or would break the chairs, (iii.) Water-pipes are fitted to one another by means of telescope joints, which allow room for expansion, (iv.) If a glass vessel is heated or cooled too rapidly, it cracks, especially if it be thick ; this arises from the fact that, since glass is a bad conductor of heat, the sides become unequally heated, and consequently unequally expanded, which causes a fracture, (v.) The cracking off of a portion of a glass tube by red-hot charcoal is due to the expansion of the heated parts, which detach themselves from the rest. When bodies have been heated to a high temperature, the force pro- duced by their contraction on cooling is very considerable ; it is equal to the force which is needed to compress or expand the material to the same extent by mechanical means. According to Barlow, a bar of malleable iron a square inch in section is stretched xTrjTy?jth of its length by a weight of a ton ; the same increase is produced by a change of temperature of about 9° C. A difference of 45° C. between the cold of winter and the heat of summer is not infrequently experienced in this counti'y. In that range, a wrought- iron bar ten inches long will vary in length by jj^jth of an inch, and will exert a stress, if its ends are securely fastened, of fifty tons. It has been calculated from Joule's data that the work done by heat in expanding a pound of iron between 0° and 100°, during which it increases about ^J^jth of its bulk, is equal to 16,000 foot-pounds ; that is, it could raise a weight of about 7 tons through a height of one foot. An application of this contractile force is seen in the mode of securing tires on wheels. The tire being made red-hot, and thus considerably ex- panded, is placed on the circumference of the wheel and then cooled. The tire, when cold, embraces the wheel with such force as not only to secure itself on the rim but also to press home the joints of the spokes into' the felloes and nave. Another interesting application was made in the case of a gallery at the Conservatoire des Arts et Metiers in Paris, the walls of which had begun to bulge outwards. Iron bars were passed across the building and screwed into plates on the outside of the walls. Each alternate bar was then heated by means of lamps, and when the bar had expanded X 3o6 On Heat [320- it was screwed up. The bars, being then allowed to cool, contracted, and in so doing drew the walls together. The same operation was performed on the other bars. 321. Compensation pendulum. — An important application of the ex- jDansion of metals has been made in the compensation pendulum. This is a pendulum in which the elongation, when the temperature rises, is so compensated that the distance between the centre of suspension and the centre of oscillation (80) remains constant, a condition which, from the laws of the pen- dulum (81), is necessar)' for isochronous oscilla- tions, and in Order that the pendulum may be used as a regulator of clocks. In fig. 315, which represents the gridiron pendulum, one of the forms of compensation pendulum, the ball, L, instead of being sup- ported bj' a single rod, is supported by a frame- work, consisting of alternate rods of steel and brass. In the figure the shaded rods represent steel ; including a small steel rod, i5, which supports the whole of the apparatus, there are six of them. The other rods, four in num- ber, are of brass. The rod i, which supports the ball, is fixed at its upper end to a horizontal cross-piece ; at its lower end it is free, and passes through the two circular holes in the lower horizontal cross-pieces. Now, from the manner in which the vertical rods are fixed to the cross-pieces, it is easy to see that the elongation of the steel rods can only take place downward, and that of the brass rods upward. Consequently, in order that the pendulum may remain of the same length, it is necessary that the elongation of the brass rods shall tend to make the ball rise, by exactly the same quantity that the elongation of the steel rods tends to lower it ; a result which is attained when the effective length A of the steel rods is to the effective length B of the brass rods in the inverse ratio of the coefficients of expansion of steel and brass, a and b ; that is, when A : ^ = b : a. The elongation of the rod may also be compensated for by means of compensating strips. These consist of two blades of copper and iron soldered together and fixed to the pendulum rod, as represented in fig. 316. The copper blade, which is more expansible, is below the iron. When the temperature sinks, the pendulum rod becomes shorter, and the ball rises. But at the same time the compensating strips become curved, as seen in fig. 317, in consequence of the copper contracting more than the iron, and two metal balls at their ends become lower. If they have the proper size in reference to the pendulum ball, the parts which tend to approach the centre Tig 315 -321] Compensation Pendulum 307 of suspension compensate those which tend to remove from it, and the centre of oscillation is not displaced. If the temperature rises, the pendulum ball Fig. 316 Fig- 317 Fig. 318 descends ; but at the same time the small balls ascend, as shown in fig. 318, so that there is always compensation. One of the simplest compensating pendulums is ^e: mercury pendulum, invented by an English watchmaker, Graham. The ball of the pendu- lum, instead of being solid, consists of a glass cylinder, containing pure mercury, which is placed in a sort of stirrup, supported by a steel rod. When the temperature rises the rod and stirrup become longer, and thus lower the centre of gravity ; but at the same time the mercury expands, and rising in the cylinder, produces an inverse effect, and as mercuiy is much more expansible than steel, a compensation may be effected without making the mercurial vessel of undue dimensions. The same principle is applied in the compensating balances of chronometers (fig. 319). The motion here is regulated by a balance or wheel, furnished with a spiral spring not represented in the figure, and the time of the chronometer depends on the elasticity of the spring, the mass of the balance, and its moment of inertia, i.e. on the distribution of its mass with regard to the axis of oscillation. Now when the temperature rises the diameter increases, and the chronometer goes slower ; and, to prevent this, part of the mass must be brought nearer the axis. The circumference of the balance consists of compensating strips, BC, consisting of two different metals, of which the more expansible is on the outside ; and towards the ends of these are small masses of metal, D, which play the same part as the balls in the above case. When the radius is expanded by heat, the small masses are brought nearer the centre in consequence of the curvature of the strips ; and as the small masses can be fixed in any position, they are easily arranged so as to compensate for the expansion of the balance. It may, however, here be observed that the chief action of heat on chronometers is to expand and soften the spring, and thereby lessen its elasticity ; this action produces five times the effect on the rate that the expansion of the balance- wheel does. Fig- 319 X 2 308 On Heat [322- CH AFTER III EXPANSION OF LIQUIDS 322. Apparent and real expansion. — A hollow space enclosed by a solid expands as if it were wholly occupied by the solid ; for consider a section of a glass tube ; we may regard this as made up of a series of innumerable concentric circles ; when the tube is heated each of these glass circles becomes larger, and in doing so must press outwards, and these expansions are the same whether there is another circle within it or not ; the hollow space will become larger just as if it were a solid glass rod. This may be illustrated by the following experiment. If a flask of thin glass, provided with a narrow stem, the flask and part of the stem being filled with some coloured liquid, be immersed in hot water (fig. 320), the column of liquid in the stem at first sinks from b to a, but then immediately after rises, and continues to do so until the liquid inside has the same tem- perature as the hot water. The first sinking of the liquid is not due to its contraction ; it arises from the expansion of the glass, which becomes heated before the heat can reach the liquid ; but the expansion of the liquid soon exceeds that of the glass, and the liquid then rises. Hence in the case of liquids we must distinguish between the apparent and the real or absolute expansion. The apparent expansion is that which is actually observed when liquids contained in vessels are heated ; the abso- lute expansion is that which would be observed if the vessel did not expand ; or, as this is never the case, it is the apparent expansion corrected for the simultaneous expansion of the containing vessel. As has been already stated, in the case of liquids the cubical expansion is alone considered ; and, as in the case of solids, the coefficient of expansion of a liquid is the increase of the unit of volume for a rise of temperature one degree ; but a distinction is here made between the coefficient of absolute expansion and the coefficient of apparent expansion. Of the many methods which have been employed for determining these two coefficients, we shall describe that of Dulong and Petit. Fig. 320 -323] Absolute Expansion of Mercury 309 323. Coefficient of absolute expansion of mercury. — In order to determine the coefficient of the absolute expansion of mercury, the influence of the envelope must be eliminated. Dulong and Petit's method depends on the hydrostatical principle that in two communicating vessels the heights of two columns of liquid in equilibrium are inversely as their densities (106), a principle independent of the diameters of the vessels, and therefore of their expansions. The apparatus consists of two glass tubes, A and B (fig. 321), joined by a narrow tube and kept vertical on an iron support, KM, the horizontality of which is adjusted by means of two levelling screws and two spirit levels, m and n. Each of the tubes is surrounded by a metal case, of which the smaller, D, is filled with ice ; the other, E, containing oil, can be heated by 't |p.J ? | Jlli Fig. 321 the furnace, which is represented in section so as to show the case. Mercury is poured into the tubes A and B ; it remains at the same level in both as long as they are at the same temperature, but rises in B in proportion as the temperature rises. The diameter of the horizontal tube is small enough to prevent any mixture of the hot and cold mercury, but freely allows hydro- static pressure to be transmitted through it. Let h and d be the height and density of the mercury in the leg A, at the temperature zero, and h' and d' the same quantities in the leg B, both heights being measured from the axis of the horizontal capillary tube. From the hydrostatic principle previously cited we have hd=hd'. But from the problem in article 319, d' = i + D/' D being the coefficient of absolute expansion of mercury ; substituting this value of d' in the equation, we have h'd i + Di' = hd, from which \\e get D = — ht 310 On Heat [323- The coefficient of absolute expansion of mercuiy is obtained from this formula, when we know the heights h' and /z, and the temperature / of the bath in which the tube B is immersed. In Dulong and Petifs experiment this tempr.ature was measured by a weight thermometer, P (325), the mercury of which overflowed into the basin, C, and by means of an air thermometer, T (336) ; the heights h' and h were measured by a catheto- meter (87). Dulong and Petit found by this method that the mean coefficient of absolute expansion of mercury between 0° and loo' C. is "0001802, but that it increases with the temperature. Between 100° and 200° it is "0001844, and between 200° and 300' it is "0001887. The same observation has been made in reference to other liquids, showing that their expansion is not regular. It has been found that this expansion is less regular in proportion as liquids are near a change in their state of aggregation ; that is, approach their freezing or boiling points. Dulong and Petit found that the expansion of mercury between —36° and 100° is practically quite uniform. Regnault repeated the experiments of Dulong and Petit with improved apparatus based on the same principle, and found that the mean coefficient between 0° and 100° is "0001815, between 100° and 200°, "0001861, and between 200° and 300°, -0001917. 324. Coefficient of the apparent expansion of mercury. — The coefficient of apparent expansion of a liquid varies with the nature of the envelope. That of mercury in glass has been nr rii.Ji^ determined by means of the appa- ratus represented in fig. 322. It consists of a glass cylinder to which is joined a bent capillary glass tube, open at the end. The apparatus is weighed first p;g_ ,2^ empty, and then when filled with mercury at zero : the difference gives the weight of the mercury, P. It is then raised to a known tempera- ture, / ; the mercury expands, and a certain quantity passes out, which is received in the capsule and weighed. If the weight of this mercury be p, that of the mercury remaining in the apparatus will be P —p. When the temperature is again zero, the mercury in cooling produces an empty space in the vessel, which represents the contraction of the weight of mercury P -p, from t° to zero, or, what is the same thing, the expansion of the same weight from o to /° ; that is, the weight p represents the expansion of the weight P -/, for f. If this weight expands in glass by a quantity p for /°, a single unit of weight would expand - i- for f, and (P-/) (■p r^ ^°'' ^ ^'"S'^ degree ; consequently, since the weight of a substance at 0° is proportional to its volume, the coefficient of apparent expansion of mercury in glass, D', = j^--p-. Dulong and Petit found the coefficient of (V -p)t apparent expansion of mercury in glass to be "0001543. -327] Coefficients of Expansion of Various Liquids 311 325. Weight thermometer. — The apparatus represented in fig. 322 is called the weight thermometer, because the temperature can be deduced from the weight of mercury which overflows. The above experiments have placed the coefficient of apparent expansion at •0001543 ; we have therefore the equation -.^—^ = '0001543, a formula which gives the temperature t when the weights P and/ are known. 326. Coefficient of the expansion of glass. — As the absolute expansion of a liquid is the apparent expansion, plus the expansion due to the envelope, the coefficient of the cubical expansion of glass is obtained by taking the difference between the coefficient of absolute expansion of mercury and that of its apparent expansion in glass. That is, the coefficient of cubical expan- sion of glass is ■0001815 - -0001543 = -0000272. Regnault found that the coefficient of expansion varies with different kinds of glass, and further with the shape of the vessel. 327. Coefficients of expansion of various liquids. ^The coefficient of apparent expansion of liquids may be determined by means of an application of the principle of the weight thermometer, and the absolute expansion is obtained by adding to this coefficient the expansion of the glass. Mean coefficients of absolute expansion of liquids for 1° C. Ether . . 0-00015 Mercury . . . o-oooi8 Water saturated with salt . . 0-00050 Sulphuric acid . 0-00063 Bisulphide of carbon', o-ooi 14 Fixed oils . 0-00080 Benzole . . 0-00125 Oil of turpentine . 0-00090 The numbers here given only hold for moderate temperatures. The co- efficient of expansion of almost all liquids increases gradually from zero, and can only be expressed with accuracy by a somewhat complicated formula, in which / is the temperature, and a, 0, and y are constants specially deter- mined for each liquid. The expansion of mercury is practically constant between - 36° and 100° C, while water contracts from zero to 4° (331), and then expands. For many physical experiments a knowledge of the exact expansion of water is of great importance. This physical constant was carefully deter- mined by Matthiessen, who found that between 4° and 30° it may be expressed by the formula Vt = I -0-00000253(2' -4) +0-0000008389(^-4)2 +0-00000007 1 73(/- 4)= ; and between 30" and 100° by ¥1 = 0-999695 + 0-0000054724/^ + 0-00000001126^'. Many liquids, with low boiling points, especially condensed gases, have very Alcohol . 0-00104 Bromine . . 0-00104 Nitric acid . o-ooiio Chloroform . o-ooui 312 On Heat [327- high coefficients of expansion. Thilorier found that liquid carbonic acid expands four times as much as air. Drion confirmed this observation, and has obtained analogous results with chloride of ethyl, liquid sulphurous acid, and liquid hyponitrous acid. 328. Correction of the barometric height — If, while atrfiospheric pressure remains constant, the temperature rises, the barometer will rise, since a longer column of the less dense mercury will be required to balance the given pressure. To render the indications of this instrument comparable in different places and at different times, they must be reduced to a uniform temperature, which is that of melting ice. The correction is made in the following manner : — Let H be the observed barometric height at P, and h its height at zero, d the density of mercury at zero, and d' its density at t^. The heights H and /; h d' are inversely as the densities (f and d' ; that is, ^^ =-=-. If we consider unit H d volume of mercury at zero, its volume at t° will be i + D/, D iDeing the co- efficient of absolute expansion of mercury. But these volumes, i + D^ and i, are inversely as the densities d and d' ; that is, ^ = — -- . Consequently If -r fj = ^— -, whence h= ^„ . Replacing D by its value, -oooiSi, we have H i + Dr i+D/ /;= -— n— = H(i- -000181/). I +•000181/ In this calculation, the coefficient of absolute expansion of mercury is taken, and not that of apparent expansion ; for the value H is the same as if the glass did not expand, the barometric height being independent of the diameter of the tube, and therefore of its expansion. If the barometric height is read off on a brass scale whose graduations are correct at 0° C, and which has a point attached to its lower end in contact with the mercury in the cistern, the reading at t° will be too low, and to obtain the correct reading at 0° the observed height must be multi- plied by I + -0000187/, since -0000187 is the coefficient of linear expansion of brass. Hence, finally /^ = H(i + -0000187/) (i --oooi8i/)==H(i- -000162/), since the term in t'^ may be neglected. 329. Correction of thermometric readings. — If the whole column of mercury of a thermometer is not immersed in the space whose temperature is to be determined, it is necessary to make a correction, which in the accurate determination of boiling points, for instance, is of great impor- tance, in order to arrive at the true temperature which the thermometer should show. That part of the stem which projects will have a tempera- ture which must be estimated, and which may roughly be taken as some- thing over that of the surrounding air. Suppose, for instance, that the actual reading is 160° and that the whole of the part over 80° is outside the \ essel, while the temperature of the surround- ing air is 15°- We will assume that the mean temperature of the stem is 25°, and that a length of i6o°-8o° is to be heated through 160-25 = 135° ; this -331] Maximum Density of Water 313 gives 80 X 135 X -000154= 1-66 (taking the coefficient of apparent expansion of mercury) ; so that the true reading is 161 •66. 330. Force exerted by liquids in expanding. — The force which liquids exert in expanding is very great, and equal to that which would be required in order to bring the expanded liquid back to its original volume. Now we know what an enormous force is required to compress a liquid to even a very small extent (96). Thus between 0° and 10°, mercury expands by 0-0017790 of its volume at 0° ; its compressibility is 0-00000295 for one atmosphere ; hence a pressure of more than 600 atmospheres would be requisite to prevent mercury expanding when it is heated from 0° to 10°. In like manner a pressure of 140 atmospheres would be required to prevent water from expanding when its temperature was raised from 4° to 14°. 33 1 . Maximum density of -water. — Water presents the remarkable pheno- menon that when its temperature sinks it contracts down to 4° ; but from that point, although the cooling continues, it expands to the freezing point, so that 4° represents the point of greatest contraction of water. Many methods have been used to determine the temperature of the maxi- mum density of water. Hope made the following experiment : — He took a deep vessel with two apertures in the sides, in which he fixed thermometers, and having filled the vessel with water at 0°, he placed it in a room at a tem- perature of 15°- As the layers of liquid at the sides of the vessel became heated they sank to the bottom, and the lower thermometer marked 4° while the upper one was still at zero. Hope then made the inverse experiment ; having filled the vessel with water at 15°, he placed it in a room at zero. The lower thermometer having sunk to 4° remained stationary for some time, while the upper one cooled down until it reached zero. Both these experiments prove that water is heavier at 4° than at 0°, for in Ijoth cases the water at 4° sinks to the lower part of the vessel. This last experiment may be adapted for lecture illustration by using a cylin- der containing water at 15° C, partially surrounded by a jacket containing bruised ice (fig. 323). Hallstrom made a determination of the maximum density of water in the following manner : — He took a glass bulb, loaded with sand, and weighed it in water of different temperatures. Allow- ing for the expansion of glass, he found that 4-1° was the temperature at which it lost most weight, and consequently this was the temperature of the maximum density of water. Despretz arrived at the temperature 4° by another method. He took a water thermometer' — that is to say, a bulbed tube containing water — and, placing it in a bath, the temperature of which was ndicated by an ordinary Fig- 323 314 On Heat [331- mercury thermometer, found that, making due allowance for the change ot volume of the glass bulb, the water contracted to the greatest extent at 4°, and that this therefore is the point of greatest density. This phenomenon is of great importance in the economy of nature. In winter the temperature of lakes and rivers falls, from being in contact with the cold air and from other causes, such as radiation. The cold water sinks to the bottom, and a continual series of currents goes on until the whole has a temperature of 4° The cooling on the surface still continues, but the cooled layers, being lighter than those below, remain on the surface, and ultimately freeze. The ice formed thus protects the water below, the lower portions of which remain at a temperature of 4°, even in the most severe winters, a temperature at which fish and other inhabitants of the water are not destroyed. Salt dissolved in water lowers the temperature of the maximum density, and sea water exhibits a maximum. According to Rosetti, this temperature is between 3-2° and 3-9° in the Adriatic. The following table of the density of pure water at various temperatures is based on several sets of observations : — Density of water between 0° and 80°. Tempe- ratures Densities Tempe- ratures Densities Tempe- ratures Densities 0-99988 12 0-99955 24 0-99738 I 0-99993 13 0-99943 25 0-99714 2 0-99997 14 0-99930 26 0-99689 3 0-99999 IS 0-99915 27 0-99662 4 I -ooooo 16 0-99900 28 0-99635 5 0-99999 17 0-99884 29 0-99607 6 0-99997 18 0-99870 30 0-99579 7 0-99994 19 0-99847 40 0-99226 8 0-99988 20 0-99827 50 0-98820 9 0-99982 21 0-99806 60 0-98232 10 0-99974 22 0-99785 70 0-97796 II 0-99965 23 0-99762 80 0-97191 Thus the mean expansion of water per degree between 0° and 80° is -000376, or a little more than twice that of mercury. -332] Problems on the Expansion of Gases 315 CHAPTER IV EXPANSION AND DENSITY OF GASES 332. Gay-Lussac's method. — The volume of a gas may be altered by change of pressure as well as by change of temperature. The relation between pressure and volume when the temperature is constant — known as Boyle's law — has been already considered. In investigating the relation between volume and temperature, care must be taken to maintain the pressure constant. The coefficient of expansion of a gas is the amount by which the unit of volume at 0° expands when its temperature is raised to 1°, the pressure being kept constant. Thus, if 7/„ = the volume at 0°, t/ts volume at t°, and a =the mean coefficient of expansion between 0° and /°, t/, = 7/o(l+a/). It is immaterial what the pressure is so long as it does not vary. This relation was discovered by Charles, and afterwards independently by Gay-Lussac and Dalton. It is generally referred to as the law of Charles. The two laws — those of Boyle and Charles — are known as the gaseous laws. Gay-Lussac determined the coefficient of the expansion of gases by means of the apparatus represented in fig. 324. In a rectangular metal bath, about 16 inches long, was fitted an air thermometer, which consisted of a capillary tube, AB, with a bulb, A, at one end. The tube ,,., .,-,-, was divided into ( ( • ■ 'r -^-^ j iCiv; -^ ^>'»■^ parts of equal ~^^^^ \ .^ -^ capacity, and the ~ "^ ■" ' ' contents of the bulb ascertained in terms of these parts. This was effected by weigh- ing the bulb and tube full of mer- ; cury at zero, and then heating slightly to expel a small quantity of mercury, which was weighed. The apparatus being again cooled down to zero, the vacant space in the tube corresponded to the weight of mercury Fig. 3i6 On Heat [332- which had overflowed ; the volume of mercury remaining in the apparatus, and consequently the volume of the bulb, was determined by calculations analogous to those made for the piezometer (96). In order to fill the thermometer with dry air it was first filled with mercury, which was boiled in the bulb itself. A tube, C, filled with calcium chloride, was then fixed on to its end by means of a cork. A fine platinum wire having then been introduced into the stem AB through the tube C, and the apparatus being slightly inclined and agitated from time to time, air entered, havmg been previously well dried by passing through the calcium chloride tube. The whole of the mercury was displaced, with the exception of a small thread, which remained in the tube AB as an index. The air thermometer was then placed in the box filled with melting ice, the index moved towards A, and the point was noted at which it became stationary. This gave the volume of air at zero, since the capacity of the bulb was known. Water or oil was then substituted for the ice, and the bath successively heated to different temperatures. The air expanded and moved the index from A towards B. The position of the index in each case was noted, and the corresponding temperature was indicated by means of the thermometers D and E. The pressure of the atmosphere was practically constant during the experiment, and, the expansion of the glass being neglected, the expan- sion of the air was obtained by subtracting from its volume at a given temperature its volume at 0°. From this the coefficient of expansion is deduced. The results obtained by Gay-Lussac in these experiments were not very exact. The coefficients of|expansion of different gases are given on p. 320. 333. Combination of formulse of Boyle and Charles. — Let /j, Wj be the pressure and volume of a given quantity of gas at temperature /, ; p^, v^ the pressure and volume at t„. Also, let w be the volume when the temperature is /j and the pressure pr^. Then, by Boyle's law, p^v^ =A^> since the temperature /, is constant ; and by Charles's law, ? — = - , since the pressure p„ is constant. Hence, eliminating w, ■^'^' = -X?!jl ; or, gene- I + a/j I + at^ rally, for a given weight of gas — — is constant, whatever changes take 1 + at place in^, v, or t. Examples. — i. The volume of a gas at t°, and under the pressure H, is V : what will be the volume V of the same gas at zero, and under the normal pressure 760 millimetres ? VT-T From the above formula it follows at once that V = ( I + a/) 760 ii. A volume of gas weighs P' at /° : what will be the weight of an equal V olume at zero, the pressure being constant .'' Let P be the desired weight, a the coefficient of expansion of the gas, d' its density at 1°, and d its density at zero. As the weights of equal -334] Reenaulfs Methods 317 volumes are proportional to the densities, we have volume of a gas at zero, its volume at t will be i + at are inversely as the volumes, — = , If I be the P d' but as the densities P' I and therefore -- = P \-\-at vhence :P'(l+a/). 334. Re^nault's methods.- -Regnault used several different methods for determining the expansion of gases. In some of them the pressure was constant and the volume variable, as in Gay-Lussac's method ; in others the volume remained the same while the pressure varied. The method described below is the same as that used by Rudberg and Dulong, but is distinguished by the care with which all sources of error are avoided. In this method both the pressure and the volume of the gas varied. The apparatus consisted of a cylindrical reservoir, B (fig. 325), termi- nating in a bent capillary tube. In order to fill the reservoir with dry air, it was placed in a hot-water bath, and the capillary tube connected by an India rubber tube with a series of drying tubes. These tubes were joined to a small air-pump, P, by which a fairly good vacuum could be pro- duced in the reservoir while at a temperature of 100°. The reservoir was first exhausted, and air afterwards admitted slowly; this. operation was repeated a great many times, so that the air in the r servoir became quite dr)', for the moisture adhering to the sides passed off in vapour at 100', and the air which entered became dry' in its passage through the U tubes. The reservoir was then kept for half an hour at the temperature of boil- ing water ; the air-pump having been detached, the drying tubes were then disconnected, and the end of the tube hermetically sealed, the height H of the barometer being noted. When the reservoir B was cool, it was placed in the apparatus represented in fig. 326. It was there quite surrounded with ice, and the end of the tube .dipped in the mercury bath, C. After the 3i8 On Heat [334- air in the reservoir B had sunk to zero, the point b was broken off by means of a pair of forceps ; the air in the interior became condensed by atmospheric pressure, the mercury rising to a height oG. In order to measure the height of this column, Q,o, which will be called h, a movable rod, go, was lowered until its point, o, was flush with the surface of the mercury in the bath ; the distance between the point o and the level of the mercury G was measured by means of the cathetometer. The point b was finally closed with wax by means of the spoon a, and the baro- metric pressure noted at this moment. If this pressure be H', the pressure of the air in B is H'->%. The reservoir was now weighed to ascer- tain P, the weight of the mercury which it contained. It was then completely filled with mercury at zero, in order to have the weight P' of the mercury in the reservoir and in the tube. If 8 be the coefficient of the cubical expan- sion of glass, and D the density of mercury at zero, the coefficient a of the cubical expansion of air is determined in the following manner : — The volume of the reservoir and of the tube at F!g. 326 zero is — , from the formula P = VD ; consequently this volume is D (i+S/) (0 at the temperature t°, assuming, as is the case, that the reservoir and tube expand as if they were solid glass (322). But from the formula P = VD, the volume of air in the reservoir at zero, and under the pressure H'— ^, is P' — P At the same pressure, but at t", its volume would be D P'-P D (i + aO; and by Boyle's law (181), at the pressure H, at which the tube was sealed, this volume must have been (P'-P)(i + aO(H'-/^) DH (2) Now the volumes represented by these formulae (i) and (2) are each equal to the volume of the reservoir and the tube at t° : they are therefore equal. Removing the denominators, we have P'(l+8/) H = (P'-P)(l+a/)(H'-/i) from which the value of a is deduced. (3) -335] Regnaulfs Methods 319 335. Regnaulfs methods {cotitiniied). — In the method described above, both the voUime and pressure of the gas were altered when the temperature changed. By other methods, which will now be described, Regnault deter- mined (l) the relation between temperature and volume when the pressure was kept constant, and (2) the relation between temperature and pressure when the volume was kept constant. Constant pressure. — In fig. 327 C is the bulb containing the gas ; it is con- nected with the manometer AB by a fine tube, F. G is a reservoir of mercury connected to the lower part of the manometer by flexible tubing ; as it is raised or lowered the height of the mercury in the limbs of the mano- meter is altered. A lateral tube, D, provided with stopcock and attached to F, allows the bulb to be put in communication with an exhausting pump, and with the gas whose co- efficient of expansion is required. The bulb C is placed in an enclosure whose temperature can be maintained at any point from 0° to 100°. First let the enclosure be filled with melting ice, and, the vessel C and tube F now containing dry gas, the surfaces of the mercury in A, B, G are adjusted to the same level. The temperature is then raised to /°, the gas expands, and the mercury tends to fall in A and rise in B and G ; but the surfaces are brought to the same level by lowering G, so as to maintain the pressure constant and equal to that of the atmosphere. The tubes F and '^'s- 327 A have been previously calibrated, so that their capacities per millimetre of length are known in terms of the capacity of the bulb C. Thus the increase of volume is measured corresponding to a given rise of temperature at constant pressure, and the coefficient of expansion is obtained from the equation •z/, = Va{i-^ at). Constant volume, — The same figure may be used to illustrate Regnault's method of determining the coefficient of increase of pressure of a gas due to change of temperature when the volume is kept constant. This coefficient is sometimes called the coefficient of expansion at constant volume. A mark is made on the tube A at S, and the mercury adjusted to S when the pressure is atmospheric and the temperature 0°. When the temperature in the bulb C rises the gas expands, but depression of the mercury in A is pre- vented by raising the reservoir G, and thus increasing the pressure to which the gas in the bulb is subjected. G is raised until the mercury in A is brought back to the mark S, and the pressure of the gas is then that due to the difference in heights in the tubes A and B, together with that of the 320 On Heat [335- atmosphere. The process is repeated with gradually rising temperatures, and a series of corresponding values of p and t obtained. The coefficient required is derived from the equation /t=/(i+a7). The following table gives both coefficients for different gases : — Coefficients of expansion of gases. Hydrogen Atmosphere-air Nitrogen Carbon monoxide „ dioxide Nitrogen monoxide . Sulphur dioxide Cyanogen Pressure Constant Volume Constant ■003661 ■003667 ■003670 •003665 — •003668 ■003669 ■003667 ■003710 •003688 ■003719 •003676 •003903 •00384s •003877 •003829 It appears from the above table that hydrogen differs from the other gases enumerated in that a is greater than a for it, while for all the rest a is the greater. We have already seen that at ordinary temperatures, -and for moderate pressure, hydrogen differs from other gases in being less com- pressible than Boyle's law requires. Regnault has further found that, at the same temperature, the coefficient of expansion of any gas increases with the pressure which it supports. Thus, while the coefficient of expansion of air under a pressure of no mm. is o'o03648, under a pressure of 3655 mm., or nearly five atmospheres, it is 0-003709. The number found by Regnault for the coefficient of the expansion of air, 0-003667, is equal to _1_ = jVh nearly ; and if we take the coefficient of expansion at 0-0036666 ... it may be represented by the fraction 3 J-J-g, which is convenient for many purposes of calculation. The small differences in the expansibility of various gases may be ascribed to the circumstance that when a gas is heated the relative positions of the atoms in the molecules are thereby altered ; and a certain amount of internal work is required for this, which is different for different gases (294). The researches of Amagat prove that at constant pressure the coefficients of expansion diminish as the temperature rises. For example, for sul- phurous acid the coefficient between 10° and 60° C. is •003903, iDut between 10° and 250° becomes •003798. The change with temperature is much less in the case of gases that are not readily liquefiable. 336. Air thermometer. — When the laws of the expansion of air are known the apparatus of fig. 327 may be used as an air thermometer, either for detei-mining directly the temperature of an enclosure or for standardising mercury thermometers and various kinds of pyrometers. Regnault found that the air and the mercury thermometer agree up to 260°, but above -338] Density of Gases 321 that point mercury expands relatively more than air. In cases where very high temperatures are to be measured, the reservoir is made of platinum. The use of an air thermometer is seen in Dulong and Petit's experiment (323) ; it was by such an apparatus that Pouillet measured the temperature corresponding to the colours which metals take when heated in a fire, and found them to be as follows : — Incipient red 525° C. Dark orange . . 1 100° C. Dull red . 700 White . • 1300 Cherry red 900 Dazzling white . 1500 In the measurement of high temperatures Deville and Troost used with advantage the vapour of iodine instead of air, and, as platinum has been found to be permeable to gases at high temperatures, they employed porce- lain instead of that metal. •5^7. Absolute zero. — If we substitute ^i, for a in the formula -£- — = ■'-" ' " I + at constant, we may write S- = constant. Hence, if temperatures are 273 + ^ measured from a point 273 degrees Centigrade belowjthe freezing point of water, we may call this latter temperature the absolute zero, and tempera- tures measured from it absolute temperatures. Thus, the absolute tempera- ture of the freezing point of water will be 273° C, and that of the boiling point of water 373° C. If temperatures measured from the absolute zero be denoted by T, the formula above becomes /w/T = constant, or pv = kT, where ^ is a constant depending on the nature and quantity of the gas. A gas for which the formula pv = kT would hold is an ideal perfect gas. The formula involves the assumption that the particles of the gas are mere points having no extension in space, and also that there are no inter- molecular forces. For the more permanent gases, nevertheless, the law expressed by the formula is very nearly true (182). 338. Density of gases. — The relative density of a gas, or its specific gravity, is the ratio of the weight of a certain volume of the gas to that of the same volume of air ; both the gas and the air being at zero and under a pressure of 760 millimetres. In order, therefore, to find the specific gravity of a gas, it is necessary to determine the weight of a certain volume of this gas at a pressure of 760 millimetres, and a temperature of zero, and then the weight of the same volume of air under the same conditions. For this purpose a large globe of about two gallons capacity is used, the neck of which is provided with a stopcock, which can be screwed to the air-pump. The globe is first weighed empty, and then full of air, and afterwards full of the gas in question. The weights of the gas and of the air are obtained by subtracting the weight of the exhausted globe from the weight of the globe filled, respectively, with air and gas. The quotient, obtained by dividing the latter by the former, gives the specific gravity of the gas. It is difficult to make these determina- tions at the same temperature and pressure, and therefore all the weights are reduced to zero and the normal pressure of 760 millimetres. The gases are dried by causing them to pass through drying tubes before they enter the globe, and air must also be passed over potash to free it from Y 322 On Heat [338- carbonic acid. And as even the best air-pumps never produce a perfect vacuum, it is necessary to exhaust the globe until the manometer in each case marks the same pressure. The globe having been exhausted, dried air is allowed to enter, and the process is repeated several times until the globe is perfectly dried. It is then finally exhausted until the residual pressure in millimetres is e. The weight of the exhausted globe is p. Air, which has been dried and purified by passing through potash and calcium chloride tubes, is then allowed to enter slowly. The weight of the globe full of air is P. If H is the barometric height in millimetres, and t° the temperature at the time of weighing, P —p is the weight of the air in the globe at the temperature ^, and the pressure H — f. To reduce this weight to the pressure 760 millimetres and the tempera- ture zero, let a be the coefficient of the expansion of air, and S the coefficient of the cubical expansion of glass. From Boyle's law the weight, which is P —p at t° and a pressure of H — e, would be ^ — ri^^-^ — under the pressure 760 millimetres and at the same temperature, t°. If the temperature is 0°, the capacity of the globe will diminish in the ratio i + 8/ to i, while the weight of the gas increases in the ratio i : i + a^, as follows from the problems in article 333. Consequently, the weight of the air in the globe at 0° and at the pressure 760 millimetres will be (P-/)- 760(1+00 _ _ ,,. ^ -^-^(H-^) (I -1-80 Further, let a be the coefficient of expansion of the gas in question ; let P' be the weight of the globe full of gas at the temperature t' and the pres- sure H', and let/' be the weight of the globe when it is exhausted to the pressure e ; the weight of the gas in the globe at the pressure 760 and the temperature zero will be fp'_-A') 76o(i + aV') /v ^ ^^H'-^)(i+80 ■ • ■ ^' Dividing the latter formula by the former we obtain the density ^ ( P'-/')(H-g)(l+ar)(l+8/ ) (P -/) (H' -«) (I -h 02') (i-H S/') ■ If the temperature and the pressure do not vary during the experiment, H = H' and / = /" ; whence D = .(|p^Kl±iL^, and, if a = a', D = %^. {P-p){l +ai) V-p 339. Regnault's method of determining the density of gases. — -Regnault so modified the above method that many of the corrections may be dispensed with. The globe in which the gas is weighed is suspended from one pan of a balance, and is counterpoised by means of a second globe of the same dimensions, and hermetically sealed, suspended from the other. These two globes, expanding at the same time, always displace the same quantity of air, and consequently variations in the temperature and pressure of the atmo- sphere do not influence the weighing. The globe, too, is filled with air or with the gas, at the temperature of zero. This is effected by placing it in a -339] Method of Determining the Density of Gases 323 vessel full of ice, as shown in fig. 328. It is then connected with a three-way cock, A, by which it may be put into communication either with an air-pump, or with the tubes M and N, which are connected with the reservoir of gas. The tubes M and N contain substances which by their action on the gas dry and also purify it. The stopcock A being so turned that the globe is only connected with the air-pump, a vacuum is produced ; by means of the same cock, the con- nection with the pump being cut off, but established with M and N, the gas soon fills the globe. But, as the exhaustion could not have been com- plete, and some air must have been left, the globe is again exhausted and the gas allowed to enter, and the process is repeated until it is thought that Fig. 328 all air is removed. The vacuum being once more produced, a differential barometer (fig. 158), connected with the apparatus by the tube E, indicates the pressure e of the residual rarefied gas. When the cock B is closed and detached, the globe is removed from the ice, and after being cleaned is weighed. This gives the weighty of the empty globe ; the globe is again replaced in the ice, the stopcock A adjusted, and the gas allowed to enter, care being taken to leave the stopcocks open long enough to allow the gas in the globe to acquire the pressure of the atmosphere, H, which is marked by the baro- meter. The stopcock A is then closed, A removed, and the globe weighed with the same precautions as before. This gives the weight P' of the gas and globe. The same operations are then repeated on this globe with air, and two corresponding weights^ and P are obtained. The only correction necessary is to reduce the weights in the two cases to the standard pressure by the Y 2 324 On Heat [339- method described in the preceding paragraph. The correction for temperature is not needed, as the gas is at the temperature of melting ice. The ratio of the weight of the gas to that of the air is thus obtained by the formula D 340. Density of gases which attack metals. — For gases which attack the ordinary metals, such as chlorine, a metal stopcock cannot be used, and vessels A\ith ground-glass stoppers (fig. 329) are substituted. The gas is introduced by a bent glass tube, the vessel being held either upright or inverted, according as the gas is heavier or lighter than air ; when the vessel is supposed to be full, the tube is withdrawn, the stopper inserted, and the weight taken. This gives the weight of the vessel and gas. If the capacity of the vessel be measured by means of water, the weight of the air which it contains is deduced, for the density of air at 0° C. and 760 millimetres pressure is -^^-^ that of distilled water under the same circumstances. The weight of the vessel full of air, less the weight of the contained air, gives the weight of the vessel itself From these three data — ^the weight of the vessel full of the gas, the weight of the air which it contains, and the weight of the vessel alone — the specific gravity of the gas is readily deduced, the necessary corrections being made for temperature and pressure. Relative de?tsity of gases at zero and at a pressure of y6o millimetres, that of air being taken as unity. Fig. 329 Air I -0000 Sulphuretted hydrogen 1-1912 Hydrogen . 0-0693 Hydrochloric acid 1-2540 Ammoniacal gas . 0-5367 Protoxide of nitrogen . 1-5270 Marsh gas . 0-5590 Carbonic acid 1-5291 Carbonic oxide 0-9670 Cyanogen . 1-8600 Nitrogen 0-9714 Sulphurous acid . 3-2474 Binoxide of nitrogen I -0360 Chlorine 3-4400 Oxygen 1-1057 Hydriodic acid 4-4430 Regnault made the following determinations of the weight of a litre of the most important gases at 0° C. and 760 mm. : — Air . 1-293187 grms. Nitrogen . 1-256157 grms. Oxygen . 1-429802 „ Carbonic acid 1-977414 „ Hydrogen . 0-089578 , —341] Fusion. Its Laws 325 CHAPTER V CHANGES OF CONDITION. VAPOUR 341. Fusion. Its laws. — The only phenomena of heat with which we have hitherto been engaged have been those of expansion. In the case of soHds it is easy to see that this expansion is hmited. For in proportion as a body absorbs heat, the kinetic energy of the molecules is increased, and ultimately a point is reached at which the molecular attraction is not sufficient to retain the body in the solid state. A new phenomenon is then produced ; melting or fusion takes place ; that is, the body passes from the solid into the liquid state. Some substances, however, such as paper, wood, wool, and certain salts, do not fuse at a high temperature, but are decomposed. Many bodies have long been considered refractory — that is, incapable of fusion ; but, in pro- portion as it has been possible to produce higher temperatures, their number has diminished. Gaudin succeeded in fusing rock crystal by means of a lamp fed by a jet of oxygen ; and Despretz, by combining the effects of the sun, the voltaic battery, and the oxy-hydrogen blowpipe, melted alumina and magnesia, and softened carbon so as to be flexible, which is a condition near that of fusion. It has been found experimentally that the fusion of bodies is governed by the two following" laws : — ■ I. Every substance begins to fuse at a certain temperature, which is invariable for each substance, if the pressure be constant. II. Whatever be the intensity of the source of heat froin the moment fusion begins, the temperature of the body ceases to rise, and remains constant until the fusion is com-plete. Melting points of certain substances. Ethylene . -169° Butter • + 33' Alcohol . .-130-5 Rubidium . 39 Ether -129 Phosphorus 44 Ammonia . ■- 75 Spermaceti 49 Mercury . - 38-8 Potassium 55 Oil of turpentine - 27 Margaric acid 57 Bromine . - 12- Stearine 60 Ice . White wax . 65 Nitrobenzene . ■ + 3-0 Wood's fusible metal . 68 Formic iacid 8-5 Stearic acid • 70 Acetic acid 17 Sodium 90 326 6 On Heat [34 Rose's fusible metal . + 94° Aluminium ■ 655° Sulphur . . 114 Magnesium ■ 750 Benzoic acid I20 Sodium chloride . 851 Indium 176 Silver 955 Tin . 232 Gold 1060 Bismuth . 269 Copper 1068 Cadmium . . 321 Potassium sulphate • 1073 Lead 328 Cast iron . . IIOO Zinc . • 419 Mild steel . • 1300 Antimony 450 Wrought iron . . 1600 Arsenic . . 500 Platinum . • 1775 Potassium iodide . 623 Iridium . ■ 1950 Some substances pass from the solid to the liquid state without showing any definite melting point ; for example, glass and iron become gradually softer and softer when heated, and pass by imperceptible stages from the solid to the liquid condition. This inter- mediate condition is spoken of as the state of vitreous fusion. Such substances may be said to melt at the lowest temperature at which perceptible softening occurs, and to be fully melted when the further elevation of temperature does not make them more fluid ; but no precise temperature can be given as that of their melting points. The determination of the melting point of a body is a matter of considerable im- portance in fixing the identity of many chemical compounds, and is moreover of fre- quent practical application in determining the commercial value of tallow and other fats. It is done as follows : — A portion of the substance is melted in a watch-glass, and a small quantity of it sucked into a fine capil- lary tube, which is then placed in a bath of clear water (fig. 330) attached to a ther- mometer, and the temperature of the bath is gradually raised until the .substance is completely melted, which from its small mass is very easily observed. The bath is then allowed to cool, and the solidify- ing point noted ; and the mean of the two is taken as the true melting point. 342. Influence of pressure on the melting point. — It follows from the principles of the mechanical theory of heat that, with an increase of pressure, the melting point of a body must be raised or lowered according as the substance expands or contracts in passing from the solid into the liquid state. Bunsen examined the influence of pressure on the melting point by means of the apparatus represented in fig. 331, somewhat resembling in appearance a siphon barometer. The tube is closed at both ends. The Fig. 330 -342] Influence of Pressure on the Melting Point 327 part from b\a c contains mercury except at the end b, where the substance under examination is put. Air occupies the portion ac, which is carefully calibrated. The lower part of the apparatus is placed in a water bath, the mercury being heated as well as the substance. The expansion of the mercury compresses the air, the elastic force of which reacts on the sub- stance and exerts on it a gradually increasing pressure. It only then remains to observe the temperature at which the substance solidifies, and the corresponding pressure at that moment. In this way Bunsen found that spermaceti, which melts at 48° under a pressure of i atmosphere, melts at 5 1 • under a pressure of 1 56 atmospheres. Hopkins found that spermaceti Fig. 331 Fig. 332 melted at 60° under a pressure of 519 atmospheres and at 80° under 792 atmospheres ; the melting point of sulphur | under these pressures was respectively 135° and 141°. Ice is a substance which contracts on melting ; hence, according to the theory, the effect of increased pressure should be to cause ice to melt at a lower temperature than 0° C. For the purpose of determining experiment- ally the relation between pressure and the temperature of fusion of ice. Lord Kelvin made use of the apparatus shown in fig. 332. It consists of a piezo- meter which, by means of a thick leaden ring, is divided into two compart- ments, the upper one containing water and the lower one crushed ice, which was thus prevented from rising. The leaden ring also served to support a thermometer enclosed in a very stout tube, and a manometer with compressed air. The pressures were exerted by means of a screw piston V. e The thermometer T indicated the temperature at which ice and water remain in presence of each other without change, i.e. the melting point of 328 On Heat [342- Fig. 333 ice. This temperature is o° C. when the pressure is atmospheric ; when the pressure was increased by means of the screw V, the temperature fell. The change was small but definite ; Lord Kelvin found that pressures of 8'i and i6-8 atmospheres lowered the melting point of ice by o'059° - I WM ~< and 0-126° respectively. These results justify the theoretical ^ previsions of his brother, Professor J. Thomson, according to S which an increase of pressure of n atmospheres lowers the w melting point of ice by o'oo74«° C, so that a pressure of 135 W atmospheres, or about 2000 pounds to the square inch, would W ,- lower the melting point 1° C. " I This lowering of the melting point is also shown by the *""■ experiment of Mousson. The apparatus consists of a stout steel tube closed at one end by a screw and with a screw piston at the other (fig. 333). The tube is filled with water and a metal bullet introduced. When the apparatus is closed it is inverted so that the bullet rests on the piston, and placed thus in a freezing mixture ; the water freezes and presses the ball against the piston. This is then turned again, and pressure is gradually applied by turning the handle of the screw. When the lower screw is opened the copper ball falls out, and is fol- lowed by a thick cylinder of ice which must have been formed at the moment of opening. Hence the ice must, by a pressure esti- mated at 13,000 atmospheres, have been converted into water at about -18° C. This influence is likewise readily demonstrated by an experiment of von Helmholtz (fig. 334). Water is boiled in a flask until all air is ex- pelled, and it is then closed. It is afterwards placed in a freezing mix- ture so that some ice forms inside. This is then allowed to melt again in great part, and the flask is placed in a vessel of water containing lumps of ice. It is then found that the still unfrozen water inside the flask freezes while that of the outside is melting. 343. Alloys. Fluxes. — Alloys are generally more fusible than any of the metals of which they are composed ; for instance, an alloy of 5 parts of tin and 1 of lead fuses at 194°. The alloy known as Ros^s fusible metal, which consists of 4 parts of bismuth, i part of lead, and i of tin, melts at 94°, and an alloy of i or 2 parts of cadmium with 2 parts of tin, 4 parts of lead, and 7 or 8 parts of bismuth, known as Woods fusible metal, melts between 66° and 71° C. An alloy of potassium and sodium in equivalent proportions is liquid at the ordinary temperature. Fusible alloys are of extended use in soldering and in taking casts. Steel melts at a lower temperature than iron, though it contains carbon, which is almost completely infusible. Fig- 334 -346] Solution 329 Mixtures of the fatty acids melt at lower temperatures than the pure acids. A mixture of potassium and sodium chlorides fuses at a lower temperature than either of its constituents ; this is also the case with a mixture of potassium and sodium carbonates, especially when they are mixed in the proportion of their chemical equivalents. An application of this property is met with in the case oi fluxes, which are much used in metallurgical operations. They consist of substances which, when added to an ore, partly by their chemical action, help the reduction of the substance to the metallic state, and, partly, by presenting a readily fusible medium, promote the agglomeration of the individual particles with the formation of a mass of metal or regulus. 344. Latent heat. — Since, during the passage of a body from the solid to the liquid state, the temperature remains constant until the fusion is com- plete, whatever be the intensity of the source of heat, it must be concluded that, in changing' their condition, bodies absorb a considerable amount of heat, the only effect of which is to maintain them in the liquid state. This heat, which is not indicated by the thermometer, is called latent heat or latent heat of fusion, an expression which, though not in strict accordance with modern ideas, is convenient from the fact of its universal recognition and employment (467). An idea of what is meant by latent heat may be obtained from the follow- ing experiment : — If a pound of water at 80° is mixed with a pound of water at zero, the temperature of the mixture is 40°. But if a pound of crushed ice at zero is mixed with a pound of water at 80°, the ice melts and two pounds of water at zero are obtained. Consequently the m.ere change of a pound of ice to a pound of water at the same temperature requires as much heat as will raise a pound of water through 80°. This quantity of heat represents the latent heat of the fusion of ice, or the latent heat of water. Every liquid has its own latent heat, and in the chapter on Calorimetry we shall show how this is determined. 345. Solution. — A body is said to dissolve when it becomes liquid in consequence of an attraction between its molecules and those of a liquid. Gum arable, sugar, and most salts dissolve in water. The weight dissolved in a given quantity of water generally increases with the temperature, as is seen from the following table : — ■ Common Salt Nitre Sodium Sulphate Copper Sulphate Zinc Sulphate O" 20 100 35 ! 13 I 6 ! 32 37 , 21 S3 42 40 247 42 i 203 115 131 654 When a liquid has dissolved as much as it can at a particular tempera- ture, it is said to be saturated. The belief formerly held that the properties of a liquid were altered when a body was dissolved in it nearly in proportion to the quantity dissolved is not confirined by the results of electrolysis. The first small quantity dis- solved produces a far greater change than a subsequent equal quantity. When a salt dissolves in water it may be supposed that the vibrations of 330 On Heat [346- its bounding molecules, which are in contact with the solvent, possibly owing" to the attraction of the solvent, or owing to capillarity, increase their ampli- tude so that they get beyond the sphere of action of the other molecules of the salt, and thereby assume a progressive motion like the molecules of a gas. Like them they then exert a pressure against the sides of the containing vessel, which is called osmotic pressure (139). During solution, as well as during fusion, a certain quantity of heat always becomes latent, and hence it is that the solution of a substance usually produces a diminution of temperature. In certain cases, however, instead of the temperature being lowered, it actually rises, as when caustic potash is dissolved in water. This depends upon the fact that two simultaneous and contrary phenomena are produced. The first is the passage from the solid to the liquid condition, which always lowers the temperature. The second is the cheinical combination of the body dissolved with the liquid, which, as in the case of all chemical combinations, produces an increase of temperature. Consequently, as the one or the other of these effects pre- dominates, or as they are equal, the temperature either rises or sinks, or remains constant. 346. Solidification. — Solidification or congelation is the passage of a body from the liquid to the solid state. This phenomenon is expressed by the two following laws : — I. Every body, under the same pressure, solidifies at a fixed temperature, •which is the same as that of fusion. II. From the commencement to the end of the solidification, the tempera- ture of a liquid remains constant. Certain bodies, more especially some of the fats, present an exception to the first law, in so far that by repeated fusions they seem to undergo a molecular change which alters their melting point. The second la\\' is the consequence of the fact that the latent heat absorbed during fusion becomes free at the moment of solidification. The application of the very low temperatures which can now be so readily procured has lessened the number of those liquids which it was formerly thought could not be solidified. By allowing liquid ethylene to boil in a vacuum, Wroblewski and Olszewski obtained a temperature of — 136° They observed that carbon disulphide solidified at —116° and fused again at about - 1 10° Absolute alcohol became viscid at - 129° and solidified at — 130-5°. Pure ether solidifies at — 129''. Water containing a salt dissolved always solidifies below zero ; the de- pression of the freezing point is proportional to the weight of salt dissolved, at any rate for weak solutions. This is known as Blagdetis law. If several salts which have no chemical action on each other be dis- solved in a given weight of water, the lowering of the freezing point is the sum of the depressions which each of them would produce [separately if dissolved in the same quantity of water. When the numbers observed in any experiment of this kind do not agree with those calculated, this points to the occurrence of some chemical action between the substances dissolved, and the observation of such deviations has been of use in questions of chemical statics. The elaborate researches of Raoult on the temperature of solidification -346] Solidification 331 of solutions of bodies in water and other solvents have led to important con- clusions. The temperature at which a solution solidifies, or its freezing point, is always lower than that of the pure solvent. If P be the weight;in|grammes of any substance dissolved in 100 grammes of a solvent, and C be the depres- sion in the freezing point observed, r then — = A IS the depression which would be produced by dissolving one gramme of the substance in 100 grammes of the solvent, and is known as the coefficient of depres- sion. A comparison of the values for A for various substances and the same solvent shows that they differ considerably ; this is not so if we compare the depressions produced by molecular weights of the sub- stances. That is, if we multiply the value of A in the above equation by M, the molecular weight of the sub- stance dissolved, we obtain the de- pression which would be produced by dissolving one gramme-mole- cule of a body in 100 grammes of the solvent, or the coefficient of molecular depression ; this is called CM P ■ Now it is found that in a very large number of cases the value of T, for one and the same solvent, is a constant number ; it has the value 19 for water, 39 for glacial acetic acid, and 49 for benzene. This relation is of great value ; by means of a simple determination of the freezing point of a solid we can calculate the molecular weight of substances which cannot be ob- tained in the gaseous state without being decomposed. This is con- veniently effected by means of the apparatus represented in fig. 335. The solvent is contained in the vessel A, and the substance to be investi- gated is introduced by the lateral aperture A'. A is surrounded by a wide glass tube B containing air, and this again is placed in a wider vessel C which contains the freezing mixture ; for experiments with benzene or glacial acetic acid as a solvent, this is bruised ice, and with water a mixture of ice T, and we have T = - Fig- 335 332 On Heat [346- and salt. The liquid from these may be drawn off by a siphon placed through b. In A is a platinum stirrer r, and a delicate thermometer D, indicating the ^-J^ of a degree. There is also a stirrer in the outer vessel. - Since C and P are known, M is determined from the formula C where T is the constant for the particular solvent employed, which is ordinary glacial acetic acid in the majority of cases. Van 't Hoff has shown that the coefficient of depression / may be 0'02T^ calculated by means of the formula t = , where co is heat of fusion, and CO T the absolute temperature of fusion. In the case of such salts as potassium chloride the molecular depressions are greater than is required by the law, being nearly twice as much as in indifferent bodies like sugar ; this is probably due to the fact that a greater or less proportion of the salt is dissociated into its constituents, a phenome- non analogous to the dissociation of vapours, to which are due abnormal vapour densities (394). 347. Crystallisation. — Generally speaking, bodies which pass slowly from the liquid to the solid state assume regular geometri- cal forms, such as the cube, prism, rhombohedron, &c. ; these are called crystals. If the crystals are formed from a body in fusion, such as sulphur or bismuth, the crystallisation is said to take place by the dry way. The crystallisation is said to be by the moist way when it takes place owing to the slow evaporation of a solution of a salt, or when a solution saturated at a higher temperature is allowed to cool slowly. Snow, ice, and many salts present examples of crystallisation. Crystallisation bears the same relation to solution that solidifi- cation does to fusion. The latent heat of solution, i.e. the heat required to effect the solution of a substance without change of temperature, is restored during the reverse process of crystallisation. 348. Retardation of the point of solidification. — The freezing point of pure water can be diminished by several degrees, if the water be previously freed from air by boiling and be then kept in a perfectly still place. In fact, it may be cooled to —15° C, and even lower, without freezing. But when it is shghtly agitated, the liquid at once solidifies. This may be conveniently shown by means of the apparatus represented in fig. 336, which consists of a delicate thermometer, round the bulb of which is a wider one containing some water. Before sealing at a the whole outside bulb was filled with water, which was then boiled out and sealed so that over the water the space is quite empty of air. The tube is pj g clamped in a retort stand, and ether is dropped on it, that which has dropped off, and become colder, being used over and over again. In this way the temperature may soon be reduced to —6°, and if then the bulb be shaken, part of the water freezes and the temperature rises to zero. The smaller the quantity of liquid, the lower is the temperature to which it can be cooled, and the greater the mechanical disturloance it -348] Retardation of the Point of Solidification 333 supports without freezing. Fournet has observed the frequent occurrence of mists formed of particles of liquid matter suspended in an atmosphere whose temperature was io° or even 15° below zero. A very rapid agitation prevents the formation of ice. This is also the case with all actions which, hindering the molecules in their movements, do not permit them to arrange themselves in the conditions necessary for the solid state. Despretz was able to lower the temperature of water contained in fine capillary tubes to — 20° without their solidifying. This experiment shows how it is that plants in many cases do not become frozen even during severe cold, as the sap is contained in very fine capillary vessels. As we have already seen, the freezing point of water containing salts in solution is lowered. Sea water freezes at —2-5° to — 3° C. ; the ice which forms is c|uite pure, and a saturated solution remains. In Finland advantage is taken of this property to concentrate sea water for the purpose of extract- ing salt from it. If water contains alcohol, precisely analogous phenomena are observed ; the ice formed is pure, and practically all the alcohol is con- tained in the residue. Dufour has observed some ver)' curious cases of liquids cooled out of contact with solid bodies. His mode of experimenting was to place the liquid in another of the same specific gravity but of lower melting point, in which it is insoluble. Drops of water, for instance, suspended in a mixture of chloroform and oil, usually solidified between —4° and —12°, while still smaller globules cooled down to —18° or -20°. Contact with a frag- ment of ice immediately set up congela- tion. Globules of sulphur (which solidifies at 115°) remained hquid at 40° ; and glo- bules of phosphorus (solidifying point 42°) at 20°. The superfusion of phosphorus may be illustrated by the experiment repre- sented by fig. 337. A long test tube containing phosphorus. A, and covered with a layer of water, is fixed along with a thermometer T in a large flask con- taining water. This flask is raised to a temperature a few degrees above the melting point of phosphorus, and is then withdrawn from the source of heat ; as its mass is considerable, the phosphorus cools very slowly, and remains liquid at tempe- ratures far below its ordinary point of solidification. A glass rod may even be dipped into it without change ; but if the liquid is touched with the smallest frag- ment of solid phosphorus, it instantaneously solidifies, and in so doinglcon- tracts and becomes opaque. When a liquid solidifies after being cooled below its normal freezing point the solidification takes place very rapidly, and is accompanied by a Fig. 337 334 On Heat [348- ■disengagement of heat, which is sufficient to raise its temperature from the point at which soHdification begins up to its ordinary freezing point. This is well seen in the case of sodium sulphate (Glauber's salt = Na.,SOj.ioH20), which melts in its own water of crystallisation at 45°, and when carefully cooled will remain liquid at the ordinary temperature of the atmosphere. If it then be made to solidify by agitation, or by adding a small fragment of the solid salt, the rise of temperature is distinctly felt by the hand. In this case the heat, which had become latent in the process of liquefaction, again] becomes free, and a portion of the substance remains melted ; for it is kept liquid by the heat of solidification of that which has solidified. 349. Change of volume on solidification and liquefaction. — The rate of expansion of bodies generally increases as they approach their melting points, and is in most cases followed by a further expansion at the moment of liquefaction, so that the liquid occupies a greater volume than the solid from which it is formed. The apparatus represented in fig. 338 is well adapted for exhibiting this phenomenon. It consists of a glass tube, ab, containing water or some other suitable liquid, to which is carefully fitted a cork with a graduated glass tube c. This forms, in fact, a thermometer, and the values of the divisions on the tube c are determined in terms of the capacity of the whole apparatus. A known volume of the substance is placed in the tube aa and the cork inserted ; the apparatus is then placed in a space at a temperature very little below the melting point of the body in question, until it has acquired its temperature, and the position of the liquid in c is noted. The temperature is then allowed to rise slowly, and the position noted when the melting is complete. Knowing then the difference in the two readings and the volume of the substance under experiment, and making a correction for the expansion of the liquid and of the glass, it is easy to deduce the increase due to the melting alone. Phos- phorus, for instance, increases about 3^4 per cent, on liquefaction ; that is, 100 volumes of solid phosphorus at 44° (the melting point) become 103-4 at the same temperature when melted. Sulphur expands about 5 per cent, on liquefying, and stearic acid about 1 1 per cent. Waterllpresents a remarkable exception ; it expands at the moment of solidifying, or contracts on melting, by about 10 per cent. One volume of ice at 0° gives 0-9178 of water at 0°, or I volume of water at 0° gives 1-102 of ice at the same temperature. In consequence of this expansion, ice floats on the surface of water. Accord- ing to Dufour, the specific gravity of ice at o'' is 0-9178 ; Bunsen found for ice which had been made from water freed from air by boiling the somewhat smaller number 0-91674. The increase of volume in the formation of ice is accompanied by an expansive force which sometimes produces powerful mechanical effects, of which the bursting of water-pipes and the breaking of jugs containing water are familiar examples. The splitting of stones, rocks, and the swelling up of moist ground during frost, are caused by the fact that water penetrates into the pores and there becomes frozen ; in short, the great expansion of Fig. 338 -350] Freezing Mixtures 335 water on freezing is the most active and powerful agent of disintegration on the earth's surface. The expansive force of ice was strikingly shown by some experiments of Major Williams in Canada. Having quite filled a 13-inch iron bomb-shell with water, he firmly closed the touch-hole with an iron plug weighing 3 pounds and exposed it in this state to the frost. After some time the iron plug was forced out with a loud explosion, and thrown to a distance of 415 feet, and a cylinder of ice 8 inches long issued from the opening. In another case the shell burst before the plug was driven out, and in this case a sheet of ice spread Fig. 339 out all round the crack (fig. 339). It is probable that under the g'reat pressure some of the water still remained liquid (342) up to the time at which the resistance was overcome ; that it then issued from the shell in a liquid state, but at a temperature below 0°, and therefore instantly began to solidify when the pressure was removed, and thus retained the shape of the orifice whence it issued. Many plans have been proposed to prevent the bursting of water-pipes in houses in severe weather. One plan is to empty the pipes, another to .allow a slow leakage through the taps ; a third method is to introduce into the exposed pipe a piece of indiarubber tubing securely closed at each end. C. V. Boys suggested making a portion of the leaden water-pipe ■of oval instead of circular section. Since the area of a circle is for a given circumference greater than the area of any other curve, the effect of expansion due to freezing would be to force the oval more or less into a ■circular form. Cast iron, bismuth, and antimony expand on solidifying, like water, and can thus be used for casting ; but gold, silver, and copper contract, and hence coins of these metals cannot be cast, but must be stamped with a die. An iron tube filled with molten bismuth and closed by a screw is broken as the bismuth becomes solid. This increase of volume when liquids solidify, and the correlated decrease ■on melting again, in the case of water and some other crystalline substances such as bismuth, are probably due to the fact that such bodies are aggregates ■of small crystalline masses, which are grouped in such a way that small interstices are formed. When the liquid melts these interstices fill up owing to the mobility of the molecules, and, notwithstanding the greater space which each individual group takes up, owing to expansion, there is on the whole a decrease of volume. 350. Freezing mixtures. — The absorption of heat in the passage of bodies from the solid to the liquid state has been used to produce artificial cold. This is effected by mixing together bodies which have an affinity for each other, and of which one at least is solid, such as water and a salt, ice and a salt, or an acid and a salt. Chemical affinity accelerates the fusion or solution ; the portion which melts or dissolves robs the rest of the mixture of a large quantity of sensible heat, which thus becomes latent. In many cases a very considerable dinnnution of temperature is produced. Parts by Weight Reduction of Temperature 8) 5) + io°to -17' 2' I + 10° to -18= 3 , 2 + 10° to -19'^ 6 5 • + 10° to -26= 4 91 4) + 10° to ~icf 336 On Heat [350- The following table gives the names of the substances mixed, their pro- portions, and the corresponding diminutions of temperature : — Substances Sodium sulphate . Hydrochloric acid . Pounded ice or sno\\- Common salt Sodium sulphate . Dilute nitric acid Sodium sulphate Ammonium nitrate Dilute nitric acid Sodium phosphate Dilute nitric acid If the substances taken be themselves previously cooled down, a still more considerable diminution of temperature is occasioned. Freezing' mixtures are frequently used in chemistry, in physics, and in domestic economy. One form of the portable ice-making machines which have come into use during the last few years consists of a cylindrical metallic vessel divided into four concentric compartments. In the central one is placed the water to be frozen ; in the next there is the freezing mixture, which usually consists of sulphate of sodium and hydrochloric acid ; 6 pounds of the former and 5 of the latter will make 5 to 6 pounds of ice in an hour. The third compartment also contains water, and the outside one contains some badly conducting substance, such as cotton, to cut off the influence of the external temperature. The best effect is obtained when fairly large quantities (2 or 3 pounds) of the mixture are used, and when the ingredients are intimately mixed. It is also advantageous to use the machines for a succession of operations. 351. Guthrie's researches. — It appears from the experiments of the late Dr. Guthrie that what are called freezing mixtures may be divided into two- classes — namely, those in which one of the constituents is liquid and those in which both are solid. The temperature indicated by the thermometer placed in a freezing mixture is, of course, due to the loss of heat by the thermometer in the liquefying freezing mixture, and is measured by the rate of such loss. The quantity of heat absorbed by the freezing mixture is obviously the heat required to melt the constituents, together with ( ± ) the heat of combination of the constituents. When one constituent is hquid, as when hydrochloric acid is added to ice, then a lower temperature is got by previously cooling the hydrochloric acid. There is no advantage in cooling the ice. But when both constituents are solid, as in the case of the- ice-salt freezing mixture, there is no advantage to be gained by cooling one or both constituents. Within verj- wide limits it is also in the latter case a matter of indifference as to the ratio between the constituents. Nor is it important whether the ice is finely powdered as snow or in pieces as large as a pea. The different powers of various salts when used in conjunction with ice as freezing mixtures appear to have remained unexplained until Guthrie -353] Vaporisation 337 showed that, with each salt, there is always a minimum temperature below which it is impossible for an aqueous solution of any strength of that salt to exist in the liquid form ; that there is a certain strength of solution for each salt which resists solidification the longest, that is, to the lowest temperature. Weaker solutions give up ice on being cooled, stronger solutions give up the salt either in the anhydrous state or in combination with water. A solution of such a strength as to resist solidification to the lowest temperature was called by Guthrie a cryohydrate. ■ It is of such a strength that when cooled below 0° C. it solidifies as a whole ; that is, the ice and the salt solidif)' together and form crystals of constant composition and constant melting and the same solidifying temperatures. The hquid portion of a freezing mixture, as long as the temperature is at its lowest, is, indeed, a melted cryohj'drate. The slightest depression of temperature below this causes solidification of the cryohydrate, and hence the temperature can never sink below the solidifying temperature of the cryohydrate. Guthrie also showed that colloid bodies, such as gum and gelatine, neither raise the boiling-point of water nor depress the solidifying point, nor can they act as elements in freezing mixtures. VAPOURS. MEASUREMENT OF THEIR PRESSURE 352. Vapours. — Vapours are the aeriform fluids into which volatile substances, such as ether, alcohol, water, and mercury, are changed by the absorption of heat. Volatile liquids are those which thus possess the property of passing into the aeriform state, and fixed liquids are those which do not form vapour at any temperature without undergoing chemical decomposition, such as the fatty oils. Ice and snow volatilise in closed spaces, forming crystals on the cooled parts. Some substances — arsenious acid (white arsenic) for example — vaporise, when heated under atmospheric pressure, without passing through the liquid condition. This process is called sublimation. In the case of arsenious acid, if the pressure is doubled the substance first liquefies and then passes into vapour. It is a question of vapour pressure (359) ; if the vapour pressure is less than that to which the substance is exposed, liquefaction takes place ; but if the vapour pressure is greater than this, the substance cannot exist in a liquid state. The vapour pressure of arsenious acid is greater than I and less than 2 atmospheres. Iodine melts at 104° and boils at 200'' under ordinary pressure, since its vapour pressure is less than 760 mm. mercury ; but if the pressure be reduced to 250 mm. the solid iodine passes direct into the vaporous state. In these conditions it is sometimes said that the boiling point of iodine is below its melting point. Vapours are transparent, like gases, and generally colourless ; there are only a few coloured liquids which also give coloured vapours. 353. Vaporisation. — The passage of a liquid into the gaseous state is designated by the general term vaporisation ; the term evaporation especi- ally refers to the slow production of vapour at the free surface of a liquid, and boiling to its rapid production in the mass of the liquid itself. We shall presently see (366) that at the ordinary atmospheric pressure, ebullition, like fusion, takes place at a definite temperature. This is not the case with evaporation, which occurs even with the same liquid at very different z 338 On Heat [353- temperatures, although the formation of a vapour seems to cease below a certain point. Mercury, for example, is stated to give no vapour below — io°, nor sulphuric acid below 30°. 354. Elastic force of vapour. Vapour pressure. — Like gases, vapours have a certain elastic force, in virtue of which they exert pressures on the sides of vessels in which they are contained. The fact of vapour pressure may be demonstrated by the following experiment : — A quantity of mercury is placed in a bent glass tube (fig. 340), the shorter leg of which is closed ; a few drops of ether are then passed into the closed leg and the tube is immersed in a water bath at a temperature of about 45°. The mercury then sinks slowly in the short branch, and the space ab is filled with a gas which has all the appearance of air, and whose elastic force counterbalances the pres- sure of the column of mercury cd, and the atmospheric pressure on d. This gas is the vapour of ether. If the water be cooled, or if the tube be removed from the bath, the vapour which fills the space ab disap- pears, and the drop of ether is reproduced. If on the contrary, the bath be heated still higher, the level of the mercury descends below b, indicating an increase in the pressure of the vapour. A gaseous substance, strictly speaking, is called a vapour when it can be liquefied by increase of pressure alone, without change of temperature ; the substance is a gas when it cannot be so liquefied. As we shall see later, whether a substance is a gas or a vapour depends on its temperature. The substance is a vapour or a gas according as its temperature is below or above its critical temperature (373). 355. Formation of vapour in a vacuum. — The change from liquid to vapour takes place very slowly when the liquid is freely exposed to the air. The atmosphere is an obstacle to the vaporisation. In a vacuum there is no resistance, and the formation of vapour is instantaneous, as is seen in tlie following experiment : — Four barometer tubes, filled with mercury, are im- mersed in the same trough, fig. 341. One of them, A, serves as a barometer, and a few drops of water, alcohol, and ether are respectively introduced into Fig- 340 Fig. 341 -356] Saturated Vapour. Maximum of Pressure 339 the tubes B, C, D. When the Uquids reach the vacuum, a depression of the mercury is at once produced. And as this depression cannot be caused by the weight of the liquid, which is an extremely small fraction of the weight of the displaced mercury, it must be due to the formation of some vapour whose elastic force has depressed the column of mercury. The experiment also shows that the depression is not the same in all the tubes ; it is greater in the case of alcohol than of water, and greater again with ether than with alcohol. We consequently obtain the two following laws of the formation of vapours : — I. In a vacuum all volatile liquids are ivtmediately converted into vapour. II. At the same temperature the vapours of different liquids have different pressures. For example, at 20° the pressure of ether vapour is 25 times as great as that of aqueous vapour. 356. Saturated vapour. Maximum of pressure. — When a very small quantity of a volatile liquid, such as ether, is introduced into a barometer tube, it is at once completely vaporised, and the column of mercury is not depressed to its full extent ; for if some more ether be introduced the depression increases. The ether, if still more be added, finally ceases to vaporise, and remains in the liquid state. There is, therefore, for a ■certain temperature, a limit to the quantity of vapour which can be formed in a given space. This space is accordingly said to be saturated. Further, when the vaporisation of the ether ceases, the depression of the mercurial column stops. And hence there is a limit to the pressure of the vapour, a limit which, as we shall presently see {358), varies with the temperature. To show that, in a closed space, saturated with vapour and containing liquid in excess, the temperature remaining constant, there is a tnaxi- mum of pressure which the vapour cannot exceed, a barometric tube is used which dips in a deep bath ,(fig. 342). This tube is filled with mercury, and then so much ether is added as to be in excess after the Torricellian vacuum is saturated. The height of the column of mercury is next noted by means of the scale graduated on the tube itself. Now, whether the tube be depressed, which tends to compress the vapour, or whether it be raised, which tends to expand it, the height of the column of mercury is constant. The pres- sure of the vapour remains constant in the two cases, for the depression neither increases nor diminishes it. Hence it is concluded that when the volume of the saturated vapour is diminished, a portion of the vapour returns to the liquid state ■ that when, on the other hand, the volume is increased, a portion of the Fig. 342 340 On Heat [366- excess of liquid vaporises, and the space occupied by the vapour is again saturated ; but in both cases the pressure and the density of the vapour remain constant. The maximum pressure is called the saturation pressure of the vapour corresponding to the particular temperature. If the vapour pressure of a liquid is spoken of without qualification, the maximum pressure is generally meant. 357. Unsaturated vapours. — It will be seen from what has been said, that vapours present two very different states, according as they are saturated or not. In the first case, where they are saturated and in contact with the liquid, they differ completely from gases, since for a given temperature their pressure and density are constant and independent of their volume. In the second case, on the contrary, where they are not saturated, they exactly resemble gases. For if the experiments (fig. 342) be repeated, only a small quantity of ether being introduced, so that the vapour is not saturated, and if the tube be then slightly raised, the level of the mercury is seen to rise, which shows that the pressure of the vapour has diminished. Similarly, by m- mersing the tube still more, the level of the mer- cury sinks. The vapour consequently behaves just as a gas would do, its pressure diminishing when the volume increases, and vice versa ; and as in both cases the volume of the vapour is inversely as the pressure, it is concluded that unsaturated vapours obey Boyle's law. When an unsaturated vapour is heated, its volume increases like that of a gas ; and the number 0-00367, which is the coefficient of the e.Kpansion of air, may be taken for that of un- saturated vapours. Hence we see that the physical properties of unsaturated \apours are comparable with those of gases, and that the formulae for the compressibility and expansibility of gases (181 and 333) also apply to unsaturated vapours. 358. Pressure of aqueous vapour below zero. In order to measure the pressure of aqueous vapour below zero, Gay-Lussac used two baro- meter tubes filled with mercury, and placed in the same reservoir (fig. 343). The straight tube, A, serves as a barometer ; the other, C, is bent, so that part of the Torricellian vacuum can be surrounded by a freezing mixture, B (350). When a little water is admitted into the bent tube, the level of the mercury sinks below that in the tube A, to an extent which varies with the temperature of the freezing mixture. At 0° the depression is . 4-54 millimetres Fig. 343 • 4-25 • 3-63 -359] Pressure of Aqueous Vapour 341 - 10" - 20° -30° These depressions, which At - 5° the depression is . 3-11 millimetres . 2-o8 „ ■ 0-84 • 0-36 must be due to the pressure of aqueous vapour in the space BC, show that even at very low temperatures there is always some aqueous vapour in the atmosphere. Although in the above experiment the part B and the part C are not both immersed in the freezing mixture, we shall presently see that when two communicating vessels are at different temperatures, the tension of the vapour is the same in both, and always corresponds to that of the lower temperature. 359. Pressure of aqueous vapour between zero and one hundred degrees. — i. Daltoris method. Dalton measured the pressure of aqueous Fig 344 Fig. 345 vapour between 0° and 100° by means of the apparatus represented in fig. 344. Two barometer tubes, A and B, are filled with mercury, and inverted in an iron bath full of mercury, which is, placed on a furnace. The tube A 342 On Heat [359- contains a small quantity of water. The tubes are supported in a cylindrical vessel, open top and bottom and full of water, the temperature of which is indicated by the thermometer. The bath being gradually heated, the water in the cylinder becomes heated too ; the water which is in the tube A vaporises, and in proportion as the pressure of its vapour increases, the mercury sinks. The depressions of the mercury corresponding to each degree of the thermometer are indicated on the scale E, and in this manner a table of aqueous vapour pressures between zero and 1 00° has been con- structed. ii. Regnaiilt's method. — Dalton's method is wanting in precision, for the temperature of the liquid in the cylinder is not everywhere the same, and consequently the exact temperature of the aqueous vapour is not shown. Regnault's apparatus is a modification of that of Dalton. The cylindrical glass vessel is replaced by a large cylindrical zinc drum, MN (fig. 345), in the bottom of which are two tubulures. The tubes A and B pass through these tubulures, and are fixed by india rubber collars. The tube containing vapour, B, is connected with a flask, a, by means of a brass three-way tube, O. The third limb of this tube is connected with a drying tube, D, containing pumice charged with sulphuric acid, which is connected with the air- pump. When the flask a contains some water, a small portion is distilled into B by gently heating the flask. Exhausting, then, by means of the air-pump, the water distils continuously from the flask and from the barometric tube towards D, which condenses the vapour. After having vaporised some quantity of water, and when it is thought that the air in the tube is with- drawn, the capillary tube which connects B with the three-way tube is sealed. The tube B being thus closed, it is experimented with as in Dalton's method. The drum, MN, being fllled with water, is heated by a spirit lamp, which is screened from the tubes by a wooden board. By means of a stirrer, K, all parts of the liquid are kept at the same temperature. In the side of the drum is a glass window, through which the height of the mercury in the tubes can be read off by means of a cathetometer ; from the difference in these heights, reduced to zero, the tension of vapour is deduced. By means of this apparatus, the elastic force of vapour between o'^ and 50° has been' determined with accuracy. 360. Pressure of aqueous vapour above 100° C. — Two methods have principally been employed for determining the pressure of aqueous vapour at temperatures above 100° ; the one by Dulong and Arago in 1830, and the other by Regnault in 1844. Fig. 346 represents a vertical section of the apparatus used by Dulong and Arago. It consisted of a copper boiler, k, with \-ery thick sides, and of about 20 gallons' capacity. Two gun-barrels, a, of which only one is seen in the drawing, were firmly fixed in the sides of the boiler, and plunged in the water. The gun-barrels were closed below, and contained mercury, in whiclr were placed thermometers, t, indicating the temperature of the water and of the vapour. The pressure of the vapour was measured by means of a mano- meter with compressed air, ot, previously graduated (185) and fitted into an iron vessel, d, filled with mercury. In order to see the height of the 361] Pressure of Aqueous Vapour 343 mercury in the vessel, it was connected above and below with a glass tube, n, in which the level was always the same as in the bath. A copper tube, /, connected the upper part of the vessel, d, with a vertical tube, c, fitted in the boiler. The tube i and the upper part of the bath d were filled with water, which was kept cool by means of a current of cold water flowing from a reservoir, and circulating through the tube b. Fig. 346 The vapour which was disengaged from the tube c exerted a pressure on the water of the tube i ; this pressure was transmitted to the water and to the mercury in the bath d, and the mercury rose in the manometer. By noting on the manometer the pressures corresponding to each degree of the thermometer, Dulong and Arago were able to make a direct measurement of the pressure up to 24 atmospheres, and the pressure to 50 atmospheres was determined by calculation. 361. Pressure of vapour below and above 100° C. — Regnault devised a method by which the pressure of vapour may be measured at temperatures either below or above 100°. It depends on the principle that when a liquid boils, the pressure of the vapour is equal to the pressure the liquid sup- ports. If, therefore, the temperature and the corresponding pressure are known, the question is solved, and the method merely consists in causing' water to boil in a vessel under a given pressure, and measuring the corre- sponding temperature. The apparatus consists of a copper retort, C (fig. 347), hermetically closed and about two-thirds full of water. In the cover are four thermometers, two of which just dip into the water, and two descend almost to the bottom. By means of a tube, AB, the retort C is connected with a glass globe, M, of about 6 gallons' capacity, and full of air. The tube AB passes through a metal cylinder, D, through which a current of cold water is constantly ,344 On Heat [361- flowing from the reservoir E. To the upper part of the globe a tube with two branches is attached, one of which is connected with a manometer, O ; the other tube, HH', which is of lead, can be attached to either an exhaust- ing or a condensing air-pump, according as the air in the globe is to be rare- fied or condensed. The reservoir K, in which is the globe, contains water at the temperature of the surrounding air. If the elastic force of aqueous vapour below ioo° is to be measured, the end H' of the lead pipe is connected with the plate of the air-pump, and the air in the globe M, and consequently that in the retort C, is rarefied. The retort being gently heated, the water begins to boil at a temperature Fig. 347 below ioo°, in consequence of the diminished pressure. And since the vapour is condensed in the tube AB, which is always cool, the pressure originally indicated by the manometer does not increase, and therefore the pressure of the vapour during ebullition remains equal to the pressure on the liquid. A little air is then allowed to enter ; this alters the pressure, and the liquid boils at a new temperature ; both these are read off, and the experi- ment repeated as often as desired up to ioo°. In order to measure the pressure above ioo° the tube H' is connected with a condensing pump, by means of which the air in the globe M and that in the vessel C are exposed to successive pressures, higher than the atmo- sphere. The ebullition is retarded (370), and it is only necessary to observe -361] Pressure of Aqueous Vapour 3.45 the difference in the height of the mercury in the two tubes of the mano- meter O, and the corresponding- temperature, in order to obtain the pressure for a given temperature. The following table by Regnault gives the pressure of aqueous vapour from — xo° to 104° Pressures of aqueous vapour from — \o° to 104° C. Tempe- ratures -10" 8 6 4 2 o + I 2 3 4 5 6 7 10 II Pl-essure in millimetres 2-078 2-456 2-890 3-955 4-600 4-940 5-302 5-687 6-097 6-534 6-998 7-492 8-OI7 8-574 9-165 9-792 Tempe- ratures 12" 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Pressure in ' Tempe- millimetres ratures 10-457 29° 1 1 -062 30 1 1 -906 31 12-699 32 13-635 33 14-421 34 15-357 35 16-346 1 40 17-391 45 18-495 50 19-659 55 20-888 60 22-184 65 23550 70 24-998 75 26-505 80 28-101 «5 Pressure in millimetres 29-782 31-548 33-405 35-359 37-410 39-565 41-827 54-906 71-391 91-982 117-479 148-791 186-945 233-093 288-517 354-643 433-410 Tempe- , Pressure in ratures ' millimetres 90" 525-45 91 : 545-78 92 566-76 93 588-41 94 610-74 95 633-78 96 657-54 97 682-03 98 707-26 98-5 720-15 99-0 733-91 99-5 746-50 1 00-0 760-00 100-5 773-71 lOI-Q 787-63 I02-0 8i6-i7 104-0 875-69 In the following table the numbers were obtained by direct observation up to 24 atmospheres ; the others were calculated by the aid of a formula of interpolation. This table and the one ne.xt following show that the elastic force increases much more rapidly than the temperature. It has been attempted to express the relation between them by formulae, but none of the formulas seems to have the simplicity which characterises a true law. Pressures in atmosptteres from 100° to 230-9° Number Temperatures of atmo- 1 spheres ' Number, Temperatures [ of atmo-j Temperatures I spheres ' ' loo-o° I 170-8° 1 12-2 I* 175-8 120-6 2 i8o-3 133-9 3 184-5 144-0 4 188-4 152-2 5 192-1 159-2 6 195-5 j 165-3 7 10 II 12 13 14 201-9 204-9 207-7 210-4 213-0 215-5 Number of atmo- spheres 15 16 17 18 19 20 21 Temperatures 217-9" 220-3 222-5 224-7 226-8 228-9 I 230-9 Number of atmo- spheres 22 23 24 25 26 27 28 346 On Heat [362- 362. Pressure of the vapours of different liquids. — Regnault deter- mined the pressure, at various temperatures, of the vapours of a certain number of liquids which are given in the following table : — Liquids Mercury Alcohol Carbon bi- sulphide Tempe- ratures Pressures in | millimetres ; 0° 0-02 ! 50 O-I I 100 074 13 50 220 100 1695 : -20 43 ! 60 132 1 164 100 3329 Liquids Ether . - Sulphurous J acid I Ammonia . -1 Tempe- Pressures in ratures millimetres -20° 68 182 60 1728 100 4950 -20 479 1165 60 8124 -3^ 876 3163 30 8832 363. Pressure of the vapours of mixed liquids. — Regnault's experi- ments on the pressure of the vapour of mixed liquids prove that (i.) when two liquids exert no solvent action on each other — such as water and carbon bisulphide^ or water and benzole — the pressure of the vapour which rises from them is nearly equal to the sum of the pressures of the two separate liquids at the same temperature ; (ii.) with water and ether, which partially dissolve each other, the pressure of the mixture is much less than the sum of the pressures of the separate liquids, being scarcely equal to that of the ether alone ; (iii.) when two liquids dissolve in all proportions, as ether and bisulphide of carbon, or water and alcohol, the pressure of the vapour of the mixed liquids is intermediate between the pressures of the separate liquids. The pressure of vapours over a convex surface, according to Lord Kelvin, is slightly greater than over a plane one. The pressure of the vapour from liquids which contain salts or other bodies in solution is less than that of the pure liquid. This may in principle be most simply demonstrated by an apparatus similar to that represented in fig. 344, in which B is a barometer into the vacuum of which the solution of a salt of known strength is introduced, while A is a similar barometer con- taining the pure liquid. With solutions of one and the same salt, Wiillner found that at a given temperature the diminution of pressure is proportional to the quantity of salt dissolved, provided the solutions are dilute. \if is the pressure of the pure solvent, and f that of the solution, and g is the percentage strength, then —I— = kg'-, where .^ is a constant. For g = \, k equals -— J^i and is the relative diminution of pressure for one per cent. , This property is of great mportancc from the connection which has been established with osmotic pressure (139). The depression is different for different salts dissolved in the same solvent, but it is found that if these various solutions are equimolecular — that is, the weights dissolved in the -364] Pressure at Different Temperatures 347 same quantity of solvent are as their molecular weights — then the depression is constant. This may also be expressed by saying that the diminution in pressure stands in the same ratio to the pressure of the solvent, as the number of molecules in the dissolved body does to the total molecules in the liquid ; that is f N + ra' where N and n are the number of molecules in the solvent and the salt respectively. Smce N = ^ and n =i-, where P and p are the weights, and M and m the molecular weights, of the solvent and salt respectively, the above equation gives / /M + Vm so that it is easy to deduce the molecular weight ni of the body dissolved. The above relations hold in strictness only for ideal solutions, or those which are so dilute that the volume of the substance is infinitely small in comparison with that of the solvent. 364. Pressure in two communicating vessels at different temperatures. — When two vessels containing the same liquid, but at different temperatures, are connected with each other, the elastic force is not that corresponding to the mean of the two temperatures, as would naturally be supposed. Thus, if there are two globes (fig. 348), one, A, containing water kept at zero by means of melting ice, the other, B, containing water at 100°, the vapour pressure, as long as the globes are not connected, is 4'6 millimetres in the first, and 760 millimetres in the second. But when they are connected by opening the stopcock C, the vapour in the globe B, from its greater pres- sure, passes into the other globe, and is there Fig. 348 condensed, so that the vapour in B can never reach a higher pressure than that in the globe A. The liquid simply distils from B towards A without any increase of pressure. From this experiment the general principle may be deduced that when two vessels containing the same liqidd, but at different temperatures, are connected, the pressure is identical in both vessels, and is the same as that 348 On Heat [364- corresponding to the lower temperature. An application of this principle has been made by Watt in the condenser of the steam-engine. 365. Evaporation. Causes which accelerate it. — Evaporation, as has been already stated (353), is the slow production of vapour at the surface of a liquid. It is in consequence of this evaporation that wet clothes dry when exposed to the air, and that open vessels containing water become empty. The vapours which, rising in the atmosphere, condense, and, becoming clouds, fall as rain, are due to evaporation from seas, lakes, rivers, and the earth. Four causes influence the rapidity of the evaporation of a liquid : i. the temperature ; ii. the quantity of the same vapour in the surrounding atmo sphere ; iii. the renewal of this atmosphere ; iv. the extent of the surface of evaporation. Increase of temperature accelerates the evaporation by increasing the pressure of the vapour. In order to understand the influence of the second cause, it is to be observed that no evaporation could take place in a space already saturated with vapour of the same liquid, and that it would reach its maximum in air completely freed from this vapour. It therefore follows that between these two extremes, the rapidity of evaporation varies according as the surrounding atmosphere is already more or less charged with the same vapour. The effect of the renewal of this atmosphere is similarly explained ; for if the air or gas, which surrounds the liquid, is not renewed, it soon becomes saturated, and evaporation ceases. Dalton found that the ratios of the evaporation in a feeble, medium, and strong draught were respectively as 270 : 347 : 424. He also observed that the quantity evaporated in perfectly dry, almost still air, at a temperature of 20°, was o-i of a gramme per square decimetre of surface in a minute. The effect of the fourth cause is self-evident. Vegetation exercises a great influence on evaporation. Schiibler found that the evaporation from a space covered with meadow grass, in the most vigorous stage of its growth, was thrice as rapid as that from an adjacent surface of water. As the plants ripened the evaporation diminished. 366. Boiling. — Ebullition, or boiling, is the rapid production of bubbles of vapour in the mass of a liquid itself When a liquid, water for example, is heated at the lower part of a vessel, the first bubbles are due to the disengagement of air which the water had previously absorbed, or which in the form of a thin film separates the liquid from the containing vessel. Small bubbles of vapour then begin to rise from the heated parts of the sides, but as they pass through the upper layers, the temperature of which is lower, they condense before reaching the surface. The formation and successive condensation of these first bubbles occasion the singing sometimes noticed in liquids just before they begin to boil. Lastly, large bubbles rise and burst on the surface, and this constitutes the phenomenon of ebullition (fig. 349). The laws of ebullition are as follows : — I. The temperature of ebullition or the boiling poi?it increases 'with the Pressure. -366] Boiling Points 549 II. For a given pressure boiling begins at a certain temperature, which varies in different liquids, but which, for equal pressures, is always the same in the same liquid. III. Whatever be the intensity of the source of heat, as soon as boiling begins the temperature of the liquid remains stationary. Fig. 349 Fig. 3SO In order to determine thejboiling points of liquids the apparatus repre- sented in fig. 350 may be used. It consists of a bulb with long neck to which is fused the tube b ; a can be connected either with a reflex or an ordinary condenser ; the condensed vapours collect in the bent part b, and flow thence into the bulb. The temperature is indicated by a delicate thermometer k passing through the cork, in which there is also a capillary glass tube ;3 ; this serves to admit a few bubbles of air from time to time, and materially prevents bumping, which is likewise prevented by a few scraps of platinum foil placed in the bulb. When the boiling point is to be determined under diminished pressure, a can be connected with an air-pump. This apparatus in suitable dimensions may also be used to determine the expansion of liquids at their boiling points. For this purpose a small pyknometer (120) is suspended from a wire, y which passes through the cork. This is weighed after having been filled with the liquid at a given temperature, and is then kept for some time in the vapour of the boiling liquid at the temperature /', and then when cooled is weighed again ; the difference in 3 so On Heat [366- the two weights represents the expansion between the two temperatures / and t' . Boiling points under the pressure ofy(x> millimetres. Fluorine . . . —187" Propionic acid 137° Oxygen. —181-4 Butyric acid 156 Nitrous oxide . —92 Turpentine . 157 Carbonic acid . —80 Methylene iodide . 182 Ammonia . . —39 AniUne . 184 Methyl chloride — 23 Iodine . . 300 Cyanogen . —20 Naphthaline . .218 Sulphurous acid . - 10 Diphenyl . 254 Ethyl chloride . +11 Benzoic acid . . 261 Aldehyde . 21 Phosphorus . 290 Ether . . -37 Diphenylamine . t 310 Carbon bisulphide 47 Strong sulphuric acid . 318 Acetone. . 56 Phenanthrene . 340 Bromine ... 58 Mercury . . 357 Methylic alcohol . 66 Phenyl phosphate . 407 Alcohol . . 78 Arsenic . . . 437 Benzole ... 81 Sulphur . . . 444 Distilled water . 100 Phosphorus pentasulphide 530 Acetic acid . . . 117 Selenium . . . 665 Amyhc alcohol . . 131 Cadmium . 756 Zinc . . . 916° Kopp pointed out that in homologous chemical compounds the same difference in chemical composition frequently involves the same difference of boiling points ; and he showed that in an extensive series of com- pounds, the fatty acids for instance, the difference of CH^ is attended by a difference of 19° C. in the boihng point. In other series of homologous compounds, the corresponding difference in the boiling point is 30°, and in others again 24°. 367. Theoretical explanation of evaporation and ebullition. — From what has been said about the nature of the motion of the molecules in liquids (294), it may readily be conceived that in the great variety of these motions, the case occurs in which, by a fortuitous concurrence of the progressive, vibratory, and rotatory motions, a molecule is projected from the surface of the liquid with such force that it overleaps the sphere of the action of its circumjacent molecules, before, by their attraction it has lost its initial velocity ; and that it then flies into the space above the liquid. Let us first suppose this space limited and originally vacuous ; it gradu- ally fills with the propelled molecules, which act like a gas and in their motion are driven against the sides of the envelope. One of these sides, however, is the surface of the liquid itself, and a molecule when it strikes against this surface will not in general be repelled, but will be retained by the attraction which the adjacent ones exert. Equilibrium will be established when as many molecules are dispersed in the surrounding space as, on the average, impinge against the surface and are retained by it in the unit of -368] Influence of Substances on the Boiling Point 351 time. This state of equilibrium is not, however, one of rest, in which eva- poration has ceased, but a condition in which evaporation and condensation, which are equally strong, continually compensate each other. The pressure is then the maximum vapour pressure of the liquid, which remains constant so long as the temperature is constant. If the space above the liquid contains air or any other gas, evaporation goes on just the same as when the space is vacuous, except that it is slower. The final pressure reached is in no way modified by the presence of other gases or vapours. What has been said respecting the surface of the liquid clearly applies to the other sides of the vessel within which the vapour is formed ; some vapour is condensed, this is subject to evaporation, and a condition ultimately occurs in which evaporation and condensation are equal. The quantity of vapour necessary for this depends on the density of vapour in the closed space, on the temperature of the vapour and of the sides of the vessel, and on the force with which this attracts the molecules. The maximum will be reached when the sides are covered with a layer of liquid, which then acts like the free surface of a liquid. 368. Influence of substances in solution on the boiling' point. — The ebullition of a liquid is the more retarded the greater the quantity of any substance it may contain in solution, provided that the substance be not volatile, or, at all events, be less volatile than the liquid itself. Water, which boils at 100° when pure, boils at the following temperatures when saturated with different salts : — Water saturated with common salt . boils at 102° „ „ potassium nitrate . „ 116 „ „ potassium carbonate „ 135 „ „ calcium chloride „ 179 Acids in solution present analogous results ; but substances merely mechanically suspended, such as earthy matters, bran, wooden shavings, &c., do not affect the boiling point. Absorbed air exerts a very marked influence on the boiling point of water. Deluc first observed that water freed from air by ebullition, and placed in a flask with a long neck, could be raised to 112° without boiling. Donny examined this phenomenon by means of the apparatus depicted in fig. 351. It consists of a glass tube CAB, bent at one end and closed at Fig. 351 C, while the other is blown into a pear-shaped bulb, B, drawn out to a point. The tube contains water which is boiled until all air is expelled, and the open end is hermetically sealed. By inclining the tube the water passes into the bent end CA ; this end being placed in a bath of chloride of calcium, the temperature may be raised to 130° without any signs of boiling. At 138° 352 On Heat [368- the liquid is suddenly converted into steam, and the water is thrown over into the bulb, which is smashed if it is not sufficiently strong. Boiled-out water, covered with a layer of oil, may be raised to 120° with- out boiling, but above this temperature it suddenly begins to boil, and with almost explosive violence. When a liquid is suspended in another of the same specific gravity, but of higher boiling point, with which it does not mix, it may be raised far beyond its boiling point without the formation of a trace of vapour. Dufour made a number of valuable experiments on this subject ; he used in the case of water a mixture of oil of cloves and linseed oil, and placed in it globules of water, and then gradually heated the oil ; in this way ebullition rarely set in below 110° or 115° ; globules of 10 millimetres' diameter very commonly reached a temperature of 1 20° or 1 30°, while very small globules of I to 3 millimetres reached the temperature of 175°, a temperature at which the pressure of vapour on a free surface is 8 or 9 atmospheres. At these high temperatures the contact of a solid body, or the production of gas bubbles in the liquid, occasioned a sudden vaporisation of the globule, accompanied by a sound like the hissing of a hot iron in water. Saturated aqueous solutions of copper sulphate, sodium chloride, &c., remain liquid at a temperature far bej'ond their boiling point, when immersed in melted stearic acid. In like manner, globules of chloroform (which boils at 61°), suspended in a solution of chloride of zinc, could be heated to 97° or 98° without boiling. It is a disputed question as to what is the temperature of the vapour from boiling saturated saline solutions. It has been stated by Rudberg to be that of pure water boiling under the same pressure. The experiments of Magnus seem to show, however, that this is not the case, but that the vapour of boiling solutions is hotter than that of pure water ; and that the temperature rises as the solutions become more concentrated, and therefore boil at higher temperatures. Nevertheless, the vapour was always found somewhat cooler than the mass of the boiling solution, and the difference was greater at high than at low temperatures. The boiling point of a liquid is usually lowered when it is mixed with a more volatile liquid than itself, but raised when it contains one which is less volatile. Thus a mixture of two parts alcohol and one of water boils at 83°, a mixture of two parts of carbon bisulphide and one part of ether boils at 38°. In some cases the boiling point of a mixture is lower than that of either of its constituents. A mixture of water and bisulphide boils at 43°, the boiling point of the latter being 46°. On this depends the following curious experiment. If water and carbon bisulphide, both at the tempera- ture 45°, are mixed together, the mixture at once begins to boil briskly. 369. Influence of the nature of the vessel on the boiling point. — Gay-Lussac observed that water in a glass vessel required a higher tempera- ture for ebullition than in a metal one. Taking the temperature of boiling water in a copper vessel at 100°, its boiling point in a glass vessel was found to be 101° ; and if the glass \essel had been previously cleaned by means of sulphuric acid and of potash, the temperature would rise to 105° or even to 106°, before ebullition commenced. A piece of metal placed in the bottom of the vessel was always sufficient to lower the temperature to -370] Influence of Pressure on the Boiling Point 353 ioo°, and at the same time to prevent the violent concussions which accom- pany the ebuDition of saHne or acid solutions in glass vessels. Whatever be the boiling point of water, the temperature of its vapour is uninfluenced by the substance of the vessels. 370. Influence of pressure on the boiling point. — We see from the table of pressures (361) that at ioo°, the temperature at which water boils under a pressure of 760 millimetres, which is that of the atmosphere, aqueous vapour has a pressure exactly equal to this pressure. This principle is general, and may be thus enunciated : A liquid boils when the pressure of its vapour is equal to the pressure it supports. Consequently, as the superin- cumbent pressure increases or diminishes, the pressure of the vapour, and therefore the temperature necessary for ebullition, must increase or diminish. Hence a liquid has, strictly speaking, an indefinite number of boiling points. In order to show that the boiling point is lower under diminished pres- sure, a small dish containing- water at 30° is placed under the receiver of an air-pump, which is then exhausted. The liquid soon begins to boil, the vapour formed being pumped out as rapidly as it is generated. A paradoxical but very simple experiment also well illustrates the dependence of the boiling point on the pressure. In a glass flask, water is boiled for some time, and when all air has been expelled by the steam, the flask is closed by a cork and inverted, as shown in fig. 352. If the bottom is then cooled by a stream of cold water from a sponge, the water begins to boil again. This arises from the condensation of the steam above the surface of the water, by which a partial vacuum is produced. It is in consequence of this dimi- nution of pressure that liquids boil on high mountains at lower temperatures. On Mont Blanc, for example, water boils at 84°, and at Quito at 90°. On the more rapid evaporation of water under feeble pressures is based the use of the air-pump in concentrat- ing those solutions which either cannot bear a high temperature, or which can be more cheaply evaporated in an exhausted space. Howard made a most important and useful application of this principle in the manufacture of sugar. The syrup, in his method, is enclosed in an air tight vessel, which is exhausted by a steam-engine. The- evaporation consequently goes on at a lower temperature, which secures the syrup from injury. The same plan is adopted in evaporating the juice of certain plants used in preparing medicinal extracts. On the other hand, boiling is retarded by increasing the pressure ; under the pressure of two atmospheres, for example, water only boils at 1 29'6°. A A Fig- 352 354 On Heat [371- 371. Franklin's experiment. — The influence of pressure on boiling may further be illustrated by means of an experiment originally made by Franklin. The apparatus consists of a bulb, a, and a tube, b, joined by a tube of smaller dimensions (fig. 353). The tube b is drawn out, and the apparatus filled with water, which is then in part boiled away by means of a spirit lamp. When it has been boiled sufficiently long to expel all the air, the tube b is sealed. There is then a vacuum in the apparatus, or rather there is a pressure due to the elastic force of aqueous vapour, which at Consequently, if the bulb, a, be Fig. 3S3 ordinary temperatures is very small. placed in the hand, the heat is sufficient to produce a pressure which drives the water into the tube, b, and causes a brisk ebullition. 372. Measurement of heights by the boiling point. — From the connection between the boiling point of water and the pressure, the heights of mountains may be measured by the thermo- meter instead of by the barometer. Suppose, for example, it is found that water boils on the summit of a mountain at 90°, and at its base at 98°. Since a liquid boils when its vapour pressure is equal to atmospheric pressure, it is only necessary, in order to ascertain the atmo- spheric pressures at the bottom and top of a mountain, to refer to a table giving corre- sponding temperatures and vapour pressures. With the help of this table a thermometer gives the same information as a barometer. The barometric pressures being thus known, the height of the mountain may be calculated by the method already given (179). An ascent of about 1080 feet produces a diminution of 1° C. in the boiling point. The instruments used for this purpose are called thermo-barometers or hypsometers, and were first supplied by WoUaston. They con- sist essentially of a small metallic vessel for boiling water (fig. 354), fitted with very deli- cate thermometers, which are only graduated from 80° to 100° ; so that, as each degree occupies a considerable space on the scale, the loths, and even the looths, of a degree Fig. 354 may be estimated, and thus it is possible to ■determine the height of a place by means of the boiling point to within about 10 feet. 373. Formation of vapour in closed tubes. — We have hitherto considered vapours as being produced in an indefinite space, or where they could -373] Formation of Vapour in Closed Tubes 355 •expand freely, and it is only under this condition that boiling can take place. In a closed vessel, the vapours produced finding no issue, their pressure and their density increase with the temperature, but that rapid disengagement of vapour which constitutes boiling is impossible. Hence, while the tempera- ture of a liquid in an open vessel can never exceed that of boiling, in a closed vessel it may be much higher. The liquid state has, nevertheless, a limit ; for, according to experiments by Cagniard-Latour and others, if either water, alcohol, or ether be placed in strong glass tubes, which are hermetically sealed after the air has been expelled by boiling, and if then these tubes are exposed to a sufficiently high temperature, a moment is reached at which the liquid suddenly disappears, and is converted into vapour. With ether this occurs at 200° ; the vapour then occupies a space less than double its volume in the liquid state, its pressure being then 38 atmospheres. Alcohol which half fills a tube is converted into vapour at 207° C. If a glass tube about half filled with water, in which some carbonate of soda has been dissolved, to diminish the action of the water on the glass, be heated, it is completely vaporised at about the temperature of melting zinc. When ethyl chloride is heated in a stout sealed tube, the upper surface ceases to be distinct at 170°, and is replaced by an ill-defined nebulous zone. As the temperature rises this zone increases in width in both directions, becoming at the same time more transparent ; after a time the liquid is completely vaporised, and the tube becomes transparent and seemingly empty. On cooling, the phenomena are reproduced in opposite order. Similar appearances are observed on heating ether in a sealed tube at 190°. Andrews made a series of observations on the behaviour of condensed gases at different temperatures, by means of an apparatus the principal features of which are represented |in fig- 355- The pure and dry gas is contained in a tube g, which is sealed at one end, and the gas is shut in by a thread of mercury. The tube is inserted in a brass end-piece, E, which is firmly screwed on a strong copper tube, R. At the other end is a similar piece, in which a steel screw works, perfect tightness being ensured by good packing. The tube is full of water, so that by turning this screw the pressure on the enclosed gas can be increased up to 500 atmospheres. In some cases the projecting capillary tube is bent downwards, so that it can be placed in a freezing mixture. Andrews found on raising liquid carbonic acid in such ; temperature of 31° C. that the surface of demarcation between the liquid and the gas became fainter, lost its curvature, and gradually disappeared The space was then occupied by a homogeneous fluid, which, when the pressure was suddenly diminished, or the temperature slightly lowered exhibited a peculiar appearance of moving or flickering striae throughout A A 2 I- ■ I ! i; i I I" i Fig- 35.-! tube to a 556 On Heat [378- its whole mass. Above 31" no apparent liquefaction of carbonic anhydride, or separation into two distinct forms of matter, could be effected, not even when the pressure of 400 atmospheres was applied. From similar observations made with other substances it seems that there exists for every liquid a temperature, the critical point or critical te7n- perature. While below this critical point a sudden transition from gas to liquid is accompanied by a sudden diminution of volume, and liquid and gas are separated by a sharp line of demarcation, above this critical point the change is connected with a gradual diminution of volume, and is quite imperceptible. The condensation can, indeed, only be recognised by a sudden ebullition when the pressure is lessened. Hence, ordinary condensa- tion is only possible at a temperature below the critical point, and it is not surprising, therefore, that mere pressure, however great, should have failed to liquefy many of the gases. These relations are shown in the case of carbonic acid by fig. 356, in which the horizontal lines, the abscissse, represent volumes, and the vertical lines, the ordinates, pressures in atmospheres. Suppose now at the particular temperature I3'l° a given quantity of gas, whose pressure and volume are indicated by the point G on the lowest curve, is subjected to gradually increasing pressure : the volume diminishes until the pressure reaches 48 atmospheres, the gas begins to liquefy, and the continued diminution of its volume completes the liquefaction (this state is represented by the line AB), after which any further increase of pressure only diminishes the volume to much the same extent as any other liquid (96). The beha- viour of the COj at 13-1° C. is denoted by the line GABQL. At a higher temperature, 21-5°, the same general results are obtained, except that a pressure of 61 atmospheres (the point A') is required for the liquefaction, and the line A'B' is shorter. On continuing the experiments It IS found that at a temperature of 30-9° there is no horizontal part, the lines merg:e into each other, and at no higher temperature is there a separa- tion into liquid and gas. This is the critical temperature, and the higher the temperature the more neady does the curve show the behaviour of a perfect gas. The phenomenon of the critical temperature may be conveniently illus- trated by the following arrangement (fig. 357), which is also well adapted for projection on a screen by means of a magic-lantern for lecture purposes. A stout glass tube about 2-5 mm. wide and 40 mm. long contains liquid sulphur dioxide, and is supported, with the drawn-out end downwards, in a test-tube by means of a wire frame. Pure melted paraffin is added to about 10 cm. above Fig. 356 -3741 PapirCs Digester 357 !l the inner tube. The whole arrangement is suspended in a retort-holder, and heat appHed with a spirit lamp. As the temperature 155° C. (the critical temperature of SO3) is approached, the liquid evaporates in the ordinary way, and there is a sharp line separating' liquid from vapour. At 155° this line vanishes, and at higher temperatures the substance is a homogeneous gas. If the tube be now left to cool, it will be noticed that, as the critical temperature is reached, stria: appear in all parts of the tube, indicating violent commotion, and immediately afterwards liquid and vapour are sharply separated from each other. With careful manipulation there is no danger, and the course of the phenomenon is readily seen through the clear paraffin. The boiling point of a body may be defined as the tem- perature above which a body passes into the state of gas, not only on the surface but in the body of the liquid ; this tempera- ture is therefore different for different pressures, and is accordingly a relative magnitude. The absolute boiling point is the temperature at which a body is converted into gas, what- ever be the pressure ; it is identical with the critical tempera- ture. Mendelejeff found that a relation existed between the absolute temperature and the capillarity of liquids. Increase of temperature diminishes the cohesion, and therefore the elevation of a liquid in a capillary tube. The elevation ultimately vanishes, and the temperature at which this takes place is the absolute boiling point. For some it is very low ; in the case of air, for instance, it is — 158° The critical pressure is that at which condensation takes place at the critical tempeature, and the volume of the saturated vapour at the critical temperature, and under the critical pressure, is called the critical volume. A vapour may be defined as being a gas at any temperature below its critical point. Hence a vapour can be converted into a liquid by pressure alone, and can therefore exist at the pressure of its own liquid, while a gas requires cooling as well as pressure to convert it into a liquid ; that is, to alter its arrangement in such a manner that a liquid can be seen to be separated from a gas by a distinctly bounded surface. Above 31° C. carbonic acid is a gas ; below this temperature it is a vapour. 374. Papin's digester. — Papin appears to have been the first to investi- gate the effects of the production of vapour in closed vessels. The apparatus which bears his name consists of a cylindrical iron vessel M (fig. 358) provided with a cover, which is firmly fastened down by the screw B. In order to close the vessel hermetically, sheet lead is placed between the edges of the cover and the vessel. A cylindrical channel through the cover is closed by a valve to which a rod u is attached. This rod presses against a lever ab, movable at a, and the pressure may be regulated by means of a weight p movable on this lever. The lever is so weighted that when the pressure in the interior is equal to six atmospheres, for example, the valve rises and the vapour escapes. The destruction of the Fig- 357 358 On Heat [374- apparatus is thus avoided, and this mechanism has hence received the name of safety-valve. The digester is filled about two-thirds with water, and is heated on a furnace. The water may thus be raised to a temperature far above 1 00°, and the pressure of the vapour in- creased to several atmospheres, according to the weight on the lever. We have seen that water boils at much lower temperatures on high moun- tains (370) ; the temperature of water boiling in open vessels in such localities is not sufficient to soften animal fibre completely and extract the nutriment, and hence Papin's digester is used in the preparation of food. It is also used in extracting gelatine. When bones are digested in this apparatus they are softened, so that the gelatine which they contain is dissolved. 375. Latent heat of vapour. — ^^As the temperature of a liquid remains constant during boiling, whatever be the source of heat (366), it follows that a consider- able quantity of heat becomes absorbed in boiling, the only effect of which is to transform the body from the liquid to the gaseous condition. And, conversely, when a saturated vapour passes into the state of liquid, it gives out a definite amount of heat. These phenomena were first observed by Black, and he described them by saying that during vaporisation a quantity of sensible heat became latent, and that the latent heat again became free during condensation. The quantity of heat which one pound of a liquid must absorb in passing from the hquid to the gaseous state, and which it gives out in passing from the state of vapour to that of liquid, is spoken of as its latent heat oj vaporisation. The analogy of these phenomena to those of fusion will be at once seen ; the modes of determining them will be described in the chapter on Calori- metry ; but the following results, which have been obtained for the latent heats of evaporation at 0°, may be here given : — Water Alcohol Benzole Acetic acid Ether 607 Carbon bisulphide . 90 236 Turpentine • 74 109 Chloroform . 67 102 Bromine . 49 94 Iodine . 24 The meaning of these numbers is, in the case of water, for instance, that it requires as much heat to convert a pound of water from the state of liquid at 0° C. to that of vapour at the same temperature, as would raise a pound of water through 607 degrees, or 607 pounds of water through one degree ; -375] Latent Heat of Vapour 359 or that the conversion of one pound of vapour of alcohol at o° into liquid alcohol of the same temperature would heat 236 pounds of water through one degree. Watt, who investigated the subject, held that the whole quantity of heat necessary to raise a given weight of water from zero to any temperature, and then to evaporate it entirely, or what is called its total heat of vaporisation, is a constant quantity. His experiments showed that this quantity is 640. Hence the lower the temperature the greater the latent heat, and, on the other hand, the higher the temperature the less the latent heat. The latent heat of the vapour of water evaporated at 100° would be 540, while at 50° it would be 590. At higher temperatures the latent heat of aqueous vapour would go on diminishing. Water evaporated under a pressure of 15 atmospheres at a temperature of 200° would have a latent heat of 440, and if it could be evaporated at 640° it would have no latent heat at all. At this temperature it would be in the critical state, being indifferently either liquid or gaseous. Regnault, who examined this question with great care, found that the total quantity of heat necessary for the evaporation of water increases with the temperature, and is not constant, as Watt had supposed. It is repre- sented by the formula Q = 6o6'5 + 0-305/, in which Q is the total quantity of heat, and t the temperature of the water during vaporisation, while the numbers are constant quantities. The total quantity of heat necessary to evaporate water at 100° is 6o6'5 + (0-305 x 100) = 637 ; at i2o° it is 643 ; at 150° it is 651 ; and at 180° it is 661. Hence the latent heat of vaporisation of water is 537 at 100°, 523 at 120°, 501 at 150°, and 481 at 180° C. The total heat of the evaporation of ether is expressed by a formula similar to that of water, namely, Q = 94 + 0-045/ ; '^"^ 'l^^^' foi^ chloroform Q = 67 + 0-1375/. The heat which is expended simply in evaporating a liquid, and which is spoken of as the latent heat, produces no rise of temperature, and only appears as doing the work of a change of state. One portion of this work is expended in overcoming the cohesion of the particles in the liquid state, and enabling them to assume the gaseous form — this is the internal work, and is by much the greater ; the other, the external work, is expended in overcoming the external pressure on the vapour formed. Knowing the increase of volume, and the pressure, the external work may be readily calculated ; for if the volumes of unit weight of the substance in the state of liquid and of vapour are respectively j and a, and the pressure p, then the external work is p{(r — s), and its heat equivalent p{(r — s)l], J being the mechanical equivalent of heat. So that, if r is the total heat of vaporisation, r = p+p{• or a freezing mixture. This is surrounded by a safety bell-jar, C. By working the force pump a pressure of 400 atmospheres can be pro- duced, which can be increased to 2500 atmospheres by means of the screw piston. When a suitable pressure has been applied, if we wait until the heat due to the compression has disappeared, and then suddenly open the screw worked by the wheel X, thereby reducing the pressure to one atmosphere, the cold produced by the sudden expansion of the gas in the tube OT' is so great as to Uquefy a portion of it, as is shown by the production of a mist. This observation was first made with nitric oxide, but similar results have been obtained with marsh gas, carbonic acid, and oxygen. 386. Pictet's method. — The principle of Pictet's method is that of libera- ting the gas under great pressure, combined with the application of a very low temperature. The essential parts of the apparatus are the following : — Two double-acting pumps, A and B (fig. 374), are so coupled together that they cause the evaporation of liquid sulphurous acid contained in the annular receiver C. By the action of the pumps the gas thus evaporated' is forced into the receiver D, where it is cooled by a current of water, and again Uquefied under a pressure of three atmospheres. Thence it passes again by the narrow tube d to the receiver C, to replace that which is ■evaporated. 372 On Heat [386- In this way the temperature of the liquid sulphurous acid is reduced to - 65°. Its function is to produce a sufficient quantity of liquid carbonic acid, which is then sub- mitted to a perfect- ly analogous pro- cess of rarefaction and condensation. This is effected by means of two simi- lar pumps, E and F. The carbonic acid gas, perfectly pure and dry, is drawn from a reser- voir through a tube not represented in the figure, and is forced into the con- denser K, which is cooled by the liquid sulphurous acid to a temperature of — 65°, and is there liquefied. H is a tube of stout copper con- FiK 374 nected with the condenser K by a narrow tube k. When a sufficient quantity of carbonic acid has been liquefied, the connection with the gasholder is cut off, and by working the pumps E and F a vacuum is created over the liquid carbonic acid in H, which produces so great a cold as to solidify it. L is a stout wrought-iron retort capable of standing a pressure of 1500 atmospheres. In it are placed the substances by whose chemical actions the gas is produced : potassium chlorate in the case of oxygen. The retort is connected with a strong copper tube in which the actual condensation is effected. This tube, the pressure in which is indicated by a specially con- structed manometer R, is closed by a stopcock N. When the four pumps are set in action, for which a steam-engine of 1 5 horse-power is required, heat is applied to the retort. Oxygen is liberated in a calculated quantity, the temperature of the retort being about 485°. Towards the close of the decomposition the manometer indicates a pressure of 500 atmospheres, and then sinks to 320. This diminution is due to the con- densation of gas, and at this stage the tube contains liquefied oxygen. If the cock N is opened, the liquid issues with violence, having the appearance of a dazzUng white pencil. This lasts three or four seconds. On closing the stop- cock the pressure, which had diminished to 400 atmospheres, now rises, and again becomes stationary proving that the gas is once more being condensed. The phenomena presented by the jet of oxygen when viewed by the electric light showed that the hght it emits was partially polarised, indicating a probable transient crystallisation of the liquid. -387] Later Researches 373 The following table exhibits some of the physical properties of sub- stances, gaseous at ordinary temperatures, when reduced to very low temperatures. Name Hydrogen . Critical tempera- ture Boiling point at atmo- spheric pressure Freezing point Density of the liquid at the boiling point Colour of liquid -235 -253 -258 to — 260 ■07 Colourless Fluorine . — -187 — ri4 Pale yellow Nitrogen . - 146-0 -194 -214-0 I'lO Colourless Carbonic oxide - 139-5 — 190 -207-0 (■') Oxygen -iiB-B -182 — 1-13 Bluish Argon -117-4 -186-1 - 190 1-212 Colourless 1 Nitric oxide - 93-5 -154 - 167-0 j Methane - 8i-8 -162 -186 0-415 J5 387. Later researches. — Wroblewski and Olszewski apparatus represented in fig. 375. The gas to be liquefied is contained in the tube qr, and is com- pressed by means of a sort of Cailletet pump coupled up with b. Liquid ethylene is contained in the reservoir x, which is surrounded by a freez- ing mixture of ice and salt ; it passes thence through the tube b\ which is surrounded by a paste of solid carbonic acid and ether, and then reaches s, cooled down to a temperature of — loo''. By means of an air-pump to which is con- nected the lead tube v this cooled liquid can be caused to evaporate under a pressure of 25 mm., so that the temperature as indicated by the hydro- gen thermometer / is -136°. The vessel in which this is effected contains calcium chloride y, the object of which is to prevent any deposition of dew on the tube. At a temperature of —136° oxygen at once liquefies under a pressure of 20 atmospheres. By still further reducing the pressure so that ethylene evaporates at a pressure of i mm. the temperature sinks to — 152° C, and now nitrogen and carbonic oxide can be directly condensed. If again the space above these liquids is rare- fied, carbonic oxide becomes solid at — 190°, and nitrogen at - 203° Dewar has carried out extensive researches on the hquefaction of gases, and has liquefied and made use of the rig. 37s even solidified air. The methods adopted do not differ in principle from 374 On Heat [387- the cold is produced by the evaporation those which have been mentioned : of liquid ethylene. Ladenburg and Kriigel (1900) determined the boiling and freezing points of a number of 'substances. They employed a thermo-electric couple, and compared its scale with a hydrogen thermometer at three temperatures,, viz. the boiling point of hquid air, — 191-25°; of ethylene, — 102-9° ; 3-"d the sublimation point of solid carbon dioxide, -77-5°. The following table gives some of their results : — Melting point ■ Substance Boiling point Oxygen -182-2 at 745 mm. Nitrous oxide . -142-8 „ 757 „ Ammonia Hydrochloric acid . - 83-1 at 755-4 „ Hydrobromic acid . - 68-1 „ 755-4,, Sulphuretted hydrogen . - 60-4 „ 755 „ ] Methane -162 „ 751 „ Ethane - 84-1 „ 749 „ Acetylene — 82-4 (sublimation point) Methyl alcohol — Ethyl alcohol . . — Ether . — -150-5 - 75-5 - III-3 - 86-13 - 82-9 - I72-I Sublimes - 93 9 -111-8 -113-1 Dewar has introduced an important improvement in surrounding the vessel in which the liquefied gas is contained by a single or double vacuum jacket, that is, a space from which the air is exhausted ; in this way liquid air may be kept and manipulated in open vessels, or, in other words, at the ordinary atmospheric pressure. Fig. 376 illustrates an arrangement by which liquid air may be kept in an open glass vessel virtually without evaporation. The smaller tube is a glass one sur- rounded by a second one, from which the air has been exhausted ; this tube contains liquid air, and, after the insertion of a glass tube and stopper, it is immersed in liquid air contained in a similar outer vacuum tube ; A is connected with the inner and B with the outer tube. As the latter receives all the radiant and conducted heat, air is continuously boiling off from the outer tube ; but as no heat reaches the inner tube there is no escape from A. By connecting B with an air-pump so as to reduce the pressure to about 10 mm., and simultaneously connecting A with an air-pump which is worked, the temperature of the liquid air is so reduced that it solidifies to a jelly-like mass. These experiments have made it possible to examine physical properties of various substances at tempera- F'g- 376 tures which approach absolute zero. It is impossible -387] Later Researches 375 here to give an account of the results obtained, but some of the most im- portant will be mentioned in their places. Qne interesting experiment may be mentioned. If a barometer is prepared in the usual way, and a sponge dipped in liquid air is applied to a portion of the outer surface of the Torri- ceUian vacuum space, a mirror of metallic mercury is immediately deposited on the inside. Linde and Hampson have constructed apparatus for the liquefaction of gases, which works continuously and depends essentially on the cooling produced when a gas expands ; it may be looked upon as the reverse of a regenerative furnace. The main features of this apparatus are represented in fig. 377. Consider, in the first case, a single round of. operations. Air supplied through the intake z, at the pressure /^ and temperature t^, is brought by the compressor F to the pressure /„ say of 50 atmospheres, thereby becom ng ^ Fig- 377 heated, but by passing' through the cooler K is restored to the temperature /j ; from this it passes through the inner tube of C, which is the charac- teristic feature of the apparatus ; meeting there a current of cooled gas proceeding in the opposite direction through the annular space of C, its temperature is lowered to t^. If the throttle valve v is opened for a moment the gas suddenly expands, its pressure is reduced to/,, and its temperature falls to t^. With this latter temperature it passes through the annular space of C, and so back to the compressor F, cooling, as already stated, the current passing in the opposite direction through the inner tube and itself becoming raised to the tem- perature t^. The gas thus reduced to this latter temperature, and at the original pressure /j, again goes through the same round of operations, again experi- encing a further reduction of temperature until liquefaction sets in. The 376 On Heat [387- operations are, in fact, continuous, and with a large apparatus of this kind several litres of liquid air have been prepared in an hour. Liquefaction of Hydrogen. — The principal feature of Hampson's or Linde's apparatus is that the gas at high pressure suddenly expands and is thereby cooled ; the expanded and cooled gas circulates round the tube containing the compressed gas, and cools it, and thus expansion at the nozzle takes place at a temperature which falls lower and lower, until finally it reaches that at which the gas liquefies. It was by making use of this principle of cooling by free expansion, combined with the cooling effect due to liquid air boiling at reduced pressure, that Dewar (igoo) succeeded in liquefying hydrogen. The difficulty arises from the extremely low critical temperature of hydrogen, viz. —235° C. Liquid air boils at about —191° under atmospheric pressure, and at —210° if the pressure is suflSciently reduced. The process then for liquefying hydrogen is as follows : — The gas at 200 atmospheres pressure is cooled to about — 205° by air boiling into a vacuum, and is then further cooled by free expansion to, say, -215° C, and returns to the gasholder.' But before doing so it begins the process of intensification by passing over the coil containing the compressed hydrogen, and giving up to this the 10 degrees of additional cooling which it had gained by expansion. Thus the high-pressure gas which succeeds it reaches the nozzle at —215° C, and expanding from a lower temperature gains by free expansion a greater amount of cooling, say 15°, so that it now passes away over the coil at — 230° C, and cools to this temperature the com- pressed gas by which it is succeeded. This intensification proceeds until the cooling reaches the boiling point of hydrogen at the pressure of the gas- holder, which is practically atmospheric. Liquid hydrogen then collects in the vessel below the nozzle. The temperature of liquid hydrogen at atmo- spheric pressure was estimated by Dewar at —253° C, or 20° absolute. Dewar also boiled liquid hydrogen at low pressure, and found it to be, like nitrogen and carbonic acid, one of the substances which readily freeze them- selves by evaporation. In the solid hydrogen thus obtained he reached the lowest temperature known, which he estimated at 13° to 15° absolute — temperatures confirmed by his subsequent observations by helium thermo- meter. One of the results of liquefying hydrogen has been to show that helium is a still more volatile gas. It is possible, therefore, to reach a lower temperature than that of liquid — ^probably even than that of solid — hydrogen, by applying to helium the same process of free expansion and continuous cooling which has been successful in the case of hydrogen. Helium has been reduced to 10° A. without freezing (Dewar). MIXTURE OF GASES AND VAPOURS 388. Laws of the mixture of gases and vapours. — Every mixture of a gas and a vapour obeys the two following laws : — L The pressure, and, consequently, the quantity , of vapour which saturates a given space are the same for the same temperature, whether this space contains a gas or is a vacuum. II. The pressure of the mixture of a gas and a vapour is equal to the -388] Mixture of Gases and Vapours 377 \ sum of the pressures which each would exert if it occupied the same space alone. These are known as Daltoris laws, from their discoverer, and are de- monstrated by the following apparatus, which was invented by Gay-Lussac : — It consists of a glass tube A (fig. 378), to which two stopcocks, b and d, are cemented. The lower stopcock is provided with a tubulure which connects the tube A with a tube B of smaller •diameter. A scale between the two tubes serves to measure the heights of the mercurial columns in these tubes. . The tube A is filled with mercury, and the stopcocks b and d are closed. A glass globe M, filled with dry air or any other gas, is screwed on by means of a stopcock in the place of the funnel C. All three stopcocks are then opened, and a little mercury is allowed to escape, which is replaced by the dry- air of the globe. The stopcocks are then closed, and as the air in the tube expands on leaving the globe, the pressure on it is less than that of the atmosphere. Mer- cury is accordingly poured into the tube B until it is at the same level in both tubes. The globe is then removed, and replaced by the funnel C, provided with a stopcock a of a peculiar con- struction. It is not perforated, but has a small cavity, as represented in n, on the left of the figure. Some of the liquid to be vaporised is poured into C, and the height of the mercury k having been noted, the stopcock b is opened and a turned so that its cavity becomes filled with liquid ; being again turned, the liquid enters the space A and vaporises. The liquid is allowed to fall drop by drop until the air in the tube is saturated, which is the case when the level k of the mercury ceases to sink (356). As the pressure of the vapour produced in the space A is added to that of the air already present, the total volume of gas is increased. It may easily be restored to its original volume by pouring mercury into B. When the mercury in the large tube has been raised to the level k, there is a diiference Bo in the level of the mercury in the two tubes which obviously represents the pressure of the vapour ; for as the air has resumed its original volume, its pressure has not changed. Now, if a few drops of the same liquid be passed into the vacuum of a barometric tube, a depression exactly equal to Bo is produced, which proves that, for the same temperature, the pressure of a saturated vapour is the same in o _ /' 0-317/ (H — /z)' If volume be measured in cubic centimetres and weight in grammes, the formula becomes p_ /(I -t- 0^)760 -ooi293'z/(H -//)' 392. Hofmann's method. — Hofmann materially improved the method of Gay-Lussac by having the mercury tube fb, in which the vapour is pro- duced, about a metre in length (fig. 382) ; it is, in fact, a barometer, and the vapour is formed in the Torricellian vacuum. This tube is sun-ounded by another glass tube a, which is connected, by a bent tube c, with a canister e, -393] Dumas' Method 383 ■so that water, amylic alcohol, or aniline, or, indeed, any substance with a constant boiling point, may be distilled through the tube a, and the vapour issues by the tube d, which is connected with a condensing arrangement not repre- sented in the figure. In this way more con- stancy in the temperatures is ensured than with the use of a mercury bath. The liquid is contained in very minute stoppered tubes, h, holding from 20 to 100 milligrammes of water ; the stoppers come out in the vacuum, and the tubes can be used over again. As, under the above conditions, the liquid vaporises into a vacuum, the vapour is formed under a very much lower pres- sure than that of the atmosphere, and therefore at a temperature much below its ordinary boiling point. Thus, the vapour-density of a body which only hoils at a temperature of 1 50° can be de- termined at the temperature of boiling water. This is of great use in the case of those bodies which decompose at their boiling point under the ordinary atmo- spheric pressure. 393. Dumas' method. — The original method of Gay-Lussac cannot be applied to liquids whose boiling point exceeds 150° or 160°. In order to raise the oil in the cylinder to this temperature it would he necessary to heat the mercury to such a degree that its vapour would be danger- ous to the operator. And, moreover, the pressure of the mercurial vapour in the graduated jar would add itself to that of the vapour of the liquid, and so far vitiate the result. The following method, devised by Dumas, can be used up to the tempe- rature at which glass begins to soften ; that is, about 400°. A glass globe is used with the neck drawn out to a fine point (fig. 383). The globe, having been dried externally and internally, is weighed, the temperature / and barometric height h being noted. This weight, W, is the weight of the glass, G, in addition to/, the weight of the air it contains. The globe is then gently warmed and its point immersed in the liquid whose vapour- density is to be determined ; on cooling, the air contracts, and a quantity of liquid enters the globe. The globe is then immersed in a bath, either of oil or fusible metal, according to the temperature to which it is to be raised. In order to keep the globe in a vertical position a metal support, on which a movable rod slides, is fixed on the side of the vessel. This rod has two rings, between which the globe is placed, as shown in the figure. There is another rod, to which a weight thermometer, D (325), is attached. Fig. 382 384 On Heat [393- Fig. 383 The globe and thermometer having been immersed in the bath, the latter is heated until slightly above the boiling point of the liquid in the globe. The vapour which passes out by the point expels all the air in the interior. When the jet of vapour ceases, which is the case when all the liquid has been converted into vapour, the point of the globe is hermetically sealed, the temperature of the bath /', and the baro- metric height h', being noted. When the globe is cooled it is carefully cleaned and again weighed. This weight, W', is that of the glass G, plus p' , the weight of the vapour which fills the globe at the temperature t' , and pressure h' , or W' = G +/'. To obtain the weight of the glass alone, the weight f of air must be known, which is determined in the following manner : — The point of the globe is placed under mercury and the extremity broken off with a small pair of pincers : the vapour being con- densed, a vacuum is produced, and mercury rushes up, completely filling the globe, if, in the experi- ment, all the air has been entirely expelled. The mercury is then poured into a carefully graduated measure, which gives the volume of the globe. From this result, the volume of the globe at the tem- perature t' may be easily calculated, and consequently the volume of the vapour. From this determination of the volume of the globe, the weighty of the air at the temperature t and pressure h is readily calculated, and this result subtracted from W gives G, the weight of the glass. Now the weight of the vapour^' is W — G. We now know the weight/' of a given volume of vapour at the temperature t! and pressure h\ and it is only necessary to calculate the weight p" of the same volume of air under the same conditions, which is easily accomphshed. The quotient •^, is the required density of the P vapour. Deville and Troost modified Dumas' method so that it can be used for determining the vapour-density of liquids with very high boiling points. The globe is heated in an iron cylinder in the vapour of mercury or of sulphur, the temperatures of which are constant respectively at 350° and 444°. In other respects the determination is the same as in Dumas' method. For determinations at higher temperatures, Deville and Troost employed the vapour of zinc, the temperature of which is 1040°. As glass vessels are softened at this temperature, they used porcelain globes with finely drawn- out necks, which are sealed by means of the oxyhydrogen flame. In the case of substances having a high boiling point, Victor Meyer has advantageously used a non-volatile substance. Wood's fvtsible alloy, which melts at 70°, instead of mercury. Habermann has introduced into Dumas' method Hofmann's modification of Gay-Lussac's, by connecting the open end of the vessel B (fig. 383) with a space in which a partial vacuum is made. Thus the vapour-density can be determined for temperatures far below the boiling point. -393] Dumas' Method 38s A method of determining vapour-density, much in use, is that devised by Victor Meyer. A long glass tube b with an enlargement at the top is fused to the cylindrical vessel C, which has a capa- city of about 100 c.c. Near the top of ^ a gas delivery tube, a, is fused, and opposite this another tube, e, closed by an india rubber tube in which a metal rod, ^, can be moved airtight. On the rod rests a small thin vessel, containing the substance whose vapour-den- sity is to be determined. For very volatile liquids small bulbs, k, of very thin glass are used ; they are filled -by being fitted through a cork to a tube in which the liquid is placed, as shown on the right of fig. 384. When k is heated, air is driven out of it ; and on cool- ing, k is filled with liquid and the endy is fused. The cork being inserted, the whole ap- paratus is suspended in the long glass vessel rr,, which contains a liquid of constant boil- ing point such as aniline or diphenyle. This is heated until it boils constantly, which is known when no air bubbles issue from the delivery tube a. When this state of things is attained a graduated tube, m, filled with water is pushed over the open end of the tube M. The rod g is then withdrawn and the small vessel falls and is broken, some asbestos being placed at the bottom to prevent a possible breakage of the vessel A itself The vapours from C issue through the bent tube shown in the figure, and are connected with a condensing arrangement not shown. When the substance vaporises a corresponding volume of air issues and is collected in the tube wz. When no more issues the tube is placed in a cylinder of water and is de- pressed until the level inside and outside is the same. The volume v is read off, and the temperature of the water /, which is also that of the room, and the barometric height H. These data, together with the weight of the| substance p, and k the pi-essure of aqueous ' vapour at t°, enable us to calculate the den- sity from the formula ■ / - / X 760 (273 + /) 'P' Fig. 384 D = ^/(o•ooI293)(H-^)273 z/(H-/z) where/,/' are expressed in grammes, and 7/ in cubic centimetres. C C 386 On Heat [393- In this case a calorimetrical determination of the temperature is made by dipping a piece of platinum in the Hquid. The volume of the vapour is obtained in the form of an equal volume of air measured at the temperature of the room, and thus neither the capacity of the vessel b nor the temperature of the vapour need be known, unless it be desired to investigate in what respect the density varies with the temperature. 394. Relation of vapour-density to molecular weight. Dissociation. — The densities of vapours, determined at temperatures a few degrees above their boiling points, and when they may be considered as obeying the gaseous laws, are governed by a simple but very important la«', that the densities of vapours are proportional to their molecular •weights. If both densities and molecular weights are referred to the same standard, that of hydrogen being taken as 2 for instance, the vapour-densities are equal to the mole- cular -weights. If the density of air is taken at i, that of hydrogen is O'o693 = -Jl- , and hence for all other gases and superheated vapours the density is _L. of the molecular weight. This law is of great importance in chemistry in fixing the molecular weights of bodies, more especially in organic chemistry. In some cases exceptions are met with ; these, when small, may be ascribed to imperfection Qf the gaseous state. A more important cause is the following : — When sal- ammoniac, NH^Cl, for instance, is strongly heated, it is resolved into ammonia, NH,, and hydrochloric acid, HCl, and it then occupies a volume double that required by the law. But there is a partial decomposition even at lower temperatures, so that the vapour consists of molecules of sal- ammoniac, mixed with molecules of free hydrochloric acid and of free ammonia. In such cases the vapour-density is said to be abnormal; and this partial decomposition, in which there is a mixture of undecomposed and of decomposed molecules, is spoken of as dissociation. Thus, sulphuric acid, SO4H,, at 325°, consists of about one half undecomposed molecules, while the other moiety decomposes into sulphuric anhydride, SO3, and water, H.,0. The dissociation of water begins at 1200° C, and is complete at 2500°. Stannic chloride, SnCl,, has the theoretical density 6-53. At 600° the density corresponds to the formula Sn^Cl^ ; as the temperature rises this diminishes, and at 1000° it represents the formula SnClj. It appears thus that the vapour exists in two forms : at 600"^ as SnjCl4, and at 1000 as SnCl^ ; as the temperature rises from 600° the molecule Sn^Cl^ is more and more dissociated, until at 1000° it is completely resolved into aSnCl.j. Dissociation does not take place suddenly, but gradually ; it increases with the temperature, and is limited by the; tendency of the components to recombine ; for each temperature the quantity dissociated is in a constant ratio to the whole. As the temperature sinks, the bodies again recombine, and at the initial temperature the body is in its original state. In this respect dissociation differs from decomposition. The temperature at which the decomposition is half completed is taken as that of dissociation. Dissociation is also met with in elementary bodies : thus at a tempera- ture of 500° C. sulphur has the vapour-density 96 (H = i), representing a molecular weight of 192 ; as the temperature increases this becomes less, and from 1000° it is constant, being then 32, which is normal, corresponding -395] Relative Densities of Liquid and Vapour 387 to a molecular weight of 64. At the lower temperature the molecule is con- sidered to be an aggregate consisting of six atoms or three molecules, while at higher temperatures this complex splits up, and at 1000° consists of the normal diatomic molecule. In like manner the density of iodine vapour, which up to 600° is 8716, is only 4-5, or about half as much, at 1500°, but then remains constant. This probably represents a dissociation of the iodine molecule, Ij, into two atoms. Densities of vapours. Air i-oooo Vapour of phosphorus . 4-3256 Vapour of water 0-6225 turpentine . 5-0130 alcohol 1-6138 anthracene . 6-OIOO acetic acid . 2 -0800 sulphur 6-6542 carbon bisulphide 2-4476 mercury 6-9760 ether . 2-5860 chrysene 8-1200 benzole 2-7290 iodine . 8-7160 anihne 3-3100 perchloriphenyle . 17-4300 The density of aqueous vapour, when a space is saturated with it, is at all temperatures |, or, more accurately, 0-6225, of the density of air at the same temperature and pressure. 395. Relation between the volume of a liquid and that of its vapour. — The density of vapour being known, we can readily calculate the ratio between the volume of a vapour in the saturated state at a given temperature and that of its liquid at zero. We may take as an example the relation between water at zero and steam at 100°. The ratio betwee^n the weights of equal volumes of air at zero, and the normal barometric pressure, and of water under the same circumstances, is as I : 773. But from what has been already said (335), the density of air at zero is to its density at ico°as i +c/ : i. Hence the ratio between the weights of equal volumes of air at 100° and water at 0° is : 773) or 0-73178 : 773- I +0-003665 X 100 Now from the above table the density of steam at 100° C, and the normal pressure, compared with that of air under the same circumstances, is as 0-6225 : I. Hence the ratio between the weights of equal volumes of steam at 100° and water at 0° is 0-73178 X 0-6225 : 773, or 0-4555 : 773, or I : 1698. Therefore, as the volumes of bodies are inversely as their densities, one volume of water at zero expands into 1698 volumes of steam at 100° C. The practical rule, that a cubic inch of water yields a cubic foot of steam, though not quite accurate, expresses the relation in a convenient form. 388 On Heat [396- CHAPTER VI HYGROMETRY 396. Province of hygrometry. — The province of hygrometry is to deter- mine the quantity of aqueous vapour contained in a given volume of air. This quantity is very variable ; but the atmosphere is seldom or never com- pletely saturated with vapour, even in our climate. Nor is it ever completely dry ; for if hygrometric substances — that is to say, substances with a great aflfinity for water, such as calcium chloride, sulphuric acid, &c. — be at any time exposed to the air, they absorb aqueous vapour. 397. Hyg^rometric state. — As the air is, in general, never saturated, the ratio of the quantity of aqueous vapour actually present in a given volume of atmospheric air to that which it would contain if it were saturated, the temperature remaining the same, is called the hygrometric state, or relative humidity of the air. The absolute moisture is measured by the weight of water actually present in the form of vapour in the unit of volume. We say the ' air is dry ' when water evaporates and moist objects dry rapidly ; and the ' air is moist ' when they do not dry rapidly, and when a slight lowering in temperature brings about deposits of moisture. The air is dry or moist according as it is more or less distant from its point of saturation. Our judgment is, in this respect, independent of the absolute quantity of moisture in the air. Thus, if in summer, at a temperature of 25° C, we find that each cubic metre of air contains 13 grammes of vapour, we say it is very dry, for at this temperature it could contain 22'5 grammes. If, on the other hand, in winter we find that the same volume contains 6 grammes, we call it moist, for it is nearly saturated with vapour, and the slightest diminution of temperature produces a deposit. When a room is warmed, the quantity of moisture is not diminished, but the humidity of the air is lessened, because its point of saturation is raised. The air may thus become so dry as to be injurious to the health, and hence it is usual to place vessels of water on the stoves used for heating. As Boyle's law applies to non-saturated vapours as well as to gases (357), it follows that, with the same temperature and volume, the weight of vapour in an unsaturated space increases with the pressure, and therefore with the pressure of the vapour itself. Instead, therefore, of the ratio of the quantities of vapour, that of the corresponding pressures may be substituted, and it may be said that the hygrometric state is the ratio of the elastic force or pressure of the aqueous vapour which the air actually contains, to the elastic force of the vapour which it would cotitain at the same temperature if it were saturated. -399] Chemical Hygrometer 389 \i f is the actual pressure of aqueous vapour in the air, and F that of saturated vapour at the same temperature, /, and E the hygrometric state ; also, if (4 be the density of aqueous vapour at 0°, w the weight of the vapour occupying the volume v, and W the weight which the vapour would have if the space were saturated, we have w=^^. /-, W=-^°^.^; therefore E = ,^ = 4 l+at 760' 1+at 760 ' W F As a consequence of this second definition, it is important to notice that, the temperature having varied, the air may contain the same quantity of vapour and yet not have the same hygrometric state. For, when the tem- perature rises, the pressure of the vapour which the air would contain, if satu- rated, increases more rapidly than the pressure of the vapour actually present in the atmosphere, and hence the ratio between the two pressures — -that is to say, the hygrometric state — becomes smaller. This also follows from the formula E =,w/W ; for though w may remain constant on rise of temperature, W will be greater. Jamin proposed to replace this ratio ^, which expresses the relative moisture, by the ratio •c^~f in which H is the barometric height ; he calls this the hygrometric richness, and contends that it brings out changes in the quantity of moisture present in the air with greater distinctness. It will presently be explained (407) how the weight of the vapour con- tained in a given volume of air may be deduced from the hygrometric state. 398. Different kinds of hygrometers. — Hygrometers are instruments for measuring the hygrometric state of the air. There are numerous varieties of them — chemical hygrometers, condensing hygrometers, and psychrometers. 399. Chemical hygrometer. — The method of the chemical hygrometer consists in passing a known volume of air over a substance which readily absorbs moisture — calcium chloride, for instance. The substance having been weighed before the passage of air, and then afterwards, the increase in weight represents the amount of aqueous vapour present in the air. By means of the apparatus represented in fig. 385 it is possible to examine any given volume of air. Two brass reservoirs, A and B, of the same size and construction, act alternately as aspirators, by being fixed to the same axis, about which they can turn. They are connected by a central tubulure, and by means of two tubulures in the axis the lower reservoir is always in con- nection with the atmosphere, while the upper one, by means of an india rubber tube, is connected with two (J tubes, N and M, filled either with calcium chloride or with pumice-stone impregnated with sulphuric acid. The first absorbs the vapours in the air drawn through, while the other, M, stops any vapour which might diffuse from the reservoirs into the tube N. The lower reservoir being full of water, and the upper one of air, the apparatus is inverted so that the liquid flows slowly from A to B. A partial vacuum being formed in A, air enters by the tubes NM, in the first of which all the vapour is absorbed. When all the water is run into B the apparatus is inverted ; the same flow recommences, and the same volume of air is drawn through the tube N. Thus, if each reservoir holds 5 litres, for 390 On Heat [399- exanaple, andjthe apparatus has been turned five times, 30 litres of air have traversed the tube N, arid have been dried. If then, before the experiment. Fig. 38s the tube with its contents lias been weighed, the increase of weight gives, the weight of aqueous vapour present in 30 litres of air at the time of the experiment. Edelmann has devised a new form of hygrometer, the principle of which is to enclose a given volume of air, and then to absorb the aqueous vapour present by means of strong sulphuric acid ; in this way a diminution in the pressure is produced which is determined, and is a direct measure of the pressure/' of the aqueous vapour previously present. Similar apparatus have been devised by Rudorfif and by Neesen. 400. Condensing' hygrometers. — When a body graduilly cools in a moist atmosphere — -as, for instance, when a lump of ice is placed in water contained in a polished metal vessel — the layer of air in immediate contact with it cools also, and a temperature is ultimately reached at which the vapour present is just sufficient to saturate the air ; the least diminution of tempera- ture then causes a precipitation of moisture on the vessel in form of dew. When the temperature rises again, the dew disappears. The mean of these two temperatures is taken as the deiv-point, and the object of condensing hygrometers is to observe this point. Daniell's and Regnault's hygrometers belong to this class. 401. Daniell's hygrometer. — This consists of two glass bulbs at the extremities of a glass tube bent t\\'ice (fig. 386). The bulb A is two-thirds ''full of ether, and a very delicate thermometer is plunged in it ; the rest of the space contains nothing but the vapour of ether, the ether having been boiled before the bulb B was sealed. The bulb B is covered with muslin, and ether is dropped upon it. The ether in evaporating cools the bulb, and the -402] Regnaulfs Hygrometer 391 vapour contained in it is condensed. The internal pressure being thus diminished, the ether in A forms vapour which condenses in the other bulb B. In proportion as the liquid distils from the lower to the upper bulb, the ether m A becomes cooler, and ultimately the temperature of the air in immediate contact with A sinks to that point at which its vapour is more than sufficient to saturate it, and it is, accordingly, deposited on the outside as a ring of dew corresponding to the surface of the ether. The temperature of this point is noted by means of the thermometer in the inside. The addition of ether to the bulb B is then discontinued, the temperature of A rises, and the tempera- ture at which the dew disappears is noted. In order to render the deposition of dew more perceptible, the bulb A is made of black glass. These two points having been determined, their mean is taken as that of the dew-point. The temperature of the air at the time of the experiment is indicated by the thermometer on the stem. The pressure f, corresponding to the temperature of the dew-point, is then found in the table of pressures (361). This pressure is exactly that of the vapour present in the air at the time of the experiment. The pressure F of vapour saturated at the temperature of the atmosphere is found by means of the same table ; the quotient obtained by dividing / by F represents the hygro- metric state of the air (397). For instance, the temperature of the air being 15°, suppose the dew-point is 5°. From the table the corresponding pressures are _/= 6-534 millimetres, and F = 12 '699 milli- metres, which gives 0-514 for the ratio of /to F, or the hygrometric state. There are many sources of error in Daniell's hygrometer. The principal are : ist, that as the evaporation in the bulb A only cools the iquid on the surface, the thermometer dipping in it does not exactly give the dew-point ; 2nd, that the observer standing near the instrument modifies the hygro- metric state of the surrounding air, as well as its temperature ; the cold ether vapour also flowing from the upper bulb may cause inaccuracy. 3rd, glass is a bad conductor of heat, hence the temperature of deposition of dew may be different from that indicated by the thermometer. 402. Regnaulfs hygrometer. — Regnaulfs hygrometer consists of two very thin polished silver thimbles 4 cm. in height and 2 cm. in diameter (fig'- 387)- In these are fixed two glass tubes D and E, in each of which is a thermometer. A bent tube. A, open at both ends, passes through the cork of the tube D, and reaches nearly to the bottom of the thimble. There is a tubulure on the side of D, fitting m a brass tube which forms a support for the apparatus. The end of this tube is connected with an aspirator G. The :g. 386 392 On Heat [402- tube E is not connected with the aspirator ; its thermometer simply indicates the temperature of the atmosphere. The tube D is then half filled with ether, and the stopcock of the aspirator opened. The water contained in it runs out, and just as much air enters through the tube A, bubbling through the ether, and causing it to evaporate. This evaporation produces a diminution of temperature, so that dew is deposited on the silver just as on the bulb in Daniell's hygrometer ; the thermometer T is then instantly to be read, and the stream from the aspirator stopped. The dew ^^■ill soon disappear again, and the thermometer T is again to be read ; the mean of the two readings is taken ; the thermometer t gives the corresponding temperature of the air, and hence there are all the elements necessary for calculating the hygrometric state. As all the ether in this instrument is at the same temperature in con- sequence of the agitation, and the temperatures may be read off at a distance by means of a tele- ' scope, and as the silver is thin and a good con- ductor of heat, the sources of error in Daniell's hygrometer are avoided. A much simpler form of the apparatus may be constructed out of a common test- tube containing a depth of i^ inch of ether. The tube is provided with a loosely fitting cork in which are. a delicate thermometer and a narrow bent tube dipping in the ether. On blowing into the ether through an india rubber tube of consider- able length, a diminu- tion of temperature is caused, and dew is ultimately deposited on the glass ; after a little practice the whole process can be conducted almost as well as with Regnault's more complete instrument. The temperature of the air is indicated by a detached thermometer. 403. Dines's hygrometer. — Dines constructed an hygrometer which is also one of condensation, but which dispenses with the use of such volatile liquids as ether. The principle of this instrument is to have a thin flat metal box, through which a small stream of cooled water is allowed to flow for a few seconds. The dew is deposited on the top of the box, which is of thin dark polished metal. By alternately stopping the flow and allowing it to continue, the disappearance and formation of the dew may be very Fig. 3B7 -404] Psychrometer. Wet-bulb Hygrometer 393 accurately observed, and the corresponding temperatures read off by a delicate thermometer placed inside. 404. Psychrometer. Wet-bulb hygrometer. —A moist body evaporates in the air more rapidly in proportion as the air is drier, and the temperature of the body sinks in consequence of this evaporation. The psychrometer, or wet-bulb hygrometer, is based on his principle, the application of which to this purpose was first suggested by Leslie. The form usually adopted in this country is due to Mason. It consists of two delicate thermometers placed on a wooden stand (fig. 388). One of the bulbs is covered with muslin, and is kept continually moist by being connected with a reservoir of water by means of a string. Unless the air is saturated v\'ith moisture the wet-bulb thermometer always indicates a lower temperature than the other, and the difference between the indications of the two thermometers is greater in pro- portion as the air can take up more moisture, and is therefore drier. The pressureyof the aqueous vapour in the atmosphere may be calculated from the indications of the two thermometers by means of the following empirical formula : — f=f' — o-ooo'/7{t - t')/i, in which _/' is the maximum pressure corresponding to the temperature of the wet-bulb thermometer, 0-00077 is a con- stant, h is the barometric height, and t and /' the respective temperatures of the dry and wet bulb thermometers. If, for example, ,4 = 750 millimetres, /= 15'' C, /= 10' C. ; ac- cording to the table of pressures (36 1),_/' = 9-165, and we have /= 9-165 - 0-00077 X 5 X 750 = 6-342. Wr^\ Q This pressure corresponds to a dew-point of about 4-5° C. If the air had been saturated, the pressure would have been 12-699, •'"d the air is therefore about half saturated with moisture. This formula expresses the result with tolerable accuracy, but the above constant 0-00077 requires to be controlled for ■different positions of the instrument ; in small closed rooms it is 0-00128, in large rooms it is o-ooioo, and in the open air without wind it is 0-00090 : the number 0-00077 is its value in a large room with open windows. Regnault found that the difference in temperature of the two bulbs depends on the rapidity of the current of air ; he also found that at a low temperature and in very moist air the results obtained with the psychrometer differed from those yielded by his hygrometer. It is probable that the indications of the psychrometer are only true for mean and high temperatures, and when the atmosphere is not too moist. A formula frequently used in this country is that given by Dr. Apjohn. It is ' orF=/- Fig. 388 F=/--^x. d h - -— X — 96 30 in which d is the difference of the wet and dry bulb thermometers in Fahrenheit degrees ; h the barometric height in inches ; f the pressure of 394, On Heat [404- vapour for the temperature of the wet bulb, and F the pressure of vapour at the dew-point, both in inches, from which the dew-point may, if necessary, be found from the tables. The constant coefficient 88 is to be used when the reading of the wet bulb is above 32° F., and 96 when it is below. According to Glaisher the temperature of the dew-point may be obtained by multiplying the difference between the temperatures of the wet and dry bulb by a constant depending on the temperature of the air at the time of observation, and subtracting the product thus obtained from this last-named temperature. The following table gives the numbers, which are known as Glaisher' s factors. Dry bulb Temperature F.° Factor 1 Dry bulb j Temperature F.° Factor Below 24'' 8-5 34 to 35 2-8 24 to 25 6-9 \ 35-40 2-5 25—26 6-5 40-45 2-2 1 26 — 27 61 45—50 2-1 j 27—28 5-6 50—55 2-0 1 28—29 5-1 55—60 1-9 29—30 4-6 60—65 1-8 30—31 4-1 65—70 1-8 31—32 37 , 70—75 ! 75-80 17 32—33 3-3 17 33—34 3-0 1 80-85 1-6 405. Absorption hygrometers. — These hygrometers are based on the property which organic substances have of elongating when moist, and of ^ again contracting as they become dry. The most common j^^ form is the Aair or Saussure's hygrometer. t^m^^it ^' f^o^sists of a brass frame (fig. 389), on which is fixed Y^^Sm\ °^ °- hair, c, fastened at the top in a clamp, a, provided with a screw, d. This clamp is moved by a screw, b. The lower part of the hair passes round a pulley, the sound. Other gases gave sounds in the order of their absorption for heat ; and, indeed, all Tyndall's results in this direction are most strikingly-confirmed. The investigations of the other experimenters, Preece, Bell and Tainter, and Mercadier, were chiefly directed to| the effects produced when the intermittent beam is allowed to fall on'solid bodies. A sort of ear-trumpet Fig. 422 Fig. 424 Fig. 423 {fig. 424) was used by Mercadier, consisting of a movable piece ab fitting over cd so that plates L of various materials could be experimented upon. The other end f was fitted with a flexible tube and bell so that it could be applied to the ear. When the intermittent beam is allowed to act on this plate it is setfin vibration and a sound is produced. This is not due, at any rate mainly, to transverse vibrations of the plate, for neither the pitch nor the quality of the note was altered when the thickness and nature of the plate were changed (284), nor was it altered when the plate was slit. The best effects were ob- tained when the diaphragm was of thin metal foil coated with lampblack on the side next the rays. Marked effects were also obtained when a transparent plate was used blackened on the side away from the rays. The effect is one of radiant heat, and is essentially due to alternate expansions and contractions 442 On Heat [451- of the layer of air in contact with the surfaces which absorb the radiant heat. The phenomenon may be very simply exhibited by blackening half the inside of a test-tube R, the open end of which is provided with a flexible tube which can be placed to the ear. When the rays fall on the blackened part a IoikI sound is heard, but very little when the bright side is exposed. The effect is also obtained when a blackened piece of foil is placed in the tube. 463] Specific Heat 443 CHAPTER IX CALORIMETRY 452. Calorimetty. Thermal unit. — Calorimetiy measures the quantity of heat which a body parts with or absorbs, when its temperature sinks or rises through a certain number of degrees, or when it changes its condition. Quantities of heat may be expressed by any of its directly measurable effects, but the most convenient is the alteration of temperature, and quan- tities of heat are usually defined by stating the extent to which they are capable of raising a known weight of a known substance, such as water. The unit chosen for comparison, and called the therinal unit, is not every- where the same ; it depends upon the units of mass and temperature adopted. A calorie is the quantity of heat required to raise the temperature of one gramme of water through one degree Centigrade ; a great calorie is 1000 times this. These units of heat are often referred to as a gramme-degree Centigrade and a kilogramme-degree Centigrade respectively. In this book we shall adopt as a thermal unit the pound-degree Centigrade, that is, the quantity of heat necessary to raise one pound of water through one degree Centigrade. 453. Specific heat. — When equal weights of two different substances, at the same temperature, placed in similar vessels, are subjected for the same length of time to the heat of the same lamp, or are placed at the same distance in front of the same fire, it is found that their temperatures will vary considerably ; thus mercury will be much hotter than water. But as, from the conditions of the experiment, they have each been receiving the same amount of heat, it is clear that the quantity of heat which is sufficient to raise the temperature of mercury through a certain number of degrees will raise the temperature of the same quantity of water only through a less number of degrees ; in other words, ,hat it requires more heat to raise the temperature of water through one degree than it does to raise the temperature of mercury by the same extent. Conversely, if the same quantities of water and of mercury at 100° C. be allowed to cool down to the temperature of the air the water will require a much longer time for the purpose than the mercury ; hence, in cooling through the same number of degrees, water gives out more heat than does mercury. It is readily seen that all bodies have not the same specific heat. If a pound of mercury at 100° is mixed with a pound of water at zero, the tem- perature of the mixture will be about 3° only ; that is to say, that while the mercury has cooled through 97°, the temperature of the water has been raised only 3°. Consequently the same weight of water requires about .32 times j as much heafas mercury does, to produce the same elevation of temperature. 444 On Heat [463- If similar experiments are made with other substances, it will be found that the quantity of heat required to effect a certain change of temperature is different for almost every substance, and we speak of the specific heat, or thermal ox calorific capacity, of a body as the quantity of heat which it absorbs when its temperature rises through a given range of temperature, from zero to 1° for example, compared with the quantity of heat which would be absorbed, in the same circumstances, by the same weight of water ; that is, water is taken as the standard for the comparison of specific heats. Thus, to say that the specific heat of lead is 0-0314, means that the quantity oif heat which would raise the temperature of any given weight of lead through 1° C. would raise the temperature of the same weight of water through only 0'03i4° C, or that '0314 thermal unit is required to heat one pound of lead through 1° C. The temperature of a body depends upon the kinetic energy of its smallest particles ; in bodies of the same temperature the atoms have the same energy of motion, the smaller mass of the lighter atoms being compensated by their greater velocity. The heat absorbed by a body not only raises its tempera- ture — that is, increases the energy of the progressive motion of the atoms — but in overcoming the attraction of the atoms it moves them further apart, and along with the expansion which this represents, some external pressure is overcome. In the conception of specific heat is included not merely that amount of heat which goes to raise the temperature but also that necessary for the internal work of expansion, and that required for the external work. If these latter could be separated, we should get the true heat of temperature, that which is used solely in increasing the energy of motion of the atoms. This is sometimes called the true specific heat. Four methods have been employed for determining the specific heats of bodies : (i.) the method of the melting of ice, (ii.) the method of mixtures, (iii.) that of cooling, and (iv.) the method of the steam calorimeter. Pre- viously to describing these methods, it will be convenient to explain the expression for the quantity of heat absorbed or given out by a body of known weight and specific heat, when its temperature rises or falls through a certain number of degrees. 454. Measure of the sensible heat absorbed byl a body. — -Let m be the mass of a body in pounds, c its specific heat, and t ts temperature. The quantity of heat necessary to raise a pound of watei through 1° C. being taken as unity, m of these units would be required to raise m pounds of water through one degree, and to raise it through t degrees, t times as much, or m.t. As this is the quantity of heat necessary to raise through / degrees m pounds of water, whose specific heat is unity, a body of the same weight, only of different specific heat, c, would [require mtc. Consequently, when a body is heated through t degrees, the quantity of heat which it absorbs is the product of its weight into the range of tem.perature into its specific heat. This principle is [the basis of all the formulas for calculating specific heats. If a body is heated or cooled from t to ( degrees, the heat absorbed or disengaged will be represented by the formula m{t' — t)c, or m{t — t')c. -456] Bunsen's Ice Calorimeter 445 455. Method of the fusion of ice. — This method of determining specific heats is based on the fact that to melt a pound of ice 80 thermal units are necessary. Black's calorimeter (fig. 425) consists of a block of ice in which a cavity is made, and which is px"Ovided with a cover of ice. The substance whose specific heat is to be determined is heated to a cer- tain temperature, and is then placed in the cavity, which is covered. After some time the body becomes cooled to zero. It is then opened, and both the substance and the cavity wiped dry with a sponge which has been previously weighed. The increase of weight of this sponge obviously repre- sents the ice which has been converted into water. Now, since one pound of ice at 0° in melting to water at 0° absorbs 80 thermal units, P pounds absorb 80 P units. On the other hand this quan- tity of heat is equal to the heat given out by the body in cooling from f to zero, which is mtc, for it may be taken for granted that in cooling from t° to zero a body gives out as much heat as it absorbs in being heated from zero to f. Consequently from 80 P Tiitc = 80 P we have c — Lavoisier and Laplace replaced the block of ice used by Black in his • experiments by a more complicated apparatus which is called the ice calorimeter. Fig. 426 represents a section. It consists of three concentric tin vessels ; in the central one is placed the body M, whose specific heat is to be determined, while the other two are filled with pounded ice. The ice in the compartment A is melted by the heated body, while the ice in the compartment B cuts off the heating influence of the surrounding atmosphere. The two stopcocks E and D give issue to the water which arises from the melting of the ice. In order to find the specific heat of a body by this apparatus, its weight, m, is first determined ; it is then raised to a given temperature, t, by keeping it for some time in an oil or water bath, or in a current of steam. . Having been quickly brought into the central com- partment, the lids are , replaced and covered with ice, as represented in the figure. The water which flows out by the stopcock D is collected. Its weight, that of the melted ice. The calculation is then made as in the preceding case. 456. Bunsen's ice calorimeter.— On the very considerable diminution of volume which ice experiences on passing into water (349), Bunsen based a calorimeter which is particularly suitable when only small quantities of a Fig. 426 P, is manifestly 446 On Heat [456- substance can be used in determinations. A small test-tube or muffle, A (fig. 427), intended to receive the substance experimented upon, is fused in the wider tube yj3, which contains pure freshly boiled distilled water, and the prolongation of this tube 0C, together with the graduated capillary tube S, contains pure mercury. It is graduated, and the volume corresponding to each division of the graduation is specially determined by calibration ; it is joined to ^C by the small mercury reservoir SD. When the apparatus is immersed in ice, and the temperature reduced to 0° C. some ether is intro- duced into A and rapidly evaporated. This abstracts heat from the^water, and a casing of ice gathers round the outside of A. The tube is then dried, and the apparatus, still surrounded by ice to prevent any rise of temperature, is left to itself until the end of the capillary column in S is stationary. A weighed quantity of a substance at a given temperature is then introduced into the tube, and sinks to zero. In doing' so it melts a certain quantity of ice, which is evidenced by a corresponding motion of the mercury along the tube S. Thus the weight of ice melted, and the weight and-original tempera- ture of the substance experimented upon, furnish all the data for calculating the specific heat. Fig. 427 Fig. 428 Let V = the diminution in volume due to melting of the ice ; u is read off from the tube S. . Since i c.c. of ice at 0° yields •9178 c.c. of water at 0°, the contraction is ■0822 c.c. Hence, if the contraction is i c.c, the water resulting from the melting is •0822 1 1 -I X z; is the volume of water in cubic centi- metres, and therefore its weight in grammes. Hence 11 ■ i ^ ■z/ x 80 = mtc, where 80 is taken as the latent heat of water, m the mass of the substance, / its original temperature, and c its specific heat. -458] Corrections 447 For heating the substance in this, and also in other calorimetrical experi- ments, the apparatus fig. 428 is well adapted. The cylindrical metal vessel •G narrows towards the top and is closed by a cork into which the test-tube R is fitted. In this glass tube, which is also closed by a cork K, the sub- stance is placed which is to be heated. The greater part of the vessel is covered by a thick mantle of felt, B. The water in the vessel is boiled, the steam emerging at d, until the substance has acquired the temperature of hoiling water, for which about twenty minutes is required. The mantle and the lamp having been taken away, the tube R is rapidly removed, and its contents tipped into the tube A of the calorimeter (fig. 427). For this method of determining specific heat a new determination of the latent heat of ice was made, and it was found to be 80-025. It was also in connection with these experiments that Bunsen made his determination of the specific gravity of ice, which he found to be in the mean 0'gi674. By the above method Bunsen determined the specific heat of several. of the rare metals forwhich a weight of only a few grains could be used. 457. Method of mixtures. — In the determination of the specific heat of a solid body by this method the substance is weighed and raised to a known temperature, by keeping it, for instance, for some time in a closed place heated by steam ; it is then immersed in a mass of cold water, the weight and temperature of which are known. From the rise of temperature of the water after mixture the specific heat of the body is determined. Let M be the mass of the body, T its temperature, c its specific heat ; and let m be the mass of the cold water, and / its temperature. As soon as the heated body is plunged into the water, the temperature of the latter rises until both are at the same temperature. Let this temperature be 6. The heated body has been cooled by T - 5 ; it has, therefore, lost a quantity of heat, M(T — 5)ir. The water has, on the contrary, absorbed a quantity of heat equal to m{6 — t), for the specific heat of water is unity. Now the quantity of heat given out by the body is manifestly equal to the quantity of heat absorbed by the water ; that is, M(T - 6)c = m{6 - 1), from which m{ 6-t) M(T-6)' 458. Corrections. — The vessel containing the water is usually a small cylinder of silver or brass, with thin polished sides, and is supported by some badly conducting arrangement. It is obvious that this vessel, which is origi- nally at the temperature of the cold water, shares its increase of temperature, and in accurate experiments this must be allowed for. The decrease of .tem- perature of the heated body is equal to the increase of temperature of the water, and of the vessel in which it is contained. If the weight of this latter be m', and its specific heat c', its temperature, like that of the water, is t : consequently the previous equation becomes Mf (T -6) = m(6 -i) + m'c'{6 - 1) ; from which, by obvious transformations, _{m + m'c') {6 — t ■^ M(T-5) 448 On Heat [458- Generally speaking, the value-?«'c\is put = fi ; that is to say, /i is the mass of water which would absorb the same quantity of heat as the vessel. This is said to be the water-equivalent of the vessel. The expression accordingly becomes {mA,i, ){6-t) M(T-e) ■ In accurate experiments it is necessary to allow also for the heat absorbed by the glass and mercury of the thermometer, by introducing into the equa- tion their water-equivalents ; and to allow for the loss of heat by radiation, a preliminary experiment is made with the body whose specific heat is sought, the only object of which is to ascertain approximately the increase of temperature of the cold water. If this increase be io°, for example, the temperature of the water is reduced by half this number — that is to say, 5° — below the temperature of the atmosphere, and the experiment is then carried out in the ordinary manner. By this method of compensation, first introduced by Rumford, the water receives»as much neat from the atmosphere, during the first-part of the experiment, as it loses by radiation during the second part. 459. Re^nault's apparatus for determining specific heats. — Fig. 429 represents one of the forms of apparatus used by Regnault in j determining specific heats by the method of mixtures. The principal part is a steam bath, AA, of which fig. 430 represents a section. It consists of three concentric compartments ; in the central one there is a small basket of brass wire, c, containing fragments of the substance whose specific heat is to be determined, in the middle of which is placed a thermometer, T. The second compartment is heated by a current of steam coming through the tube e from a boiler B, and passing into a worm, a, where it is condensed. The third compartment, ii, is an air chamber to hinder the loss of heat. The steam bath, AA, rests on a chamber, K, with double sides, EE, forming a jacket which is kept full of cold water, in order to exclude the heat from AA, and from the boiler, B. The central compart- ment of the steam bath is closed by a damper, r, which can be opened at pleasure, so that the basket c can be lowered into [the chamber K. On the left of the figure is represented a small and very thin brass vessel, D, suspended by silk threads on a small carriage, which can be moved out of, or into, the chamber K. This vessel, which serves as a calorimeter, con- tains water, in which is immersed a thermometer, t. Another thermometer at the side, /', gives the temperature of the air. When the thermometer T shows that the temperature of the substance in the bath is stationary, the screen h is raised, and the vessel D moved to just below the central compartment of the steam bath. The damper r is then withdrawn, and the basket c and its contents are lowered into the water in the vessel D, the thermometer T remaining fixed in the cork. The carriage and the vessel D are then moved out, and the water agitated until the thermometer t becomes stationary. The temperature which it indicates is 6. This temperature known, the rest of the calculation is made in the manner described in article 452, care being taken to make all the necessaiy corrections. -460] Method of Cooling 449 In determining the specific heat of substances — phosphorus, for instance — which could not be heated without causing them to melt, or undergo some change which would interfere with the accuracy of the result, Regnault adopted an inverse process : he cooled them down to a temperature con- siderably below that of the water in the calorimeter, and then observed the diminution in the temperature of the latter, which resulted from immersing the cooled substance in it. I UUIllllll ilhiJ I Fig. 429 In determining the specific heat of substances, which, like potassium, would decompose water, some other liquid must be used, such as turpentine or benzole. These liquids have the additional advantage of having a lower specific heat than water, so that an error in determining the temperature of the cooling liquid has a less influence on the value of the specific heat of the substance. With this view use has been made of mercury, the specific heat of which is only one-thirtieth that of water. 460. Method of cooling.— Equal weights of different bodies whose specific heats are different will occupy different times in cooling through the same number of degrees. Dulong and Petit applied this principle in determining the specific heats of bodies in the following manner :— A small polished silver vessel, V (fig. 431), is filled with the substance in a state of fine powder, and a thermometer placed in the powder, which is pressed down. G G Fig. i 4SO On Heat [460- This vessel is heated to a certain temperature, and is then introduced into a copper vessel, E, in which it fits hermetically, being suspended by silk threads. This copper vessel is exhausted through the tube tt', and maintained at the constant temperature of melting ice, MN, and the time noted which the substance takes in falling through a given range of temperature, from ,15° to 5° for example. The times ..which equal weights of different bodies require for cooling, through the same range of tem- perature, when the radiating surface is the same in each case, are directly as their specific heats. Regnault proved that this method does not give trustworthy results with solids ; it assumes, which is not quite the case, that the cooling in all parts is equal, and that all substances part with their heat to the silver case with equal facility. The method may, however, be employed with success in the determina- tion of the specific heat of liquids. Since the emissive power of the silver vessel is the same in all cases, as is also the temperature-fall, the quantity of heat lost is proportional to the time. Hence, if m, tn' be the masses of the substances (powders or liquids) just filling the vessel V ; c, c' their specific heats, and /, t' the respective times of cooling from 6' to 6, mc{e' -ff) = kt, {k being a constant), and jii' c' {6' - 6) = kt' ; :. ^=^. m c t If, for example, the second substance is water, c' =1, and m'm' is the density (o-) of the substance whose specific heat is required, at' In an investigation of the specific heats of various soils, Pfaundler found that a soil of low specific heat heats and cools rapidly, while earth of higher specific heat undergoes slow heating and slow cooling ; that moist earths rich in humus have a high specific heat, amounting in the case of turf to as much as 0-5 ; while dry soils free from humus, such as lime and sand, have a low specific heat, not more than about 0-2. 461. Condensation method. — The determination of specific heat by the condensation of steam has been in recent years carried out with success by J. Joly (1886). The principle of the method is as follows : — A known weight of the substance whose specific heat is required, at a known temperature, is suddenly enveloped in saturated steam, some of which condenses upon it. It is now weighed in the steam, and weighs more than before, in consequence of the steam condensed upon it. If lu is the increase of weight, w'L represents the quantity of heat given up by the steam in condensing ; and if W is the weight of the body at the low temperature (/,), 4 the temperature of the steam, and c the specific heat of the substance, Wc(/2 - /j) = heat -462] Specific Heat of Liquids 45 1 Steam absorbed by the substance, and this must be equal to wL, whence c is determined. In its simplest form Dr. Joly's apparatus consists of a thin metal enclosure or chamber, A (fig. 432), in which there hangs from the arm of a balance by a fine platinum wire, a, a platinum pan B, carrying the body whose specific heat is required. Steam is admitted into the chamber by a wide tube, C, and escapes through a tube at the bottom, D. The aperture id) at the top of the chamber is so small that very little steam escapes there, and what does escape is prevented from condensing on the suspend- ing wire by a contrivance (not shown in the figure) which enables the wire to be heated by a fine platinum spiral through which an electric current flows. At the beginning of an experi- ment a known weight (a few grammes) of the substance is placed in the pan, and when the temperature has become steady, as shown by the sensitive thermo- ^'=' '•^^ meter, b, steam is suddenly admitted, so that the whole chamber becomes filled with saturated vapour. Condensation at once begins on the substance, and the resulting water is caught in the pan B, weights being added to the other pan of the balance to restore equilibrium. During this process the steam is admitted very slowly into the chamber, so that the pan may not be subjected to any steam draught. After four or five minutes the condensa- tion is complete, and no further increase of weight takes place. The specific heat is determined from the equation (W^ + m) (/j — ^]) = ^L, where ;« is the water equivalent of the platinum pan, the other letters having the meanings given to them above ; 4, the temperature of the steam, is determined by the barometric pressure from Regnault's table ; L = 59673 --601/2 (468). A correction must be introduced in consequence of the first weighing being made in air at t°, while w is weighed in steam at t°. 462. Specific heat of liquids. — The specific heat of liquids may be determined either by the method of cooling, by that of the ice calorimeter, or by that of mixtures. In the last-named case they are contained in a small metal vessel, or a glass tube, which is placed in the central compartment {fig. 430), and the experiment then made in the usual manner. A method devised by Pfaundler of determining the specific heat of G G 2 452 On Heat [462- liquids, which under certain circumstances is advantageous, depends on the fact that an electric current heats any conductor through which it passes. In two equal calorimeters containing the liquids to be tested, together with suitable thermometers and stirrers, two equal spirals of fine platinum wire are placed. These being connected in series with a voltaic battery by means of copper wires, the heat produced in the wires by the current will be equal, and the rise in temperature in the liquids will then be inversely as the specific heats. One of the liquids is usually water. It will be seen from the table in the following article that water and a few other liquids have a much greater specific heat than other substances, and more especially than the metals. From its great specific heat water requires a long time in being heated or cooled, and for the same weight and tempera- ture it absorbs or gives out far more heat than'other substances. This double property is applied in the hot-water apparatus, and it plays a most important part in the economy of nature. 463. Specific heats of bodies. — The list contained in the next article (464) gives the specific heats of a great number of elementary substances. We give here the specific heats of a few substances, mostly liquids : — Specific heat Specific heat Alcohol . . 0-620 Carbon bisulphide 0-24S Glycerine • 0-S55 Thermometer glass 0-198 Ether . 0-516 Steel . 0-II8 Turpentine 0-426 Brass 0-094 The specific heat of water is commonly taken at unity, which is not strictly correct. According to recent determinations the mean specific heat between 0° and / is expressed by the formula i -1- 0-00015^. These numbers, as well as those in 464, represent the mean specific heats between 0° and 100°. It was shown by Dulong and Petit that the specific heats increase with the temperature. Those of the metals, for instance, are greater between 100° and 200° than between 0° and 100°, and are still greater between 200° and 300° ; that is to say, a greater amount of heat is required to raise a body from 200° to 250° than from 100° to 150°, and still more than from 0° to 50°. For silver, the mean specific heat between 0° and 100° is 0-057, while between 0° and 200° it is 0-061 1. The following table gives the specific heats at various temperatures : — Copper . . . 0-0910 4- 0-000046/ Zinc . 0-0865 -*" 0-000088/ Lead . .... 0-0286 + 0-000038/ Platinum . . . 0-03 1 7 h- 0-0000062/ Water 1+0-00015/ The increase of specific heat with the temperature is greater as bodies are nearer their fusing point. Any action which increases the density and molecular aggregation of a body diminishes its specific heat. Thus hard steel with the density 7-798 has the specific heat 0-1175 ; while that of soft steel of density 7-861 is 0-1165. The specific heat of copper is diminished by its being hammered, but it regains its original value after the metal has been again heated. -463] Specific Heats of Bodies 453 The specific heat of a liquid increases with the temperature much more rapidly than that of a solid. H. T. Barnes has shown that the specific heat of water is a minimum at 37'5° C. If we take its value at 16° as ujiity, the mean value between 0° and 100° is l'oooi2, that is practically the same as at 16°. The most remarkable examples of the influence of temperature on the specific heat are afforded by carbon, boron, and silicon. Weber has found that at 600° the specific heat of carbon is 7 times, and that of boron 25 times, as great as their respective specific heats at — 50°. The specific heat of diamond is 0-0635 ^t - 5°° 0-1318 at 33°, 0-2218 at 140°, and 0-3026 at 247°. Although the specific heat increases thus rapidly between - 50° and 250°, beyond that point the rate of increase is slower ; and beyond 600°, or at an incipient red heat, it seems to be pretty constant, or at any rate to exhibit no greater variations with the temperature than are afforded by other sub- stances. Thus while at 600° the specific heat is 0-441, at 985° it is 0-459. Graphite also has at 22° the specific heat 0-168 ; this increases, but at a gradually diminishing rate, to 642°, where its specific heat is 0-445. Like diamond, an incipient red heat seems to be a limiting temperature beyond which graphite exhibits only the ordinary variation with the temperature. Weber has also found that, in their thermal deportment, there are only two essentially different modifications of carbon — the transparent one (diamond), and the opaque ones (graphite, dense amorphous carbon, and porous amor- phous carbon). Crystallised boron is similar in its deportment to carbon ; its specific heat increases from 0-1915 at —40° to 0-2382 at 27', and to 0-3663 at 233°. The- rate of increase is very rapid up to 80° ; it increases beyond that temperature, but at a gradually diminished rate, and, no doubt, tends to an almost constant value of 0-5. The specific heat of silicon also varies with the temperature.; between — 40° and 200° it increases from 0-136 to 0-203 5 '^e rate of increase is less rapid with higher temperatures, being at 200° only one-fourteenth what it is at 10°. At 200° it reaches its limiting value. The specific heat of substances is greater in the liquid than in the solid state, as will be seen by the following table : — Solid Liquid Water . 0-502 i-ooo Sulphur 0-203 0-234 Bromine . 0-084 o-iio Iodine . . . 0-054 0-008 Mercury . . 0-031 0-033 Phosphorus . . 0-190 0-212 Tin . . . . . 0-056 0-064 Lead ... ... 0-031 0-040 It also differs with the allotropic modification ; thus, at ordinary tem- peratures, the specific heat of red phosphorus is 0-19, and that of white 0-17 ; of crystallised arsenic 0-083, ^^^ of amorphous 0-058 ; of crystallised selenium 0-084, and of amorphous 0-0953 > of wood charcoal 0-241 ; of graphite 0-202 ; and of diamond o- 1 47. Pouilletused the specific heat of platinum for measuring high temperatures. 454 On Heat [463- Supposing 200 ounces of platinum had been heated in a furnace and had then been placed in 1000 ounces of water, the temperature of which it had raised from 13° to 20°. From the formula we have M = 200, m= 1000 ; 6 is 20, and i? is 13. The specific heat of platinum is 0-033, ^"^ we have there- fore, from the equation, Mc{T-6) = m{e-t) r^_m(d — /) + Mc0_^7ooo+ 132 _ 7132 _ j-g_o It is found, however, that the mean specific heat of platinum at tempera- tures up to about 1200° is 0-0377 ; if this value, therefore, be substituted for c in the equation, we have .7150-8- 7-54 948° C. By this method, which requires great skill in the experimenter, Pouillet determined a series of high temperatures. He found, for example, the temperature of melting iron to be 1500° to 1600° C. 464. Dulong and Petit's la-w, — A knowledge of the specific heat of bodies became of great importance in consequence of Dulong and Petit's discovery of the remarkable law, that the product of the specific heat of any solid element into its atomic weight is approximately a constant number, as will be seen from the following table : — Specific heat Atomic weight Atomic heat Aluminiuiji 0-2I43 27-4 5-87 Antimony 0-0513 122 6-26 Arsenic . 0-0822 75 6-17 Bismuth . 0-0308 210 6-47 Bromine . 0-0843 80 6-74 Cadmium 0-0567 112 6-35 Cobalt . 0-1067 58-7 6-26 Copper 0-0939 63-5 5-99 Gold ... 0-0324 197 6-38 Iodine . 0-0541 127 6-87 Iron 0-1 138 56 6-37 Lead .... 0-0314 207 6-50 Magnesium 0-2475 24 5 '94 Mercury . 0-0332 200 6-64 Nickel . 0-1092 58-7 6-41 Phosphorus 0-1740 31 5-39 Platinum 0-0324 197-5 6-40 Potassium 0-1655 39' I 6-47 Silver .... 0-0570 108 6-16 Sulphur .... 0-1780 32 570 Tin 0-0555 118 6-55 Zinc .... 0-0950 65-2 6-23 It will be seen that the number is not a constant, but varies between 5-39 and 6-87. These variations may depend partly on the difficulty of getting -466] Specific Heat of Compound Bodies 455 the elements in a state of perfect purity, and partly on errors incidental to the determination of the specific heats, and of the atomic weights. Again, the specific heats of bodies vary with the state of aggregation of the bodies, and also with the temperatures at which they are determined ; some, such as potassium, have been determined at temperatures very near their fusing ' points ; others, like platinum, at temperatures much removed from them. A prominent cause, therefore, of the discrepancies is doubtless to be found in the fact that all the determinations have not been made under corresponding physical conditions. The specific heats of the non-metallic elements at ordinaiy temperatures do not conform to the law of Dulong and Petit. Thus, the specific heat of carbon (graphite) at atmospheric temperature is •16S, and its atomic iieat 2-oi6 ; but at high temperatures the specific, heat rises to and remains approximately constant at o'46, giving an atomic heat of 5-52, which approximates to the value found for metallic elements. The results obtained with boron and silicon show a similar agreement with the law. The atomic weights of the elemerits represent the relati^•e weights of equal numbers of atoms of these bodies, and the product, pc^ of the specific heat, f, into the atomic weight, p, is the atomic heat, or the quantity of heat necessary to raise the temperature of the same number of atoms of different substances by one degree ; and Dulong and Petit's law may be thus ex- pressed : the same quantity of heat is needed to heat an atom of all simple bodies to the same extent. The atomic heat of a body, when divided by its specific heat, gives the atomic weight of a body. Regnault proposed to use this relation as a means of determining the atomic weight, and it certainly is of great service in deciding on the atomic weight of a body in cases where the chemical relations permit a choice between two or more numbers. On modern views, the heat imparted to a body is partly expended in external work ( = Pz/, where P is atmospheric pressure and v the expansion), which in the case of a solid would be extremely small ; secondly, the internal work, or the heat used in overcoming the attraction of the atoms for each other, and forcing them apart ; and thirdly, there is the true specific heat, or the heat applied in increasing the temperature — that is, in increasing the energy of the molecules (453). By far the most considerable of these is the last ; the amount of heat consumed in the two former operations is small, and the variations with different bodies must be inconsiderable. Until, however, the relation between the various factors is made out, absolute identity in the numbers for the atomic heat cannot be expected. Weber holds that even when due allowance has been made for these circum- stances, the variations are too great to be accounted for, and he considers that they point for their explanation to an alteration in the constitution of the atom, and render probable a changing valency of the atom of carbon. 465. Specific heat of compound bodies. — In compound bodies the law also prevails : the product of the specific heat into the equivalent is an almost constant number, which varies, however, with different classes of bodies. Thus, for the class of oxides of the general formula RO, it is 11 -30 ; for the sesquioxides R^O^ it is 37-15 ; for the sulphides RS, it is i8-88 ; and for the 4S6 On Heat [465- carbonates RCO^, it is 21-54. The law, which is known as Neumann! s law, may be expressed in the following general manner : — • With compounds of the same formula, and of a similar chemical constitution, the product of the 7nolecular weight into the specific heat is a cottstant quantity. This includes Dulong and Petit's law as a particular case. Kopp propounded the following law, which is an extension of that of Neumann : — The molecular heats of all solid bodies are equal to the sum of the molecular heats of the elements contained in them.. Dulong and Petit's law that all elements have the same atomic heat he does not consider universally valid. He assigns the number 6'4 to all elements excepting the following : with sulphur and phosphorus it is S-4, fluorine 5'0, oxygen 4-0, silicon 3-8, boron 27, hydrogen 2-3, and carbon i 8. Even with this modification it is found that the calculated heats of com- pounds differ more from the observed ones than can be ascribed to errors in the determination of the specific heats. This is probably due to the fact that some of the heat is expended in internal work, and that it is this which brings about the discrepancies. With mixtures of alcohol and water in certain proportions, the specific heat is greater than that of the water ; thus, that of a mixture containing 20 per cent, of alcohol was found by Dupr^and Page to be i"0456. No general law can be laid down for solutions of acids or of salts in water ; the specific heat is most frequently less than that calculated from the constituents. 466. Specific heat of gases. — The specific heat of a gas may be referred either to that of water or to that of air. In the former case it represents the quantity of heat necessary to raise a given mass of the gas through one degree, as compared with the heat necessary to raise the same mass of water one degree. In the latter case it represents the quantity of heat necessary to raise a given volume of the gas through one degree, compared with the quantity necessary for the same volume of air treated in the same manner. De la Roche and Berard determined the specific heats of gases in re- ference to water by causing known volumes of a given gas under constant pressure, and at a given temperature, to pass through a spiral glass tube placed in water. From the increase in temperature of this water, and from the other data, the specific heat was determined by a calculation analogous to that given under the method of mixtures. They also determined the specific heats of different gases relatively to that of air, by comparing the quantities of heat which equal volumes of a given gas, and of air at the same pressure and temperature, imparted to equal weights of water. Subsequently to these researches, De la Rive and Marcet applied the method of cooling to the same determination ; and Regnault made a series of investigations on the calorific capacities of gases and vapours, in which he adopted, but with material improvements, the method of De la Roche and Berard. Fig. 433 represents this apparatus. The gas issues from a gas-holder, not shown in the figure, through the tube a, and enters the heating space E, which is filled with oil ; the gas passes here through a serpentine tube, and thus acquires the temperature, which is kept uniform by a stirrer, D. From this it passes into the calorimeter, W, which consists of a metal box divided into a series of compartments, and forming in effect a serpentine, so specific Heat of Gases 457 that the gas has to traverse a long path before emerging into the air. The temperature of this bath is indicated by a deUcate thermometer, and is kept uniform by moving the stirrer. The pressure of the gas is noted on a manometer. Regnault thus obtained the following results for the specific heats of the various gases and vapours, compared first with the specific heat F'g- 433 of an equal mass of water taken as unity ; secondly, with that of an equal volume of air, referred, as before, to its own mass of water taken as unity : — Simple gases Air [Oxygen . J Nitrogen I Hydrogen I Chlorine Specific heats Equal masses Equal volumes 0-2374 0-2374 0-2I74 0-2405 0-2438 0-2370 3-4090 0-2359 0-I2I0 0-2962 45 8 On Heat [466- Compound gases Vapours I Nitric oxide . Carbonic oxide Carbonic acid Hydrochloric acid . Ammonia Ethylene Water Ether Alcohol Turpentine . Carbon bisulphide \ Benzole . Specific Equal masses heats Equal volumes 0-2315 0-2406 0-2450 0-2370 0-2163 0-1845 0-5083 0-3307 0-2333 0-2966 0-4040 0-4805 0-4810 0-4106 0-2984 I -2296 0-4534 0-5061 O-7171 2-3776 0-1570 0-4140 0-3754 I -01 14 In making these determinations the gases were under a constant pressure, but variable volume ; that is, the gas as it was heated could expand, and this is called the specific heat under constant pressure. But if the gas when being heated is kept at a constant volume, its pressure or elastic force then necessarily increasing, it has a different capacity for heat ; this latter is spoken of as the specific heat under constant volume. That this latter is less than the former is evident from the following considerations: — Suppose a given quantity of gas to have had its temperature raised t° • while the pressure remained constant, this increase of temperature will have been accompanied by a certain increase in volume. Supposing now that the gas is so compressed as to restore it to its original volume, the result of this compression will be to raise its temperature again to a c^tain extent, say t'°. The gas will now be in the same condition as if it had been heated and had not been allowed to expand. Hence, the same quantity of heat which is required to raise the temperature of a given mass of gas, t°, while the pressure remains constant and the volume alters, will raise the temperature t + t' degrees if it is kept at a constant volume but variable pressure. The specific heat, therefore, of a gas at constant pressure, c, is greater than the specific heat under constant volume, c,, and they are to each other as t+t': t, ^, . ■ <: t+t' that IS — = - . c, t Elementary gases do not obey Dulong and Petit's law. Dewar has, however, shown that, at the temperature of liquid air, the specific heat of hydrogen is 6, and of nitrogen -43, so that their atomic heats are respectively 6x1=6 and -43 X 14 = 6-02, and thus at this low temperature are in agree- ment with the law. 467. Latent heat of fusion. — Black was the first to observe that during the passage of a body from the solid to the liquid state a quantity of heat disappears, so far as thermometric effects are concerned, and is accordingly said to become latent. In one experiment he suspended in the room at a temperature 8-5° two glass flasks, one containing water at o^, and the other the same weight of ice at 0°. After half an hour the temperature of the water had risen -467] Latent Heat of Fusion 459 4°, that of the ice being unchanged, and it was io| hours before the ice had melted and attained the same temperature. Now the temperature of the room remained constant, and it must be concluded that both vessels received the same amount of heat in the same time. Hence 21 times as much heat was required to melt the ice and raise it to 4° as was sufficient to raise the same weight of water through 4°. So that the total quantity of heat imparted to the ice was 21 x 4 = 84 ; and as only 4 of this was used in raising the temperature, the remainder, 80, was used in simply melting the ice. He also determined the latent heat by immersing 119 parts of ice at 0° in 135 parts of water at 877° C. He thus obtained 254 parts of water at 1 1 -6° C. Taking into account the heat received by the vessel in which the liquid was placed, he obtained the number 7944 as the latent heat of lique- faction of ice. The method which Black adopted is essentially that which is now used for the determination of latent heats of liquids ; it consists in placing the substance under examination at a known temperature in the water (or other liquid) of a calorimeter, the temperature of which is sufficient to melt the substance if it is solid, or to solidify it if liquid ; and when uniformity of temperature is established in the calorimeter, this temperature is determined. Thus, to take a simple case, suppose it is required to determine the latent heat of the liquidity of ice. Let M be a certain weight of ice at zero, and m a weight of water at /' sufficient to melt the ice. The ice is immersed in the water, and as soon as it has melted, the final temperature (P is noted. The water and calorimeter, in cooling from /° to 6 , have parted with a quantity of heat, {m-¥ fi){t — 6\ where fx, is the water equivalent of the calorimeter. If x be the latent heat of water, the ice absorbs, in liquefying, a quantity of heat Mjr ; but, besides this, the water which it forms has risen to the temperature 6^, and to do so has required a quantity of heat, repre- sented by M5°. We thus get the equation lslx+yi6 = {in^ ti)(i -ff), from which the value x is deduced. By this method Desains and De la Provostaye found that the latent heat of the liquefaction of ice is 79'25 : that is, a pound of ice in liquefying" absorbs the quantity of heat which would be necessary to raise 79'25 potmds of water 1°, or, what is the same thing, one pound of water from zero to 79'25°. Bunsen's latest determination gave 80-025 (456). This method is thus essentially that of the method of mixtures ; the salne apparatus may be used, and the same precautions are required, in the two cases. In determining the latent heat of liquefaction of most solids, the dif- ferent specific heats of the substance in the solid and in the liquid state require to be taken into account. In such a case, let m be the weight of the water in the calorimeter (the water equivalents of the calorimeter and thermometer, supposed to be included) ; M the weight of the substance worked with ; t the original and 6 the final temperature of the calorimeter ; T the original tem- perature of the substance ; % its melting (or freezing) point ; C the specific heat of the substance in the solid state between the temperature % and 6 ; c its specific heat in the liquid state between the temperatures T and ffi ; and let L be the latent heat sought. 460 On Heat [467- If the experiment be made on a melted substance which gives out heat to the calorimeter and is thereby solidified (it is taken for granted that a body gives out as much heat in solidifying as it absorbs in liquefying), it is plain that the quantity of heat absorbed by the calorimeter, m{6 - /), is made up of three parts : first, the heat lost by the substance in cooling from its original temperature T to the solidifying point % ; secondly, the heat given out in sohdification, ML ; and, thirdly, the heat it loses in sinking from its solidifying point % to the temperature of the water of the calorimeter. That is : whence n{6-t) = M^T- cy + L + (C - ^)C] L = '-^^^ - (T - my- (ts: - e)c. Tin . . . • 14-25 Cadmium 13-66 Bismuth . 12-64 Sulphur 9-37 Lead 5-37 Phosphorus 5-03 . 2-83 The following numbers have been obtained for the latent heats of fusion of the substances specified : — Water .... 80-03 Sodium nitrate . 62-97 Potassium nitrate . 47-37 Zinc . . . 28-13 Platinum . 27-18 Silver . . . .21-07 Mercury The potential energy which bodies acquire in the act of melting is strictly comparable to that gained by a weight when work has been spent in •raisijig it. When the liquid soHdifies, it reproduces the heat which had been expended in liquefying the solid : just as when a stone falls it produces by its impact against the ground the heat, the equivalent of which in work had been expended in raising it, and a similar explanation applies to the latent heat of vaporisation. 468. Determination of the latent heat of vapour. — Liquids, as we have seen, in passing into the state of vapour, absorb a very' considerable quantity of heat, which is termed their latent heat of vaporisation. In deter- mining the heat absorbed in vapours, it is assumed that a vapour in liquefying gives out as much heat as the liquid had absorbed in becoming converted into vapour. The method employed is essen- tially the same as that for determining the specific heat of gases. Fig. 434 represents the apparatus used by Despretz. The vapour is produced in a retort, C, where its temperature is indicated by a thermometer. It passes into a worm, SS, immersed in cold water, where it condenses, imparting Fig- 434 -468] Determination of the Latent Heat of Vapour 461 its latent heat to the condensing water in the vessel B. The condensed vapour is collected in a vessel, A, and its weight represents the quantity of vapour which has passed through the worm. The thermometers in B give the change of temperature. Let M be the weight of the condensed vapoui', T its temperature on entering the worm, which is that of its boiling point, and x the latent heat of vaporisation. Similarly, let m be the weight of the condensing water (comprising the weight of the vessel B and of the worm SS reduced to their equivalent in water), let i° be the temperature of the water at the beginning, and 6^ its temperature at the end of the experiment. It i^to be observed that, at the commencement of the experiment, the condensed vapour passes out at the temperature t°, while at the conclusion its temperature is ff' ; we may, however, assume that its mean temperature during the experiment is > ' . The vapour M after condensation has 2 therefore parted with a quantity of heat M(T -— — Jc, while the heat disengaged in liquefaction is represented by Mx. The quantity of heat absorbed by the cold water, the worm, and the vessel is m{6 — t). Hence Wlx + V{.{^ -i±l-'\c = m(6- ■t), from which x is obtained. Despretz found that the latent heat of steam at 100° is 540 ; that is, a pound of water at 100° absorbs in vaporising as much heat as would raise 540 pounds of water throughi". The values for the latent heat of aqueous vapour obtained by Regnault at temperatures between 65° and 100°, and more recently by Dieterici at 0°, and by E. H. Griffiths at intermediate temperatures, are represented with great accu- racy by the formula L = 59673 — 0'6oi /. Thus, at 100°, L = 536-63. Bertholet used the apparatus represented in fig. 435 for determining latent heats of vapori- sation. The liquid in the flask D is heated by the ring burner B, and the vapour which forms passes through the tube ab into the serpen- tine S, where it condenses and collects in the bulb R. These are contained in the calori- meter C, the top of which is closed by a wooden cover, HH, and a layer of felt, NN' ; they cut off any heat from the flask D and from the burner B. As the serpentine SR can be de- tached from ab, it is easy to determine the weight of the distillate ; from this, and from the rise in temperature of the water in the calorimeter, the latent heat can be readily calculated. rig- 435 462 On Heat [468- In the conversion of a body from the hquid into the gaseous state, as in the analogous process of fusion, as the temperature rises to that of boihng, one part of the heat is used in increasing the temperature and another in internal work. For vaporisation, the greater portion is consumed in the internal work of overcoming the reciprocal attraction of the particles of liquid, and in removing them to the far greater distances apart in which they exist in the gaseous state. In addition to this there is the external work — namely, that done against the external pressure, usually that of the atmo- sphere ; and as the increase of volume in vaporisation is considerable, this is large. Vaporisation may take place without external work being done, as when it is effected in vacuo ; but whether the evaporation is under a high or under a low pressure, on the surface of a liquid or in the interior, there is always a great consumption of heat in internal work. 469. Latent heat of vaporisation of liquefied gases. — Mathias has deter- mined the heat of vaporisation of certain liquefied gases, and its variation with the temperature between 0° and 33°, by means of the apparatus represented in fig. 436. Fig. 436 The liquefied gas is contained in a cylindrical gilt copper reservoir R, capable of sustaining a pressure of over 100 atmospheres, and connected with a long narrow serpentine tube coiled round it. The whole is immersed in a calorimeter. The serpentine is soldered to a screw valve A, which by means of a junction and a copper tube identical with that round the reservoir is connected with another and larger screw valve B. F is a glass flask containing sulphuric acid, and during the course of the experiment, while the liquefied gas is evaporating the sulphuric acid drops into the water of the calorimeter, care being taken to mix by means of the -470] Favre and Silbermami s Calorimeter 463 thermometer ; in this way the temperature may be kept constant to within a few hundredths of a degree ; the escape of the gas is regulated by the screw valve B, the regularity of the flow being ascertained by a wash bottle Z containing glycerine. The loss in weight of R gives the weight of the liquid vaporised, and from the loss of weight of F the heat due to the dilution of the sulphuric acid can be calculated. These two furnish the data for calculating the heat of evaporation of the liquefied gas at the constant temperature t°. At ordinary temperatures the determination can be made between 0° and 22° ; beyond these limits special precautions are required. E.xperiments were made with sulphurous acid, carbonic acid, and nitrous oxide ; they show that the heat of evaporation constantly decreases, the decrease bemg linear for SO„, and extremely rapid for the other two gases. The formula X= 117(31 -^) — 0-47(31 — /)- gives the heat of evaporation of CO., from the critical temperature to temperatures much below 0°. 470. Favre and Silbermann's calorimeter. — The apparatus (fig. 437) furnishes a very dehcate means of determining- the calorific capacity of Fig. 437 liquids, latent heats of evaporation, and the heat disengaged in chemical actions. The principal part is a spherical iron reservoir, A, full of mercury, of which it holds about 50 pounds, and represents, therefore, a volume of about half a gallon. On the left there are two tubulures, B, in which are 464 On Heat [470- fitted two sheet-iron tubes or muffles, projecting into the interior of the bulb. Each can be fitted with a glass tube for containing the substance experi- mented upon. In most cases one muffle and one glass tube are enough ; the two are used when it is desired to compare the quantities of heat produced in two different operations. In a third vertical tubulure, C, there is also a muffle, which can be used for determining calorific capacities by Regnault's method (460), in which case it is placed beneath the r of fig- 430. The tubulure d contains a steel piston ; a rod turned by a handle, m, and provided with a screw thread, transmits a vertical motion to the piston, but, by a peculiar mechanism, gives it no rotatory motion. In the last tubulure is a glass bulb, a, in which is fitted a long capillary glass tube, bo, divided into parts of equal capacity. The mercury calorimeter is thus essentiall)' a thermometer with a very large bulb and a capillary stem : it is therefore extremely delicate. It differs, however, from a thermometer in the fact that the divisions do not indicate the temperature of the mercury in the bulb, but the number of thermal units imparted to it by the substances placed in the muffle. This graduation is effected as follows : — By working the piston the mercury can be made to stop at any point of the tube, bo, at which it is desired the graduation should commence. Having then placed in the iron tube a small quantity of mercury, which is not afterwards changed, a thin glass tube, e, is inserted, which is kept fixed against the buoyancy of the mer- cury by a small wedge not represented in the figure. The tube being thus adjusted, the point of a bulb tube (see fig. 438) is introduced, con- taining" water which is raised to the boiling point ; turning the posi- tion of the pipette, then, as represented in n', a. quantity of the liquid flows into the test-tube. The heat thus imparted to the mercuiy makes it expand ; the column of mercury in bo is lengthened by a number of divisions, n. If the water poured into the test-glass be weighed, and if its temperature be taken when the column bo is stationary, the product of the weight of the water into the number of degrees through which it has fallen indicates the number of thermal units which the water gives up to the entire apparatus. Dividing by n this number of thermal units, the quotient gives the number, a, of thermal units corresponding to a single division of the tube bo. In determining the specific heat of liquids, a given Aveight, JVI, of the liquid in question is raised to the temperature T, and is poured into the tube C. Calling the specific heat of the liquid c, its final temperature 0, and Fig. 438 -471] Examples 465 n the number of divisions by which the mercurial column bo has advanced, we have M(:(T — ff) = na. from which c = ^-^^^^ — :r, ^ ' ' M(T-ey The boards represented round the apparatus are hinged so as to form a box, which is lined with eider-down or wadding, to prevent any loss of heat. It is closed at the top by a board, which is provided with a suitable case, also lined, which fits over the tubulures d and a. A small magnifying glass, which slides along the latter, enables the divisions on the scale to be read off. 471. Examples. — I. What weight of ice at zero must be mixed with 9 pounds of water at 20° in order to cool it to 5° ? Let M be the weight of ice necessary ; in passing from the state of ice to that of water at zero, it will absorb 80M thermal units ; and in order to raise it from zero to 5°, 5M thermal units will be needed. Hence the total heat which it absorbs is 8oM + 5M = 85M. On the other hand, the heat given up by the water in cooling from 20° to 5° is 9 x (20— 5)= 135. Con- sequently 85M = 135 ; from which M = 1-588 pounds. II. What weight of steam at 100° is necessary to raise the temperature of 208 pounds of water from 14° to 32° ? Letp be the weight of the steam. The latent heat of steam is 540°, and consequently j!5 pounds of steam in condensing into water give up a quantity of heat, 540/, and form p pounds of water at 100°. But the temperature of the mixture is 32°, and therefore p gives up a further quantity of heat ^(100 — 32) = 68/, for in this case c is unity. The 208 pounds of water in being heated from 14° to 32° absorb 208(32 — 14) = 3744 units. Therefore 540^ -H 68/ = 3744 ; from which/ = 6-58i pounds. H H 466 On Heat [472- CHAPTER X STEAM ENGINES 472. Steam engines. — Steam, engines are machines by which heat energy, obtained by the combustion of some fuel, is turned into mechanical work, aqueous vapour being used as a working fluid for effecting the trans- formation. In all but a few very exceptional cases the mechanical means used for the transformation of the one form of energy into the other are as follows : — the heat of combustion is, as far as possible, imparted to water in a closed vessel called the boiler ; the water is thereby converted into steam, occupying an enormously greater volume, and this steam is allowed to pass from the boiler as fast as it is formed, and to act alternately on the two sides of a movable piston working backwards and forwards in a cylinder. As soon as the piston has been pushed to either end of the cylinder by the incoming steam acting on one side of it, the communication between that side and the boiler is shut off, and another communication opened either to a condenser or to the atmosphere. In either case the steam rushes out of the cylinder and the pressure- against the piston falls, so that it can be pushed back by fresh steam from the boiler acting on its opposite side. If the purpose of the engine is merely to work pumps, or any other apparatus requiring only a reciprocating motion, a rod from the piston can be connected directly, or through a lever, to the pump to be worked. If, however, as in a majority of cases, the engine has to drive something having a rotary motion, a simple mechanism is used to change the reciprocating motion of the piston into the rotation of a crank. In this change itself there is no loss of energy (478), the work of the steam on the piston being exactly equal to the work done at the rotating crank-pin, minus only the lost work spent in overcoming the friction of the joints of the mechanism. We shall first consider the boiler, or apparatus for generating steam, and then the engine itself 473. Steam boiler. — Figs. 439 and 440 show one of the forms of boiler most commonly used in this country for supplying steam to stationary engines. This type of boiler is called Cornish, having been first used for pumping engines in Cornwall. Fig. 439 shows a longitudinal section of the boiler and the brick flues in which it is set, and fig. 440 shows on the left a half-front view of the boiler and on the right a half-cross section. The boiler consists of an outer cylindrical shell A of wrought iron or steel plates riveted together, and a smaller internal flue or furnace B. The latter is open at both ends, and is crossed by a series of vertical tubes C, called Galloway tubes, which allow the water to circulate from the lower to the upper part of the boiler. The fire is placed on a grate D in the front part of the flue, the grate ending -473] Steam Boiler 467 in a firebrick bridge over which the gases have to pass. These hot gases find their way past the tubes to the back of the boiler, and then are com- pelled to diverge sideways and return by the side flues K to nearly the front of the shell, where the flues are diverted downwards, as shown in fig, 439, and thence they return by thfe lower flue L to the chimney M. By thus Fig- 439 «ncircling the boiler with flues it is endeavoured to get all the heat possible from the gases before they are allowed to pass away up the chimney. The i^xxncv^ai fittings or mountings of the boiler are indicated in the figures, and are as follows : G is a dome on which stands the stop-valve N through which the steam is carried to the engine. The object of the dome is to take the steam from a point far away from the water line, so that it may be as dry as possible. P is a safety vg.lve, held down on its seat by the action of a weighted lever, and so ad- justed that as soon as the pressure of steam reaches its intended maximum and tends to rise beyond it, the valve is lifted and the steam rushes away into the air. Q is a manhole door by which access is had to the interior •of the boiler, when it is empty and out of use, for cleaning and repair. R is ^pressure gauge or indicator, standing in front of the shell, showing, bya hand working in front of a dial plate, the ' boiler pressure ' or amount by which the pressure of steam inside the boiler exceeds that of the atmosphere surrounding it. S is a water gauge, a glass tube connected at top and bottom to the boiler, its upper end to the steam space and the lower end to the water space. The water stands in the glass tube at the same level as in the boiler, and the fireman can see at a glance whether it is at the right height. This matter is of great importance, because an accidental fall of water-level is a frequent cause of boiler explo- ;sions. If, for instance, the water fell so low as to leave the top of the furnace B uncovered, the plates would get red-hot and soften so much as to collapse Fig. 440 468 On Heat [473- under the action of the steam pressure, with consequences that might be most serious. In marixfc boilers^ when it is of the greatest importance to get as much heating surface as possible into a small space, and similarly in the locomotive boiler to be presently described, the hot gases after leaving the fiirnace are made to pass through a number of small tubes instead of one large one as in fig. 439. Such boilers are called multitubular boilers. Of late years the shells of large boilers have frequently been made ot ' mild steel,' produced by the Bessemer or Siemens-Martin processes, rather than of wrought iron. In locomotive boilers, where the combustion is very rapid and intense, the fire-boxes are frequently made of copper, a much better conductor of heat than either iron or steel. 474. Cornish engine. — Fig. 441 shows the oldest of all the types- |of engines still in use, the Cornish pumping engine, which is worth examina- tion both for its historical interest and on account of the special way in ' „ t4l which it works. (In the figure all details except those absolutely necessaiy to illustrate the action of the engine are omitted.) The engine has a vertical cyUnder A (often of very great size, and with as much as 10 or 1 1 feet stroke), in which works a piston P, whose rod is connected by a chain to a sector on the end of a beam B. Beside the cylinder is a chamber C containing the valves for admitting and discharging steam, whose mode of working will be presently described. At the further end of the beam a second sector is -474] Cornish Engines 469 connected with the pump-rod, at the upper end of which is placed a heavy counterweight Q. Below the cylinder a pipe M leads to a chamber N called the condenser, into which a jet of water from the tank in which it stands continually plays. The condenser in its turn is connected with a pump called an air-pump, worked from the beam by the rod E, and fitted with suction and discharge valves, and valves in its piston in the usual way. , We] can follow the working of the engine easily by supposing the piston to start at the top of its stroke. The valves are then in the position shown, m open, n and o closed. Steam passes from the boiler through the pipe T to the top of the piston, and forces it down against the small pressure of the steam below it, this steam escaping into the condenser through the valve o and the pipe M. The pump-rods or pit work, and the weight Q, are thus lifted to the top of their stroke. When the piston arrives at the bottom of its stroke the valves m and are shut and n is opened.- This allows free communication between the two sides of the piston, and so puts it into equilibrium. The counterweight Q, together with the pump-rods, is made somewhat heavier than the piston and rod plus the whole weight of the column of water to be lifted. It therefore falls slowly (the whole affair thus becoming an Atwood's machine (79) on an enormous scale), and forces up the water through the pumps. As soon as the piston has once more got to the top of its stroke, by which time of course all the steam has been transferred to its under side, the position of the valves is again reversed and the piston once more begins to fall. The steam below the piston is suddenly put into communication with the condenser N, into which a jet of cold water is always playing. It is therefore reduced in temperature almost instantaneously, much of it is condensed into water, and the rest, which still fills the space below the piston, is necessarily reduced to a pressure of only about 3 pounds per square inch or about | of an atmosphere. As the pres- sure of the steam coming direct from the boiler in such engines is often 50 pounds per square inch above that of the atmosphere, it follows that the differ- ence of pressure on the two sides of the piston in such a case is 50 h- 15 — ^ = 62 pounds per square inch, and it is this difference of pressure which compels the piston to move downwards and lift all the weight at the other end of the beam. The condensed steam and the condensing water fall together at the bottom of the condenser, and are continually removed (alone with the uncondensed steam and any air that may be present) by the air- pump, which is a simple lift pump with a valve in its piston (217). In all modern Cornish engines the beams are of iron, and the sector and chains are replaced by an arrangement of iron links forming 3. parallel moiion which it is not necessary here to describe. The simple arrangement for working the valves, shown in outline in the figure, is also replaced by a much more complicated apparatus in which, by means of cataracts, any required length of pause can be made between the strokes of the engine a matter which is sometimes of importance in heavy pumping work. It will be noticed that by the peculiar single-acting method of working adopted in the Cornish engine, the velocity of the down stroke (also called the steam stroke, or the indoor stroke) depends — other things being equal — upon the steam pressure, but the velocity of the up stroke {eqtdlibritcm or outdoor stroke) depends solely on the overplus weight put on the outer end of the 470 On Heat [474- beam. In this way a slow and quiet upward motion can be given to the water, no matter how quickly the steam may move the piston. 475. Ordinary horizontal engine. — The engines now most largely used in factories for driving machinery differ altogether in their action from the Cornish engine. In them the cylinder is generally horizontal, and the crank is driven through a connecting rod only, without the intervention of any beam. Such an engine is shown in fig. 442. Here A is the steani cylinder, B the valve chest, or chamber in which works the valve whose mode of action is described in the next article. D is the main shaft, on the inner end of which is the crank driven by the connecting rod E. C is an eccentric (fig. 444), which works the valve by the rod N. F is a governor controlling the admission of steam to the cylinder by the valve H. M is the bedplate or frame of the engine, and L the flywheel. A few words are necessary about the governor. This apparatus, an invention of James Watt's, consists of two weighted arms hinged at the top. Fig. 442 which fly outward when the speed of rotation is increased and drop together when it is reduced. The outward or inward motion of the arms is caused by a simple arrangement to turn the spindle G and so to close or open the valve H, which admits steam through K to the cylinder. In this way the engine automatically controls its own speed (477). 476. Distribution of steam. Slide valves. — Figs. 443 and 444 show details as to the working of the valve and the distribution of the steam in the engine just described. The former is a longitudinal section of the cylinder shown in fig. 442. A is the cylinder itself, B the piston, C the piston-rod, D the stuffing-box through which the piston passes steam-tight. It will be seen that a port or passage L communicates between each end of the cylinder and the surface on which the \ahe works, or valve face. On this face and between the two steam-ports, comes a third point M, communi- cating directly with the atmosphere or with a condenser as the case may be. The \alve G is shaped in section something like an irregular D, and is often -476] Distribution of Steam. Slide Valves 471 called a ' D ' valve in consequence. It is moved continuously backwards and forwards upon the valve face by the valve-rod H working in the stuffing- box K. When in the position shown in the figure, the steam enters by F, and passes into the left-hand end of the cylinder (past the edge of the valve) and pushes the piston from left to right. The steam at present in the cylinder (as shown by the arrows) passes out at L, and through the under part of the valve G to the exhaust port M. As the piston moves on, the valve at first moves in the same direction, opening the port a little wider, then gradually moves back again and closes the admission port altogether. The point at which this occurs is called the point of cut off. No more steam is allowed to enter the cylinder for that stroke, the piston being pushed forward by the pressure of the elastic steam expanding behind it. By the time the piston has got to the end of its stroke, the position of the valve is just reversed from that in which it is shown, and steam passes into the cyhnder through the right-hand port, driving the piston from right to left, while the steam which has already done duty in the left-hand end of the cylinder passes away, in its turn, through the exhaust. IS, ."l l4 f^ j s> - Fig- 443 Fig. 444 The eccentric from which the valve receives its motion (lettered C in fig. 443) is shown in detail in fig. 444. Here D is the crankshaft and A a disc (solid or ribbed) fixed eccentrically on it so as to revolve with it. Encircling this disc (which is the eccentric) is a strap or ring B (made in two pieces for the sake of getting on and off), rigidly connected with a rod C, which is coupled by a pin to the valve-rod E. In each revolution of the eccentric the valve-rod is moved backwards and forwards through a space equal to twice the eccentricity of the eccentric, or distance between the centres of D and of A. The eccentric is thus equivalent exactly to a crank having a radius equal to its eccentricity. It is used instead of a crank because it does not require any gap to be left in the shaft, as a crank would do, but allows it to be carried continuously on. In locomotive or marine engines two eccentrics are commonly used, one so placed as to give the valve the right motion when the shaft rotates in one direction, and one rightly placed for the other. By apparatus called reversing gear either one or the other can be caused to move the valve, so that the engine can be made, at pleasure, to turn the shaft in one or the other direction. 472 On Heat [477- 477- Locomotives. — Locomotive engines, or simply locomotives, are steam engines which, mounted on a carriage, propel themselves by trans- mitting their motion to wheels. The whole machine, fig. 445, boiler and engine, is fixed to a wrought-iron frame, which, therefore, is made strong enough to carry the whole weight, and which in turn transmits that weight to the axle-boxes (or bearings in which the axles turn), by means of springs, and thence through the wheels to the rails. The boiler is of a special type, adopted in order to get the greatest possible heating surface in a very limited -477] Locomotives 4^3 space. It consists of three parts — the^re-dox, barrel, and smoke-box. The fire-box, in the left of the engraving, is generally a more or less rectangular box, with a flat top, placed inside a second box of somewhat similar shape, but with a semi-cyli;idrical, or, as in the figure, domed top. In the inner fire-box are the fire-bars, on which the fuel is placed through a door in front. The space between the inner and outer boxes is filled with water to a height considerably over the top of the inner one, and communicates freely with a long cylindrical barrel, closed at the other end by the smoke-box. This barrel, which forms the main bulk of the boiler, is filled with water to within nine or ten inches of its upper side. It is traversed from end to end by a great number of small tubes (about ij inch in diameter) which communicate with the inner fire-box at the one end, and with the smoke-box at the other. They therefore are entirely immersed in the water from end to end. The gases of combustion, formed in the inner fire-box, pass through these tubes to the smoke-box, and thence up the chimney, and impart most of their heat to the water as they pass along. There are two steam cylinders, one on each side of the frame, each one with its piston and connecting rod, &c., being simply an ordinary high-pressure horizontal engine. Their exhaust steam is discharged through a blast pipe into a nozzle inside the chimney near its base, and this serves to excite the fierce draught which is required in order that the necessary heat may be developed by the very small furnace. The two cylinders work cranks at right angles to each other, so that one may be in full action when the other is at its dead point. A locomotive such as that shown in the figure is called an outside cylinder engine, on account of the position of its cylinders. In England many engines have cylinders placed inside the frames, which are then called inside cylinder locomotives. In express engines the cylinders frequently drive only one very large pair of wheels, as is shown in the figure. These are called driving wheels, those on the front axle being leading wheels, and on the rear axle trailing wheels. In the case of goods engines, however (as well as in many other instances), when less speed but a greater pull is required, two or more pairs of wheels of the same diameter are connected together by coupling rods, so that two or more axles may be directly or indirectly actually driven by the engine. Such engines are called coupled engines. The action of the engine upon the wheels may cause them either to slip round on the rails (in which case the engine, of course, does not move onwards) or to roll on them in the usual way. To prevent slipping occurring it is necessary to make the friction between the wheels and the rails as great as possible, This is done by making as large a proportion of the whole weight as possible rest on the driving or the coupled wheels, and also — when bad weather causes the rails to be greasy or otherwise unusually slippery — by increasing the coefficient of friction (49) between the wheels and the rails by pouring sand on the latter. All locomotives are furnished with a sand- box for this purpose. The steam pressure in locomotives is greater than that commonly used in any other engines, being often 120 to 130 pounds per square inch above the atmosphere. In marine engines 70 to 80 pounds is often used, in stationary engines seldom quite so much. 474 On Heat [477- The following is an explanation of the reference letters in fig. 445 : — A, the main steam-pipe, conveying steam to the cylinder F, in which Avorks a piston P, driving the crank M through the connecting-rod K, r^ are the piston-rod guides, V the stuffing-box. The exhaust steam is discharged through the pipe E. (It will be remembered that the cylinder and all this gear are duplicated on the other side of the engine.) DZ is the outer fire- box and X the barrel of the boiler, both covered with felt and wood or sheet iron to prevent loss of heat by radiation. The small tubes are seen at a, Y is the smoke-box, and Q the chimney or funnel. TT are the springs which transmit the weight of the frame to the axle-boxes. Of the smaller details, GI is the arrangement for closing or opening the steam-admission valve, BiJC the reversing gear, RR feed-water pipes, N coupling rod for attaching tender and rest of train, ei safety valves, g whistle, m steps, n water gauge, t cocks for blowing water out of cylinders, H cock for blowing out boiler when needful. It is perhaps hardly necessary to explain that the breaking away of part of the fire-box, cylinder, &c., is done in the drawing only for the sake of showing clearly the internal construction. 478. Various kinds of steam engine. — Three types of steam engine have been described : the Cornish engine, the ordinary horizontal engine, and the locomotive engine. Others ought to be mentioned, although they cannot be here described in detail. Compound engines are those in which the steam is first used in the ordinary way in one cylinder and then trans- ferred — of course at a comparatively low pressure^to another cylinder and used in it before being sent away to the condenser. This type is practically universal for marine purposes, and is very common for stationary engines. Its main advantage is a thermodynamic one. In an ordinary engine the cylinder walls are exposed alternately to the hot steam from the boiler and the cool vapour passing to the condenser. The latter so reduces the temperature of the iron, that when the first rush of fresh steam comes into the cylinder, much of it is immediately condensed on the cool metal, and an enormous quantity of heat is thereby lost. By passing the steam through an intermediate, or low-pressure^ cylinder on its way to the condenser, the sides of the first or high-pressure cylinder are never exposed to condenser temperature, but only to that of the steam as it passes to the low-pressure cylinder ; they therefore are not so much cooled, and the loss of steam by condensation on them is very much reduced. There is no mechanical gain, as has sometimes been stated, in the use of two cylinders instead of one. Sometimes the cylinder of an engine is enclosed in a second, slightly larger, cylinder, and fresh steam at boiler pressure admitted to the annular space so formed outside the working cylinder. The object of this is to reduce still further the condensation in the cylinder just alluded to. Such an engine is said to be steam-jacketed. - A surface-condensing engine is one in which the steam is condensed by contact with the surface of a number of small tubes through which cold water is kept continually circulating without being itself actually mixed with the condensing water. By this arrangement the condensed steam is kept by itself, and being di'stilled water it can be used very advantageously to feed the boiler again. Compound marine engines are almost invariably surface- -479] Work of an Engine. Horse-Pozver 475 condensing. In this case the air-pump only takes away the condensed steam, a separate pump, called a circulating pump, being- used to force the condensing water through the tubes. Engines without any condenser, like that shown in fig. 445, in which the steam is exhausted directly into the atmosphere after it has done its work,, are often c.zS\&d. high-pressure engines, but high pressures (of 80 to 90 pounds per square inch) are now frequently used in condensing engines, so that the name may be somewhat misleading. In such an engine as is shown in fig. 445 we have seen that the governor keeps the speed constant, by closing or opening an exterior valve through which the steam passes on its way to the main valve. An artificial resis- tance is in this way opposed to the passage of the steam, by increasing which the pressure can be reduced, and therefore the work done by the steam, so that the engine will not run too fast if the resistance to its motion be diminished (as by disconnecting some of the machines it is driving, &c.). The actual weight of steam passing into the cylinder at each stroke remains unchanged, but the amount of ziseful work the steam can do is diminished artificially by giving it some useless work to do in addition, in forcing" its way through a constricted passage. This is now known to be a wasteful way of controlling speed. In modern engines, therefore, the governor is frequently made to act by regulating the quantity of steam ad- mitted by each stroke, and thus making the consumption of steam as nearly as possible proportional to the work done. Engines so arranged, of which the Corliss engine is one of the best known examples, are said to be fitted with automatic cut-off gear. There is a popular misconception, that somehow or other work is lost in an engine of the ordinary type between the piston and the crank, the latter receiving less work than is done on the former in consequence of the nature of the mechanism connecting them. It is probably unnecessary to point out here the fallacy of this notion, but it has received sufficient acceptance to lead to the invention of a host of rotary engines, in which it is endeavoured to obtain the desired rotary motion in a somewhat more direct fashion. Reuleaux has shown that in almost every case the mechanisms used in the rotary engines are the same as those of ordinary engines, although disguised in form, so that the idea of mechanical advantage is doubly a mistake, while in almost every case the rotary engines possess such grave mechanical defects that none of them have practically come into use. 479. Work of an engine. Horse-power. — The unit of work by which the performance of an engine is measured is in this country always the foot- pound. The number of foot-pounds of work done by the engine in any given time is equal to the average effective pressure upon its piston during that time, multiplied by the total distance through which the piston has moved under that pressure. By average effective pressure is meant the average value of the diflference between the pressures on its two sides. Taking the time as one minute, this quantity of work in foot-pounds is equal to : — Area of piston x mean intensity of pressure on piston x length of stroke X number of strokes per minute. The stroke must be taken in feet. If the area is in square feet, the 4;6 On Heat [479- pressure must be in pounds per square foot ; if the area is in square inches, the pressure must be in pounds per square inch. If the strokes are double strokes, each corresponding, that is, to one whole revolution of the shaft, the length of stroke must be multiplied by 2. To find, for example, the work done in one minute by an engine with cylinder 16 inches diameter and 24 inches stroke, making 50 (double) strokes per minute with a mean pres- sure of 52 pounds per square inch, we have (8^ X 3-1416) X 52 X / ?^^? J X 50 = 2,091,000 ft.-lbs. The rate at which an engine does work is often measured in horse-power of 33,000 ft.-lbs. per minute, an arbitrary unit supposed to represent the maxi- mum rate at which work could actually be done by a horse. In the case supposed the horse-power would be "' " ' — =bvA.. 33,000 On the Continent the unit of work is a kilogrammetre, which is very closely equal to 'l\ ft.-lbs. The horse-power used abroad, of 75 kilo- grammetres per second, is nearly 2 per cent, smaller than that in use in this country. 480. Indicator. Brake. — By the expression iiiark done by an engine we may mean either of two things, viz. the total work done by the engine, or what is called its useful, or effective, work. The total work is the actual work done by the steam on the piston and obtained by calculation, as described in the last paragraph. The useful work is what remains of this total after deduction has been made of the work necessary to drive the engine itself against its own frictional resistances. The total work of an engine is mea- sured by means of an apparatus called an indicator, invented by Watt, of which fig. 446 shows one of the most recent forms (Richard's), omitting a number of constructional details. The steam-engine indicator consists of a small cylinder A, half a square inch in area, in which works a piston B, the under side of which can be put into full communication with the cylinder of the engine by opening the cock C. Between the top side of the piston and the under side of the cylinder-cover is a spiral spring. The motion of the piston-rod is transferred to a parallel motion DD, and so causes a point E to move in a straight line up and down, its stroke being about four times as great as that of the small piston. The indicator is fixed on to the cylinder of the steam engine near one end, so that when the cock C is opened, there is the same pressure of steam on the indicator piston as on the engine piston. This pressure forces up the piston, and the amount of com- pression of the spring so caused is proportionate to the pressure causing it. The upward motion of E, therefore, is proportional to the steam pressure In front of E is a vertical drum F, on which a strip of paper cah be fixed, and this drum is caused to rotate about its axis by attaching the cord G to any suitable part of the engine. The paper thus moves horizontally under the pencil, with a motion proportional to the stroke of the engine, while the pencil moves up and down on the paper with a motion proportional to the steam pressure on the piston. The two motions occurring simul- taneously, the pencil traces on the paper a curve whose horizontal and vertical ordinates are proportional to the two quantities just named, and -480] Indicator. Brake 477 whose area is therefore proportional to the product of these quantities, or, which is the same thin^, to the work done by the piston as defined in the last paragraph. The curve is called an indicator card, or indicator diagram, and while its area shows the whole work done by the steam, its form shows the engineer what iJ happening within the cylinder at each point of the stroke, which he may often require to know. Figs. 447 and 448 show two forms of indicator diagram. The curves themselves, as drawn by the indicators, are lettered ABCD. Beside them a scale of pressure in atmospheres is placed. In fig. 447 the steam is expanded about seven times, and the back pressure is about \ of an atmo- sphere, the pressure during admission being 5 atmospheres. The engine is a condensing one, and the diagram is fairly good. Fig. 448 is for a non- condensing engine, the back pressure being above that of the atmosphere. |Fig- 447 1 A B 5,w r ^~"--\^^^ c \p zy"" S r =^ Fig. 446 Fig. 448 The steam is cut off (at B) only at about J of the stroke, so that it is not working economically, and from the roundness of its corners the diagram would be considered a poor one. The useful work of an engine is measured by an entirely different piece of apparatus, called a dyjtamomeier. This is used in many forms, but fig. 449 shows the principle upon which the majority act. The apparatus shown in the figure is known as a Pronys friction brake. A is the shaft, the usual work transmitted by which we require to find. Upon the shaft is a fixed pulley B, embraced by two blocks B, and B^, which can be tightened up by the screws at C, and €3. To the lower block is fixed a lever D, from which hangs a weight, and which has at its extremity a small pointer work- ing against a short scale F. If such an apparatus be .set in motion by turning the shaft A, one of two things must happen : either the pulley must 478 On Heat [480- slipjround in the blocks, or it must so grip them as to carry both them and the lever D round its own axis. The moment of resistance to the former is rY, if r be the radius of the pulley and F the frictional resistance at its Fig. 449 periphery ; that of the latter is RW, where R is the radius of the weight and W the weight itself. In practice the screw Cj is loosened sufficiently to keep the weight just lifted from the ground, while the pulley is always turning round in the blocks, so that, therefore, rF = RW. The work done at the brake per minute is equal to the frictional resistance multiplied by the distance through which it is overcome in the same time, •or, if n be the number of revolutions per minute, = 2TTr7n - 27rRW«. It is therefore just the same as if a resistance = W were continually being overcome at the periphery of a wheel of radius R, making n turns per minute. As the values of all the quantities in the expression 2n-RW« are very readily determined, it will be seen that this brake affords a very simple way of measuring the net work transmitted through the shaft of an engine. The ratio useful work work shown by brake ,is called the efficiency total work ' " work shown by indicator' of the engine as a machine, or its mechanical efficiency. It is often as much as o'85 and sometimes even higher than o-g or go per cent., being g-enerally greatest in large engines. 481. Efficiency of heat engines.^ — There is another ratio of efficiency connected with the steam engine, namely the ratio Total work done by engine Total heat expended ' what is called the efficiency of the engine as a lieat engiiie or its thermo- dynamic efficiency. If Tj and T^ be respectively the absolute temperatures (337) of the steam and the feed water in any engine, then it can be shown -483] Gas Engines 479 that such an engine, if working quite perfectly, could transform no more than ( ^ ~ — -- \ of the heat which it receives into work. This fraction in the case of a steam engine is seldom more than about o'25. The value of the actual efficiency of the engine is often from o-io to 0-14 ; while, therefore, an ordinary steam engine, with such an efficiency, turns into work only from jij to ^ of the whole heat it receives, yet it may be turning into work J or more of the whole heat which it could possibly transform into work if it were perfect. To increase the economy of steam engines we require to make the value (T — T \ ^— — 5. I larger. This is done either by raising Tj or by lowering Tj, or both. The chief difficulty is that we cannot raise Tj without increasing the steam pressure, whicn it is often not convenient to do, while we cannot lower Tj below such a temperature, 50' to 60'' F., as can readily be obtained naturally at all seasons of the year. 482. Hot-air engines. — The difficulty as to Tj just mentioned is got over by the use of some fluid whose pressure is not a function of its temperature, and naturally air is the most convenient fluid for the purpose. Many ' hot- air' engines have been designed, and some have found a considerable measure of success commercially, as Rider's, Hock's, and Lehmann's. In all cases the engines consist essentially of one (or two) chambers placed so that one end can be heated by a furnace and the other cooled by a refrige- rator. The air is compelled to move from the cold space to the hot and back again continually. When hot it is allowed to expand and push forward a piston ; when cold it is compressed by pushing back the piston again to its original position. The difference between these two quantities of work is the whole work done by the engine. By making Tj a very high temperature, (T — T \ — ';= — ^1 of an air engine may be made much higher than that of a steam engine. But it is so much more difficult to attain the theoretical efficiency in the air than in the steam engine, that its actual efficiency is generally much lower than that of a steam engine. There are constructive difficulties connected with the hot-air chambers, and with the regulation of the speed, and these, as well as the large bulk of most air engines in proportion to their power, have stood greatly in the way of their development. No doubt, however, much more improvement would have taken place in these engines had not gas engines come into prominence of late years and proved much more convenient. 483. Gas engines. — Gas engines, like steam engines and air engines, are heat engines, but in them the working fluid is ordinary coal gas mixed with air, in the proportion of about i to 1 1 by volume. The principle of action is very simple : — The explosive mixture after being drawn into the cylinder is set light to, the heat generated by the very rapid combustion, which we call an explosion, causes the mixed gases to expand and drive forward the piston. The great difficulty for many years was that the explosion was so rapid that the comparatively slow-going piston could not keep up with it, and the greater part of the energy of the explosion was lost by radiation and conduction. In the more modern gas engines, however (Otto's and Clerk's 48o On Heat [483- and others), this difficulty is got over by compressing the charge before igniting it, a treatment which is found to decrease very much the rapidity of the explosion and so greatly increase the actual efficiency of the engine. Fig. 450 shows the principal parts of an Otto ' Silent ' gas engine, as now made. A is the cylinder, open at front and single-acting, in which works a deep piston F, driving a crank in the usual manner. The' cylinder is surrounded by a water jacket, to prevent it from getting too hot. At the back of the cylinder is a slide valve B, worked by a cam, not shown in drawing, on the lay shaft G. The valve B is kept up against its face by spiral springs E. D is a chamber in which a small jet of gas for igniting the mixture is con- tinually burning. Cj is the cock for admission of gas, and C^ an india rubber bag to equalise the gas pressure. The working of the engine is as follows : — the piston moves from left to right and draws into the cylinder the explosive mixture. On the return stroke it compresses the mixture to about 3 atmospheres. The igniting flame is then allowed to come for an instant Fig. 450 into contact with the compressed mixture, which burns very rapidly (or explodes slowly, whichever expression be preferred) and pushes the piston forward again, the pressure rising to 10 or 12 atmospheres. On the next return stroke the burnt gases are pushed out through the opening shown in the drawing, and the process begins once more. There are many ingenious arrangements about this type of engine which our space will not allow us to mention in detail. It must suffice to say that the engine has proved distinctly economical, and has such very great conveniences as may fairly account for the rapid way in which its use (and that of other gas engines) has extended. In conclusion, it is as well to point out that, as long as they work between the same temperatures, there is no difference between steam, air, and gas engines as to theoretical economy. The last two gain by the possibility of using higher limits of temperature than can be employed in a steam engine, Ijut, so far, have lost by constructive and mechanical difficulties which prevent their theoretical efficiency from being attained. 485] Heat due to Friction 481 CHAPTER XI SOURCES OF HEAT AND COLD 484. Different sources of heat. — The following different sources of heat may be distinguished : i. the mechanical sources, comprising friction, percussion, and pressure ; ii. the physical sources — that is, solar radiation, terrestrial heat, molecular actions, change of conditions, and electricity ; iii. the chemical sources, or molecular combinations, and more especially combustion. In what follows it will be seen that heat may be produced by reversing its effects ; as, for instance, when a liquid is solidified or a gas compressed (486) ; though it does not necessarily follow that in all cases the reversal of its effects causes heat to be produced — instead of it, an equivalent of some other form of energ)- may be generated. In like manner heat may be forced to disappear, or cold be produced when a change such as heat can produce is brought about by other means, as when a liquid is vaporised or a solid liquefied by solution ; though here also the disappearance of heat is not always a necessary consequence of the production, by other means, of changes such as might be effected by heat. MECHANICAL SOURCES 485. Heat due to friction. — The friction of two bodies, one against the other, produces heat, which increases with the pressure and with the rapidity of motion. For example, the axles of carriage wheels, by their fric- tion against the boxes, often become so strongly heated as to take fire. By rubbing together two pieces of ice in a vacuum below zero. Sir H. Davy partially melted them. In boring a brass cannon Rumford found that the heat developed in the course of 2\ hours was sufficient to raise 26J pounds of water from zero to 100°, which represents 2650 thermal units (452). Mayer raised water from 12° to 13° by shaking it. At the Paris Exhibition, in 1855, Beaumont and Mayer exhibited an apparatus, which consisted of a wooden' cone covered with hemp, and moving with a velocity of 400 revolutions in a minute, in a hollow copper cone, which was fixed and immersed in the water of an hermetically closed boiler. The surfaces were kept covered with oil. By means of this apparatus 88 gallons of water were raised from 10° to 130°' in the course of a few hours. In the case of flint -and steel, the friction of the flint against the steel' raises the temperature of the metallic particles which fly off, heated to such; an extent that they take fire in the air. I I 482 On Heat [485- The luminosity of aerolites is considered to be due to their friction against the air, and to their condensation of the air in front of them (486), their velocity attaining as much as 150 miles in a second. Tyndall devised an experiment by which the great heat developed by friction is illustrated in a striking manner. A small brass tube closed at one end- (fig. 451) is fixed on a small wheel. The tube, three parts full of water, Fig. 451 is closed by a cork, and is pressed between a wooden clamp, while the wheel is rotated with some rapidity. The water rapidly becomes heated by the friction, and its temperature soon exceeding the boiling-point, the cork' is projected to a height of several yards by the elastic force of the steam. 486. Heat due to pressure and percussion. — If a body be so com- pressed that its density is increased, its temperature rises according as the volume diminishes. Joule verified this in the case of water and of oil, which were exposed to pressures of 15 to 25 atmospheres. In the case of water at I '2° C, increase of pressure caused lowering of temperature — a result which agrees with the fact that water contracts by heat at this temperature. Similarly, when weights are laid on metal pillars, heat is evolved, and absorbed when they are removed. So in like manner the stretching of a metal wire is attended with a diminution of temperature. The production of heat by the compression of gases is easily shown by means of the -pneumatic syringe (fig. 452). This consists of a glass tube with thick sides, closed hermetically by a leather piston. At the bottom of this there is a cavity in which a small piece of cotton, moistened with ether or bisulphide of carbon, is placed. The tube being full of air, the piston is suddenly plunged downwards ; the air thus compressed disengages so much heat as to ignite the cotton, which is seen to burn when the piston is rapidly withdrawn. The ignition of the cotton in this experiment indicates a temperature of at least 300°. The rise of temperature produced by the compression in the above -486] Heat due to Pressure and Percussion 483 experiment is sufficient to effect the combination, and therefore the detonation, of a mixture of hydrogen and oxygen. A curious apphcation of the principle of the pneumatic syringe is met with in the American powder ram for pile-driving. On the pile to be dri\en is fixed a powder mortar, above which is suspended at a suitable distance an iron rammer, shaped like a gigantic stopper, which just fits in the mortar. Gunpowder is placed in the mortar, and when the rammer is detached it falls into the mortar, compresses the air, producing so much heai: that the powder is exploded. The force of the gases projects the rammer into its original position, where it is caught by a suitable arrangement ; at the same time the reaction of the mortar on the pile drives this in with far greater force than the fall of the rammer. After adding a fresh charge of powder, the rammer is again allowed to fall, again produces heat, explosion, and so forth, so that the driving is effected in a surprisingly short time. Percussion is also a source of heat. In firing shot at an iron target, a sheet of flame is frequently seen at the moment of impact ; and Sir J. Whit- worth used iron shells which are exploded by the concussion on striking an iron target. A small piece of iron hammered on the anvil becomes very hot. Fig. 452 The heat due to the impact of bodies is not difficult to calculate. When- ever a body moving with a velocity v is suddenly arrested in its motion, its kinetic energy is converted into heat. This holds equally whatever be the cause to which the motion is due : whether it be that acquired by a stone falling from a height, by a bullet fired from a gun, or the rotation of a copper disc by means of a turning table. The energy of any moving body is expressed by or in foot-pounds by ^— , where p is the weisrht in 2 ig ° pounds, V the velocity in feet per second, and ^is about 321(32) ; and if the whole of this be converted into heat, its equivalent in thermal units will be pv^ — Suppose, for instance, a lead ball weighing a pound be- fired 2^X 1390 " to 6 f from a gun, and strike against a target, what amount of heat will it produce ? We may assume that its velocity will be about 1600 feet per second ; then I X 1 600^^ its kinetic energy will be = 40,000 foot-pounds. Some of this will 2 X 32 have been consumed in producing the vibrations which represent the sound of the shock, some of it also in its change of shape ; but neglecting these two as being small, and assuming that the heat is equally divided between the ball 484 On Heat [486- and the target, then, since 40,000 foot-pounds is the equivalent of 287 thermal units, the share of the ball will be 14-3 thermal units ; and if, for simplicity's sake, we assume that its initial temperature is zero, then, taking: its specific heat at 0-0314, we shall have I X 0-0314 je/= 14-3, or ;; = 457°, which is a temperature considerably above that of the melting point of lead (341). By allowing a lead ball to fall from various heights on an iron plate, both experience an increase of temperature which may be measured by the thermopile ; and from these increases it may be easily shown that the heat is directly proportional to the height of fall, and therefore to the square of the velocity. By similar methods Mayer calculated that if the motion of the earth. were suddenly arrested the temperature produced would be sufficient to melt and even volatilise it ; while, if it fell into the sun, as much heat would be produced as results from the combustion of 5000 spheres of carbon the size of our globe. PHYSICAL SOURCES 487. Solar radiation. — The most intense of all sources of heat is the sun. Pouillet made the first accurate measurements of the heat of the sun by means of an instrument called the fyroheliovieter. The form represented in fig. 453 consists of a flat cylindrical metal box 3 inches in diameter and i an inch deep, containing a known weight of water. To it is fitted a metal tube which contains the stem of a deli- cate thermometer, the bulb of which dips in the liquid of the box, being fitted by means of a cork. The tube works in two collars, so that by means of a milled head it can be turned, and with it the vessel, and the liquid thus be uniformly mixed. The face of the vessel is coated with lampblack, and is so adjusted that the sun's rays fall perpendicularly upon it. This can be ascertained by observing when the shadow exactly covers the lower disc which is fitted to the same axis. The instrument was exposed for five minutes at a time to the sun's rays ; knowing the weight of the water, and the rise of temperature, we may easily calculate the heat absorbed by it. Corrections were necessary for the heat reflected by the lampblack, and also for the heat absorbed by the|air. The solar constant Q is the quantity of heat in gramme-degrees which a F'g- 453 -487] Solar Radiation 485 square centimetre of a perfect absorbent would receive in a minute from the vertical sun's rays at the limit of the atmosphere. On the surface of the earth the value Q is less, but by determining it at various heights and combining the observations, the absorption by the atmosphere can be deter- mined and Q ascertained. The most trustworthy experiments give for this value 3 gramme calories. When the sun is in the zenith about one-third is absorbed and two-thirds reach the earth. Of older data, Pouillet calculated from the results of experiments with his apparatus that if the total quantity of heat which the earth receives from the sun in the course of a year were employed to melt ice, it would be capable of melting a layer of ice all round the earth of 35 yards in thickness. Another statement is that the heat emitted by the sun is equal to that produced by the combustion of 1500 pounds of coal in an hour on each square foot of its surface. But from the surface which the earth exposes to the sun's radia- tion, and from the distance which separates the earth from the sun, the quantity of heat which the earth receives can only be fjgj^ooooo °^ ^^^ ^ie^aX emitted by the sun. Violle calculated the thickness of ice melted by the sun's heat at the equator, apart from absorption by the atmosphere, at 55 metres in thickness ; and, deducting this absorption, at 37 metres. Faraday calculated that the average amount of heat radiated in a day on each acre of ground in the latitude of London is equal to that which would be produced by the combustion of sixty sacks of coal. The heat of the sun cannot be due to combustion, for even if the sun consisted of hydrogen, which of all substances gives the most heat in com- bining with oxygen, it can be calculated that the heat thus produced would not last more than 3000 years. Another supposition is that originally put forth by Mayer, according to which the heat which the sun loses by radiation is replaced by the fall of aerolites against its surface. One class of these is what we know as shooting stars, which often appear in the heavens with great brilliancy, especially on August 14 and November 15 ; the term meteoric stone or aerolite being properly, restricted to the bodies which fall on the earth. They are often of considerable size, and are even met with in the form of dust. Although some of the sun's heat may be restored by the impact of such bodies against the sun, the amount must be very small, for Lord Kelvin has proved that a fall of 0-3 gramme of matter in a second on each square metre of surface would be necessary for this purpose. The effect of this would be that the mass of the sun would increase, and the velocity of the earth's rotation about the sun would be accelerated to an extent which would be detected by astronomical observa- tions. Helmholtz considers that the heat of the sun was produced originally by the condensation of a nebulous mass, and is kept up by a continuance of this contraction. A sudden contraction of the primitive nebular mass of the sun to its present volume would produce a temperature of 28 millions of degrees Centigrade ; and a contraction of xttJct of its mass would be sufficient to supply the heat radiated by the sun in 2000 years. This amount of contraction could not be detected even by the most refined astronomical methods. 486 On Heat [488- 488. Terrestrial heat. — Our globe possesses heat peculiar to it, which is called terrestrial heat. The heat from the sun penetrates slowly by conduc- tion into the interior, and accordingly the maximum temperature will be at different depths at different times. Thus with four thermometers sunk at depths of 3, 6, 12 and 25-5 feet in the porphyry rock of the Calton Hill, Edin- burgh, the registered maximum temperatures were on August 1 9, September 8, October 19, and January 4 respectively. But some of the heat is retained in each layer and raises the temperature so that the yearly valuations diminish with the depth. For the above thermometers these were 8'2', 5-6°, 27°, and 07° From observations of this kind it is concluded that the solar heat does not penetrate below a certain internal layer, which is called the layer of constant amuial tejnperature ; its depth below the earth's external surface varies, of course, in different parts of the globe ; at Paris, it is about 30 yards, and the temperature is constant at 11 '8' C. Below the layer of constant temperature, the temperature is observed to increase, on the average, 1° C. for every 90 feet. The most rapid increase is at Irkutsk in Siberia, where it is 1° for 20 feet, and the slowest in the mines at Mansfield, where it is about i^ C. for 330 feet. This increase has been verified in mines and artesian wells. According to this, at a depth of 3000 yards the temperature of a corresponding layer would be 100°, and at a depth of 20 to 30 miles there would be a temperature sufficient to melt all substances which exist on the surface. Hot springs and volcanoes confirm the existence of this central heat. Various hypotheses have been proposed to account for the existence of this central heat. The one usually admitted by physicists is that the earth was originally in a liquid state in consequence of the high temperature, and that by radiation the surface has gradually solidified, so as to form a solid crust. The cooling must be very slow, owing- to the small conductivity of the crust. For the same reason the central heat does not appear to raise the temperature of the surface more than J^ of a degree. Fourier calculated that the heat given off by the earth in 100 years would be sufficient to melt a layer of ice 3 metres in thickness, which therefore is only j^Vtt of '1^^' received by the sun in the same time. 489. Heat produced by absorption and imbibi- tion. — Molecular phenomena, such as imbibition, absorption, capillary actions, are usually accom- panied by disengagement of heat. Pouillet found that whenever a Uquid is poured on a finely divided solid, an increase of temperature is produced which varies with the nature of the substances. With in- organic substances, such as metal, the oxides, the earths, the increase is -^ of a degree ; but with organic substances, such as sponge, flour, starch roots, dried membranes, the increase varies from i to 10 degrees. The absorption of gases by solid bodies presents the same phenomena. Fig. 454 -490] Chemical Combination. Combustion 487 Dobereiner found that when platinum, in the fine state of division known as platinum black, is placed in oxygen, it absorbs many hundred times its volume, and that the gas is then in such a state of density, and the tem- perature so high, as to give rise to strong combustion. Spongy platinum produces the same effect. A jet of hydrogen directed on it takes fire. The apparatus known as Dobereiner's lamp depends on this property of finely divided platinum. It consists of two glass vessels (fig. 454). The first, A, fits in the lower vessel by means of a tubulure which closes it hermetically. At the end of the tubulure is a lump of zinc, Z, immersed in dilute sulphuric acid. By the chemical action of the zinc on the dilute acid hydrogen gas is generated, which, finding no issue, forces the liquid out of the vessel B into the vessel A, so that the zinc is not in contact with the liquid. The stopper of the upper vessel is raised to give exit to the air in proportion as the water rises. On a copper tube, H, fixed in the side of the vessel B, there is a small cone, a, perforated by an orifice ; above this there is some spongy platinum in the capsule, c. As soon now as the cock, which closes the tube H, is opened, the hydrogen escapes, and, coming in contact with the spongy platinum, is ignited. The condensation of vapours by solids often produces an appreciable rise of temperature. This is particularly the case with humus, which, to the benefit of plants, is warmer in moist air than the air itself Favre found that when a gas is absorbed by charcoal the amount of heat produced by the absorption of a given weight of sulphurous acid, or of nitrous oxide, greatly exceeds that which is disengaged in the lique- faction of the same weight of gas ; for carbonic acid, the heat produced by absorption exceeds even the heat which would be disengaged by the solidi- fication of the gas. The heat produced by the absorption of these gases cannot, therefore, be explained by assuming that the gas is liquefied, or even solidified in the pores of the charcoal. It is probable that it is in part due to that produced by the liquefaction of the gas, and in part to the heat due to the imbibition in the charcoal of the liquid so produced. CHEMICAL SOtTRCES 490. Chemical combination. Combustion. — Chemical combinatiojis are usually accompanied by a rise of temperature. When these combinations take place slowly, as when iron oxidises in the air, the heat produced is imperceptible ; but if they take place rapidly, the disengagement of heat is very intense. The same quantity of heat is produced in both cases, but when evolved slowly it is dissipated as fast as formed. Combustion is chemical combination attended with the evolution of light and heat. In ordinary combustion in lamps, fires, candles, the carbon and hydrogen of the coal, or of the oil, &c., combine with the oxygen of the air. But combustion does not necessarily involve the presence of oxygen. If either powdered antimony or a fragment of phosphorus be placed in a vessel of chlorine, it unites with chlorine, producing thereby heat and flame. Many combustibles burn with flame. K flame is a gas or vapour raised to a high temperature by combustion. Its illuminating power varies with the nature of the product formed. The presence of a solid body in the flame 488 On Heat [490- increases the illuminating power. The flames of hydrogen, carbonic oxide, and alcohol are pale, because they only contain gaseous products of com- bustion. But the flames of candles, lamps, coal gas, have a high illuminating power. They owe this to the fact that the high temperature produced decomposes certain of the gases, with the production of carbon, which, not being perfectly burnt, becomes incandescent in the flame. Coal gas, when burnt in an arrangement by which it obtains an adequate supply of air, such as a Bunsen's burner, is almost entirely devoid of luminosity. A non-lumi- nous flame may be made luminous by placing in it platinum wire or asbestos. The temperature of a flame does not depend on its illuminating power. A hydrogen flame, which is the palest of all flames, is the hottest. Chemical decomposition, in which the attraction of heterogeneous mole- cules for each other is overcome, and they are moved further apart, is an operation requiring an expenditure of work or an equivalent consumption of heat ; and conversely, in chemical combination, motion is transformed into heat. When bodies attract each other chemically their molecules move towards each other with gradually increasing velocity, and when impact has taken place the progressive motion of the molecules ceases, and is converted into a rotating, vibrating, or progressive motion of the molecules of the new body. The heat produced by chemical combination of two elements may be compared to that due to the impact of bodies against each other. Thus the action of the atoms of oxygen, which in virtue of their progressive motion, and of chemical attraction, rush against ignited carbon, has been likened by Tyndall to the action of meteorites which fall into the sun. 491. Heat disengaged during chemical action. — Many physicists, more especially Lavoisier, Rum- ford, Dulong, Despretz, Hess, Favre and Silbermann, Berthelot, Thomsen, and Andrews, have in- vestigated the quantity of heat dis- engaged by various bodies in chemical actions. Lavoisier used in his experi- ments the ice calorimeter already described. Rumford used a calori- meter known by his name, which consists of a rectangular copper canister filled with water. In this canister there is a worm which passes through the bottom of the box, and terminates below in an inverted funnel. Under this funnel is burnt the substance experimented upon. The products of combustion, in passing through the worm, heat the water of the canister, and from the increase of Fig. 455 -491] Heat disengaged during Chemical Action 489 its temperature the quantity of heat evolved is calculated. Despretz and Dulong successively modified Rumford's calorimeter by allowing the com- bustion to take place, not outside the canister, but in a chamber placed in the liquid itself; the oxygen necessary for the combustion entered by a tube in the lower part of the chamber, and the products of combustion escaped by another tube placed at the upper part and twisted in a ser- pentine form in the mass of the liquid to be heated. Favre and Silbermann improved this calorimeter very greatly (470), not only by avoiding or taking- account of all possible sources of error, but by arranging it for the deter- mination of the heat evolved in such chemical actions as take place between gases and vapours. The gases enter by tubes BB' and CC, fig. 455, into a metal chamber A, where the reaction takes place, the course of which can be watched through a glass plate which closes a wider tube FK. The gaseous products before passing into the air traverse a long serpentine tube H, at the lower end of which is a small box G which receives the liquids arising from the condensation of the vapours. The cylinder A and the serpentine are contained in a known mass of water contained in a calori- meter, and from the rise in temperature of this water the heat developed can be calculated. To avoid any loss of heat this is placed within a metal case, MM, containing swan's down. The whole is contained in a vessel of water NN in which is a thermometer, to eliminate the influence of changes in the temperature of the air. The experiments of Favre and Silbermann are the most trustworthy, as having been executed with the greatest care. They agree very closely with those of Dulong. Taking as thermal unit the heat necessary to raise the temperature of a pound of water through one degree Centigrade, the following- table gives the heat disengaged by a pound of each of the substances while burning in oxygen : — Hydrogen . . 34,462 Marsh gas . . i3)063 Ethylene . 11,858 Petroleum . . 11,000 Oil of turpentine . 10,853 Olive oil . . 9860 Ether . . . 9030 Anthracite . . 8460 Charcoal . 8080 Coal . . 8000 Tallow .... 8000 Graphite 7797 Diamond . . . 7770 Absolute alcohol . . 7180 Coke . . 7000 Phosphorus . . 5750 Coal gas . . 5600 Wood, dried at 1 20° . 3616 Carbon bisulphide . . 3401 Wood, ordinary . 2756 Carbonic oxide . . 2400 Sulphur . . . 2220 Zinc . . 1300 Iron . . 1 181 Bunsen's calorimeter (456) has been used with advantage for studying the heat produced in chemical reactions, in cases in which only very small quantities are available. For experiments. Ion the heat of neutralisation of acids and bases the apparatus represented in fig. 456 may be used. W is a large vessel of vi^ater of constant temperature ; the beaker glass, B, which is the calorimeter, rests on a cork in the outer one, A. On the wooden lid, H, are two weights, Sj 490 On Heat [491- and Sj, to keep A down in the water ; c and d are tubes placed in holes in the lid, and contain weighed quantities of the two liquids ; b \% a. delicate thermometer. After the tubes c and d have acquired the temperature, of the water t, their contents are poured into B through an aperture in the lid for this purpose. When the reaction is complete, the temperature indicated by the thermometer, which reaches to the middle of B, rises to /„ so that, when we know the weight of the substances, and the rise of temperature i"] — t, the quantity of heat produced in the reaction is easily determined. Fig- 456 Fig. 457 492. Berthelot's calorimetric bomb. — This apparatus, represented in section in fig. 457, is small enough to be inserted in the water of a calori- meter. It consists of a steel reservoir C lined with platinum, which can be hermetically closed by a screwed cover B. At the centre is a cylinder in which a tube can be turned, serving to admit the gases to be worked with. Near this is a carefully insulated platinum wire, which ends near the side of the apparatus ; when an electric spark is passed it sets up the chemical reaction, the heat due to which is to be measured. For this purpose the bomb before the experiment is placed in a calorimeter, and from the rise in temperature of the known weight of water the quantity of heat can be deduced. If a solid is to be burned it is placed in a platinum capsule, and the combustion set up by passing a current through a veiy fine platinum wire in contact with it. 493. Endothermic and exothermic actions. — -AH chemical actions, whether -493] Endothermic and Exothermic Actions 491 of combination or of decomposition, are attended by a disturbance of the thermal equihbrium ; and the quantity of heat disengaged is a measure of the physical and chemical work. In most cases the act of chemical combination is attended by a rise of temperature, and the quantity of heat is a measure of the energy developed in the reaction. Thus in the formation of one molecule of water there are lilDerated 68,924 thermal units, which may be written thus, H, + O = VLfi + 68,924. Those reactions which take place with disengagement of heat are said to be exothermic ; there are, however, cases Avhere bodies do not directly com- bine without the intervention of extraneous heat — for instance, iodine and hydrogen to form hydriodic acid ; the equation for this is I + H + 6ooo=IH. Such reactions are called endothermic. Those bodies are most stable in the formation of which most heat is developed ; thus the iron and zinc oxides, in the formation of which 1 1 8 1 and 1300 units are respectively developed, are much more stable than silver oxide, in the formation of which only 27 units are developed. The heat of decomposition is the reciprocal of that of combination ; those bodies which develop most heat in their formation require conv;rs;ly an equivalent quantity to decompose them ; decompositions which require an expenditure of heat to produce them are called endothermic. Those com- pounds, on the contrary, which absorb heat in their formation, develop an equivalent quantity in being decomposed, and the reactions are exothermic ; they often take place with explosive violence, as in the case of the nitrogen chlorides and iodide. An exothermic reaction gives rise to an endothermic compound ; and, conversely, an endothermic reaction forms an exothermic compound. The oxidising compounds in most ordinary explosives, potassium chlorate and nitrate, are endothermic, evolving heat during decomposition which thus helps the reactions. If there be any system of bodies which act on each other without the supply of extraneous energy, then that body or set of bodies results, in the formation of which most heat is produced. This is called the principle of greatest chemical action. The heat developed in any chemical reaction depends on the relation between the initial and the final products, and is independent of the nature and succession of the intermediate stages. It is equal to the sum of the quantities of heat produced in each stage, regard being had to the negative quantities due to such processes as solution and gasification. Thus a gramme of carbon in burning to carbonic acid produces 8080 calories. If the same weight of carbon burns so as to form carbonic oxide, it forms 2473 ; and the combustion of the carbonic oxide resulting from this reaction yields 5607, making together 8080. Potassium combiries directly with chlorine to form potassium chloride? the heat of formation of which is 1 5,000 and is equal to that produced by the same weight of salt, whether this be formed by the direct union of hydro- 492 On Heat [493- chloric acid and potash, or whether it be produced by the action of potassium on aqueous solution of hydrochloric acid. The heat of combustion of a compound is not always equal to the sum of that of each of its constituents. The heat of combustion of carbon bisulphide is 3401, while that calculated from its constituents is 3145 ; the compound accordingly possesses more energy than its constituents, and its formation is due to an endothermic reaction. Metanieric bodies are those which contain the same number of elements but in different groupings ; thus acetic acid and methylic formate have each the composition C^H^Oj ; but the heat of combustion of the latter is 4157, and that of the former 3505 ; from this it is to be inferred that the grouping of the atoms to form acetic acid has been attended with the expendi- ture of more energy than in the case of methylic formate. Polymeric bodies are those which have the same elements and the same percentage composition but differ in the number of atoms which form a molecule. Thus the more complex the molecule the smaller is the quantity of heat. That of amylene, for instance, C^Hm, is 11,401, and that of metamylene, CjqH^o, is 10,908. Many chemical elements, such as carbon, sulphur, and phosphorus, exist in modifications which are essentially different from each other in their physical properties, but which form, when they enter into combination with other elements, identical chemical products. Such bodies are said to have graphite or different allotropic forms which have different thermal values. The heat liberated when one allotropic form is changed into another — for instance, when charcoal is converted into diamond — cannot be directly deter- mined, but must be arrived at by indirect methods. A given weight of carbon, whether it be charcoal or diamond, produces exactly the same weight of carbonic acid, though the heat of combustion is different. Thus, when a gramme each of charcoal, graphite, and diamond are severally burnt in oxygen in the calorimetric bomb, the heats produced are respectively 8137, 7900, and 7860 thermal units ; hence 237, the differ- ence between the two former values, represents the heat developed in the transformation of one gramme of charcoal into graphite, and 40, the corre- sponding number, in the change from graphite to diamond. The temperature of combustioti, or, in the case of gases, the temperature of the flame, is the upper limit of the temperature which can be attained by the combustion of a body. This can be deduced from the heat of combus- tion, and from the specific heats of the bodies produced. The theoretical temperature of combustion of hydrogen in oxygen is calculated at 6715° ; this, however, is never even approximately reached, for at much lower temperatures aqueous vapour is dissociated (394) into its constituents, and the combustion cannot exceed a certain limit of temperature. 494. Animal heat.— In all the organs of the human body, as well as those of all animals, processes of oxidation are continually going on. Oxygen passes through the lungs into the blood, and so into all parts of the body. In like manner the oxidisable bodies, which are principally hydrocarbons, pass by the process of digestion into the blood, and likewise into all parts of the body, while the products of oxidation, carbonic acid and water, are eliminated by the skin, the lungs, &c. Oxidation in the muscle produces motions of the -496] Fireplaces 493 molecules, which are changed into contraction of the muscular fibres ; all other oxidations produce heat directly. When the body is at rest, all its functions, even involuntary motions, are transformed into heat. When the body is at work, the more vigorous oxidations of the working parts are transferred to the others. Moreover, a great part of the muscular Avork is changed into heat, by friction of the muscles and of the sinews in their sheaths, and of the bones in their sockets. Hence the heat produced by the body when at work is greater than when at rest. The blood distributes heat uniformly through the body, which in the normal condition has a temperature of 36'9° C. = 98-4° F. The^blood of mammalia has the same temperature, that of birds is somewhat higher. In fever the temperature rises to 42° to 43°, and in cholera, or when near death, sinks as low as 35°. The function of producing work in the animal organism was formerly considered as separate from that of the production of heat. The latter was held to be specially due to the oxidation of the hydrocarbons of the fat, while the work was ascribed to the chemical activity of the nitrogenous matter. This view has now been generally abandoned ; for it has been found that during work there is no increase in the secretion of urea, which is the result of the oxidation of nitrogenous matter ; moreover, the organism while at rest produces less carbonic acid, and requires less oxygen than when it is at work ; and the muscle itself, both in the living organism and also when removed from it and artificially stimulated, requires more oxygen in a state of activity than when at rest. For these reasons the production of work is ascribed to the oxidation of the organic matter generally. The process of vegetation in the living plant is not in general connected with any oxidation. On the contrary, under the influence of the sun's rays the green parts of plants decompose the carbonic acid of the atmosphere into free oxygen gas and into carbon, which, uniting with the elements of water, form cellulose, starch, sugar, and so forth. In order to effect this, an expenditure of heat is required which is stored up in the plant, and which reappears during the combustion of the wood, or of the coal arising from its decomposition. At the time of blossoming a process of oxidation goes on, which as in the case of the blossoming of the Victoria regia, is attended with an appre- ciable rise of temperature. HEATING 495. Different kindsj of heating;. — Heating is the art 01 utilising for domestic and industrial purposes the sources of heat which nature offers to us. Our principal source of artificial heat is the combustion of coal, coke turf, wood, and charcoal. 496. Fireplaces. — Fireplaces are open hearths built against a wall under a chimney, through which the products of combustion escape. However much they may be improved, fireplaces will always remain the, most imperfect and costly mode of heating, for they render a\ailable only 13 per cent, of the total heat yielded by coal or coke, and 6 per cent, of that by wood. This enormous loss of heat arises from the fact that the current of air necessary for combustion always carries with it a large quantity of the heat produced, which is dissipated in the atmosphere. Hence Franklin said 494 On Heat [496- ' fireplaces should be adopted in cases where the smallest quantity of heat was to be obtained from a given quantity of fuel.' Notwithstanding their want of economy, however, they will always be preferred as the healthiest and pleasantest mode of heating, on account of the cheerful light which they emit, and the ventilation which they ensure. 497. Draught of fireplaces. — The draught of a fire is the upward current in the chimney caused by the ascent of the products of combustion ; when the current is rapid and continuous, the chimney is said to draw well. The draught is caused by the difference between the temperature of the inside and that on the outside of the chimney ; for, in consequence of this difference, the gaseous bodies which fill the chimney are lighter than the air of the room, and consequently equilibrium is impossible. The weight of the column of gas CD, fig. 458, in the chimney being less than that of the external column of air AB of the same height, there is a pressure from the out- side to the inside which causes the products of combustion to ascend the more rapidly in proportion as the difference in weight of the two gaseous masses is greater. The velocity of the draught of a chimney may be determined theoretically by the formula v= ^2ga{t' — i)k, in which g is the acceleration of gravity, a the coefficient of the expansion of air, h the height of the chimney, t' the mean temperature of the air inside the chimney, and / the temperature of the surrounding air. The currents caused by the difference in temperature of two communi- cating gaseous masses may be demonstrated by placing a candle near the top and near the bottom of the partially opened door of a warm room. At the top, the flame will be turned from the room to- wards the outside, while the contrary effect will be produced when the candle is placed on the ground. The two effects are caused by the current of heated air which issues by the top of the door, while the cold air which replaces it enters at the bottom. In order to have a good draught, a chimney ought to satisfy the following con- ditions : — i. The section of the chimney ought not to be larger than is necessary to allow an exit for the products of combustion ; other- wise ascending and descending currents are produced in the chimney, which cause it to smoke. It is advantageous to place on the top of the chimney a conical pot narrower than the chimney, so that the smoke may escape with sufficient velocity to resist the action of the wind. ii. The chimney ought to be sufficiently high, for, as the draught is caused by the excess of the external over the internal pressure,Jthis excess is greater in proportion as the column of heated air is longer. iii. The external air ought to pass into the chamber with sufficient Fig. 458 -500] Heating by Hot Air 495 rapidity to supply the wants of the fire. In an hermetically closed room combustibles would not burn, or descending currents would be formed which would drive the smoke into the room. Usually air enters in sufficient quantity by the crevices of the doors and windows. iv. Two chimneys should not communicate, for if one draws better than the other, a descending current of air is produced in the latter, which carries smoke with it. For the strong fires required by steam boilers and the like, very higb chimneys are needed ; of course the increase in height would lose its effect if the hot column above became cooled down. Hence chimneys are often made with hollow walls — that is, of separate concentric layers of masonry or brickwork — the space between them containing air. 498. Stoves. — Stoves are apparatus for heating with a detached fire, placed in a room to be heated, so that heat radiates in all directions round the stove. At the lower part is the draught-hole by which the air necessary |for combustion enters. The products of combustion escape by means of iron chimney-pipes. This mode of heating is one of the most economical, but it is by no means so healthy as that by open fireplaces, for the ventilation is very bad, more especially where the stoves are fed from the outside of the room. These stoves also emit a bad smell, arising in part from the decomposition of organic substances which are always present in the air by their contact with the heated sides of the chimney-pipes ; or possibly, as Deville and Troost's researches seem to show, from the diffusion of gases through the heated sides of the stove. The heating is very rapid with blackened metal stoves, but they also cool very rapidly. Stoves constructed of polished earthenware, which are common on the Continent, heat more slowly, but more pleasantly, and they retain the heat longer. 499. Heating by steam. — Steam, in condensing, gives up its latent heat of vaporisa- tion, and this property is used in heating baths, public buildings, hothouses, &c. For this purpose steam is generated in boilers like those used for steam engines, and is then made to circulate in pipes placed in the room to be heated. The steam condenses, and in doing so imparts to the pipes its latent heat, which becomes free, and thus heats the surround- p.- ing air. 500. Heating- by hot air. — Heating by hot air consists in heating the air in the lower part of a building, whence it rises to the higher parts in 496 On Heat [500- The apparatus is arranged as represented in virtue of its lessened density. fig- 459- A series of tubes, AB, only one of which is shown in the figure, is placed in a furnace F, in the cellar. The air passes into the tubes through the lower end, A, where it becomes heated, and, rising in the direction of the arrows, reaches the room M by a higher aperture, B. The various rooms to be heated are provided with one or more of these apertures, which are placed as low in the room as possible. The conduit O is an ordinary chim- ney. These apparatus are- more economical than open fireplaces, but they are less healthy, unless special provision is made for ventilation. SOI. Heating by hot water. — This consists of a continuous circulation of water, which, having been heated in a boiler, rises through a series of tubes, and then, after becoming cool, passes into the boiler again by a similar series. Fig. 460 represents an apparatus for heating a building of several stories. The heating apparatus, which is in the basement, con- sists of a bell-shaped boiler, o, with an in- ternal flue, F. A long pipe, M, fits in the upper part of the boiler, and also in the reservoir Q, placed in the upper part of the building to be heated. At the top of this re- servoir there is a safety valve, s, by which the pressure of the vapour in the interior can be regulated. The boiler, the pipe M, and a portion of the reservoir Q, being filled with water, as it becomes heated in the boiler an ascending current of hot water rises to the reservoir Q, while at the same time descending currents of colder and denser water pass from the lower part of the reservoir Q into receivers 6, d,/, filled with water. The water from these passes again through pipes into other receivers, a, c, e, and ultimately reaches the lower part of the boiler. During this circulation the hot water heats the pipes and the receivers, which thus become true water-stoves. The number and the dimensions of these parts are determined from the fact that a cubic foot of water in falling through a temperature of one degree can theoretically impart the same in- crease of temperature to 3200 cubic feet of air (466). In the interior of the Fig. 460 -503] Cold produced by the Expansion of Gases 497 receivers, a, b, c, d, e,f, there are cast-iron tubes which communicate with the outside by pipes, P, placed underneath the flooring. The air becomes heated in these tubes, and issues at the upper part of the receiver. The principal advantage of this mode of heating is that of giving a temperature which is constant for a long time, for the mass of water only cools slowly. It is much used in hot-houses, baths, artificial incubation, drying rooms, and generally wherever a uniform temperature is desired. SOURCES OF COLD 502. Various sources of cold. — Besides the cold caused by the passage of a body from a solid to the liquid state, of which we have already spoken, cold is produced by the expansion of gases, by radiation in general, and more especially by radiation at night. 503. Cold produced by the expansion of ^ases. Ice machines. — We have seen that when a gas is compressed the temperature rises (486). The re- verse of this is also the case : when a gas is i-arefied, a reduction of temperature ensues, because a quantity of sensible heat disappears when the gas becomes increased to a larger volume. This may be shown by placing a delicate Breguet's thermometer under the receiver of an air-pump, and exhausting ; at each stroke of the piston the needle moves in the direction of zero, and regains its original position when air is admitted. The production of cold when a gas is expanded has been extensively applied in machines for artificial refrigeration on a large scale. By Wind- hausen's ice machine, from 15,000 to 150,000 feet of air can be cooled in an hour, through 40 to 100 degrees in temperature, by means of a steam engine of from 6 to 20 horse-power. The essential parts of this machine are repre- sented in fig. 461. The piston B in the cylinder A is worked to the right^by -^CT Fig. 461 a steam engine and to the left by a steam engine and by the compressed air. As it moves towards the right the \alve a opens, and air under the ordinary atmospheric pressure enters the space Aj. When this is full the piston moves towards the left, the air in A is compressed to about 2 atmospheres, the valve a is closed, the valve b opens, and air passes in the direction of the K K 498 On Heat [503- arrows into the cooler, C. By its compression it has become strongly heated, and the necessary cooling is effected by means of pipes through which cold water circulates, entering at 5 and emerging at 6. The air, thus compressed and cooled, passes out through the valve c, which is automatically worked by the machine, into the space Aj, where, in conjunction with the steam engine, it moves the piston to the left, and compresses the air in Aj ; for at a certain position of the piston the valve c is closed, the compressed air in the cylinder A^ expands, and thereby is cooled far below the freezing point. As the piston moves again to the right, the valve d is opened by the working of the machine, and the cooled air emerges through the tube 4 to its destination. If it passes into an ordinary room, by condensing the moisture it fills it with snowflakes. Machines of this kind are extensively employed in the arts ; in breweries, oil refineries, in the artificial production of ice, and in cooling rooms on board ship for the transport of dead meat, &c., which has become an industry of the greatest importance. In the Linde machine the material used is ammonia gas, which is liquefied by compression and surface condensation. This liquid ammonia being allowed to evaporate takes the heat for this change of state from the surrounding bodies, which are thereby cooled. The ammonia vapour thus formed is again liquefied, and flowing back to the refrigerator is again evaporated, so that a small quantity of ammonia is always passing through the same cycle of operations. A machine of this kind worked by a steam engine of half a horse-power can cool in an hour 3400 cubic yards of air from 10° to 5° C, or 1400 cubic yards from 6° to - 4° C. ; or it will produce i cwt. of ice in the same time. The larger machines are relatively more advantageous. 504. Cold produced by radiation at nig^ht. — During the day the ground receives from the sun more heat than it radiates into space, and the temperature rises. The reverse is the case during night. The heat which the earth loses by radiation is no longer compensated, and consequently a fall of temperature takes place, which is greater according as the sky is clearer, for clouds send towards the earth rays of greater intensity than those which come from the celestial spaces. In some winters it has been found that rivers have not frozen, the sky having been cloudy, although the thermometer had been for several days below — 4° ; while in other less severe winters the rivers freeze when the sky is clear. The emissive power exercises a great influence on the cold produced by radiation ; the greater it is, the greater is the cold. In Bengal, the cooling by night is used in manufacturing ice. Large flat vessels containing water are placed on non-conducting substances, such as straw or dry leaves. In consequence of the radiation the water freezes, even when the temperature of the air is 10° C. The same method can be applied in all cases with a clear sky. The Peruvians, in order to preserve the shoots of young plants from freezing, light great fires in their neighbourhood, the smoke of which, pro- ducing an artificial cloud, hinders the cooling produced by radiation. 505. Absolute zero of temperature. — As a gas is increased ji^^j of its volume for each degree Centigrade, it follows that at a temperature of 273° C. the volume of any gas measured at zero is doubled, supposing the pressure -505] Absolute Zero of Teinperature 499 to remain constant. In like manner, assuming the gaseous laws to continue to hold, we should have at 273' below zero, P V = o (332) ; that is, either the gas would shrink into nothing or it would be subjected to no pressure. We are not, however, driven to either of these conclusions, since we know that all gases are liquefied before a temperature of — 273° is reached. Nevertheless, this temperature —273' C. is a very important one, and is called the absolute zero of temperature. Thermodynamical considerations, apart from the behaviour of any particular gas, point to the conclusion that at this temperature all substances lose the whole of their molecular motion, i.e. are entirely deprived of heat. Absolute temperatures are obtained by adding 273 to the temperature on the Centigrade scale. Thus —35° C. is 238^^ on the absolute scale of temperature, and+ 15° C. is 288°. K K 2 Soo 071 Heat [506- CHAPTER XII MECHANICAL EQUIVALENT OF HEAT 506. Mechanical equivalent of heat. — If the various instances of the production of heat by motion be examined, it will be found that in all cases mechanical energy is expended. Thus in rubbing- two bodies against each other motion is apparently destroyed by friction ; it is not, however, lost, but appears in the form of a motion of the particles of the body ; the motion of the mass is transformed into a motion of the molecules. Again, if a body be allowed to fall from a height, it strikes against the ground with a certain velocity. According to older views, its motion is destroyed, vis viva is lost. This, however, is not the case ; the vis viva of the body or its kimtic emrgy appears as energy of its molecules. In the case, too, of chemical action, the most productive artificial source of heat, it is not difficult to conceive that there is, in the act of combining, an impact of the dissimilar molecules against each other, an effect analogous to the production of heat by the impact of masses of matter against each other (486). In like manner, heat may be made to produce motion, as in the case of the steam engine, and the propulsion of shot from a gun. Traces of a view that there is a connection between heat and motion are to be met with in the older writers. Bacon for example ; and Locke says, ' Heat is a very brisk agitation of the insensible parts of the object, which produces in us that sensation from whence we denominate the object hot ; so that what in our sensation is heat, in the object is nothing but motion.' Rumford, in explaining his great experiment of the production of heat by friction, was unable to assign any other cause for the heat produced than motion ; and Davy, in the explanation of his experiment of melting ice by friction in vacuo, expressed similar views. Carnot, in a work on the steam engine published in 1824, also indicated a connection between heat and work. The views, however, which had been stated by isolated writers had little or no influence on the progress of scientific investigation, and it is in the year 1842 that the modern theories may be said to have had their origin. In that year Dr. Mayer, a physician in Heilbronn, formally stated that there exists a connection of simple proportionality between heat and work ; and he it was who first introduced into science the expression ' mechanical equi- valent of heat.' Mayer also gave a method by which this equivalent could be calculated ; the particular results, however, are of no value, as the method, though correct in principle, was founded on incorrect data. In the same year, too, Colding of Copenhagen published experiments on -506] Mechanical Equivalent of Heat SOI the production of heat by friction, from which he concluded that the evohi- tion of heat was proportional to the mechanical energy expended. About the same time as Mayer, but quite independently of him. Joule commenced a series of experimental investigations on the relation between heat and work. These first drew the attention of scientific men to the subject, and were admitted as a proof that the transformation of heat into mechanical energy, or of mechanical energy into heat, always takes place in a definite numerical ratio. Subsequently to Mayer and Joule, several physicists, by their theoretical and experimental investigations, have contributed to establish the mechanical theory of heat : namely, in this country. Lord Kelvin and Rankine ; in Germany, Von Helmholtz, Clausius, and Holtzmann ; and in France, Clapeyron and Regnault. The following are some of the most important and satisfactory of Joule's experiments. A copper vessel, B (fig. 462), was provided with a brass paddle-wheel (indicated by the dotted lines), which could be made to rotate about a Fig. 462 vertical axis. Two weights, E and F, were attached to cords which passed over the pulleys C and D, and were connected with the axis A. These weights in faUing caused the wheel to rotate. The height of the fall, which in Joule's experiments was about 63 feet, was indicated on the scales G and H. The roller A was so constructed that by detaching a pin the weights could be raised without moving the wheel. The vessel B was filled with water and placed on a stand, and the weights allowed to sink. When they had reached the ground, the roller was detached from the axis, and the weights again raised, the same operations being repeated twenty times. The heat produced was measured by ordinary calorimetric methods (457). The work expended is measured by the product of the weight into the height through which it falls, or ph, less the work lost by the friction of the various parts of the apparatus. This is diminished as far as possible by the use of friction wheels (79), and its amount is determined by connecting C S02 On Heat [506- and D without causing them to pass over A, and then determining the weight necessary to communicate to them a uniform motion. In this way it has been found that a thermal unit — that is, the quantity of heat by which a pound of water is raised through i° C. — is generated by the expenditure of the same amount of work as would be required to raise 1392 pounds through i foot, or i pound through 1392 feet. This is expressed by saying that the mechanical equivalent of the thermal unit is 1392 foot- pounds. The friction of an iron paddle-wheel in mercury gave 1397 foot-pounds, and that of the friction of two iron plates gave 1395 foot-pounds, as the mechanical equivalent of one thermal unit. In another series of experiments, the air in a receiver was compressed by means of a force-pump, both being immersed in a known weight of water at a known temperature. After 300 strokes of the piston the heat, C, was measured which the water had gained. This heat was due to the compres- sion of the air and to the friction of the piston. To eliminate the latter in- fluence, the experiment was made under the same conditions, but leaving the receiver open. The air was not compressed, and 300 strokes of the piston developed C thermal units. Hence C - C is the heat produced by the com- pression of the gas. Representing the foot-pounds expended in producing this heatby W, we have -=; — -, for the value of the mechanical equivalent. By this method Joule obtained the number 1442. The mean number which Joule adopted for the mechanical equi\alent of one thermal unit on the Centigrade scale is 1390 foot-pounds ; on the Fahrenheit scale it is 772 foot-pounds. The number is called JoiMs equi- valent, and is usually designated by the symbol J. On the metric system 424 metres are usually taken as the height through which a kilogramme of water must fall to raise its temperature i degree Centigrade. This is equal to 41,600,000 ergs, or 4-16 x 10' grammes raised through a height of a centimetre, taking ^= 981. Professor Rowland of Baltimore has recently made a very careful and complete determination of the mechanical equivalent of heat, by Joule's method, in which he has examined and allowed for all possible sources of error. His results give 4-269 x 10' grammes centimetre or 1401 foot-pounds as the mean value of this constant for the latitude of Baltimore ; and this value is in close agreement with a still more recent determination by Mr. E. H. Griffiths, who found, by an electric method, 4'i99 x 10' ergs, or 1403-6 foot-pounds for the latitude of Greenwich (^=981-17), and by Micalescu, who found 4-187 x 10' for the latitude of Paris (^=980-96). Him made the following determination of the mechanical equivalent by means of the heat produced by the compression of lead. A large block of sandstone, CD (fig. 463), is suspended vertically by cords ; its weight is P. E is a piece of lead, fashioned so that its temperature may be determined by the introduction of a thermometer. The weight of this is n, and its specific heat c. AB is a cylinder of cast iron, whose weight is p. If this is raised to A'B', a height of h, and allowed to fall again, it compresses the lead, E, against the anvil, CD. It remains to measure on the one hand the work spent, and on the other the heat gained. -506] Mechanical Equivalent of Heat 503 The hammer AB be ng raised to a height h, the work of its fall is ph ; but as, by its elasticity, it rises again to a height ^„ the work is p{h-h^. The anvil CD, on the other hand, has been raised through a height H to CD', and has required in so doing PH units of work. The work, W, definitely absorbed by the lead is/(/z-/^i)-PH. On the other hand, the lead has been heated by 6, it has gained Uc6 thermal units, c being the specific heat of lead, and the mechanical equivalent J is equal to the quotient A series of six experiments gave 1394 foot-pounds Centigrade for the Uc6 mechanical equivalent as thus obtained. The experiments of Cantoni and Gerosa in this direction are the simplest. They allowed mercury to fall from a funnel through a narrow tube into a \'essel below, when its temperature was measured. In this way the number 1390 was obtained. Experiments in the opposite direction have also been made, in which the work produced by one thermal unit was determined. This was done on a large scale by Hirn by means of a steam engine of one hundred horse-power. He determined the quantity of heat contained in the steam before its action, and then the amount contained in the water after its condensation. This was less, for some had been expended in work ; and this work as measured by the dynamometer was equivalent to that which had disappeared, the number 13907 being thus obtained. The following is the method which originally Mayer employed in calcu- lating the mechanical equivalent of heat. It is taken, with slight modifica- tions, from Tyndall's work on Heat, who, while strictly following Mayer's reasoning, has corrected his data. Let us suppose that a rectangular vessel with a section of a square foot contains at 0° a cubic foot of air under the ordinary atmospheric pressure ; and let us suppose that it is inclosed by a piston without weight. Suppose now that the cubic foot of air is heated until its volume is doubled ; from the coefficient of expansion of air we know that this is the case at 273° C. The gas in doubling its volume will have raised the piston through a foot in height ; it will have lifted the atmospheric pressure through this distance. But the atmospheric pressure on a square foot is in round S04 On Heat [506- numbers 15 x 144 = 2160 pounds. Hence a cubic foot of air in doubling its volume has lifted a weight of 2160 pounds through a height of a foot. The quantity of heat which will double the volume of a cubic foot of air, and in so doing will lift 2160 pounds through a height of a foot, is 5-29 thermal units, taking the specific heat of air to be 0-24 at constant pressure. Now in the above case the gas has been heated under constant pressure, that is, when it could expand freely. If, however, it had been heated under constant volume, its specific heat would have been less in the ratio i : i'4i4 (466), so that the quantity of heat required under these circumstances to raise the temperature of a cubic foot of air would be 5-29 x - =374. Deducting this from 5-29, the difference 1-55 represents the weight of water which would have been raised 1° C. by the excess of heat imparted to the air when it could expand freely. But this excess has been consumed in the work of raising 2160 pounds through a foot. Dividing this by 1-55 we have 1393. Hence the heat which will raise a pound of water through 1° C. will raise a weight of 1393 pounds through a height of a foot ; a numerical value of the mechanical equivalent of heat agreeing as closely as can be expected with that which Joule adopted as the most certain of his experimental results. Fig. 464 The value of J, the mechanical equivalent of heat, as determined by Joule and also by more recent observers (Griffiths, Rowland, Barnes, &c.), is given in the subjoined table in various units. Recent Joule observers Foot-pounds Fahrenheit 772 779 „ „ Centigrade 1390 1403 Kilogramme-metres Centigrade . 424 428 Ergs 4-16 X 10' 4'2 X 10 -606] Mechanical Equivalent of Heat 505 A convenient practical unit of work or energy is 10' ergs ; it is called a joule. One calorie = 42 x 10'' ergs = 4'2 joules. A variety of experiments may in like manner be adduced to show that whenever heat disappears work is produced. For example, suppose that the air in a reservoir immersed in water be compressed to the extent of 10 atmospheres, and that, when the compressed air has acquired the tempera- ture of the water, it be allowed to act upon a piston loaded by a weight, the result is that the weight is raised. At the same time the water becomes cooler, showing that a certain quantity of heat had disappeared in producing the mechanical effort of raising the weight. This may also be illustrated by the following experiment (fig. 464), due to Tyndall : — A strong metal box is taken, provided with a stopcock, on which can be screwed a small condensing pump. Having compressed the air since it becomes heated by this process, the box is allowed to stand for some time, until it has acquired the temperature of the surrounding medium. On opening the stopcock the air rushes out ; it is expelled by the expansive force of the internal air : in short, the air drives itself out. Work is there- fore done by the air against external pressure, and there should be a dis- appearance of heat ; and if the jet be allowed to strike against the thermopile, the galvanometer is deflected, and the direction of its deflection indicates a cooling (fig. 464). A similar effect is observed when, on opening a bottle of soda water, the carbonic acid gas which escapes is allowed to strike against the thermopile. If, on the contrary, the experiment is made with an ordinary pair of bellows, and the current of air is allowed to strike against the pile, the deflection of the galvanometer is in the opposite direction, indicating an increase of temperature (fig. 465). In this case the hand of the experimenter performs the work, which is converted into heat. Fig. 46s Joule placed in a calorimeter two equal copper reservoirs, which could be connected by a tube. One of these contained air at 22 atmospheres, the other was exhausted. When they were connected, they came into equilibrium So6 On Heat [506- under a pressure of 1 1 atmospheres ; but as the gas in expanding had done no work, there was no alteration in temperature. When, however, the second reservoir was full of water, the air in entering was obliged to expel it and thus perform work, and the temperature sank, owing to an absorption of heat. 507. Isothermal and adiabatic lines. — Reference has already been made to isothermal lines in connection with the experiments of Dr. Andrews on carbonic acid. We will now examine the subject more generally. An iso- thermal line of a substance is a line drawn in reference to two co-ordinate axes in such a way that, however the properties of the substance — denoted by lengths measured along the co-ordinate axes — vary, its temperature remains always the same. If pressures are measured along the vertical, and volumes along the horizontal line, the isothermal lines of a gas for which Boyle's law is true {pv = const.) are rectangular hyperbolas. In fig. 466 the curve LL' represents the behaviour of a certain quantity of the gas at constant temperature i^. Whatever be its volume and pressure, the state of the gas will be de- noted by some point on this curve, the form of the curve being fixed by the fact that Op^ x Ov, = Op.j X Ov,, wherever A and B may be. If the temperature is raised and kept constant at /, we get another isothermal, MM', which will be farther away from the axes, since for a given volume the pressure will be greater than at the lower temperature. Thus, for a perfect ideal gas the isothermal lines are a series of rect- angular hyperbolas farther and farther away from the axes as the temperature is higher. For a real gas, far removed from its temperature of liquefaction, the isothermal lines do not differ materially from those shown, but the deviation from the hyperbolic forin becomes marked as the tem- perature of liquefaction is approached. The isothermal lines for carbonic acid are shown in fig. 356 ; GA represents the substance in the gaseous condition at 13° C, AB the sub- stance partly liquefied, and£L entirely liquid. Similarly we may draw lines to represent the variations of pressure and volume of any other substance, whether solid, liquid, or gaseous, at any constant temperature. If the changes of volume and pressure of a substance (say a gas) occur in such a way that no heat is gained or lost, they are said to take place adiabatically , and the curves exhibiting the variations of pressure and volume under these conditions are called adiabatic lines. In fig. 467 let <^,, <^ . . . be adiabatics of a gas, and let B denote the state of the gas at temperature, pressure, and volume, t^ p^ v.-,, respectively. If the volume be reduced to v^ and no heat escapes, the temperature will rise and Fig. 466 Fig. 467 -508] Carnot's Cycle S07 the pressure become p^ ( = 0^1); greater than it would have been with iso- thermal contraction. Thus the adiabatic through B is steeper than the isothermal, and so for other points. The equation to an adiabatic line, that is, the relation between p and v which characterises it, is ^■2/'' = const., where 7 = CfjC,^, the ratio of the specific heat of a gas at constant pressure to its specific heat at constant volume (466). 508. Carnot's cycle. — Referring to fig'. 466, let the state of the substance be denoted by A, that is, let/, w, /, be its pressure, volume, and temperature respectively. Suppose the substance to recei\e heat and to expand without change of temperature from w-, to v^, then work is done by the expanding substance, the amount of which may be proved to be equal to the area Az/jZ/jBA. If work be done upon the substance so that it contracts from 7'., to ■z/j, the work so done is represented by the same area. Similarly, if the substance expand or contract adiabatically (fig. 467), the work done is equal to the area enclosed between the curve, the horizontal axis and the ordinates of the points representing the initial and final states. Imagine a heat engine, whose working substance may be any fluid, to perform a series or cycle of operations, that is, to receive or give out heat and to 'do work or have work done upon it in such a. way that at the end of the series the substance is in exactly the same state as to pressure, volume, and temperature as at the beginning. Then we are sure that on the whole no internal work has been done, and we may draw conclusions as to the heat given or received, and the work done by the substance or spent upon it. There are many ways in which such a series might be arranged ; that chosen by Carnot, and known as Carnot's cycle, involves four distinct operations. Let the state of the substance be denoted by the point A (fig. 468), its temperature, volume, and pressure being' t^ "ij^p^. 1. Let work be done on the substance, and its volume diminished from w, to v„. If the heat produced by the compression is not allowed to escape, the substance will be heated ; let its temperature rise from t^ to t. Its state is now represented by the point B, AB being an adiabatic. The work done is the area BAz/jWoB. 2. The substance expands at constant temperature t, receiving a quantity of heat, H calories ( = JH ergs), and its volume increases from v„ to v^ The line BC is an isothermal, and the work done hy the substance is Bt/^t/jCB. 3. The supply of heat is now cut off, and the substance continues to expand, neither receiving nor giving out heat, until its temperature falls to ^i. Its state is denoted by D, the line CD being an adiabatic. The work done by the substance is Cv^J^C 4. The substance is compressed isothermally at /„ a quantity of heat Hj being taken from it to keep its temperature constant. Eventually the temperature and volume become what they were at first. Thus the cycle is 5o8 On Heat [508- completed, the state of the working substance being in all respects the same at the end as it was at the beginning. The total work done by the expanding substance is Bw^z'^DCB ; that done upon it during contraction, Bz/^^/^DAB ; the difference between these is the area ABCD, which therefore represents the work done by the engine during the cycle = W. The heat H was taken in at the higher temperature /, and Hj given up at the lower temperature ^, ; H — Hj calories, or J(H — Hj) ergs, is therefore the quantity utilised. Hence W = J(H — H,) by the first law. Suppose that in the above set of operations we had proceeded in the reverse direction, that is, allowed the substance to expand from A to D, supplying it with heat H, to keep its temperature constant, then compressed it adiabatically from D to C and isothermally from C to B, taking from it during the isothermal compression a quantity H of heat, and finally bringing it back to the state A. In this case work equal to ABCD ( = W) has been done upon the substance, heat Hj has been given to it and H withdrawn from it ; therefore W + JHi = JH. The engine works equally satisfactorily in this case, but every operation is reversed. For this reason Carnot's cycle is called a reversible cycle. A reversible engine is in a certain sense a perfect engine, for its efficiency is greater than that of any other engine working between the same tempera- tures. This Carnot proved by supposing two engines, one reversible, the other non-reversible, working between the temperatures /and /j, to be coupled together, the latter driving the former. He showed that (on the assumption that the non- reversible engine has the greater efficiency) the result must be that by the simple action of the two engines heat is transferred from the cold body at /, to the hot body at t, without any work being done by any external agency. This is contrary to experience. The efficiency of an engine may be defined as that fraction of the total amount of heat received which is converted into work. If H = heat received and Hj = that given up, heat TJ U" utilised as work = H - Hj ; hence efficiency = - — 1. H The efficiency of Carnot's engine clearly depends upon the difference of temperature t — t^; for / being kept constant, and H, as before, being received from the source, if we take an isothermal corresponding to a lower tempera- ture ?j the area ABCD becomes larger. Hence E, the efficiency, = C(/-/,), where C is a constant known as Carnot's function ; it is equal to i//, if/ and /j are measured from the absolute zero of temperature. Hence T-» H — H, /— /i/o\ H / ^^--H-^=-/-^('*'')'°'-Hr/7 The efficiency of Carnot's engine depends only on the temperatures at which heat is taken in and rejected, and not on the properties of the working' substance. This constitutes what is know as Carnot s principle. The second law of thermodynamics has not so far been defined, though it has been assumed. The enunciation of it has taken many forms. Clausius put it thus : — No engine can of itself, without the aid of external agency, transfer heat from a body at a low temperature to a body at a high -509] Dissipation of Energy 509 temperature. Another form of the second law is the statement of the impossibility of any engine being more efficient than a reversible engine. 509. Dissipation of energy. — Rankine made the following interesting observations on a remarkable consequence of the mutual convertibility which has been shown to exist between heat and other forms of energy : — Lord Kelvin has pointed out the fact that there exists, at least in the present state of the known world, a predominating tendency to the conversion of all other forms of physical energy into heat, and to the uniform diffusion of heat throughout all matter. The form in which we generally find energy originally collected is that of a store of chemical power consisting of uncom- bined elements. The combination of these elements produces energy in the form known by the name of electrical currents, part only of which can be employed in electrolysing chemical compounds, and thus reconverted into a store of chemical power ; the remainder is necessarily converted into heat ; and again, only a part of this heat can be employed in electrolysing compounds or in reproducing electric currents. If the remainder of the heat be employed in expanding an elastic substance, it may be converted entirely into visible motion, or into a store of visible mechanical power (by raising weights, for example), provided the elastic substance is enabled to expand until its temperature falls to the point which corresponds to the absolute privation of heat ; but unless this condition is fulfilled a certain proportion only of the heat, depending on the range of temperature through which the elastic body works, can be converted, the rest remaining in the state of heat. On the other hand, all visible motion is of necessity ultimately converted into heat by the agency of friction. There is, then, in the present state of the known world, a tendency towards the conversion of all physical energy into the sole form of heat. Heat, moreover, tends to diffuse itself uniformly by conduction and radia- tion, until all matter shall have acquired the same temperature. There is consequently, so far as we vmderstand the present condition of the universe, a tendency towards a state in which all physical energy will be in the state of heat, and that heat so diffused that all matter will be at the same temperature ; so that there will be an end of all physical phenomena. Vast as this speculation may seem, it appears to be soundly based on experimental data, and to truly represent the present condition of the uni- verse as far as we know it. Sio On Light [510- BOOK VII ON LIGHT CHAPTER I TRANSMISSION, VELOCITY, AND INTENSITY OF LIGHT 510. Theories of light Light is the agent which, by its action on the retina, excites in us the sensation of vision. That part of physics which deals with the properties of light is known as optics. In order to explain the origin and transmission of light, various hypo- theses have been made, the most important of which are the emission or corpuscular theory, and the iindulatory theory. On the emission theory it is assumed that luminous bodies emit, in all directions, an imponderable substance, which consists of molecules of an extreme degree of tenuity : these are propagated in right lines with an almost infinite velocity. Penetrating into the eye they act on the retina, and deter- mine the sensation which constitutes vision. On the undulatory theory, all bodies, as well as the celestial spaces, are filled by an extremely subtle elastic medium, which is called the luminiferous ether. The luminosity of a body is due to an infinitely rapid vibratory motion of its molecules, which, when communicated to the ether, is propagated in all directions in the form of spherical waves, and this vibratory motion, being thus transmitted to the retina, calls forth the sensation of vision. The vibrations of the ether take place not in the direction in which the wave is travelling, but in a plane at right angles to it. An idea of these may be formed by shaking a rope at one end. The vibrations, or to and fro move- ments, of the particles of the rope, are at right angles to fbe length of the rope, but the onward motion of the wave's form is in the direction of the length. See the remarks in articles 69, 226, 433. On the emission theory the propagation of light is effected by a motion or translation of particles of light thrown out from the luminous body, as a bullet is discharged from a gun ; on the undulatory theory there is no pro- gressive motion of the particles themselves, but only of the state of disturb- ance which was communicated by the luminous body ; and this is transmitted by the vibratory motion of the particles of the luminiferous ether. The luminiferous ether penetrates all bodies, but on account of its extreme tenuity it is uninfluenced by gravitation ; it occupies space, and although it presents no appreciable resistance to the motion of the denser bodies, it is possible that it hinders the motion of the smaller comets. It has -613] Propagation of Light in a Homogeneous Medium 511 been found, for example, that Encke's comet, whose period of revolution is about 3j years, has its period diminished by about oti of a day at each successive rotation, and this diminution is ascribed by some to the resistance of the ether. Graetz has calculated that the density of ether is 9 x io~^'^ that of water. From a formula of Lord Kelvin it is calculated to be greater than lo-'** ; it may accordingly be admitted to be io~^'. While the air over a square metre weighs 10,000 kilogrammes, the ether in it, taking the height of the atmosphere at 30 miles, would weigh only 0'0022 milligramme. Kelvin concludes that if the density of the air followed Boyle's law, and the tem- perature were constant, at a height equal to that of the earth's radius it would be only io~''°° that of water. The ether is therefore far more dense than air so rarefied. He calculated that a volume equal to that of the earth cannot contain less than 2775 pounds of ether. The fundamental principles of the undulatory theory were enunciated by Huyghens, and subsequently by Euler. The emission theory, principall)- owing to Newton's powerful support, was for long the prevalent scientific creed. The undulatory theory was adopted and advocated by Young", who showed how a large number of optical phenomena, particularly those of diffraction, were to be explained by that theory. Subsequently, too, though independently of Young, Fresnel showed that the phenomena of diffraction, and also those of polarisation, are explicable on the same theory, which since his time has been generally accepted. 511. Luminous, transparent, translucent, and opaque bodies. — Lumi- nous bodies are those which emit light, such as the sun and ignited bodies. Transparent or diaphanous bodies are those which readily transmit light, and through which objects can be distinguished ; water, gases, polished glass are of this kind. Translucent bodies transmit light, but objects cannot be distinguished through them : ground glass, oiled paper, &c., belong to this class. Opaque bodies do not transmit light ; for example, wood, metals, &c. No bodies are quite opaque ; they are all more or less translucent when cut in sufficiently thin leaves. Foucault showed that when the object-glass of a telescope is thinly silvered, the layer is so transparent that the sun can be viewed through it without danger to the eyes, since the metallic surface reflects the greater part of the radiation which falls upon it. 512. Luminous ray and pencil. — k. luminotcs ray is the direction of the line in which light is propagated ; a luminous pencil is a collection of rays from the same source ; it is said to be parallel when it is composed of parallel rays, divergent when the rays separate from each other, and co7i- vergent when they tend towards the same point. Every luminous body emits divergent rectilinear rays from all its points, and in all directions. 513. Propagation of light in a homogeneous medium. — A medium is any space or substance which light can traverse, such as a vacuum, air, water, glass, &c. A medium is said to be homogeneous when its chemical com- position and density are the same in all parts, and to be isotropic when its properties at all points are the same in all directions ; when this is not the case it is said to be anisotropic or ceolotropic. In every homogeneous medium light is propagated in a right line. For, SI2 On Light [613- if an opaque body is placed in the right line which joins the eye and the luminous body, the light is intercepted. The hght which passes into a dark room by a small aperture is visible from the light falling on the particles of dust suspended in the atmosphere. Light changes its direction on meeting an object which it cannot pene- trate, or when it passes from one medium to another. These phenomena will be described under the heads reflection and refraction. 514. Shadow, penumbra. — When light falls upon an opaque body it cannot penetrate into the space immediately behind it, and this space is called the shadow. Fig. 469 In determining the extent and the shape of a shadow projected by a body, two cases are to be distinguished : that in which the source of light is a single point, and that in which it is a body of any given extent. In the first case, let S (fig. 469) be the luminous point, and M a spherical body which causes the shadow. If an infinitely long straight line, SG, Fig. 470 moves round the sphere M tangentially, always passing through the point S, this line will trace a conical surface, which, beyond the sphere, separates that portion of space which is in shadow from that which is illuminated. In the present case, on placing a screen, PQ, behmd the opaque body the limit of the shadow HG will be sharply defined. This is not, however, usually the case, for luminous bodies have always a certain magnitude, and are not mere luminous points. -514] Shadozv, Penumbra 513 Suppose that the luminous and illuminated bodies are two spheres, SL and MN (fig. 470). If an infinite straight line, AG, moves tangentially to both spheres, always cutting the line of centres in the point A, it will pro- duce a conical surface with this point for a summit, and which traces behind the sphere MN a perfectly dark space MGHN. If a second right line, LD, which cuts the line of centres in B, moves tangentially to the two spheres, so as to produce a new conical surface, BDC, it will be seen that all the space outside this surface is illuminated, but that the part between the two conical surfaces is neither quite dark nor quite Hght. So that if a screen, PQ, is placed behind the opaque body, the central portion GH of the screen is quite in the shadow, while the annulus of breadth HC receives Hght from certain parts of the luminous body, and not from others. It is brighter than the true shadow, and not so bright as the rest of the screen, and it is accord- ingly called the peiiumbra. Shadows such as these are geometrical shadows ; physical shadows, or those which are really seen, are by no means so sharply defined. A certain quantity of light passes into the shadow, even when the source of light is a mere point, and con- versely the shadow influ- ences the illuminated part. This phenomenon, which will be afterwards described, is known by the name of diffraction (660). The explanation of the phenomena of eclipses follows directly from the theory of shadows. When the opaque disc of the moon comes, according to the conditions, between the sun and the earth, the shadow cast by the moon causes a more or less complete solar eclipse on those parts of the earth which it meets. Let S be the sun, T the earth, and L the moon placed in a position favourable for an eclipse (fig. 471). If we can suppose the three bodies represented with their relative magnitudes and distances, we need only repeat the graphical construction of this figure to determine the dimensions of the cone of the shadow, and of the penumbra of the moon. The length LI of the cone of the shadow varies between 57 and 59 terrestrial radii, according to the relative positions of the earth and its satellite ; the distance between the two planets varies between 55 and 62 such radii ; hence, under favour- able conditions the cone of the shadow may reach the earth, and in those points of the earth thus touched, m, there is a total eclipse of the sun. As this area has relatively a small extent, an eclipse which is visible by the inhabitants of this area is not seen by those in the neighbourhood. After the lapse of a time which never exceeds 3m. 13s. the cone will have left the place m and will pass to m', which is not necessarily on the same parallel of latitude. It will thus sweep over the surface of the earth, in virtue of the special motion of the two heavenly bodies, along a line which astronomers can determine beforehand. On all points along this line L L Fig. 471 SH Oil Light [514- (fig. 472) there will successively be a total eclipse ; for adjacent ones, which are within the cone of the penumbra the eclipse will be partial. Fig. 472 If the cone of the shadow does not reach the earth, there will nowhere be a total eclipse ; but on a point m' (fig. 473) there will be no light from the central part of the sun ; this will then appear like a black circle surrounded b}' a bright ring (fig. 474), and forms what is called an annular eclipse. Fig- 473 Fig- 474 Total or partial eclipses of the moon are produced by the total or partial immersion of the moon in the cone of the shadow cast by the earth ; for jin observer on the moon they would constitute total or partial eclipses of the sun ; loialax those parts of the moon in the shadow, ^ar/za/ at those in the penumbra. The transits of Venus or of Mercury over the sun are phenomena of the same kind as eclipses, being produced by the projection on the earth of the penumbi'al cones of shadow of those planets. The eclipses of the satellites of certain planets such as Jupiter are identical with the eclipses of the moon. The shadow of a body, a sphere for instance, in sunlight is about no times as long as the body is broad. This follows from the proportion Distance of the sun _ Diameter of the sun Length of the shadow Diameter of the sphere' 515. Images produced by small apertures. — When rays of light which pass into a dark chamber through a small aperture are received upon a screen, they form images of external objects. These images are inverted ; their shape is always that of the external objects, and is independent of the shape of the aperture- -515] Images produced by Small Apertures S15 The inversion of the images arises from the fact that the luminous rays proceeding from external objects, and penetrating into the chamber, cross one another in passing the aperture, as shown in fig. 475. Continuing in a straight line, the rays from the higher parts meet the screen at the lower parts and conversely, those which come from the lower parts meet the Fig- 475 higher parts of the screen. Hence the inversion of the image. The arrangement forms what is known as a camera obscura. In order to show that the shape of the image is independent of that of the aperture, when the latter is sufficiently small and the screen at an ade- quate distance, imagine a triangular aperture, O (fig. 476), made in the door of a dark chamber, and let ab be a screen on which is received the image of a flame, AB. A divergent pencil from each point of the flame passes through the aperture, and forms on the screen a triangular image resembhng the Fig. 476 aperture. But the union of all these partial images produces a total image of the same form as the luminous object. For if we conceive that an infinite straight line moves round the aperture, with the condition that it is always tangential to the luminous object AB, and that the aperture is very small, the straight line describes two cones, the apex of which is the aperture, while one of the bases is the luminous object and the other the luminous object on the screen — that is, the image. Hence, if the screen is per- pendicular to the right line joining the centre of the aperture and the centre of the luminous body, the image is similar to the body ; but if the screen is obhque, the image is elongated in the direction of its obliquity. This is what is seen in the patches of light on the ground when solar light falls upon foliage ; the rays of the sun passing through the minute interstices between the leaves produce images of the sun, which are either round or elliptical, L L 2 516 On Light [515- according as the ground is perpendicular or oblique to the solar rays ; and this is the case whatever be the shape of the aperture through which the light passes. 516. Velocity of light. — Light moves with such a velocity that at the surface of the earth there is, to ordinary observation, no appreciable interval between the occurrence of any luminous phenomenon and its perception by the eye. The knowledge that the velocity of light is not infinite was acquired as the result of astronomical observation. Romer, a Danish astro- nomer, in 1675, first deduced the velocity of light from observations of the eclipses of one of Jupiter's satellites. Jupiter is a planet, round which five satellites revolve, as the moon does round the earth. In Romer's time only four were known. Of these the first, E (fig. 477) (we should now call it the second), suffers occultation — that is, passes into Jupiter's shadow — at equal intervals of time, which are 42h. 28m. 36s. Romer constructed a table giving the exact times at which occultations would occur for a year in advance, and compared the observed with the calculated times. While the earth, T, moves in that part of its orbit nearest Jupiter, its distance from that planet does not materially alter in 42 hours, and the intervals between two successive occultations of the satellite are approximately the same ; but, in proportion as the earth moves away in its revolution round the sun, j, the apparent interval between two occultations increases, and when, at the end of six months, the earth has passed from the position T to the position T', a total retardation of i6m. 36s. is observed between the time at which the phenomenon is seen and that at which it is calculated to take place. But when the earth was in the position T, the sun's light reflected from the satellite E had to traverse the distance ET, while in the second position the light had to traverse the distance E'T'. This distance exceeds the first by the diameter of the earth's orbit. Consequently, light requires i6m. 36s. to travel the diameter TT' of the terrestrial orbit, or twice the distance of the earth from the sun, which gives for its velocity 190,000 miles in a second. The stars nearest the earth are separated from it by at least 206,265 times the distance of the sun. Consequently, the light which they send -517] Apparatus for determining the Velocity of Light 517 requires more than three years to reach us. Those stars which arfe only visible by means of the telescope are possibly at such a distance that thousands of years would be required for their light to reach our planetary system. They might have been extinguished for ages without our knowing it. 517. Foucault's apparatus for determining the velocity of light. — Not- withstanding the prodigious velocity of light, Foucault succeeded in deter- mining it experimentally by the aid of an ingenious apparatus, based on the use of the rotating mirror, which had been invented by Wheatstone for measuring the velocity of electricity. In the description of this apparatus, a knowledge of the principal pro- perties of mirrors and of lenses is presupposed. Fig. 478 represents the chief parts of Foucault's arrangement. The window shutter, K, of a dark chamber is perforated by a rectangular slit, behind which the platinum wire o is stretched vertically. A beam of sunlight reflected fi'om the out- side by a mirror enters the dark room by the slit, meets the platinum Fig. 478 t"ig. 479 wire, and then traverses an achromatic lens, L, with a long focus, placed at a distance from the platinum wire less than double its focal length. The image of the platinum wire, more or less magnified, would thus be formed on the axis of the lens ; but the pencil of light, having traversed the lens, impinges on a plane mirror, m, rotating with great velocity ; it is reflected from this, and forms in space an image of the platinum wire, which is displaced with an angular velocity double that of the mirror (530). This image is reflected by a concave mirror, M, whose centre of curvature coincides with the axis of rotation of the mirror ;«, and with its centre of figure. The pencil reflected from the mirror M returns upon itself, is again reflected from the mirror ;«, traverses the lens a second time, and forms an image of the platinum wire, which appears on the wire itself so long as the mirror m is at rest or turns slowly. In order to see this image without hiding the pencil of light which enters by the aperture in K, a thin plate of unsilvered glass, V, is placed between Si8 On Light [517- the lens and the wire, and is inclined so that the reflected rays fall upon a powerful eyepiece, P. The apparatus being arranged, if the mirror m is at rest, the pencil after meeting M is reflected to w, and thence returns along its former path, till it meets the glass plate V in a, and being partially reflected, forms at d — the distance ad being equal to ao — an image of the wire, which the eye is enabled to observe by means of the eyepiece, P. If the mirror wz, instead of being fixed, is moving slowly round — its axis being at right angles to the plane of the paper — there will be no sensible change in its position during the brief interval elapsing while light travels from we to M and back again, but the image will alternately disappear and reappear. If now the velocity of jti is increased to upwards of 30 turns per second, the interval between the disappearance and reappearance is so short that the impression on the eye is persistent, and the image appears perfectly steady. Lastly, if the mirror turns with sufficient velocity, there is an appreciable displacement of the image, owing to the fact that now the mirror m has moved through a small angle during the time the light took to travel from it to M and back again ; the return ray, after its reflection from the mirror m, takes the direction mb, and forms its image at i ; that is, the image has undergone a total displacement di. Speaking precisely, there is a deviation of the ray as soon as the mirror turns, even slowly ; but it is only appreciable when the velocity of rotation is sufficiently rapid, or the distance M»2 sufficiently great, for the deviation necessarily increases with the time which the light takes in traversing 2mM. In Foucault's experiment the dis- tance Mm was only 135 feet ; when the mirror rotated with a velocity of 600 to 800 turns in a second, displacements of 0-2 to 0"3 mm. were obtained. Taking Mm = /, Lm = /', oh = r, and representing by n the number of turns- in a second, by 8 the observed displacement of the image of the wire, and by V the velocity of light, Foucault arrived at the formula SwPnr Y-. ?+/')' from which the velocity of light is calculated at 185,157 miles in a second ; this number agrees remarkably well with the value deduced from newer determinations of the value of the solar parallax. The mechanism by which the mirror was turned consisted of a small steam turbine, bearing a sort of resemblance to the siren, and, like that mstrument, giving a higher sound as the rotation is more rapid : in fact, it is by the pitch of the note that the velocity of the rotation is determined. In this apparatus liquids can be experimented upon. For that purpose a tube, AB, 10 feet long, and filled with distilled water, is placed between the turning mirror m, and a concave mirror M', identical with the mirror M. The luminous rays reflected by the rotating mirror, in the direction mM', traverse the column of water AB twice before returning to V. But the return ray then becomes reflected at c, and forms its image at A : the displacement is consequently greater for rays which have traversed water than for those which have passed through air alone ; hence the velocity of light is less in water than in air. This is the most important part of these experiments. It is a necessary -519] Laws of the Intensity of Light 519 consequence of the undulatory theory that the velocity of light must be less in the more highly refracting medium (652), while the opposite is a necessary consequence of the emission theory. Hence Foucault's experiment may be regarded as a crucial test of the validity of the undulatory theory. 518. Experiments of Fizeau. — In 1849 Fizeau measured directly the velocity of light, by ascertaining the time it took to travel from Suresnes to Montmartre and back again. The apparatus employed was a toothed wheel, capable of being turned with great and measurable angular velocity. The teeth were made of precisely the same width as the intervals between them-j The apparatus being placed at Suresnes, a pencil of rays was transmitted through an interval between two teeth to a mirror placed at Montmartre^ The pencil, directed by a properly arranged system of lenses, returned to the wheel. As long as the apparatus was at rest the pencil returned exactly through the same interval as that through which it first set out. But when the wheel was turned sufficiently fast, a tooth was made to take the place of an interval, and the ray was intercepted. As the wheel was turned still more rapidly, the light reappeared when the interval between the next two teeth had taken the place of the former tooth at the instant of the return of the pencil. The distance between the two stations was 28,334 feet. From a knowledge of this distance, the dimensions of the wheel, its velocity of rotation, &c., Fizeau found the velocity of light to be 196,000 miles per second — a result agreeing with that given by astronomical observation as closely as can be expected in a determination of this kind. Cornu recently investigated the velocity of light by Fizeau's method, but with improvements so that the probable error did not exceed ^'^■^ of the total amount ; the two stations, which were 6'4 miles apart, were a pavilion of the Ecole Polytechnique and a room in the barracks of Mont Valerien. By means of electro-magnetic arrangements the rotation of the toothed disc, and the times of obscuration and illumination, were registered on a blackened cylinder, on the principle of the method described in article 245. Cornu thus obtained the number 185,420 miles — a result closely agreeing with that of Foucault, and supported by calculations based on the results of astronomical observations of the transit of Venus in 1 874. Newcomb improved Foucault's method by using a slightly concave mirror instead of a plane one, by which the image of the slit was brighter ; it was observed by a telescope through a distance of 4,000 metres. The rotations also were reversed, by which the angle between the two positions of the telescope was observed with greater accuracy ; he thus obtained the number 186,364 miles, while Michelson repeated a former determination and found 186,354, a difference of only about 10 miles. 519. Laws of the intensity of light. — The intensity of illumination is the quantity of light received on the unit of surface ; it is subject to the following laws : — I. The intensity of illumination on a given sicrface dice to a point-source of light is inversely as the square of its distance from the source. II. The intensity of illuminatioft which is received obliquely is propor- tional to the cosine of the angle which the luminous rays make with the normal to the illuminated surface. 520 On LigJit [519- In order to demonstrate the first law, let there be two circular screens, CD and AB (fig. 480), one placed at a certain distance from a source of light, L, regarded as a point, and the other at double this distance, and let s and S be the areas of the two screens. If a be the total quantity of light which is emitted by the source in the direction of the cone ALB, the in- tensity of the light on the screen CD — that is, the quantity which falls on the unit of surface — is , and Fig. 480 the intensity on the screen AB is t- Now as the triangles ALB and CLD are similar, the diameter of AB is double that of CD ; and as the surfaces of circles are as the squares of their diameters, the surface S is four times s, consequently the intensity - is one- fourth that of - . s Fig. 480 shows that it is owing to the divergence of the luminous rays emitted from the same source that the intensity of light is inversely as the square of the distance ; the illumination of a surface placed in a beam of parallel luminous rays is the same at all distances in a vacuum In air and in other transparent media the intensity of light decreases, in consequence of absorption, more rapidly than the square of the dis- tance. The second law of intensity corresponds to the law which we have found to prevail for heat : it may be theoretically deduced as follows : — Let DA, EB (fig. 481) be a pencil of parallel rays falling obliquely on a surface, AB, and let om be the normal to this surface. If S is the section of the pencil, a the total quantity of light which falls on the surface AB, and I that which falls on the unit of surface — that is, the intensity of illumination — we have I = — =^. But AB as S is only the projection of AB on a plane perpendicular to the pencil, we S Fig. 481 know from trigonometry that S = AB cos a, from which AB = This cos a value substituted in the above equation gives i = ^ cos a demonstrates the law of the cosine, for as a and S I is proportional to cos a. The law of the cosine applies also to rays emitted obliquely by a luminous surface ; that is, the rays are less intense in proportion as they are more a formula which are constant quantities, -520] Photometers S2I inclined to the surface which emits them. In this respect they correspond to the third law of the intensity of radiant heat (420). 520. PKotometers. — A photometer is an apparatus for measuring the relative illuminating powers of different sources of light. The illuminating power of a source is the quantity of light received by unit area at unit distance from the source, the rays falling perpendicularly on the area. Rumford'' s photometer. — This consists of a ground-glass screen, in front of which is fixed an opaque rod (fig. 482) ; the lights to be compared — for instance, a lamp and a candle — are placed at a certain distance in such a manner that each projects on the screen a shadow of the rod. The shadows thus projected are at first of unequal intensity, but by altering the position of the lamp it may be so placed that the intensity of the two shadows is the same. Then, since the shadow thrown by the lamp is illuminated by the candle, and that thrown by the candle is illuminated by the lamp, the illu- mination of the screen due to each light is the same. The illuminating powers of the two sources — that is, the illuminations which they would give at equal distances— are then directly proportional to the squares of their Fig. 482 distances from the shadows ; that is to say, if the lamp is three times the distance of the candle, its illuminating power is nine times as great For if i and i' are the illuminating powers of lamp and candle respectively and d and d' their distances from the shadows, it follows, from the first law of the intensity of light, that the amount of light received from the i i lamp at the distance d is - and that from the candle -,,-- at the distance d' . On the screen these are equal ; hence ^ = -_ or _ = - — , which was to be proved. Bunsen's photometer. — When a grease-spot is made on a piece of bibu- lous paper, if the paper be illuminated by a light placed in front, the spot appears darker than the surrounding space ; if, on the contrary, it be illuminated from behind, the spot appears light on a dark ground. If the 522 On Light [620- greased part and the rest appear unchanged, the illumination on both sides is the same. Bunsen's photometer depends on an application of this prin- ciple. Its essential features are represented in fig. 483. A circular spot is made on a paper screen by means of a solution of spermaceti in naphtha : on one side of this is placed a light of a certain intensity, which serves as a standard ; in London it is a sperm candle | of an inch in diameter, and burning 120 grains in an hour. The light to be tested — a petroleum lamp, or a gas burner consuming a certain volume of gas in a given time — is then moved in a right line* to svich a distance on the other side of the screen that there is no difference in brightness between the greased part and the rest of the screen. By measuring the distances of the lights from the screen ,,/,,:■! I, , ,.l . , , , I ., , , I < , , ,1 , , , , I, p I |l Fig- 483 by means of the scale, their relative illuminating powers are respectively as the squares of their distances from the screen. The difficulty of constructing candles capable of giving a light sufficiently uniform for standard purposes has led Harcourt to adopt as unit the light formed by burning a mixture of 7 volumes of pentane gas and 20 volumes of air, at the rate of half a cubic foot in an hour, in a specially constructed burner so as to produce a flame of a definite height. This has been found to answer well in practice. By this kind of determination the degree of accuracy which can be attained is not so great as in many physical determinations, more especially when the lights to be compared are of different colours ; one, for instance, yellow, and the other of a bluish tint. In Germany a paraffin candle 2 centimetres in diameter, and having a flame 5 centimetres high, or a Hefner Alteneck lamp equal to I '2 candles, is much used as standard ; the combustible in the lamp is amylic acetate or artificial pear oil, and a flame of constant height is produced in a burner of special construction. The French Carcel lamp is equal to 92 candles. The absolute unit of light adopted by the International Congress of Electricians in 1884, proposed by M. VioUe, is that emitted by a square centimetre of melted platinum at the moment of its solidification. It is equal to about 15 standard candles. Wheatsione's photometer. — The principal part of this instrument is a steel bead P (fig. 484), fixed on the edge of a disc, which rotates on a pinion, o, working in a larger toothed wheel. The wheel fits in a cylindrical brass box which is held in one hand, while the other works a handle. A, Fig. 484 -521] Relative Intensities of various Sources of Light 523 which turns a central axis, the motion of which is transmitted by a spoke, <2, to the pinion o. In this way the latter turns on itself, and at the same time revolves round the circumference of the box ; the bead shares the double motion and consequently describes a curve in the form of a rose (fig. 48s). Now, let M and N be the two lights whose intensities are to be com- pared ; the photometer is placed between them and rapidly rotated. The brilliant points produced by the reflection of the light on the two opposite sides of the beads give rise to two luminous bands, arranged as represented in fig. 485. If one of them is more bril- liant than the other — that which proceeds from the light M, for instance — the instrument is brought nearer the other light until the two bands exhibit the same brightness. The distance of the photo- meter from each of the two lights being then pleasured, their candle-powers are proportional to the squares of the distances. 521. Relative intensities of various sources of light. — The light of the sun is 600,000 times as powerful as that of the moon ; and 16,000,000,000 times as powerful as that of a Centauri, the third in brightness of all the stars. The moon is thus 27,000 times as bright as this star ; the sun is 5,500 million times as bright as Jupiter, and 80 billion times as bright as Neptune. Its light is estimated to be equal to 670,000 times that of a wax candle at a distance of i foot. According to Fizeau and Foucault the electric light produced by 50 Bunsen's cells is about \ as strong as sunhght. The relative luminosities of the following stars are as compared with Vega=i: Pole Star 0-13, Aldebaran 0-30, Saturn 0-47, Arcturus 079, Mars 2-93, Sirius 4'29i, Jupiter 8-24, Venus 38-9. A difference in the strength of light or shadow is perceived when the duller light is f g of the brightness of the other, and both are near together, especially when the shadow is moved about. Our requirements as regards illumination are constantly on the increase ; thus for public receptions of a state character in recent times in Paris, a number of lamps was used corresponding to over 13 candles per square yard, which is six times as much as was used on the occasion of the marriage of the Dauphin in 1745 ; the former, however, is still far removed from perfect illumination, that of daylight, which is estimated at about 180 candles per square yard. 524 On Light [522- CH AFTER II REFLECTION OF LIGHT. MIRRORS 522. Laws of the reflection of light. — When a ray of light meets a polished surface, it is reflected according to the two following laws, which, as we have seen, also hold for heat. I. The angle of reflection is equal to the angle of incidence. II. The incident and the reflected ray are both in the same plane, which is perpendicular to the reflecting surface. The words are here used in the same sense as in article 423, and need no further explanation. First proof . — The two laws may be demonstrated by the apparatus represented in fig. 486. It consists of a graduated circle in a vertical plane. Two brass slides move round the cir- cumference ; on one of them there is a piece of ground glass, P, and on the other an opaque screen, N, in the centre of which is a small aperture. Fixed to the latter slide there is also a mirror, M, which can be more or less inclined, but always remains in a plane perpendicular to the plane of the gra- duated circle. Lastly, there is a small polished metallic mirror, m, placed horizontally in the centre of the circle. In making the experiment, a pencil of solar or any suitable artificial light, S, is caused to fall on the mirror M, which is so inclined that the reflected light passes through the aperture in N, and falls on the centre of the mirror, tn. The luminous pencil then experi- ences a second reflection in a direction otP, which is ascertained by moving P until an image of the aperture is found in its centre. The number of degrees comprised in the arc AN is then read off, and likewise that in AP ; these being equal, it follows that the angle of reflection AotP is equal to the angle of incidence KmM.. The second law follows from the arrangement of the apparatus, the plane of the rays M»z and mV being parallel to the plane of the graduated circle, and consequently perpendicular to the mirror m. Second proof . — The law of the reflection of light may also be demonstrated =^^-jg:^^Jg ^= Fig. 486 -524] Formation of Images by Plane Mirrors 525 by the following experiment, which is susceptible of greater accuracy than that just described : — In the centre of a graduated circle, M (fig. 487), placed in a vertical position, there is a small telescope movable in a plane parallel to the limb ; at a suitable distance there is a vessel D full of mercury, which forms a perfectly horizontal plane mirror. Some particular star of the first or second magnitude is viewed through the telescope in the direc- tion AE, and the telescope is then inclined so as to receive the ray AD coming from the star after being reflected from the brilliant surface of the mercury. Fig. 4S7 In this way the two angles formed by the rays EA and DA, with the hori- zontal AH, are found to be equal, from which it may easily be shown that the angle of incidence E'DE is equal to the angle of reflection EDA. For if DE is the normal to the surface of the mercury, it is perpendicular to AH, and AED, ADE are the complements of the equal angles EAH, DAH : therefore AED, ADE are equal ; but the two rays AE and DE' may be considered parallel, in consequence of the great distance of the star, and therefore the angles EDE' and DEA are equal, for they are alternate angles and consequently the angle E'DE is equal to the angle EDA. REFLECTION OF LIGHT FROM PLANE SURFACES 523. Mirrors. Images. — Mirrors are bodies with polished surfaces which show by reflection objects presented to them. According to their shape, mirrors are divided into plane, spherical {concave and convex\ parabolic, conical, &c. Rays of light diverging from any point of the object and falling upon a mirror are caused by reflection either to converge to, or to appear to diverge from, a second point. In either case the second point is called the image of the first point. 524. Formation of images by plane mirrors.- — The determination of the position and size of images resolves itself into investigating the images of a series of points. And first, the case of a single point. A, placed in front of a plane mirror, MN (fig. 488), will be considered. Any ray, AB, incident from this point on the mirror is- reflected in the direction BO, making the angle of reflection DBO equal to the angle of incidence DBA. 526 On Light [524- If now a perpendicular, AN, be let fall from the point A on the mirror, and if the ray OB be prolonged below the mirror until it meets this perpen- dicular in the point a, two triangles are formed, ABN and BNa, which are equal, for they have the side BN common to both, and the angles ANB, ABN, equal to the angles aNB, aBN ; for the angles ANB and sNB are right angles, and the angles ABN and aBN are each equal to the angle OBM. From the equality of these triangles, it follows that aN is equal to AN ; that is, that any ray, AB, takes such a direction after being reflected, that its prolongation below the mirror cuts the perpendicular ka in the point a, which is at the same distance from the mirror as the point A. This applies also to the case of any other ray from the point A ; AC, for example. Fig. 488 Fig. 489 From this the important consequence follows, that all rays from the point A, reflected from the minor, follow, after reflection, the same direction as if tJiey had all proceeded from the point a. The eye is deceived, and sees a reproduction of the point A at a, as if it were really situated at a. Hence in plane mirrors the image of any point is formed behind the mirror at a distance equal to that of the given point, a7id on the perpendicular let fall from, this point on the m,irror. It is manifest that the image of any object will be obtained by construct- ing, according to this rule, the image of each of its points, or, at least, of those which are sufficient to determine its form. Fig. 489 shows how the image ab of any object, AB, is formed. It follows from this construction that in plane mirrors the image is of the same size as the object ; for if the trapezium ABCD be applied to the trape- zium T)Cab, they are seen to coincide, and the object AB agrees with its image. A further consequence is, that in plane mirrors the image is sym- metrical in reference to the object, and not inverted. 525. Virtual and real images. — There are two cases relative to the direction of rays reflected by mirrors according as the rays after reflection are convergent or divergent. In the latter case the reflected rays do not meet, but if they are supposed to be produced on the other side of the mirror, their prolongations meet in the same point, as shown in figs. 488 and 489. The eye is then affected just as if the rays proceeded from this point, and it sees an image. But the image has no real existence, the luminous rays do not come from the other side of the mirror : this appearance is called the virtual image. The images of real objects produced by plane mirrors are of this kind. -526] Multiple Images from two Plane Mirrors 527 In the second case, where the reflected rays converge, as we shall soon see in concave mirrors, the rays meet at a point in front of the mirror and on the same side as the object. They form there an image called the real image, for it can be received on a screen. The distinction may be expressed by saying that real images are those formed by the reflected rays themselves, and virtual images those formed by their prolongations. 526. Multiple images from two plane mirrors. — When an object is placed between two plane mirrors, which form an angle with each other, either right or acute, images of the object are formed, the number of which increases with the inclination of the mirrors. If they are at right angles to each other, three images are seen, arranged as represented in fig. 490. The rays OC and OD from the point O, after a single reflection, give the one an image O', and the other an image O", while the ray OA, which has undergone two reflections at A and B, gives the third image O'" When the angle of the mirrors is 60°, five images are produced, and seven if it is 45°. The number of images continues to increase in proportion as the angle diminishes, and when it is zero — that is, when the mirrors are parallel — the number of images is theoretically infinite. In general, if two mirrors are inclined to each other at an angle which is an exact submultiple of 180° {e.g. 30°, 45°, 60°, 90°), the number of images they produce^counting for this purpose the object as one image — is equal to the number of times the angle between them is contained in 360. The kaleidoscope, invented by Sir D. Brewster, depends on this property of inclined mirrors. It consists of a tube, in which are three mirrors inclined at 60°, or sometimes two inclined at 30° ; one end of the tube is closed by a piece of ground glass, and the other by a cap provided with Fig. 490 an aperture. Small irregular pieces of coloured glass are placed at one end between the ground glass and another glass disc, and when looked at through the aperture, the other end being held towards the light, the objects and their images are seen arranged in beautiful symmetrical forms ; 528 On Light [526- by turning the tube, an almost endless variety of these shapes is obtained. 527. Multiple images in two plane parallel mirrors. — In this case the number of images of an object placed between them is theoretically infinite. Physically the number is limited, for as the incident light is never totally reflected, some of it being always absorbed, the images gradually become fainter, and are ultimately quite extinguished. Fig. 491 shows how the pencil La reflected once from M gives at I the image of the object L at a distance wI = »2L; then the pencil 'Lb reflected once from the mirror M, and once from N, furnishes the image I' at a distance nV = n\ ; in like manner the pencil Lc, after two reflections on M, and one on N, forms the image I" at a distance ml" = ml', and so on for an infinite series. The images i, i', i" are formed in the same manner by rays of light which, emitted by the object L, fall first on the mirror N. Each virtual image formed by one mirror acts as a real object towards the other mirror. 528. Irregular reflection. Diffused light. — The reflection from the surfaces of polished bodies, the laws of which have been just stated, is called the regular or specular reflection ; but the quantity thus reflected is less than that of the incident light. The light incident on an opaque body separates, in fact, into three parts : one is reflected regularly ; another irregularly — that is, in all directions ; while a third is extinguished, or absorbed by the reflecting body. If light falls on a transparent body, a considerable portion is transmitted with regularity. The irregularly reflected hght is called scattered or diffused light : it is that which makes bodies visible. The light which is reflected regularly does not give us the image of the reflecting surface, but that of the body from which the light proceeds. If, for example, a beam of sunlight be incident on a well-polished mirror in a dark room, the more perfectly the light is reflected the less visible is the mirror in the different parts of the room. The eye does not perceive the image of the mirror, but that of the sun. If the reflect- ing power of the mirror be diminished by sprinkling on it a light powder, the sun's imag-e becomes feebler, and the mirror is visible from all parts of the room. Perfectly smooth, polished reflecting surfaces, if such there were, would be invisible. The beam of light itself is only seen in the room owing to irregular reflections from the particles of dust, and the like, which are floating in the air. Tyndall showed that when this floating matter in the air in an enclosed space is completely removed, the beam of sunlight or the electric light is quite invisible. The atmosphere diffuses the light which falls on it from the sun in all directions, so that it is light in places which do not receive the direct rays of the sun. Thus, the upper layers of the air difflise the light which they receive before sunrise and after sunset, and accordingly give rise to the phenomena of twilight. 529. Intensity of reflected light. — The intensity of the light reflected is always less than that of the incident light, for some of the latter is absorbed, as heat, by the reflecting body. The amount of reflected light increases with the obliquity of the incident beam. For instance, if a sheet of white paper be placed before a candle, and be 'looked at very obliquely, an image of the flame is seen by reflection, which is not the case if the eye receives less oblique rays. -531] The Sextant 529 Fig. 492 The quantity of the reflected Hght varies with different bodies, even when the degree of polish and the angle of incidence are the same. Thus with per- pendicular incidence, the light reflected from a metal mirror is f of the incident light, f from mercury, ^5 from glass, and -^ from water. It also varies with the nature of the medium which the ray is traversing before and after reflection. Polished glass immersed in water loses a great part of its reflecting power. In the case of scattered reflection the actual lustre or brightness of a luminous surface is only a fraction of the light which falls upon it, and depends on the nature of the surface. If we call the incident light 100, we have for the brightness of freshly fallen snow 78, white paper 70, white sandstone 24, por- phyry II, and ordinary earth 8. 530. Reflection of a. ray of light in a. rotating mirror. — When a horizontal ray of light falls on a plane mirror which can rotate about an axis, if the mirror is turned through any angle, the reflected ray is turned through double the angle. Let nm (fig. 492) be the first position pf the mirror, n'm' its position after it has been turned through the angle a ; and let OD be the fixed incident ray. Suppose that at first the incident ray falls normally on the mirror ; the corresponding reflected ray will be along DO. When the mirror has turned through an angle a, its normal, DM, will have turned through the same angle, and the reflected ray DA through 2a. The statement which is here shown to be true in a particular case may be proved true generally. 531. The sextant. — This instrument is used to measure the angular distance of any two distant objects ; its principle is as follows. Suppose A (fig. 493) is a small mirror half silvered, so that the eye at B' can see through the free part. B is a second mirror which can turn about an axis- at right angles to the plane pf the figure. When its plane is parallel to that of A, the ray EB of a distant object, which we will call L, is reflected from B to A, so that the eye sees the distant object L both directly through the unsilvered part of A, and also by reflection from the silvered mirrors B and A, L being assumed to be so distant that E,B' and EB are parallel. If B is not parallel to A, but in the position represented by the shading, the eye receives rays not from E but from some other object, L', in the direction BF. M M Fig- 493 530 On Light [631- If /3 is the angle through which the mirror B has been turned, the angular distance between L and L' is 2fl (530). Thus the angular distance between any two distant objects is determined by turning the mirror B through such an angle that the eye looking along B'A sees one object directly and the other by reflection from the two mirrors. Fig. 494 represents one form of sextant which derives its name from the fact that only one sixth of the circle is used. It consists of a graduated metal sector AA, on which plays the index arm F ; this is provided with a vernier and a micrometer screw by which the index may be accurately -adjusted and also clamped ; G is a lens for reading the vernier. The mirror B, which is called the index glass, is rigidly fixed to the arm BF and moves with it. The telescope DE is fixed to one arm as shown, and on the other arm opposite is the horizon glass C, also rigidly fixed, the lower half of which is silvered. The axis of the telescope just traverses the boundary of the silvered and unsilvered part of the mirror. K and L are dark glasses, turning about hinges b and c, for shading off the sun's light. In making an ob- servation the sextant is held by the handle, H, so that its plane passes through both the objects whose angular distance is to be mea- sured. The index arm being at the zero of the graduation, the two mirrors are parallel. One of the objects, a point on the horizon for instance, is viewed through the telescope and the unsilvered part of the mirror C. The index arm is then moved until the eye sees simultaneously with this the image of another body, the sun or a star for example, which reaches the eye after successive reflections from the mirror B, and from the silvered part of the mirror C. The angle between the two is twice the angle through which the index arm has been turned, and is read off directly from the graduated arc, 60° on the arc being graduated as 1 20° A great advantage of this instrument is that a slight agitation does not affect the measurement of the angle ; it can accordingly be used on ship- board, is indispensable for use at sea, and in travelling where the use of a stand is objectionable. 532. Measurement of small ang^les by reflection from a mirror. — An important application of the laws of reflection in measuring small angles of deflection in magnetic and other observations was first made by Gauss. Fig. 494 Fig- 495 ray -533] Mance's Heliograph 531 The principle of this method will be understood from fig. 495, in which AO represents a telescope, underneath which, and at right angles to its axis, is fixed a graduated scale ss ; the centre of which, the zero; corresponds to the axis of the telescope. Let NS be the object whose angular deflection is to be measured, a magnet for instance, and let mm represent a small plane mirror fixed at right angles to the axis of the magnet. If now, at the begin- ning of the observation, the telescope is ad- justed so that the image of the zero ap- pears coincident with the cross-wires, its axis is perpendicular to the mirror. Now when the mirror is turned, by whatever cause, through an angle a, the eye will see, through the tele- scope, the image of another division of the scale, a for instance, the proceeding from which makes with the line cQK the angle 2a. From the distance of this division Oa from the zero of the scale and the distance Oc from the mirror we have tan 20 = . Thus, for instance, if Oa is 12 millimetres and Oc 5000 millimetres, then tan 2a = , from which 5000 2a = 8' 15". As a practised eye can "easily read ^ of a millimetre, it is pos- sible by such an arrangement to read off an angular deflection of two seconds. Another plan for reading the small angle through which a suspended magnet or other rotating body moves, is to replace the telescope by an oil or glow lamp, and the plane mirror by a concave spherical mirror. The light of the lamp passes through a circular aperture across which a vertical fine wire is drawn, and the mirror produces a sharp image of the illuminated wire on a graduated scale, which is generally placed immediately above the aperture. Such a lamp and scale are illustrated in fig. 496. 533. Mance's heliograph. — The reflection of light from mirrors has been applied by Sir H. Mance in signalling at great distances by means of the sun's light. The apparatus consists essentially of a mirror about 4 inches in diameter mounted on a tripod, and provided with suitable adjustments. So that the sun's light can be received upon it and reflected to a distant station. An M M 2 Fig. 496 532 On Light [533- observer then can see through a telescope the reflection of the sun's rays as a spot of light. The mirror has an adjustment by which it can be made to. follow the sun in its apparent motion. There is also a lever key by which the signaller can deflect the mirror through a very small angle either to the right or left, and thus the observer at the distant station sees corresponding, flashes to the right or left. Under the subject of Telegraphy it will be seen how these alternate motions can be used to form an alphabet. The heliograph has proved of essential service in the campaigns in. Afghanistan and South Africa. Instead of any special form of apparatus, an ordinary shaving mirror or handglass is frequently used ; and the proper inclination having been given so as to send the sun's rays to the distant station, which is very easily effected, the signals are produced by obscuring, the mirror by sliding a piece of paper over it for varying lengths of time;.. In this way longer or shorter flashes of light are produced, which, properly combined, form the alphabet. Of course this mode of signalling can only be used where the sun's light is available, but it has the advantage of being cheap, simple, and portable- Signals have been sent at the rate of twelve words a minute, through dis- tances, in very fine weather, of forty miles. REFLECTION OF LIGHT FROM CURVED SURFACES 534. Spherical mirrors. — It has been already stated (523) that there are several kinds of curved mirrors ; those most frequently employed are spherical and parabolic mirrors. Spherical mirrors are those whose curvature is that of a sphere ; their surface may be supposed to be formed by the revolution of an arc MN (fig. 497) about the radius CA, which unites the middle of the arc to the centre of the circle of which it is a part. According as the reflection takes place from its internal or from its external face, the mirror is said to be cott- cave or convex. C, the centre of the hollow sphere of which the mirror forms part, is called the centre of curvature : the point A is ^'^' 49^ the centre of the mirror.. The infinite right line AL, which passes through A and C, is the principal axis of the mirror ; any right line which simply passes through the centre C and not through the point A, is a secondary axis. The angle MCN,, formed by joining the centre and extremities of the mirror, is the aperture.. A principal section is the section made by a plane through its principal, axis. In speaking of mirrors those lines alone will be considered which lie in the same principal section. 535. Reflection from a concave spherical mirror. — We shall first take the- case when the object is a luminous point situated at L (fig. 498), on the principal axis of the mirror. Of the rays which proceed from L, some fall upon the mirror and are reflected ; the reflected rays, if we consider only — S35] Reflection from a Concave SpJierical Mirror 533 those which strike the mirror in the neighbourhood of A, the centre of the mirror, meet in a point which is the image of the point L. Since a point is determined by the intersection of two Hnes, it is only necessary to ■draw two incident rays from L and find out the point where the correspond- ing reflected rays meet. Let one of the two rays iDe that which passes •through the centre of curvature, C, of the mirror ; this strikes the mirror normally at A ^nd is reflected along its original path, so that AL is the reflected ray corresponding to the incident ray LA. Draw any other in- Fig. 49S cidentray, LI; join IC, and make the' angle CI/ equal to the angle CIL, and let 1/ meet AL in the point / ; then / is the image of L. All other rays from L will, after reflection from the mirror, pass approximately through /, provided the aperture of the mirror be small. L and / are called conjugate points or conjugate foci : for there is this connection between them, that if / is the source of light, L will be its image, that is, will be the point to which rays after reflection will converge. We will now obtain a numerical relation between the distances of L and / from the mirror. Let AL =p, PJ=p', and AC = r ; then, since in the triangle LI/ the angle at I is bisected by IC, we have by geometry LI : I/=LC : Cl=p — r : r—p'. Now, 1/ is greater than Kl ; but if I be taken very near to A — that is, if we consider only those rays which are close to the principal axis — we may assume 1/ and A/ to be equal, and also IL and AL. Thus the equation above becomes AL : Kl=p — r : r—p, or p : p' =p — r : r—p; whence ... / I I 2 fir—p) =p'{p — r), or pr +p'r = 2pp , and dividing by pp r, -+—=-. p p r This formula enables us to find the position of / when that pf L is known. Let us now consider how the point / moves when the source L is placed in different positions. If L moves away from the mirror along the axis, th^ angle of incidence LIC increases, and therefore the angle Cl/increases also, that is, / moves towards the mirror ; this is seen also from the formula, for, since - -1- -. is constant, if p increases, p' must diminish. Suppose L to be p p removed to an infinite distance, then p is infinite, and - = o ; hence _, = ^ or 2 p' r /' = -. That is, if the point from which the light comes is infinitely distant, and the incident rays are parallel to each other and to the principal axis the reflected rays converge to a point halfway between the centre of the 534 On Light [535- mirror and the centre of curvature. This case is illustrated in fig. 497. The point of convergence F is called the- principal focus of the mirror ; its distance from the mirror is the focal length. Thus the focal length of a mirror is half its radius of curvature, or, if/ denote the focal length, If the point L returns towards the mirror, /, its image, moves from F to meet it. Since the angles of incidence and reflection are always equal, it follows that L and / arrive at C together, and object and image coincide. The formula also tells us that \i p = r, p' must also = r. When the luminous point moves from C towards A, its image or conjugate focus moves away from C ; and if the luminous point coincide with F, the reflected rays are parallel and the image is formed at an infinite distance away. Virtual image. — If the luminous point is between the principal focus and the mirror (fig. 499), we see — taking two incident rays LA and LM and proceeding as before — the reflected rays AL and ME do not meet, but are divergent. This is the case with all rays from the point L, and hence L has no real image ; but if the reflected rays are conceived to be prolonged on the other side of the mirror, their prolongations will intersect in a point / on the axis, and an eye looking in the direction KA experiences the same impression as if the rays were directly emitted from the point /. Hence a virtual image or focus is formed quite analogous to those formed by plane mirrors. Fig. 499 The formula ■ - may J be written p' = —-^ , from which p p r f p-f we see that if / is greater than /, p' will_be positive ; that is, that if the luminous point is farther away from the mirror than the principal focus, there will be a real image formed on the same side of the mirror. If p =f, p' is infinite, and the reflected rays are parallel when the luminous point coincides v.ith the principal focus ; if^ is less than _;^ that is, if L is between the mirror and its principal focus,/' is negative, and the image — a virtual image in this case — is formed on the other side of the mirror. It is convenient to consider all lines drawn in the direction from which the light is proceeding to|be positive, and those drawn in the opposite direction to be negative. In figs. 498 and 499 the light Fig. 500 which falls upon the mirror is coming from the right — hence all distances measured to the right, as /, p', r,f, are positive. If the mirror faces the left, distances measured to the left are positive. But no' ambiguity will arise if we remember that the positive direction is that from which the light is coming. -637J Formation of Images of Objects in Concave Mirrors 535 Hitherto the luminous point has been supposed to be placed on the principal axis, but it is easy to find the position of its image when it is not so situated. In fig. 500, let ACK be the principal axis, L the luminous point, LCB a secondary axis through L. As before, it is only necessary to draw two incident rays from L and find where the corresponding reflected rays meet. If LCB be one of the incident rays, its corresponding reflected ray will be BCL ; let LM, parallel to the principal axis, be the other. Since all rays parallel to the principal axis converge after reflection to the principal focus, LM will be reflected along MF. Hence /, where MF and BC meet, is the image of L. If L be not far removed from ACK, we may use the same formula as before to find the position of /, measuring p and p' along the principal axis. 536. Reflection from convex mirrors. — In convex mirrors only virtual images are formed. Let MM' (fig. 501) be a convex spherical mirror, with centre of curvature at C, and let L be a luminous point on the principal axis, CK. Of the rays diverging from L, consider one, LM, and draw the normal, CM. LM will be reflected along a line which makes the same angle with CM that the incident ray LM makes. The incident ray drawn towards C is reflected along its own path. The reflected rays do not meet, but their prolongations backwards *'s- 501 meet at /, which is therefore the (virtual) image of L. F, halfway between C and the mirror, is the principal (virtual) focus of the mirror. The formula already proved for a concave mirror, viz. I i. = 2 _ I ~p P'~'r- y holds in this case also, if the sign of r or / be reversed, p and/' being, . as before, the distances of L and / from the mirror. Hence - + —.= — ,. or p' = — , Kl=p', KQ, = r, QL^^ CL _ p-r . ql CI r ~ p' ' butsince I+\ = 5, l_i='-J., ■ P-J-^t ■6 p r p r r p r-p' p'' by geometiy -542] Spherical Aberration. Caustics 539 Hence, if O and I represent the linear dimensions of object and image respectively, ^=^^=|-. Thus, size of the image (linear) _ distance of the image from the centre of curvature size of the object distance of the object from the centre of curvature _ distance of the image from the mirror distance of the object from the mirror The term magnification — that is, the ratio of the linear size of the image to that of the object — is used whether the image be greater or less than the object. Zero magnification means that the image is infinitely small as com- pared with the object ; unit magnification., that the object and image are the same size. The relation given above holds whether the image be real or virtual, and for convex as well as concave mirrors. 541. Discussion of the formulae for mirrors. — The formulae in question I I 2 I , V and b = J- • • ■ . • • ■ ^'^ These hold for convex as well as concave mirrors, and for virtual as well as real images ; but the convention with regard to signs must be attended to. Equation ( l) may be written p' = -— , = — — , /,-. i. Concave mirror ; /"positive. If the object is at an infinite distance on the axis, p= oz, the incident rays are parallel, and^' =/; that is, the reflected rays converge at the principal focus and (from equation 2) the image is infinitely small, in other words a mere point. As the object approaches the centre of curvature, so does the image. As p' < p, the image is smaller than the object. VJ'h&a. p = r = 2f, p' = 2/ ; that is, object and image coincide at the centre, arid the magnification = unity. As the object approaches F, the image moves off to infinity and grows indefinitely in size. When the object is nearer the mirror than the principal focus, p < f and (equation 3) p' is negative, and the image rapidly diminishes. lip =/l2, p' = —/, and the magnification = 2. When the luminous object is in contact with the mirror, so is the image. ii. Convex mirror ; /negative. Equation (3) becomes p'=-JJ =-^„ P from which we see that, / being positive, p' is always negative, that is, the image is always virtual. When / is infinite, p' = — / and the magnification is zero. As the object approaches the mirror the image increases in size, but cannot be greater than the object. Object and image coincide when^ = o. 542. Spherical aberration. Caustics. — In the foregoing explanation of the formation of images by spherical mirrors, it has been assumed that the aperture of the mirror does not exceed 8 or 10 degrees, since it is only when the incident rays are \ery close to the principal axis that 540 On Light [542- the reflected rays meet in a single point. With a larger aperture the rays reflected near the edges meet the axis nearer the mirror than those that are reflected at a small distance from the centre of the mirror. Hence arises a want of sharpness in these images, which is called spherical aberration by reflection, to distinguish it from the spherical aberration by refrac- tion, which occurs in the case of lenses. Every reflected ray cuts the one next to it (fig. 509), and their '^' ^°' points of intersection form in space a curved surface which is called tne cailstic by reflection. The curve FM represents one of the branches of a section of this surface made by the plane of the paper. When the light of a candle is reflected from the inside of a teacup or a glass tumbler, a section of the caustic surface can be seen by partly filling the cup or tumbler with milk. 543. Applications of mirrors. Heliostat. — The applications of plane mirrors in domestic economy are well known. Mirrors are also frequently used in physical apparatus for sending light in a certain direction. We have already seen an application of this in the heliograph (533). The light of the sun can only be sent in a constant direction by making the mirror movable. It must have a motion which compensates for the continual change in the direction of the sun's rays produced iby the apparent diurnal motion of the sun. This result is obtained by means of a clockwork motion, to which the mirror is fixed, and which causes it to follow the course of the sun. Such an apparatus is called a heliostat. The reflection of light is also used to measure the angles of crystals by means of the instruments known as reflecting goniometers. Concave spherical mirrors are also often used. They are applied for magnifying mirrors, as in the older forms of shaving mirrors. They have been employed for burning mirrors, and are still used in telescopes. They also serve as reflectors, for conveying light to great distances, by placing a luminous object in their principal focus. The search light used by steamers in passing through the Suez Canal by night, and by war ships, consists of a powerful electric light placed at the principal focus of a concave spherical reflector. Parabolic reflectors, though theoretically preferable, are not much used for this purpose on account of the difficulty of working the parabolic surface. The images of objects seen in concave or convex mirrors appear smaller or larger, but otherwise similar geometrically, except in the case where some parts of a body are nearer the mirror than others. The distortion of features observed on looking into a spherical garden mirror is more marked the nearer we are to the glass. Objects seen in cylindrical or conical mirrors appear ludicrously distorted. From the laws of reflec- tion the shape of such a distorted figure can be geometrically constructed. In like manner distorted pictures of objects can be constructed which, seen in such mirrors, appear in their normal proportions. They are called anamorphoses. -544] Parabolic Mirrors 541 544. Parabolic mirrors.^ — Parabolic mirrors are concave mirrors whose surface is generated by the revolution of the arc of a parabola, AM, about its axis AX (fig. 510). It has been already stated that in spherical mirrors the rays parallel to the axis converge only approxi- mately to the principal focus ; and reciprocally, when a source of light is placed in the principal focus of these mirrors, the reflected rays are not exactly parallel to the axis. Parabolic mirrors are free from this defect ; they are more difficult to construct, but are better for reflec- tors. It is a property of a parabola Fig_ 510 that the right line FM, drawn from the focus F to any point M of the curve and the line ML, parallel to the axis AF, make equal angles with the tangent TT' at this point.' s^Hence all rays parallel to the|axis after reflection meet in the focus of the -mirror F ;, and conversely, when a source of light is placed in the focus, the rays incident on the mirror are reflected exactly parallel to the axis. The light thus reflected tends to maintain its intensity even at a great distance, for it has been seen (519) that it is the divergence of the luminous rays which principally weakens the intensity of light. From this property parabolic mirrors are used in carriage lamps, and in the lamps placed in front of and behind railway trains. These reflectors were formerly used for lighthouses, but have been replaced.by lenticular glasses. When < two equal parabolic mirrors are cut by a plane perpendicular to the axis passing through the focus, and are then united at their intersections as shown in fig. 511, so that their foci coincide, a system of reflectors is obtained with which a single directions at once. This arrangement is used in lighting staircases and passages. Fig. 511 lamp illuminates in two 542 On Light [545- CH AFTER III SINGLE REFRACTION. LENSES 545. Phenomenon of refraction. — Refraction is the deflection or bending which the rays of light experience in passing obliquely from one medium to another : for instance, from air into water (fig. 513). If the incident ray is perpendicular to the Fig. 512 Fig- 513 surface separating thp two media, it is not bent, but continues its course in a right line (fig. 512). The incident ray being represented by SO (fig. 514), the re- fracted ray is the di- rection OH which light takes in the second medium ; and of the angles SOAand HOB, which these rays form with the normal AB, to the surface which separates the two media, the first is the angle of incidence, and Fig. su the other the angle of refraction. According as the refracted ray approaches or deviates from the normal, the second medium is said to be more or less refringent or refracting than the first. All the light which falls on the surface of a refracting substance does not completely pass into it ; one part is reflected, regularly or diffiisely (528), while another penetrates into the medium. -547] Index of Refraction 543 In uncrystallised media, such as air, liquids, ordinary glass, the luminous ray is singly refracted ; but in certain crystallised bodies, such as Iceland spar, selenite, &c., the incident ray gives rise to two refracted rays. The latter phenomenon is called double refraction, and will be discussed in another part of the book. We shall here deal exclusively with single refraction. 546. Laws of single refraction.^ — When a luminous ray is refracted in passing from one medium into another of a different reflective power, the following laws prevail : — ■I. Whatever the obliquity of the incident ray, the ratio which the sine of the incident angle bears to the sine of the angle of refraction is constant for the same two media, and the same coloured light, but varies with different media. 1 1. The i7icident and the refracted rays are itt the same plane, which is perpendicular to the surface separating the two media. These have been known as Descartes's laws ; they are, however, really due to Willibrod Snell, who discovered them in 1620 ; they are demon- strated by the same apparatus as that used for the laws of reflection (522). The plane mirror in the centre of the graduated circle is replaced by a semi- cylindrical glass vessel, filled with water to such a height that its level is exactly the height of the centre (fig. 515). If the mirror, M, be then so inclined that a reflected ray, MO, is directed towards the centre, it is refracted on passing into the water, but it passes out without refraction, because its direction is then at right angles to the curved sides of the vessel. In order to observe the course of the refracted ray, it is received on a screen, P, which is moved until the image of the aperture in the screen N is formed at its centre. In all positions of the screens N and P, the sines of the angles of incidence and refraction are measured by means of two graduated rules, movable so as to be always horizontal, and hence perpendicular to the diameter AD. On reading off the lengths which are proportional to the sines of the angles MOA and DOP in the scales I and R, the numbers are found to vary with the position of the screens, but their ratio is constant ; that is, if the sine of incidence becomes twice or three times as large, the sine of refraction increases in the same ratio, which demonstrates the first law. The second law follows from the arrangement of the apparatus, for the plane of the graduated limb is perpendicular to the surface of the liquid in the semi- cylindrical vessel. 547. Index of refraction. — The ratio between the sines of the incident and refracted angles is called index of refraction, or refractive index of the Fig- 515 544 On Light [547- second medium with respect to the first. Thus if n be the refractive index, and / and r the angles of incidence and refraction, sin i = n sin r. The refrac- tive index varies with the media ; for example, from air to water it is f , and from air to glass it is |. If the media are considered in an inverse order — that is, if light passes from water to air, or from glass to air — it follows the same course, but in a contrary direction, PO becoming the incident and OM the refracted ray. Consequently the index of refraction is reversed ; from water to air it is then f , and from glass to air f . On the undulatory theory of light, the index of refraction of one medium with regard to another is the ratio of the velocity with which light travels in the second medium to that with which it travels in the first. Thus the velocity of light in glass is twO-thirds and in water three-fourths of its velocity in empty space. 548. Effects produced by refraction. — In consequence of refraction, bodies immersed in a medium more highly refracting than air appear nearer the surface of this medium, but they appear to be more distant if immersed in a less refracting medium. Let L (fig. 516) be an object immersed in a mass of water. In passing thence into air, the rays LA, LB . . . diverge from the normal to the point of incidence, and take the direction AC, BD . . . , the prolongations of which intersect approxi- mately in the point L', placed on the perpendicular L'K. Supposing the points A, B . . . are not far removed from the normal KL, an eye looking vertically downwards and receivmg these rays sees the image of L at L'. If the eye looks obliquely at the object, the image rises, and the greater the obliquity of the rays LA, LB . . , the higher the object appears. For the same reason a stick placed obliquely in water appears bent, the immersed part appearing raised. It is easy to show that the apparent dis- tance of the point L below the surface is less than the true distance in the ratio i/m, where n is the refractive index of water. For if NN' (fig. 517) be the normal to the surface at A, the angle LAN' is the angle of i|ncidence, and NAc the angle of refraction of the incident ray sin NAf Fig. 516 But Fig. 517 sin NAf cosL 'AO cos LAO LA, and OA AL' sin LAN' AL _ AL OA AL OL if A is sufficiently sin LAN' near to O. Hence, if p and p' are the respective distances of a point and its image from the surface of water, p = np'. Thus a stream or pond that appears to the eye looking vertically down to be 3 feet deep is in reality 4 feet deep. If the eye looks obhquely at the object the image rises, and is slightly nearer to the observer. Thus, when a stick is placed obliquely and partly -549] Multiple Images formed by Glass Mirrors 545 Fig. 518 immersed in water, not only does the stick appear to be broken at the surface, but the part immersed appears to be bent. An experimental illustration of the effect of refraction is the following : — A coin is placed in an empty porcelain basin, and the eye placed so that the coin is just not visible. If now, the position of the eye remaining unaltered, water be poured into the basin, the coin becomes visible. A consideration of fig. 516 will suggest the ex- planation of this phenomenon. Owing to an effect of refraction, stars are visible to us even when they are below the horizon. For as the layers of the atmo- sphere are denser in proportion as they are nearer the earth, and as the refractive power of a gas increases with its density (561), it follows that on entering the atmosphere the luminous rays become bent, as seen in fig. 518, describing a curve before reaching the eye, so that we can see the star at S' along the tangent of this curve instead of at S. In our climate the atmospheric re- fraction does not raise the stars when on the horizon more than half a degree. The effect of refraction is that objects at a distance appear higher than they are in reality ; our horizon is thereby widened. When individual layers of air refract more strongly than usual, objects may thereby become visible which are usually below the horizon. Thus, from Hastings, ' the coast of France, which is at a distance of 56 miles, is not unfrequently seen. 549. Multiple images formed by glass mirrors. — Metal rriirrors which have but one reflecting surface give only one image ; glass mirrors give rise to several images, which are readily observed when the image of a candle is looked at obliquely in a looking-glass. A very feeble image is first seen, and then a very distinct one ; behind this there are several others, whose intensities gra- dually decrease until they disappear. This phenomenon arises from the looking-glass having two reflecting surfaces. When the rays from the point A meet the surface, fig. 5 19, a part is reflected and forms an image, a, of the point A, on the prolongation of the ray i5E, reflected' by this surface ; the other part passes into the glass and is reflected at c from the layer of metal which covers the back surface of the glass, and reaching the eye in the direction dii, gives the image a'. This image is distant from the first by double the thickness of the glass. It is brighter, because metal reflects better than glass. In regard to other images it will be remarked that whenever light is trans- mitted from one medium to another — for instance, from glass to air — (547), only some of the rays get through ; the remainder are reflected at the surface which bounds the two media. Consequently when the pencil cd, reflected from c, attempts to leave the glass at d, most of the rays composing it pass N N Fig 519 546 On Light [549- into the air, but some are reflected at d, and continue within the glass. These are again reflected by the metallic surface, and form a third image of A ; after this reflection they come to MN, when many emerge and render the third image visible ; but some are again reflected within the glass, and in a similar manner give rise to a fourth, fifth, &c., image, thereby completing the series above described. It is manifest from the above explanation that each image must be much feebler than the one preceding it, and consequently only a small number are visible — ordinarily not more than eight or ten in all. This multiplicity of images is objectionable in observations, and, accord- ingly, metal mirrors, or right-angled prisms (556), are to be preferred in optical instruments. 550. Total reflection. Critical angle. — When a ray of light passes from one medium into another which is less refracting, as from water into air, it has been seen that the angle of incidence is less than the angle of refraction. Hence, when light is propagated in a. mass of water from S to O (fig. 520), there is always a value of the angle of incidence SOB, such that the angle of refrac- tion AOR is a right angle, in which case the re- fracted ray emerges parallel to the surface of the water. This angle, SOB, is called the critical angle, since for any greater angle, POB, the incident ray cannot emerge, but undergoes an internal reflection, which is called total reflection because the incident light is entirely reflected. From the formula sin j = «sinr we see that if 2 = 90° sin z= I, and Mr,, is the corresponding value of;-, i.e. the critical angle, sin r,, = -. From water to air the critical angle is 48° S3' ; from glass to air, 41" 48'. The occurrence of this internal reflection may be observed by the follow- ing experiment : — An object. A, is placed before a rectangular glass vessel filled with water (fig. 521) ; the surface of the liquid is then looked at as shown in the figure, and an image of the object A is seen at a, formed by the rays re- flected at OT, in the ordinary manner of a mirror. In total reflection there is no loss of light from absorption or transmission, and accordingly it produces the greatest brilliancy. If an empty test-tube be water, its surface, when looked at from above, shines as brilliantly as pure mercury ; those rays which fall obliquely on the side at an angle greater than the critical angle cannot pass into the air inside the tube, and are, thei'efore, totally reflected upwards. If a little water be passed into the tube, that portion of it loses its lustre. Bubbles, again, in water glisten like pearls, and cracks in transparent bodies like strips of silver. Fig. 520 Fig. 521 placed in a slanting position in -551] Mirage 547 for the oblique rays are totally reflected. The lustre of transparent bodies bounded by plane surfaces, such as the lustre of chandeliers, arises mainly from total internal reflection. This lustre is the more frequent and the more brilliant the smaller the critical angle, that is, the greater the refractive index ; the lustre of diamond, therefore, is the most brilliant. The erecting prism used with projection apparatus (6i6) is an interesting application of the principle of total internal reflection ; also the camera lucida (615). 551. Mirag^e. — The wznrg-^ is an optical illusion by which inverted images of distant objects are seen as if below the ground or in the atmosphere. This phenomenon is of most frequent occurrence in hot climates, and more espe- cially on the sandy plains of Egypt. The ground there has often the aspect of a tranquil lake, on which are reflected trees and the surrounding villages. Monge, who accompanied Napoleon's expedition to Egypt, was the first to give an explanation of the phenomenon. It is due to refraction, which results from the unequal density of the dif- ferent layers of the air when they are expanded by contact with the heated Fig. 522 5oil. The least dense layers are then the lowest, and the pencil of light from an elevated object, A (fig. 522), traverses layers which are gradually less refracting ; for, as will be shown presently (561), the refracting power of a gas diminishes with lessened density. The angle of incidence accordingly increases from one layer to the next, and ultimately reaches the critical angle, beyond which internal reflection succeeds to refraction (550). The pencil then rises, as seen in the figure, and undergoes a series of successive refractions, but in the direction contrary to the first, for it now passes through layers which are gradually more refracting. The pencil then reaches the eye with the same diiection as if it had proceeded from a point below the ground, and hence it gives an inverted image of the object, just as if it had been reflected from the surface of a tranquil lake. The effect of the mirage may be illustrated artificially, though feebly, as Wollaston showed, by looking' along the side of a red-hot poker at a word or object ten or twelve feet distant. At a distance less than three-eighths N N 2 548 On Light [551- of an inch from the line of the poker, an inverted image was seen, and within and without that an erect image. A better arrangement than a red-hot poker is a flat sheet-iron box, about 3 feet in length by 5 to 7 inches in height and breadth (fig. 523) ; it is filled with red-hot charcoal ^^ . and held at about . ^ the level of the eye. Looking over the lid of the box in the direction pm a direct, and in the is seen. The same c Fig. 523 -/m- direction pm' an inverted image of a distant point, z;z phenomenon is observed by looking along the sides. Mariners sometimes see in the air inverted images of ships and distant objects which are still below the horizon ; this is due to the same cause as the mirage, but is in a contrary direction. The lower layers of the air being in contact with the water are cold and dense. The rays of an object, a ship for instance, bent in an upward direction are more and more bent away from the vertical as they are continually passing into gradually less dense layers, and ultimately fall so obliquely on an upper attenuated layer that they are totally reflected downwards, and can thus reach the eye of an observer on the sea or on the shore. Scoresby observed several such cases in the Polar seas. The twinkling or scintillation of the fixed stars is also to be accounted for by alterations in the direction of their light due to refraction. 552. Refraction at a curved surface. — We have seen that when light undergoes refraction at a single plane surface, like that of water, the image of a point in the water, seen normally, is only _ , or |, of its true distance n from the surface, and the question arises. How will the apparent distance be related to the true distance if the surface of the medium is curved ? We will answer the question by taking a specific example. Let AD (fig. 524) be a sphere of glass, and let P be a small air bubble in it. An eye look- ing along the diameter APC will see not P but its image Q, and we have to find the position of Q. From P draw any ray PB, also CB, the normal at B ; PB, on emerging from the glass into air, will be bent away from the normal, and its direction Q is then the (virtual) image of P. Let also let AP=/, AQ=p', AC = r; the- n = -.^:. = '-|^^-|r = !"!l! ^^r' '^ *e angles are all small r Fig. 524 produced backwards meets PA in Q the angle PBC = ^, and QBC = fl; refractive index = « = -.HL_ sm (j> sin PBC angle PBC But angle = arc radius n ( z APB - i ACB) = l AQB - A /. CB. , when the angle is formed at the centre of a circle ; and —654] Prism 549 if B is very near to A, we may assume BQ = AQ and BP = AP, therefore /arc AB _ a rc AB \ ^ / arc AB _ arc AB\ ^ \ p r I \^p' r ) /I i\ I I . n I n—\ \ p r / p r P P ^ Example. — Let r = 6 inches, p = ^ inches, n = f , n- I I and n = -. — (549). I _ n P'' p It the surface instead of being spherical had been plane, p' would have been = 3. This follows from the formula on putting r = oc In the case here considered, AP and AC are both measured in the positive direction, and the light passes from a more dense to a less dense medium. But the formula holds in all cases. We shall have to use it again in considering the images formed by lenses. TRANSMISSION OF LIGHT THROUGH TR.\NSPARENT 5IED1A 553. Media with parallel faces.^ — Any transparent medium bounded by two parallel plane surfaces is called a plate. When light traverses a plate of any substance, the emergent rays are parallel to the incident rays. Let SA be a ray incident on one face of a glass plate (fig. 525), and DB the emergent ray, / and r the angles of incidence and of refraction at the entrance of the ray, and, lastly, i' and r' the corresponding angles at its emergence. At A the light undergoes a first refraction, At D it is refracted sm r ' a second time, and the index is then . sm r But we have seen that the index of re fraction of glass with respect to air is the reciprocal of the index of air with respect to glass ; hence sin i' _ sin r sin r' sin z' Fig. 525 But as the two normals AG and DE are parallel, the angles r and i' axe. equal, as being alternate interior angles. As the numerators in the above equation are equal, the denominators must also be equal ; the angles r' and i are therefore equal, and hence DB is parallel to SA. 554. Prism. — In optics a prism is any transparent medium l^'S- 5^6 Fig. 527 (*mprised between two plane faces inchned to each other. The intersection of these two faces is the edge of the prism, and their inclination is its SSO On Light [554- refracting angle. Every section perpendicular to the edge is called a principal section. The prisms used for experiments are generally right triangular prisms of glass, as shown in fig. 526, and their principal section is a triangle (fig. 527). In this section the point A is called the stimmit of the prism, and the right line BC is called the base : these expressions have reference to the triangle ABC, and not to the prism. 555. Path of rays in prism. Angle of deviation. — When the laws of refraction are known, the path of the rays in a prism is readily determined. Let O be a luminous point (fig. 527) in the same plane as the principal section ABC of a prism, and let OD be an incident ray, let us suppose, of monochromatic light. This ray is refracted at D, and approaches the normal, because it passes into a more highly refracting medium. At K it experiences a second refraction, but it then deviates from the normal, for it passes into air, which is less refractive than glass. The light is thus refracted twice in the same direction, so that the ray is deflected towards the base, and consequently the eye which receives the emergent ray KH sees the Fig. 52S Fig. 529 virtual image of O, which is formed at O' ; that is, objects seen through a pris?!i appear deflected towards its summit. The angle OEO', which the incident and eriiergent rays form with each other, expresses the deviation of light caused by the prism, and is called the angle of deviatioji. In ordinary light, objects seen through a prism appear bordered with colour: this phenomenon, known as dispersion, will be afterwards described (574)- The angle of deviation increases with the refractive index of the material of the prism, and also with its refracting angle. It also varies with the angle under which the luminous ray enters the prism. That the angle of deviation increases with the refracti\e index may bfe shown by means of the polyprism. This name is given to a prism formed -557] Conditions of Emergence in Prisms 5 5 1 of several prisms of the same angle connected at their ends (fig. 528). These prisms are made of unequally refracting substances, such as flint glass, rock crystal, or crown glass. If any object — a horizontal line, for instance — be looked at through the polyprism, its different parts are seen at unequal heights. The highest portion is that seen through the flint glass, the refractive index of which is greatest ; then the rock crystal ; and so on in the order of the decreasing refractive indices. The prism with variable angle (fig. 529) is used for showing that the angle of deviation increases with the refracting angle of the prism. It consists of two parallel brass plates, B and C, fixed on a support. Between these are two glass plates, moving on a hinge with some friction against the plates, so as to close it. When water is poured into the vessel the angle may be varied at will. If a ray of light, S, be allowed to fall upon one of them, by inclining the other more the angle of the prism increases, and the deviation of the ray is seen to increase. 556. Use of right-angled prisms as reflectors.— Prisms whose principal section is an isosceles right-angled triangle afford an important application of total reflection (550). For let ABC (fig. 530) be the principal section of such a prism, O a luminous point, and OH a ray at right angles to the face BC. This ray enters the glass without being re- fracted, and makes with the face AB an angle equal to B — that is, to 45° — and therefore greater than the critical angle of glass, which is 41° 48' (550). Fig. 530 The ray OH undergoes, therefox'e, at H total reflection, which imparts to it a direction HI perpendicular to the second face AC. Thus the hypotenuse surface of this prism produces the effect of the most perfect plane mirror, and an eye placed at I sees O', the image of the point O. This property of right- angled prisms is frequently used in optical instruments, such as the camera lucida (615), the Newtonian telescope (611), and the prismatic compass (732), instead of metal reflectors, which readily tarnish. They are also largely used with the limelight or electric- light lantern for projection in order to erect images that would otherwise be inverted (616). The newer light- house lenses are partly made up of such prisms. 557. Conditions of emergence in prisms. — In order that any mono- chromatic ray refracted at the first face of a prism may emerge from the p. second, it is necessai-y that the re- fractive angle of the prism be less than twice the critical angle of the sub- stance of which the prism is composed. For if LI (fig. 531) be the ray incident on the first face, IE the refracted ray, PI and PE the normals, the ray IE can only emerge from the second face when the incident angle lEP 552 On Light [557- is less than the critical angle (550). But as the incident angle LIN in- creases, the angle EIP also increases, while lEP diminishes. Hence, according as the direction of the ray LI tends to become parallel with the face AB, does this ray tend to emerge at the second face. Let LI be now parallel to AB, the angle r is then equal to the critical angle / of the prism, because it has its maximum value. Further, the angle EPK, the exterior angle of the triangle IPE, is equal to r + i'; but the angles EPK and A are equal, because the sides which contain them are at right angles to each other, and therefore Pi. = r + i' ; therefore also A = /+/', for in this case r = l. Hence, if A = 2/ or is >2/, we shall have z' = /or >/, and therefore the ray would not emerge at the second face, but would be parallel to AC or would undergo internal reflection, and emerge at a third face, BC. This would be much more the case with rays whose incident angle is less than BIN, because we have already seen that i' would continu- ally increase. Thus in the case in which the refracting angle of a prism is equal to 2/ or is greater, no luminous ray could pass through the faces of the refracting angle. As the critical angle of glass is 41° 48', and twice this angle is less than 90^ objects cannot be seen through a glass prism whose refracting angle is a right angle. As the critical angle of water is 48° 35', light could pass through a hollow right-angled prism formed of three glass plates and filled with water. If we suppose A to be greater than / and less than 2/, then of rays inci- dent at I, some within the angle NIB will emerge from AC, others will not emerge, nor will any emerge that are incident within the angle NIA. If we suppose A to have any magnitude less than /, all rays incident at I within the angle NIB will emerge from AC, as also will some of those incident within the angle NIA. 558. Minimum deviation. — When a pencil of monochromatic light passes through an aperture A, in the side of a dark chamber (fig. 532), the pencil may be focused by a lens, F, on a distant screen at C. But if a vertical prism be interposed between the lens and the screen, the pencil is deviated towards the base of the prism, and the image is projected at D, at some distance from the point C. If the prism be turned so that the incident angle decreases, the disc of light approaches the point C up to a certain position, E, from which it reverts to its original position even when the prism is rotated in the same direction. Hence there is a deviation, EBC, less than any other. It may be proved mathematically that this minimum deviation takes place when the angles of incidence and of emergence at the faces of the prism are equal. The angle of minimum deviation may be calculated when the incident Fig- 532 -559] Measurement of the Refractive Index of Solids 553 angle and the refracting angle of the prism are known. For when the deviation is a minimum, then since the angle of emergence r' is equal to the incident angle i (fig. 531), r must equal z'. But it has been shown above (557) that A = r + z' ; consequently A = 2r (i) If the minimum angle of deviation LD/ be called d, this angle being exterior to the triangle DIE, we readily obtain the equation d=i—r-^r' — i^ li— 2r, d= 21 -X whence (2) which gives the angle d, when i and A are known. From the formulae (i) and (2) a third may be obtained, which serves to calculate the index of refraction of a prism when its refracting angle and the minimum deviation are known. The index of refraction, n, is the ratio of the sines of the angles of incidence and refraction ; hence n = — .'P-^ ; sm r replacing z and ^ from their values in the above equations (i) and (2) we set {^) A (3) 559. Measurement of the refractive index of solids. Spectrometer. — By means of the preceding formula (3) the refractive index of a solid may "be calculated when the angles A and d are known, and these may be determined by means of the spectrometer. The spectrometer is in appearance similar to the spectroscope illustrated in fig. 567. Supported on a vertical upright is a horizontal graduated disc, T (fig. 533), and at its centre a smaller circular table, D, which can be turned about a central -vertical axis and clamped in any desired position. A is a collimator with vertical slit at the end a and convex lens at b, the slit being at the principal focus of the lens (563). Bis a telescope which can be moved round the circle in such a way that its axis is always directed to- wards the centre of the circle ; it can be clamped anywhere on the circle, and its position read off by a vernier (not shown) moving over the graduations of the scale. The prism ■whose refracting angle is to be measured is placed on the central table with its edge near the centre in such a way that, when the slit a is illuminated "by monochromatic, e.g. sodium, light, the parallel rays which emerge from l> fall partly on one and partly on the other face of the prism. The telescope Fig. 533 554 On Lifrht [569- — which has previously been focused for parallel rays — is moved to the position B, so that an observer may see through it an image of the slit a by the rays reflected from the left-hand side of the prism. The telescope is then moved to C, and an image of the slit is again seen, this time by the rays reflected from the right-hand face. It is not difficult to prove that the angle BC through which the tele- scope has been turned is twice the angle of the prism. Thus the angle A is determined. To find the minimum deviation d, the prism is placed as shown in fig. 534 and the telescope adjusted at C so that the image of the slit seen by refraction coincides with the cross-wires of the telescope. The angle between C and the zero graduation is the deviation. The observer, in order to make this a minimum, turns the small table one way or the other, each time adjusting the telescope, until C is brought as near to the zero as possible. Thus the minimum deviation is found. It is usual, having measured rf on one side, to turn the table D round and reverse the position of the prism, the telescope C bemg now on the left-hand side of the zero. The minimum deviation is again found, and the mean of the two values taken. The values of A and d, substituted in the equation (3) (558), give the value oin. 560. Measurement of the refractive index of liquids. — Biot applied Newton's method to determining the refractive index of liquids. For this purpose a cylindrical cavity, O, of about 075 inch in diameter, is perforated in a glass prism, PQ (fig. 535), from the incident face to the face of emergence. This cavity is closed by two plates of thin glass which are cemented on the sides of this prism. Liquids are introduced through a small stoppered aperture, B. The refracting angle and the minimum deviation of the liquid '^' ^^^ prism in the cavity O having been deter- mined, their values are introduced into the formula (3), which gives the index. 561. Measurement of the refractive index of gases. — A method for this purpose, founded on that of Newton, was devised by Biot and Arago. The apparatus which they used consists of a glass tube (fig. 536), bevelled at its two ends, and closed by glass plates, which are at an angle of 143°. This tube is connected with a bell-jar, H,in which there is a siphon barometer,, and with a stopcock by means of which the apparatus can be exhausted, and different gases introduced. When the tube, AB, has been exhausted, a ray of light, SA, is transmitted through it, which is bent away from the normal through an angle r - z at the first incidence, and towards the normal through an angle i' — r' at the second. These two deviations being added, the total deviation, d^ is r-i + i' -r'. In the case of a minimum deviation, i = r' -561] Measurement of the Refractive Index of Gases 555 and r = i', whence d=K-ii, since r-^i' = K (557)- The index from vacuum to air, which is eA-idently sm r sin i has therefore the value . A . rA-d\ (4) Hence, in order to deduce the refractive index n from vacuum into air, which is the absolute index of air, it is merely necessary to know the refracting angle, A, and the angle of minimum deviation, d. To obtain the absolute index of any other gas, we first produce a vacuum, and then introduce the gas ; the angles A and d having been measured, the above formula gives the index of refraction from the gas to air. Dividing the index of refraction from vacuum to air by the index of refraction from the gas to air, we obtain the index of refraction from vacuum to the gas ; that is, its absolute index. It appears probable that certain relations exist between the refractive index, n, and the density, d^ of a body. These relations are of considerable importance in questions of theoretical chemistry regarding the constitu- tion of bodies. They are expressed by the formula R = ' . - , which is known as the »'- + 2 d Fig. 536 constant of refraction. If this is multiplied by a, the atomic weight, we have the atojnic refraction — ■— ; or, if by the molecular weight, ?«, ■ 2 d %\e have the molecular refraction ' in n' + 2 ' d' The following table gives the refractive indices for the three principal Fraunhofer lines (585), the red, yellow, and violet ; the last column gives the dispersion (577), or the difference between the extreme red, «A) "ind the extreme %iolet, tin, rays. A D ' H »H-«A Water 1-329 I-33I ' 1-344 0-015 Alcohol 1-360 1-364 '-375 0-015 Crown glass (light) 1-510 I-S75 I-53I 0-02I „ (heavy) I-61O I -61 2 I -63 1 0-02 1 Rock salt 1-538 I-S45 1-569 0-031 Flint glass (light) . 1-599 I -609 \ 1-640 0-041 „ (hea\'y) 1-735 1-751 , I-81I 0-076 Calcspar (ordinary) 1-650 1-659 ! 1-683 0-033 „ (extraordinary) 1-483 1-483 ' 1-498 0-015 Carbon bisulphide I-6l2 1-631 ; 1-703 0-091 SS6 On Light [561- The following are the mean values for a few other substances, and correspond nearly to the E line : — Ice . . . . 1-310 Turpentine 1-363 Solution of nitre . . i"355 Rock crystal 1-545 Vitreous humour of the eye . i -339 Benzole 1-586 Aqueous „ „ „ 1-357 Oil of cassia 1-621 Crystalline lens „ „ i"384 Diamond . 2-750 Mean refractive indices of gases Vacuum i -000000 Carbonic acid . I -000449 Hydrogen 1-000138 Hydrochloric acid . I -000449 Oxygen . 1-000272 Nitrous oxide . 1-000503 Air 1-000294 Sulphurous acid . 1-000665 Nitrogen. . 1-000300 Ethylene I -000678 Ammonia . 1-000385 Chlorine . I -000772 LENSES. THEIR EFFECTS 562. Different kinds of lenses. — Lenses are transparent media which, from the curvature of their surfaces, have the property of causing the luminous rays which traverse them either to converge or to diverge. According to their curvature they are either spherical, cylindrical, elliptical, or parabolic. Those used in optics are exclusively spherical. They are commonly made either of crown glass, which is free from lead| or oi flint glass, which con- tains lead, and is more refractive than crown g'lass. The combination of spherical surfaces, either with each other or with plane surfaces, gives rise to six kinds of lenses, sections of which are M W Fig- 537 represented in fig. 537 ; four are formed by two spherical surfaces and two by a plane and a spherical surface. M is a double convex, N is a plano-convex, O is a converging concavo- convex, P is a double concave, Q is a plano-concave, and R is a diverging concavo-convex. The lenses O and R are also called meniscus lenses, from their resemblance to the crescent-shaped moon ; O is also called a periscopic lens. The first three, which are thicker at the centre than at the borders, are converging or convex lenses ; the others, which are thinner in the centre, are diverging or concave. In the first group the double convex lens only need be considered, and in the second the double concave, as the properties of each of these lenses apply to all those of the same group. In lenses whose two surfaces are spherical, the centres for these surfaces —563] J^onnulcs for Lenses 557 are called centres of acrvaitire, and the right line which passes through these two centres is the. principal axis. In a plano-concave or plano-convex lens the principal axis is the perpendicular let fall from the centre of curvature of the spherical face on the plane face. Suppose a luminous point to be situated on the principal axis of a convex or concave lens. Rays from the point fall upon the lens, and, after refraction at the first and second surfaces, converge to or diverge from a point, which is the image of the luminous point. We proceed, before describing the phenomena of lenses, to obtain a formula which shall give the relation between the distances of object and image from the lens and be applicable both to convex and to concave lenses. 563. Formulae for lenses. — Let MAB be a lens (fig. 538). A convex lens of this shape is chosen because each of its faces has a positive curvature, that is, the radii of curvature of both faces are drawn in the direction from which the Ught is coming. Let O be the centre of curvature of the first face, LB, O' of the second, MA, and let OB = r, O'A = s. P is a luminous point on the principal axis, and an incident ray, PL, is bent at the point of incidence towards the normal along LM. Another incident ray, PP, enters the glass without refraction. The two rays BA and LM are divergent, but if produced backwards, meet at a point Q, which is therefore the virtual image of P by refraction at the first surface of the lens. Let BP =p, BQ = q, and let n = the refractive index of the glass. We may apply the formula of article 552 to this case, remembering however that here the rays are passing from air into glass, whereas in 552 they were passing from glass into air ; hence instead of n we must use i/«. The formula then becomes I I n. I ^^~^or — -^--^~" • (') p q ~ r p q r The point Q may now be treated as if it were a real source of light in a medium of glass, emitting rays which fall upon the second surface, AM, of the lens, and after refraction into air converge to a point R on the axis. In the elementary theory of lenses it is assumed that the lenses are very thin, so that the distance of a point from the lens is the same from whichever side of the lens it is measured. On this assumption BQ = AQ = ^, and let 55 8 On Light , [563- AR=^. Then, applying the same formula to this case of refraction from glass into air, we have — --i = , since AO =-r (2) q p s Combining the two formulas and eliminating -, we have y)r^-<4) ■ (3) This is a general formula, applicable to all cases both of convex and conca\'e lenses, provided it be borne in mind that all distances measured from the lens to the right (supposing the incident light to come from the right) are positive and to the left negative. If the lens is convex, and the incident beam parallel to the principal axis, the refracted rays converge to a point on the negative side of the lens, called the principal focus. Its distance from the lens is called the focal length of the lens. The \'alue of the focal length, / is given by the formula, on putting /> = oc, or \\p = o; then^-, = -L = («- i) ( 1 — i Y p J .r s J Thus the focal length of a lens depends on the curvature of the two faces and on the refractive index of the material of the lens. Replacing (?z - i) ( -) by in formula (3), we have 1 _ I _ I p' -p-y- For convex lenses f is negative ; when parallel rays fall upon a concave lens the rays diverge after refraction, but the virtual focus is on the same side of the lens as that from which the light comes, hence for concave lenses /is positive. 564. Particular cases. — Fig. 539 illustrates the case in which the incident rays LB, MN, &c., are parallel to the principal axis. P", the point to which the)' converge on the other side of the lens, is the principal focus. There is of course a similar principal focus on the left-hand side of the lens, to which parallel rays would converge if they came Fig. 539 from the right. In the figure the rays are ■drawn as if they were incident at all parts of the lens from the centre to the edge, but in practice it is only the central part of the lens which is used ; unless the angle DFE is confined to 10° or 12°, the refracted rays do not •even approximately pass though a single point. -565] Concave Lenses 5S9 If the incident rays start from a point L on the principal axis (fig. 540), which is at a finite distance than the lens but beyond the principal focus, the point of convergence is at /, also on the principal axis, but farther away than Fig- 54° F ; L and /are called conjugate foci, for if either is a source of light the other is its image. According as the point of light comes nearer the lens, the convergence of the emergent rays decreases, and the focus / becomes more distant ; when the point L coincides with the principal focus, the emergent rays on the other side are parallel to the axis, and there is no focus, or, what is the same thing, it is infinitely distant. Fig. 54" As the refracted rays are parallel in this case, the intensity of light only decreases slowly, and a simple lamp can illuminate great distances. It is merely necessary to place it in the focus of a double convex lens, as shown in fig. 541. Virtual foci. — When a luminous point is placed between the lens and its principal focus, the image or focus of the point is virtual, as shown in fig. 542. In this case the incident rays make with the normal greater angles than those made with the rays FI from the principal focus ; hence, when the former rays emerge, they move farther from the axis than the latter, and form a diverging pencil, HK,GM. Fig. 542 These rays cannot pro- duce a real image, but their prolongations intersect in some point, /, on the axis, and this point is the virtual focus of the point L (535). 565. Concave lenses. — In concave or diverging lenses there are only virtual foci, whatever the distance of the object. Let SS' be any pencil of 56o On Light [565- rays parallel to the axis (fig. 543) ; any ray, SI, is refracted at the point of incidence, I, and approaches the normal, CI. At the point of emergence it is also refracted, but diverges from the normal GC, so that it is twice refracted in a direction which moves it from the axis, CC. As the same Fig: 543 '''ig- 544 thing takes place for every other ray, S'KMN, it follows that the rays, after traversing the lens, form a diverging pencil, GHMN. Hence there is no real focus, but the prolongations of these rays cut one another in a point F, which is the principal virtual focus. In the case in which the rays proceed from a point, L (fig. 544), on the axis, it is found by the same construction that a virtual focus is formed at /, which is between the principal focus and the lens. 566. Optical centre, secondary axis. — In or near every lens there is a point called the optical centre, which is situate on the axis, and which has the property that any luminous ray passing through it experiences no angular deviation ; that is, that the emergent ray is parallel to the incident ray. The existence of this point may be demonstrated in the following manner : — Let two parallel radii of curvature, CA and C'A' (fig. 545), be drawn to the two surfaces of a double convex lens. Since the two tangent planes to the surface of the lens at A and A' are parallel, as being perpendicular to two parallel right lines, it will be granted that the refracted ray AA' is propagated in a medium with parallel faces. Hence a ray KA, which reaches A at such Fig- 545 Fig. 346 an inclination that after refraction it takes the direction AA', will emerge parallel to its first direction (553) ; the point O, at which the right line cuts the axis, is therefore the optical centre. The position of this point may be determined for the case in which the curvature of the two faces is the same, which is the usual condition, by observing that the triangles COA and C'OA' are equal, and therefore that OC = OC, which gives the point O. If the curvatures are unequal, the triangles COA and COA' are similar, and either CO or CO may be found and therefore also the point O. -567] Formation of Images by Double Convex Lenses 561 In double concave or meniscus lenses the optical centre may be determined by the same construction. In lenses with a plane face this point is at the intersection of the axis by the curved face. Every right line, PP' (fig. 546), which passes through the optical centre without passing through the centres of curvature, is a secondary axis. As in all cases here considered the thickness of the lens is supposed to be extremely small, we may, in determining geometrically the positions of images, consider the optical centre to lie halfway between the two surfaces of the lens, and that rays passing through the optical centre suffer no bending or displacement. So long as the secondary axes only make a small angle with the principal axis, all that has hitherto been said about the principal axis is applicable to them ; that is, that rays emitted from a point P (fig. 546) on the secondary axis PP' nearly converge to a certain point of the axis, P', and according as the distance from the point P to the lens is greater or less than the focal length, the image thus formed will be conjugate or virtual, and that the formula already investigated for points on the principal axis applies also to secondary axes. This principle is the basis of what follows as to the formation of images. 567. Formation of images by double convex lenses. — In lenses, as well as in mirrors, the image of an object is the collection of the images of its several points ; hence the determination of the images furnished by lenses resolves itself into determining the position of a series of points, as was the case with mirrors (537). i. Real image. — Let AB (fig. 547) be placed beyond the principal focus. Of the rays from the point A which fall upon the lens, that which passes through the centre undergoes no bending. If AC be drawn parallel to the principal axis, it will after refraction pass through F, the principal focus. The rays DF and AO meet at a, which is therefore the image of A. Proceeding simi- larly with the rays ^'s- ^^ from B, we shall find that after refraction they meet in the point b, which is therefore the image, or conjugate focus, of B ; and as the points between A and B have their foci between a and b, a real but inverted image of AB will be formed at ab. To see this image, it may be received on a white screen, on which it will be depicted, or the eye may be placed in the path of the rays emerging from it. Conversely, if ab were the luminous or illuminated object, its image would be formed at AB. Two consequences important^for the theory of optical instruments follow from this : — viz. ist, if an object, even a very large one, is at a sufficient distance from a double convex lens, the real and inverted image which is obtained of it is very small — it is near the prin- cipal focus, but somewhat beyond it ; 2nd, if a very small object be placed 00 S62 On Light [567- Fig. 548 near the prmcipal focus, but a little in front of it, the image which is formed is at a great distance — it is much larger, and that itt proportion as the object is near the principal focus. In all cases the object and the image are in the same proportion as their distances from the lens. These two principles are experimentally confirmed by receiving on a screen the image of a lighted candle, placed successively at various distances from a double convex lens. ii. Virtual image. — There is another case in which the object AB (fig. 548) is placed between the lens and its principal focus. All rays from A which fall upon the lens diverge on emerging from the second face, as if from some point a. We can find this point most easily by dx-awing a ray, AC, parallel to the principal axis, and another, AO, through the centre of the lens ; the latter suffers no bending, the former after refraction passes through F, the principal focus. The divergent rays CF, ON, on being produced backwards, meet at a, the position of which is thus found. Tracing the rays from B in the same way, its virtual image will be found at b. There is therefore a -virttcal image of AB at ab ; // is erect, and larger than the object. The magnifying power is greater in proportion as the lens is more convex, and the object nearer the principal focus. We shall presently show how the magnifying power may be calculated by means of the formulae relating to lenses (569). Double convex lenses, used in this manner as magnifying glasses, are called simple microscopes. 568. Formation of images in concave lenses. — A concave lens, like a convex mirror, only gives virtual images, whatever the distance of the object. Let AB (fig. 549) be an object placed in front of such a lens. From A draw two rays, one parallel to the prin- cipal axis, which emerges from the other side of the lens as if coming from F, the principal focus ; the other through the centre of the lens. The prolongations backwards of these meet at a, which is therefore the image (virtual) of A. Similarly for B and other points of the object. Thus, an eye receiving the rays emerging from the left-hand side of the lens sees the image, of AB at ab, erect, virtual, and diminished. 569. Discussion of formulae. — i. Convex lens. — In the case of a convex lens,y"is negative, and the formula connecting^ and/' is Fig. 549 I I -)-"*"fh--f\ J p~ p -569] Discussion of Formula 5^3 If p is infinite, Z = o and p' = -/; that is, the refracted rays intersect at the P principal focus on the negative side. \ip = if,p'=-lf; hence, if the object is placed at a distance from the lens equal to twice the focal length, the image is the same distance on the other side. Also, since s>55^fii^Mii|l££E.) = magnification = ^, size of object (Imear) p it follows that the image is in this case the same size as the object, or the magnification is unity. If ^ > 2/, /' < 2/, and the image is diminished. If p>fa.-nA <7f, p' is between —2/ and negative infinity, i.e. there is magnifi- cation. When/ =7^ p' = cxz, the emergent rays being parallel. When p 0,>=(^^-:)(-l^i)=-(.^-:)(i-i); in the last case s>r, and therefore for all convex lenses y is negative. Similarly for the concave lenses P, Q, R,/is positive. 570. Spherical aberration. Caustics. — In speaking about foci, and about the images formed by different kinds of spherical lenses, it has been hitherto assumed that the rays emitted from a single point intersect also after refraction in a single point. This is virtually the case with a lens whose aperture — that is, the angle obtained by joining the edges to the principal focus — does not exceed 10^ or 12°. Where, however, the aperture is larger, the rays which traverse the lens near the edge are refracted to a point F (fig. 550) nearer the lens than the point G, which is the focus of the rays which pass near the axis. The phenomenon thus produced is named spherical aberration by refraction ; it is analogous to the spherical aberration produced by reflection (542). The luminous sur- faces formed by the intersection of the refracted rays are termed caustics by refraction. Spherical aberration is prejudicial to the sharpness and definition of an image. If the image of an obiect produced by a convex lens is received on a ground - glass screen, and is sharply defined in the centre, it will be indistinct at the edges ; and, vice versa., if the image is sharp at the edges, it will be indistinct in the centre. This defect is very objection- able, more especi- ally in lenses used for photography. It is partially obviated by placing in front of the lenses diaphragms provided with a central aperture called stops, which admit the rays passing near the centre, but cut off those which pass near the edges. The image thereby becomes sharper and more distinct, though the illumina- tion is less. If a screen be held between the light and double convex lens, which quite covers the lens, but has two concentric series of holes, two images are obtained, and may be received on a sheet of paper. By closing one or the other series of holes by a flat paper ring, it can be easily ascertained which image arises from the central, and which from the marginal rays. When the paper is at a small distance the marginal rays produce the image Fig- 550 -672] Determination of Focal Length of a Lens 565 in a point, and the central ones in a ring ; the former are converged to a point, and the latter not. At a somewhat greater distance the marginal rays produce a ring, and the central ones a point. It is thus shown that the focus of the marginal rays is nearer the lens than that of the central rays. Spherical aberration is diminished by substituting for a lens of short focus two lenses of double focal length, which are placed at a little distance apart. Greater length of focus has the result that for the same diameter the aperture and also the aberration are less ; and as it is not necessary to stop a great part of the lens there is a gain in luminosity, which is not purchased by indistinctness of the images, while the combination of the two lenses has the same focus as that of the single lens (571). Lenses which are free from spherical aberration are called aplanatic. 571. Combination of lenses. — If parallel rays fall on a convex or concave lens A, which has the focal length _/J and then on a lens B, convex or concave, with the focal distance _/', at a distance d from A, and the distance from the lens B at which the image is formed is F ; then F / /W If the lenses are close together, so that d=o, Y f f I 2 If the lenses have the same curvature, that is f=f , then - = _ ; that is to say, the focal length of the combination is half that of the single lenses. If A is convex and B concave,/ is negative and/' positive. Hence F f' f ff ' thus, as the focal length of the convex lens is greater or less than that of the concave, the combination is concave or convex. By the aid of this formula we can determine the focal length of a concave lens by combining with it a convex lens of such convexity that the combination is convex. The reciprocal of the focal length is called the power of the lens. The power of a combination of two lenses in contact is the sum of the powers of the separate lenses. 572. Determination of the focal length of a lens, and of the refractive index of its material. — i. Convex lens. — ia) Let the lens be exposed to the sun's rays so that they are parallel to its axis. The emergent penqil being received on a ground-glass screen, the point to which the rays converge is readily seen ; it is the principal focus. A stop should be used to cut off all rays except those near the centre. ib) If a luminous object, such as a candle or gas flame, be placed on one side the lens, and a screen on the other, and the screen be moved until a sharp image of the object is formed on it, the focal length may be deter- mined from the formula — — — = -j. If we consider/, /', and/ to be all p p J positive quantities, we must change the signs of/' and /; thus the formula becomes — + -,7 = -,, where now /, p\ and / are mere numerical lengths p p J S66 On Light [572- without regard to the direction in which they are drawn. When / and^' are measured, the value of /"is at once deduced. {c) In the last arrangement we may alter the relative positions of lens and screen so that the object and image are the same size ; each is then distant 2/ from the lens, or, to obtain f, we may divide distance between object and image by 4. {d) Another method is to place on one side of the lens, and a little beyond its principal focus, a brightly illuminated scale, which is best of glass, on which a strong light falls ; on the other side a screen is placed at such a distance as to produce a greatly magnified distinct image of the scale. Then if I and L are the lengths of the scale and its image respectively, and d the distance of the screen from the lens, ii. Concave lens. — We have already (571) indicated a method by which the focal length of a concave lens may be found. It depends upon our Fig- 551 being able to employ, in contact with the concave lens, a convex lens of sufficient power to render the combination convex. The focal lengths of the single convex lens and of the combination are determined by one of the methods given above, and that of the concave lens deduced from the formula i^_' + -. If/, and F refer to the convex lens and to the combination respectively, each must have the negative sign prefixed ; whence /. I 7," I F XF' and this is positive since F >/j iii. Refractive index. — We can measure the curvatures of the two faces of a lens by a small spherometer (11), and its focal length by one of the above -573] Laryngoscope 567 methods. The formula _=(«-i) (_ — ) then enables us to find «, the / \r s/ refractive index of the glass. 573. Laryngoscope.— As an application of lenses may be adduced the laryngoscope, which is an instrument invented to facilitate the investigation of the larynx and other cavities of the mouth. It consists of a plano- convex lens L, and a concave reflector M, both fixed to a ring which can be adjusted to any convenient lamp (fig. 551). The flame of a lamp is in the principal focus of the lens, and at the same time is at the centre of curvature of the reflector. Hence the divergent pencil proceeding from the lamp to the lens is changed after emerging into a parallel pencil. Moreover, the pencil from the lamp, impinging upon the mirror, is reflected to the focus of the lens, and traverses the lens, forming a second parallel pencil which is superposed on the first. This being directed into the mouth of a patient, its condition may be readily observed. S68 On Light [574- CHAPTER IV DISPERSION AND ACHROMATISM 574. Decomposition of white light. Solar spectrum. — The phenomenon of refraction is by no means so simple as we have hitherto assumed. When white light, or that which reaches us from the sun, passes from one medium into another, it is decomposed into several kinds of light, a phenomenon to which the name dispersion is given. In order to show that white light is decomposed by refraction, a pencil of the sun's rays, SA (fig. 552), is allowed to pass through a small aperture in the window shutter of a dark chamber, as in Newton's original experiment. This pencil tends to form an oval and colourless image of the sun at K ; but if a flint-glass prism arranged horizontally be interposed in its path, the beam, on emerging from the prism, be comes refracted to- wards its base, and produces on a distant screen a vertical band rounded at the ends, coloured in all the tints of the rainbow, which is called the solm spectrum (see Plate I.). In this spectrum there is, in reality, an infinity of different tints, which Fig. 552 imperceptibly merge into each other, but it is customary to distinguish seven principal colours. These are violet, indigo, blue, green, yellow, orange, red ; they are arranged in this order in the spectrum, the violet being the most refrangible, and the red the least so. They do not all occupy an equal extent in the spectrum, violet having the greatest extent, and orange the least. 575. The colours of the spectrum are simple, and unequally refrangible. — If one of the colours of the spectrum be isolated by intercepting the others by means of a screen E, as shown in fig. 553, and if the light thus isolated be allowed to pass through a second prism, B, a refraction will be observed, but the light remains unchanged ; that is, the image received on the screen H is violet if the violet pencil has been allowed to pass, blue if the blue -576] The Colours of the Spectrum S69 pencil, and so on. Hence the colours of the spectrum are simple \ that is, they cannot be further decomposed by the prism. Moreover, the colours of the spectrum are unequally refrangible ; that is, the glass of the prism possesses a dif- ferent refractive index for each of the rays of which white light is composed. The elon- gated shape of the spectrum would be sufficient to prove the p; unequal refrangibility of the simple colours, for it is clear that the violet, which is most deflected towards the base of the prism, is also most refrangible ; and that red, which is least deflected, is least refrangible. But the unequal refrangibility of simple colours may be shown by numerous experiments, of which the two following may be adduced : — i. Two narrow strips of coloured paper, red and violet, are fastened close to each other on a sheet of black paper. On looking at them through a prism, they are seen to be unequally displaced, the red band to a less extent than the violet ; hence the red rays are less refrangible than the violet. ii. The same conclusion may be drawn from Newton's experiment with crossed prisms. On a prism A (fig. 554), in a horizontal position, a pencil of white light, S, is received, which, if it had merely traversed the ' prism A, would form the spectrum rv, on a dis- tant screen But if £ secondprism B, be placec in a vertical position be- Fig. 354 hind the first, in such a manner that the refracted pencil passes through it, the spectrum rv becomes deflected towards the base of the vertical prism ; but, instead of being deflected in a direction parallel to itself, as would be the case if the colours of the spectrum were equally refracted, it is obliquely refracted in the direction r'v' , proving that from red to violet the colours aramore and more refrangible. These different experiments show that the refractive index differs in dif- ferent colours ; even rays which are to perception indistinguishable may differ S70 On Light [575- in refrangibility. In the red band, for instance, the rays at the extremity of the spectrum are less refracted than those which are nearer the orange zone. 576. Production of a pure solar spectrum. — In the above experiment the spectrum formed is built up of a series of overlapping coloured images of the sun, and the colours are confused and indistinct. In order to obtain a pure spectrum, the slit, in the shutter of the dark room through which light enters, should be of rectangular form, from 15 to 25 mm. in height and from i to 2 mm. in breadth. The sun's rays are directed upon the slit by a mirror, or still better by a heliostat (543). An achromatic double convex lens is placed at a distance from the slit of double its own focal length, which should be about a metre, and a screen is placed at the same distance from the lens. An image of the slit of exactly the same size is thus formed on the screen (569). If now there is placed near the lens, between it and the screen, a prism with an angle of about 60°, and with its refracting edge parallel to the slit, a very beautiful, sharp, and pure spectrum is formed on the screen. The prism should be placed so that it produces the minimum deviation for the mean rays. 577. Dispersive power. — With transparent prisms of different substances, or with hollow glass prisms filled with various colourless liquids, spectra are obtained formed of the same colours, and in the same order ; but when the deviation produced is the same, the length of the spectrum varies with the substance of which the prism is made. The angle of separation of two selected rays (say in the red and the violet) produced by a prism is called the dispersion, and the ratio of this angle to the mean deviation of the two rays is called the dispersive power. This ratio is constant for the same substance so long as the refracting angle of the prism is small. For the deviation of the two rays is proportional to the refracting angle ; their difference and their mean vary in the same manner, and therefore the ratio of their difference to their mean is constant. The spectra which are formed by artificial lights rarely contain all the colours of the solar spectrum ; but their colours are found in the solar spectrum, and in the same order. Their relative intensity is also modified. The shade of colour which predominates in the flame predominates also in the spectrum ; yellow, red, and green flames produce spectra in which the dominant tint is yellow, red, or green. A - A + ^ The formula for a prism, ;? sin — = sin (558), may, if A be small enough, be written n ^= — i-, or Aqueous humour . . I '3365 Vitreous humour . . . . 1'3365 Cornea . . . 13365 External coating of the lens i "3930 Centre of the lens . . i'454i Mean refraction of the lens . . . ''437' From this it will be noticed that the refractive indices of all the media excepting the lens are the same. 627. Curvatures and dimensions of various parts of the human eye. — According to the latest tables of Von Helmholtz (188S), these are : — min. Radius of curvature of the cornea . . . 7-83 „ „ anterior surface of the crystalline . . icoo „ „ posterior surface „ „ . 6'oo Distance from apex of the cornea to the anterior surface of the lens . 3-60 „ „ „ posterior „ „ . 7-20 Thickness of the crystalline lens . . . . 3-60 628. Path of rays in the eye. — From what has been said as to the structure of the eye, it may be^^compared to a camera obscura (614), of which A Fig. 622 the pupil is the aperture, the crystalline is the condensing lens, and the retina is the screen on which the image is formed. Hence the effect is the same as when the image of an object placed in front of a double convex lens is formed at its conjugate focus. Let |AB (fig. 622) be an object placed -630] Optic Axis, Optic Angle, Visual Angle 627 before the eye, and let us consider the rays emitted from any point of the object A. Of all these rays, those which are directed towards the pupil are the only ones which penetrate the eye, and are operative in producing vision. These rays, on passing into the cornea, experience a first refraction which brings them near the secondary axis A« drawn through the optic centre of the crystalline ; they then traverse the crystalline, which again refracts them like a double convex lens, and, having experienced a final refraction by the vitreous humour, they meet in a point a, and form the image of the point A. The rays issuing from the point B form in like manner an image of it at the point b, so that a very small real and inverted image is formed exactly on the retina, provided the eye is in its normal condition. 629. Inversion of images. — In order to show that the images formed on the retina are really inverted, the eye of an albino or any animal with pink eyes may be taken ; this has the advantage that, as the choroid is destitute of pigment, Hght can traverse it without loss. This is then deprived at its posterior part of the cellular tissue surrounding it, and fixed in a hole in the shutter of a dark room ; by means of a lens it may be seen that the inverted images of external objects are depicted on the retina. The inversion of images in the eye has greatly occupied both physicists and physiologists, and many theories have been proposed to explain how it is that we do not see inverted images of objects. The chief difficulty seems to have arisen from the conception of the mind or brain as something behind the eye, looking into it, and seeing the image upon the retina ; whereas really this image simply causes a stimulation of the optic nerve, which produces some molecular change in some part of the brain ; and it is only of this change, and not of the image as such, that we have any conscious- ness. The mind has thus no direct cognisance of the image upon the retina, or of the relative positions of its parts, and, sight being supplemented by touch in innumerable cases, it learns from the first to associate the sensations brought about by the stimulation of the retina (although due to an inverted image) with the correct position of the object as taught by touch. 630. Optic axis, optic angle, visual angle. — The principal optic axis of an eye is the axis of its figure ; that is to say, the straight line in reference to Fig. 623 which it is symmetrical. In a well-shaped eye it is the straight line passing through the centre of the pupil and of the crystalline. The lines ka, B6 (fig. 622) are secondary axes. The eye sees objects most distinctly in the direction of the principal optic axis, since rays of light following this direc- tion impinge upon the yellow spot where vision is most acute. s s 2 628 On Light [630- The optic angle is the angle BAC (fig. 623) formed between the prin- cipal optic axis of the two eyes when they are directed towards the same point. This angle is smaller in proportion as the objects are more distant. The visttal angle is the angle AOB (fig. 624) under which an object is seen ; that is to sayj the angle formed by the secondary axes drawn from the optic centre of the crys- talline to the oppo- site extremities of the object. For the same distance, this angle increases with the magnitude of the object,, and for the same object it decreases as the distance increases, as is the case when the object passes from AB to A'B'. It follows, therefore, that objects appear smaller in proportion as they are more distant ; for as the secondary axes AO, BO, cross in the centre of the crystalline, the size of the image projected on the retina depends on the size of the visual angle AOB. 631. Estimation of the distance and size of objects. — The estimation of distance and of size depends on numerous circumstances : these are the visual angle, the optic angle, the comparison with objects whose size is familiar to us. To these must be added the effect of what is called aerial perspective ; that is, a more or less vaporous medium which enshrouds the distant objects, and thereby not only diminishes the sharpness of the out- lines, but also softens the contrast .between light and shade, which close at hand are marked. When the size of an object is known, as the figure of a man, the height of a tree or of a house, the distance is estimated by the magnitude of the visual angle under which it is seen. If its size is unknown, it is judged relatively to that of objects which surround it. A colonnade, an avenue of trees, the gas-lights on the side of a road, appear to diminish in size in proportion as their distance increases, because the visual angle decreases ; but the habit of seeing the columns, trees, &c., in their proper height, leads our judgment to rectify the impression produced by vision. Similarly, although distant mountains are seen under a very small angle, and occupy but a small space in the field of view, our familiarity with the effects of aerial perspective enables us to form a correct idea of their real magnitude. As regards the estimation of near objects, the muscular senses of accom- modation (634) and convergence (635) play a very important part. Thus it is well known that people who lose the sight of one eye experience great difficulty in estimating the distance of objects near at hand. This any one can prove for himself by covering up one of his eyes, and then attempting to thread a needle. The explanation of this difficulty is very simple. When one eye is destroyed or covered up, then owing to the absence of binocular vision there is no optic angle, and therefore convergence ceases to be called into play. Now the two chief guides for estimating the distance of near objects are the stereoscopic relief of objects due to binocular vision, and -632] Schemer's Experiment 629 the muscular sense of convergence. When only one eye is used both these factors are wanting. Nevertheless, it is only by long custom that we can establish a relation between our distance from the objects and the corre- sponding motion of the eyes. It is a curious fact that persons born blind, whose sight has been restored by the operation for cataract, imagine at first that all objects are at the same distance away. Vertical distances are estimated too low compared with horizontal ones ; on high mountains and over large surfaces of water, distances are estimated too low owing to the want of intervening objects. Practice and experience have great influence on our correct estimation of magnitude and distance. As we ascend mountains much less frequently than we walk on the level, we err more easily in estimating a height than in judging a horizontal distance. A room filled with furniture appears larger than an empty room of the same size. We cannot recognise the true form of an object if, with moderate illu- mination, the visual angle is less than half a minute. A white square, a metre in the side, appears at a distance of about five miles under this angle as a bright spot which can scarcely be distinguished from a circle of the same size. A very bright object, however, such as an incandescent platinum wire, is seen in a dark ground under an angle of 2 seconds. So, too, a small dark object is seen against a bright grovmd ; thus a hair held against the sky can be seen at a distance of i or 2 metres. 632. Scheiner's experiment. — If we look at a small object placed either within or beyond the point on which the eye is focused, through a number of minute openings in a diaphragm, arranged so close together that they fall within the circumference of the pupil, the object appears multiple, each object furnishing a separate retinal image. This forms what is known as Scheiner's experiment. It may be made as follows : By means of a sewing needle, two small holes are pricked in a piece of cardboard, not more than jJg of an inch apart, i.e. less than the diameter of the pupil. The card is held before one eye with the holes horizontally in front of the pupil, and with the other hand a needle is held at ordinary reading distance in the line of vision. If the eye is fixed on the needle itself, it appears single and clearly defined ; as soon, however, as we look at a more distant object, the needle appears double, and at the same time blurred. If we block out the right-hand hole, the left-hand image disappears, and vice versa. If we now fix the eye on an object nearer than the needle, the latter again appears double and blurred, and blocking either hole causes the image on the same side to vanish. The explanation of these phenomena may be simplified by the following diagram. Let AB (fig. 625) be the two holes in the card CC, O a luminous point in the needle, OA, OB the pencils of rays passing through the apertures in the card. Let H, E, M represent the position of a hypermetropic, normal, and myopic eye respectively. When the normal eye E is accommodated for O, the rays OA, OB meet at the point E, and the needle appears sharply defined and single. If the eye is fixed on a point beyond, or, what amounts to the same thing, if the eye is hypermetropic, the retina may be considered to lie no longer at E, but in front at H, and the rays OA/ not only do not 630 On Light [632- Fig, 62, meet in a focus at p, but do not meet the rays OB/' ; hence the luminous spot O will be seen at two points, and the points themselves being out of focus will appear blurred. More- over, the rays passing through the right-hand hole A will cut the retina at /, and will appear to the mind on the i-everse side, i.e. on the left ; therefore block- ing the right- hand hole A causes a disappearance of the left-hand image, and vice versa. For similar treasons, if the eye is accommodated for a point nearer the eye than O, or, what amounts to the same thing, if the eye is myopic, the retina may be considered to lie behind E at M, and the image will again be seen doubled and blurred ; only in this case blocking out the right-hand hole A will cause the right-hand image to disappear. Stampfer constructed an optometer based on this principle. He employed a tube containing two diaphragms, one furnished with two slits i mm. apart, the other with a single slit covered with ground glass. The diaphragm is moved to or from the eye until the slit is seen single. This distance from the eye is the measure of distinct vision. 633. Distance of distinct vision. — The distance of distinct vision., as already stated (598), is the distance at which objects must be placed so as to be seen with the greatest distinctness. It varies in different individuals, and in the same individual it is often different in the two eyes. For small objects such as print, it is from 10 to 12 inches in normal cases. Persons who see objects distinctly only at a very short distance away are called tnyopic, or short-sighted, and those who see objects distinctly at a long distance are hypermetropic, or long-sighted (643). Sharp7iess of sight may be compared by reference to that of a normal eye taken as a unit. Such a standard eye, according to Snellen, recognises quadrangular letters when they are seen under an angle of 6' ; if, for instance, such letters are i cm. high at a distance of 6 metres. The sharpness of vision of one who recognises these letters at a distance of 6 metres is then said to be — , and in like manner, if the letters can only be distinctly seen when they subtend an angle of 9', 12', or 18', the sharpness of vision would be indicated by the equation V = _, , and respectively. 634. Accommodation. — By this term are meant the changes which occur in the eye to fit it for seeing distinctly objects at different distances from it. If the eye be supposed fixed and its parts immovable, it is evident that there could only be one surface whose image would fall exactly upon the retina ; the one distance at which objects could be distinctly seen being -634] Accommodation 63 1 dependent on the refractive indices of the media and the curvatures of the refractive surfaces of the eye. The image of any point nearer the eye than this distance would fall behind the retina ; the image of any more distant point would be formed in front of it. Experience, however, shows us that a normal eye can see distinct images of objects at very different distances. We can, for example, see a distant tree through a window, and also a scratch on the pane, though not both dis- tinctly at the same moment ; for when the eye is arranged to see one clearly, the image of the other does not fall accurately upon the retina. An eye completely at rest seems adapted for seeing distant objects ; the sense of effort is greater in a normal eye when a near object is looked at, after a distant one, than in the reverse case ; and in paralysis of the nerves govern- ing the accommodating apparatus, the eye is persistently adapted for distant sight. There must, therefore, be some mechanism in the eye by which it can be voluntarily altered, so that the more divergent rays proceeding from near objects shall come to a focus upon the retina. There are several con- ceivable methods by which this might be effected ; it is actually brought about by a drawing forwards of the crystalline lens and a greater convexity of its front surface. This is shown by the following experiment : — If a candle is placed on one side of the eye of a person looking at a distant object, and his eye is observed frbm the other side, three distinct images of the flame will be seen : the first, virtual and erect, is reflected from the anterior surface of the cornea ; the next, erect and less bright, is reflected from the anterior surface of the lens ; the third, inverted and brilliant, is due to the posterior surface of the lens. If now the person looks at a near object, no change is observed in the first and third images, but the second image becomes smaller and approaches the first ; which shows that the anterior surface of the crystalline lens becomes more convex and approaches the cornea. In place of the candle, Von Helmholtz throws light through two holes in the screen upon the eye, and observes the distance on the eye between the two shining points, instead of the size of the flame of the candle. This change in the lens is effected chiefly by means of a circular muscle (ciliary muscle), the contraction of which relaxes the suspensory ligament, and so allows the front surface of the lens to assume more or less of that greater convexity which it would normally exhibit were it not for the drag exercised upon it by the ligament. Certain other less important changes occur, tending to make the lens more convex and to push it forwards, which cannot, however, be explained without entering into minute anatomical details. When the eye is accommodated for near vision, the pupil contracts and so partially remedies the greater spherical aberration. The range of accommodation, called by Donders _, is measured by first of all determining the greatest distance, R, at which a person can see dis- tinctly. In this case the ciliary muscle is in a state of rest, that is, the accommodation is relaxed to the utmost. The shortest distance, P, is observed at which the person can see distinctly. In this case the ciliary muscle is contracted to its utmost power, that is, the accommodation has arrived at its maximum. The total accommodation power which an eye can bring into 632 On Light [634- play is therefore represented by the difference between the refraction of the eye when at rest, and when it is at the maximum effort of accommodation ; then III Here each of the three terms represents a lens expressed by the inverse of its focal distance. By the dioptric method (644) this formula is simplified, and becomes where a is the number of diopters represented by the range of accommoda- tion ; /= the number represented by the eye when accommodated to its maximum, and r= the number of diopters when relaxed to see th&pttnctum remotum ; in other words, a is the difference between the powers of the eye when viewing near and distant objects. 635. Binocular vision. — A single eye sees most distinctly any point situated on its optical axis, and less distinctly other points also, towards which it is not directly looking, but which are still within its circle of vision. It is able to judge of the direction of any such point, but unable by itself to estimate its distance. Of the distance of an object it may, indeed, learn to judge by such criteria as loss of colour, indistinctness of outline, decrease in magnitude, &c. ; but if the object is near, the single eye is not infallible, even with these aids. When the two eyes are directed upon a single point, we then gain the power of judging of its distance as compared with that of any other point, and this we seem to gain by the sense of greater or less effort required in causing the optical axes to converge upon the one point or upon the other. Now a solid object may be regarded as composed of points which are at different distances from the eye. Hence, in looking at such an object, the axes of the two eyes are rapidly and insensibly varying their angle of con- vergence, and we as rapidly are gaining experience of the difference in distance of the various points of which the object is composed, or, in other words, an assurance of its solidity. Such kind of assurance is necessarily unattainable in monocular vision. 636. The principle of the stereoscope. — Let any solid object, such as a small box, be supposed to be held at some short distance in front of the two eyes. On what- ever point of it they are fixed, they will see that point the most distinctly, and other points more or less clearly. But it is evident that, as the two eyes see from different points of view, there will be formed in the right eye a picture of the object different from that formed in the left ; and it is by the apparent union of these two dissimilar pictures that we see the object -637] The Reflecting Stereoscope 633 Fig. 627 in relief. If, therefore, we delineate the object, first as seen by the right eye, and then as seen by the left, and afterwards present these dissimilar pictures again to the eyes, taking care to present to each eye that picture which was drawn from its own point of view, there would seem to be no reason why we should not see a representation of the object,, as we saw the object itself, in relief. Experiment confirms the supposi- tion. If the object held before the eyes were a truncated pyramid, r and / (fig. 626) would repre- sent its principal lines, as seen by the right and left eyes respectively. If a card is held between the figures, and they are steadily looked at, r by the right eye, and / simultaneously by the left, for a few seconds, there Avill be seen a single picture having the unmistakable appearance of relief. Even without a card interposed, the eye, by a little prac- tice, may soon be taught so to combine the two as to form this solid picture. Three pictures will in that case be seen, the central one being solid, and the two outside ones plane. Fig. 627 will explain this. Let r and / be any two corresponding points, say the points marked by a large dot in the figures drawn above ; R and L the positions of the right and left eyes ; then the right eye sees the point r in the direction Ro, and the left eye the point / in the direction Lo, and accordingly each by itself judging only by the direc- tion, they together see these two points as one, and imagine it to be situated at 0. But the right eye, though looking in the direction Rr, also receives an image of / on another part of the retina, and the left eye in the same way an image of r, and thus three images are seen. A card, however, placed in the position marked by the dotted line will, of course, cut off the two side pictures. To assist the eye in combining such pairs of dissimilar pictures, both mirrors and lenses have been made use of, and the instruments in which either of these are adapted to this end are called stereoscopes. 637. The reflecting stereoscope. — In the reflecting stereoscope plane mirrors are used to change the apparent position of the pictures, so that they are both seen in the same direction, and their combination by the eye is thus rendered easy and almost inevi- table. If ab, ab (fig. 628) are two plane mirrors inclined to each other at an angle of 90°, the two arrows, x,y, would both be seen by the eyes situ- ated at R and L in the position marked by the dotted arrow. If, instead of the arrows, we now substitute such a pair of dissimilar pictures as we have spoken of above, of the same solid object, it is evident that, if the margins of the pictures coincide, other corre- sponding points of the pictures will not. <- a' I. B. Fig. 628 The eyes, however, almost without effort, soon bring such points into coincidence, and in so doing make them 634 On Light [637- ■ la H Fig. 629 appear to recede or ad\-ance, as they are farther apart or nearer together than any two corresponding points (tlie right-hand corner, for instance) of the ^. margins when the pictures are placed side by side, as in the diagram, fig. 628. It will be plain, also, on considering the position for the arrows in fig. 628, that to adapt such figures as those in fig. 627 for use in a reflecting stereoscope one of them must be re- versed, or drawn as it would be seen through the paper if held up to the light. 638. The refracting stereoscope. — Since the rays passing through a convex lens are bent always towards the thicker part of the lens, any segment of such a lens may be readily adapted to change the apparent position of any object seen through it. Thus, if (fig. 629) two segments be cut from a double convex lens, and placed with their edges together, the arrows, x, y, would both be seen in the position of the dotted arrow by the eyes at R and L. If we substitute for the arrows two dissimilar pictures of the same solid object, or the same landscape, we shall then, if a diaphragm, ai, be placed between the lenses to prevent the pictures being seen crosswise by the eyes, see but one picture, and that apparently in the centre, and magnified. As before, if the margins are brought by the power of the lenses to coincide, other corresponding points will not be coincident until combined by an almost insensible effort of the eyes. Any pair of corresponding points which are farther apart than any other pair will then be seen farther back in the picture, just as any point in the background of a landscape would be found (if we came to compare two pictures of the landscape, one drawn by the right eye, and the other by the left) to be represented by two points farther apart from each other than two others which represented a point in the foreground. It will be instructive to notice that there is also a second point on Ms side of the paper, at which if a person look steadily, the diagrams in fig. 630 will combine, and form quite a different stereoscopic pic- ture. Instead of a solid pyramid, a hollow pyramidal box will then be seen. The point may easily be found by experiment. Here again two external images will also be seen. If we wish to shut these out, and see only their central stereoscopic combination, we must use a diaphragm of paper held parallel to the plane of the picture with a square hole in it. This paper screen must be so adjusted that it may conceal the right-hand figure from the left eye, and the left-hand figure from the right eye, while the central stereoscopic picture may be seen through the hole. It will be plain from the diagram (fig. 630) that o is the point to which the eyes must be directed, and at which they will imagine the point to be situated, which is formed by the combination of the two points r and /. The dotted line shows the posi- tion of the screen. A stereoscope with or without lenses may easily be Fig. 630 -639] Persistence of Impressions on the Retina 635 constructed, which will thus give us, with the ordinary stereoscopic slides, a reversed picture ; for instance, if the subject be a landscape, the foreground will retire and the background come forward. When the two retinas view simultaneously two different colours, the im- pression produced is that of a single mixed tint. The power, however, of combining the two tints into a . single one varies in different individuals, and in some is extremely weak. If two white discs at the base of the stereo- scope be illuminated by two pencils of complementary colours, and if each coloured disc be looked at with one eye, a single white one is seen, showing that the sensation of white light may arise from two complementary and simultaneous chromatic impressions on each of the two retinas. Dove found that if a piece of printing and a copy are viewed in the stereo- scope, a difference in the distance of the words, which is not apparent to the naked eye, causes them to stand out from the plane of the paper. 639. Persistence of impressions on the retina. — When an ignited piece of charcoal is rapidly rotated, we cannot distinguish it ; the appearance of a circle of fire is produced ; similarly, rain, in falling di'ops, appears in the air like a series of liquid threads. In a rapidly rotating toothed wheel the individual teeth cannot be seen. But if, during darkness, the wheel be suddenly illuminated, as by the electric spark, the individual parts may be clearly made out. The following experiment is a further illustration of this property : — A series of equal sectors are traced on a disc of glass, and they are alternately blackened ; in the centre there is a pivot, on which a second disc is fixed of the same dimensions as the first, but completely blackened with the exception of a single sector ; then placing the apparatus between a window and the eye, the second disc is made to rotate. If the movement is slow, all the transparent sectors are seen, but only one at a time ; by a more rapid rotation we see simultaneously two, three, or a greater number. These various appearances are due to the fact that the impression of these images on the retina remains for some time after the object which has produced them has disappeared or become displaced. The duration of the persistence varies with the sensiti\'eness of the retina and the intensity of light. Plateau investigated the duration of the impression by numerous similar methods, and has found that it is, on the average, half a second. Among many curious instances of these phenomena, the following is one of the most remarkable. If, after having looked at a brightly illuminated window, the eyes are suddenly closed, the image remains for a few instants — that is, a sashwork is seen consisting of luminous panes surrounded by dark frames ; after a few seconds the colours become interchanged, the same framework is now seen, but the frames are now bright, and the glasses are perfectly black ; this new appearance may again revert to the former one. The impression of colours remains as well as that of the form of objects ; for if circles divided into sectors are painted in different colours, they become confounded, and give the sensation of the colour which would result from their mixture. Yellow and red give orange ; blue and red violet ; the seven colours of the spectrum give white, as shown in Newton's disc (fig. 559). This is a convenient method of studying the tints produced by mixed colours. A great number of pieces of apparatus are founded on the persistence 636 On Light [639- of sensation on the retina ; such are the thaumatrope, the phenakistoscope^ Faradafs wheel, the kaleidophone, and the zoetrope. The zoetrope, or wheel of life, is very convenient for representing a number of vibratory motions. It consists of an open cylinder which can be rotated about its vertical axis with a number of vertical slits at the top. If the successive positions of a vibrating pendulum, for instance, are drawn on a narrow strip of paper, equal in length to the circumference, and this is placed inside the cylinder, when the wheel is rapidly rotated, we see on looking through the slits the pendulum as if it were steadily vibrating. In the kinematograph a rapid succession of photographs of moving objects are taken, and successively projected in the same order on a screen, which allows a certain fixed short time of exposure to each picture before the next picture appears. In this way the most interesting and varied phenomena are vividly reproduced with lifelike accuracy. 6401 Accidental images. — When a coloured object placed upon a black ground is steadily looked at for some time, the eye is soon tired, and the intensity of the colour is enfeebled ; if now the eyes are directed towards . D = — and F = — . Hence, to find the number- of diopters which represent the focal length in inches, we must divide 39'37 by that focal distance, and, conversely, to find the number of inches correspond- ing to a given number of diopters, we have only to divide 39'37 by this latter. In choosing spectacles it is necessary in practice to adapt them to the special requirements of a patient rather than to correct the absolute error of refraction of the eye. The following rules, therefore, only represent the theoretical values necessary to correct the error of refraction (ametropia) present for seeing near or distant objects. In myopia the defect is measured by the distance of the farthest point of distinct vision firom the eye {pimctum remotuvi) (F, fig, 633). Thus, if the punctum remotum (p.r.) be situated at 50 cm., the myopia equals J^, or 2 di- opters, and we correct it by a concave lens having a power = — 2D, or a focal +B Fig. 633 length = 50 cm. For if a concave lens be placed in front of the eye, parallel rays will enter the eye as if they came from the focus of the lens, i.e. from the punctum remotum. But all rays from the p.r. meet on the retina, and the eifect of the —2D lens is to cause rays proceeding from infinity to diverge after passing through the lens as if they came from the p.r. — in other words, distant objects will appear sharply defined on the retina. A concave pair of spectacles will, therefore, be the proper correction to order. In high myopia the distance between the spectacles and the eye must be taken into account. Let the distance of the p.r. from the eye be 100 mm. = -VW-D, or loD, and let the spectacle glass be placed 13 mm. in front of the eye — the correcting glass will need to have a focal length of 100—13 = 87 mm., i.e. a power of -'■§^1^, or ii-5D. A concave lens of 11-50 will therefore be necessary to correct a myopia of loD. In hypermetropia the whole case is reversed. The retina being situated -646] Achromatopsy 641 in front of the focus, it would be necessary, in order that the image should fall on the retina, that the parallel incident rays coming from infinity should be made to converge by means of a convex lens, for convergent rays do not exist in nature. The punctum remotum in this case is therefore negative, i.e. it is situated behind the retina (F, fig. 634). The defect is, therefore, measured by a convex lens whose focus coincides with the punctum remotum. Parallel Fig. 634 rays proceeding from infinity will then enter the eye as if they came along the path of rays which converge to the p.r. — -in other words, distant objects will appear sharply defined on the retina. Suppose the p.r. be situated 125 mm. behind the eye, the hypermetropia = Aifyy-, i.e. 8D, and a lens of that refractive power will correct the error. But as the spectacles are placed about 13 mm. in front of the eye, the correcting lens will need to have a focal length of 125 + 13=138 mm., or about 7D. In lower degrees of hypermetropia the distance of the lens from the eye may be disregarded. 645. Diplopia. — Diplopia is an affection of the eye which causes objects to be seen double ; that is, that two images are seen instead of one. Usually the two images are almost entirely superposed, and one of them is much more distinct than the other. Diplopia is usually due to a want of power in one or more of the ocular muscles, but it may be due to the prismatic action of badly centred spectacles. 646. Achromatopsy. — Achromatopsy., or colour blindness, is a curious defect of vision which shows itself in the inability to distinguish between certain colours which, to persons not so affected, are quite dissimilar. In other respects their vision may be quite normal. Four forms of colour blindness have been described, viz. red blindness, greeji blindness, violet blindness, and total colotir blindness. By far the commonest form of this defect is that of red blindness. Dalton suffered from this defect, and from the fact that he very carefully described it the defect has been called Daltonism. Persons so affected are unable to distinguish between certain shades of red and green, being blind for two particular groups of hues which are complementary. Green or bluish green and red colours to them vary only in shade, but not in colour. Thus red cherries on a green tree are distinguishable only by their form and shade. If such a person be examined with the spectroscope the red end is found to be more or less shortened, and the whole spectrum appears to consist of two distinct colours only, yellow and blue. In many cases the two colours are separated by a neutral band of greyish colour. Blue yellow blindness, or violet blindness, as it is called by some, is an exceedingly rare phenomenon. It is characterised by the inability to T T 642 On Light [646- distinguish blue and its shades, from yellow, but red and green, with all their shades, are clearly defined. In this form the spectrum is shortened at the violet end. Green blindness has also been described, but as in colour blind- ness the complementary colours are always defective, it is difficult to dis- tinguish such cases from red bhndness, and what appears to be green blind- ness by one test may be considered to be red blindness by another. Total colour blindness. — Lastly, cases have been occasionally met with in which all sensation of colour is absent, the spectrum appearing to such persons as a greyish band of varying brightness. In such cases the vision will be somewhat impaired as well. Colour blindness occurs chiefly in the male sex. It is usually congenital, and is found to affect from 3 to 4 per cent, of the community. When acquired it is almost always due to disease. Owing to the danger which may arise from the faulty observation of coloured signals on railways and at sea, numerous methods have been proposed for the qualitative and quantita- tive observation of the colour sense. The best test for ordinary use is to give the patient a standard skein of wool of a particular tint, green, rose, or red, and to require him to match it with others which appear to him of the same tint, among a large bundle of skeins of many colours. Coloured glasses which can be rotated in front of a lantern to imitate railway signals are also largely used for this purpose. 647. Ophthalmoscope. — This instrument, as its name indicates, is de- signed for the examination of the eye, and was invented in 185 1 by Von Helmholtz. It consists : — i. Of a concave spherical reflector of glass or metal, M (figs. 635, 636), in the middle of which is a small hole about a sixth of an inch in diameter. The focal length of the reflector is from 8 to 10 inches. 2. Of a converging lens, 0, which is held in front of the eye of the patient. To make use of the ophthalmoscope, the patient is placed in a dark room, and a lamp put beside him, E. The screen serves to shade the light from his head, and keep it in dark- ness. The observer. A, holding in one hand the re- flector, em- ploys it to con- centrate the hght of the lamp near the ^'^- '35 eye, B, of the patient, and with his other hand holds the achromatic lens, o, in front of the eye. By this arrangement the back of the eye is lighted up, and its structure can be clearly discerned. -647] Ophthalmoscope 643 Fig, 636 shows how the image of the back of the eye is produced, which the observer, A, sees on looking through the hole in the reflector: Let db be the part of the retina on which the light is concentrated, pencils of rays proceeding from ab would form an inverted and aerial image ai ab aX a b'. These pencils, however, on leaving the eye, pass through the lens 0, tod thus the image a"b" is in fact formed, inverted, but distinct, and in a position fit for vision. Fig. 636 Modern ophthalmoscopes are now usually provided with either one or more discs of metal carrying a complete series of convex and concave lenses, or with a similar series of lenses forming a chain of discs fitted in the body of the instrument. These lenses are so arranged that the obseirver by rotating a small wheel can bring a lens of any focal length he pleases behind the aperture of the mirror. This mirror is usually of a much shorter focal length than in the instrument previously described, and is tilted at an angle so that its plane is not parallel to the lenses behind the mirror. In consequence of this, the ophthalmoscope can be held almost touching the patient's eye, while the light can still be reflected into the eye from the mirror. In this form of ophthalmoscope the lens o is dispensed with, and by placing behind the mirror the lens which corrects the sum (or difference) of the refractive errors of the patient's and the observer's eye, the observer's eye is rendered emmetropic for the pencils of light which reach it. In this case the rays of light from the lamp are reflected from the mirror directly on the back of the patient's eye, and proceeding from ab, are converged by the lens placed behind the mirror in such a manner that they form an erect image enlarged about twenty times, while in the former indirect method the image is inverted and enlarged only about four or five times. By a simple contrivance in the form of a swivel carrying the two kinds of mirrors, either can be at once rotated in front of the aperture, and thus the same instrument can be employed for both methods of e.xamination. The direct method just described affords a ready means of estimating the refraction of the patient's eye, or, in other words, of ascertaining at once the focal length of the lens necessary to enable the patient to see distant objects. To find this, all that is necessary is that the observer should previously ascertain the exact number of diopters necessary to correct his eye for distant vision, and to accustom himself to relax his accommodation to the full when using the instrument. On the patient's part this relaxation occurs insensibly. The eye of both persons being adjusted for (distant objects, the observer now looks through the aperture of the mirror, holding the instrument as close to the patient's eye as possible. Should both eyes be emmetropic (normal), the rays of light which are practically parallel would be focused on the 044 On Light [647- retiftse of both the eyes, and no correcting lens would be needed. Should the observer's eye be at fault, the lens which will correct it for parallel rays will enable him to see the details of the patient's retina. Should both eyes jrant coiTCCting, then the number of diopters which are found necessary to add to or subtract from the number which correct the observer's eye will indicate the error in the patient's eye. By thus correcting for the vessels in the retina which run in every direction, both the axis and the amount of astigmatism present may be readily ascertained. -649] Phosphorescence 645 CHAPTER VII SOURCES OF LIGHT. PHOSPHORESCENCE' 648. Various sources of light. — The various sources of light are the sun, the stars, heat, chemical combination, phosphorescence, electricity, and meteoric phenomena. The last two sources will be treated under the articles Electricity and Meteorology. The origin of the light emitted by the sun and by the stars is unknown ; the sun is the chief source ; its temperature is estimated at hundreds of thousands of degrees. The ignited envelope by which the sun is surrounded is gaseous, because the light of the sun, like that emitted from all gaseous bodies, gives no trace of polarisation in the polarising telescope, chap. viii. Terrestrial bodies become sources of light when they are raised to a sufficiently high temperature ; according to Draper all bodies begin to glow with a red heat at 525°, or according to more recent observers at aboiit 490" C. ; the light is brighter as the temperature is higher, and at 1170° a body is white-hot. The luminous effects witnessed in many chemical combinations arq due to the high temperatures produced. Ordinary luminous flames are essentially gases containing solids heated to incandescence. 649. Phosphorescence. — Certain bodies have the property of becoming luminous in the dark without any considerable rise of temperature. This phenomenon, which is well seen in phosphorus, is for this reason known as phosphorescence. Here it is undoubtedly due to a slow oxidation, for it ceases in spaces where no oxygen is present. Phosphorescence is also ex- hibited under certain conditions by decaying animal and vegeta;ble matter. This is also due to slow oxidation. Phosphorescence is observed in living animals, of which the best known case is that of the glowworm ; here it is very intense, and the, brightness seems to depend on the will. Its light consists of a continuous spectrum from C to near h, and is particularly rich in blue and green rays. In tropical climates the sea is often covered with a bright phosphorescent, light due to myriads of small luminous infusoria {Noctiluca miliaris), Langley showed that in ordinary oil or gas flames more than 99, per cent. of the total energy is expended as heat, and is lost as regards light ; and in sources at a high temperature, such as the arc and incandescent electric lights, the proportion although less is still considerable. The light of the fire- fly (Pyrophorus noctilucus), which is found abundantly in Cuba, when ex- amined by the spectroscope and bolometer is found to be devoid of red and infra-red rays, that is, to contain only luminous rays. It thus represents an 646 On Light [649- economical form of light. As the more refrangible rays are those which affect the eye, it is desirable to obtain as much energy in this form as pos- sible, and it is in this direction that improvement in artificial illumination is to be loc^ied for. At present, to use the striking comparison of Professor Lodge, we are in the position of an organist who, in order to produce a few very high notes of the organ, has to turn on the whole of the register. Phosphorescence by rise of temperature. This is best seen in certain species of diamonds, and particularly in cldorophane, a variety of fluorspar, which, when heated to 300° or 400°, suddenly becomes luminous, emitting a greenish-blue light which lasts for several days. Hagenbach examined the spectrum of phosphorescent fluorspar, and found that it consisted of only nine bands : four blue, two green, two yellow, and one orange. As the relative intensities of these bands are continually changing, it is easy to understand the different colours presented by different specimens of this mineral. Phosphorescence by mechanical effects, such as friction, percussion, cleavage, &c. ; for example, when two crystals of quartz are rubbed against each other in darkness, when a lump of sugar is broken, or when a plate of mica is cleft. To this category belongs also the disengagement of light when arsenipus acid crystallises. Phosphorescence by electricity, like that which results from the friction of mercury against the glass in a barometric tube. 650. Phosphorescence by insolation. — A large number of substances^ after having been exposed to the direct action of sunlight, or even of the diffused light of the atmosphere, emit in darkness a phosphorescence the colour and intensity of which depend on the nature and physical condition of these substances. This was first observed in 1604 in Bolognese phosphorus (barium sulphide), but it also exists in a great number of substances. Calcium and strontium sulphides are those which present it in the highest degree. They must be pi^epared in the dry way and at high temperatures. Wlien well prepared, after being exposed to the light, they are luminous for several hours in darkness. But as this phosphorescence takes place in a vacuum as well as in a gaseous medium, it cannot be attributed to a chemical action, but-rather to a temporary modification which the body undergoes from the action of light. A phosphorescent calcium sulphide is prepared for industrial purposes, and is known as BahnairHs luminous paint. After the substances above named, the best phosphorescents are the following, in the order in which they are placed : a large number of diamonds (especially yellow ones), and most specimens of fluorspar ; then arragonite, calcareous concretions, chalk, apatite, heavy spar, dried calcium nitrate and dried calcium chloride, calcium cyanide, a large number of stron- tium " or barium compounds, magnesium and its carbonate, &c. Besides these a large number of organic substances also become phosphorescent by insola:tion ; for instance, dry paper, silk, cane-sugar, milk-sugar, amber, the teeth, &c. Dewar has shown that at - 180° C. all substances are phosphor- esceht. The different spectral rays are not equally well fitted to render substances phosphorescent. The maximum effect takes place in the violet rays, or even -650] Phosphorescence by Insolation 647 a little beyond ; while the light emitted by phosphorescent bodies generally corresponds to rays of a smaller refrangibility, that is, of greater wave-length, than those of the light received by them and giving rise to the action. The tint which phosphorescent bodies assume is very variable, and even in the same body it changes with the manner in which it is prepared. In strontium compounds green and blue tints predominate ; and orange, yellow, and green tints in the barium sulphides. The duration of phosphorescence varies also in different bodies. In calcium and strontium sulphides, phosphorescence lasts as long as thirty hours : with other substances it does not exceed a few seconds, or even a fraction of a second. The colour emitted by an artificial phosphorescent alters with the tem- perature during insolation. Thus with strontium sulphide the light is dark violet at — 20° C, bright blue at + 40°, bluish-green at 70°, greenish-yellow at 100°, and reddish-yellow of feeble luminosity at 200° C. When a phosphorescent body has been heated the light emitted is brighter, but the greater the emission of light the shorter is the duration of the phos- phorescence. Heat, therefore, produces a more rapid radiation of the light. Phosphoroscope. In experimenting with bodies whose phosphorescence lasts a few minutes or even a few seconds, it is simply necessary to expose them to solar or diffused light for a short time, and then place them in dark- ness : their luminosity is very apparent, especially if care has been taken to close the eyes previously for a few moments. But in the case of bodies whose phosphorescence lasts only a very short time, this method is inadequate. Becquerel invented an mgenious apparatus, the phosphoroscope, by which bodies can be viewed immediately after being exposed to light : the mterval which separates the insolation and observation can be made as small as possible, and can be measured with great precision. This apparatus consists of a closed cylindrical box, AB (fig. 637), of blackened metal ; on the ends are two apertures opposite each other which have the form of a circular sector. One only of these, o, is seen in the figure. The box is fixed, but it is traversed in the centre by a movable axis, to which are fixed two circular screens, MM and PP, of blackened metal (fig. 638). Each of these screens is perforated by four apertures of the same shape as those in the box ; but while the latter correspond to each other, the apertures of the screens alternate, so that the open parts of the one correspond to the closed parts of the other. The two screens, as already mentioned, are placed in the box, and fixed to the axis, which by means of a train of wheels, worked by a handle, can be made to turn with any velocity. In order to investigate the phosphorescence of any body by means of this instrument, the body is placed on a stirrup interposed between the two rotating screens. The light cannot pass simultaneously through the opposite apertures of the sides A and B, because one of the closed parts of the screen MM, or of the screen PP, is always between them. So that when a body, a, is illuminated by light from the other side of the apparatus, it could not be seen by an observer looking at the aperture, <7, for then it would be masked by the screen PP. Accordingly, when an observer saw the body a, it would not be illuminated, as the light would be intercepted by the closed 648 Oil Light [660- parts of a screen MM. The body a would alternately appear and disappear ; it would disappear during the time of its being illuminated, and appear when it was no longer so. The time which elapses between the appearance and disappearance depends on the velocity of rotation of the screens. Suppose, Fig. 637 for instance, that they made 1 50 turns in a second ; as one revolution of the screens is effected in jj^ of a second, there would be four appearances and four disappearances during that time. Hence the length of time elapsing between the time of illumination and of observation would be ^ of i^^y of a second, or o-ooo8 of a second. Observations with the phosphoroscope are made in a dark chamber, the observer being on that side on which is the wheelwork. A ray of solar or electric light is allowed to fall upon the substance a, and, the screens being made to rotate more or less rapidly, the body a appears luminous in a con- tinuous manner, when the interval between insolation and observation is less than the duration of the phosphorescence of the body. By experiments of -650] Phosphorescence by Insolation 649 this kind, Becquerel found that substances which usually are not phosphor- escent appear so in the phosphoroscope ; such, for instance, as Iceland spar. Uranium compounds present the most brilliant appearance in this apparatus ; they emit a very bright luminosity when the observer can view them 0^03 or 0-04 of a second after insolation. But a large number of bodies produce no effect in the phosphoroscope ; for instance, quartz, sulphur, phosphorus, metals, and liquids. 6s o On Light [651- CHAPTER VIII DOUBLE REFRACTION. INTERFERENCE. POLARISATION 651. The undulatory theory of light. — 1 1 has been already stated (510) that the phenomenon of Hght is ascribed to waves or undulations propagated through an exceedingly rare medium called the luminiferous ether, which is supposed to pervade all space, and to exist between the molecules of the ordinary forms of matter. It is held, in short, that light is due to undulations of the ether, just as sound is due to undulations propagated through the air In the latter case, the undulations cause the drum of the ear to vibrate and produce the sensation of sound. In the former case, the undulations cause points of the retina to vibrate and produce the sensation of light. The two cases differ in this, that in the case of sound there is independent evidence of the existence and vibration of the medium (air) which propagates the undulation ; whereas in the case of light the existence of the medium and its vibrations is assttvied, because that supposition connects and explains in the most complete manner a long series of very various phenomena. There is, however, no independent evidence of the existence of the luminiferous ether. The analogy between the phenomena of sound and light is very close ; thus, the intensity of a sound is greater as the amplitude of the vibration of each particle of the air is greater, and the intensity of light is greater as the amplitude of the vibration of each particle of the ether is greater. Again, a sound is more acute as the length of each undulation producing the sound is less, or, what comes to the same thing, according as the number of vibrations per second is greater. In like manner, the colour of light is different accord- ing to the length of the undulation producing the light : a red light is due to a comparatively long undulation, and corresponds to a deep sound, while a violet light is due to a short undulation, and corresponds to an acute sound. Although the wave-length cannot be observed directly, yet it can be inferred from certain phenomena with great exactness. The following table gives the lengths, in inches and millimetres, of the undulations corresponding to the light at the principal dark lines of the spectrum : — Dark line A . . . B . C D, . . E F . . . G . H, . Wave- length in inches Wave- length in millimetres 0-0000299 0-0007504 0-0000271 0-0006874 0-0000258 0-0006562 0-0000232 0-0005897 0-0000207 0-0005271 O-OOOOI9I 0-0004862 0-0000169 0-00043 ' I 0-0000159 0-0003969 -652] Physical Explanation of Single Refraction 65 1 It will be remarked that the limits are very narrow within which' the lengths of the undulations of the ether must be comprised, if they are : to be capable of producing the sensation of light. In this respect light is in marked contrast to sound. For the limits are very wide within which the lengths of the undulations of the air may be comprised when they produce the sensation of sound (244). The colour of a body is due to the power it has of absorbing certain vibrations, and of reflecting others ; and the body appears of the colour pro- duced by the coexistence of the reflected vibrations. A body appears white when it reflects all different vibrations in the proportion in which they are present in the spectrum ; it appears black when it reflects light in such small quantities as not to affect the eye. A red body is one which has the property of reflecting in predominant strength those vibrations which pro- duce the sensation of red. This is seen in the fact that, when a piece of red paper is held against the daylight, and the reflected light is caught on a white wall, this also appears red. A piece of red paper in the red part of the spectrum appears of a brighter red, and a piece of blue paper held in the blue part appears a brighter blue ; while a red paper placed in the violet or blue part appears almost black. In the last case the I'ed paper can only reflect red rays, while it extinguishes the blue rays, and as the blue of the spectrum is almost free from red, so little is reflected that the paper appears black. When light falls upon a transparent body, the body appears colourless if all the vibrations are transmitted in the proportion in which they exist in the spectrum. But if some of the vibrations are checked ot-- extinguished, the emergent light will be of the colour produced by the coexistence of the un- checked vibrations. Thus, when a piece of blue glass is held before the eye, the vibrations producing red and yellow are extinguished, and the colour is due to the emergent vibrations which produce blue light. The undulatory theory also accounts for the reflection and refraction of light, as well as other phenomena which are yet to be described. The ex- planation of the refraction of light is of so much importance that we shall devote to it the next article. 652. Physical explanation of single refraction. — The explanation of this phenomenon by means of the undulatory theory of light presupposes that of the mode of propagation of a plane wave. Now, if a disturbance originated at any /oz«/ of the ether, it would be propagated as a spherical wave in all directions round that point with a uniform velocity. If, instead of a single point, we consider the front of a plane wave, it is evident that disturbances originate simultaneously at all points of the front, and that spherical waves proceed from each point with the same uniform velocity. Consequently, all these spheres will at any subsequent instant be touched by a plane parallel to the original plane. The disturbances propagated from the points in the first position of the wave will mutually destroy each other, except in the tangent plane ; consequently the wave advances as a plane wave, its successive positions beir^g the successive positions of the tangent plane. If the wave moves in any medium with a velocity w, it will describe a space vt in a time t, in a direction at right angles to the wave- front. 65^ On Light [652- In any given moment let mn (fig. 639) be the position of the wave-front of a beam of light, which, moving through any medium, meets the plane surface AB of any denser refract- ing medium. In the same moment in which the wave-front reaches «, m becomes the centre of a spherical wave system which moves in the second medium ; and, as the elas- ticity of the second me- dium is different from that of the first, the velo- '^' '' cities of propagation of the wave in the two media will be different. While the plane wave moves from n to K, the corresponding wave starting from m reaches the surface of a sphere the radius of which is less than «K, if the second medium is denser than the first. The incident wave in like manner reaches m' and n' simul- taneously, and while n' moves to K, m' moves to o' on the surface of a sphere, the radius of which, ni'o\ is to mo as ;z'K is to «K. All the elementary waves proceeding from points intermediate to n and K which arise from the same incident wave, touch one and the same plane K<)V, and the refracted ray proceeds in the new medium perpendicular to this tangent plane. Now «K and mo are proportional to the velocities of light in the two media respectively ; let mK. be taken as unit of length, then «K = sin «otK and mo = sin tnKo. Now nmK is the angle of incidence of the ray, and mKo is the angle of refraction, and nK and mo are proportional to the velocities of light in the two niedia respectively ; hence we see that these velocities are to each other in the same ratio as the sines of the angles of incidence and refraction ; a conclusion which agrees with the results of direct observation (518), and forms a beautiful confirmation of the truth of the undulatory theory. DOUBLE REFR.4CTI0N 653. Double refraction. — It has been ah'eady stated (545) that a large number of crystals possess the property of double refraction, in virtue of which a single incident ray in passing through any one of them is divided into two, or undergoes bifiircation, whence it follows that, when an object is seen through one of these crystals, it appears double. The fact of the existence of double refraction in Iceland spar was first stated by Bartholin in 1669, but the law of double refraction was first enunciated exactly by Huyghens in his treatise on light, written in 1678 and published in 1690. Crystals which possess this peculiarity are said to be double-refracting. It is found to a greater or less extent in all crystals which do not belong to the cubical system. Bodies which crystallise in this system, and those which, like glass, are destitute of crystallisation, have no double refraction. The property can, however, be imparted to them when they are unequally compressed, or when they are cooled quickly after having been heated, in -656] Ordinary and Extraordinary Ray 653 which state glass is said to be unannealed. Of all substances, that which possesses it most remarkably is Iceland spar or crystallised calcium carbonate. In many substances, the power of double refraction can hardly be proved to exist directly by the bifurcation of an incident ray ; but its existence is shown indirectly by their action on polarised light (677). Fresnel explained double refraction by assuming that the ether in double- refracting bodies is not equally elastic in all directions; from which it follows that the vibrations, in certain directions at right angles to each other, are transmitted with unequal velocities ; these directions being de- pendent on the constitution of the crystal. This hypothesis is confirmed by the property which glass acquires of becoming double-refracting by pressure and when unannealed. 654. Uniaxial crystals. — In all double-refracting crystals there is one direction, and in some a second direction, possessing the following property : — When a point is looked at through the crystal in this particular direction, it does not appear double. The lines fixing these directions are called optic axes ; and sometimes, though not very properly, axes of double refraction. A crystal is called U7tiaxial when it has one optic axis ; that is to say, when- there is one direction within the crystal along which a ray of light can proceed without bifurcation. When a crystal has two such axes, it is called a biaxial crystal. The uniaxial crystals most frequently used in optical instruments are Iceland spar, quartz, and tourmaline. Iceland spar crystal- lises in rhombohedra, whose faces form with each other angles of 105° 5' or 74° 55'. It Fig. 640 has eight solid angles (see fig. 640). Of these, two, situated at the extremi- ties of one of the diagonals, are severally contained by three obtuse angles. A line drawn within one of these two angles in such a manner as to be equally inclined to the three edges containing the angle is called the axis of the crystal. If all the edges of the crystal were equal, the axis of the crystal would coincide with the diagonal, ab. Brewster showed that in all uniaxial crystals the optic axis coincides with the axis of crystallisation. The principal plane with reference to a point of any face of a crystal, whether natural or artificial, is a plane drawn through that point at right angles to the face and parallel to the optic axis. If in fig. 640 we suppose the edges of the rhombohedron to be equal, the diagonal plane a^;:^ contains the optic axis {ab), and is at right angles to the faces «^^and chbg; conse- quently it is parallel to the principal plane at any point of either of those two faces. For this reason abed is often called the principal plane with respect to those faces ; any plane parallel to this is also a principal plane. 655. Ordinary and extraordinary ray. — One of the two rays into which an incident ray is divided on entering a uniaxial crystal is called the ordinary, and the other the extraordinary ray. The ordinary ray follows the laws of single refraction ; that is, with respect to that ray the sine of the angle of incidence bears a constant ratio to the sine of the angle of refraction, and the plane of incidence coincides with the plane of refraction. Except in 6S4 On Light [655- particular positions, the extraordinary ray follows neither of these laws. The images corresponding to the ordinary and extraordinary rays are called the ordinary and extraordinary images respectively. If a transparent specimen of Iceland spar be placed over a dot of ink, on a sheet of white paper, two images will be seen. One of them, the ordinary image, will seem slightly nearer to the eye than the other, the extra- ordinary image. Suppose the spectator to view the dot in a direction at right angles to the paper, then, if the crystal, with the face still on the paper, be turned round, the ordinary image will continue fixed, and the extraordhiary image will describe a circle round it, the line joining them being always in the direction of the shorter diagonal of the face of the crystal, supposing its edges to be of equal length. In this case it is found that the angle between the ordinary and extraordinary ray is 6° 12'. 656. The laws of double refraction in a uniaxial crystal. — These pheno- mena are found to obey the following laws : — i. Whatever be the plane of incidence, the ordinary ray always obeys the two general laws of single refraction (546). The refractive index for the ordinary ray is called the ordinary refractive index. ii. In every section perpendicular to the optic axis the extraordinary ray also follows the laws of single refraction. Consequently, in this plane, the extraordinary ray has a constant refractive index, which is called the extra- ordinary refractive index. iii. In every principal section the extraordinary ray follows the second law only of single refraction ; that is, the planes of incidence and refraction coincide, but the ratio of the sines of the angles of incidence and refraction is not constant. Huyghens gave a very simple geometrical construction, by means of which the directions of the refracted rays can be determined when the direc- tions of the incident ray and of the axis are known relatively to the face of the crystal. This construction was not generally accepted by physicists until WoUaston, and subsequently Malus, showed its truth by numerous exact measurements. 657. Positive and negative uniaxial crystal. — The term extraordinary refractive index has been defined in the last article. For the same crystal, its magnitude always differs from that of the ordinary refractive index ; for example, in Iceland spar the ordinary refractive index is l'654, while the extraordinary refractive index is I •483. In this case the ordinary index exceeds the extraordinary index. When this is the case the crystal is said to be negative. On the other hand, when the extraordinary index exceeds the ordinary index, the crystal is said to be positive. The following list gi\es the names of some of the principal uniaxial crystals : — Negative Uniaxial Crystals ' Iceland spar Ruby Pyromorphite Tourmaline Emerald Potassium ferrocyanide Sapphire Apatite Sodium nitrate Positive Uniaxial Crystals Zircon Apophyllite Titanite Quartz Ice Boracite -659] Interference of Light 65 5 658. Double refraction in biaxial crystals. — A large number of crystals, including all those belonging to the trimetric, the monoclinic, and the tricUnic systems, possess two optic axes \ in other words, in each of these crystals there are two directions along which a ray of light passes without bifurcation. A line bisecting the acute angle between the optic axes is called the medial line ; one that bisects the obtuse angle is called the supplementary line. It has been found that the medial and supplementary lines and a third line at right angles to both are closely related to the fundamental form of the crystal to which the optic axes belong. The acute angle between the optic axes is different in different crystals. The following table gives the magnitude of this angle in the case of certain crystals : — Nitre . 5° 20' Mica . • 45° 0' Strontianite , • 6 56 Sugar . ■ 50 Arragonite . • . 18 18 Selenite 60 Anhydrite . . 28 7 Epidote . 84 19 Heavy spar . 37 42 Iron sulphate 90 When a ray of light enters a biaxial crystal, and passes in any direction not coinciding with an optic axis, it bifurcates ; in this case, however, neither ray conforms to the laws of single refraction, but both are extra- ordinary rays. To this general statement the following exception must be made : — In a section of a crystal at right angles to the medial line one ray follows the laws of ordinary refraction, and in a section at right angles to the supplementary line the other ray follows the laws of ordinary refraction. INTERFERENCE AND DIFFRACTION 659. Interference of lig^ht. — The name interference is given to the re- ciprocal action which two rays of light exert upon each other when they are emitted from two neighbouring sources, and meet each other under a very small angle. This action may be obser\'ed by means of the following ex- periment : — In the shutter of a dark room two very small apertures of the same diameter are made close to each other. The apertures are closed by pieces of coloured glass — red, for example — by which two pencils of homogeneous light are introduced. These two pencils form two divergent luminous cones which meet at a certain distance ; they are received on a white screen a little beyond the place at which they meet, and in the segment common to the two discs which form upon this screen some very well-defined alternations of red and black bands are seen. If one of the two apertures be closed, the fringes disappear, and are replaced by an almost uniform red tint. From the fact that the dark fringes disappear when one of the beams is intercepted, it is concluded that they arise from the interference of the two pencils which cross obliquely. This experiment was first made by Grimaldi, but was modified by Young. Grimaldi had drawn from it the conclusion that light added to light may produce darkness. The full importance of this principle remained for a long time unrecognised, until these inquiries were resumed by Young and by Fresnel, of whom the latter, by a modification of Grimaldi's experi- ment, rendered it an experijnenticm crucis of the truth of the undulatory hypothesis. 656 On Light [669- In Grimaldi's experiment diffraction (660) takes place, for the luminous rays pass by the edge of the aperture. In the following experiment, which is due to Fresnel, the two pencils interfere without the possibility of diffraction. Two plane mirrors, AB and BC (fig. 641), of metal, are arranged close to each other, so as to form a very obtuse angle, ABC, which must be very little Fig. 641 less than 180°. A pencil of monochromatic light — red, for instance — which passes into the dark chamber, is brought to a focus, F, by means of a lens, L. On diverging from F the rays fall partly on AB, and partly on BC. If BA is produced to P and FPFj is drawn at right angles to AP, and if PFj is made equal to PF, then the rays which fall on AB will, after reflection, pro- ceed as if they diverged from Fi. If a similar construction is made for the rays falling on BC, they will proceed after reflection as if they diverged from Fj. A little consideration will show that F, and F, are very near each otlier. Suppose the reflected rays to fall on a screen SS, placed nearly at right angles to their directions. Every point of the screen which receives light from both pencils is illuminated by both rays, viz. one from Fj, the other from F^ : thus the point H is illuminated by two rays, as also are K and I. Now the combined action of these two pencils is to form a series of parallel bands alternately light and dark on the screen (fig. 642). They are distributed sym- metrically in refer- ence to one of them cc, which is more briUiant than the Pig 5^^ others, and which is called the central fringe. This is the fundamental phenomenon of inter- ference : and that it results from the joint action of the two pencils is plain -659] Interference of Light 657 for if the light which falls upon either of the mirrors is cut off, the dark bands altogether disappear. The experiment may also be made by means of Ohm's prism or the bi- prism, which is a prism in which the refracting angle is very nearly 180°. A very simple arrangement of a mirror for experiments on the interference of light is thus constructed. Four small wax pellets, a, b^ c, d, are placed on a small block of wood, and on this two strips of plate glass, which accurately fit along the line be (fig. 643). A larger glass plate is then laid on this, and the finger moved with gentle pressure along this line. In this way the two mirrors form a very slight angle with each other, and give in sunlight the coloured pjg 5^3 fringes. The above remarkable experiment is explained in the most satisfactory manner by the undulatory theory of light. The explanation exactly resembles that already given of the formation of nodes and loops by the combined action of two aerial waves (262) ; the only difference being that in that case the vibrating particles were supposed to be particles of air, whereas in the present case the vibrating particles are supposed to be those of the luminiferous ether. Consider any point K on the screen, and first let us suppose the distance of K from Fj and F^ to be equal. Then the undulations which reach K will always be in the saxne. phase, and the particle of ether at K will vibrate as if the light came from one source : the amplitude of the vibration, however, will be increased in exactly the same manner as happens at a loop or ventral point ; consequently, at K the intensity of the light will be increased. The same will be true for all points on the screen, such that the difference between their distances from the two images equals the length of one, two, three, &c., undulations. If, on the other hand, the distances of K from F, and F, differ by the length of half an undulation, then the two waves would reach K in exactly opposite phases. Consequently, whatever velocity would be com- municated at any instant to a particle of ether by the one undulation, an exactly equal and opposite velocity would be communicated by the other undulation, and the particle would he. permanently at rest, or there would be darkness at that point ; this result being produced in a manner precisely resembhng the formation of a nodal point already explained. The same will be true for all positions of K, such that the difference between its dis- tances from Fj and F^ is .equal to three halves, or five halves, or seven halves, &c., of an undulation. Accordingly, there will be on the screen a succession of alternations of light and dark points, or rather lines — for what is true of points in the plane of the paper (fig. 642) will be equally true of other points on the screen, which is supposed to be at right angles to the plane of the paper. Between the light and dark lines the intensity of the light will vary, increasing gradually from darkness to its greatest intensity, and then decreasing to the second dark line, and so on. If instead of red hght any other coloured light were used — for example, violet light — an exactly similar phenomenon would be produced, but the dis- tance from one dark line to another would be less than before. If white light were used, each separate colour tends to produce a different set of dark lines. Now these sets being superimposed on each other, and not coinciding, the U U 6s8 On Light [659- dark lines due to one colour are illuminated by other colours, and instead of dark lines a succession of coloured bands is produced. The number of coloured bands produced by white light is much smaller than the number of dark lines produced by a homogeneous light ; since at a small distance from the middle band the various colours are completely blended, and a uniform white light produced. 65o. Diffraction and fringes. — Diffraction is a modification which light undergoes when it passes the edge of a body, or when it traverses a small aperture^a modification in virtue of which the luminous rays appear to become bent, and to penetrate into the shadow. This phenomenon may be observed in the following- manner :— A beam of sunhght is allowed to pass through a very small apertm"e in the shutter of a dark room, where it is received on a condensing lens, L (fig. 644), with a Fig. 644 short focal length. A red glass is placed in the aperture so as to allow only red light to pass. An opaque screen, e, with a sharp edge a — a razor, for instance — is placed behind the lens beyond its focus, and intercepts one portion of the luminous cone, while the other is projected on the screen b, of which B represents a front view. The following phenomena are now seen : — Within the geometrical shadow, the limit of which is represented by the hne ab, a faint light is seen, which gradually fades in proportion as it is farther from the hmits of the shadow. In the upper part of the screen-^which, being above the line ab, might be expected to be uniformly illuminated — a series of alternate dark and light bands or fringes is seen parallel to the line of shadow, which gradually become more indistinct and ultimately disappear. The limits between the light and dark fringes are not quite sharp lines : there are parts of maximum and minimum intensity which gradually fade off into each other. All the colours of the spectrum give rise to the same phenomenon, but the fringes are broader in proportion as the light is less refrangible. Thus with red light they are broader than with green, and with green than with violet. Hence, with white light, which is composed of different colours, the dark spaces of one tint overlap the light spaces of another, and thus a series of prismatic colours will be produced. If, instead of placing the edge of an opaque body between the light and the screen, a ^'ery narrow body be interposed, such as a hair or a fine metal wire the phenomena will be different. Outside the space corresponding to the geometrical shadow, there is a series of fringes, as in the former case. But within the shadow also there is a series of alternate light and dark bands. They are called interior fringes, and are much narrower and more numerous than the external fringes. -861] Gratings 6S9 ii^iilllllllii ffllfl^Mflf When a small opaque circular, disc is interposed, white light being used, its shadow on the screen shows in the middle a bright spot surrounded by a series of coloured concentric rings ; the bright spot is of various colours according to the relative positions of the disc and screen. The haloes some- times seen round the sun and moon belong to this class of phenomena. They are due, as Fraunhofer showed, to the diffraction of light by small globules of fog in the atmosphere. Fraunhofer even gave a method of estimating the mean diameter of these globules from the dimensions of the haloes. 66i. Gratings. — ^Phenomena of diffraction of another class are produced iDy allowing the pencil of light from the luminous point to traverse an aper- ture in the form of a narrow slit in an opaque screen. The diffracted light may be received on a sheet of white paper, but the images are much better seen through a small telescope placed be- hind the aperture. If the aperture is very small, the telescope may be dispensed with, and the figure may be viewed by placing the aper- Fig- 645 ture before the eye. If now monochromatic light (583)— red, for instance— be allowed to fall through such a narrow slit, a bright band of red hght is seen, and right and left of it a series of similar bands gradually diminishing in brightness and separated by dark bands. The breadth of these bands differs with the nature of the light, being narrower and nearer together in violet than in green, and these again nar- rower and nearer than in red, as shown in fig. 645. If ordinary white light be used, then the colours are hot exactly superposed, but a series of equidistant spectra is formed on each side of the bright line, with their violet side turned inwards. In order to explain this, let us refer to fig. 646, which represents the formation of the first dark band. When light is in- cident on the slit, AB, the particles of ether there, which we will represent by the dotted lines, will be set in vibration, and each point will become the centre of a new series of oscillations. Consider now the undulations which constitute a ray proceeding at right angles to the plane of the slit : all such undulations will form a band of light on the screen MN. Those which are not parallel but proceed at equal inclinations, and meet at the point r, will be in the same phase and will reinforce each other, and the line of maximum brightness will be at r. Consider, however, a pencil of rays which proceeds Fig. 646 66o On Light [661- from the slit in an oblique direction and which meets the screen, or the retina, in the point s, and let us suppose that the difference between the lengths of the paths of the undulations proceeding from the edges b and a — that is, bs and as — is equal to the length of an undulation. Make sc = sb and join be ; then ac is the length of the undulation. Let us suppose that the whole set of undulations which proceeds from the slit ab is divided at d into two equal groups of undulations. Then a little consideration will show that at any part of the path there will be a dif- ference of phase of half an undulation between the ray from the margin a, and that from the centre d ; and to each of the undulations constituting the group on the left there will be a corresponding one among the groups on the right, which just differs from it by half an undulation ; the general effect will be that the group on the left will be half an undulation behind the group on the right, and both arriving at the screen in opposite phases neutralise each other and produce darkness. When the difference between the paths of the marginal undulations is equal to half a wave-length, a partial destruction of light takes place ; the luminous intensity corresponding to this obliquity is a little less than half that of the undiffracted light. If the marginal distance is one and a half undulations, we can, as before, conceive the whole pencil divided into three parts, of which two will neutralise each other, and the third only will be effective. There will be a luminous band, but one of less intensity. In like manner where the marginal undulations differ by two whole wave- lengths, they will again extinguish each other, and a dark band will be the result. Thus there will be formed a series of alternate dark and bright bands of rapidly diminishing intensity. In general, when the difference of path of the rays proceeding from the margin of the slit amounts to n wave- lengths, n being any whole number, we have a dark band, and when it amounts to n + ^ wave-lengths, a bright band. The phenomena of diffraction produced when other than straight lines are used are often of great beauty. They were more particularly examined by Schwerdt, and the whole of the phenomena are in exact accordance with the undulatory theory, though the explanation is in many cases somewhat intricate. The theory renders it possible to predict the appearance which any particular aperture will produce, just as astronomy enables us to foretell the motions of the heavenly bodies. Some of the simpler forms — such as straight lines, triangles, squares— may be cut out of tinfoil pasted on glass, and apertui-es of any form may be produced with great accuracy by taking on glass a collodion photograph of a sheet of paper on which the required shapes are drawn in black. Looking through any of these apertures at a luminous point, we see it surrounded with coloured spectra of very various forms, and of great beauty. The beautiful colours seen on looking through a bird's feather at a distant source of light, and the colours of striated surfaces, such as mother- of-pearl, are due to a similar cause. A beautiful phenomenon of the same kind is the aureole observed on looking at a candle flame through lycopodium powder strewn on glass. Two crossed gratings give a splendid picture in which a bright point is surrounded in all directions by spectra. -662] Diffraction Spectra 66 1 662. Diffraction spectra. — The most important of these figures are the gratings proper, which may be produced by arranging a series of fine wires parallel to each other, or by careful ruling on a piece of smoked glass, or by photographic reduction. Nobert has made such gratings by ruling lines on glass with a diamond, in which there are 12,000 lines in an inch in breadth. The late Dr. Stone constructed such gratings for reflection, by ruling lines on plates of nickel ; this metal has the advantage of hardness, non-liability to tarnish, and great reflecting power. If a grating be used instead of a single slit, as above described, the phenomena are in general the same, though of greater brilliancy. With homogeneous light and such a grating, there is seen, on each side of the central bright line, a series of sharply defined narrow bands and lines of light, gradually increasing in breadth and diminishing in intensity as their distance from the central line increases. If white light be used the white band is seen in the centre, and on each side of it a sharply defined isolated spectrum with the violet edges inwards. Next to this, and separated by a dark interval, is on each side a somewhat broader but similar spectrum, and then follow others which become fainter and broader and overlap each other. The brightness and sharpness of these spectra depend on the close- ness of the lines, and on the opacity of the intermediate space. In those which are ruled by diamond on glass, the parts scratched represent the opaque parts. For objective representation the image of a slit in a dark shutter, through which the sunlight enters, is focused by means of a convex lens on a screen at a distance, and then a grating is placed in the path of the rays. The spectra produced by means of a grating are known as diffraction spectra. Very accurate gratings can now be easily and cheaply prepared by means of photography, and their use for scientific purposes is extending. There are many points of difference between these spectra and those produced by the prism, and for scientific work the former are preferable. A diffraction spectrum is the purer the greater the number of lines in the grating, provided they are equidistant. To obtain the maximum brightness, the opaque intervals should be as opaque and the transparent ones as trans- parent as possible. The spectra are, however, not more than jL as bright as prismatic spectra. By the use of sensitive photographic dry plates (622), even faint lights can be made visible and this objection removed. On the other hand, in diffraction spectra, the colours are uniformly dis- tributed in their true order and extent according to the difference in their wave-lengths, and according therefore to a property which is inherent in the light itself ; while in prismatic spectra the red rays are concentrated, and the violet ones dispersed. In diffraction spectra the centre is the brightest part. Fig. 647 represents a grating spectrum, together with an equally long spectrum produced by a flint-glass prism ; the upper one being that produced by the grating. It will be seen that D in the one spectrum is in almost exactly the same position as F in the other. Diffraction spectra have, moreover, the advantage of giving a far larger number of dark lines, and of giving them in their exact relative positions. Thus, in a particular region in which Angstrom had mapped 118 lines, 662 On Light [662- Draper, by means of a diffraction spectrum, was able to photograph at least 293. Diffraction spectra also extend farther in the direction of the ultra- violet, and give more dark lines in that region. Fig. 647 The most perfect gratings were constructed by the late Professor Rowland, of Baltimore, by means of a machine specially planned and constructed for the purpose, the chief feature in which is a practically perfect screw. Using this machine, he has been able to rule gratings with as many as 43,000 lines to the inch, nor does this represent the limit of the power of the machine. Gratings with 14,000 or 28,000 lines give, however, the best definition. Another great improvement is to rule the gratings on curved instead of on flat surfaces ; in this way the spectrum can be formed without a tele- scope, which is a matter of great importance, as telescopes interfere with a great many experiments. The spectroscope is thus reduced to its simplest form, so that an instrument of very high power may be constructed at a small cost. By means of his gratings Professor Rowland was able to resolve lines in the spectrum which had never hitherto been separated. It has been proposed to use the fine quartz threads prepared by Mr. Boys (89) for making gratings. 663. Determination of wave-length. — The relative positions of these bright and dark lines furnish a means of calculating the wave-length or length of undulation of any particular colour. We must first of all know the distance rs (fig. 646) of the first dark band from the bright one. The bands are not uniform in brightness or darkness, but there is in each case a position of maximum intensity, and it is from these that the distances are measured. If the bands are viewed through a telescope, the angle is observed through which the axis must be turned from the position in which the cross wire coincides with the centre of the bright band to that in which it coincides with the centre of the dark band. From this angle, which can be very accurately measured, the distance is easily calculated. When the diffraction bands are received on a screen, the distance may be directly measured, and most accurately by taking half the distance between the centres of the first pair of dark bands. We have thus the similar triangles abc and rds, in which ac : bc-rs : rd -664] Colours of Thin Plates. Newton's Rings 663 (fig. 646). Now be may be taken equal to ab, the width of the sHt, which can be measured directly with great accuracy by means of a micrometer screw (i i), and rd is the distance of the screen. Hence rs-K. ab ac= = — rd Now ac, the difference between as and sc, is equal to the length of an undu- lation of this particular colour. In one experiment with red light the width of the slit ab was 0-015 '"ch, the distance rs 0-15 inch, and the distance of the screen 93 inches, which gave ac= ° ^^ i =0-000024 inch as the wave- length of red light. Using blue light the distance of rs was found to be o-i, which gives o-ooooi6. Knowing the length of the undulations, we can easily calculate their number in a second, n, from the formula n = - (226), where v is the velocity of light. Taking this at 1 86,000 miles, we get for the red corresponding to the dari; line B 434,420,000,000,000 as the number of oscillations in a second, and for the H in the violet 758,840,000,000,000 undulations. If, instead of a single slit, gratings be used, we have the possibility of more accurate results, for the contrast is greater, and thus the distance is more easily determined. The width of the slit is easily calculated by count- ing th^ number of lines in a given space. 664. Colours of thin plates. Newton's rings. — All transparent bodies, solids, liquids, or gases, when in sufficiently fine laminas, appear coloured with very bright tints, especially by reflection. Crystals which cleave easily, and can be blatained in very thin plates, such as mica and selenite, show this phenomenon, which is also well seen in soap-bubbles and in the layers of air in cracks in glass and in crystals. Steel, in being tempered, becomes covered with a very thin layer of oxide, and exhibits the colour of thin plates, which change during heating as the oxide changes its thickness. A drop of oil spread rapidly over a large sheet of water exhibits all the colours of the spectrum in a constant order. A soap-bubble appears white at first, but, in proportion as it is blown out, brilliant iridescent colours appear, especially at the top, where it is thinnest. These colours are arranged in horizontal zones around the summit, which appears black when there is not thickness enough to reflect light, and the bubble then suddenly bursts. Newton, who first studied the phenomena of the coloured rings in soap- bubbles, wishing to investigate the relation between the thickness of the thin plate, the colour of the rings, and their extent, produced them by means of a layer of air interposed between two glasses, one plane and the other slightly convex (fig. 648). Fig. The two surfaces being cleaned and exposed to ordinary light in front of a window, so as to reflect light, there is seen at the point of contact a black spot surrounded by six or seven coloured rings, the tints of which become 664 On Light [664- gradually less strong. If the glasses are viewed by transmitted light, the centre of the rings is white, and each of the colours is exactly complementary of that of the rings by reflection. The lens and the glass plate are usually arranged in a brass mount, which by means of three screws allows the pressure to be regulated. With homogeneous light, red for example, the rings are successively black and red ; the diameters of corresponding rings are less as the colour is more refrangible ; but with white light the rings are of the different colours of the spectrum, which arises from the fact that, as the rings of the different simple colours have different diameters, they are not exactly superposed, but are more or less separated. Fig. 649 For experiments on Newton's rings the apparatus represented in fig. 649 is suited. The glasses, N, for producing the rings are placed on the sliding part of a dividing machine. A pencil of monochromatic light from B, made parallel by the lens L, is thrown vertically downwards by the plate G. Above this is a totally reflecting prism, P, which sends the rays from N towards the telescope F. The telescope is sighted so that the cross wire goes through the centre of the first ring ; then by turning the screw the ten innermost bright and dark rings are successively brought in position ; the respective diameters are then very easily determined by reading off on the scale the corresponding divisions. It is usual to speak of the successive rings as the first, second, third, &c. By the first ring is understood that of least diameter. The thickness of the layer of air which corresponds to any particular ring is obtained as follows : — -666] Polarisation by Double Refraction 66s Fig. 650 Let GH (fig. 650) be the plane glass surface on which is laid the convex glass lens AEB, the radius, R, of which is ME. Let DFbe the radius, p, of any given ring ; FC = DE, or e is the thickness of the layer of air corresponding to this ring. Now from a well-known geo- metrical principle, p' = e -^ {2^ — e) ; but since e is infinitely small, the formula may be written p^ = ^x2R, so that knowing p and R it is easy to calcu- late e. Newton found that the thicknesses corresponding to the successive dark rings are proportional to the numbers o, 2, 4, 6 , while for the bright ^ rings the thicknesses were proportional * to I, 3, 5 He found that for the first bright ring the thickness was ttsVtjxt of ''II inch, when the light used was the brightest part of the spectrum, that is, the part on the confines of the orange and yellow rays. If the focal length of the lens is from three to four yards, the rmgs can be seen with the naked eye ; but if the length is less, the rings must be looked at with a lens. If the space between the lens and the plate contains, instead of air, a liquid of greater refrangibility, the rings contract owing to the shorter wave- length. 665. Explanation of Newton's rings.T— Newton's rings, and all pheno- mena of thin plates, are simple cases of interference. In fig. 651, let MNOP represent a thin plate of a transparent body, on \vhich a pencil of parallel rays of homogeneous light, ab, impinges ; this will be partially reflected in the direction be, and partially refracted towards d. But the refracted ray will undergo a second reflection at the surface, OP ; the reflected ray will emerge at e in the same direction as the pencil of light reflected at the first surface ; and consequently the two pencils be and ef will augment or diminish each other's effect according as they are in the same or opposite phases. We shall A thus have an effect produced similar to that of fringes (660). POLARISATION OF LIGHT 666. Polarisation by double refraction. — It has been already seen that when a ray of light passes through a crystal of Iceland spar (655), it becomes divided into two rays of equal intensity ; viz. the ordinary ray, and the extraordinary ray. These rays are found to possess other peculiarities, which are expressed by saying they are polarised ; namely, the ordinary ray in a principal plane, and the extraordinary ray in a plane at right angles to a principal plane. The phenomena which are thus designated may be 4/ Ist Fig. 651 666 On Light [666- described as follows : — Suppose a ray of light which has ym&sx%0Vi& ordinary refraction in a crystal of Iceland spar to be allowed to pass through a second crystal, it will generally be divided into two rays ; namely, one ordinary, and the other extraordinary, but of unequal intensities. If the second crystal be turned round until the principal planes of the two crystals coincide — that is, until the crystals are in similar or in opposite positions — then the extra- ordinai-y ray disappears, and the ordinary ray is at its greatest intensity ; if the second crystal is turned farther round, the extraordinary ray reappears, and increases in intensity as the angle increases, while the ordinary ray diminishes in intensity until the principal planes are at right angles to each other, when the extraordinary ray is at its greatest intensity and the ordinary ray vanishes. These are the phenomena produced when the ray which ex- perienced ordinary refraction in the first crystal passes through the second. If the ray which has experienced extraordinary refraction in the first crystal is allowed to pass through the second crystal, the phenomena are similar to those above described ; but when the principal planes coincide, an extra- ordinary ray alone emerges from the second crystal, and when the planes are at right angles, an ordinary ray alone emerges. These phenomena may also be thus described : — Let O and E denote the ordinary and extraor4inary rays produced by the first crystal. When O enters the second crystal, it generally gives rise to two rays, an ordinary {Oo) and an extraordinary (O^), of unequal intensities. When E enters the second crystal, it likewise gives rise to two rays, viz. an ordinai-y (Eo) and an extraordinary (E^), of unequal intensities, the intensities varying with the angle between the principal planes of the crystals. When the principal planes coincide, only two rays, viz. Oo and 'Ke, emerge from the second crystal, and when the planes are at right angles, only two rays, viz. Oe and Eo, emerge from the second crystal. Since O gives rise to an ordinary ray when the principal planes are parallel, and E gives rise to an ordinary ray when they are at right angles, it is manifest that O is related to the principal plane in the same manner that E is related to a plane at right angles to a principal plane. This phenomenon, which is produced by all double-refracting crystals, was first observed by Huyghens in Iceland spar, and in consequence of a suggestion of Newton's was afterwards called polarisation. It remained, however, an isolated fact until the discovery of polarisation by reflection recalled the attention of physicists to the subject. The latter discovery was made by Malus in 1808. 667. Polarisation by reflection. — When a ray of light, ab (fig. 652), falls on a polished unsilvered glass surface, fghi, inclined to it at an angle of 35° 25', so that the angle of incidence is 54° 35', it is reflected, and the reflected ray is polarised in the plane of reflection. If it were transmitted through a crystal of Iceland spar, it would pass through without bifurcation, and undergo an ordinary refraction, when the principal plane coincides with the plane of reflection ; it would also be transmitted without bifurcation, but undergo extraordinary refraction, when the principal plane is at right angles to the plane of reflection ; in other positions of the crystal it would give rise to an ordinary and an extraordinary ray of different intensities, according to the angle between the plane of reflection and the principal -668] Angle of Polarisation 667 Fig. 652 plane of the crystal. The peculiar property which the light has acquired by reflection at the surface fghi can also be exhibited as follows : — Let the polarised ray be be received at c, on a second surface of unsilvered glass, at the same angle, viz. 35° 25'. If the surfaces are parallel, the ray is reflected ; but if the second plate is caused to turn round the line cb, the intensity of the reflected ray continually diminishes, and when the glass surfaces are at right angles to each other, no light is reflected. By continuing to turn the upper mirror the intensity of the reflected ray gradually increases, and attains a maximum value when the surfaces are again parallel. The above statement will serve to describe the phenomenon of polarisation by reflection so far as the principles are concerned ; the apparatus best adapted for exhibiting the phe- nomenon will be described farther on. 658. Angle of polarisation. — -The polarising angle of a substance is the angle which the incident ray must make with the perpendicular to a plane polished surface of that substance in order that the polarisation may be complete. For glass this angle is 54° 35', and if in the preceding experi- ment the lower mirror were inclined at any other angle than this, the light would not be completely polarised in any position ; this would be shown by its being partially reflected from the upper surface in all positions. Such light is said to be partially polarised. The polarising angle for water is 52° 45' ; for quartz, 57° 32' ; for diamond, 68° ; and it is 56° 30' for obsidian, a kind of volcanic glass which is often used in these experiments. Light which is reflected from the surface of water, from a slate roof, from a polished table, or from oil paintings, is all more or less polarised. The ordinary light of the atmosphere is frequently polarised, especially in the earlier and later periods of the day, when the solar rays fall obliquely on the atmosphere. Almost all reflecting surfaces may be used as polarising mirrors. Metal surfaces form, however, an important exception. Brewster discovered the following remark- ably simple law in reference to the polarising angle : — The polarising angle of a substance is that angle of incidence for which the reflected polarised ray is at right angles to the refracted ray. Thus, in fig. 653, if si is the incident, ir the refracted, and if the reflected ray, the polarisation is most complete when fi is at right angles to ir. Ths plane of polarisation \i the plane of Fig- 653 reflection in which the light becomes polarised ; it coincides with the plane of incidence, and therefore contains the polarising angle. 668 On Light [668- A simple' geometrical consideration will show that the above law may be thus expressed : — The tangent of the angle of polarisation of a substance is equal to its refractive index. As the refractive index differs with the dif- ferent colours, it follows that the angle of polarisation cannot be the same for all colours. This explains why a ray of white light is never completely polarised. 669. Polarisation by single refraction. — When an unpolarised pencil of light falls upon a glass plate placed at the polarising angle, one part is reflected ; the other part becomes refracted in passing through the glass, and the transmitted light is now found to be partially polarised. If the light which has passed through one plate, and whose polarisation is very feeble, be transmitted through a second plate parallel to the first, the effects become more marked, and by ten or twelve plates are tolerably complete. A bundle of such plates, for which the best material is the glass used for covering microscopic objects, fitted in a tube at the polarising angle, is frequently used for examining or producing polarised light. If a ray of light fall at any angle on a transparent medium, the same holds good with a slight modification. In fact, part of the light is reflected and part refracted, and both are found to be partially polarised, eqital quan- tities in each being polarised, and their planes of polarisation being at right angles to each other. It is, of course, to be understood that the polarised portion of the reflected light is polarised in the plane of reflection, which is likewise the plane of refraction. 670. Polarising instruments. — Every instrument for investigating the properties of polarised light consists essentially of two parts — one for polarising the light, the other for ascertaining or exhibiting the fact of the light having undergone polarisation. The former part is called the polariser, the latter the analyser. Thus in art. 666 the crystal producing the first refraction is Xhe polariser, that producing the second refraction is the analyser. In art. 667 the mirror at which the first reflection takes place is the polariser, that at which the second reflection takes place is the analyser. Some of the most convenient means of producing polarised light will now be described, and it may be remarked that any instrument that can be used as a polariser can also be used as an analyser. The experimenter has, therefore, consider- able liberty of selection. 671. Norremberg's apparatus. — The simplest instrument for polarising light is that invented by Norremberg. It may be used for repeating most of the experiments on polarised light. It consists of two brass rods, b and d (fig. 654), which support an unsil- vered mirror, n, of ordinary glass, movable about a horizontal axis. A small graduated circle indicates the angle of inclination of the mirror. Between the feet of the two columns there is a silvered glass, p, which is fixed and horizontal. At the upper end of the columns is a graduated plate, i, in which a circular disc, o, rotates. This disc, in which there is a square aperture, supports a mirror of black glass, m, which is inclined to the vertical at the polarising angle. An annular disc, k, can be fixed at different heights on the columns by means of a screw. A second ring, a, may be moved around the axis. It supports a black screen, in the centre of which there is a circular aperture. -672] Tourmaline 669 When the mirror n makes with the vertical an angle of 35° 25', which is the complement of the polarisingL angle for glass, the rays of light, S«, which meet the mirror at this angle become polarised, and are reflected in the direction np towards the mirror p, which sends them in the direction ^«r. After having passed through the glass, «, the polarised ray- falls upon the blackened glass m under an angle of 35° 25', because the mirror makes ex- actly the same angle with the vertical. But if the disc, o, to which the mirror, ?«, is fixed, be turned horizontally, the in- tensity of the light reflected from the upper mirror gradually diminishes, and totally disap- pears when it has been moved through 90°. The position is that represented in the diagram : the plane of incidence on the upper mirror is then perpendi- cular to the plane of incidence, ^7tp, on the mirror, n. When the upper mirror is again turned, the intensity of the light increases until it has passed through 180°, when it again reaches a maxi- mum. The mirrors 711 and n are then parallel. The same phenomena are repeated as the mirror m continues to be turffed in the same direction, until it again comes into its original position ; the intensity of the reflected light being greatest when the mirrors are parallel, and being reduced to zero when they are at right angles. If the mirror in is at a greater or less angle than 35° 25', a certain quantity of light is reflected in all positions of the plane of incidence. 672. Tourmaline. — The primary foym of this crystal is a regular hex- agonal prism. Tourmaline, as already stated, is a negative uniaxial crystal, and its optic axis coincides with the axis of the prism. For optical purposes a plate is cut from it parallel to the axis. When a ray of light passes through such a plate, an ordinary ray and an extraordinary ray are produced polarised in planes at right angles to each other ; viz. the former in a plane at right angles to the plate parallel to the axis, and the latter in a plane at right angles to the axis. The crystal possesses, however, the remarkable property of rapidly absorbing the ordinary ray ; consequently, when a plate of a certain thickness is used, the extraordinary ray alone emerges — in other words, a beam of common light emerges from the plate of tourmaline polarised in a plane at right angles to the axis of the crystal. If the light Fig. 654 670 On Light [672^ thus transmitted be viewed through another similar plate held in a parallel position, little change will be observed, excepting that the intensity of the transmitted light will be about equal to that which passes through a plate of double the thickness ; but if the second tourmaline be slowly turned, the light will become feebler, and will ultimately disappear when the axes of the two plates are at right angles. The objections to the use of the tourmaline are that it is not very trans- parent, and that plates of considerable thickness must be used if the polarisa- tion is to be complete. For unless the ordinary ray is completely absorbed the emergent light will be only partially polarised. . Herapath discovered that iodoquinine sulphate has the property of polarising light in a remarkably degree. Unfortunately, it is a very fragile substance, and difficult to obtain in large crystals. 673. Double-refracting prism of Iceland spar. Double image prism. — When a ray of light passes through an ordinary rhombohedron of Iceland spar, the ordinary and extraordinary rays emerge parallel to the original ray, con- sequently the separation of the rays is proportional to the thickness of the prism. But if the crystal is cut so that its faces are inclined to each other, the deviations of the ordinary and extraordinary rays will be different, they will not emerge parallel, and their separation will be greater as their distance from the prism increases. The light, however, becomes de- composed in passing through the prism, and the rays will be coloured. It is therefore necessary to achrotitatise (595) the prism, which is done by combining it with a prism of glass with its refracting angle turned in the contrary direc- tion (fig. 656). In order to obtain the greatest amount of divergence, the prism should be cut with its refracting edge * ' parallel to the optic axis, and this is always done. Let us suppose that a ray of polarised light passes along the axis of the cylinder (fig. 656), and let us suppose that the cylinder is caused to turn slowly about its axis ; then the resulting phenomena are exactly like those already described (656). Generally there will be an ordinary and an extra- ordinary ray produced, whose relative intensities will vary as the tube is turned. But in two opposite positions the ordinary ray alone will emerge, and in two others at right angles to the former the extraordinary ray will alone emerge. When the ordinary ray alone emerges, the principal plane of the crystal — that is, a plane at right angles to its face, and parallel to its refracting edge — coincides with the original plane of polarisation of the ray. Consequently, by means of the prism, it can be ascertained both that the ray is polarised, and likewise in which plane it is polarised. A com- pound prism constructed in the manner described is called a double-image prism. 674. Nicol's prism. — The Nicol's prism is one of the most valuable means of polarising light, for it is perfectly colourless, it polarises light completely, and it transmits only one beam of polarised light, the other being entirely suppressed. It is constructed from a rhombohedron of Iceland spar, about an inch in height and \ of an inch in breadth. This is bisected in the plane which passes through the obtuse angles as shown in fig. 657, that is, along the -676] Physical Theory of Polarised Light 6yi plane ab (fig. 658). The two halves are then again joined in the same order by means of Canada balsam. The principle of the Nicol's prism is this : — The refracti\'e index of Canada balsam, I -549, is less than the ordinary index of Iceland spar, i'654, Fig. 6S7 Fig. 658 but greater than its extraordinary index, i '483. Hencc when a luminous ray SC (fig. 658) enters the prism, the ordinary ray is totally reflected on the surface, ab, and takes the direction CdO, by which it is refracted out of the crystal, while the extraordinary ray, Ce, emerges alone. Since the Nicol's prism allows only the extraordinary ray to pass, it may be used, like a tour- maline, as an analyser or as a polariser. Foucault replaced the layer of Canada balsam by one of air, the two prisms being kept together by the mounting. The advantage of this is that the section ab (fig. 658) need not be so acute, so that the prism becomes shorter, and therefore cheaper. Nicol's prism is the most important feature of most polarising apparatus, It is better than the polarising mirror on accoimt of its more complete polarisation, and has the advantage over tourmaline of giving a colourless field of view. 675. Physical theory of polarised light. — The explanation of the dark bands produced by the interference of light in art. 659 resembles that of the formation of nodes and loops given in art. 278. It might hence be supposed that the vibrations producing light are quite similar to those producing sound. But this is by no means the case. In fact, no assumption is made* in art. 659 as to the direction in which the vibrating particles move, and accordingly the explanation is equally true whether the particles vibrate in the direction AB, BA, along which the disturbance is travelling, or at right angles to AB. As a matter of fact, the former is the case with the vibrations producing sound, the latter with the vibrations producing light. In other words, the vibrations producing sound take place in the direction of propagation, the vibrations producing light are transversal to the direction of propagation. This assumption as to the direction of the vibration of the particles of ether producing light is rendered necessary, and is justified, by the pheno- mena of polarisation. When a ray of light is polarised, all the particles of ether in that ray \ibrate in straight lines parallel to a certain direction in the front of the «ave corresponding to the ray. When a ray of light enters a double-refracting medium, such as Iceland spar, it becomes divided into two, as we have already seen. Now it can be shown to be in strict accordance with mechanical principles that, if a medium 672 On Light [675- possesses unequal elasticity in different directions, a plane wave produced by transversal vibrations entering that medium will give rise to two plane waves moving with different velocities within the medium, and the vibrations of the particles in front of these waves will be in directions parallel respec- ti\ely to two lines at right angles to each other. If, as is assumed in the undulatory theory of light, the ether exists in a double-refracting crystal in such a state of unequal elasticity, then the two plane waves will be formed as above described, and these, having different velocities, will give rise to two rays of unequal refrangibility (652). This is the physical account of the phenomenon of double refraction. It will be remarked that the vibrations corresponding to the two rays are transversal, rectilinear, and in directions perpendicular to each other in the rays respecti\ely. Accordingly the same theory accounts for the fact that the two rays are both polarised, and in planes at right angles to each other. It is a point still unsettled whether, when a ray of light is polarised with respect to a given plane, the vibrations take place in directions v/ithin or per- pendicular to that plane. Fresnel was of the latter opinion, and the evidence is on the whole in favour of his view. It is, however, convenient in some cases to regard the plane of polarisation as that plane in which the vibrations take place. COLOURS PRODUCED BY THE INTERFERENCE OF POLARISED LIGHT 676. Laws of the interference of polarised rays. — After the discovery of polarisation, Fresnel and Arago tried whether polarised rays presented the same phenomena of interference as ordinary rays. They were thus led to the discovery of the following laws in reference to the interference of polarised light, and, at the same time, of the brilliant phenomena of colora- tion, which will be presently described. I. When two rays polarised in the same plane interfere with each other, they produce, by their interference, fringes of the very same kind as if they were common light. II. When two rays of light are polarised at right angles to each other, they produce no coloured fringes in the same circumstances in which two rays of common light would produce them. When the rays are polarised in planes inclined to each other at any other angles, they produce fringes of intermediate brightness ; and if the angle is made to change, the fringes gradually decrease in brightness from 0° to 90°, and are totally obliterated at the latter angle. III. Two rays originally polarised in planes at right angles to each other may be subsequently brought into the same plane of polarisation without acquiring the power of forming fringes by their interference. IV. Two rays polarised at right angles to each other, and afterwards brought into the same plane of polarisation, produce fringes by their inter- ference like rays of common light, pro\ided they originated in a pencil the whole of which was originally polarised in any one plane. V. In the phenomena of interference produced by rays that have suffered double refraction, a difference of half an undulation must be allowed, as one of the pencils is retarded by that quantity, from some unknown cause. -678] Effect produced when the Crystal is very thin 673 677. Effect produced by causing^ a pencil of polarised rays to traverse-a double-refracting crystal. — -The following important experiment may be made most conveniently by Norremberg's apparatus (fig. 654). At g (fig. 655) there is a Nicol's prism. A plate of a double-refracting crystal cut parallel to its a.\is is placed on the disc at e. In the first place, however, suppose the plate .of the crystal to be removed. Then, since the Nicol's prism allows only the extraordinary ray to pass when it is turned so that its principal plane coincides with the plane of reflection, no light will be transmitted (674). Place the plate of doubly refracting crystal, which is supposed to be of moderate thickness, in the path of the reflected ray at e. Light is now transmitted through the Nicol's prism. On turning the plate, the intensity of the transmitted light varies ; it reaches its maximum when the principal plane of the plate is inclined at an angle of 45° to the plane of reflection, and disappears when these planes either coincide with or are at right angles to each other. The light in this case is white. The same or eq livalent phe- nomena are produced when any other analyser is used. Thus, assume the double-image prism to be used, and suppose the crystal to be removed. Then, generally, two rays are transmitted ; but if the principal plane of the analyser is turned in the plane of primitive polarisation, the ordinary ray only is trans- mitted, and then when turned through 90° the extraordinary ray only is trans- mitted. Let the analyser be turned into the former position, then, when the plate is interposed, both ordinary and extraoi'dinary rays are seen, and when the plate is slowly rotated, the ordinary and extraordinary rays are seen to vary in intensity, the latter vanishing when the principal plane of the polarising plate either coincides with, or is at right angles to, the plane of primitive polarisation. 678. Effect produced when the plate of crystal is very thin. — In order to exhibit this, take a thin film of selenite or mica between the twentieth and sixtieth of an inch thick, and interpose it as in the last article. If the thickness of the film is uniform, the light now transmitted through the analyser will be no longer white, but of a uniform tint ; the colour of the tint being different for different thicknesses — for instance, red, or green, or blue, or yellow, according to the thickness ; the intensity of the colour de- pending on the inclination of the principal plane of the film to the plane of reflection, being greatest when the angle of inclination is 45°. Let us now suppose the crystalline film to be fixed in that position in which the light is brightest, and suppose its colour to be red. Let the analyser (the Nicol's prism) be turned round, the colour will grow fainter, and when it has been turned through 45°, the colour disappears, and no light is transmitted ; on turning it further, the complementary colour, green, makes its appearance, and increases in intensity until the analyser has been turned through 90° ; after which the intensity diminishes until an angle of 135° is attained, when the light again vanishes, and, on increasing the angle, it changes again into red. Whatever be the colour proper to the plate, the same series of pheno- mena will be observed, the colour passing into its complementary when the analyser is turned. That the colours are really complementary is proved by using a double-refracting prism as analyser. In this case two rays are transmitted, each of which goes through the same changes of colour and intensity as the single ray described above ; but whatever be the colour and X X 674 On Light [678- inteiisity of the one ray in a given position, the other ray will have the same when the analyser has been turned through an angle of 90°. Consequently, these two rays give simultaneously the appearances which are successively presented in the above case by the same ray at an interval of 90°. If now the two rays are allowed to overlap, they produce white light ; thereby proving their colours to be complementar)'. Instead of using plates of different thicknesses to produce different tints, the same plate may be employed inclined at different angles to the polarised ray. This causes the ray to traverse the film obliquely, and, in fact, amounts to an alteration in its thickness. With the same substance, but with plates of increasing thickness, the tints follow the laws of the colours of Newton's rings (665). The thickness of the plate must, however, be different from that of the layer of air in the case of Newton's rings to produce corresponding colours. Thus corresponding colours are produced by a plate of mica and a layer of air when the thickness of the former is about 400 times that of the latter. In the case of selenite the thickness is about 230 times, and in the case of Iceland spar about 13 times, that of the corresponding layer of air. 679. Explanation of the phenomena described above. — The phenomena described in the last articles admit of complete explanation by the undulatory theory, but not without the aid of abstruse mathematical calculations. What follows will show the nature of the explanation. Let us suppose, for con- venience, that in the case of a polarised ray the particles of ether vibrate in the plane of polarisation (675), and that the analyser is a double-image prism, with its principal plane in the plane of primitive polarisation ; then the vibrations, being wholly in that plane, have no resolved part in- a plane at right angles to it, and, consequently, no extraordinary ray passes through the analyser ; in other words, only an ordinary ray passes. Now take the crystalline plate cut parallel to the axis, and let it be interposed in such a manner that its principal plane makes any angle {&) with the plane of primitive polarisation. The effect of this will be to cause the vibrations of the primitive ray to be resolved in the principal plane and at right angles to the principal plane of the crystal, thereby giving rise to an ordinary ray (O) and an extraordinaiy ray (E), which, however, do not become separated on account of the thinness of the plate. They will not form a single plane polarised ray on leaving the plate, since they are unequally retarded in pass- ing through it, and consequently leave it in different phases. Since neither of the planes of polarisation of O and E coincides with the principal plane of the analyser, the vibrations composing them will again be resolved, viz. O gives rise to Oo and Oe, and E gives rise to Eo and Eg. But the vibra- tions composing Oo and Eo, being in the same phase, give rise to a single ordinary ray, lo, and in like manner Oe and Et^ give rise to a single extra- ordinary ray, I^. Thus the interposition of the plate of crystal restores the extraordinary ray. Suppose the angle 6 to be either 0° or 90°. In either case the vibrations are transmitted through the plate without resolution ; consequently they remain wholly in the plane of primitive polarisation, and on entering the analyser cannot give rise to an extraordinary ray. If the Nicol's prism is used as an analyser, the ordinary ray is suppressed -680] Coloured Rings 675 by mechanical means. Consequently only \e will pass through the prism, and that for all values of 6 except 0° and 90°. A little consideration will show that the joint intensities of all the rays existing at any stage of the above transformations must continue constant, but that the intensities of the individual rays will depend on the magnitude of 6 \ and when this circumstance is examined in detail, it explains the fact that \e increases in intensity as 6 increases from 0° to 45°, and then decreases in intensity as 6 increases from 45° to 90°. In regard to the colour of the rays it is to be observed that the formulas for the intensities of \o and \e contain a term depending on the length of the wave and the thickness of the plate. Consequently, when white light is used the relative intensities of its component colours are changed, and therefore \o and \e will each have a prevailing tint, which will be different for different thicknesses of the plate. The tints will, however, be complementary, since the joint intensities of \o and \e being the same as that of the original ray, they will, when superimposed, restore all the components of that ray in their original intensities, and therefore produce white light. 6S0. Coloured rings produced by polarised light in traversing double- refracting films. — In the experiments with Norremberg's apparatus which have just been described (679), a pencil of parallel rays traverses the film of crystal perpendicularly to its faces, and as all parts of the film act in the same manner, the tint is everywhere the same. But when the inci- dent rays traverse the plate under dif- ,,,11,.^ ct-^ ferent obliquities, which comes to the same thing as if they traversed '^' ^' plates differing in thickness, coloured rings are formed similar to Newton's rings. The best method of observing these new phenomena is by means of the tourmaline pincette or tongs (fig. 659). This is a small instrument consisting of two tourmalines, cut parallel to the axis, each of them being fitted in a copper disc. These two discs, which are perforated in the centre, and blackened, are mounted in two rings of silvered copper, which is coiled, as shown in the figure, so as to form a spring, and press together the tourma- lines. The tourmalines turn with the disc, and may be so arranged that their axes are either perpendicular or parallel. The crystal to be experimented upon, being fixed in the centre of a cork disc, is placed between the two tourmalines, and the pincette is held before the eye so as to view diffused light. The tourmaline farthest from the eye acts as polariser and the other as analyser. If the crystal thus viewed is uniaxial, and cut perpendicularly to the axis, and a homogeneous light — red, for instance — is looked at, a series of alternately dark and red rings is seen. With another simple colour similar rings are obtained, but their diameter decreases as the refrangibility of the colour increases. On the other hand, the diameters of the rings diminish when the thickness of the plates increases, and beyond a certain thickness no more rings are produced. If, instead of illuminating the rings by homogeneous light, white light be 676 On Light [680- used, then, since the rings of the different colours produced have not the same diameter, they are partially superposed, and pi'oduce very brilliant variegated colours. The position of the crystal has no influence on the rings, but this is not the case with the relative position of the two tourmalines. For instance, in experimenting on Iceland spar cut perpendicular to the axis, and from I to 20 millimetres in thickness, when the axes of the tourmalines are perpen- dicular, a beautiful series of rings is seen, brilliantly coloured, and traversed by a black cross, as shown in fig. i, Plate II. If the axes of the tourma- lines are parallel, the rings have tints complementary to those they had at first, and there is a white cross (fig. 2, Plate II.) instead of a black one. In order to understand the formation of these rings when polarised light traverses double-refracting films, it must first be premised that these films are traversed by a converging conical pencil, whose summit is the eye of the observer. Hence it follows that the virtual thickness of the film which the rays traverse increases with their divei'gence ; but for rays of the same obliquity this thickness is the same ; hence there result different degrees of retardation of the ordinary with respect to the extraordinary ray at different points of the plate, and therefore different colours are produced at different distances from the axis, but the same colours will be produced at the same distance from the axis, and consequently the colours are arranged in circles round the axis. The arms of the black cross are parallel to the optic axis of each of the tourmalines, and are due to an absorption of the polarised light in these directions. When the tourmalines are parallel the vibrations are transmitted, and hence the white cross. Analogous effects are produced with all uniaxial crystals ; for instance, tourmaline, emerald, sapphire, beryl, mica,pyromorphite, and potassium ferro- cyanide. 681. Rings in biaxial crystals. — In biaxial crystals, coloured rings are also produced, but their form is more complicated. The coloured bands, instead of being circular and concentric, have the form Oi curves, with two centres, the centre of each system corresponding to an axis of the ciystal. Figs. 4, 5, and 6, Plate II., represent the curves seen when a plate of eitlier cerussite, topaz, or nitre, cut perpendicularly to the medial line (658), is placed between the two tourmalines, the plane containing the axis of the crystal being in the plane of primitive polarisation. When the axes of the two tourmalines are at right angles to each other, fig. 4, Plate II., is obtained. On turning the crystal without altering the tourmalines, fig. 5, Plate II., is seen, which changes into fig. 6, Plate II., when the crystal has been turned through 45°. If the axes of the tourmalines are parallel, the same coloured curves are obtained, but the colours are complementary, and the black cross changes into white. The angle between the optic axes in the case of nitre is only 5° 20', and hence the whole system can be seen at once. But when the angle exceeds 20° to 25°, the two systems of curves cannot be simultaneously seen. There is then only one dark brush instead of the cross, and the bands are not oval, but circular. Fig. 3, Plate II., represents the phenomenon as seen with arragonite. Sir John Herschel, who measured the rings produced by biaxial crystals Pi. 11, -682] Colours produced by Compressed or Unannealed Glass 677 leferred them to the kind of curve known in geometry as the lemniscate, in strict accordance with the principles of the undulatory theory of light. The observation of the system of rings which plates of crystals give in polarised light presents a means of distinguishing between optical uniaxial and optical biaxial crystals, even in cases in which no conclusion can be drawn as to the system in which a mineral crystallises from mere morpho- logical reasons. In this way the optical investigation becomes a valuable aid in mineralogy ; as, for example, in the case of mica, of which there are two mineralogical species, the uniaxial and the biaxial. All the phenomena which have been described are only obtained by means of polarised light. Hence, a double refracting film, with either a Nicol's prism or a tourmaline as analyser, may be used to distinguish between polarised and unpolarised light, that is, as a polariscope. 682. Colours produced by compressed or by unannealed glass. — Ordinary glass is isotropic, and is therefore not endowed with the power of double refraction. It acquires this property, however, if by any cause its elasticity becomes more modified in one direction than in another. Glass may become anisotropic by being strongly compressed in a given direction, or curved, or tempered, that is to say, cooled after having been heated. If the glass is then traversed by a beam of polarised light, effects of colour are obtained which are entirely analogous to those described in the case of doubly refracting crystals. They are, however, susceptible of far greater variety, according as the plates of glass have a circular, square, rectangular, or triangular shape, and according to the degree of tension of their particles. Fig. 660 Fig. 661 Fig. 662 Fig. 663 Fig. 665 When the polariser is a mirror of black glass, on which the light of the sky is incident, and the analyser is a Nicol's prism, and a square plate of compressed glass is placed between polariser and analyser, the appearances represented in figs. 660, 661, 663 are successively presented ; figs. 662 678 On Light [682- and 665 represent the appearances produced by a circular plate under the same circumstances ; and fig. 664 that produced when one rectangular plate is superposed on another. This figure also varies when the system of plates is turned. In consequence of being rapidly cooled, glass often acquires a Strained condition. Hence, when the masses of glass, more especially the larger ones from which lenses are made, are examined by polarised light, the existence of strains may be revealed which would render it useless to go to the trouble and expense of working such masses, as they would probably break in the operation. ELLIPTIC, CIRCULAR, AND ROTATORY POLARISATION 683. Definition of elliptic and circular polarisation In the cases hitherto considered, the particles of ether composing a polarised ray vibrate in parallel straight lines ; to distinguish this case from those we are now to consider, such light is frequently caWe^A platie polarised light. It sometimes happens that the particles of ether describe ellipses about their positions of rest, the planes of the ellipses being perpendicular to the direction of the ray. If the axes of these ellipses are unequal and parallel, the ray is said to be elliptically polarised. In this case the particles which, when at rest, occupied a straight line, are, when in motion, arranged in a helix round th^ line of their original position as an axis, the helix exchanging from instant to instant. If the axes of the ellipses are equal, they become circles, and the light is said to be circulariy polarised. If the minor axes become zero, the ellipses coincide with their major axes, and the light becomes plane polarised. Consequently, plane polarised light and circulariy polarised light are par- ticular cases of elliptically polarised light. 684. Theory of the orig^ of elliptic and circular polarisation. — Let us in the first place consider a simple pendulum (56) vibrating in any plane, the arc of vibration being small. Suppose that, when in its lowest position, it received a blow in a direction at right angles to the direction of its motion, such as would make it vibrate in an arc at right angles to its arc of primitive vibration, it follows from the law of the composition of velocities that the joint effect will be to make it vibrate in an arc inclined at a certain angle to the arc of primitive vibration, the magnitude of the angle depending on the magnitude of the blow (58). If the blow communicated a velocity equal to that with which the body is already moving, the angle would be 45°. Next suppose the blow to communicate an equal velocity, but to be struck when the body is at its highest point, this will cause the particle to describe a circle, and to move as a conical pendulum. If the blow is struck under any other circumstances, the particle will describe an ellipse. Now as the two blows would produce separately two simple vibra- tions in directions at right angles to each other, we may state the result arrived at as follows : — -If two rectilinear vibrations are superinduced on the same particle in directions at right angles to each other, then : i. If they are in the same or opposite phases, they make the point describe a rectilinear vibration in a direction inclined at a certain angle to either of the original vibrations. 2. But if their phases differ by 90 ' or a quarter of a vibration, the particle will describe a circle, provided the vibrations -685] Fresnel's Rhomb 679 are equal. 3. Under other circumstances the particle will describe an ellipse. To apply this to the case of polarised light. Suppose two rays of light polarised in perpendicular planes to coincide, any particle in the common path of the rays will have simultaneously two motions in directions at right angles to each other. Consequently — i. If the vibrations are in the same or opposite phases, the light resulting from the two rays is plane polarised. 2. If the rays are of equal intensity, and their phases differ by 90°, the result- ing light is circularly polarised. 3. Under other circumstances the light is elliptically polarised. As an example, if reference is made to arts. 679 and 680, it will be seen that the rays denoted by O and E are superimposed in the manner above described. Consequently, the light which leaves the depolarising plate is elliptically polarised. If, however, the principal plane' of the depolarising plate is turned so as to make an angle of 45° with the plane of primitive polarisation, O and E have equal intensities ; and if, further, the plate is made of a certain thickness, so that the phases of O and E may differ by 90°, or by a quarter of a vibration, the light which emerges from the plate is circulai-Iy polarised. This method may be employed to produce circularly polarised light. Circular or elliptic polarisation may be either right-handed or left- handed, or what is sometimes called dextrogyrate and lavogyrate. If the observer looks along the ray in the direction of propagation, from polariser to analyser, then, if the partitles move in the same direction as the hands of a watch with its face to the observer, the polarisation is right-handed. 685. Fresnel's rhomb. — This is a means of obtaining circularly polarised light. We have just seen (684) that, to obtain a ray of circularly polarised light, it is sufficient to decompose a ray of plane polarised light in such a manner as to produce two rays of light of equal intensity polarised in planes at right angles to each other, and differing in their paths by a quarter of an undulation. Fresnel effected this by means of a rhomb which has received his name. It is made of glass ; its acute angle is 54^, and its obtuse 126°. If a ray (a, fig. 666) of plane polarised light falls perpendicularly on the face of AB, it will undergo two total internal reflections at an angle of about 54", one at E, and the other at F, and will emerge perpendicularly from the face CD. If the plane ABCD be inchned at an angle of 45° to the plane of polarisation, the polarised ray will be divided into two coincident rays, with their planes of polarisation at right angles to each other, and it appears that one of them loses exactly a quarter of F'g- 666 an undulation, so that on emerging from the rhomb the ray is circularly polarised. If the ray emerging as above from Fresnel's rhomb is examined, it will be found to differ from plane polarised light in this, that, when it passes through a double image prism, the ordinary and extraordinary rays are Of equal intensity in all positions of the prism. Moreover, it differs from ordinary light in this, that, if it pass through a 68o On Light - [685- second rhomb placed parallel to the first, a second quarter of an undulation will be lost, so that the parts of the original plane polarised ray will differ by half an undulation, and the emergent ray will be plane polarised ; more- over the plane of polarisation will be inclined at an angle of 45° to ABCD, but on the other side from the plane of primitive polarisation. 686. Elliptic polarisation. — In addition to the method already men- tioned (685), elliptically polarised light is generally obtained whenever plane polarised light suffers reflection. Polarised light reflected from metals becomes elliptically polarised, the degree of ellipticity depending on the direc- tion of the incident ray, and of its plane of polarisation, as well as on the nature of the reflecting substance. When reflected from silver, the polarisation is almost circular, and from galena almost plane. If elliptically polarised light be analysed by the Nicol's prism, it never vanishes, though at alternate positions it becomes fainter ; it is thus distinguished from plane and from circular polarised light. If analysed by Iceland spar, neither image disappears, but they undergo changes in intensity. Light can also be polarised elliptically in Fresnel's rhomb. If the angle between the planes of primitive polarisation and of incidence be any other than 45', the emergent ray is elliptically polarised. 687. Rotatory polarisation. — Rock crystal or quartz possesses a remark- able property which was long regarded as peculiar to itself among all crystals, though it has been since found to be shared by tartaric acid and its salts, together with some other crystallised bodies. This property is called rotatory polarisation, and may be described as follows : — Let a ray of homogeneous light be polarised, and let the analyser, say a Nicol's prism be turned til! the light does not pass through it. Take a thin section of a quartz crystal cut at right angles to its axis, and place it between the polariser and the analyser with its plane at right angles to the rays. The light will now pass through the analyser. The phenomenon is not the same as that pre- viously described (677) ; for, if the rock crystal is turned round its axis, no effect is produced, and if the analyser is turned, the ray is found to be ■pla7ie polarised in a plane inclined at a certain angle to the plane of primitive polarisation. If the light is red, and the plate i millimetre thick, this angle is about 17°. In some specimens of quartz the plane of polarisation is turned to the right hand, in others to the left hand. Specimens of the former kind are said to be right-handed, those of the latter kind left-handed (684). This difference corresponds to a difference in crystallographic structure. The property possessed by rock crystal of turning the plane of polarisation through a certain angle was investigated by Biot, who, amongst other results, arrived at this : — For a given colour, the angle through which the plane of polarisation is turned is proportional to the thickness of the quartz. 688. Physical explanation of rotatory polarisation. — The explanation of the phenomenon described in the last article is as follows : — When a ray of polarised light passes along the axis of the quartz crystal, it is divided into two rays of circularly polarised light of equal intensity, which pass through the crystal with different velocities. In one the circular polarisation is right- handed, in the other left-handed (684). The existence of these rays was proved by Fresnel, who succeeded in separating them. On emerging from -690] Coloration produced by Rotatory Polarisation 68 1 the crystal they are compounded into a plane polarised ray ; but, since they move with unequal velocities within the crystal, they emerge in different phases, and consequenth- the plane of polarisation will not coincide with the plane of primitive polarisation. This can be readily shown by reasoning similar to that employed in art. 684. The same reasoning will also show that the plane of polarisation will be turned to the right or left, according as the right-handed or left-handed ray moves with the greater velocity. Moreo\-er, the amount of the rotation will depend on the amount of the retardation of the ray whose velocity is least ; that is to say, it will depend on the thickness of the plate of quartz. In this manner the phenomena of rotatory polarisation can be completely accounted for. 689-690. Coloration produced by rotatory polarisation. — The rotation is different with different colours ; its magnitude depends on the refrangibility, and is greatest with the most refrangible rays. In the case of red light a plate I millimetre in thickness will rotate the plane 17°, while a plate of the same thickness will rotate it 44° in the case of violet light. Hence with white light there will, in each position of the analysing" Nicol's prism, be a greater or less quantity of each colour transmitted. In the case of a right- handed crystal, when the Nicol's prism is turned to the right, the colours will successively appear from the less refrangible to the more so — that is, in the order of the spectrum, from red to violet ; with a left-handed crystal in the reverse ordei". Obviously in turning the Nicol's prism to the left, the reverse of these results will take place. When a quartz plate cut perpendicularly to the axis, and traversed by a ray of polarised light, is ^. looked at through a doubly refracting prism, two brilliantly coloured images are seen, of which the tints are complementary ; for their images are partially superposed, and in this position there is white light (fig. 667). When the prism is turned from left to right, the two images change colour and assume successively all the colours of the spectrum. This will be understood from what has been said about the different rotation for different colours. Quartz rotates the plane of polarisation for red 1 7° for each millimetre, and for violet 44° ; hence from the great difference of these two angles, when the polarised light which has traversed the quartz plate emerges, the various simple colours which it contains are polarised in different planes. Consequently, when the rays thus transmitted by the quartz pass through a double-refracting prism, they are each decomposed into two others polarised at right angles to each other : the various simple colours are not divided in the same proportion between the ordinary and extraordinary rays furnished by the prism ; the two images are, therefore, coloured ; but, since those which are wanting in one occur in the other, the colours of the images are perfectly complementary. These phenomena of coloration may be well seen by means of Norrem- berg's apparatus (figs. 654, 655). A quartz plate, s, cut at right angles to the axis and fixed in a cork disc, is placed on a screen, e ; the mirror n being then so inclined that a ray of polarised light passes through the quartz, the latter is viewed through a double-refracting prism, ^; when this tube is turned, the 682 On Light [690- complementary images furnished by the passage of polarised Hght through the quartz are seen. 691. Rotatory power of liquids. — Biot found that a great number of hquids and solutions possess the property of rotatory polarisation. He futher observed that the deviation of the plane of polarisation can reveal differences in the composition of bodies where none is exhibited by chemical analysis. For instance, one of the two sugars obtained by the action of dilute acids on cane-sugar deflects the plane of polarisation to the right, and the other to the left, although their chemical composition is the same. The rotatory power of liquids is far less than that of quartz. In con- centrated syrup of cane-sugar, which possesses the rotatory power in the highest degree, the power is ^ that of quartz, so that it is necessary to operate upon columns of liquids of considerable length — 8 inches, for example. Fig. 668 represents an apparatus devised by Biot for measuring the rotatory power of liquids. On a metal groove, g, fixed to a support, r, is a brass tube, rf, 20 centimetres long, tinned inside, in which is contained the liquid experimented upon. This tube is closed at each end by glass plates fastened by screw collars. At m is a mirror of black glass, inclined at the polarising angle to the axis of the tubes bd and n, so that the ray re- flected by the mirror III, in the direction bda, is polarised. In the centre of the graduated circle //, inside the tube a, and at right angles to the axis bda, is a double refracting a.chromatic prism (673), which can be turned about the axis of the appa- ratus by means of a button n. The latter is fixed to a limb c, on which is a vernier, to indicate the number of degrees turned through. Lastly, from the position of the mirror ?«, the plane of polarisation, Sod, of the reflected ray is vertical, and the zero of the graduation of the circle h is on this plane. Before placing the tube d in the groove g, the e.xtraordinary image furnished by the double-image prism disappears whenever the limb c corre- sponds to the zero of the graduation, because then the double-refracting prism is so turned that its principal section coincides with the plane of polarisation Fig. 668 -692] SoleU's Saccharimeter 683 (690). This is the case also when the tube d is full of water or any other inactive liquid, like alcohol, ether, &c., which shows that the plane of polar- isation has not been turned. But if the tube be filled with a solution of cane- sugar or any other active liquid, the extraordinary image reappears, and to •extinguish it the limb must be turned to a certain extent either to the right •or to the left of zero, according as the liquid is right-handed or left-handed, showing that the polarising plane has been turned by the same angle. With solution of cane-sugar the rotation takes place to the right ; and if with the same solution tubes of different lengths are taken, the rotation is found to increase proportionately to the length, in conformity with art. 687 ; further, with the same tube, but with solutions of various strengths, the rotation increases with the quantity of sugar dissolved, so that the quantitative -analysis of a solution may be made by means of its angle of rotation. In this experiment homogeneous light must be used ; for, as the various tints of the spectrum are rotated to different extents, white light is decomposed in traversing an active liquid, and the extraordinary image does not dis- -appear completely in any position of the double-refracting prism — it simply changes the tint^ The transition tint (692) may, however, be observed. To avoid this inconvenience a piece of red glass is placed in the tube between the eye and the analyser, which only allows red light to pass. The extra- -ordinary image disappears in that case, whenever the principal section of the prism coincides with the plane of polarisation of the red ray. Since for a given coloured light and at a given temperature the rotation depends upon the quantity of active substance present, we may write a = klx, where / is the length of the tube (in decimetres), x the number of grammes of active substance per cubic centimetre of solution, and k a constant, which is called the specific rotation of the substance. 692. Soleil's saccharimeter. — Soleil constructed an apparatus, based upon the rotatory power of liquids, for analysing saccharine substances, to which the name saccharimeter is applied. Fig. 669 represents the sac- charimeter fixed horizontally, and fig. 670 gives a longitudinal section. The principle of this instrument is not that of observing the amplitude of the rotation of the plane of polarisation, as in Biot's apparatus, but that of compensation ; that is to say, a second active substance is used, acting in the opposite direction to that analysed, whose thickness can be altered until the contrary actions of the two substances completely neutralise each other. Instead of measuring the deviation of the plane of polarisation, the thick- ness is measured which the plate of quartz must have in order to produce perfect compensation. The apparatus consists of three parts — a tube containing the liquid to be analysed, a polariser, and an analyser. The tube m, containing the liquid, is made of copper, tinned on the inside, and closed at both ends by glass plates. It rests on a support, k, terminated at both ends by tubes, r and a, in which are the crystals used as polariser and analyser, and which are represented in section (fig. 670). In front of the aperture S (fig. 670) is placed an ordinary lamp. The light emitted by this lamp in the direction of the axis first meets a double- 684 On Light [692- refracting prism r, which serves as polariser (670). The ordinary image alone meets the eye, the extraordinary image being projected out of the field ot vision in consequence of the largeness of the angle which the ordinary Fig. 669 makes with the extraordinary ray. This polariser is placed in such a position that the plane of polarisation is vertical, and passes through the axis of the apparatus. Emerging from the double-image prism,, the polarised ray meets a disc of quartz formed of two half-circles of the same thickness, but of opposite rotations, the line of separation being vertical and in the same plane as the axis of the apparatus. These plates, cut perpendicularly to the axis, have a thickness of 3'65 millimetres, corresponding to a rotation of 90°, and give a rose-violet tint, called the tint of passage, or transition tint. As the quartz, whether right-handed or left-handed, turns always to the same extent for the same thickness, it follows that the two quartz plates a and b (fig. 673) turn the plane of polarisation equally, one to the right and the other to- the left. Hence, looked at through a double-image prism, they present exactly the same tint. Having traversed the quartz, q, the polarised ray passes into the liquid in the tube 111, and then meets a single plate of quartz, z, of any thickness, the use of which will be seen presently. The compensator, it, which destroys- the rotation of the column of liquid, m, consists of two quartz plates, with the same rotation either to the right or the left, but opposite to that of the plate i. These two quartz plates, a section of which is represented in fig. 671, are obtained by cutting obliquely a quartz plate with parallel sides so as to formi two prisms of the same angle, N, N', which is called a biqtiartz ; super- posing, then, these two prisms, as shown in the figure, a single plate is- -692] SoleU's Saccharimeter 68s obtained with parallel faces, the thickness of which can be varied at will. Each prism is fixed to a slide, so as to move either way without disturbing the parallelism, the motion being effected by means of a double rackwork and pinion turned by a milled head, b (figs. 669, 670). When these plates move in the direction indicated by the arrows (fig. 671) it is clear that the sum of their thicknesses increases, and that it diminishes when the plates are moved in the contrary direction. A scale and a vernier Fig, 670 Fig. 673 follow the plates in their motion, and measure the thickness of the compen- sator. This scale, represented with its vernier in fig. 672, has two divisions with a common zero, one from left to right for right-handed liquids, the other from right to left for left-handed. When the vernier is at zero, the sum of the thicknesses of the plates NN' is exactly equal to that of the plate z, and as the rotation of the latter is opposed to that of the compensator, the effect is zero. But by moving the plates of the compensator in one or the other direction either the compensator or the quartz, z', preponderates, and there is a rotation from left to right. Behind the compensator is a double-refracting prism, c (fig. 670), serving as analyser to observe the polarised ray which has traversed the liquid and the various quartz plates. In order to understand more easily the object of the prism c, we will neglect for a moment the crystals and the lenses on the left of the drawing. If at first the zero of the vernier v coincides with that of the scale, and if the liquid in the tube is inactive, the actions of the com- pensator, and of the plate i, neutralise each other ; and, the liquid having no action, the two halves of the plate §■, seen through the prism c, give exactly the same tint as has been observed above. But if the tube filled with in- active liquid be replaced by one full of solution of sugar, the rotatory power of this solution is added to that of one of the halves (a or b) of the plate q (viz. that half which tends to turn the plane of polarisation in the same direction as the solution), and subtracted from that of the other. Hence the two halves of the plate q no longer show the same tint ; the half a, for instance, is red, while the half b is blue. The prisms of the compensator are then moved by turning the milled head b, either to the right or to the left, until the difference of action of the compensator and of the plate i compensates 686 On Light 692- the rotatory power of the solution, which takes place when the two halves- of the plate q, with double rotation, revert to their original tint. The direction of the deviation and the thickness of the compensator are measured by the relative displacement of the scale e and of the vernier v. Ten of the divisions on the scale correspond to a difference of i millimetre in the thickness of the compensator ; and as the vernier gives itself tenths of these divisions, it therefore measures differences of ^-^ in the thickness of the compensator. When once the tints of the two halves of the plate are exactly the same, and therefore the same as before interposing the solution of sugar, the division on the scale corresponding to the vernier is read off, and the corre- sponding number gives the strength of the solution. This depends on the experimental fact that i6'47i grains (1-067 grammes) of pure and well-dried sugar-candy being dissolved in water, and the solution diluted to the volume of 100 cubic centimetres, and observed in a tube of 20 centimetres in length, the deviation produced is the same as that effected by a quartz plate a milli- metre thick. In making the analysis of raw sugar, a weight of i6'47i grains of sugar is taken, dissolved in water, and the solution made up to 100 cubic centimetres, with which a tube 20 centimetres in length is filled, and the number indicated by the vernier read off, when the primitive tint has been obtained. This number being 42, for example, it is concluded that the amount of crystallisable sugar in the solution is 42 per cent, of that which the solution of sugar-candy contained, and, therefore, i6'47i grains x ^^, or 6'9i8 grains ("499 gramme). ' This result is only valid when the sugar is not mixed with uncrystallisable sugar or some other left-handed substance In that case the crystallisable sugar, which is right-handed, must be, by means of hydrochloric acid, converted into uncrystallisable sugar, which is left-handed ; and a new determination is made, which, together with the first, gives the quantity of crystallisable sugar. The arrangement of crystals and lenses, o,g,f, and a, placed behind the prism c, forms what Soleil calls the producer of sensitive tints. For the most delicate tint — that by which a very feeble difference in the coloration of the two halves of the rotation plate can be distinguished — is not the same for all eyes ; for most people it is of a \iolet-blue tint, like flax blossom ; and it is important either to produce this tint, or some other for which the eye of the observer is equally sensitive. This is effected by placing in front of the prism, c, at first a quartz plate, o, cut perpendicular to the axis, then a small Galileo's telescope consisting of a double convex glass, g, and a double concave glass, f, which can be approximated or removed from each other according to the distance of distinct vision of each observer. Lastly, there is a double-refracting prism, c, acting as polariser in reference to the quartz, and the prism a as analyser ; and hence, when tlie latter is turned either right or left, the light which has traversed the prism t, and the plate o, changes its tint, and finally gives that which is the most delicate for the experimenter. 693. Polarisation of heat. — The rays of heat, like those of light, may become polarised by reflection and by refraction. The experiments on this subject are difficult of execution ; they were first made by Malus and -693] Polarisation of Heat 68; Berard in 1810 ; after the death of Malus they were continued by the latter philosopher. In his experiments, the heat rays reflected from one mirror were re- ceived upon a second, just as in Norremberg's apparatus ; from the second they fell upon a small metallic reflector, which concentrated them upon the bulb of a differential thermometer. Berard observed that heat was not reflected when the plane of reflection of the second mirror was at right angles to that of the first. As this phenomenon is the same as that presented by light under the same circumstances, Berard concluded that the heat rays became polarised in being reflected. The double refraction of heat may be shown by concentrating the sun's rays by means of a heliostat on a prism of Iceland spar, and investigating the resultant pencil by means of a bolometer or of a thermopile, which must have a sharp narrow edge. In this case also there are an ordinary and an extraordinary ray, which follow the same laws as those of light. In the optic axis of the calcspar, heat is not doubly refracted. A Nicol's prism can be used for the polarisation of heat as well as for that of hght : a polarised ray does not traverse the second Nicol if the plane of its principal section is perpendicular to the vibrations of the ray. The phenomena of the polarisation of heat may also be studied by means of plates of tourmaline and of mica. The angle of polarisation is virtually the same for heat as for light. In all these experiments the prisms must be very near each other. The diffraction, and therefore the intei-ference, of rays of heat has been established by the experiments of Knoblauch and others. And Forbes, who repeated Fresnel's experiment with a rhombohedron of rock salt, found that by two total internal reflections, heat is circularly polarised, just as is the case with light. 688 On Magnetism. [694- BOOK VIII ON MAGNETISM CHAPTER I PROPERTIES OF MAGNETS 694. Natural and artificial magnets. — Magnets are substances which have the property of attracting iron, and the term magnetism is applied to the cause of this attraction and to the resulting phenomena. The property exists in a high degree in an ore of iron which is known in chemistry as the magnetic iron oxide. Its composition is represented by the formula FejOj. This mineral, which is also called lodesione., was first found at Magnesia, in Asia Minor, the name magnet being derived from this circumstance. The name lodestone, which is applied to this natural magnet, was given on account of its being used when suspended as a guiding or leading stone, from the Saxon Icedati, to lead ; so also the word lodestar. Lodestone is met with in the older geological formations, especially in Sweden and Norway, where it is worked as an iron ore, and furnishes the best cjuality of iron. A piece of steel may, by suitable means, which will be presently described, have this property of attracting iron conferred upon it ; it then laecomes an artificial magnet. Artificial magnets can be made more powerful than natural magnets, and, as they are also more convenient, they will be exclusively referred to in describing the phenomena of magnetism. They may be made of any shape : a bar magnet is a rectangular strip with square ends, say eight or ten inches long, an inch broad, and an eighth of an inch thick ; it becomes a horseshoe magnet when its ends are bent round towards each other. A magnetic needle is a thin strip of magnetised steel with pointed ends, suspended by a string, or supported on a pi\ot, in such a way that it can turn in a horizontal plane ; it is often called a. compass needle. 695. Poles and neutral lines. — When a small piece of soft iron is sus- pended by a thread and a bar magnet is approached to it, the iron is attracted towards the magnet, and some force is required for its removal. The force of the attraction varies in different parts of the magnet ; it is strongest at the two ends, and is totally wanting in the middle. -696] Reciprocal Action of two Poles 689 This variation may also be seen very cleariy when a bar magnet is placed in iron filings (fig. 674) ; the filings cling round the ends of the bar in feathery tufts, diminishing in amount towards the middle, where there are none. That part of the surface of the bar which is free from filings is called the neutral line or neutral plane ; and the parts near the ends of the bar where the attraction ^^|i(||jl,| | ,j| ,1 1 n ni .il| is greatest are called the poles. Every magnet, whether natural or arti- '®' ''* ficial, has two poles and a neutral line. The experiment of the iron filings shows that the two ends of the magnet are exactly alike in their action on the fihngs, there being nothing to indicate any difference between them. But a magnet, suspended by a string in such a way that it can move in a horizontal plane, is found to come to rest after some oscillations in nearly a north and south position, one particular end pointing to the north. We must therefore distinguish one end of a magnet from the other. The end which points to the north is called the north or red pole, the other being the south or blue pole. 696. Reciprocal action of two poles. — When a small magnetic needle, ab (fig. 675), is suspended by a fine thread, and the north pole, A, of another needle is brought near its north pole, a, repulsion takes place. If, on the contrary, A is brought near the south pole, b, of the movable needle, the latter is strongly attracted. It may be shown in the same manner that the two poles of the magnet A are also different, by successively presenting them to the same pole, a, of the movable needle. In one case there is repulsion, in the other attraction. Hence the following law may be enunciated : — Poles of the same name repel, and poles of contrary ilames attract, one another. The setting of a magnetic needle north and south would be intelligible in the light of the above law, if there were in the northern regions of the earth a magnet polev- a blue pole — attracting the red end of the needle and repelling the blue end, and in the southern part of the earth a red pole attracting the blue and repelling the red end of the needle ; in other words, if the earth were a natural magnet with blue polarity in the Arctic and red polarity in the Antarctic regions, and we know that the earth is such a magnet. Faraday called the north end of a magnet the marked end, and dis- tinguished it by a transverse notch, the other end being the icmnarked end. Lord Kelvin calls the end which points to the north the true south pole, and the end which points to the south the true north pole. Such nomenclature Y Y Fig. 675 690 On Magnetism [696- is liable to cause confusion. Sir George Airy introduced the names red and blue. For practical purposes Lord Kelvin has adopted these names ; he paints the magnets which are used for the correction of ships' compasses half red and half blue. On the same principle the earth's magnetism would be represented by a globe painted blue in the northern and red in the southern hemisphere. We shall call the end of a magnet which points to the north the red or north pole indifferently, except when we are dealing with the earth's magnetism, in which case blue and red are preferable terms. 697. Experiments with broken magnets. — We have seen that the two halves of a bar magnet have opposite polarities, although the action is greatest at the ends, and diminishes to zero at the centre. We might hence expect that if a magnet were broken in two, each half would retain the magnetism it possessed in the unbroken bar, and so exhibit polarity of one kind only. That this is not so, but that each of the broken parts possesses all the pro- perties of a complete magnet, is evident from the following experiment : — A steel knitting-needle (fig. 676) is magnetised by rubbing it with one of the poles of a magnet, and then, the existence of the two poles A, B, and of the neutral line N having been ascertained by means of iron filings, it is broken in the middle. But now, on presenting successively the two halves to a magnet, each will be found to possess two opposite poles A, B', and A', B, with a neutral line N, and to be in fact a perfect magnet. If these new magnets are broken in turn into two halves, each will be a complete magnet AB" and A"B' with its two poles and neutral line, and so on, as far as the division can be continued. Further, the piece A"B' from near the centre is just as strong as the piece AB" near the end. If the magnetised knitting-needle be converted into filings, each bit is still a perfect magnet. In imagination we may carry the division farther, and assert that when the attenuation has gone so far that the molecule is reached, each ultimate particle contains the two magnetisms ; that magnetism, in short, is a phenomenon the cause of which resides in the elementary particle or molecule itself Each molecule is a magnet. It follows also from this experiment that it is impossible to obtain one pole of a magnet without the other, in other words that unipolar magnets have no existence. In practice, however, and for experimental purposes, we may assume that one end of a magnet, the length of which is 50 times its diameter, acts as an isolated or single pole. 698. Theories of magnetism. — To explain the phenomena, it was usual at one time to assume the existence of hypothetical magnetic fluids each of which acts repulsively on itself, but attracts the other fluid, and to imagine each molecule of the magnetic substance in the unmagnetised state to be surrounded by equal quantities of the two fluids, so as to mutually neutralise each other. The fluids could be more or less separated from each other by the action of magnetising forces, but were not able to leave the molecule. Fig. 676 -698] Theories of Magnetism 6g i The fluids were completely separated when the substance was magnetised to saturation. Another way in which the phenomena may be regarded is to suppose every particle of a magnetic substance such as iron to be intrinsically a magnet having a north (or red) pole at one end, and a south (or blue) pole at the other end. In the unmagnetised bar these molecular magnets have their axes pointing in directions depending on their mutual actions, and the bar exhibits no resultant external magnetic effect, since, on the whole, the particles point as much in one direction as in another. When, however, the bar is subjected to an external magnetic force, the molecular magnets tend to be twisted round into the direction of magnetisation, which tendency is greater the greater the applied force. If the applied force is so great that all the tiny magnets have their axes brought completely round into the direction of the force, the bar is magnetised to saturation. We need not trouble ourselves with the question as to how the molecules of a magnetic substance become magnets. We have only to suppose that the magnetic character of each molecule is an inherent and permanent property of the substance, like its hardness, or opacity, or electric conductivity. This mode of regarding what takes place in a magnetic substance when it is magnetised may be illustrated by nearly filling a glass tube with steel magnetised filings, obtained by filing up a steel magnet. The tube will be found to behave like a rod of iron, showing no polarity. But if the particles are shaken while being subjected to a strong magnetic force, if for instance the tube, held vertically, be sharply tapped against the south pole of a strong bar magnet, so that the filings are more or less free to move at the moment when they are acted upon by a downward magnetic force, it will be found that the tube has become a permanent magnet, with a north pole at the bottom and a south pole at the top. The effect of the applied force has been to draw downwards to a greater or less extent the north poles of the filings. But on shaking the tube, or turning out the filings, and putting them in again so as to destroy the regularity, every trace of polarity will disappear. It seems therefore that the polarity at each end of a magnet is caused by the fact that the resultant action on a magnetic body is strongest near the ends, and does not arise from any accumulation of magnetisms at the ends. Rupture of the glass tube may be guarded against by placing a piece of cloth on the bar magnet. The same point may be illustrated by the following experiment, which is due to the late Sir W. Grove : — In a glass tube with plate glass ends is placed water in which is diffused magnetic oxide of iron. Round the out- side of the tube is coiled some insulated wire. When the tube is shaken the liquid appears dark and muddy by transmitted light, but beconies clearer when a current of electricity is passed through the wire. This is due to the fact that by the magnetising action of the current the mag- netic particles set with their longest dimension parallel to the axis of the tube, in which position they obstruct the passage of light to a less extent. The ultimate particles of a piece of iron are not in absolute contact with each other. We are assured of this by the fact that the volume of an iron rod diminishes when its temperature falls. Hence the ultimate particles have y Y 2 692 On Magnetism [698- a certain freedom of motion. Joule showed that when a bar of iron is mag- netised it is increased in length, which is accounted for by supposing that the molecular magnets turn round with their magnetic axes in the direction of magnetisation. The more recent experiments of Mr. Shelford Bidwell will be described later (906). 699. Magnetic field. Lines of force. — The space round a magnet through which it exercises its property of attracting or repelling a magnetic pole is called the magnetic field due to the magnet. The magnetic field is pervaded by magnetic force, so that if a magnetic pole is placed at any point in it, the pole begins to move in a definite direction, which is the dii-ection of the force at the point. A red pole would move in one direction, a blue pole in the opposite, and a small compass needle would set so as to show the direction of the line of force at the point. Thus, if a small magnet about an inch long is pivoted on a point and put on a table on which a bar magnet is supported, the needle and magnet being in the same horizontal plane, the needle shows the direction of the magnetic force, which in this case is due jointly to the bar magnet and to the earth. By gradually moving the little needle in the direction in which it points, a line is traced which indi- cates at any point the direction of the resultant magnetic force. If we repeat the operation, starting at some fresh point, we trace another line of magnetic force, and so the whole field, or rather the horizontal section of it in which the exploring needle moves, may be mapped out. Near the poles of the bar magnet the exploring needle points directly towards the pole ; at places equidistant between the poles it lies parallel to the bar. The general appearance of the lines of force, as thus traced, is shown in fig. 679. The intensity of the magnetic force is greatest near the poles, and diminishes as the distance increases. By the term strength of a field at a poi7it is meant the intensity of the magnetic force at that point. 700. Magnetic induction. — A rod of iron introduced into a magnetic field at once becomes a magnet, and is said to be magnetised by induction, its magnetism being induced magnetism.. When the iron is removed from the field, as a rule the induced magnetism disappears and the rod ceases to have any magnetic polarity. The amount of the induced magnetism is greater when the rod is parallel to the lines of force than when it lies across them, and is greatest when it is in contact with one end, say the north pole^ of the bar ; the rod, if not too large, will then be supported by the magnet, and will itself be a magnet, as may be tested by iron filings, with south pole at the top and north pole at the bottom, and remain so as long as the contact continues. This rod will sup- port a second, and that a third, and so on (fig. 677), the Fig. 677 magnetic attraction becoming feebler as the distance from the bar increases. Each of these rods has become a magnet by induction, with a south pole at the top and a north pole below. But they are magnets only so long as they -700] Magnetic Induction 693 Fig. 678 remain under the influence of the bar ; when removed from it they lose all their polarity. The formation of the tufts of iron filings which become attached to the poles of magnets is due to induction. The particles in contact with the magnet are converted into magnets ; these act inductively on the adjacent particles, and these on the next, and so on, producing a filamentary arrangement of filings. The bush-like appearance of these filaments is due to the repulsive action which the free poles exert upon each other. Any piece of magnetic substance like iron, while being attracted by a magnet, is for the time being converted into a magnet. Magnetic action can only take place between magnets, not between a magnet and a piece of matter. Fig. 678 illustrates the effect of superposing two magnetic fields. A is the north pole of a bar magnet to which a piece of iron, a key for example, is attached, being rendered a magnet by induction, with a south pole at the top. When a second similar mag- net is slid over the first with its south pole B gradually approaching the north pole A, the magnetism induced in the key is weakened and the key presently falls. Two magnets placed in contact with opposite poles together produce practically no external field, that is, iron is not magnetised in their neighbourhood. The distribution of magnetic force in the field due to a bar magnet may be well shown by means of iron filings, since these become magnets when introduced into the field. If a stout sheet of paper stretched on a frame is held over a bar magnet, and then some very fine iron filings are strewn on the paper, on tapping the frame the filings will be found to arrange them- selves in thread-like curved lines, stretching from pole to pole (fig. 679). These lines form what are called magnetic curves. The direction of the curve at any point represents the direction ai magnetic force at this point. To render these curves permanent, the paper on which they are formed should be waxed ; if then a hot iron plate is held over them, the wax is melted, and rises by capillary attraction (132) between the particles of filings, and, on subsequent cooling, connects them together. They may also be fixed by carefully placing on Fig. 679 694 On Magnetism [700- them a sheet of paper coated with paste, which is then gently pressed and Ufted off ; it should be quickly dried to prevent the iron from rusting. These curves are a graphic representation of the law of magnetic attrac- tion and repulsion with regard to distance ; for under the influence of the two poles of the magnet each particle becomes itself a minute magnet, the poles of which arrange themselves in a position dependent on the resultant of the forces exerted upon them by the two poles, and this resultant varies with the distance of the two poles respectively. A small magnetic needle placed in any position near the magnet will take a direction which is the tangent to the curve at this place. We must picture to ourselves a permanent magnet as having permanently associated with it a definite set of lines of force, which are not merely bound up with the fact that their existence is revealed by iron filings. Lines of force must be conceived as acting like stretched elastic threads repelling each other in a direction at right angles to their lengths. An illustration of this is furnished by suspending two long thin magnetised needles from threads at the ends ; when these are brought near each other, with like poles opposite, the direction of the lines of force is the same in each, and the needles repel each other. In fig. 680 the magnetic curves represent the direction of the lines of force in the field due to two opposite poles, Fig. 680 Fig, 681 while fig. 681 represents that due to two similar poles, both figures being taken from photographs of actual fields. The expression ' lines of force ' or ' lines of magnetic force ' is used in much the same sense as that in which we speak of rays of light. And just as we might express the illumination of any surface by the number of rays which fall upon it, so also we may say that the strength of the magnetic field at any point is proportional to the number of lines of force which pass through a given area placed transversely to the lines and enclosing the point, A uniform rnagnetic field is one in which the lines of force are parallel and uniformly distributed. This is practically the case with a small portion of the field at a considerable distance from the pole of a magnet, or between the poles of a horseshoe magnet It is also the case in the interior of a long magnetising coil (901) except near the ends. The direction of a line of force is the direction in which a red pole would move along the line ; it is usual to speak of the lines as starting at the north pole and ending at the south pole. It will be seen later that we must -701] Magnetic Substances 695 regard a line of force, not as starting at one point and ending at another, but as a continuous line running through the substance of the magnet. Fig. 679 shows only the external portions of the lines, but each of these has its counterpart in the steel itself, so that the lines run in the magnet from the south to the north pole, and externally from the north to the south. If the bar is very long in comparison with its cross section, the lines emerge and enter at the ends only ; but with an ordinary bar magnet the lines escape before they reach the end, as is indicated by the smaller curves in fig. 679. When a bar magnet is plunged into filings none of them cling to the centre, because no lines of force escape there ; where lines of force escape, there filings cling. Hence all the lines associated with a magnet pass through the middle ; here they are parallel, but they diverge towards the ends and complete the magnetic circuit outside. 701. Magnetic substances. — Iron is not the only substance which is attracted by a magnet. Nickel and cobalt exhibit the same property, and, to a less degree, manganese. Faraday showed that there are a great many other substances which are also magnetic ; but in them the attraction is so feeble that special means must be employed to show it. Again, there are other substances which are repelled instead of attracted by a magnet, bismuth being the most noteworthy ; such substances are said to be diatnagnetic. Thus, as regards magnetic properties, all substances may be put into one of three classes : — 1. Ferromagnetic substances, or those which are strongly acted on by a magnet. These are iron, nickel, cobalt, and, to a less extent, manganese, at ordinary temperatures ; alloys of iron with carbon (different kinds of steel) and other substances, and salts of iron. 2. Paramagnetic substances. — These are also attracted by a magnet, but so slightly that the action cannot be observed except under special con- ditions. In this class are the metals platinum and aluminium, many salts, oxygen and ozone, and the ferromagnetic metals, iron, nickel, and cobalt, when heated above their critical temperatures (712). 3. Diaw.ag72ctic substances, or those which are repelled by the pole of a magnet. A rod of a diamagnetic substance tends to place itself at right angles to the lines of force in- a magnetic field, as a rod of iron places itself along the lines of force. Among diamagnetic substances are bismuth, phos- phorus, antimony, water, and many gases. The subject of Diamagnetism is treated in Chapter XIII. Magnetic substances have no action on each other. If a rod of iron be dipped into filings none of them adhere ; but if the rod be brought near to one of the poles of a compass needle the pole is attracted and the needle deflected. This is due to the fact that when the rod is brought into the magnetic field of the needle it becomes a magnet by induction. The end nearest to the north pole of the needle becomes a south pole, and so attraction ensues ; but the magnetism comes and goes quite freely owing to the small coercive force (702) of the iron, so that when the same end is pre- sented to the south pole of the needle it becomes a north pole, and again attrac - tion occurs. If the iron rod had been a magnet, either end of it would have attracted one end of the needle, and repelled the other. Thus the phenomenon of repulsion enables us to determine when a rod of iron or 696 On Magnetism [701- steel has or has not any permanent magnetism. But this is sometimes misleading ; for instance, if a rod of iron have a certain very small amount of permanent magnetism it may repel one of the poles of a magnet at a certain distance, but attract it when brought nearer, owing to the induced magnetism overpowering the small amount of permanent magnetism. The best way of testing a rod of magnetic substance for a trace of permanent magnetism is to place it at right angles to the magnetic meridian (727), so that its end is equidistant from the two poles of a small sensitive compass needle. Under these conditions it will have no magnetism induced in it by the needle, and therefore if it is free from permanent magnetism the needle will not be de- flected. A deflection of the needle must be due to permanent magnetism in the rod. 702. Coercive force.- — We have seen from the above experiments that soft iron becomes magnetised under the influence of a magnet, but that this magnetism is not permanent, and ceases when the magnet is removed. Steel likewise becomes magnetised when near to a magnet ; but to a much less extent, and the less as the steel is more highly tempered. Placed in contact with a magnet, a steel bar acquires magnetic properties to a shght extent only ; to make the magnetism more powerful the steel must be rubbed with one of the poles. But the greater part of the magnetism thus evoked in steel is permanent, and does not disappear when the inducing force is removed. These different effects in soft iron and steel are ascribed to a kind of resistance, analogous to friction, which is called coercive force and which, in a magnetic substance, offers a hindrance to the rotation of the molecular magnets, but which also prevents their return to their former positions when once moved. In steel this coercive force is very great ; in soft iron it is very small or almost absent. By oxidation, stretching, pressure, torsion, or hammering, a certain amount of coercive force may be imparted to soft iron ; and by heat the coercive force may be lessened, as will be afterwards seen. -706] Method of Separate Touch 697 CHAPTER II METHODS OF MAGNETISATION 703. Magnetisation. — There are various methods by which the ferro- magnetic substances — iron, steel, nickel, and cobalt — may be converted into magnets. We have already seen that a piece of iron becomes a magnet, by induction, when brought into a magnetic field, and that the amount of magnetism induced is greatest (for a given position in the field) when the iron lies along the lines of force. But the magnetism thus produced is as a rule not permanent. The principal methods of converting a bar of steel into a permanent magnet are (i) those known by the technical names of single touch, separate touch, and double totcch, and (2) those in which an electric current is employed. 704. Method of single touch. ^ — This consists in moving the pole of a powerful magnet from one end to the other of the bar to be magnetised, and repeating this operation several times always in the same direction. The molecular magnets are thus gradually rotated throughout all the length of the bar, and that end of the bar which was touched last by the magnet is of opposite polarity to the end of the magnet by which it has been touched. This method only produces a feeble magnetic power, and is, accordingly, only used for small magnets. 705. Method of separate touch. — This method, which was first used by Dr. Knight in 1745, consists in placing the two opposite poles of two equally strong magnets in the middle of the bar to be magnetised, and then moving them simultaneously towards the opposite ends of the bar. Each magnet is then placed in its original position and the operation repeated. After several rubbings on both faces the bar is magnetised. In Knight's method the magnets are held vertically. Duhamel improved the method by inclining the magnets, as represented in fig. 682 ; and still Oi'LJ Fig. 682 more by placing the bar to be magnetised on the opposite poles of two fixed magnets, the action of which strengthens that of the movable magnets. If 698 ; On Magnetism [705- all the magnets are arranged in the magnetic meridian with their north poles (A) towards the north, additional advantage is gained from the inductive action of the earth's magnetism. The relative position of the poles of the magnets is indicated in the figure. This method produces the most regular magnets. 706. Method of double touch. — In this method, which was invented by Mitchell, the two magnets are placed with their opposite poles together in the middle of the bar to be magnetised. But, instead of being moved in opposite directions towards the two ends, as in the method of separate touch, they are kept at a fixed distance by means of a piece of wood placed between them (fig. 682), and are simultaneously moved first towards one end, then from this to the other end, the operation being repeated several times, and finished in the middle, care being taken that each half pf the bar receives the same number of frictions. Epinus, in 1758, improved this method by supporting the bar to be mag- netised, as in the method of separate touch, on the opposite poles of two powerful magnets, and by inclining the bars at an angle of 1 5° to 20°. In practice, instead of two bar magnets, it is usual to employ a horseshoe magnet which has its poles conveniently close together. Whichever of the above three methods is employed, it will be found that, after five or six rubbings on each side, the bar has received as much magnetism as can be imparted to it by the particular method employed. This can be tested by placing the bar on a table at right angles to the magnetic meridian, at the distance of about 40 or 50 cm. from a small com- pass iieedle, The deflection of the needle, which is a measure of the magnetism of the bar, increases with the number of rubbings up to five or six, but not beyond. If in the method' of separate or double touch two similar poles are used, two red poles for example, the result is that the steel bar acquires a blue pole at each end and a red pole in the middle. The magnet is then said to have consequent poles. In the method of double touch, even when two unlike poles are used, it often happens that consequent poles are developed. Hence this method is not in general so satisfactory as that of separate touch, 707. Magnetisation by electricity. — In the methods of touch described above, the bar of steel was magnetised by suitably agitating its particles when it was in the field of the magnet or magnets employed, and the amount of induced magnetism was limited by the strength of these magnets. If stronger magnets are used, or if by other means the strength of the magnetic field surrounding the steel be increased, more magnetism may be induced. A bar of steel is said to be magnetised to saturation when its magnetism cannot be increased by any possible means. On the molecular- magnet theory we see that this condition will be reached when the molecules are turned round so that their magnetic axes are all parallel to the direction of magnetisation, that is, to the length of the bar. An electric current supplies us with the most satisfactory means of applying a magnetic field. A tube made of brass or glass or other non- magnetic materia! is wound with from ten to twenty turns per cm. of insulated copper wire, the ends of which terminate in binding screws as represented -709] Armatures 699 at A (fig. 966). When a current from a battery passes through this coil' a magnetic field is produced inside and all round it, but the field is strongest in the hollow of the tube where the lines of force are parallel to the length of the tube. The strength of the field depends upon two things, viz. the number of turns of wire in the coil and the strength of the electric current, that is, upon the number of ampere-turns (902). Thus for a given coil we can, by increasing the current, make the field as strong as we wish. The bar of steel to be magnetised is placed inside the coil, and on removal, after the circuit has been broken and completed several times, is found to be strongly magnetised. 708. Magnetic battery. — A magnetic battery consists of a number of magnets joined together by their similar poles. Sometimes they have the form of a horseshoe, and sometimes a rectilinear form. The battery repre- sented in fig. 683 consists of five superposed steel plates. That in fig. 684 consists of twelve plates, arranged in three layers of four each. The horseshoe form is best adapted for supporting a weight, for then both poles are used at 'once. In both the bars are magnetised separately, and then fixed by screws. The force of a magnetic battery consisting of n similar plates equally magnetised is not n times as great as that of a single one, but is somewhat smaller. These magnets mutually en- feeble each other ; manifestly because each north pole evokes south mag- netism in the adjacent north pole, and thereby diminishes some of its north polarity. At the same time the strength is greater than if the steel is in one co- herent mass ; the reason doubtless is that thin plates of steel are more easily mag- netised to saturation than thick ones, as the inducing action does not extend deep. The separate plates should not be in contact, as the enfeeblement of the mag- netism is thereby less. It is also advisable to connect the pieces by a mass of soft iron as shown in fig. 684. The magnetism of a plate which has formed part of such a battery will be found to be materially less than it was originally. Thus Jamin found that six equal plates, which separately had each the portative force (7io)>of 18 kilos., only lifted 64 kilos, when arranged as a battery, instead of 108; Fig, and «hen removed from the battery, each of them had onlyi the portative force 9 to 10 kilos. The force is increased by making the lateral plates i or 2 centimetres shorter than the one in the middle (fig. 683). 709. Armatures. — After a steel bar has been brought to its limit of satura- tion, it gradually loses its magnetism. To prevent this, armatiires or keepers are used ; these are pieces of soft iron, A and B (fig. 684), which are placed 70O On Magnetism [709- Fig. 684 Fig. 685 in contact with the poles. Acted on inductively, they become powerful temporary magnets, possessing opposite polarity to that of the inducing pole ; they thus react in turn on the permanent magnetism of the bars, preserving and even increasing it. The lines of force between opposite poles, instead of spreading out in widely extended curves, are now for the most part confined to the soft iron keepers, and there is comparatively little external field. Iron is more permeable to lines of force than air (721). When the magnets are in the form of bars, they are arranged in pairs, as shown in fig. 685, with opposite poles in juxtaposition, and the magnetic circuit is completed by two small bars of soft iron, AB. A horseshoe magnet has A,,>° » .. ^.uM -^1 " a keeper attached to it, which is usually arranged so as to support a weight. The keeper becomes magnet- ised under the influence of the two poles, and adheres with great force : the weight which it can support being more than double that which a single pole would hold (fig. 683). In respect to this weight, a^singular phenomenon has been observed. When contact is once made, and the keeper is charged with its maximum weight, any further addition would detach it ; but if left in contact for a day, an additional weight may be added without detaching it, and by slightly increasing the weight every day it may ulti- mately be brought to support a far greater load than it would originally. But if contact be once broken, the weight it can now support does not much exceed its original charge. It is advantageous that the surface of the magnet and armatures which are in contact should not be plane but very slightly cylindrical, so that they touch along a line. In providing a natural magnet with a keeper, the line joining the two poles may first be approximately determined by means of iron filings ; it may also be determined by bringing it near a magnetic needle, and ascertaining the positions in which its action is greatest. Two poles of soft iron (fig. 686), each terminating in a massive shoe, are then applied to the faces corresponding to the poles. Under the influence of the natural magnet, these plates become magnetised, and if the letters A and B represent the position of the poles of the natural magnet, the poles of the armature are a and b. 710. Portative force. — The portative force is the greatest weight which a magnet can support. It can be determined by suspending to the keeper a vessel to which shot or sand or water is gradually added, until the keeper is detached (fig. 683). Hacker found that the portative force of a saturated Fig. 686 -711] Circumstances which influence the Power of Magnets 701 horseshoe magnet, which, by repeatedly detaching the keeper, had become constant, may be represented by the empirical formula m which P is the portative force of the magnet, p its own weight, and a a coefficient which varies with the nature of the steel and the mode of mag- netising. Hence a magnet which weighs 1000 ounces supports only 25 times as much as one weighing 8 ounces or ^-Jj as heavy, and 25 such bars would support as much as a single one which is as heavy as 125 of them. It appears immaterial whether the section of the bar is quadratic or circular, and the distance of the legs is of inconsiderable moment ; it is important, however, that the magnet be suspended vertically, and that the load be exactly in the middle. In Hacker's magnets the value of a was iO'33, while in Logemann's it was 23. By arranging together several thin magnetised plates Jamin constructed bar magnets which supported 15 times their own weight. The attraction between the plane pole face of a magnet and an iron armature m contact with it may be shown to be -5 — , where S is the area of on" the surfaces in contact and B the magnetic induction (72 1 ), that is the number of lines of force per square centimetre of the surfaces. In the case of a horseshoe magnet the surface S is that of both limbs. 711. Circumstances which influence the power of magnets. — All bars do not attain the same magnetic state under the same magnetising forces, for their coercive force varies. Twisting or hammering imparts to iron or steel a considerable coercive force. But the most powerful of these in- fluences is the operation of tempering (93). Coulomb found that a steel bar tempered at dull redness, and magnetised by a given field, made ten oscilla- tions in 93 seconds. The same bar tempered at a cherry-red heat, and similarly magnetised, took only 63 seconds to make ten oscillations. Hence it would seem that the harder the steel the greater is its coercive force ; it undergoes magnetisation less readily, but retains it more effectually. It appears, however, from Jamin's experiments that no general rule of this kind can be laid down ; for each specimen of steel there seems, according to the proportion of carbon which it contains, to be a certain degree of tempering which is most favourable for the development of permanent mag- netisation. Very hard steel bars have the disadvantage of being very brittle, and in the case of long thin bars a hard tempering is apt to produce consequent poles (706). Compass needles are usually tempered at a blue heat — that is, about 300° C. — by which a high coercive force is obtained without great fragility. The steel rods used by Lord Kelvin for compass correction are made as hard as possible ; before being magnetised they are raised to -a bright red heat and quenched in cold water. The hardness of steel, and the proportion of carbon which it contains, exert an important influence on the degree to which it can be magnetised. For the same degree of hardness, the magnetisation increases with the pro- portion of carbon in the steel. Holtz magnetised plates of English corset steel to saturation and determined their magnetic moment ; they were 702 On Magnetism [711- then placed in dilute hydrochloric acid, by which the iron was eaten away, and the magnetic moment determined when the plate had been magnetised to saturation after each such treatment. It was thus found that, with a diminution in the proportion of iron, there was an increase in the magnetic moment for the unit of weight. Holtz found, however, that perfectly pure iron prepared by electrolysis can acquire permanent magnetism. Ferro- manganese, or iron alloyed with about 12 per cent, of manganese, is quite destitute of magnetic properties. Hopkinson showed that nickel steel con- taining 25 per cent, of nickel and a small percentage of carbon is magnetic or non-magnetic at ordinary temperatures, depending on its previous treat- ment. If a specimen of magnetic nickel steel is raised to a sufficiently high temperature it loses its magnetic susceptibility (722), and does not regain it on cooling, so that at ordinary temperatures it is now non-magnetic. It recovers, however, its capacity for being magnetised if cooled down to -20° C. Jamin found that magnetisation extends deeper in a bar than has been usually supposed ; in soft and annealed steel it penetrates deeply: The depth diminishes with the hardness of the steel and the proportion of carbon it contains. Holtz made some experiments on the influence of solid bars as against hollow tubes in the construction of permanent steel magnets. The latter are to be preferred ; they are decidedly cheaper, as they need not be bored, but may be bent from steel plates. A bar and a tube of the same steel, 125 mm. in length by 13 mm. diameter, the tube being 175 mm. thick, were magnetised to saturation, and their magnetic moments determined by the method of oscillation (719), the tube being loaded with copper. The magnetism of the tube was to that of the bar as i-6 : I. The tubes also retained their mag- netisation better. After the lapse of six months the ratio of the magnetism of the tube to that of the bar was as 27 : i. A magnetised steel tube filled with a soft iron core has scarcely any directive force. Holtz considers that the iron acts as a keeper. Percussion and torsion. — When a steel bar is hammered while being magnetised it acquires a much higher degree of magnetisation than it would without this treatment. Conversely when a magnet is let fall, or is otherwise violently disturbed, it loses some of its magnetisation. Wiedemann has inves- tigated in a very complete manner the relations of torsion and magnetisation. Torsion exerts a great influence on the magnetisation of a bar, and the inter- esting phenomenon has been observed that the influence of torsion on mag- Tietism is reciprocal. Thus the permanent magnetisation of a steel bar is diminished by torsion, but not proportionately to the increase of torsion. In like manner the torsion of twisted iron wires is diminished by their being magnetised, though less so than in proportion to their magnetisation. Repeated torsions in the same direction scarcely diminish magnetisation, but a torsion in the opposite direction produces a new diminution of the magnetism. In a perfectly analogous manner, repeated m.agnetisations in the same direction scarcely diminish torsion, but a renewed magnetisation in the opposite direction does so. 712. Effect of temperature. — Increase of temperature always produces a diminution of the magnetism of a steel magnet. If the changes of tempera- -713] Distribution of Free Magnetism 763 ture are small — those of the atmosphere, for instance — the magnet is not permanently altered. Kuppfer allowed a magnet to oscillate, in the earth's field, at different temperatures, and found a definite decrease in its moment with increased temperature, as indicated by its slower oscillations. In the case of a magnet ih inches in length, he observed that with an increase of each degree of temperature the duration of 800 oscillations was 0-4 second longer. If n be the number of oscillations at zero, and n^ the number at /, then 72 = yZj ( I — ct\ where t is a constant depending in each case on the magnet used. This formula has an important application in the correction of the observations of magnetic force which are made at different places and at different temperatures, and which, in order to be comparable, must first be reduced to a uniform temperature. When a magnet has been more strongly heated, it does not regain its original moment (720) on cooling to its original temperature ; and when heated to bright redness, it is demagnetised. This was first shown by Coulomb ; it is the most satisfactory method of demagnetising' a steel magnet. The magnet, after being heated to bright redness (about 800° C), may be cooled either slowly or rapidly, but in either case it should be held in such a position as not to be subjected to any magnetic force. Substances which are ferromagnetic at ordinary temperatures lose their magnetic quality, or rather become paramagnetic (701), like copper. &c., when their temperature is sufficiently raised. Gilbert showed that at a red heat iron is incapable of being magnetised. As the temperature of iron is raised the susceptibility slightly increases, but falls suddenly to zero when the tem- perature reaches 790°. The point at which this sudden loss of magnetic quality occurs is called the critical temperature for the particular metal. The critical temperature of nickel is 350° ; for cobalt it is above a white heat. The suddenness with which iron loses its magnetic quality depends upon the intensity of the field. In a very feeble field the magnetic susceptibility rises to a very high value just before the critical temperature is reached, and then falls abruptly to zero. 713. Distribution of free magnetism. — Coulomb investigated the dis- tribution of magnetic force by placing a large magnet in a vertical position ; he then took a small magnetic needle suspended by a cocoon thread, and fixed at right angles to a stout copper wire so as to retard the oscillations (fig. 687) ; and having ascertained the number of its oscillations under the. influence of the earth's magnetism alone, he presented it to different parts of the magnet. The oscillations were fewer as the needle was nearer the middle of the bar, and when they had reached that position their number was the same as under the influence of the earth's magnetism S ^ alone. For magnetised bars of more than 7 inches in •''S- ^^7 length the distribution could always be expressed by a curve whose abscissa; were the distances from the ends of the magnet, and whose ordinateS were the force of magnetism at these points. With magnets of the above 704 On Magnetism [713- dimensions the poles are at the same distance from the end ; Coulomb found the distance to be i -6 inch in a bar 8 inches long. He also found that, with shorter bars, the distance of the poles from the end is ^ of the length ; thus with a bar of 3 inches it would be half an inch. These results presuppose that the other dimensions of- the bar are very small as compared with its length, that it has a regular shape, and is uniformly magnetised. When these conditions are not fulfilled, the positions of the poles can only be determined by direct trials with a magnetic needle. With lozenge-shaped magnets the poles are nearer the middle. Coulomb found that these lozenge-shaped bars have a greater directive force than rectangular bars of the same weight, thickness, and hardness. A short magnet is defined by Coulomb as one whose length is less than 50 times its diameter. Kohlrausch found that the pole of a magnet, as far as its action at a distance is concerned, is -^ of its length from the end. Jamin investigated the distribution of force in magnets by suspending from one arm of a delicate balance a small iron ball, and then ascertain- ing what force, applied at the other arm, was required to detach the ball when placed in contact with various parts of the magnet to be investi- gated. 714. Mayer's floating magfnets. — The reciprocal action of magnetic poles may be conveniently illustrated by an elegant method devised by Professor A. M. Mayer. Steel sewing-needles are magnetised so that their points are north poles, and their eyes, which are thus south poles, just pro- ject through minute cork discs, so that when placed in water the magnets float in a vertical position. If the north pole of a strong magnet is brought near a number of these floating magnets, they are attracted by it, and take up , t"" 6* 5« ,,«, *' '\ \ • ♦- • •, ..•„ »■ • ,»■ < ,*' '^ ? f' ^ • • • j A • • • •' *. ■•' 8" %b 18 a lib Fig. 688 definite positions, forming figures which depend on the reciprocal' repulsion of the floating magnets, and on their number. Some of them are repre- sented in fig. 688. As the number of needles increases, various arrangements are possible which are not equally stable, the letters a, b, and c indicating the decreasing order of stability. A slight shock often causes one form to pass into another and more stable form. -715] Professor Ewtng's Experiments 705 These figures not only illustrate magnetic actions, but suggest an image of the, manner in which alteration of molecular groupings may give rise to physical phenomena, such as those of superfusion (348). Such floating magnets as are here described are delicate tests of mag- netisation, and are convenient for investigating the distribution of the poles in bodies of irregular shape. 715. Professor Ewing's experiments. — We may here give an account of Professor Ewing's experiments in illustration of magnetic properties, which explain them without requiring any other assumption than that magnetism is a molecular property, each molecule being a perfect magnet with a north and south pole. He used a number of small magnets made of steel wire not more than ^ of an inch in diameter and 2 inches long, bent in the middle as shown in fig. 689, so as to bring the centre of gravity below the point of support, which was a small sewing-needle fixed in a Fig. 689 lead base, a small depression being punched in the bend. By placing' a number of such small magnetic needles near each other, he found that when left to themselves they set in various configura- tions, each of which is stable, but has no external action. If one part of such a system is disturbed, a new arrangement is established. Each separate magnet takes up a position of stable equilibrium, after oscillations of greater or less amplitude. If now any given configuration is submitted to the action of a gradually increasing magnetic field, produced by passing a voltaic current through a series of parallel wires, the magnets are at first deflected progressively, but if the current is stopped these magnets revert to their original arrangement, and there is no permanent effect on the system. This illustrates the case of slight temporary magnetism. When, however, the strength of the field is further increased, a certain stage is reached at which equilibrium is destroyed, and a fresh configuration is formed in which many of the elementary magnets are in the direction of ' the field. From this stage any increase in the strength of the field only makes the observation more marked. On gradually weakening the field, the system does not return through the same stages ; it tends towards that configuration in which the magnets are parallel to the field. This illustrates the case of permanent magne- tisation. If the system is quite homogeneous — that is, if the molecular magnets are uniformly arranged — the passage to parallelism is comparatively easy ; this represents the case of soft iron. If the system is not homogeneous and the magnets form unequal groups, they do not follow the action equally and at the same time ; the magnetisation is prolonged, and the remanent magnetism is also more stable. This represents the case of steel. The action of heat on a magnetic substance may be explained by the supposition that it acts in two ways, by increasing the distance of the z z 7o6 On Magnetism [715- molecular magnets from each other, and by setting them in oscillation. The first cause facilitates the action of the field, the second diminishes the mag- netic moment : one or the other predominates, according to the strength of the field. To account for the disappearance of magnetic properties at the critical temperature, it may be assumed that the oscillations gradually increase until they change into a rotatory motion of the molecules. -718] The Torsion Balance 707 CHAPTER III LAWS OF MAGNETIC ACTION 716. Poles of a mag'net. — We have spoken of the ends of a bar magnet, where its attraction for iron filings appears to be greatest, as the poles of the magnet. But it is necessary to be more precise. All parts of a bar magnet, from the neutral plane to one end, say the red end, repel a red pole with a force which increases from the middle to the end. If we imagine an isolated red pole to be situated at a definite distance from the magnet, and draw lines from each point of the red half of the magnet to the pole, and take lengths along these lines to represent the magnitudes of the several forces we can by ordinary mechanics find the direction of the resultant of these forces. The point in which the line of the resultant cuts the magnetic axis of the bar may be called the red pole of the magnet. Similarly for the blue pole. But it is found that the position of the poles as so defined is not constant ; it varies with varying distance of the pole acted upon, being nearer the end of the bar as the point in question approaches. To obviate this uncer- tainty it is usual to consider the pole acted upon to be at an infinite distance from the magnet. The lines of action of all the component forces are then parallel, and the centre of these parallel forces is defined as the pole of the magnet. The poles of an ordinary bar magnet may be taken as being about ^ of its length from each end. The poles of a long steel rod, whose length is great in comparison with its cross section — for example, one 30 cm. long and I mm. in diameter — may be regarded as being at the ends. If such a magnetised wire be dipped into iron filings, the filings form small tufts at the ends only. The magnetic axis of a magnet is the straight line which passes through its two poles. 717. Laws of magnetic force. — Consider two long thin magnetised steel wires : we may regard their poles as points, situated at their extremities. The two red poles repel each other with a force which varies inversely as the square of the distance between them. This law of repulsion between two similar poles — the same law holds in the case of attraction between two dissimilar poles — was proved experimentally by Coulomb by two methods : (i) that of the torsion balance, (2) that of oscillations. 718. The torsion balance. — This apparatus depends on the principle that, when a wire is twisted through a certain angle, the moment of the couple resisting torsion is proportional to the angle through which the wire z z 2 7o8 On Magnetism [718- has been twisted (89). It consists (fig. 690) of a glass case closed by a glass top, with an aperture wz near the edge, to allow the introduction of a mag- net, A. In another aperture in the centre of the top a glass tube fits, provided at its upper extremity with a torsion head. This consists of two circular pieces : d, which is fixed, is divided on the edge into 360°, while on one e, which is mov- able, there is a mark, c, to indicate its rotation. D and E represent the two pieces of the torsion head on a larger scale. On E there are two uprights connected by a horizontal axis, on which is a very fine silver wire supporting a mag- netic needle, ab. On the side of the case there is a graduated scale, which indicates the angle of the needle ab, and hence the torsion of the wire. When the mark c of the disc E Fig. 690 is at zero of the scale D, the case is so arranged that the wire supporting the needle and the zero of the scale in the case are in the magnetic meridian. The needle is then removed from its stirrup, and replaced by an exactly similar one of copper, or any non-magnetic substance ; the tube, and with it the pieces D and E, are then turned so that the needle stops at zero of the graduation. The magnetic needle ab, being now replaced, is exactly in the magnetic meridian, and the wire is without torsion. Before introducing the magnet A, it is necessary to investigate the action of the earth's magnetism on the needle ab, when the latter is removed out of the magnetic meridian. This will vary with the magnetic moment of the needle, with the dimensions and nature of the particular wire used for suspension, and with the intensity of the earth's magnetism in the place of observation. Accordingly the piece E is turned until ab makes a certain angle with the magnetic meridian. Coulomb found in one of his experiments that E had to be turned 36° in order to move the needle through 1° ; that is, the earth's magnetism was equal to a torsion' of the wire corresponding to 35°. As the couple of torsion is proportional to the angle of torsion when the needle is deflected from the meridian by 2, 3 . . . degrees, the directive action of the earth's magnetism is equal to 2, 3 . . times 35°. The action of the earth's magnetism having been determined, the magnet A is placed in the case so that similar poles are opposite each other. In one e.Kperiment Coulomb found that the pole a was repelled through 24'. Now the force which tended to bring the needle into the magnetic meridian was represented by 24° + 24 x 35° = 864, of which the part 24° was due to the torsion of the wire, and 24 x 35° was the equivalent in torsion of the directive force of the earth's magnetism. As the needle was in equilibrium, it is clear that the repulsive force which counterbalances these forces must be equal -719] Method of Oscillations 709^ to 864°. The torsion head was then turned until ab made an angle of 12°. To effect this, eight complete turns of the disc were necessary. The total force which now tended to bring the needle into the magnetic meridian was com- posed of: — 1st, the 12° of torsion by which the needle was distant from its starting point ; 2nd, of 8 x 360' = 2880° the torsion of the wire ; and 3rd, the force of the earth's magnetism, represented by a torsion of 12 x 35°. Hence the forces of torsion which balance the repulsive forces exerted at a distance of 24' and of 1 2° are — 24° . . . 864 12' . . 3312 Now, 3312 is very nearly four times 864 ; hence for half the distance the repulsive force is four times as great. In the above calculation several assumptions are made which are not strictly justifiable. In the first place, the moment of the earth's couple on the magnet ab is proportional not to the deflection but to the sine of the deflection (726). The difference between an angle and its sine may be neglected when the angle does not exceed 5° or 6°, but not for angles so large as 24°. Secondly, the distance between the actjng poles has been measured along an arc instead of along a chord of a circle ; and thirdly, the action between the poles A and a only has been taken into account, that between A and b being neglected. 719. Method of oscillations. — A magnetic needle oscillating under the influence of the earth's magnetism may be considered as a pendulum, and the laws of pendulum motion apply to it (56). The method of oscilla- tions consists in causing a magnetic needle to oscillate first under the influence of the earth's magnetism alone, and then successively under the combined influence of the earth's magnetism and of a magnet placed at unequal distances. The following determination by Coulomb will illustrate the use of the method. A magnetic needle was used which made 1 5 oscillations in a minute under the influence of the earth's magnetism alone. A magnetic bar about 2 feet long was then placed vertically in the plane of the magnetic meridian, p- , so that its north pole was downwards and presented to the south pole b of the oscillating needle (fig._69i), so as to concur in its action with that of the earth. He found that at a distance of 4 inches the needle made 41 oscillations in a minute, and at a distance of 8 inches 24 oscillations. Now, from the laws of the pendulum, the intensities of the forces are inversely as the squares of the times of oscillation. Hence, if we call H the force of the earth's magnetism, Fj the force due to the magnet at the distance of 4 inches, F„ at the distance of 8 inches, we have H : H-hF, = i52: 4I^ and H:H + F,= i5-=:24'; eliminating H, Fi : F2 = 4i=-i5- : 242-i5- = i456 : 351=4 : i nearly, or Fi : Fj = 4 : I. \ 7IO On Magnetism [719- In other words, the force acting at 4 inches is quadruple that which acts at double the distance. It will be observed that the influence of the upper pole S in modifying" the field at o has been neglected, and therefore we can only expect the results to agree approximately with the inverse square law ; this law, indeed, cannot be said to be strictly proved by either of the experimental methods employed by Coulomb. A more satisfactory proof will be given later (725). The attraction or repulsion between two poles at a given distance apart depends on the product of the strengths of the two poles ; for, clearly, if either pole is doubled or trebled, the force in action would be twice or thrice as great as before, but if one were doubled while the other was trebled, the force would be increased sixfold. Thus, finally, the force of repulsion, F, between two similar poles, of strengths m^, m^, whose distance apart is r, varies as — L_- or we may write if the units are properly chosen. Suppose the force to be measured in dynes (63), r in centimetres, and that the poles are'equal in strength, and each equal to m ; then F (dynes) = ^. Let r= 1 cm., and let the value of m be increased or diminished until F is exactly equal to i dyne : then I = — , or m= 1 ; that is, the pole is of unit strength. 720. Unit pole. Magnetic moment. — We thus have a definition of um'/ pole ; it is a pole of such strength that it would repel another pole exactly like itself with a force of i dyne if they were i centimetre apart. A pole of strength m would repel unit pole at unit distance with a force of ;« dynes. The mome7it of a magnet is the product of the strength of either pole into the distance between them. If M is the moment, m the strength of each pole, and / their distance apart, M = ml. As a rule we cannot detei-mine either / or m, but their product is a readily measured magnitude. We can picture mentally an isolated pole by thinking of one end of a magnetised steel wire, the other end of which is too remote to be considered. Lines of force radiate from an isolated pole (say of strength m) equally in all directions, the intensity of the resulting magnetic field, at any distance r from the pole, being _. But the intensity of a magnetic field is also defined as the number of lines which pass through the unit of area (i sq. cm.) held at right angles to the field. By comparing these two modes of expressing the intensity of a magnetic field, we arrive at an expression for the number of lines of force which radiate from a magnetic pole. For suppose an isolated pole, /«, to be the centre of a sphere of radius r (cm.), and N to represent the total number of radiating lines. Since the surface -722] Magnetic Susceptibility 7 1 1 of the sphere is 47r?'- (sq. cm.) and the lines are uniformly distributed, the number per square centimetre, or intensity of magnetic field at distance ' r = : but this is equal to - ; .'. N = 47r7«. Thus there are 47r ( = I2'6) 4jrr'- r' lines of force proceeding from each unit magnetic pole. 721. Mag^netic permeability. — When various substances, such as glass, wood, cardboard, or copper, are brought into the magnetic field, the lines of force proceed through them as if there were air in their place. But if a bar of soft iron is brought into the field the lines of force pass through it in larger quantities, the distribution of the field is thereby altered, and within a certain range the other lines are deflected. The iron attracts them as it were, causing those lines in the neighbourhood to make their way through it ; the iron is more. per7neable to lines of magnetic force. This may be illustrated by considering the case of a stream of water with a steady flow, in which is a quantity of river weed, which offers resistance to the flow ; if the weed is removed from a certain space in the middle, the resistance which it offers is also removed, the water flows more easily there, and the direction of the lines of flow in the neighbouring parts is now deflected towards the free part. The lines of force thus falling on a piece of soft iron converge towards the iron and emerge at the other end. Where the lines enter is a south and where they emerge a north pole. A magnetic needle free to move and brought near the magnet takes up such a position that the lines of force have undisturbed course through it. With soft iron this is also the case ; the molecular magnets are rotated, so that they offer as little hindrance as possible. If a soft iron ring is placed in a magnetic field, its plane being parallel to the field, the lines of force make their way through the iron and very few enter the interior, as may be seen by means of iron filings. A massive iron cylinder acts thus as a ?nagnetic screen, shielding magnets placed in the interior against the action of the magnetic field. The magnetic permeability of a substance is defined as the ratio of the number of lines of force passing through a mass of it to the number which would pass through the same Volume of air or other non-magnetic material, the magnetising force being the same in each case. It is denoted by the symbol ^i. If H represent the strength of a magnetic field, that is, the number of lines per sciuare centimetre of cross section, and B represent the number of lines per square centimetre passing through a mass of iron placed in the field, B/H=/i = the magnetic permeability. B is called the magnetic, ittdiiction, or flux-density . The permeability of iron is not a constant quantity, but depends upon the quality of the iron, the way in which it has been treated, and the strength of the field. For soft iron the permeability may be as high as 3000, and for steel in a strong field as low as 2. The permeability of air and other non- magnetic materials is . approximately unity, while bismuth — a diamagnetic substance — has a permeability less than unity, viz. -99982. 722. Magnetic susceptibility. — In considering the permeability of a sub- stance our attention is drawn to the facility with which lines of force pass 712 On Magnetistn [722- through it ; but there is another aspect in which we may regard the effect of the field on the magnetic substance. A piece of iron in the magnetic field becomes a magnet, with a south pole at the end where the lines enter, and a north pole at the end where they emerge, and has a definite magnetic moment. The magnetic moment acquired per unit volume is called the intensity of magnetisation, and is denoted by I. If M is the magnetic M moment, and V the volume of the iron m cubic centimetres, I = ,— . If the iron is in the form of a rod of length / and cross section A, and if we suppose the poles to be situated at its ends and to have each a strength in, then M = mL and V = /A, or I =— , from which it is seen that the intensity of A magnetisation is equal to the pole strength of the specimen per unit of cross section. It is clear that the intensity of magnetisation of a magnetic substance in a magnetic field depends upon two things, viz. the nature and condition of the substance and the strength of the field. So we may write I = kH, where H is the field, and k a coefficient depending on the material, and called the magnetic susceptibility of the substance. The relation between /i and k, the coefficients of permeability and susceptibility, may be readily found as follows : — The pole strength m per square centimetre of a rod in a magnetic field H is 1, as was proved above, and therefore the number of lines of force proceeding from it is 4^1 (720). Hence the total number of lines, due to the field and to the induced magnetism, is H + 47rI, but this is equal to B. Hence B = H + 47rl ; but by definition B =/jH and I = kH, .'. /i = I + 47rK. For hard steel in a strong field, for which « = 2, k = approximately 12-5 = 'oS ; for soft steel, where u = 2000, k = ~~ - 160. 12-5 723. Magnetic force at a point in a magnetic field due to a short bar magnet. — We shall consider two cases : (i) when the point is on the axis ^ produced of the magnet, (2) when it is on the line § = E J drawn perpendicular to the '— —J '^ magnet through its middle p; g point. In each case it is assumed that the magnet is small compared with the distance of the point from it. (i) ' End on' position {fig. 6g2). — Let SN be the magnet, A its middle point, m the strength of each of its poles, and 2/ the distance between them so that its moment = M = 2lm. Let there be a red pole of strength m' at O, and let AO = r. The force between N and O is ^ ""^,^. ,, that between S and (r ~ /)- -724] Ois -mm' Comparison of Moments of Magnets 713 Hence, the force on pole in at O due to the magnet SN , 4r/ iin'y\.r mti ^ — _ {r+lf The direction of the force is along NO, (f>-Pf {r'-r^f If /- is negligible in comparison with r\ F="'"^ , or the force on unit pole {i.e. the strength of field) at O is 2M With regard to the suppression of P above, let us take the case in which 2/ = 8 cm. N and r = 40 cm., then ^ = 1600 and /-=i5; hence in neglecting l^ we are making an error of I per cent. If we desire greater accuracy the complete formula must be used. (3) ' Broadside on' position (fig. 693). — The force between N and O = Fig. 693 r' + /• along NO S O = r' + r^ " These have a resultant along OT, whose magnitude F' imm T-r%o limn' I m'M. OS. r' + P if we neglect f. r^r\c- 2mm cosTOS = - ~^, r' + (^ {f + Z-^)* {r^ + fyi M Hence the strength of the magnetic field at O is — , and its direction is parallel to the length of the magnet. . Thus the field due to a bar magnet varies inversely as the cube of the distance from the centre of the magnet, and, for a given distance, is twice as great along the axis as at right angles to it. 724. Comparison of moments of mag^nets. — Let M, Mj represent the moments of the magnets to be compared, H the earth's field, and let the magnet M be placed in the end on position with regard to the magnetic needle AB, length /, the strength of each of _^ whose poles is m. The needle is then sub- jected to two magnetic fields, H due to the earth, and F = ^^ j due to the magnet, and will be deflected from the meridian by an angle 6. The couple due to 2M H is H7« X / sin 5 ; that due to F is ¥m x / cos fl= -„ . ml cos 6 ; since 714 On Magnetism [724- the needle is in equilibrium these couples are equal, .■.F = H tan 6 or, ^ = Jr* tan 6. . : ■ (l> H Let the second magnet, of moment Mj, be similarly placed at such a distance r^ as to produce the same deflection ; then '^' = i^i'tanfl, .-. M/Mi = r'K^ If the magnets are placed in the broadside on position the formula becomes = r' tan d. H Or, we may compare the moments of the two magnets by placing them iii the same time in the end on position with regard to a compass needle, one on each side, at such distances that the needle undergoes no deflection. It is then only necessary to measure the distances (r, r-^ of the centres of the magnets from the centre of the needle, and M/Mjsr'/ri'. It is assumed that the lengths of the magnets to be compared are sufficiently small for /- to be neglected in comparison with r'K The moments of two magnets may also be compared by means of the torsion balance (7i8) as follows : — Suspend the first magnet (JVI) in the balance so that there is no twist in the wire, and turn the torsion head E (fig. 690) through such an angle a that the needle is deflected 6 from the meridian ; the torsion in the wire is then a — 6. The couple due to the earth's magnetism tending to turn the magnet into the meridian is MH sin 5; the torsional couple tending to twist the wire in the opposite direction is proportional to the angle of torsion, and may be written k{a. - fl), where k is a. constant. These two couples are equal ; therefore MH sin 6 = kia — ff). Now replace the magnet M by M,, and let uj be the] angle through which the torsion head must be twisted to cause the same deflection (5) as before. Then M,H sin 6 = k{a.^-6); hence M/Mi = (a-fl)/(ai -5). It will be seen later (736) how the moment of a magnet may be determined in absolute measure. 725. Gauss's proof of the inverse square law. — In determining the magnetic force due to a bar magnet, we have assumed that the force between two magnetic poles varies inversely as the square of the distance between them. But suppose we make no such assumption, but write force = , where n may be any whole or fractional number : if we then r"- determine the force due to the magnet in the ' end on ' and ' broadside on ' positions successively, we shall arrive at the results : F (end on) =?M_ M Fj (broadside on) = — - j -725] Gauss's Proof of the Inverse Square Laiv 7 1 5 thus the force in the 'end on' position is proved to be n times that in the 'broadside on' position. Introducing these values into the formulse of the last article, we obtain : — end on H n broadside on H tanfi, When the experiment is made, it is found that tan 6 is exactly twice tan 6^ ; hence « = 2, and the law of force between two magnetic poles is that of the inverse square of the distance. This method of experimental proof admits of much greater accuracy than that of the torsion balance (718). 7i6 On Magnetism [726- CHAPTER IV TERRESTRIAL MAGNETISM 726. Directive action of the earth on magnets. — When a magnetic needle is suspended by a thread, as represented in fig. 675, or is placed on a pivot on which it can oscillate freely (fig. 695), it ultimately sets in a position which is more or less north and '?■ south. If removed from this position it always returns to it after making a certain number of oscillations. Analogous observations have been made in different parts of the globe, from which the earth has been compared to an immense mag- net, Avhose poles are very near the terrestrial poles, and whose neutral line virtually coin- cides with the equator. Suppose that the needle, instead of being constrained by the mode of its sus- pension to move only in a horizontal plane, is free to move in any direction, it will be found to take an inclined position, its red end dipping downwards and its axis making an angle of about 67° with the horizon. The earth being a magnet is surrounded, like any other magnet, by its own field of magnetic force. The lines of force proceed from the red pole, which is near the terrestrial south pole, and sweeping round reach the earth again at the blue pole in the neighbourhood of the north terrestrial pole. But, as in the case of a bar magnet the lines of force do not leave and enter the bar exclusively at the ends, but to a diminishing extent from the ends to the middle ; so with the earth. A magnetic needle freely suspended in a magnetic field always places itself along or parallel to the lines of force in the field, and therefore we may conclude that the lines of force due to the earth's mag- netism are, in England, inclined to the horizontal plane at an angle of about 67^, and are inclined downwards, since it is the red end of the needle which dips. In fig. 696 let ab be the direction in which a compass needle lies, and ac the direction which the needle takes when it is free to move in the plane of the magnetic meridian ; then, if ac represent not only the direction but the magnitude of the earth's field, it is clear, from the parallelogram of forces, that ab will represent the horizontal component, and be the vertical component, of the field. If the experiment described above \ 1 I \ I \ I \ ! \ I \ 1 .^ Fig. 696. is made at different parts of a -728] Variations in Declination 717 room, it will be found that the direction of the needle is the same in all cases ; hence the lines of the earth's force are at the same place parallel to each other, and the field is a uniform field. Imagine a room filled with wires or threads, all stretched straight and parallel to the axis of a freely suspended magnetic needle and uniformly distributed, so that there are exactly as many, per unit of area at right angles to them, at one part as at another ; such an arrangement would represent the local field of the earth's magnetism. And as we may resolve a force represented by ac (fig. 696) into a horizontal force ab and a vertical force be, so we may consider the earth's magnetic field, represented by uniformly distributed lines parallel to ac, as being equivalent to two fields, one horizontal with uniformly distributed lines parallel to ab, the other vertical with' uniformly distributed lines parallel to be. In most cases we have to deal only with compass needles and the horizontal field. That it is a uniform field is shown by placing a magnet horizontally on a cork floating in water : the magnet will at first oscillate, and then gradually settle in the magnetic meridian, and will not (provided that no iron is in the neighbourhood) show any tendency to move either towards the north or towards the south. The couple acting on a needle deflected through an angle 6 from the meridian is MH sin 6, which is often referred to as the terrestrial magnetic couple. It represents the twisting eflTect on the needle when it is inclined to the meridian ; its maximum value is MH, when the needle is at right angles to the meridian. If the horizontal field were not uniform, the forces acting at A and B (fig. 69s) would not be equal and parallel, and consequently would have a resultant causing the needle to move in a definite direction. But no such motion can be detected ; hence the field is uniform. 727. Magnetic elements. Declination. — In order to specify the magnetic state at any point of the earth's surface, three things must be known ; these are — i. Declination ; ii. Inclination or Dip ; iii. Force or Intensity, These three are termed the magnetic elements of the place. We shall explain them in the order in which they stand. The geographical meridian of a place is the imaginary plane passing through this place and through the two terrestrial poles, and the meridian is the outline of this plane upon the surface of the globe. Similarly the magtietic meridian of a place is the vertical plane passing at this place through the two poles of a compass needle in equilibrium. In general the magnetic meridian does not coincide with the geo- graphical meridian, and the angle which the magnetic makes with the geographical meridian — that is to say, the angle which the direction of the needle makes with the geographical meridian — is called the declination or variation of the magnetic needle. The declination is said to be east or west, according as the north pole of the needle is to the east or west of the geographical meridian. 728. Variations in declination. — The declination of the magnetic needle, which varies in different places, is at present west in Europe and in Africa, but east in Asia and in the greater part of North and South America. It shows further considerable variations even in the same place. These varia- tions are of two kinds : some are regular, and are either secular, annual, or 7i8 On Magnetism [728- diurnal ; others, which are irregular, are due to what are called niagiutic storms (738). Secular variations. — In the same place the declination varies in the course of time and the needle appears to make oscillations to the east and west of the meridian, the duration of which extends over centuries. The declination has been known at London since 1580, and the following table represents the variations which it has undergone : — Year Declination Year Declination 1580 11° 17' E. 1815 24° 27' w. 1634 4° 5' ' 1820 24° II' 1657 0° 183I 24° 0' 1672 2° 30' W. 1865 20° 34' 1700 9° 40' 1871 19° 42' 1720 13° 0' 1880 18° 33' 1760 19° 30' 1883 18° 15' 1790 23° 39' 1S96 16° 56' 1800 24° 36' igoi 16° 24' 1806 24" 28' This table shows that since 1580 the declination has varied at London as much as 36°, and that the greatest westerly declination was attained in 1800, since which time the north end of the needle has gradually tended towards the east. At Paris the changes have been similar to those at London. In 1580 the needle showed an easterly declination of 11° 30' ; in 1663 it was at zero ; from that time it gradually tended towards the west, and reached its maxi- mum declination of 22° 34' in 1814 ; since then it has steadily diminished, and is now (1901) 14° 40', the decrease at present being a little more than 5' per year. At Yarmouth and Dover the variation is about 40' less than at London ; at Hull and Southampton about 20' greater ; at Newcastle and Swansea about 1° 45', and at Liverpool 2° o', at Edinburgh 3° o', and at Glasgow and Dublin about 3° 50' greater than at London. The following are the observations of the magnetic elements at Kew extending over thirty-seven years : — Year Declination 1865 20° 59' 1875 19° 41' 1 1880 18° 59' i 1885 18° 26' i 1890 17° 51' 1895 17° 17' ' 1898 17° I' i 1900 16° 53' ! 1 901 16° 48' i Inclination 68° 7' 67° 48' 67° 42' 67° 38' 67° 33' 67° 24' 67° 17' 67° 11' 67° 9' Horizontal force 0-1765 0-1791 0-1797 o-i8o6 0-1817 0-1828 0-1836 0-1843 0-1846 -730] Declination Compass ^ig In certain parts of the earth the magnetic coincides with the geographical meridian. These points are connected by an irregularly curved imaginary line, called a line of no variation or agonic line. Such a line cuts the east of South America, and, passing east of the West Indies, enters North America near Cape Hatteras, and traverses Hudson's Bay ; thence it passes through the Arctic regions, entering the Old World east of the White Sea, traverses the Caspian, cuts the east of Arabia, turns then towards Australia, and passes across the Antarctic circle, to complete the circuit. Isogo7iii lines are lines connecting those places on the earth's surface at which the declination is the same. Maps on which such isogonic lines are depicted are called declination or variation maps ; and a comparison of these in various years is well fitted to show the variation which this magnetic element undergoes. The first of the kind were constructed in 1700 by Halley. Plate IV. represents a map on Mercatoi's projection giving these lines for the year 1895. It will be seen that the surface of the globe is divided by these lines into two regions : one, the smaller, in which the variation is westerly, as indicated by the continuous lines ; the other, in which the variation is easterly, as indicated by the dotted lines. There is also a closed agonic line in the East of Asia, enclosing Japan and a portion of China. Within this curve the declination is westerly. This chart is useful to the mariner as not only giving him the declination in any place, but also as showing him the places on the globe where the declination changes most rapidly. Of these the most remarkable are the coast of Newfoundland, the Gulf of St. Lawrence, the seaboard of North America, and the English Channel and its approaches. 729. Annual and diurnal variations. — Cassini first discovered in 1780 that the declination is subject to small annual variations. At Paris and London it is greatest about the vernal equinox, diminishes from that time to the summer solstice, and increases again during the nine following months. It does not exceed from 15' to 18', and it varies somewhat at different epochs. The daily variations were first discovered by Graham in 1722. In this country the north pole moves every day from east to west from sun- rise until one or two o'clock ; it then tends towards the east, and at about ten o'clock regains its original position. During the night the needle is almost stationary. Thus the westerly declination is greatest during the warmest part of the day. The amount of the daily variation depends on the season of the year, ranging from 25' in summer to 5 'or less in winter. The mean annual value of the daily range varies from year to year, oscillating between maximum values which occur every ten and a half or eleven years. Years of maximum mean daily variation coincide with years of maximum sunspot area (738). The amplitude of the daily variation decreases from the poles towards the equator, where it is very slight. Thus in the island of Rewak it never exceeds 3' to 4'. 730. Declination compass. — The declination compass is an instrument by which the magnetic declination of any place may be determined when its astronomical meridian is known. The form represented in fig. 697 •consists of a brass box, AB in the bottom of which is a graduated circle, M. 720 On Magnetism [730- In the centre is a pivot on which oscillates a very light lozenge-shaped magnetic needle, ab. To the box are attached two uprights supporting a horizontal axis, X, on which is fixed an astronomical telescope, L, movable in a vertical plane. The box rests on a foot, P, about which it can turn in a horizontal plane, taking with it the telescope. A fixed circle, QR, which is called the azimuth circle, measures the number of degrees through which the telescope has been turned, by means of a vernier, V, fixed to the box. The inclination of the telescope, in reference to the horizon, may be measured by another vernier, K, which moves with the axis of the telescope, and is read off on a fixed gradu- ated arc, X. The first thing in deter- mining the declination is to adjust the compass horizon- tally by means of the screws SS, and the level n. The astronomical meridian is then found, either by an observa- tion of the sun at noon exactly,, or by any of the i-eady methods known to astronomers. The box AB is then turned until the telescope is in the plane of the astronomical meridian. The angle made by the magnetic needle with the diameter N, which corresponds with the zero of the scale, and is exactly in the plane of the telescope, is then read off on the graduated limb, and this is east or west, according as the pole a of the needle stops at the east or west of the diameter N. 731. Correction of errors. — These indications of the compass are only correct when the magnetic axis of the needle— that is, the right line passing through the two poles — coincides with its axis of figure, or the line connect- ing its two ends. This is not usually the case, and a correction must there- fore be made, which is done by the method of reversion. For this puipose the needle is not fixed in the cap, but merely rests on it, so that it can be removed and its position reversed ; thus what was before the lower is now the upper face. The mean between the observations made in the two cases gives the true declination. For, let NS be the astronomical meridian, ab the axis of figure of the needle, and mn its magnetic axis (fig. 698). The true declination is not the arc Na, but the arc N»z, which is greater. If now the needle be turned, the line mn makes the same angle with the meridian NS ; but the north end of -~- ^ t.«.\vQ>^:;>.\ Fig. 697 -732] Mariner's Compass 72! the needle, \\hich was on the right of jnn, is now on the left (fig. 699), so that the declination, which was previously too small by a certain amount, is now too large by the same amount. Hence, pro- vided the error be small, the true declina- tion is given by the mean of these two ob- servations. 732. Mariner's com- pass. — The magnetic action of the earth has received its most im- portant application in the marincr^s compass. This is a declination compass used in guiding the course of a ship. Fig. 700 represents a view of the whole, and fig. 701 a vertical section. It consists of a cylindrical case, BB', which is supported on gimbals so as to keep the compass in a horizontal position in spite of the rolling of the vessel. These are two concentric Fig. 698 I'i^, 700 rings, one of which, attached to the case itself, moves about the axis jr^? which pjays in the outer ring AB, and this moves in the supports PQ, about the aixis mn, at right angles to the first. In the bottom of the box is a pivot, on which is placed, by means of an agate cap, a magnetic bar, ab, which is the needle of the compass. On this is fixed a disc of mica, called the compass card, a little larger than the length of the needle, on which is traced a star or rose, with thirty-two branches, making the eight points or rhumbs of the wind, the demi-rhumbs, and the quarters. The branch ending in a small star, and called N, corresponds to the magnetic axis of the bar ab, which is underneath the disc. There are several objections to the compass just described, of which one 3 A ' 722 On Magnetism [732 is that the magnet ab must be pierced at the centre for fitting the agate cap, and that its magnetic character is thereby altered. Another objection is the uncertainty as to the direction of the magnetic axis of the magnet. En-ors from these causes may be avoided by using two magnets instead of one. They are rectangular in form, and are attached at right angles to the card, parallel to each other, and equidistant from the centre. The box or bowl in which the compass card is supported is made of copper, to produce electrodynamic damping of the needle or needles (963). In Lord Kelvin's compass, the card and its attachments are made as light as possible, to diminish the friction at the pivot and so render the compass more sensitive. The card consists of a thm aluminium circular rim with silk strings extending radially from it to a small aluminium disc at the centre, to which is fitted an agate or sapphire cap. A thin paper annulus is gummed to the strings, and on this are marked the points of the compass. The pivot on which the cap rests is made of platinum-iridium, to ensure hardness and freedom from oxidation. There are eight magnets, of the thickness of a knitting-needle, and of lengths ranging from 8 cm. to 5 cm., placed symmetrically on each side of the centre and connected together by silk strings ; they are supported from the aluminium ring by silk strings, and lie in a plane about 3 cm. below the card. The weight of card, magnets and all, is not more than 180 grains, or I li- grammes. Since the needles are some way below the point of suspension the card remains horizontal even when the earth's vertical force {i.e. the tendency of the needles to dip) is considerable. The period of vibration of the card is greater than in the older form of compass card ; but, owing to the comparative absence of friction, the needles always point in the direction of the horizontal field. The bowl of Lord Kelvin's compass has a compartment at its base partially filled with a viscous liquid {e.g. castor oil), to prevent oscillations. The prismatic compass is greatly used for surveying, more especially for military purposes ; it differs from the mariner's compass mainly in its dimensions, and in the way in which obser- ■ vations are made. It consists of a shallow metal box about 2^ inches in diameter (fig. 702) ; the needle, which is fixed below the compass card, plays on a pivot much as in Fig. 701 Fig. 702 fig. 701. On the left of fig. 702 is seen a metal frame across which is stretched a horsehair, forming a sight-vane. Exactly opposite this is a right-angled prism P enclosed in a metal case, with an eyehole and a slit as represented at the side of the figure When an observation is to be made, the compass is held horizontally, and so that the slit in the prism, the hair of the sight-vane, and the distant object o 'A 3 '_/) a z -733] Inclination or Dip. Magnetic Equator 723 are seen to be in the same line ; the observer, looking through the eyehole, notes the angle which the needle makes ; a similar observation is made with- another object, and thus the angle between them, or their bearing, is given. The sight-vane moves on a hinge, and can be turned down, when it presses a spring which lifts the magnet from the pivot and keeps it rigid, so that the compass can be transported in any position. As the image is seen through the convex face of the prism it is magnified, and as it is seen by reflection it is reversed, so that in order to read the figures correctly they must be reversed on the card ; the reflection being total there is little loss of light. 733. Inclination or dip. Magnetic equator. — If the needle be so arranged that it can move freely in a vertical plane about a horizontal axis, it will be seen that, although the centre of gravity of the needle lies in the axis of suspension, the north pole in our hemisphere dips downwards. In the southern hemisphere the south pole is inclined downwards. • The angle which the magnetic needle makes with the horizon, when the vertical plane, in which it moves, coincides with the magnetic meridian, is called the inclination or dip of the needle. In any other plane than the magnetic meridian the Inclination increases, and is 90° in a plane at right angles to the magnetic meridian. For the magnetic inclination represents the direction of the total magnetic force, which may be resolved into two forces, one acting horizontally and the other vertically. When the needle can only move in a plane at right angles to the magnetic meridian, the horizontal component can only act in the direction of the axis of suspen- sion, and therefore cannot affect the needle, which is then solely influenced by the vertical component, and consequently stands vertical. The value of the dip, like that of the declination, differs in different localities. It is greatest in the polar regions, and decreases with the latitude to the equator, where it is approximately zero. In London at the present time (1901) the dip is 67° 7'. In the southern hemisphere the inchnation is again seen, but in a contrary direction ; that is, the south pole of a needle dips below the horizontal line. The magnetic poles of the earth are those places in which the dipping- needle stands vertical, that is, where the dip is 90°. In 1831 the first of these, the magnetic north pole, was found by Sir James Ross in 96° 43' west longitude and 70^ north latitude. The same observer found in the South Sea, in 76° south latitude and 168 ' east longitude, that the inclination was 88° 37'. From this and other observations, it has been calculated that the position of the magnetic south pole was at that time in about 154° east longitude and 75^° south latitude. The line of no declination (agonic line) passes through these poles, and the lines of equal declination (isogenic lines) converge towards them. The magnetic equator, or aclinic line', is the line which joins all those places on the earth where there is no dip : that is, all those in which the dipping-needle is horizontal. It is a somewhat sinuous line, not differing much from a great circle inclined to the equator at an angle of 12°, and cutting it on two points nearly opposite each other — one in the Atlantic and one in the Pacific (see Plate V.). These points appear to be gradually moving their position, and travelling from east to west. 3 A 2 724 On Magnetism [733- Lines connecting places in which the dip is the same are called isoclinic lines. They have a certain analogy and parallelism with the parallels of latitude, and the term magnetic latitude is sometimes used to denote positions on the earth with reference to the magnetic equator. Plate V. is an inclina- tion map for the year. 1895, the construction of which is quite analogous to that of the map of declination. The inclination is subject to secular variations, like the dechnation, as is readily seen from a comparison of maps of inclination for different epochs. At Paris, in 1671, the inclination was 75° ; since then it has been continually decreasing : in 1835 it was 67° 24' ; in 1849, 67° ; in 1859, 66° 16' ; in 1869, 65° 43' ; in 1879, 65° 32' ; in 1883, 65° 17' ; in 1891, 65° 11 ; in 1893, 65° 8' ; in 1895, 65° 5' ; in 1896, 65° 2' ; in 1897, 65° i' ; and in 1901, 64° 54'. The following table gives the secular changes in the inclination at London, from which it will be seen that since 1723, in which it was at its maximum, it has continually diminished by an average of something more than three minutes in each year : — Year Inclination Year Inclination 1576 71° 50' 183B 69° 17' 1600 72° 1854 68° 31' 1676 73° 30' 1859 68° 21' 1 1723 74° 42' 1874 67° 43' ! ; 1773 72° 19' 1876 67° 39' 1780 72° 8' 1878 67° 36' 1790 71° 33' 1880 67° 35' ! 1800 70° 35' 1883 67° 31' ! 1821 70° 31' 1896 67° 10' 1828 69° 47' I90I 67° 7' 734. Inclination compass. — An inclination compass, or dip circle, is an instrument for measuring the magnetic inclination or dip. One form, repre- sented in fig. 703, though not best adapted for the most accurate measure- ments, is well suited for illustrating the principle. It consists of a graduated horizontal brass circle wz, supported on three legs, provided with levelling screws. Above this circle there is a plate A, movable about a vertical axis, and supporting, by means of two columns, a, second graduated circle M, which measures the inclination. The axle of the needle rests on agate plates on a frame r. To observe the inclination, the magnetic meridian must first be deter- mined, which is effiscted by turning the plate A on the circle m until the needle is vertical, which is the case when it is in a plane at right angles to the magnetic meridian (733). The plate A is then turned go° on the circle m, by which the vertical circle M is brought into the magnetic meridian. The angle dca, which the magnetic needle makes with the horizontal diameter, is the angle of inclination. There are here several sources of error, which must be allowed for. The most important are these : — i. The magnetic axis of the needle may not coincide with its axis of figure ; hence an error which is corrected by -735] Force of the EdrtKs Magnetism 725 reversing the needle on its bearings, ii. The centre of gravity of the needle .may not coincide with the axis of suspension, and then the angle dca is too great or too small, according as the centre of gravity is below or above the centre of suspension ; .for in the first case the action of gravity is in the same direction as that of the magnetic force, and in the second it is in the opposite direction. To correct this error, the poles of the needle must be reversed by remag- netising it in such a way that what was a north is now made a south pole. The inclination is now redetermined, and the mean taken of the results ob- tained in the two groups of operations. iii. The line of zeros may not be horizontal. To correct the error that Would arise from this cause, the posi- tion of the needle is observed when the circle M is facing east, and also when it is facing west. Fig. 703 The Kew dip circle is in principle like the instrument just described, but is much more sensitive. The needle is 3 inches long and turns about an axle, consisting of a fine steel cylinder, resting on agate edges. The vertical circle is enclosed in a glass box, and the positions of the ends of the needles are observed by means of microscopes. 735. Force of the earth's magnetism. — If a magnetic needle be moved from its position of equilibrium, it will revert to it after a series of oscilla- tions, which follow laws analogous to those of the pendulum (56). If the magnet be removed to another place, and caused to oscillate during the same length of time as the first, a different number of oscillations will be observed. And the earth's magnetic force in the two places will be respec- tively proportional to the squares of the number of oscillations. If at M the number of oscillations in a minute had been 25 = ^, and at another place M ', 24 = ;z', we should have — Force of the earth's magnetism at M _ifi _625 _ ,.-0, " -"="576" Force of the earth's magnetism at M' That is, if the force of the magnetism at the second place is taken as unity, that of the first is fo85. If the magnetic condition of the needle had not changed in the interval between the two observations, this method would give the relation of the forces at the two places. In 'these determinations of the force, it would be necessary to observe the oscillations of the dip-needle, which are produced by the total force 726 On Magnetism [735- of the earth's magnetism. These, however, are difificult to obtain with accuracy, and therefore those of the dechnation needle are usually taken. The force which makes the declination needle oscillate is only a portion of the total magnetic force, and is smaller in proportion as the inclination is greater. If a line «(r = T (fig. 704) represent the total force at the place M, the angle i the inclination, then the horizontal component Yi.=ab = 'X cos i. Hence, if n and n' represent the number of vibrations, in a given time, of a declination needle at the two places, at which the total forces are T T' respectively, we shall have — ■ Tcos i n" , T ;z-cos i' - ■ hence - - T'cos i' n'- ' T' 7z'^cos z That is to say, having observed in two different places the number of oscillations, n and «', that the same needle makes in the same time, the ratio of the magnetic forces in the two places will be found by multiplying the ratio of the square of the number of oscillations by the inverse ratio of the cosines of the angle of dip. Plate VI. is a chart representing the distribution of hori- zontal force over the earth's surface. The lines of equal horizontal force are somewhat irregular, especially in the neighbourhood of the equator andjn extreme latitudes. The horizontal force diminishes as we proceed from the equator either northwards or southwards. If its value in the south of England is taken as unity, its maximum value (2-1) occurs in Borneo, and there is another maximum (rg) on the west side of Panama. At the Cape of Good Hope the horizontal force is nearly the same as in England. Its change with place is most rapid in the region of Australia. When the angle of dip z is known, the total force T, or the vertical force Z, in any place, may be obtained from the values in the chart by the formula T = H sec i ; and Z = H tan i. The total force is least near the magnetic equator, and, increasing with the latitude, is greatest near, but not quite at, the magnetic poles ; the places of maximum intensity are] named the magnetic foci. There are two magnetic foci in the northern hemisphere, called respectively the American focus and the Siberian focus. The American focus is in north latitude 54° and longitude 94° W. ; the Siberian focus in 66 ' north latitude and 1 1 5° east longi- tude. There are probably also two foci in the southern hemisphere ; they are near to the south magnetic pole and not far from each other. The lines connecting places of equal total force are called isodynamic lines. They are not parallel to the magnetic equator, but seem to have about the same direction as the isothermal lines. According to Kuppfer, the force appears to diminish as the height of the place is greater ; a needle which made one oscillation in 24 seconds vibrated more slowly by o-oi of a second at a height of 1000 feet ; but, according to Forbes, the force is only -^-Jt^ less at a height of 3000 feet. There is, however, some doubt as to the accuracy of these observations, owing to uncertainty as to the correction for temperature. The intensity varies in the same place with the time of day : it attains its > o Z tq o Z o D - z -736] Determination of Horizontal Force 727 maximum between 4 and 5 in the afternoon, and is at its minimum between 10 and II in the morning. It is probable, though it has not yet been ascertained with certainty, that the force undergoes secular variations. From measurements made at Kew it appears that on the whole the total force experiences a very slight annual increase. 736. Determination of the horizontal force in absolute measure. — The relative values of the earth's horizontal magnetic force at two places may be determined, as we have seen, by causing a compass needle, whose moment is assumed to remain constant, to vibrate at the two places and taking the ratio of the squares of the number of vibrations in a given time. The chart (Plate VI.) shows the distribution of horizontal force on the earth's surface for the year 1895, the force at London being taken as unity. But it is possible to determine the horizontal force in absolute measure — that is, in terms of the fundamental units of length, mass, and time — without referring to its value at any particular place, and without assuming the constancy of the moment of any particular magnet. For this purpose two experiments are necessary: (i) the vibration experiment, (2) the deflection experiment. Vibration experiment. — When a bar magnet suspended by a thread without torsion, free to oscillate in a horizontal plane, is deflected from its position of equilibrium and then left to itself, it vibrates through its position of equilibrium, making oscillations which, if small, are isochronous like those of the pendulum. The number of these oscillations in a given time depends on the mass and dimensions of the bar, on its magnetic moment, and on the intensity of the earth's magnetism in the place of observation. The time, t, of a complete oscillation of such a magnet is represented by the formula t=- 2w\ I ^nnr,-, where 1 is the moment of inertia of the magnet, V HM M the magnetic moment of the bar, and H is the horizontal force of the earth's magnetism. Hence t" The moment of inertia of a magnet may be determined from its mass and linear dimensions if the magnet is homogeneous in structure and of a regular geometrical shape ; or it may be determined experimentally by first observing the time of oscillation of the magnet under the influence of the earth's magnetism, and then the time when it has been loaded with a mass the moment of inertia of which is known, and which does not alter the magnetic moment of the bar. Now the value of HM depends on the nature of the bar, and on the force of the earth's magnetism in the place in question. If the magnetism of the bar were increased or diminished, or if the same bar were removed to a different locality, the product would have a different value. We must therefore find some independent relation between H and M, whereby M, the magnetic moment of the bar, may be got rid of, and an absolute value be obtained for H. Such a relation may be obtained from the deflection which the bar magnet produces in a magnetic needle. 728 On Magnetism [736- Dejlection experiment. — Place the magnet, whose time of vibration has been determined, in the ' end on ' position (723) with regard to a small compass needle, and note the deflection 6. It has been shown that with this M arrangement ^^ = hr^ tan 6, where r is the distance between the centre of H the magnet and the centre of the needle. It is not necessary to know either the magnetic moment or any other property of the needle employed. In the two equations which have now been obtained, \i2. MH = 47r^I M and ti = \r^ tan 6, H the only variables are M and H, for d,ir and tan 6 are mere numbers. I has been evaluated once for all, / has been determined in seconds, and r in centimetres. Thus M and H are separately determined in absolute C.G.S. units : 2 1 H =- IN r r^ tan 6 and M=:^. ^"i?ltim#. Thus the same operations which determine H determine M also in absolute measure. The total force is determined in absolute measure when| the dip, z', is known, from the formula T = . cos z The value of H at Greenwich for the year 1902 is 0-185, that is, the hori- zontal magnetic field at Greenwich is such that a free unit magnetic (red) pole, submitted to its action, would begin to move in a horizontal northerly direction, and at the end of one second would have acquired a velocity of -185 cm. per second. The total force at the same place is -477. If British units — namely, the foot, grain, second — be employed, the unit of force is that which by acting for a second on a grain gives to it a velocity of a foot per second, and the unit magnetic pole is such that if placed one foot from a second equal pole it will repel it with a force equal to the unit just defined. To convert the value of H, when expressed in centimetres, grammes, and seconds, into the equivalent value referred to British units, we must raultiph- by 21-69. Ill like manner, to convert magnetic forces referred to British units into the corresponding values expressed in centimetres, grammes, and seconds, we must multiply by 0-0461 = — - . 21-69 737. Dimensions of magnetic magnitudes. — The dimensions of force, momentum, energy, &c., in terms of length L, time T, and mass M, were given in art. 63. From there we can readily deduce the dimensions of magnetic magnitudes. From Coulomb's la\\- we have F = — -, where F is the -738] Magnetic Observatories 729 force between two magnetic poles, each of strength m. Now the dimensions of F are ^=, /. the dimensions of magnetic pole, m, are \l -r^ • L^ or T Again, the magnetic force at a point in a magnetic field was defined (720) as the force on the unit pole at that point. Hence, ^. , mechanical force magnetic force = and its dimensions are pole ML T ^ M*L" ^ Let N be the number of lines of force passing through an area A, H the number per square centimetre of that area, then N = AH. Hence, i _i .1 3 dimensions of magnetic flux = L'' x ="!'„• See also art. 1,000. 738. Magnetic observatories. — During the last few years great attention has been devoted to the observation of the magnetic elements, and observa- tories for this purpose have been fitted up in different parts of the globe. These observations have led to the discovery that the magnetism of the earth is in a state of constant fluctuation, like the waves of the sea or the pressure of the atmosphere. In studying the variations of the declination, &c., the mean of a great number of observations must be taken, so as to eliminate irregular disturbances and bring out the general laws. The principle on which magnetic observations are automatically recorded is as follows : — Suppose that in a dark room a bar magnet is suspended horizontally, and at its centre is a small mirror ; suppose further that a lamp sends a ray of light to this mirror, the inclination of which is such that the ray is reflected, and is received on a horizontal drum placed underneath the lamp. The axis of the drum is at right angles to the axis of the magnet ; it is covered with sensitive photographic paper, and is rotated uniformly by clockwork. If now the magnet is quite stationary, as the drum rotates, the reflected spot of hght will trace a straight line on the paper with which the revolving drum is covered. But if, as is always the case, the position of the magnet varies during the twenty-four hours, the effect will be to trace a sinuous line on the paper. These lines can afterwards be fixed by ordinary photographic methods. If we know the distance of the mirror from the drum, and the length of the paper band which comes under the influence of the spot of light in a given time — twenty-four hours, for instance — the angular deflection at any given moment may be deduced by a simple calculation (532). The observations made in the English magnetic observatories were reduced by Sabine, and revealed some ourious facts in reference to mag- netic storms and the daily range of magnetic declination. He found that the latter exhibits a certain periodicity, and attains its greatest value about every ten years. Independently of this, .Schwabe, who for many years studied the subject, found that the spots on the sun, seen on looking at 730 On Magnetism [738- it through a coloured glass, vary in their number, size, and frequency, but attain their maximum about every ten or eleven years. Now Sabine establfshed the interesting fact that the period of their greatest frequency coincides with the period of greatest mean daily range of declination. Another phenomenon is the simultaneous occurrence of magnetic pertur- bations in \'ery distant countries. Thus Sabine mentioned a magnetic disturbance which was felt simultaneously at Toronto, the Cape, Prague, and Van Diemen's Land. Such simultaneous perturbations have received the. name of magnetic storms. Other remarkable connections between the sun and terrestrial magnetism have been observed ; one, especially, of recent occurrence has attracted considerable attention. It was the flight of a large luminous mass across a vast sunspot, while a simultaneous perturbation of the magnetic needle was observed in the observatory at Kew ; subsequent examination of magnetic observations in various parts of the world showed that within a few hours one of the most violent magnetic storms ever known had prevailed. It seems, however, that these accidental variations in the declination cannot be due to changes in any direct action of a possible magnetic condition of either the sun or the moon. Foi it can be shown that if the magne- tisation of the latter were as powerful as that of the earth, the deflection which it could produce would not amount to the jipth of a second, a quantity which cannot be measured. In order to produce a variation of lo', such as is frequently met with, the magnetisation of the sun or of the moon must be 12,000 times that of the earth ; in other words, a more powerful degree of magnetisation than that of powerfully anagnetised steel bars. Magnetic storms are nearly always accompanied by the exhibition of the aurora borealis in high latitudes ; that this is not universal may be due to the fact that many auroras escape notice. The converse of this is true, that no great display of the aurora takes place without a violent magnetic storm. The centre or focus towards which the rays of the aurora converge lies approximately in the prolongation of the direction of the dipping-needle ; and it may be mentioned in this connection that the appearances of the aurora borealis have the same periods as the sunspots. 739. Magnetisation by the action of the earth. — The action of the earth on magnetic substances resembles that of a magnet, and hence the terrestrial magnetism is constantly tending- to produce magnetisation in soft iron and in steel. But as the coercive force is very considerable in the latter substance, the action of the earth is inadequate to produce more than slight magnetisation. This is not the case with perfectly soft iron. When a bar of this metal is held in the magnetic meridian parallel to the dip needle, the bar becomes at once endowed with magnetic polarity. The lower extremity is a north pole, and if the north pole of a small magnetic needle be approached, it will be repelled. This magnetism is of course unstable, for if the bar be turned the poles are inverted, as pure soft iron is nearly destitute of coercive force. While the bar is in this position, a certain amount of coercive force may be imparted to it by giving it several smart blows ^^■ith a hammer, and the bar retains for a short time the magnetism which it has thus obtained. But -740] Deviation of the Compass in Iron Ships 7^1 the coercive force thus developed is very small, and after a time the mag- netism disappears. If a bar of soft iron is twisted vifhile held vertically, or, better, at the angle of dip, it acquires a feeble permanent magnetisation. It is this magnetising action of the earth which develops the magnetism frequently observed in steel and iron instruments, such as fire-irons, rifles, lamp-posts, railings, gates, lightning conductors, &c., which remain for some time in a more or less vertical position. They become magnetised with their north pole downwards, just as if placed over the pole of a powerful magnet. The magnetism of native black iron o5cide (694) has doubtless been pro- duced by the same cause ; the very different magnetic power of different specimens being partly attributable to the different positions of the veins of ore with regard to the line of dip. The ordinary irons of commerce are not quite pure, and possess a feeble coercive force ; hence a feeble magnetic polarity is generally found to be possessed by the tools in a smith's shop. Cast iron, too, has usually a great coercive force, and can be permanently magnetised. The turnings, also, of wrought iron and of steel produced by the .powerful lathes of our ironworks are found to be magnetised. 740. Deviation of the compass in iron ships. — The magnetic properties of the mild steel now so largely used in the construction of ships are similar to those of soft iron, which was at one time generally employed. The coercive force of mild steel is small and its permeability considerable. A vertical plate of such steel placed in the magnetic meridian, in the northern hemisphere, will become magnetised, by the inductive action of the earth, with blue polarity in the upper part and towards the south, and with red polarity in the lower part and towards the north, the neutral line being at right angles to the earth's total force. Each plate which enters into the construction of an iron or steel ship is subjected to much mechanical violence in the processes of hammering, boring, riveting, &c., and consequently acquires an increased coercive force, and retains the induced magnetism. The ship, which is the aggregate of the steel and iron plates and masses used in its construction, becomes a huge magnet, and its magnetism is to a considerable extent perma7ienf. The direction of its polarity depends upon its position in building. If it has been built head north, the bow will have red and the stern blue magnetism — blue magnetism always predominating in the upper part and red towards the keel, if the ship has been built in the northern hemisphere. Here, then, is a cause of deviation of the compass. Let us suppose, to take an example, that the ship has a blue pole near the bow and a red pole near the stern. In these circumstances there will be no error of the compass when the ship is sailing in a northerly (magnetic) direction ; but if she turns eastwards the red end of the compass needle will be pulled towards the east, and the error will increase to a maximum, and then diminish to zero, as the ship's head turns from north, through east, to south. In the whole of this semicircle the error is easterly ; in the remaining semicircle it is westerly. Hence, the error of the compass due to this cause is called semi- circular, since it changes its sign in each semicircle. This error is compensated by placing hard steel magnets in the binnacle under the compass bowl, in such number and at such distances that the field 732 On Magnetism [740- they produce at the position of the compass needles is exactly equal and opposite to that produced by the permanent magnetism of the ship. Error of the compass is brought about not only by the permanent magnetism of the ship, but by magnetism temporarily induced in vertical or horizontal masses of iron or steel in the ship, due to the vertical or horizontal components of the earth's magnetic force. Consider, first, vertical masses — the sides of the ship, steel ribs, masts, funnels, davits, &c. — acted on by the vertical component Z (735). Each becomes a magnet with blue polarity at the top (in the northern hemisphere) and red polarity at the bottom. The effect of all these vertical magnets on the compass will depend upon the position of the latter in the ship, but in any case is such as could be produced by a single vertical rod of iron suitably placed. Assuming all the iron of the ship to be symmetrically placed with regard to the central vertical fore-and-aft plane of the ship, the resultant vertical rod will be in this plane, and the error it causes will be semicircular in character, being zero at N and S and a maximum near the east and west points, but of opposite signs in the east and west semicircles. The error due to this cause is corrected by a vertical bar of soft iron — called a Flinders bar — placed immediately forward of or immediately abaft the binnacle, with its upper or lower end on a level with the needles ,of the compass, and of such length as to produce exact compensation. Sometimes the length of the Flinders bar is fixed, and its distance from the binnacle variable. In the Royal Navy the Flinders bar is fixed in position, but its length may be varied from 24 inches downward. The error due to induction in vertical iron vanishes at the magnetic equator, where Z, the vertical component, =0. It varies with the tangent of the dip. In the southern hemisphere the sign of the error changes. Horizontal masses of iron acted on by the earth's horizontal force become temporarily magnetised with red polarity towards the north and blue towards the south, and produce an effect on the compass which a little consideration will show to be a maximum at the intercardinal points NE, SE, SW, and NW, and to vanish at the cardinal points N, E, S, W. The error due to this cause is called guadrantal, because it changes sign in every quadrant : if it is to the east when the ship's head is in the NE quadrant, it will be to the west in the SE quadrant, to the east in the SW, and to the west again in the NW. The error due to this cause is for a given ship the same in all parts of the world, for although the induced magnetism increases with the horizontal force, the tendency of the compass to return to the meridian increases in the same ratio. Hence the error is constant, and if compensated by suitably placed masses of iron — generally iron spheres attached to the port and starboard sides of the binnacle — at any one place, is compensated for all parts of the world. It was stated above that the magnetism acquired by an iron or steel ship in the process of building is permanent. This is not strictly correct, for a certain proportion of it is generally lost during the first voyage, being shaken out by the buffeting of the waves and the vibration of the engines. The magnetism which remains undergoes very little subsequent diminution, and -740] Deviation of the Compass in Iron Ships 733 this is called its permanent magnetism, in opposition to the subpermanent "hich it loses. Before a ship leaves port for a long voyage, she is ' swung for the adjust- ment of compasses.' The process consists' in observing the direction of the standard compass on board, as the ship's head points N, NE, E, &c., and comparing it with that of an undisturbed compass on shore. In this ■\\'ay the error of the compass on each point is ascertained and a table of errors drawn. By analysis of this table the navigating officer finds out how much of the error is due to the permanent magnetism of the ship and how much to temporary induction in vertical and horizontal iron. The several errors are compensated (i) by permanent magnets in the binnacle, (2) by a Flinders bar, and (3) by the port and starboard iron spheres. 734 Frictional Electricity [741- BOOK IX FRICTIONAL ELECTRICITY CHAPTER I FUNDAMENTAL PRINCIPLES 741. Electricity. Its nature. — Electricity is a powerful physical agent which manifests itself mainly by attraction and repulsion, but also by luminous and heating effects, by violent shocks, by chemical decomposition, and many other phenomena. It is evoked in bodies by a variety of causes, among which are friction, pressure, chemical action, heat and magnetism. Thales, 600 B.C., knew that when amber was rubbed with silk it acquired the property of attracting light bodies ; and from the Greek word (^XfKrpov) for this substance the term electricity has been derived. This is nearly all the knowledge left by the ancients ; it was not until towards the end of the sixteenth century that Dr. Gilbert, physician to Queen Elizabeth, showed that this property was not limited to amber, but that other bodies, such as sulphur, wax, glass, &c,, also possessed it in a greater or less degree. 742. Development of electricity by friction. — When a glass rod, or a stick of sealing-wax or shellac, is held in the hand, and is rubbed with a piece of flannel or with the skin of a cat, the parts rubbed will be found to have the property of attracting light bodies, such as pieces of silk, wool, feathers, paper, bran, gold leaf, &c., which, after remaining a short time in contact, are again repelled. They are then said to have become electrified. In order to ascertain whether bodies are electrified or not, instruments called electroscopes are used. The simplest of these, the electric pendulum (fig. 705), consists of a pith ball attached by means of a silk thread to a glass support. When an electrified body is brought near the pith ball, the latter is instantly attracted, but after momentary contact is again repelled (fig. 706). A solid body may also be electrified by friction with a liquid or with a gas. In the Torricellian vacuum a movement of the mercury against the sides of the glass produces a disengagement of electric light visible in the dark ; a tube exhausted of air, but containing a few drops of mercury, becomes also luminous when agitated in the dark. If a quantity of mercury in a dry glass vessel is connected with a gold- Conductors and Nonconductors 735 -743] leaf electroscope (748) by a wire, and a dry glass rod be immersed in it, no indi- cations are observed during the immersion, but on smartly withdrawing the rod, the leaves increasingly diverge, attaining their maximum when the rod leaves the mercury. Some substances, particularly metals, do not seem capable of receiving the electric excitement. When a rod of metal is held in the hand, and r\ Fig. 705 Fig. 706 rubbed with silk or flannel, no electric effects are produced in it ; and bodies were divided by Gilbert into idioelectrics, or those which become electrified by friction ; and anelectrics, or those which do not possess this property. These distinctions no longer obtain in any absolute sense ; under appropriate conditions, all bodies may be electrified by friction (743). 743. Conductors and nonconductors. — When a dry glass rod, rubbed at one end, is brought near an electroscope, it will be seen that that part only is electrified which has been rubbed ; the other end produces neither attraction nor repulsion. The same is the case with a rod of shellac or of sealing-wax. In these bodies electricity does not pass from one part to another — they do not conduct electricity. Experiment shows that when a metal has received electricity in any of its parts the electricity instantly spreads over its entire §urface. Metals are hence said to be good cofidticiors of electricity. Bodies have, accordingly, been divided into conductors and nonconductors ■or insulators. This distinction is not absolute, and we may advantageously consider bodies as offering a resistance to the passage of electricity which varies with the nature of the substance. Those bodies which offer little Teslstance are conductors, and those which offer great resistance are non- conductors or insulators : electric conductivity is accordingly the inverse of electric resistance. There is no such thing as an absolute nonconductor of electricity, any more than there is an absolute nonconductor of heat. 736 Frictional Electricity [743- We are to consider that between conductors and nonconductors there is a quantitative and not a qualitative difference ; there is no conductor so good but that it offers some resistance to the passage of electricity, nor is there anj- substance which insulates so completely but that it allows some electricit)- to pass. The transition from conductors to nonconductors is gradual, and no line of sharp demarcation can be drawn between them. In this sense we are to understand the following table, in which bodies are conveniently classed as conductors^ semiconductors, and nonconductors • those bodies being designated as conductors which, when applied to a charged electroscope, discharge it almost instantaneously ; semiconductors being those which discharge it in a short but measurable time — a few seconds, for instance ; while nonconductors effect no perceptible discharge in the course of a minute. Conductors Semiconductors Nonconductors Metals. Alcohol and ether. Dry oxides. Well-burnt charcoal. Powdered glass. Ice at- 25° C. Graphite. Flour of sulphur. Lime. Acids. , Dry wood. India rubber. Aqueous solutions. Paper. Air and dry gases. Water...,' Ice at o". Dry paper. Snow. Silk, Vegetables. Diamonds and p Animals. stones. Soluble salts. Glass. Linen. Wax. Cotton. Sulphur. Resin. Amber. Shellac. precious This list is arranged in the order of decreasing conductivity, or, what is the same thing, of increasing resistance. The arrangement, however, is not invariable. Conductivity depends on many physical conditions. Glass, for example, which does not conduct at ordinary temperatures, does so at 200° to 300° C. To show this, platinum wire is coiled on a glass rod to within a couple of inches from the end. If the finger touches the coiled part, and the free end when at the ordinary temperature is applied to a charged electroscope, it does not affect it ; but if the free end be heated by placing it in a Bunsen's flame, it will now be found to discharge the electroscope. Shellac and resin do not insulate so well when they are heated. Water, which is a good conductor, conducts but little in the state of ice at o , and very badly at -25°. Powdered glass and flour of sulphur conduct very well, while in compact masses they are nonconductors ; probably because in a state of powder each particle becomes covered with a film of moisture that acts as a conductor. The nonconducting power of glass is also greatly influenced by its chemical composition. Some specimens have an appre^ ciable conductivity even if dry and at the ordinary temperature. -745] Distinction of the two kinds of Electricity 717 Heat acts indirectly by drying, by which many bodies lose their conduc- tivity either partially or wholly. 744. Insulating bodies. Common reservoir. — Bad conductors are called insulators, for they are used as supports for bodies in which electricity is to be retained. A conductor remains electrified only so long as it is sur- rounded by insulators. If this were not the case, as soon as the electrified body came in contact with the earth, which is a good conductor, the elec- tricity would pass into the earth, and diffuse itself through its whole extent. On this account, the earth has been named the common reservoir. A body is insulated by being placed on a support with glass feet, or on a cake of resin, or by being suspended by silk threads. No bodies, however, insulate perfectly ; all electrified bodies lose their electricity more or less rapidly by means of the supports on which they rest. An insulating stand consists of a metal or wooden disc, or platform, supported on a pillar of some insulating material. If this material is glass it should be washed in dilute acid (to get rid of any adhering alkah) and in water, dried, and coated with a thin layer of shellac varnish to prevent deposition of moisture on it. Ebonite is frequently used for insulating purposes, but it ceases to insulate after long exposure to light, owing to the formation of a thin film of sulphuric acid (due to the action of oxygen and moisture on the sulphur of the ebonite) on its surface. Brown shellac and paraffin wax are ex- cellent insulators. The loss of electricity from a charged conductor in a moist atmosphere is due chiefly to leakage by the support, and not to the conductivity of the moist air. Mascart's insulator is admirably adapted for supporting bodies charged with electricity. It consists of a glass vessel of special shape (fig. 707), to the glass vase of which is fused the stem. This passes through the neck and supports the plate, P ; the neck is enclosed by an ebonite stopper, and inside the vessel is sulphuric acid, so that the stem A is always dry. From their great conductivity metals do not seem to become electrified by friction. But if they are insulated, by being held in the hand by an India rubber glove or a silk handkerchief and then rubbed, they give good indi- cations. This may also be seen by the following experiment (fig. 708). A brass ''Imumijii^' la ^a^^^^Bsa tube is provided with a glass handle by which it is held, and is then rubbed with '^' '° silk or flannel. On bringing the metal near an electric pendulum (fig. 705), the pith ball will be attracted. If the metal is held in the hand, electricity is indeed produced by friction — but it immediately passes through the body into the ground. If, too, the cap of a gold-leaf electroscope be briskly flapped with a dry silk handkerchief, the gold leaves will diverge. 745. Distinction of the two kinds of electricity. — When a glass rod is rubbed with silk, both glass and silk are electrified, for each attracts a pith-ball pendulum when brought near to it. To ensure success in this experiment 3B Fig. 707 73^ Frictional Electricity [745- the operator should wear an india rubber glove, for the purpose of insulating the silk ; otherwise the electricity developed on it may escape to the floor of the room. The pith ball after contact with the glass rod is repelled by it, but is still attracted by the silk. Similarly, if when the pith ball is neutral the silk touches it, the ball acquires some of the electricity of the silk and is repelled by it, though it is attracted by the glass rod. If instead of glass and silk we make the experiments with glass and flannel, we find that both these substances become electrified by friction with each other, and that the pith ball when charged by contact with the sealing-wax is repelled by it, and attracted by the flannel, while, if it has first touched the charged flannel, it is repelled by the flannel and attracted by the sealing-wax. Further, if glass be rubbed with silk and sealing-wax with flannel, the pith ball, after touching the glass, is repelled by the glass and attracted by the sealing-wax, and after touching the sealing-wax, is repelled by it and attracted by the glass. By experiments of this nature it becomes clear that we must distinguish between two kinds of electrification, and recognise that the glass and silk are differently electrified, as are also wax and flannel, but that the kind of electrification developed on the glass by friction with silk is of the same kind as that developed on flannel when it is made to rub sealing-wax, and also that the electricities produced on the sealing-wax and on the silk are identical. Dufay gave the names vitreous and resinous to these two respectively. 746. Theories of electricity. — To account for the different effects of electricity, Franklin supposed that there exists a peculiar, subtle, imponder- able fluid, which acts by repulsion on its own particles, and pervades all matter. This fluid is present in every substance in a quantity peculiar to it, and when the substance contains this normal quantity it is in the natural, or unelectrified, state. When two substances are rubbed together, the one acquires an additional quantity of the fluid, and is said to be positively electrified ; the other loses an equal quantity, and is said to be negatively electrified. Positive electricity is represented by the sign -t- , and negative electricity by the sign — ; a designation based on the algebraical principle, that when a plus quantity is added to an equal minus quantity zero is produced. The theory of Symmer assumes that every substance contains an inde- finite quantity of a subtle, imponderable matter, which is called the electric fluid. This fluid is formed by the union of two fluids — the positive and the negative. When they are combined they neutralise each other, and the body is then in the natural or neutral state. By friction, and by several other means, the two fluids may be separated, but one of them can never be excited without a simultaneous production of the other. There may, how- ever, be a greater or less excess of the one or the other in any body, and it is then said to be electrified positively or negatively. As in Franklin's theory, vitreous corresponds to positive and resinous to negative electricity. This distinction is merely conventional : it is adopted for the sake of con- venience, and there is no other reason why resinous electricity should not be called positive electricity. It must be added that these theories are quite hypothetical ; but for purposes of instruction the adoption of one or other of them is for the present justified by the convenient explanation which they give of electric phenomena. -748] Gold-leaf Electroscope 719 A* At Fig B ^B 747. Attraction and repulsion. — The phenomena of attraction and repulsion naay be enunciated in the following law : — Two bodies charged with the same electricity repel each other;, two bodies charged with opposite electricities attract each other. These attractions and repulsions take place in virtue of the action which the two electricities exert on themselves, and g not in virtue of their action on the particles of matter. The repulsion between similarly electrified bodies may be exhibited in the following experiments : — i. If the pith balls, A and B (fig. 709), be suspended, close together, by long silk fibres, and a charged glass rod is brought up from below, as soon as the pith balls touch the glass they are both charged with + electricity, and repel each other to the positions A' B'. ii. Hold a narrow strip of silk ribbon, a yard long, by its middle, so that the two halves hang vertical in the unelectrified state. When electrified by friction with India rubber they stand out from each other at an angle, both being charged with the same (positive) electricity. To secure this result, a good plan is to cover the first and second fingers of the right hand with pieces of large rubber tubing and to pass the ribbon between them. A similar experiment may be made with a strip of gutta-percha tissue by passing it between the fingers. 748. Gold-leaf electroscope. — An electroscope is an apparatus (i) for detecting the presence of electrification, and (ii) for indi- cating differences of potential (757). The gold-leaf electroscope is much more sensitive as a detector of electrification than the pith-ball pendulum which has so far been used. A convenient form of it, and one which may be used -for lantern projection, consists of a brass cylinder A (fig. 710), about 10 cm. in diameter, with plate-glass ends 8 cm. apart. It is surmounted by a short brass tube plugged with paraffin wax, through the centre of which passes a brass rod. This rod has a small brass ball, a, at the top, and at the bottom carries two parallel strips of gold leaf 3 cm. long and •; cm. broad. The part d of the rod which supports the cylinder is made of ebonite, so that when necessary the brass case may be insulated from the ground. The rod below d fits into a tube g, and can be clamped so that the gold leaves may be at any desired height from the table. Fine copper wires are drawn horizontally across the inner sides of the glass ends of the cylinder, the object being to surround the gold leaves with a metallic environment, all parts of which are connected * '"° together, and may be earthed when necessary. There is a small hole at the 3 B 2 740 Frictional Electricity [748- Fig. 711 top of a for the insertion of a wire, and scope. It is found that A is entirely free Pig. yiy from charge, the whole of the charge having passed to the hemispheres. This experiment was first made by Cavendish, but the apparatus is commonly known as Biof s. Another form of apparatus to illustrate the same fact is represented in fig. 718, in which A is a hollow brass hemisphere resting on a support of ebonite, and is electrified by being flapped with catskin ; a similar hemi- sphere, B, provided with a glass handle, is placed over it. By means of a metal spring with an ebonite button, E, the outer and inner hemispheres may be brought into contact with each other. On afterwards reijioving B, and examining the two hemispheres, we find all the electricity on B. iv. The distribution of electricity on the surface may also be shown by means of the following apparatus : — It consists of a metal cylinder on in- sulating supports, on which is fixed a long strip of tinfoil which can be rolled up by means of a small insulating handle (fig. 719). A quadrant electroscope (748) is fitted in metallic communi- cation with the cylinder. When the strip is rolled up, a charge is imparted to the cylinder, by which a certain divergence is produced. On unrolling the tinfoil this divergence gradually diminishes, and increases as it is again rolled up. The quantity of electricity remaining the same, the electric charge, on each unit of sur- face, is therefore less as the surface is greater, v. The following ingenious experiment by Faraday further illustrates this law : — A metal ring is fitted on an insulating support, and a conical gauze bag, such as is used for catching butterflies, is fitted to it (fig. 720). By means of a silk thread, the bag can be drawn inside out. After electrifying the bag, it is seen by means of a proof plane that the electricity is on the exterior ; but if the positions are reversed by drawing the bag Fig. 718 -756] Electric Density 749 inside out, so that the interior has now become the exterior, the electricity will still be found on the exterior. The property of electricity, of accumulating on the outside of bodies, is ascribed to the repulsion which the particles exert on each other. Elec- tricity tends constantly to pass to the surface of bodies, whence it continually tends to escape, but is prevented by the resistance of the feebly conducting atmosphere. To the statement that electricity resides on the surface of bodies, two exceptions may be noted. When a steady current flows through a wire the flow takes place throughout the whole mass of the condvictor. Also a body placed inside another may, if insulated from it, receive charges of Fig. 720 electricity. On this depends the possibility of electric experiments in ordinary rooms. Also the inside of a hollow conductor may receive an induced charge (762). 755. Electric density.— On a metal sphere the distribution of the electricity is everywhere the same, simply from its symmetry. This can be demonstrated by means of the proof plane and electroscope. A metal sphere placed on an insulating support is electrified, and touched at different parts of its surface with the proof plane, which each time is applied to the cap of the electroscope. As the divergence observed is in all cases sensibly the same, it is concluded that the proof plane each time receives the same quantity of electricity. In the case of an elongated ellipsoid (fig. 721) it is found that the distribution of electricity is different at different points of the surface. The electricity accumulates at the most acute points. This is demonstrated by successively touching the ellipsoid at different parts 750 Frictional Electricity [755- Fig. 721 with the proof plane, and then bringing this to the electroscope. It is found that the greatest deflection is produced when the proof plane has been in contact with the point a, and the least by contact with the middle space e. The electric dejtsity at any part of a surface is the term used to express the quantity of electricity per unit area at that part of the surface. If S represents the surface in square centimetres, and Q the quantity of electricity on that surface in terms of the unit already defined (752), then, assuming that the electricity is equally distri- buted, as on a sphere, its electric- density is equal If the distribu- tion varies rapidly the electric density at any particular spot is equal to the quantity which would be present on a square centi- metre embracing that spot, if the distribution were uniform throughout the square centimetre and the same as at the spot in question. On an insulated cylinder, terminated by two hemispheres, the density of the electric layer at the ends is greater than in the middle. On a circular disc the density is greatest at the edges. 756. Force outside an electrified body. — The force F which a sphere, charged with a quantity of electricity Q, exerts on unit charge at a distance ^from its centre, is -j; ; this is equal to ^ if S is the area of the sphere, and o- the density of electricity on its surface. Now the area of the sphere is 417 R^ ; and if the distance d is equal to the radius R, then the force outside the surface but close to it = ^''Y„ = Ana-. K' It may be shown in like manner that the force due to any closed con- ductor on unit charge, placed just outside it, is 4770-. On an insulated conductor, where the electricity is in equilibrium, a particle of electricity will have no tendency to move along the surface, for otherwise there would be no equilibrium. But the electricity does exert a pressure on the external non-conducting medium, which is always directed outwards, and is called the electrostatic pressure or electric tension, and represents the endeavour of the charge of electricity to violently break through the insulation of the dielectric. The amount of this pressure is 2n-o-* for unit area, o- being the electric density at the point considered. The effect of this on a soap-bubble, for instance, if electrified with either kind of -757] " Potential 751 electricity, is to enlarge it. In any case the electrification constitutes a deduction from the amount of atmospheric pressure which the body experi- ences when unelectrified. The terms electric density and electrostatic pressure are often confounded. The latter ought rather to be restricted, as Maxwell proposed, to express the state of stress or pressure exerted upon a dielectric in the neighbourhood of an electrified body producing a strain which, if continually increased, tends to disruptive discharge. It varies as the square of the electric density, and is equal to 27ro-^ per unit area. The electric force just outside a charged con- ductor — that is, the mechanical force on the unit charge — is, as we have seen above, 4!rcr, and varies as the simple power of the electric density. Electro- static pressure may thus be compared to the strain on a rope which supports a weight ; and the dielectric medium which can support a certain tension and no more is said to have a certain electric strength in the same sense as a rope which bears a certain weight without breaking is said to have a certain strength. 757. Potential. — If one end of a wire be connected to the cap of a gold- leaf electroscope, and the other end, held in insulating tongs, be allowed to touch the surface of the elongated conductor (fig. 721), we find that whatever part is touched the divergence of the leaves is the same. It has been already seen that the electric density is greatest at the pointed end, and varies as the curvature of the surface. It has also been seen that when the sphere (fig. 716) is charged, the charge resides on the surface, and there is no electricity inside. But whether the wire connected with the electroscope touches the inside or outside of the hollow sphere, the indication of the electroscope is the same. It is clear, therefore, that there is some property of the charged conductor which is the same at all parts of its surface, however unequally the electricity may be distributed on that surface. This property is called electric potential. Two conductors, A and B, have the same potential when, on connection being made between them by a wire, no electricity passes from the one to the other. If positive electricity passes from A to B, A is at a higher potential than B. The earth and all things in conducting connection with it are said to be at zero potential. If A is posi- tively charged and is earth-connected, there is a flow of positive electricity from it to the earth ; it must therefore have been at a higher potential than the earth, or at a positive potential. On the other hand, if it is negatively charged, it is at a lower potential than the earth, or at a negative potential, because, if it were earthed, positive electricity would' flow from the earth to it. When electricity, without qualification as to sign, is spoken of, positive electricity is always meant. Potential is analogous to level in mechanics and hydrostatics. As water only flows from places at a higher to places at a lower level, so electricity only flows from places at a higher to places at a lower potential. If two water tanks are connected by a pipe, there will be a flow of water from the tank in which the water level is higher to that in which it is lower, and the flow will continue until the level is the same in both. The flow does not depend upon the quantities of water in the tanks. So when two conductors are charged with electricity, there will only be a flow of electricity from one to the other when there is a difference of potential between them, however 752 Frictional Electricity [757- different the charges may be. The cause of flow of water is, of course, hydro- static pressure, and this is proportional to difference of level. If two vessels containing air or steam or any other gaseous substance, at different pressures, be joined by a pipe with a stopcock, the difference in pressure will cause a flow of gas from one to the other when the stopcock is opened, and the flow will take place from the vessel of higher to that of lower pressure. Quantity of gas is here the analogue of quantity of (positive) electricity, and difference of pressure the analogue of difference of potential. Electrical engineers con- stantly refer to the difference of potential which causes a flow of electricity as electric j>ressicre. It must be carefully distinguished from electrostatic pressure (756). We cannot speak of potential in the abstract, any more than we can speak of any particular level without at least some tacit reference to a standard of level. Thus, if we say that such and such a place is 300 feet high, we usually imply that this is the height above sea level. So, too, we refer the longitude of a place to some definite meridian, such as that of Greenwich, either expressly or by implication. In like manner we cannot speak of the potential at a point without at least an implied reference to a standard of potential. The standard is usually the earth, which is taken as being at zero potential, or the same as the potential at an infinite distance. If we speak of the potential at a given point, the difference between the potential at this point and the earth is meant. The relation between quantity of electricity and electric potential may be further illustrated by reference to certain well-known thermal phenomena. In the interchange of heat between bodies of different temperatures the final result is that heat passes only from bodies of higher to bodies of lower temperature. So also electricity passes only from bodies of higher to bodies of lower potential. Potential is as regards electricity what temperature is as regards heat, and might indeed be called electric temperature. We may have a small quantity of heat at a high temperature ; thus a short thin wire heated to incandescence has a far higher heat potential, or temperature, than a bucket of hot water, but the latter will possess a much larger quantity of heat. The quantity of electricity in a flash of lightning is small, but the potential is very high. 758. Measure of potential. — We have already seen, that in order td lift a certain mass against the attraction of gravity (60-62) there must be a definite expenditure of work, and the equivalent of this work is met with in the energy which the lifted mass retains, or what is called the potential energy of position. Let us now suppose that we have a large insulated conductor charged with positive electricity, and that, at a distance which is very great in com- parison with the size of the sphere, there is a small insulated sphere charged with the same kind of electricity. If we move the small sphere, which we will suppose to have unit charge (752), towards the conductor, we must do a certain amgunt of work upon it to overcome the repulsion between the two charges. The potential of the conductor is numerically equal to this work, if the small sphere be moved from an infinite distance, that is, from a place where the potential is zero, close up to the conductor. And ;generally, if V is the potential at any point, either on a conductor or in a dielectric. -758] Measure of Potential 755 V units of work (ergs) would have to be done against electric forces to bring the unit charge from an infinite distance to that point. If in the above case the sphere were charged with negative electricity, then instead of its being needful to do work in order to bring a unit of posi- tive electricity towards it, work would be done by electric attraction, and the potential of the point near the charged sphere would thus be negative. The potential at any point may also be said to be the work done against electric force, in moving unit charge of negative electricity from that point to an infinite distance. The amount of work required to move the unit of positive electricity against electric force from any one position to any other, is equal to the excess of the electric potential of the second position over the electric potential of the first. This is, in effect, the same as has been said above, for at an infinite distance the potential is zero. Here it is immaterial along what path the electricity is moved, whether by the shortest one or not ; just as in the analogous case of moving a body against gravity the work done only depends on the initial and final position of the body moved. It may be proved that the potential at a point A (fig. 722), distant ^ from a charge, 5?, of positive electricity, is I, That is, ^ ^ X represents the work which must be done upon a unit of positive electricity to bring it from an infinite dis- ^'^' ''^^ tance to A against the repulsive force of a charge q situated at B. To determine the potential at A due to several independent causes, we must write down the value of the potential due to each separate cause, and take the algebraic sum of these to repre- sent the actual potential If there are three charges, -(- q^, - q^, + q^., situated at the points B, C, D (fig. 723), distant respectively r^, r^, r.j from A, the potential at A is ?i _ ?2 + £s It must be noted that although potential is measured in terms of work, it is not of Fig. 723 ■ the same nature or dimensions as work ; potential is equal to work done upon a definite quantity of electricity, or V = ^^^^ , or QV = W, if Q = quantity of electricity and W = work. electric charge Now the dimensions of work are (63) ML'/T^' and since F = -- ■ (753), the a dimensions of the square of an electric charge are equal to (the dimensions of) F(/*, or are -=5- x L^ ; therefore the dimensions of electric charge are Mi U J r , ..• , ML2 . Mi U Mi Li ,„ , ^ \ it ^ i — =_, and of potential, __ -v- — _ — = — — (See also art. 1,000.) Fre- quently the unit charge is assumed, and we speak of the potential as so many ergs, but it must be remembered that this is accurate only in the sense in which it is accurate to speak of a velocity of so many miles \^per hour being under- stood], or a pressure of so many pounds Yper square inch being understood]. 3C 754 Frictional Electricity [759- 759. Electric field. Lines of electric force. — A region in which force is exercised is called a. field of force. The space round the earth is a field of gravitational force due to the earth's attraction. The lines along which force is exercised are called lines of force, and the field is uniform when the lines of force are parallel to each other and uniformly spaced. The earth's gravitational field of force is uniform over a given small area. An electric field is a region in which electric force is exerted. Electric force acts upon electric charges as mechanical or gravitational force acts upon matter. Mechanical force has no action upon a charge of electricity, any more than electric force acts upon matter. Let a sphere be charged with a quantity Q of positive electricity. The electric force at any distance r from Fig. 724 its centre is ~ thus the force rapidly falls off as the distance from the sphere increases. The lines of force due to a positively charged sphere are straight lines radiating as from the centre of the sphere. They start, however, not from the centre but from the surface, are directed outwards, and are uni- formly spaced (fig. 724). If the charge were doubled, the number of lines would be doubled. If the charge is negative the arrows will be directed to- wards the sphere, since the direction of a line of force is the direction in which a positive charge moves along it. The lines of force in the field due to two spheres a short distance apart equally charged, one with posi- tive and the other with negative electricity, are Fig. 725 shown in fig. 725, and fig. 726 illustrates the distribution of the lines when the charges are both positive or both negative. -759] Electric Field. Lines of Electric Force 755 The lines of electric force may be made visible in the dark by placing^ two small balls at a distance from each other in conducting communication Fig. 726 with an electric machine at work, and then sifting lycopodium powder through a fine sieve while the space is at the same time illuminated by the lime or the electric light. They may also be shown experimentally by the apparatus represented in fig. 727 : two stout wires terminated in small knobs are fitted to the sides of a flat glass dish in which is placed turpentine with quinine sulphate uniformly diffused in it ; when the wires are connected with the electrodes of an Fig. 727 electric machine (776), which is very slowly worked, the white crystals arrange themselves in lines which are the lines of force of the field in question. An cquipotential surface is a surface such that the potential is the same at all parts of it ; and the trace of an equipotential surface on a plane is an eguipotential line. If a small test charge is moved along an equipotential surface no work is done by or against electric force. Lines of force are everywhere perpendicular to equipotential surfaces. In the case of an insulated electrified sphere the successive equipotential surfaces are spherical shells of gradually increasing radii. Fig. 728 illustrates the case of a sphere of radius i cm., with a charge numerically equal to 10 units. The potential is equal to 10, and the equipotential circles (portions of them only are shown in the figure) are drawn so that the difference of potential between successive surfaces is unity. The fall of potential is very rapid near the sphere, but falls off slowly at distances exceeding 5 cm. from the centre. At this distance the potential is 2, at 10 cm. it is i, and at a distance of a metre from A the potential is only -^ (758). 3 C2 756 Frictional Electricity [759- If the force in a field has everywhere the same direction, the equipoten- tial surfaces are parallel planes, the lines of force are parallel, and we have a uniform field. Figfc 728 The case we have selected for illustrating the subject of equipotential lines is the simplest that could be chosen. But, bearing in mind that an equipotential line cuts lines of force at right angles, it is easy to trace the equipotential lines in less simple cases — such as that of the ellipsoidal con- ductor in fig. 721 — when the lines of force in the field have been drawn, or of the similarly and dissimilarly charged spheres of figs. 725 and 726. The surface of a conductor is always an equipotential surface. 760. Electric capacity.'^ — When a conductor, away from the neighbourhood of other conductors, is charged with positive electricity the potential -rises as the charge increases, and is directly proportional to the charge. If two conductors, not near each other, are charged with equal quantities of positive electricity, they are not raised to the same potential unless they have one property in common, which is called electric or electrostatic capacity. The capacity of a conductor depends upon its size and shape, and upon its position with regard to other conductors ; it depends also upon the nature of the surrounding medium. The electrostatic capacity of a conductor is measured by, and is numerically equal to, the quantity of electricity which must be communicated to the conductor to raise by unity its potential above the potential of surrounding conductors. Thus, if C represents the capacity of a conductor, Q the quantity of electricity with which it is charged, and V the difference between its potential and that of neighbouring bodies, the relation Q = CV holds. It has already been stated (758) that the potential at a distance rf from the centre of a sphere charged with a quantity Q of electricity is Q / rf ; if d- r, the radius of the sphere, the potential (which is now that of the sphere itself) is ^. Comparing this with the formula above, we see that the r capacity of a sphere surrounded by air and away from other conductors is equal to its radius. Electrostatic capacity is analogous to the capacity of a liquid measure. Imagine a litre jar or cylinder graduated in cubic centimetres, with the graduation 1000 some little distance from the top. The capacity of this -761] Action of Points 757 vessel is said to be i litre, being measured by, the quantity of liquid which must be poured into it to fill it up to the mark looo. In the same way the electrostatic capacity of a conductor is measured by the quantity of electricity which must be communicated to the conductor to raise it from zero to unit potential, or more generally to raise its potential by unity, any conductors which are near to it being supposed to be at zero potential. There is an analogy between heat and electricity, as regards capacity, but there are also important differences ; thus the capacity of a body for heat is influenced by the temperature (463), being generally greater at higher temperatures, while the capacity of a body for electricity does not depend on the potential. Again, the thermal capacity depends solely on the mass of a body, and in bodies of the same material and shape is proportional to the cube of homologous dimensions ; the capacity for electricity is directly proportional to such dimensions, and not to the weight or volume. Thermal capacity is proportional to a specific coefficient, which varies with the mate- rial, but is independent of its shape ; while electric capacity varies with the shape of a body, but not with its material, provided the electricity can move freely upon it. Thermal capacity is unaffected by the proximity of other bodies, while the electric capacity depends on the position and shape of all the adjacent conductors. If we have a series of bodies at a considerable distance from each other, whose capacities and potentials are respectively c, c', c", &c., and v, v', v", &c., then, if they are all connected by fine wires of no capacity, they all instantly acquire the same potential V, which is determined by the equation The analogy of this to the equalisation of temperature which takes place when bodies at different temperatures are mixed together is directly apparent. It may be further illustrated by supposing a series of tubes of different diameters, and connected by very narrow tubes, in which are stopcocks to cut off communication. If, while in this state, water is poured into the tubes to different heights above the common level, it will be manifest that they will hold very various quantities of water. If, however, the stopcocks are opened, the tubes will still contain quantities of water pro- portional to their capacities, but the level or potential in all will be the same. 761. Action of points. — Since the electric density at any part of the surface of a conductor increases with the curvature of the part, the density at a fine point in connection with a conductor must tend to become infinitely great ; but the greater the density the greater will be the tendency of electricity to overcome the resistance of the air, and escape, for the electro- static pressure is proportional to the square of the density (756). If the hand is brought near a point on a conductor connected with an electric machine in action, a slight wind is felt ; and if the disengagement of electricity takes place in the dark a luminous brush is seen. If an electrified conductor is to retain its electricity, all sharp points and edges must be avoided ; on the other hand, to facilitate the outflow of electricity in apparatus and experiments, frequent use is made of this action of points. A flame acts like a very fine point in diffusing electricity. For experiments illustrating the action of points, see article 780. 758 Frictional Electricity [762- CH AFTER III ELECTROSTATIC INDUCTION OR INFLUENCE. ELECTRIC MACHINES 762. Electrostatic induction. — When a conductor is brought into the electric field produced by a charged body it becomes thereby electrified with a positive charge at one end and a negative charge at the other, the two charges being separated by a region in which there is no electrification. The process is called electrostatic induction or influence, the electrification is induced, and the charged body which produces the field is the inducing body. The elementary facts of electrostatic induction may be demonstrated by the apparatus illustrated in fig. 729. A is the charged body which pro- duces the field ; it is represented here as a sphere charged positively, but in practice may be an excited glass rod. B is an insulated uncharged cylinder ; it becomes electrified by induction, and we may test the distribution of elec- tricity on it by the proof plane and electroscope. For this purpose let the proof plane, after touching the remote the cap of an electroscope. The leaves electricity, as is rendered evident by the fact that the divergence increases when a small charge from an excited glass rod is applied to the cap. When the charge at the near end of B is similarly tested, it is found to be negative. Between the two ends of B is a neutral region, from which no electricity can be carried away by the proof plane. That the charges on B are equal to each other is shown by the fact that when the cylinder is removed fi-om the field of A it is found to be without charge. The neutral region on B is generally on the side of it nearer to A, for though the negative and positive induced charges are equal, they are unequally distributed, that nearer to A being the denser, and therefore occupying less surface. If, while B is under induction, any point of it is momentarily touched with the finger, positive electricity will flow from it to the earth, reducing it to zero potential. This must be so, since B, being in the field of A, is at a positive potential. But, although, after being touched, B is at zero potential, it still retains a negative charge at the end near A. This result follows what- ever part of it is touched, since connecting one part to earth means connect- ing every other part to earth. If now the sphere and cylinder be separated Fig. 729 end of B, be brought to diverge, and with positive -762] Electrostatic Induction 759 Fig. 730 the negative charge at the end of B spreads over its surface, and the potential of the cylinder becomes negative. The experiments described above may easily te made with a gold-leaf electroscope and a charged body, glass or sealing-wax. Fig. 730 illustrates the case when an excited rod of sealing-wax is held at a little distance above the cap of the electroscope. The conductor, which takes the place of the cylinder B in fig. 729, here consists of the knob, rod, and leaves of the electroscope. The cap acquires a positive and the leaves a negative charge, the whole conductor being at a negative potential. The leaves diverge because their potential is different from (lower than) that of the earth (787), the angle of divergence being a rough measure of the differ- ence. When C is touched the poten- tial rises frpm a negative value to zero, and the leaves collapse, although a positive charge still resides on the cap. This charge cannot be got rid of so long as A remains ; but when A is removed, the potential of C — which, notwithstanding the positive charge, was kept down at zero by the influence of the negatively charged rod — at once rises, the. electricity spreads over the whole conductor, and the leaves diverge with a positive charge. Thus a body can be charged with electricity by induction as well as by conduction. But, in the latter case, the charging body loses part of its electricity, which remains unchanged in the former case. The electricity imparted by conduction is of the same kind as that of the electrified body, while that excited by induction is of the opposite kind. To impart electricity by conduction, the body must be quite insulated ; while in the case of induction it must be in connection with the earth — at all events momentarily. A body electrified by induction acts in turn on bodies placed near it, separating the two electricities in a manner shown by the signs on the cylinder B (fig. 729). What has here been said has reference to the inductive action exerted on good conductors. Bad conductors are not so easily acted upon by induction, owing to the great resistance they present to the circulation of electricity ; but, when once charged, their electric state is more permanent. This is analogous to what is met with in magnetism ; a magnet instan- taneously magnetises a piece of soft iron, but the magnetisation is only temporary, and depends on the continuance of the action of the magnet ; a magnet magnetises steel with far greater difficulty, but this magnetisation is permanent. The attraction of a pith-ball pendulum (fig. 705) is explained by induc- tion. Let M be a charged body and N a pith ball (fig. 731). o 760 Frictional Electricity [762- If the pendulum is suspended by an insulating thread, such as dry silk, M, acting inductively on N, attracts the negative and repels the positive electricity, so that the maxima of density are respectively at the points a and b. Now a is nearer >z£z£zj?r£>-+-f.ilL-u induction (fig. 740), and there is practically La. -fe .,-^r^,.-t— ^j^ A^j jio transfer of electricity to it from the ebonite ; F'g- 74° when it is touched the induced negative only passes to earth, the equal positive charge re- maining on the under face. This positive electricity, when the cover is raised, becomes free, and may be withdrawn in the form of a spark. The electrophorus is more efficient when the ebonite is provided with its metal backing than when it is not so provided, for in the latter case the inductive action described above cannot take place, or takes place (through the ebonite to the table on which it rests) to a less extent, the negative charge produced by friction is not so great, and the inductive action on the cover is diminished. The electrophorus is a good instance of the conversion of mechanical into electric energy. When the cover is lifted from the excited cake work must be expended in order to overcome the attraction of the electricity in the cake for the opposite electricity developed by induction on the cover ; and the equivalent of this work appears in the energy of the electricity thus detached. Of course, in raising the cover, work has to be done against gravity, but this work is the same whether the cover is electrified or not. When it is electrified, additional work must be done against electric force, and this is the work which is converted into energy of electric separation. The best way to discharge the plate of an electrophorus is to pass rapidly the flame of a Bunsen burner over its surface. 773. Lord Kelvin's water-dropping collector. — In the electrophorus it is seen how we may, given an initial charge, obtain by intermittent inductive action an indefinitely large amount of electricity. Lord Kelvin's water- dropping collector may be given as another arrangement for the same purpose. -774] The Replenisher 771 Fig. 741 A and B (fig. 741) are insulated metal cylinders called the inductors, and are in metallic connection with two cylinders a and b, also insulated, called the receivers, each having a funnel the nozzle of which is in the centre of the cylinder. Water from the pipe £ falls in drops through the metal taps c and d, the nozzles of which are in the centre of the cylinders A and B. Take first the case of the cylinder A, and suppose it to possess a small positive charge at the outset, the drops as they fall will be charged negatively by induction, the corresponding positive going to earth, through e. Falling on the funnel of the receiver b they impart to it the whole of their charge, and the water as it issues will be nevitral. But the negative charge of b is shared with B, which is thus negatively electrified, and the drops which fall through it are positively electrified and give up their posi- tive charge to a, which strengthens the positive of A. By this means even with a very slight original charge they will strengthen each other, until sparks pass. It is not even necessary to give a charge at the outset ; the ordinary electricity of the atmosphere is generally sufficient. The energy in this apparatus is derived from that of the falling body, and would be exactly equivalent to it if there were no loss, and if the drops reached the funnel without any velocity. 774. The replenisher. — For the purpose of maintaining constant the potential of the needle of the quadrant electrometer (796) Lord Kelvin •devised a simple and interesting form of influence machine which is illustrated in fig. 742, while fig. 743 shows a horizontal section. A and B are conducting supports to which are attached portions of two insulated half-cylinders of brass. Slots are cut in the cylinders, through which springs, a and b, attached to the external supports, pass ; e and / are other springs which pass through openings at the bottom of the cylinders (fig. 742), and are in metallic connection \vith each other. The two metallic wings C and D can be rotated by means •of the spindle P, and during the rotation come into successive contact with the springs a, e, b, f. Suppose that the conductor A is connected with the needle of the electrometer which is charged with positive electricity, and that the spindle is rotated in the direction of the arrow. Also, let B be earth-connected. Neither of the wings C and D has 3D2 Fig. 742 772 Frictional Electricity [774- Fig. 743 afty charge in the position shown in the figure ; but as soon as C touches ^, it receives a negative charge, while an equal positive charge passes by the M'ire^tothe springy" and the wing D. As the rotation continues, D Avith its positive charge comes in contact witli the spring a, and the whole of its charge passes to A. The negative charge of C goes to earth through B, or, increases the negative charge of B if B is in sulated, and the same process is repeated as the rotation is continued. Thus, at each half-x'evolution the charge on A is increased by a small amount, and its potential and that of the needle connected with it may be, by the continued rotation of the spindle, raised to any desired amount. The friction of the spindle bearings is so small that the wings may be rapidly spun round by applying the finger to the milled head at the top of the spindle seen in the centre of the cover in fig. 742. 775. Holtz's electric machine. — We proceed to describe some of the more powerful machines for producing electricity of high potential, the action of which depends upon continuous electrostatic induction. The form represented in fig. 744 was invented by Holtz, of Berlin. It consists of two circular plates of thin glass at a distance of 3 mm. from each other ; the larger one, AA, which is 2 feet in diameter, is fixed by means of four wooden rollers a, resting on glass axes and glass feet. The diameter of the second plate, BB, is 2 inches less ; it turns on a horizontal axis, which passes through a hole in the centre of the large fixed plate without touching it.. In the plate A, on the same diameter, are two large apertures or windims^ F F'. Along the lower edge of the window F, on the posterior face of the plate, a band of paper, p, is glued, to which is connected a tongue (A ^\n cardboard, n, joined to / by a thin strip of paper, and pro- tecting into the window. At the upper edge of the window, F', there are corresponding parts, p' and n' . The papers^ and^' constitute the armatures. The two plates, the armatures, and their tongues are covered with shellac \arnish, but more especially the edges of the tongues. In f^'pnt of the plate B, at the height of the armatures, are two brass combs, O O', supported by two conductors of the same metal, C C. In the front end of these conductors are two moderately large brass knobs, through which pass two brass rods terminated by smaller knobs, rr', and provided with ebonite handles, K K'. These rods, besides mo\ing with gentle friction in the knobs,' can also be turned so as to be more or less near and inclined towards each other. The plate BB is turned by means of a winch M, and a series of pulleys which transmit its motion to the axis ; the velocity which it thus receives is 12 to 15 turns in a second, and the rotation should take place in the direction indicated by the arrows, that is, towards the points of the cardboard tongues nn'. -775] Holts's Electric Machine 77: To work the, machine, one of the armatures p p' must be firsl primed, that is, positively or negatively electrified. This is effected by means of s. plate of ebonite, which is excited by striking it with catskin ; the two knobs rr' having been connected so that the two conductors C C form only one, ^ Fig. 744 ' as seen in fig. 745, which shows by a horizontal section, through the axis of rotation, the relative arrangement of the plates and of the conductors. The electrified ebonite is then brought, near one of them— ^, for instance — and the plate B is turned. The ebonite is charged with negative electricity, and Kg. 7;s this withdraws the positive electricity of the armature and charges it nega- tively. This latter, acting by induction through the plate BB as it turns on the conductors OCC'O' (fig. 745), produces positive electrification . on the points O, which collects on the front face of the movable plate ; while at 774 Frictional Electricity [775- the same time negati\'e electricity, discharged from the comb O', collects, like the former, on the front face of the plate B. Hence, the two electricities being carried along by the rotation, at the end of half a turn all the lower half of the plate B, from p to F' (fig. 746), is positively electrified, and its upper surface from p' to F negatively. But the two opposite electricities above and below the window F' concur in decomposing the electricity of the armature /'»' ; the part/' is positively electrified, while negative electricity is liberated by the tongue n', and is deposited on the -inner face of the plate BB, which from its thinness almost completely neutralises the positive electricity on the anterior face. The second armature thus becomes primed, and the same effect as at F' is produced at F on the armature /^z— that is, that the opposite electricities above and below p 71 decomposing a new quantity of neutral electricity, the negative charge of the part p increases, while the positive electricity which is liberated by the tongue n neutralises the negative electricity which comes from F' towards F ; and so forth, until, the machine having attained its maximum charge, there is equili- brium in all its parts. From that point it only keeps itself up, and in perfectly dry air it may work for a long time without its being neces- sary to employ the ebonite plate. If this is removed, and the knobs r and / are moved apart (fig. 745) to a distance de- pendent on the power of the machine, while the rotation is continued, a torrent of sparks strikes across from one knob to the other. With plates of equal dimensions Holtz's machine is far more powerful than the ordinary electric machine (768). The power is still further increased by suspending to the conductors C C two condensers (781), or small Leyden jars, H H', which consist of two glass tubes coated with tinfoil, inside and out, to a fifth of their height. Each of them is closed by a cork through which passes a rod, communicating at one end with the inner coating, and suspended to one of the conductors by a crook at the other end. The two external coatings are connected by a conductor, G. They are, in fact, only two small Leyden jars (786), one of them, H, becoming charged with positive electricity on the inside and negative on the outside ; the other, H', with negative electricity on the inside and positive on the outside. The jars must be charged up to the potential of the machine before a discharge between the knobs r r' can occur. Without the jars the machine gives relatively thin and non-luminous sparks. -776] Wimshurst's Machine 775 The current of the machine is utiUsed by placing in front of the frame two brass uprights, Q Q', with binding screws in which are copper wires ; then, by means of the handles K K', the rods which support the knobs r r' are inclined, so that they are in contact with the uprights. The current being then directed by the wires, a battery of six jars can be charged in a few minutes, water can be decomposed, a galvanometer deflected, and Geissler's tubes illuminated. Kohlrausch found that a Holtz machine with a plate 16 inches in diameter, and making 5 turns in three seconds, produced a constant current capable of decomposing water at the rate of 3J millionths of a milligramme in a second, that is, equal to -00034 ampfere (940) approximately. Rossetti, who made a series of measurements with a Holtz machine, found that the strength of the current is nearly proportional to the velocity of the rotation ; it increases a little more rapidly than the rotation. The ratio of the velocity of rotation to the strength of the curreiit is greater when the hygrometric state increases. The current produced by a Holtz machine is comparable with that of a voltaic couple. Its electromotive force and resistance are constant, provided the velocity of rotation and the hygrometric state are constant. The electromotive force is independent of the velocity of rotation, but diminishes as the moisture increases ; it is nearly 52,000 times as great as that of Daniell's cell. The internal resistance is independent of the moisture, but diminishes, rapidly with increased \elocity of rotation. Thus with a velocity of 120 turns, in a minute it is represented by 2810 million ohms (850), and with a velocity of 450 turns it is 646 million ohms. Holtz's machine is very much affected' by the moisture of the air ; but Ruhmkorff found that by spreading- on the table a few drops of petroleum, the vapours which condense on the machine protect it against the moisture of the atmosphere. Holtz's machine affords a means of making a curious experiment on reversibility. If the. two combs of a machine in the ordinary, state are con- nected with the. poles, of a second similar one, which is then set in action, the combs of the first become luminous,. and the plate begins to rotate, but in the opposite direction to its ordinary course ; the electricity thus transmits the motion of the second machine to the, first : the one expends what the other produces. It may also be observed that the two machines are connected by opposite poles, and the system constitutes a circuit which is traversed in a definite direction by a continuous electric current. A very simple and efficient machine of this kind is made by Voss of Berlin. One with a plate of to inches diameter produces a spark of 4 to 5 inches. 776. Wimshurst's machine. — This is the simplest and most efficient of all induction machines. It consists (fig. 747) of two circular glass discs, P and P', mounted on a fixed horizontal spindle in such a way as to be rotated in opposite directions at a distance of not more than a quarter of an inch apart. Both discs are well varnished, and attached to the outer surface of each, near the cir- cumference, are narro\\ radial sectors of tinfoil arranged at equal angular distances apart. 776 Frictional Electricity [776- Attached to the fixed spindle on which the discs rotate is a bent conduct- ing rod, at the ends of which are two fine wire brushes ; twice during each revolution two diametrically opposite conductors are put in connection with each other by means of this conductor, as they just graze the tips of the brushes. At the back is a similar one at right angles to that . in front, and there is a position of maximum efficiency, which is when they make an angle of 45° with the fixed collectors. These diametral conductors need not be specially insulated. There are two forks provided with combs, p p\ directed towards each other, and towards the two discs which rotate between Fig- 747 them ; they are shown in fig. 748. B and B' are Leyden jars which may be connected to the electrodes of the machine by metal rods, or may be detached at pleasure. The machine is self-exciting, and requires neither friction, nor the spark from any outside exciter, to start it. It is one of the most remark- able features of this machine, that under ordinary conditions it attains its fiill power after the second or third turn. The initial charge is probably obtained from the electricity of the air, or from the frictional resistance against it. With a machine having plates 17 inches in diameter, a powerful spark -776] Wimskurst's Machine 777 discharge passes between the two spark balls, d d, when they are 4 to 5 inches apart, in regular succession, at the rate of 2 or 3 for every turn of the handle. A machine with 12 plates, 30 inches in diameter, when driven at a Fig. 748 speed of 200 turns per minute, produces sparks between the terminals of i^i inches in length. The action of the machine may be explained as follows : — In fig. 749 Fig. 749 the plates P P' are indicated by sections of cylinders ; b^Cb^ and b\Cb'..:\.r:^ plate, which has been twisted or bent, reverts to its original state when the stress which brought about the '^' ''° deformation ceases to act, but not at once quite com- pletely. A certain length of time is required for this alteration to take place, but the change is promoted by any gentle mechanical action, such as tapping, which gives the molecules a certain freedom of motion. Dr. Hopkinson made an experiment with a Leyden jar which is quite analogous to this. A glass vessel (fig. 770) contains sulphuric acid, and in it is placed a thinner -791] The Universal Discharger 791 •one, about half full of the same liquid. Platinum wires dip in the two liquids, one of them being in connection with the prime conductor of an •electric machine, while the other is connected with the earth. The arrange- ment forms, in short, a condenser, the coatings of which are sulphuric acid. When, after being thus charged, the jar is discharged, a residual discharge may be taken after some time by again connecting the wires ; if, however, the inner jar be gently tapped with a piece of wood, the residue makes its appearance much more rapidly. 790. Electric batteries. — The charge which a Leyden jar can take depends on the extent of the coated surface, and is inversely proportional to the thickness of the insulator. Hence, the larger and thinner the jar the greater the capacity and the more powerful the charge, for a source of given potential. But very large jars are expensive, and liable to break ; .and when too thin, the accumulated electricities discharge themselves through the glass, especially if it is not quite homogeneous. Leyden jars have usually from ^ to 3 square feet of coated surface. For more powerful charges electric batteries are used. An electric battery consists of a number of Leyden jars whose internal .and external coatings are respectively connected with each other (fig. 771). They are usually placed in a wooden box lined on the bottom with tinfoil, which is connected with two metal handles in the sides of the box. The inner coatings are ■connected with each ■other by metal rods, and the battery is charged by con- necting them with the prime conduc- tor, while the outer coatings are con- nected with the ground by means of .a chain fixed to the handles. A Hen- ley's electroscope (fig. 711) indicates the charge of the battery. The larger and more numerous the jars the longer ^'S- ^^i is the time required to charge the battery, but the effects are so much the more powerful (801). To discharge a battery, the coatings are connected by means of the dis- charging rod, the outside coating being touched first. Care is required, for with large batteries serious and even fatal accidents may occur. 791. The universal discharger. — This is an almost indispensable appa- ratus in experiments with the electric battery. On a wooden stand (fig. 772) are two glass legs, each provided with universal joints, in which movable brass rods are fitted. Between these legs is a small ivory table, on which is 794 Frictional Electricity [791- placed the object under experiment. The two metal knobs being directed towards the objects, one of them is connected with the outer coating of the battery, and the moment communication is made between the outer and the inner coating by means of the glass discharging rod, the discharge passes through the object on the table. Fig. 772 792. Charg-ing Leyden jars in series or cascade. — A number of Leyden jars are placed each on a separate insulating support. The knob of the first,/ (fig. 773), is in connection with the prime conductor of the machine, and its outer coating joined to the knob of the second, the outer coating of the second to the knob of the third, and so on, the outer coating of the last, /„ communicating with the ground. The inner coating of the first receives a charge of positive electricity from the machine, and the corresponding positive electricity set free by induction on its outer coating, ' instead of escaping to the ground, passes to the inner coating of the second, which, acting in like manner, develops a charge in the third jar, and so on to the last, where the positive electricity developed by induction on the outer coating passes to the ground. The jars may be discharged either singly by connecting the inner and outer coatings of each jar, or simultaneously by connecting the inner coating of the first with the Fig. 773 -793] Measurement of the Cfiarge of a Battery 795 outer of the last. In this way the quantity of electricity necessary to charge one jar is available for charging a series of jars. It must not be supposed, however, that each jar contains as much electricity as a single jar would if charged in the usual way to the same potential of the machine. Suppose there are four similar jars, each of capacity C, and that the machine is worked until its potential rises to V, which may be indicated by a deflection of (say) 30° of a Henley's electroscope (748). In the case where a single jar is charged by itself, the drop of potential between the inner and outer coatings is V, since the outer coating is earthed ; but when four jars are arranged in cascade, the same drop takes place in four stages, and the difference of potential between the inner and outer coatings of any one of the jars is V/4. The quantity in any one jar is CV/4, and the sum in the four jars CV, which is exactly equal to the quantity any one of the jars would have had, had it been charged by itself to the potential indicated by the electroscope. 793. Measurement of the charge of a battery. Lane's electrometer. — When the outer and inner coatings of a charged Leyden jar are gradually brought nearer each other, at a certain distance a discharge ensues. The distance is called the striking or sparking distance. For the same charge it is inversely proportional to the pressure of the air, and, with the same jar, but different charges, directly proportional to the electric density of that point of the inner coating at which the discharge takes place. As the density of any point of the inner coating, other things remaining the same, is proportional to the entire charge, the striking distance is proportional to the quantity of electricity in a jar. The measurement of the charge of a battery, however, by means of the striking distance, can only take place when the charge disappears. By means of Lane's electrometer, which depends on an application of this principle, the charge put into a jar or battery may be measured. This apparatus, c (fig. 774), consists of an ordinary Leyden iar, near which there is a vertical metallic support. At the upper end is a brass rod, with a knob at one end, which can be placed in metallic con- nection with the outside of the jar : the rod being movable, the knob can be kept at a measured distance from the knob of the inner coating, such as to ensure that a comparatively small dif- ference of potential between the two coatings will give rise to a spark and so discharge the jar. Fig. 774 represents the operation of measuring the charge of a jar or battery by means of this apparatus. The jar b, whose charge is to be measured, is placed on an insulated stool with its outer coating in metallic connection with the inner coating of Lane's jar c, the outer coating of which is put to earth ; a is the conductor of the machine. When the machine is worked, positive electricity passes into the jar or battery b, and from the outer coating of b into c. When the charge 796 Frictional Electricity [793- in c has reached a certain limit, it discharges itself between the two knobs, and as often as such a discharge takes place, the same quantity of positive electricity will have passed from the machine into the battery ; hence its charge is proportional to the number of discharges of the electrometer. 794. Harris's unit jar. — Harris's unit jar (fig. 775) is an application of the same principle, and is often convenient for measuring quantities of electricity. It consists of a small Leyden phial, 4 inches in length and ■J inch in diameter, coated to about an inch from the end, so as to expose about 6 inches of coated surface. It is fixed horizontally on a long insulator, ||b and the charging rod connected at P with the conductor of the machine, while the outer coating is connected with the jar or battery by the rod t p. When the charge of electricity in the interior has reached a certain potential depending on the distance of the two balls in and «, a discharge ensues, and marks a certain quantity of electricity received as a charge by the battery, in terms of the charge of the small jar. 795. Volta's condensing electroscope. — -The condensing electroscope invented by Volta is a modification of the ordinary gold-leaf electroscope (748). The rod to which the gold-leaves are affixed terminates in a disc instead of in a knob, and there is another disc of the same size provided with an insulating glass handle. The discs, which are covered with a layer of insulating shellac varnish (fig. 776), form a condenser, with air and shellac as the dielectric. By this association of a condenser with the gold-leaf electroscope, differ- ences of potential may be indicated, and roughly measured, too small to be shown by the unaided electroscope. Suppose, for instance, we wish to measure the difference of potential between the poles of an insulated voltaic battery. Let wires, connected to the poles and held by insulating tongs, be brought into contact with the upper and lower plates, the positive pole (say) with the upper plate, and the negative with the lower. The plates will become charged with positive and negative electricity respectively, and the difference of potential between them will be that which we wish to measure, but there will be no divergence of the leaves. Now let the wires be carefully detached and the upper plate removed by its glass handle ; the leaves at once diverge with negative electricity, which was set free by the removal of the upper plate. Indeed, when the upper plate was removed, the electro- static capacity of the electroscope was very much reduced; and, as the charge of negative electricity on it was not altered, its potential rose in the same proportion as its capacity fell, and became sufficiently large to cause a deflection of the leaves. If the lower plate be connected with the positive pole, and the upper with the negative, and the same operations be repeated, the leaves will diverge to the same extent as before, but with positive elec- tricity. With his condensing electroscope Volta showed that if strips of zinc and -796] Quadrant Electrometer 797 copper be soldered together, they become oppositely electrified. The zinc was held in the hand, and the lower plate touched with the copper, while the upper plate was touched with the finger. On removal of strip and upper plate, the leaves diverged with negative electricity (813). Fig. 776 Fig. 777 796. Quadrant electrometer. — Lord Kelvin devised a very sensitive electrometer by which accurate measurements of potential may be made. One form of this instrument, represented in fig. 778, consists of two pairs of quadrants, AA' BB', of thin sheet metal, which together form a flat cylin- drical box, cut into four quadrants by diametral sections at right angles to each other. Each of these quadrants is suspended to the top of the case by a glass stem, and the alternate pairs are connected with each other by wires. Each of the pairs is also connected with an insulated binding- screw, so that connection can be made with bodies on the outside. In the middle of the quadrant is hung, by a bifilar suspension, what is called the needle, which consists of a thin sheet of aluminium shaped as shown in fig. 779 ; for the sake of lightness, parts of the needle, indicated by the dotted lines in the figure, are cut out. If all the quadrants are in the same electric condition, the adjustment is made so that the two fibres of the suspension are in the same plane which is symmetrical with reference to the space between the quadrants. If now the two pairs of quadrants are at different potentials, as when, for instance, they are connected with the two poles of a voltaic cell by means of the binding screws, and if the needle is charged to a given potential, which is usually positive and much higher than that of either pair of quadrants. 798 Frictional Electricity [796- one end of the needle will be repelled by the pair of quadrants which are electrified like itself and will be attracted by the other pair. It will thus be subject to the action of a couple tending to set it obliquely to the slit. In order to render the slightest motion of the needle visible, a small silver concave mirror with a radius of about a metre is connected with it. The light of a petroleum lamp, not represented in the figure, strikes against this, and is reflected as a spot on a horizontal scale. Any deflection of the needle, either on one side or the other, is indicated by the motion of the sjjot of light on the scale (532). In order that the potential of the needle may be kept as constant as possible, a platinum wire attached to the needle dips into a glass vessel containing strong sulphuric Fig. 778 Fig. 779 acid, and coated externally with tinfoil. The sulphuric acid keeps the electrometer dry, and acts as the inner coating of a Leyden jar, the tinfoil outer coating being uninsulated. When the jar is charged the needle will have the same potential as the sulphuric acid, and the leakage will be slow. The more complete forms of instrument are provided with a replenisher (774), whereby the potential of the jar and needle can be brought to any required value, and also a subsidiary electrometer (the gauge) which shows when the right value is attained. If A and B represent the potentials of the quadrants, and C the potential of the needle, it may be proved that d=k{h.- B)(C — V where d is the deflection of the needle, and k a constant depending on the instrument. The Leyden jar of the electrometer is generally charged by two or three sparks from an electrophorus, and is thus raised to a potential of some hundreds (or even thousands) of volts. If, in comparison with C, A and B are small, we may neglect (A + B)/2 in comparison with C, and the formula -797] Thomson's Absolute Electrometer 799 becomes <3?=/i'(A— B)C. Hence, if C can be kept constant by a replenisher, the deflection of the needle is directly proportional to the difference of poten- tial between the quadrants. 797. Thomson's absolute electrometer. — Another class of electrometers, also invented by Lord Kelvin, give a direct measure of electric constants in absolute jneasure. Fig. 780 represents a modified form of the electrometer for class experiments. Two plane metal discs A and B, about 10 cm. in diameter, are kept at a distance from each other, which is small in proportion to their diameters, but which can be very accurately measured. Out of the centre of the upper one is cut a disc c ; this is suspended by insulating threads from one end of the arm a 6 of a. balance, at the other end of which is a counterpoise, or a scalepan^. .\t the end of the arm is a fork, across which is stretched a fine wire ; when the disc is exactly in the plane of the circular band or ring which surrounds it, which is called the guard ring, this fine wire is exactly across the interval between two marks in the upright, and its position can be accurately determined by means of the lens C. The disc and the guai-d ring are in contact with each other by means of a bridge of very fine wire (not shown in the figure), and are kept at a constant poten- tial, being connected by a wire with a constant source of electricity, while the plate B can be kept at any poten- tial or put to earth. Suppose now that the whole system is at the same potential, and that the disc is exactly balanced so as to be in the plane of the guard ring. If now A is electrified to a given potential, while the plate B is connected with the earth, c will be attracted towards B ; and in order to retain it exactly in the plane of the guard ring the force applied at the other end of the lever must be increased. This may be done by altering the distance of the counterpoise, or by adding weights to a scalepan, and the additional weight thus applied is a measure of the attractive force. By reason of the guard ring the electric field between c and B will be uniform, the lines of force being straight, uniformly spaced, and perpen- dicular to the plates. If ' heating one of the junctions of a metallic circuit, consisting of two metals soldered together, an electric current was produced. This phenomenon may be shown by means of the apparatus represented in fig. 855, which consists of a plate of copper, mn, the ends of which are bent and soldered to a plate of bismuth, op. Inside the circuit is a magnetic needle, a, moving on a pivot. When the apparatus is ' placed in the magnetic meridian, and one of the solderings gently heated, as shown in the figure, the needle is deflected in a manner which indicates the passage of a current from n to m — that is, from the heated to the cool junction in the copper. If, instead of heating the junction n, it is cooled by ice, or by placing upon it cotton-wool moistened with ether, the other junction remaining at the ordinary temperature, a current is produced, but in the opposite direction— that is to say, from m to n ; in both cases the current is in general stronger in proportion as the difference in temperature of the solderings is greater. Seebeck gave the name thermo-electric to this current, and to the couple which produces it, to distinguish it from the ordinary voltaic current and couple. 869. Thermo-electric series. — If small bars of two different metals are soldered together at one end while the free ends are connected with the wires of a galvanometer, and if the point of junction of the two metals is heated, a current is produced, the direction of which is indicated by the deflection of the needle of the galvanometer. Moreover, the strength of the current, calculated from the deflection of the galvanometer, is proportional to the electromotive force of the thenno-coitple. By experimenting in this way with different metals, we may form them into a list such that the current passes from any one to another lower in the list through the hot junction. The E.M.F. in a circuit of two metals depends upon the difference of -870] Thermo-electric Inversion 877 temperature of the junctions and upon the nature of the substances employed ; it also depends upon the 7nean temperature of the junctions. If the mean temperature of the junctions of two metals is t° and one junction is half a degree above, the other half a degree below t°, so that the difference of temperature is one degree, the electromotive force in the circuit is called the thermo-electric power of the two metals at t°. If P denotes the thermo-electric power of two metals at the mean tem- perature t°, and 7- is the difference of temperature between their junctions, the E.M.F. acting on the circuit is Pt. Thermo-electric power is thus the rate of change of the thermo-electro- motive force with temperature. The following table gives approximately the thermo-electric powers for certain metals at the mean temperature 20° C. They are expressed in micro-volts (848) per degree, and are referred to that of lead as zero. Bismuth • +97 Copper -I Cobalt . 22 Silver . -2-5 Nickel . 22 Iron -14 German Silver 12 Antimony -25 Lead . Tellurium -500 Tin . . . — I Selenium -800 Thus with whatever metal in the above list bismuth is associated to form a thermo-couple, the current will always pass from it to the other metal through the warmer junction. With a bismuth-antimony couple at a mean temperature of 20°, the E.M.F. per degree is 97 — (-25)= 122 micro volts. It will be observed how great is the thermo-electric power of the highly crystalline metals. Alloys are not always intermediate to the metals of which they are composed, and therefore the position of the metals is greatly affected by slight admixtures. The thermo-electric behaviour of substances is greatly affected by hardness, direction of crystallisation, and so forth, and to this are no doubt due many of the discrepancies in the lists given by different observers. Of all the bodies mentioned in the above series, bismuth and selenium produce the greatest electromotive force ; but from the expense of this latter element, and on account of its low conducting power and the difficulty of making good joints, antimony is generally substituted. When rods, AB, A'B', of two metals have their ends A, A', joined together, the other ends B, B', being connected by copper wires to the terminals of a galvanometer, and the junction A A' is heated to, and main- tained at, a definite temperature, the deflection of the galvanometer needle will be constant, so long as the points B, B', and the rest of the circuit are at the same temperature, which may be higher or lower than that of the junction A A'. Further, the electromotive force is the same whether A and A' are merely in contact, or are soldered together, or joined by any other metal, provided all parts of the junction are at the same temperature. 870. Thermo-electric inversion. — For small differences the E.M.F. of a thermo-electric pair is proportional to the difference of temperature of the junctions, but for greater ranges this rule no longer holds, even though the mean temperature is kept constant. In some cases the E.M.F. increases 878 Dynamical Electricity [870- more rapidly than the temperature-difference ; in others the rate of increase with rising temperature of the hot junction diminishes, until at a certain temperature it becomes zero and changes sign. Let one junction of a copper- iron couple be kept at 0° while the other is gradually heated ; the E.M.F. increases until the temperature reaches 276°, and then diminishes, becoming zero when the temperature is 552°. If one junction is as much above 276° as the other is below it, there will be no E.M.F., and no current, in the circuit. This temperature is called the neutral te7nperature. When the mean temperature of the circuit is the neutral temperature there will be no E.M.F., however great may be the difference of temperature between the hot and cold junctions. If the temperature in the above case is pushed beyond 552°, a negative E.M.F. is developed, increasing with temperature. This phenomenon is known as thermo-electric inversion, and is easily exhibited by twisting together the ends of copper and iron wires, and connecting the free ends to a low-resistance reflecting galvanometer. If the junction is gradually heated in a spirit flame, the spot of light will be seen to adv3.nce, first quickly, then more slowly, reach a limiting position, return, pass the zero, and proceed in the opposite direction. 871. Causes of thermo-electric currents. — Thermo-electric currents are probably to be attributed to an electromotive force produced by the contact of heterogeneous substances, a force which varies with the temperature. When all the parts of a circuit are homogeneous, no current is produced on heating, because the heat is equally propagated in all directions. This is the case if the terminals of the galvanometer are connected by a simple copper wire. But if we destroy the uni- formity of this wire by coiling it in a spiral, or by knotting it (fig. 856), the needle indicates by its deflection a current going from the heated part to that in which the homogeneity has been destroyed by the twisting produced ; this is not seen with platinum wire. If the ends of the galvanometer wires are coiled in a spiral, and one end is heated and touched with ^'S- ^56 the other, the current goes from the heated to the cooled end. If one part of a piece of brass wire, whose ends are connected to a galvano- meter, is annealed, and the junction between annealed and unannealed is heated, a current is produced flowing from unannealed to annealed through the hot junction. Svanberg found that the thermo-electromotive force is influenced by the crystallisation ; for instance, if the cleavage of bismuth is parallel to the face of contact, it is greater than if both are at right angles, and the reverse is the case with antimony. Thermo-electric couples may be con- structed of either two pieces of bismuth or two pieces of antimony, if in the one the principal cleavage is parallel to the place of contact, and in the other is at right angles. Hence the position of metals in thermo-electric series is influenced by their crystalline structure. Many crystallised minerals have great electromotive force when heated -873] NoMli's Thermo-electric Pile 879 with metals or with each other. Thus the combination copper pyrites- copper, when heated in a spirit lamp, has an electromotive force of 0-12, and copper pyrites-iron pyrites of o-i8 of a volt. 872. Thermo-electric battery. — From what has been said it will be understood that a thermo-electric couple consists of two metals soldered together, the two ends of which can be joined by a conductor. Fig. 857 represents a bismuth- copper couple ; fig. 858 represents a series of couples used by Pouillet. The former consists of a bar of bismuth bent twice at right angles, at the ends of which are soldered two copper strips, c, d, which terminate in two binding screws fixed on some insulating material. When several of these couples are joined so that the second copper of the first is soldered to the bismuth of the second, then the second copper of this to the bismuth of the third, and so on, this arrangement constitutes a thermo-electric battery, which is worked by keeping the odd solderings, for instance, in ice, and the even ones in water heated to 100°. The electromotive force of each couple under these conditions is about •01 volt. Fig. 857 Fig. 858 873. Nobili's thermo-electric pile. — Nobili devised a form of thermo- electric battery, or pile, as it is usually termed, in which there are a large number of couples in a very small space. For this purpose he joined the couples of bismuth and antimony in such a manner that, after|having formed a series of five couples, as represented in fig. 860, the bismuth from b was soldered to the antimony of a second series arranged similarly ; the last bismuth of this to the antimony of a third, and so on for four vertical series containing together 20 couples, commencing by antimony, finishing] by bismuth. 88o Dynamical Electricity [873- Thus arranged, the couples are insulated from one another by means of small paper bands covered with varnish, and are then enclosed in a copper frame, P (fig. 859), so that only the solderings appear at the two ends of the pile. Two small copper binding screws, m and ;/, insulated in an ivory ring, communicate in the interior, one with the first antimony, representing the positive pole, and the other with the last bismuth, repre- senting the negative pole. Covers, not shown in the figure, fit on the ends Fig. S59 Fig. 860 Qf the frame to protect the faces of the pile from accidental changes of temperature. The E.M.F. of a single bismuth-antimony pair for 1° difference of tempe- rature is about 122 micro- volts, and for a pile of 20 pairs 2,440 micro- volts. If the terminals were connected to a moderately sensitive galvanometer — of, say, 5 ohms resistance, and having a reduction factor of -5 micro-ampere per division (841) — the deflection would be 1,000 divisions, so that a deflection of I division would correspond to a difference of temperature of -001° C. be- tween opposite faces of the thermo-pile. The most sensitive arrangement of this class is the radiomicrometcr invented by Mr. Boys. It consists of a light thermo-junction suspended by a thin quartz thread (89) between the poles of a strong horseshoe magnet ; it resembles in fact D'Arsonval's galvanometer (fig. 897). With the slightest difference in the temperature of the two ends of the bars of the thermo-pair a current is produced in its circuit, and this being in a magnetic field is deflected like any current under the influence of a field. And as the force tending to deflect it depends upon the product of the current into the strength of the field, it follows that with a strong field only an extremely feeble current is necessary to produce a considerable deflection. By its means Mr. Boys can detect differences of less than one-millionth of a degree Centigrade. It will clearly respond to a quantity of heat not greater than that which would be received on a halfpenny by the flame of a candle at a chstance of 1,530 feet. 874. Clamond's thermo-electric battery. — Of the attempts which have been made to apply thermo-electric currents to directly practical purposes, perhaps the most successful has been Clamond's, which has been used for telegraphic purposes and also for electroplating. Its characteristic features are the construction and arrangement of the elements, and the manner in which the heating is effected. The negative element of the couple consists Fig. 861 Fig. 862 of an alloy of two parts of antimony and one of zinc, forming a flat spindle-shaped bar from 2 to 3 inches in length by f inch in thickness (fig. 862). The positive metal is a thin strip or lug of tin-plate, stamped as represented at a a' in fig. 861 ; this is then bent in as shown at c, and being held in a mould, the alloy, which ..lo -874] Clamond's Thermo-electric Battery melts at 260" C, is poured in. The individual elements have then' the appearance represented in fig. 862, and to connect them together the tin lugs are bent into shape, and joined in a circle of elements (fig. 863), being kept in their position by a paste of asbestos and soluble glass ; flat rings of this composition are also made, and are placed between each series of rings piled over each other ; the connection between the individual elements and between the sets of rings is made by soldering' together the projecting ends of the tin lugs. Thin plates of mica are placed between the alloy and the tin-plate, excepting at the place of soldering. Looked at from the inside, the faces of the battery present the appearance of a perfect cylinder. The heating" is effected by means of coal gas, admitted through an earthenware tube, A B, fig. 864, perforated by numerous small holes : this is surrounded by a somewhat larger iron tube, C D, reaching nearly to the top of the cylinder, which is closed by a lid, E F. Air enters at the bottom Fig. S63 Fig. 864 of this tube, and the heated gases, passing up the tube, curl over the top, descend on the outside, and escape by a chimney, G H. This arrangement economises gas and prevents danger from overheating, as the gas-jets do not impinge directly on the metallic junctions. The supply of gas is regulated by an automatic arrangement, so that the temperature is not higher than about 200°. Although sometimes convenient, thermo-electric batteries are by no means an economical source of electricity. Thus a Clamond's battery of 130 ele- ments has an E.M.F. of 8 volts, and a resistance of 3-2 ohms ; its maximum available work can be shown to be 5 watts per second ; and the consump- tion of gas per hour is 180 litres. The heat of combustion of a litre of gas gives 5,200 gramme calories ; the heat expended per second is, therefore, 260 calories, which would correspond to 1,084 watts. The yield is there- fore only about ijj^ of the heat supplied. 3 '■ 882 Dynamical Electricity [874^ . Taking the ordinary price of gas in large towns, the cost of producing a horse-power by a thermo-electric battery would be nearly three shillings an hour for gas alone. 875. Becquerel's electric pyrometer. — This apparatus consists (fig. 865) of two wires, one of platinum and the other of palladium, each two metres in length and a sq. mm. in section. They ai-e not soldered at the ends, but firmly tied for a distance of a centimetre with fine platinum wire. The palladium wire is enclosed in a thin porcelain tube ; the platinum wire is on the outside, and the whole is enclosed in a larger porcelain tube, P. At the end of this F!g. 865 is the junction, which is adjusted in the place the temperature of which is to be investigated. At the other end project the platinum and palladium wires m and n, which are soldered to two copper wires that lead the current to a galvanometer, G. These wires at the junction are placed in a glass tube immersed in ice, so that, being both at the same temperature, they give rise to no thermo-electromotive force. The galvanometer, which was devised by Weber, consists of a magnetised bar, ab, placed within a copper frame, which damps the oscillations (963) and rests on a stirrup, H, which in turn is suspended Irom a long and very fine -877] Thermo-electric Diagram 883 platinum wire. On the stirrup is fixed a mirror, M, which moves with the magnet, and gives by reflection the image of divisions traced on a horizontal scale, E, at a distance. These divisions are observed by a telescope. With this view, before the current passes the image of the zero of the scale is made to coincide with the micrometer wire of the telescope ; then the slightest deflection of the mirror gives the image of another division, and therefore the angular deflection of the bar magnet. This angle is always small, and should not exceed 3 or 4 degrees : a result which is secured by placing, if necessary, a rheostat or a resistance coil in the circuit. The angular deflec- tion being known, the intensity of the current and the temperature of the junction are deduced from pyrometric tables. These are constructed by interpolation when the strengths are known which correspond to two tempe- ratures near those to be observed. The indications of the pyrometer extend to the fusing point of palladium. Lechatellier has greatly improved this method by using a couple of platinum associated with an alloy of platinum with 10 per cent, of rhodium, both in the form of wires. These are connected with a D'Arsonval's dead- beat galvanometer (897). The couple is placed in various metals and salts at their melting points, the temperatures of which are known, and from the observed deflections a scale is empirically gradu- ated. In this way temperatures up to 1,200° C. may be determined which are accurate to within 10°. The principle of the arrangement known as Bec- querel's thermo-electric needle is adapted for tempera- tures below the boiling point of water. Two identical couples are joined in series in opposition to each other. The junction A being placed at the point whose tem- perature is to be determined, the junction B is placed in a bath, the temperature of which can be varied until there is no deflection of the galvanometer. The temperature of the two junctions is then the same. - -876.- Properties and uses ..of thermo-electric currents.— ^Thermo-electric currents are of extremely low potential, but of great constancy ; for the oppo- site junctions of thermo-electric couples can easily be kept at 0° and 100° C. by means of melting ice and boiling water. On this account. Ohm used them in the experimental establishment of his law. They can produce all the actions of the ordinary batteiy in kind, though in less degree. By means of a thermo-electric pile consisting of 769 elements of iron and German silver, the ends of which differed in temperature by about 10° to 15°, Kohlrausch proved the presence of free positive and negative electricity at the two ends of the open pile respectively. He found that the E.M.F. was nearly proportional to the number of elements, and also that the electromotive force of a single couple under the above circumstances was about ^-i^-s that of a single Daniell's cell. On account of their low potential, thermo- electric piles produce only feeble chemical actions. Botto, however, with 1-20 platinum and iron wires, decomposed water. 877. Thermo-electric diagram. — Thermo-electric relations may be very conveniently illustrated by means of what is called the thermo-electric 3 L2 884 Dynamical Electricity [877- diagram. In fig. 867 the abscissse represent the temperatures of the junctions on the Centigrade scale, and ordinates represent thermo-electric powers in terms of micro-volts per degree Centigrade. Lead, for a reason to be presently explained (879), is taken as the metal of reference. The different metals are represented by straight lines and the significance of the diagram may be illustrated by taking an example. At 50° the ordinate of the iron curve is — 13, which means that if we make a circuit of the two metals iron and lead, and if one junction be at 49^° and the other at 5oJ°, so that the temperature difference is 1° and the mean temperature 50°, the E.M.F. in the circuit will be 13 micro-volts, and the current will flow from lead to copper through the warmer junction. If, instead of iron, we take copper at the same temperature, the E.M.F. is i micro-volt ; and if the metals employed are iron and copper. Fig. 867 the diagram tells us that at 50° the E.M.F. per degree \% y y' = 13 — i = 12 micro-volts, that is, it is the area of a narrow strip 1° wide as\A.y y' in length. If one junction is at o and the other at 100° the mean temperature is still 50°, and the E.M.F. = 12 x 100= the area o, jr, x-^, —15 ; this area increases, but at a diminishing rate, as the temperature of the hot junction is raised above 100°, the other junction still kept at o, and reaches its maximum value when it is equal to the triangle o, «, —15. The neutral temperature (276° C.) has now been attained, and on further heating, say to 400°, it will be necessary to subtract the area n, y, y' from the triangle o,n, — 1 5, in order to get the area representing the electromotive force. It is clear that if the temperature is raised to 552° ( = twice 276°) the E.M.F. vanishes, and beyond this temperature is reversed in sign. 878. Peltier's experiment. — When on a bar of bismuth, BB', cut halfway -878] Peltier's Experiment 885 B B Fig. 868 through at its centre (fig. 868), is soldered a bar of antimony with a similar cut, and when the ends A and B are connected with a galvanometer, the needle of the galvanometer is deflected in one direction when the junction is heated, and in the other when it i§ cooled.^ Peltier found by means of this apparatus, which is known as Peltier's cross, that when the end A' was connected with one pole, and B' with the other pole of a voltaic element, so that a current passed from A' through the junction to B', the needle was deflected in such a direction as to show that the junction was heated when the cell current passed from A' to B', while it was cooled when the current passed in the opposite direction. This is called the Peltier effect. In order to show the cooling effect, this experiment may be made by hermetically fixing, in two tubulures in an air thermometer, a compound bar consisting of bismuth and antimony soldered together in such a manner that the ends project on each side. The projecting parts are provided with binding screws, so as to allow a current to be passed through. When the current passes from the antimony to the bismuth, the air in the bulb is heated, it expands, and the liquid in the stem sinks ; but if it passes in the opposite direc- tion the air is cooled, it contracts, and the liquid rises in the stem. The current must not be too strong ; that of a single Bunsen's cell is usually sufficient ; it is best regulated by a rheostat (857). By making a small hole at the junction of a bismuth and antimony bar, in whidi were placed a drop of water and a small thermometer, the whole being Cooled to zero, Lenz found that when a current was passed from bismuth to antimony the water was frozen and the thermometer sank to — 3'5° C. The Peltier experiment may also be illustrated by interposing an iron wire between two copper wires, and surrounding the first with water at o"^,- and the second with ice at 0°. On passing a feeble current, it is found that as much ice melts at one junction as is produced at the other. The Peltier efiect is independent of the heating effect which is produced when a current traverses any conductor, and which may be called the/rictional heating or Joule effect. The heat due to this cause is proportional to the square of the current, C, to the re- sistance, R, and to the time, t, and is independent of the direction of the current (860) ; while the Peltier effect M^ is proportional to the strength of the current and to the time, and is rever- sible with its direction. This suggests a method of determining the effect in question. It is equal to ^C^, where ^ is a constant which is called the coefficient of the Peltier effect. The frictional heat is equal to C^R/. Hence, if the current is passed so that in one case the Peltier effect coincides with the Joule effect, while in the other it is opposed to that effect, we shall have for the total heat H and H' in the Fig. 869 886 Dynamical Electricity [878— two cases : measured in dynamical units H = C^R^ + ^C^, and H' = CR^— ^C^, from which c H-H' ^Ct That the Peltier effect is independent of the Joule heating has been established by Edlund, by a method the principle of which is represented in fig. 869. M and N are two bulbs, and are connected by a narrow glass tube, in which is a drop of liquid serving as index. The rods of metal A and B are fixed airtight in the bulbs, and are soldered at in and n, while the free ends can be connected with a battery. If the pieces m and n inside the glass vessels offer the same resistance, and these vessels are of the same size, when the current passes the Joule effect is the same in each case, and consequently the index is equally pressed in opposite directions, and there- fore does not move. But the Peltier effect is opposite in the two vessels, and produces a displacement of the index, from which the change of tem- perature can be deduced. The Peltier effect, as will be seen, is greater as the term 2C/', or the strength of the current, is less, and hence it can only be shown with feeble currents. These experiments form an interesting illustration of the principle, that whenever the effects of heat are reversed heat is produced ; and whenever the effects ordinarily produced by heat are otherwise produced, cold is the result ; for cooling takes place when the current is in the same direction as the thermo-current which would be produced by heating the junctions, and heating when the current is in the opppsite direction. 879. Thomson effect. — If we take two bars of the same metal A B and A' B', which are connected at the ends B B' by a wire, so that a current can be passed through them, N^ then the temperature of each part of the bars due to the Joule effect would be the same when the stationary condition is attained. If the ^ I I / B '•^° ends B B' are kept at a ^'^^- H^^ii^^l*IMllilll»|illll nninr ~ ^li 1 11 ^l constant temperature of 100° by being immersed in boiling water, while the others A A' are placed in melting ice, and are thus at 0° and if now a thermopile is placed with its two opposite faces in contact with symmetrical portions of the two bars, it will be found that when a current passes through the system at ABB' A', the galvanometer of the thermopile is deflected, showing that there is a difference of temperature at the two ends of the pile— that is, the corre- sponding parts of the bars are not at the same temperature. In the case of copper, silver, zinc, and antimony the point would be hotter on that bar along which the current passes from hot to cold ; in the case of tin, aluminium. -879] Thomson Effect 887 platinum, bismuth, and iron it is hotter when the current passes from cold to hot. This phenomenon, which is known as the Thomson effect from its dis- coverer, Lord Kelvin, is most marked in antimony among positive metals and in iron ; it is a sort of electric convection of heat ; in copper the current carries heat along with it. In iron heat apparently travels against the current. Cold copper behaves towards hot copper in the same way as bismuth behaves towards antimony, so that when a current is passed from the hot to the cold end of a bar of copper there is an evolution of heat at all points along the bar. In a bar of iron under similar conditions there is an absorption of heat. In the case of those metals whose lines slope downwards in the thermo- electric diagram (fig. 867), such as copper, zinc, etc., heat travels with the electricity when the current passes from the hotter to the colder portion of an unequally heated bar. In the case of those metals whose curves slope upwards, iron, platinum, etc., heat travels in the opposite direction. Le Roux found that lead has no Thomson effect — that is, there is no motion of heat either with or against the current. This is why lead is chosen as the standard in the thermo-electric diagram. Le Roux also showed that the Thomson effect is proportional to the Strength of the current. 888 Dynamical Electricity [880- CHAPTER VI ELECTRODYNAMICS 880. Electrodynamics. — By the term electrodynamics are understood the laws of electricity in a state of motion, or the action of electric currents upon each other and upon magnets, while electrostatics deals with the laws of elec- tricity in a state of rest. The action of one electric current upon another was first investigated by Ampfere, shortly after the discovery of Oersted's celebrated fundamental Fig. 871 experiment (835). All the phenomena, even the most complicated, follow from two simple laws, which are — I. Two currents which are parallel^ and in the same direction, attract one another. II. Two currents parallel, but in contrary directions, repel one another. In order to demonstrate these laws, the circuit which the current traverses must consist of two parts, one fixed and the other movable. This is effected -881] Rogefs Vibrating Spiral 889 Fig 872 by the apparatus (fig. 871), which is .a modified and improved form, of one originally devised by Ampere. It consists of two brass columns, A and D, between which is a shorter one. The column D is provided with a rectangular frame, MN, on which is wound a number of turns of insulated wire (fig. 873), the sensitiveness of the instrument increasing with the number of turns. This frame can be adjusted at any height, and in any position, by means of a universal screw clamp (see figs. 873-876). The short column is hollow, and in its interior slides a brass tube termi- nating in a mercury cup, c, which can be raised or lowered. On the column A is another mercury cup, represented in section at fig. 872 in its natural size. In the bottom is a capillary aperture through which passes the point of a sewing-needle fixed to a small copper ball. This point extends as far as the mercury, and turns freely in the hole. The movable part of the circuit consists of a copper wire proceeding from a small ball, and turning in the direction of the arrows from the cup a to the cup c. The two lower branches are fixed to a thin strip of wood, and the whole system is balanced by two copper balls, sus- pended to the ends. These details being known, the current from a battery of 6 or 8 volts ascending by the column A (fig. 873) to the cup a, traverses the circuit BC, reaches the cup c, descends the central column, and thence passes by a wire, P, to the coil MN, whence it returns to the battery by the wire Q. Now, if, before the current passes, the movable circuit has been arranged in the plane of the coil, with the sides B and M opposite each other, when the current passes, the side B is re- pelled, which demonstrates the second law ; for in the branches B and M the currents, as indicated by the arrows, are proceeding in opposite directions. To demonstrate the first law the experiment is arranged as in fig. 873 — that is, the multiplier is reversed ; the current is then in the same direc- tion both in the multiplier and in the movable part ; and when the latter is removed out of the plane of the multiplier, so long as the current passes it tends to return to it, proving that there is attraction between the two parts. 881. Roget's vibrating spiral. — The attraction of parallel currents may also be shown by an experiment known as that of Rogei's vibrating spiral^ 890 Dynamical Electricity [881- fig. 874. A copper wire about 07 mm. in diameter is coiled in a spiral of about 30 coils of 25 mm. in diameter. At one end it is hung vertically from a binding screw, while the other just dips in a mercury cup. On passing a current of 2 or 3 amperes through ^^ 1. the spiral by means of the mercury ^^^SMB cup and the binding screw, its coils I ; are traversed by parallel currents ; ^R they therefore attract one another, and rise, and thus the contact with the mercury is broken, and a small spark occurs. The current having thus ceased, the coils no longer attract each other, they fall by their own weight, contact with the mercury is re-established, and the series of phenomena is indefinitely reproduced. The experiment is still more striking if an iron rod the thickness of a pencil is intro- duced into the interior, as shown in the figure. The self-induction (967) of the circuit being increased, the sparks are much more vivid and noisy. 882. Laws of angular currents. I. Two rectilinear currents, the directions of which form an angle with each other, attract one another when both approach or recede from the apex of the angle. II. They repel one another if one approaches and the other recedes from the apex of the angle. These two laws may be demonstrated by means of the apparatus above described, replacing the movable circuit by the circuit BC (fig. 875). If then the rectangular frame is placed horizontally, so that its current is in the same direction as in the movable current, on remov- ing the latter it quickly approaches the fixed coil, which verifies the first law. To prove the second law, the coil is turned so that the currents are in opposite directions, and then repulsion ensues (fig. 875). Fig. 374 Fig. 875 -884] Action of Infinite Rectilinear Current 891 Fig. 876 Both laws are included in the statement that the two circuits tend to become parallel to each other with their currents in the same direction. 883. Laws of sinuous currents. — The action of a sinuous current is equal to that of a rectilinear current of the same length in projection. This principle is demon- strated by arranging the fixed coil vertically and placing near it a movable circuit of insulated wire half sinuous and half rectilinear (fig. 876). It will be seen that there is neither attraction nor repulsion, showing that the action of the sinuous portion mn is equalled by that of the rectilinear portion. An application of this principle will presently be met with in the appara- tus called solenoids (893), which are formed of the combination of a sinuous with a rectilinear current. 884. Action of an infinite rectilinear current on a rectangular or circular current. — It is easy to see that a horizontal infinite current exer- cises the same directive action on a rectangular current movable about ii vertical axis (fig. 877) as that which has been above stated. For from the direc- tion of the currents indicated by the arrows, the part QY acts by attraction not only on the horizontal portion YD [law of angular currents), but also on the vertical portion AD. This latter statement will be evident if we suppose a line to be drawn perpendicular both to YQ and to AD ; it will be the shortest line between their directions. The part of the current QY which is on the right of this line will attract AD, for both currents are moving in the same direction, and the part on the left will repel AD, for one IS moving towards, and the other from, the shortest line between them. Hence, from both causes, AD will move to the right. The same action evidently takes place between the part PY and the parts CY and BC. Hence, the Jixed current PQ tends to direct the movable rectangular current ABCD into a position Jiarallel to PQ, and such that in the wires CD a?zd PQ the direction of the two currents is the same. This principle is readily demonstrated by placing the circuit ABCD on the apparatus with two supports (fig. 877), so that at first it makes an angle with the plane of the supports. On passing a somewhat powerful ■current below the circuit in the same plane as the supports, the movable part Fig. S77 892 Dynamical Electricity [884— passes into that plane. It is best to use the circuit in fig. 873, which is astatic, while that of fig. 877 is not. What has been said about the rectangular current in fig. 877 applies also to circular currents, and is demonstrated by the same experiments. 885. Motion of currents in a magnetic field. — The phenomena of the attraction and repulsion of currents described in the preceding ai'ticles may also be explained by reference to the magnetic fields produced by the currents. A current through a straight wire is accompanied by a magnetic field, the lines of force in which are circles in planes at right angles to the wire, with their centres in the wire (834). A north magnetic pole placed in such a field tends to move round the current along a line of force and the direction of motion is given by Ampere's i-ule, which states that if we imagine a swimmer in the wire swimming in the direction of the current, and looking at the north pole, the pole will move towards his left hand. In this case the current is supposed to be fixed, and the pole movable, but the action between the two is reciprocal — that is, if the pole is fixed, and the wire carrying the current capable of motion, it will move to the right hand of the swimmer. And generally a movable straight conductor carrying a current in a magnetic field, and capable of moving parallel to itself, will move towards the right hand of the hypothetical swimmer who, swimming with the current, places himself so that the lines of force in the field pass through him from front to back. Applying this rule to the cases- represented in figs. 871, 873, where the lines of force due to the current in M or N are closed curves threading through the frame MN and the swimmer is in the movable conductor B, apparent repulsion of B in fig. 871 and attraction in fig. 873 must occur. The motion of the rectangular coil, ABCD in fig. 877, follows the same rule, for the circular lines of force due to the current QP are coming up towards the swimmer in YC, and his right hand is therefore directed towards the direction of P and away from Q, whatever be the position of the rectangle. The rectangle will be at rest, and in a position of minimum potential energy with regard to the current QP, when it is parallel to the latter, and in these circumstances more lines of force due to QP pass through it than when the rectangle has any other position. Moreover, its own lines of force due to the current flowing through it (835) are in the same direction as those proceeding from QP, so that in its position of rest it has the maximum number of lines of force passing through it. This is in conformity with a principle of universal application,, which may be stated thus : — When a circuit in a magnetic field is traversed by a current, it will alter its position and configuration so as to enclose the greatest possible number of lines of force. The principle is illustrated in the following experiment : — If the ends of two copper wires connected to the terminals of a battery are joined by a loop of a flexible conductor, such as the thin tinsel used in embroidery, the loop will probably hang down in such a way as to enclose a very small area ; but, if a current passes through the circuit, the loop swells out so as to present a larger area and to increase the number of lines of force through it. If the material were perfectly flexible, it would take a circular form. In order to use a fairly strong current in this experiment, and at the same time to avoid the risk of fusion, it is better to immerse the fine wire in water^ -887] Rotation of Magnets by Currents 893 •which will carry off the heat by convection as fast as it is produced, and is practically a non-conductor of electricity. 886. Rotation of a vertical current by a horizontal circular current. — A horizontal circular current, acting on a rectilinear vertical, also imparts to it a continuous rotatory motion. In order to show this, the apparatus represented in fig. 878 is used. It consists of a brass vessel, round which are coiled several turns of in- sulated copper wire, through which a current passes. In the centre of the vessel is a brass support, a, terminated by a small cup containing mercury. In this dips a pivot supporting a copper wire, b,b, bent at its ends in two ver- tical branches, which are soldered to a very light copper ring immersed in acidulated water contained in the vessel. A current entering through the wire VI passes through the coil A, and, terminates at B, which is connected by a wire underneath with the lower part of the column a. Ascending in this column, it passes by the wires b,b into the copper ring, and through the acidulated water to the sides of the vessel, whence it returns to the battery by the strip D. The circuit be- ing thus closed, the wire bb and the ring tend to turn in a direction contrary to that of the fixed current. This may be explained by reference to the various attractions and repulsions between the circular currents and those in the wire ; but the result follows at once from the con- sideration that the current in the coil A produces a magnetic field, the lines ■of force in which come upwards through the coil. In the neighbourhood of the centre they are nearly straight, and towards the circumference they curl over and enter the coil underneath. If Ampere's swimmer is placed anywhere on the wire bb and faces the lines, his right hand will indicate the direction of motion, which will be against that of the current in A. 887. Rotation of magfuets by currents. — Faraday proved that currents impart the same rotatory motions to magnets that they do to currents. This maybe shown by means of the apparatus represented in fig. 879. It consists of a large glass vessel, almost filled with mercury. In the centre of this is immersed a magnet, A, about eight inches in length, which projects a little above the surface of the mercury, and is loaded at the bottom with a platinum cylinder. At the top of the magnet is a small cavity containing mercury ; the current ascending the column m passes into this cavity by the rod C. From the magnet it passes by the mercury to a copper ring, G, when it emerges by the column n. When the current flows the magnet begins to rotate round its own axis with a velocity depending on its magnetic power and on the strength of the current. Instead of making the magnet rotate on its axis, it may be caused to Fig. 878 894 Dynamical Electricity [887- rotate round a line parallel to its axis by arranging the experiment as shown (fig. 880). This rotatory motion is readily intelligible on Ampere's theory of mag- netism (894), according to which, a magnet is traversed on its surface by an infinity of circular currents in the same direction, in planes perpen- dicular to the axis of the magnet. At the moment at which the current passes from the magnet into the mercury, it di- vides on the surface of the mercury into an infinity of rec- tilinear currents proceeding from the axis of the magnet to the circumference of I the glass. Figs. 881 and 882> which corre- spond respec- tively to figs. 879 and 880,. give on a larger scale, and on a horizontal plane passing through the surface of the mercury, the direction of the currents to which the rotation is due. In fig. 879, the north pole being at the top, the Amperian currents pass round the magnet in the reverse direction to that of the hands of a watch, as indi- cated by the arrow z (fig- 881), while the currents which radiate from the rod C towards the metal ring GG' have the direction CD, CE, etc. Thus (881) any given element e of the magnetic current of the bar A is attracted by the current CE and repelled by the current CD ; hence results a rotation of the bar about its axis in the same direction as the hands of a watch. In fig. 882 the currents CD, CF, being in the oppo- site direction to those of the bar, would repel the latter, which would be attracted by the currents CE, CH. Hence the bar rotates in a circular direction, shown by Fig. 879 Fig. 880 Fig. 882 the arrow j, about the vertical axis which passes through the rod C. If the north pole is below, or if the direction of the current is altered, the rotation of the magnet is in the opposite direction. These motions may also be explained by applying Ampere's rule to the -888] Directive Actions of Magnets on Currents 895 lines of force due to the magnet. In fig. 881 the current enters the magnet at C, the middle of its north end. Lines of force emerge from all parts of the end, so that a swimmer in the current which enters at C will be looking at a north pole in whatever direction he faces, and the point to which he looks must move towards his left hand. Hence the magnet rotates in the direction stated. The reader will have no difficulty in explaining in a similar way the motion of the magnet in the second case, fig. 882. 888. Directive actions of magnets on currents. — Not only do currents act upon magnets, but magnets also act upon currents. In Oersted's funda- mental experiment (fig. 871), the magnet being movable while the current is fixed, the former is directed and tends to set at right angles to the current. If, on the contrary, the magnet is fixed and the current movable, the latter is directed and sets across the direction of the magnet. This may be illus- trated by the apparatus represented in fig. 883. This is the original form Fig. 884 of Ampere's stand, and is frequently used in experimental demonstration. It needs no explanation. The circuit which the current traverses is movable, and below its lower branch a powerful bar magnet is placed ; the circuit immediately begins to turn, and stops after some oscillations in a plane perpendicular to the axis of the magnet. It is then in a position in which the lower rectangle contains as many as possible of the lines due to the magnet. The current in the upper rectangle of the movable frame is opposite to that in the lower, and thus diminishes the action between the magnet and the lower circuit, but, owing to its greater distance, does so to a comparatively small extent. For demonstrating the action of magnets upon currents, De la Rive's floating battery (fig. 884) is well adapted. It consists of plates of zinc and copper which are immersed in dilute sulphuric acid contained in a glass bulb slightly loaded with mercury to keep it upright, and which can float freely on water. With the plates can be connected either circular or 896 Dynamical Electricity [888- rectangular wires, coils, or solenoids ; they are then traversed by a current, and can be subjected to the action either of magnets or of currents. 889. Rotation of currents by magnets. — Not merely can currents be directed by magnets, but they may also be made to rotate, as is seen from the following experiment, devised by Faraday (fig. 885). On a base with levelling screws, and resting on. an ivory support, is a copper rod, BD. It is surrounded in part of its length by a bundle of magnetised wires, AB, and at the top of it is a mer- cury cup. A copper frame, EF, balanced on a steel point, rests in the cup, and the other ends of the circuit, which terminate in steel points, dip in an annular trough full of mercury. The apparatus being thus arranged, a. current of 2 or 3 amperes enters at the bind- ing screw b ; it thence rises in the rod D, descends by the two branches, reaches the mercury by the steel points, whence it passes by the framework, which is of copper, to the battery by the binding screw a. If now the magnetised bundle is raised, the circuit EF rotates in a direction depending on the polarity of A. There is a mechanical force acting on the wire E or F, the direction of which is given by Ampere's rule. It is proportional to the current and to the pole strength of the magnet. In this experiment the magnetised bundle may be replaced by a solenoid (893) or by an electromagnet, in which case the two binding screws in the base of the apparatus on the left give entrance to the current which is to traverse the solenoid or electro- magnet. The motion of a movable current in a magnetic field is also illustrated by Barloit/s wheel, represented in fig. 886. It consists of a light toothed metal wheel which can rotate about a horizontal axis, and is so arranged that one or more teeth dip in a mercury trough. The two branches of a horseshoe magnet are on opposite sides of the trough, and when the poles of a battery are connected with the axis and mercury respectively, the wheel at once rotates. If the current flows from the centre to the circumference of the wheel, and the north pole is in front, the wheel rotates in a direction opposite that of the hands of a watch. Faraday's disc (fig. 887) is similar ; the current arrives and departs by two springs, one B which presses against the axis, and the other A against the cir- cumference of the wheel. H represents the direction of the lines of force of the field. Let H, which represents the direction of the lines of force, denote also the strength of the field. Then the magnetic flux passing through the disc Fig, SSs -891] Directive Action of the Earth on Vertical Currents 897 is n-r^H, r being the radius ; and if C be the current, the torque or moment of the couple tending to make the disc rotate is tt^'^HC. The direction of motion is given by Ampfere's rule. 890. Electrodynamic and electromagnetic rotation of liquids. — The condi- tion of a linear current assumed in the previous experiments is not necessary. This may be illustrated by a simple form of experiment devised by Clerk Maxwell. At the bottom of a small beaker, a copper disc is placed with an insulated tongue bent at right angles, and connected with a similar zinc disc supported about an inch above the copper. Dilute acid is placed so as to cover both discs and some fine sawdust having been added to the liquid, the whole is placed on the pole of an electromagnet. The rotation of the liquid is then, shown by that of the sawdust. 891. Directive action of the earth on vertical currents. — The earth, which exercises a directive action on magnets (726), a,cts also upon currents, giving them in some cases a fixed direction, in others a continuous rotatory motion. The first of these two actions may be thus enunciated : Every vertical V \\ Fig. 8S6 current movable about an axis parallel to itself places itself under the direc- tive action of the earth in a plane through this axis perpendicular to the magnetic meridian, and stops after some oscillations, on the east of its axis of rotation when it is descending, and on the west when it is ascending. This may be demonstrated by means of the apparatus represented in fig. 88g, which consists of two brass vessels of somewhat different diameters. The larger, a, about 13 inches in diameter, has an aperture in the centre, through which passes a brass support, b, insulated from the vessel a, but communicating with the vessel K. This column terminates in a small cup, in which a light wooden rod rests on a pivot. At one end of this rod a fine wire is coiled, each end of which dips in acidulated water, with which the two vessels are respectively filled. The current arriving by the wire m passes to a strip of copper, which is connected underneath the base of the apparatus with the bottom of the column b. Ascending in this column, the current reaches the vessel K • and the acidulated water which it contains ; it ascends from thence in the wire c, redescends by the wire e, and, traversing the acidulated water, it 3 M 898 Dynamical Electricity [891- reaches the sides of the vessel a, and so back to the battery through the wire n. The circuit being thus closed, the wire e moves round the column b^ and stops to the east of it, when it descends, as is the case in the figure. This result follows from the principles explained in article 885. The horizontal component of the earth's magnetic field only is concerned, and the movable circuit bee places itself so as to add its own lines of force to those of the earth. It tends therefore to remain in an east and west plane, with the current as you look at it from the south going round in the same direction as the hands of a watch, that is with the wire e on the east side. If the direction of the current be reversed e will rest on the west side. T Fig. 8SS If the rod with a single wire, in fig, 889, is replaced by one with two wires as in fig. 888, the i"od will not move, for as each wire tends to place itself on the east of the column ff, two equal and contrary effects are produced which counterbalance one another. 892. Action of the earth on currents movable about a vertical axis. — The action of the earth on horizontal currents is not directive, but gives ilicm a continuous rotatory motion. This may be illustrated by means of the apparatus represented in fig. 890, which only differs from that of fig. 88g in having but one vessel containing „_ ^ acidulated water. The current, ascending by the column a, traverses the two wires cc, and de- scends by the wires bb, from which it|regains the battery ; the circuit bccb then begins a continuous rotation anti-clockwise Fig. 890 ox clockwise, according as in the wires cc the current goes from the centre, as is the case in the figure, or goes towards it. -893] Solenoid 899 which is the case when the current enters by the wire m instead of by n. In this case we have to consider the vertical component of the earth's field ; for the two circuits branching from a round; to the acid on each side neutralise each other so far as the horizontal component is concerned (891). To face the vertical lines the swimmer in c must look upwards, and since he moves to his right the rotation is anti-clockwise. When a circle of wire such as is shown in fig. 8gi is supported so as to be movable about a vertical axis and a current passed through it, the circuit places itself in a plane perpendicular to the magnetic meridian with the current descending on the east side, for in this position the magnetic flux through the circuit is greater than in any other. From the directive action which the earth exerts on circuits it is necessary, in many experiments, to neutralise this action. This is effected by arranging the movable circuit symmetrically about its axis of rotation, so that the directive action of the earth tends to turn the two branches in opposite directions. This condition is fulfilled in the circuit in fig. 885. Such circuits are hence called astatic circuits. 893. Solenoid. — A solejioid or electromagnetic cylinder is a system of equal and parallel circular currents formed of the same piece of covered copper wire and coiled in the form of a helix or spiral, as represented in fig. 892. A solenoid, however, is only complete when part of the wire BC passes in the direction of the axis in the interior of the helix. With this arrangement, when the circuit is traversed by a current it follows from what has been said about sinuous currents (883) that the action of a solenoid in a longitudinal direction, AB, is counterbalanced by that of the rectilinear current BC. This action is accordingly null in the direction of the length — that is, there is no magnetic field Fig. 892 m a plane perpendicular to the magnetic axis, all the lines of force lying in planes containing the axis. The system of lines of force due to a circular current are shown in fig. 824. When a current flows through a number of parallel rings forming a solenoid (fig. 893), the direction of the current being the same in each ring, the lines of force due to the successive circles unite to form a system which traverses the interior of the solenoid from end to end, emerge at A, and, curving round in all directions, re-enter the solenoid at B. Thus the solenoid is associated with a system of lines of force precisely like that already described in the case of a bar magnet, and which is delineated in fig. 679. The solenoid shown in fig. 893 is constructed so that it can be suspended on two pivots in the cups a and c, and be freely movable about a vertical axis. When the circuit is complete the solenoid begins to move, and finally sets with its axis in the magnetic meridian and the end A towards the north. When deflected from this position it returns to it after some oscillations. The solenoid, in fact, behaves exactly like a magnet 3M2 900 Dynamical Electricity [893- with a north pole at A, where the lines of force emerge. It is to be observed that in the position of equilibrium the current is descending on the east side of the coil — ^that is, as we look at the end A, which corresponds to the north pole of a magnetic needle, we see that the cur- rent is going round in a direc- tion opposite to that of the hands of a watch. Further, it may be noted that the posi- tion of equilibrium of the solenoid is in agreement with the fundamental principle that a movable coil carrying a current in a magnetic field places itself in such a position that the maximum number of lines of force passes through it. For the earth's horizontal lines run from south to north, and therefore in the position of equilibrium the solenoid is full of the earth's lines. If a current is passed through a wire PQ (fig. 893) stretched north and south under the solenoid, Oersted's experiment (835) may be repeated, the solenoid taking the place of the magnetic needle. If the direction of the current in PQ is from south to north, the north end (A) of the solenoid is deflected to the east, and takes up a new position of equilibrium under the combined action of the magnetic fields due to the earth and to the current in PQ. The result may also be regarded as an illustration of one of Ampere's fundamental laws — namely, that angular currents tend to become parallel and to flow in the same direction. Fig. 893 Fig. 894 The same phenomena of attraction and repulsion exist between solenoids and magnets as between magnets themselves. For if one of the poles of a magnet is presented to a movable solenoid, traversed by a current, attraction or repulsion will take place, according as the poles of the magnet and of the solenoid are of contrary or of the same name. The same phenomenon -895] Terrestrial Current 901 takes place when a solenoid traversed by a current and held in the hand is presented to a movable magnetic needle. When two solenoids traversed by a current are allowed to act on each other, one of them being held in the hand and the other being movable about a vertical axis, as shown in fig. 894, attraction and repulsion will take place just as in the case of two magnets. 894. Ampere's theory of magnetism. — Ampere propounded a theory based on the analogy between solenoids and magnets, by which all magnetic phe- nomena may be referred to electrodynamic principles. Instead of attributing magnetic phenomena to the existence of two fluids Ampfere assumed that each individual molecule of a magnetic substance is traversed by an electric current, which circulates without meeting with resistance and therefore without the expenditure of eYiergy. The molecular currents, which thus remain of constant strength, are free to move about the centres of the molecules. The coercive force, however, which is little or nothing in soft iron, but considerable in steel, opposes this motion, and tends to keep the molecular currents in any position in which they happen to be. When the magnetic substance is not magnetised, these currents, under the influence of their mutual attractions, occupy such positions that their' total action on any external magnetic substance is null. Magnetisation consists in giving to these molecular currents a parallel direction, and the stronger the magnetising force the more perfect the parallelism. The limit of mag- netisation is attained when the currents are completely parallel. The resultant of the actions of all the molecular currents is equivalent to that of a single current which traverses the outside of a magnet. For by inspection of fig. 895, in which the molecular currents are re- presented by a series of small internal circles in the two ends of a cylindrical bar, it will be seen that the adjacent parts of the currents oppose one another and cannot exercise any external electrodynamic action. This is not the case with the surface ; there the molecular currents at ab are not neutralised by other currents, and as the points abc are infinitely near, they form a series of elements in the same direction situated in planes perpendicular to the axis of the magnet, thus constituting a true solenoid. 895. Terrestrial current. — In order to explain terrestrial magnetic effects on this supposition, the existence of electric currents is assumed, which continually circulate round our globe from east to west perpendicular to the magnetic meridian. The resultant of their action is a single current travers- ing the magnetic equator from east to west. They are supposed by some to be thermo-electric currents due to the variations of temperature caused by the successive influence of the sun on the different parts of the globe from east to west. Dynamical Electricity [895- 902 These currents direct magnetic needles ; for a suspended magnetic needle comes to rest when the molecular currents on its under-surface are parallel and in the same direction as the terrestrial currents. As the molecular currents are at right angles to the direction of its length, the needle places its greatest length at right angles to east and west, or north and south. Natural magnetisation is probably imparted in the same way to iron minerals. 8g6. Electrodynamometers. — The principle of the electrodynamometer is that of determining the strength of a current by measuring the attraction or repulsion between parallel branches through which the current flows, one branch being fixed and the other movable. Fig. 896 represents the main features of a form devised by Siemens for this purpose ; w is a coil of stout copper wire, and w' a single wire ; nn are mercury cups, and kk binding screws, by which connection is made with the main circuit LL. The wire w' is surmounted by a spiral spring,^ which is connected at one end with this wire, and at the other with a torsion head, j ; the latter is provided with an index, z, which moves over a graduated scale, S. An index, z' z', is also fixed to the wire w' ; on the right of the lower part of fig. 896 is seen the end of the wire z'z', which projects and moves over the graduated disc, S. At the outset both indexes point to zero ; when the current passes the movable coil tends to place its plane parallel to that of the fixed coil with the currents in the two flowing in the same direction, and the point z' is displaced along the scale. By turning the screw j it is brought back to zero, and the angle through which z is moved is a measure of the torsion of the spiral spring f, and this angle is proportional to the square of the strength of the current traversing the circuit. This electrodynamometer is not intended for the mea- surement of very minute currents ; it has the advantage that its indications are independent of the external mag- netic field, and when the two coils are traversed by the same current they are also independent of the direction of the current, and can accordingly be used with advantage in measuring alternating currents. It will be noticed that the movable coil, w'w', is always in the same position — viz. at right angles to the fixed coil — when a reading is taken, and, therefore, the electro-magnetic torque on the movable circuit, which is proportional to C'-' (since the current C flows both in the fixed and movable coils), is always exactly balanced by the torsion of the spiral spring which is proportional to the angle of torsion, that is C = le'd, or, C = k^6, where /■ is a constant and 6 the angle through which the torsion head has been turned. If a current, whose strength in amperes is known, is passed through the instrument, and 6 is noted, k is determined. An electrodynamometer devised by Giltay on a principle first introduced by Bellati is remarkable for its great sensitiveness. A bundle of fine iron wires hangs by a bifilar suspension inside the coil of a multiplier, the plane Fig. 896 -897] Suspended Coil Galvanometer 903 Fig. 8g7 of which is at an angle of 45° with the magnetic meridian. The bundle itself is at an angle of 45° with the plane of the coils, and is thus at right angles to the magnetic meridian. When alternating currents are passed through the coil they magnetise the wires with alter- nate poles, so that the bundle is always deflected in the same direction. The deflections are read off by a mirror and scale, and when small are directly proportional to the square of the current. The apparatus is so . sensitive that deflections of 18 cm. on the scale, placed at the usual distance from the mirror of the instrument, are produced by the currents of an ordinary telephone. In Lord Kelvin's Ampere Balance the attraction between two parallel coils, through which the current to be measured passes, is weighed. The apparatus consists of a balance beam, pivoted at the centre, in a manner to be presently described, and carrying a flat horizontal coil at each end. Above and below each of these terminal coils is a fixed coil, so that there are altogether six coils, of which four are fixed and two move in the spaces between the fixed coils, and the current to be measured flows through all of them. The wire is so wound that the coil at one end of the beam is repelled by the upper, and attracted by the lower fixed coil, while that at the Other end is attracted by the upper, and repelled by the lower coil. The deflected beam is restored to the horizontal position by means of a sliding weight, and the position of the latter on the beam enables the strength of the Current to be determined. The instrument really measures the square of the strength of the current, since the current flows through both the attracting and attracted coils. The chief difficulty in instruments of this class is to provide means for the current to enter and leave the moving coil or coils. In Siemens' Electro- dynamometer the device of mercury cups is adopted, but this is unsatisfactory in many ways. In the ampere balance the beam is suspended by two sets of fine parallel copper-wires, through which the current enters and leaves the moving system. These copper-wire ligaments are extremely flexible, and leave the beam almost as much freedom as if it were suspended on knife- edges ; and the number of wires in the ligament can be increased, without affecting its flexibility, so as to enable it to carry a strong current. 897. Suspended coil galvanometer. — In the galvanometers already described (841), the coils through which the current passes are fixed, and the needle is movable. A suspended coil galvanometer is one in which a fixed and strong magnetic field is provided by a permanent steel 904 Dynamical Electricity [897- magnet between the poles of which is suspended a coil carrying the current to be measured. The coil when traversed by a current tends to place itself at right angles to the field. To this class belong the galvanometers of Deprez and D'Arson\al represented in fig. 897. Between the branches of a strong horseshoe magnet is a soft iron cylinder, which is supported independently and becomes magnetised by induction. Between this and the magnet is a light rectangular wire coil, supported above and below by wires conveying the current into and out of the moving coil. When the current passes, the coil is deflected and equilibrium is established when the electro-magnetic torque is equalled by the torsion of the wire. The motion of the coil can be read off by a spot of light reflected from a mirror (532) attached to it, and for small angles the current is proportional to the angle of deflection. Induction currents due to the motion of the coil in the field are produced, and as these are powerful when the circuit is closed by a small resistance, the galvanometer IS virtually dead-beat (963). These instruments are practically independent of external magnetic fields, and may therefore be used in the neighbourhood of dynamos. 898. Weston Ammeter. — The principle of this instrument is the same as that of the D' Arsonval galvanometer already described. Fig. 898 shows the instrument with the cover Y (fig. 899) removed, while fig. 900, which is on a larger scale, enables the coil and pole-pieces to be seen. The aluminium frame on which the coil is wound, instead of being suspended by wires, is pivoted top and bottom in jewelled centres, J, and controlled by two hair- springs, S, S, made of non-magnetic material, the springs also serving to lead the current into and out of the moving coil. To the ends of the horse-shoe magnet M, M, curved iron pole-pieces, P, P, are attached, and in the centre of the moving coil is a stationaiy soft iron cylinder I, so that the lines of magnetic force in the region in which the coil moves are nearly radial. A long pointer attached to the coil moves over the scale, X, which is graduated in amperes, or fractions of an ampere. The instrument illustrated is a milli-ammeter, the divisions on the scale being milli-amperes, or thousandths of an ampere. The clearance — that is, the space between the poles P, P, and the core I, in which the coil moves — is very small. This enables the magnetic field to be made strong, and constant in strength. The instrument is dead-beat, and as the moving system is carefully balanced, may be used in any position. 899. Wattmeter. — A wattmeter is an instrument for measuring the power absorbed by any conductor or circuit when an electric current passes through it. If C be the current in the conductor or circuit in amperes, and e the difference of potential between its ends in volts, Ce is the power absorbed, in watts. C and e might be measured separately by an ammeter and voltmeter respectively, and the values multiplied together to gain the watts. A wattmeter gives the product directly. It is essentially an electrodynamometer, in which, however, the fixed and movable coils, instead of being in series with each other, are entirely separate. One of the coils, of low resistance, is in series with the circuit in ques- tion ; the other, of high resistance, is in parallel with the circuit. Since the current in the high-resistance coil is proportional to the difference of poten- -900] Hall's Experiment 90s tial, e, at its ends, and since the torque on the movable Coil, when restored by torsion to its zero position, is proportional to the product of the currents in the two coils, it follows that the angle through which the pointer, attached to the torsion head, has been moved, is proportional to Ce. 900. Hall's experiment. — In the action of magnets on currents which Fig. 399 Fig. 900 From Ayrtoii s ' Practical Electricity ' has been described in the foregoing sections, we have been concerned with the action of the magnet on the body which conveys the current. Professor Hall of Baltimore has made the following experiment to determine whether the path of a current itself in the body of a conductor is or is not deflected when it is exposed to the direct action of a magnetic field. A strip of gold leaf A B, 9 centimetres in length by 2 centimetres broad go6 Dynamical Electricity [900- (fig. 901), is fastened on a glass plate placed between the poles of an electro- magnet in such a manner that the plane of the strip is at right angles to the lines of force of the magnetic field. A difference of potential of from i to 2 volts is established between the ends A and B. Two wires leading to a galvanometer a and b are connected with two equipotential points at the opposite edges of the strip ; that is to say, at two points, found by trial, in which there is no deflection in the galvanometer. Fig. 902 shows the general direction of the lines of flow of the current when the electro- Fig, goi Fig. 902 magnet is not excited, the dotted lines being equipotential lines. When the electromagnet is excited by passing a current through it, a distinct deflection is produced in the galvanometer, showing that the position of the equipoten- tial lines is varied (fig. 903), and that the paths of the current in the conducting strip have been deflected. This deflection is permanent, and cannot there- fore be due to induction, and its direction is reversed when the current in the electromagnet is reversed (fig. 904).' cT- ^ Fig. 903 The magnetic field acts thus upon the current in the gold leaf in such a manner as to displace it towards one edge or the other, and to cause a small portion to pass through the circuit of the galvanometer. The electricity is displaced in the direction of the electromagnetic force, due to the magnet, from «? to b through the galvanometer in the case of iron, zinc, and cobalt, but from b Xo a through the galvanometer, with nickel, gold, and bismuth. Of all metals, bismuth shows the phenomenon in far the highest degree. -901] Electromagnets 907 CHAPTER VII ELECTROMAGNETS. MAGNETISATION OF IRON. TELEGRAPHS goi. Electromagnets. — If insulated copper wire is wound in the form of a spiral on a tube of non-magnetic material, and a current is passed through it, the spiral becomes a magnet. Such an arrangement is commonly called a solenoid, though it does not strictly conform to the conditions for a solenoid laid down in article 893. The coil is said to be right-handed (fig. 905) or left-handed (fig. 906), •mssm'sm PS iw^mi Fig. go5 according as the direction of the successive turns, to an observer looking at one end, is with or against the motion of a clock hand. But whatever the direction of the coiling, the polarity is easily found by the following rule : 7/ a person swimming in the current looks at the axis of the spiral^ the north pole is always on his left. If the wire is not coiled regularly, but if its direction is reversed, at each Fig. 906 change of direction a consequent pole (706) is formed in the magnet. The simplest method of remembering the polarity produced is as follows : What- ever be the nature of the helix, whether right or left handed, if the end facing the observer has the current flowing in the direction of the hands of a watch it is a south pole, and vice versd. The lines of force pass through the interior of the coil in straight lines, emerge at the north pole and, spreading round, enter again at the south pole, each line of force being a continuous curve. If the coil contains an iron core, the latter becomes magnetised, its polarity being the same as that of the coil ; but the lines of force are considerably increased in number. An arrangement of a long length of copper wire wound on a bar or core of soft iron forms what is called an electromagnet. The magnetisation of the iron is only temporary ; when the current ceases the magnetisation ceases also, and the iron reverts almost wholly to its ordinary magnetic but unmagnetised condition. From its property of producing a powerful magnetic field, the coil in 9o8 Dynamical Electricity [901- this experiment constitutes a magnetising coil or spiral ; and the mag- netisation of the iron by its means is an appHcation of the principle of magnetic induction. From the fact that electromagnets are far more powerful than permanent magnets, and, still more, that their magnetisation can be instantaneously evoked and de- stroyed, they have met with a host of applications of the very greatest im- portance ; and the form, dimensions, and strength of such electromagnets vary greatly with the purpose for which they are intended. There are, however, two principal types : t/ar magnets, as in fig. 905, or horseshoe magnets, either in one piece, as shown in fig. 907, or else formed of two straight electromagnets, each joined to a cross-piece of soft iron or yoke, T, as shown in fig. 909. It is better to have the iron in one piece, but the bending of large masses is difficult, and is apt to increase the coercive force, so that the other plan is gener- ally adopted, great care being taken that the surfaces in contact be very accurately fitted to each other. In order that the poles at the two ends may be of opposite kinds, the wire must go round each branch in the same direction as it would do if the core had been bent after the winding had been finished. The windings ought to appear in opposite directions on the two legs to an observer who is looking at the two ends (fig. 908), the current going like the hands of a watch round the south pole, and in the opposite direction round the north pole. Fig. 910 represents a compact form '.*Q\ti S ^z^. Fig. 907 Fig. 90S Fig. 909 of electromagnet devised by Joule, the core and armature of which may be constructed by sawing a piece of wrought-iron tubing lengthwise. There must be space enough to contain the wire necessaiy. The magnetism in solid and in hollow cylinders of the same diameters is —902] Magneto-motive Force 909 the same, provided in the latter case there is sufficient thickness of iron for the development of the magnetisation. With currents below a certain strength, wide tubes of sheet-iron are far more powerfully magnetised than solid rods of the same length and weight ; but with more powerful currents the magne- tism of the latter preponderates. 902. Magnetic force inside a magnetising coil. Magneto-motive Force. — The magnetic force, that is, the force on unit pole, is the same at all points in the interior of a long coil, except near the ends ; and, further, is independent of the diameter of the coil. Its Pig g^, value is 47r«,C|, where «, is the number of turns per centimetre of length of the coil, and C, is the current in absolute measure. If / is the length of the coil, supposed to be wound uniformly, n the total number of turns, n = «,/, and if the current C is measured in amperes, then, since 10 amperes are equal to i absolute unit of Current, the magnetic force, or strength of the magnetic field, inside the coil IS ;— ■ Let this be called H. When there is no iron in the coil this expression gives also the number of lines of force per square centimetre of cross-section ; but if the coil surround an iron core the number of lines is increased to an extent corresponding to the increased permeability (721). If B represents the magnetic induction, and p. the permeability, If a soft iron ring or tore is coiled round with insulated wire through which a current is passed, it is the seat of a very powerful magnetic in- duction, though it has no poles, and therefore no external action. Such a system forms a closed magiutic circuit ; the arrangement represented in fig. 907, where the two poles of an electromagnet are connected by an arma- ture, also forms such a circuit, and an interesting analogy may be made between it and a closed electric circuit. For if N represent the total number of lines passing through the iron whose cross-section is S, N = BS, therefore N = BS = 47[^CS = i^r^C/io ^ M_ 10/ l_ Z an expression analogous to Ohm's formula for currents — viz. C = - M is R called the magnetomotive force, and Z the magnetic resistance or reluctance. The magnetomotive force is the product of current and total number of turns of wire multiplied by a constant ; the reluctance varies directly as the length, and inversely as the cross-section of the iron, and also inversely as u, the permeability of the iron. The reciprocal of \j. is the specific rehiciance of the iron, corresponding to specific resistance in the analogous case. If N 9IO Dynamical Electricity [902— the total number of wires passing through the iron, is called the magnetic flux, the above relation may be written „ . ,, magnetomotive force magnetic iiux = — 5 reluctance Flux-density is a better term for B than magnetic induction. The analogy between electric and magnetic circuits also holds if we consider the magnetic circuit as made up of bodies of different permeabilities ; Z in this case being the sum of expressions like — ?^. For example, in the Weston Ammeter (898) the magnetic circuit consists of the steel magnet M, the pole-pieces PP, the iron cylinder P, and the two air-gaps separating the pole-pieces from the cylinder ; for each of these /, fi, and S must be determined, and as the i"eluctance of air is very great as compared with that of iron or steel, we see the importance of making the air-gap as narrow as possible. The analogy fails, however, in one important respect ; electric resist- ance is quite independent of electromotive force, while permeability differs in value with the value of the magnetomotive force. Hence the analogy is rather formal than real ; it is, however, useful in dealing M'ith calculations about electromagnets. The expression 47r«C shows that we get the same magnetic effect whether we have a small number of turns of wire with a strong current, or a great number of turns with a weak current. Thus, with a given bar the same effect is produced by one turn conveying a current of one ampere a.s by ten turns with a current of one-tenth of an ampere. In the case of electro- magnets the magnetising force is usually defined by the number of ampere- turns used. Taking the permeability of air as unity, that of iron is many hundred times as great ; hence the introduction of a layer of air in a magnetic circuit is analogous to the introduction of a bad conductor in an electric circuit. Iron being the most permeable of all substances, a magnetic circuit should have as much iron as possible. The junctions also should be made close and true, since each joint increases the magnetic reluctance. 903. Ammeters. — -A variety of instruments have been constructed for measuring current, which depend upon the principle that a piece of iron partially or entirely enclosed in a coil through which the current passes strives to place itself in the strongest part of the magnetic field thereby created, the tendency being approximately proportional to the strength of current. A pointer attached to the piece of iron, and moving over a graduated scale, serves to indicate the strength of current. The control, that is, the force opposing the motion of the iron, is supplied either by a spring or a weight. Instruments of the latter class are called gravity ammeters. We proceed to describe one of these, devised by Mr. Evershed. Its working parts are shown in figs. 91 1 and 912. Along the axis of the coil is a staff, S, S, pivoted in jewelled bearings, carrying near one end the pointer, P, P, and controlling weight, W. Rigidly attached to this is the needle A, B, a half-cylinder of thin-sheet soft iron. This is enclosed in a fixed brass cylinder, T, T, seen in fig. 912, but removed from fig. 91 1. Another soft iron -903] Ammeters 911 cylinder or collar, C, D, part of which is cut away, and which, consequently, has the shape shown in fig. gii, fits closely on the outside of the brass tube. Fig. 911 shows the relative positions of the iron needle A,B, and the iron collar C, D, when the index points to zero of the scale, that is, when no current is passing. When a current flows round a coil, the needle is pulled round|magnetically, so as to fill up, to a greater or less extent, the space where the iron has been cut away from the collar C, D, its motion being controlled by the weight W, which is rigidly attached to the axis. The scale is V p Fig. 912 From Ayrion's ' Practical Electricity ' graduated empirically. Ammeters with gravity control must be rigidly fixed, and;are generally secured to a vertical wall. In instruments to be used on board ship a spring control is substituted. An ammeter, devised by Professors Ayrton and Perry, depends on the principle that when a portion of an iron core is partly within and partly without a magnetising coil, it is drawn inwards when a current. is passed through the coil. The magnetic field not being uniform, the iron is urged towards the strongest part of the field. The essential feature of the 912 Dynamical Electricity [903- apparatus is a coil of insulated wire, in the axis of which is a spiral attached at one end to an index moving over a graduated scale. At the other end of the spiral is a brass cap to which is attached a thin cylinder of sheet iron, which is in fact the core ; it encircles the spiral and projects outside the coil. The spiral itself is formed of a ribbon of thin phosphorus bronze coiled so as to form a very narrow cylinder. This construction gives it the property that, unlike ordinary spirals, when its length increases the free end rotates through a considerable distance. Accordingly, when the current passes through the coil, the iron tube is drawn within the spiral to an extent varying with the strength of the current ; this thereby elongates the spiral to which it is attached, and the index attached to the latter moves over the scale, finally taking up a position which depends on the strength of the current. Such instruments are graduated empirically and within 16000 1 — 1 ^_ J _,_ -1 15000 14000 13000 CO 12000 O II 000 is O 10000 D — 9000 O 1- 8000 — ' ^ • — ■^ / ^ / r — / 1 1 1 I ; ~' "^ 6000 p 5000 3 4000 UJ Ul d: 3000 2000 fOOO 1 '■ — - J\ _i_ U 12 5 ^A 5 6 7 a 9 10 II 12 15 1-* 15 16 17 la 13 20 MACNETifivNO Force H Fig. 913 From Slingo and Brooker's ' Electrical Engineering ' any desired range by observing the deflection caused by passing through them currents of known strength. 904. Magnetisation curve. — If we take a given magnetising spiral, at right angles to the magnetic meridian, and place at some distance from it, and in the line of its axis, a small magnetic needle, on passing a current through the spiral the needle is deflected, and this deflection (or, more strictly, its tangent) is a measure of the magnetic moment acquired by the spiral ; if the current is gradually increased the deflection will also be increased, and in proportion to the strength of the current. If, however, the spiral contains a bar of soft iron, the case is not so simple. On plotting the curve which represents the ratio of the magnetising force to the magnetisation, as measured by the deflection of the needle, it will be -904] Magnetisation Curve 913 found that at first the magnetisation is proportional to the magnetising force ; then a stage is reached when the magnetisation increases more rapidly than in direct proportion to the magnetising force, but the rate of increase gradu- ally becomes less, and the magnetisation ultimately approaches a limit which is not materially exceeded, even by a considerable increase in the magnetising force. This represents a state of saturation (698), and it corresponds to the case in which the axes of the molecular magnets are all strictly parallel to the axis of the spiral. The following table gives a number of results obtained for a specimen of soft iron examined by Professor Ewing by the above method, which is known as the magnetometer method. In the first column magnetising forces (H), which are directly proportional to the magnetising current, are given. From the deflection of the magnetometer needle the magnetic moment of the iron can be deduced, and hence the intensity of magnetisation (I), of the iron, since I = magnetic moment ^j^^ ^^j^^^ ^^ j ^^^ ■^_^ j^ ^j^^ second volume column. The third column contains the values of the magnetic susceptibility of the iron, obtained by dividing I by H. The values of B are obtained from the formula B = H + 4!rl, and those of /j by dividing B by H. H I -^i B -i ■32 3 9 40 120 •84 13 15 170 200 1-37 33 24 420 310 2-14 93 43 1,170 550 2-67 295 no 3,710 1,390 i 3-24 581 179 7,300 2,250 3-89 793 204 9,970 2,560 4-50 926 206 11,640 2,590 ^•17 1,009 195 12,680 2,450 6-20 1,086 175 13,640 2,200 7-94 1.155 145 14,510 1,830 979 1,192 122 14,980 1,530 11-57 1,212 105 15,230 1,320 15-06 1,238 82 15,570 1,030 19-76 1,255 64 15,780 800 21-70 1,262 58 15,870 730 This table presents many points of interest, some of which are better seen when the results are plotted in the form of a curve. This has been done in fig. 913, in which abscissas represent magnetising forces (H), and ordinates represent corresponding values of B, the magnetic induction. Near the origin the curve is a straight line, showing that the magnetism produced by a small force is proportional to the force. The change in the magnetising force from 2 to 5 units causes an extremely rapid rise in the resulting magnetisation, but as the magnetising force is further in- creased the curve tends to become parallel to the axis of magnetising force. When this parallelism is attained the iron is saturated with magnetism, and 3N 914 Dynamical Electricity [904- its permeability is unity. The last column in the table shows that the permeability of soft iron increases with the magnetic field and then di- minishes. Its maximum value, 2,590, was reached when the magnetising force was 4-5, and when this was raised to 217 the permeability fell to 730. Ewing and others, applying magnetising forces as high as 20,000 to wrought iron, reduced its permeability to nearly 2. The intensity of the magnetisation which can be imparted to a bar is about 1,700 C.G.S. units in the case of wrought iron, 1,240 with cast iron, and 5 1 5 in the case of nickel. Steel can acquire pretty much the same intensity of magnetisation as wrought iron, and retains about one-half in the form of permanent or residual magnetism. Soft iron almost wholly loses its mag- netisation when the current ceases, and the more so the purer the iron, and the more carefully it is annealed. In many applications it is of great importance that the cessation of the magnetisation with the current should be as complete as possible. Permanent and residual magnetism are in fact the same, but the former expression is used when it is desired to retain the magnetism, and the latter when its presence is objectionable. Residual magnetism is greater in long magnets, that is to say, those in which the diameter is small in comparison with the length. Hence for rapid demagnetisation the cores should be short and thick. A bundle of soft iron wires is more rapidly demagnetised than a massive bar of the same size. Residual magnetism is greater when the magnetising current is not stopped suddenly, as is usually the case, but is gradually brought back to zero by successively introducing increasing resistances. 905. Portative force. — The attraction between a magnet and a soft iron keeper depends only on the area of the surfaces in contact, and on the magnetic induction (or flux-density) B. If S represents the area, and if a weight of M grammes is required to drag the keeper from the magnet, the SB' attractive force = M^ dynes, where ^ = 981 (81), and M^ = t, — . When an armature is not in contact with the poles the attraction di- minishes very rapidly with the distance ; for in the first place the attraction is inversely proportional to the distance, and then the effect of this distance is to introduce a layer of air which from its very great reluctance greatly lessens the induction in the magnetic circuit. According to the researches of Bidwell, it appears that for low degrees of magnetisation the portative force increased less rapidly than the current strength up to a certain point, at which the field was about 240 units and the load supported 14,000 grammes per square centimetre. From this point the magnetising current and the load increased in the same ratio. When the field had an intensity of 585 units, the greatest weight supported was 1 5,900 grammes per sq. cm., or 226 pounds per square inch. 906. Change of length of an iron rod in a magnetic field.— Joule found that under a magnetising force which he considered sufficient to saturate the iron, but which appears to have been less than 100 units, the length of an iron bar was increased by iiif-^-^-a. When the bar with its coil was placed in a sort of water thermometer consisting of a glass flask provided with a capillary tube. Joule found, using the same magnetising force as before, that allowing for the expansion of water due to the heat of the current, there was no motion in the capillary tube ; from this he concluded -907] Magnetic Hysteresis 91S that the vohime of the iron was unaltered by magnetisation, and also that since its length was increased, its diameter must have diminished. In Shelford Bidwell's investigation of these phenomena, a far higher magnetising force was employed (up to nearly 1,500 units), and the results showed that Joule's conclusions required modification. Bidwell found that the length of a rod of soft iron increased as the magnetising force was raised to 80 units and then diminished, regaining its original value when the magnetising force was about 300 units. Beyond this point the iron rod contracted, and continued to do so until the magnetising force was about 1,000 units, after which it remained constant. The maximum elongation varied in different specimens, ranging from to the ^■^S^s-^ part of the length of the rod. The amount of tne J7rxn7-jj7x the retraction under strong force was utAjTriy of ^'^ length. The diameter of the rod is also changed ; with small forces it is diminished, and with large forces increased, but the longitudinal and transverse changes of dimensions are not often related in such a manner as to leave the volume of the bar unaltered. A magnetising force of 80 or 90 units has indeed generally no effect upon the volume ; with a smaller force, however, the volume is diminished, while with a larger one it is increased. Steel behaves in much the same way as iron, but suffers less elongation under moderate forces. The behaviour of cobalt is the reverse of that of iron, contracting under small and lengthening under great magnetic forces. A nickel rod is always shortened, whether the magnetising force is great or small. 907. Cyclic Changes. Magnetic Hysteresis. — Suppose that a rod of iron has been subjected to gradually increasing magnetising forces and that its magnetisation curve is represented by OA, fig. 914, in which, as before, abscissse represent magnetising forces, and ordinates the corre- sponding magnetisations. If at the point A the magnetising force is gradually diminished, the curve OA is not retraced, but the ordinates of the descending curve are greater than those of the ascending curve for equal values of the current. When the current is zero there is still a certain amount of magnetisation left-(residual magnetism), and to reduce this to zero a mag- netising force must be applied in the opposite direction. Let this force be increased to — F, then diminished to zero, and then increased positively until the point A is again reached. The iron is now in the same state as it previ- ously was at the point A, having passed through a complete cycle of changes. It may be shown that the area of the loop, ACA'BA, is a measure of the energy which has been spent in carrying each cubic centimetre of the iron through the cycle — that is, the difference between the energy spent in mag- netising and that which is recovered in the reverse process. It will thus be seen that the magnetisation of a bar for a given force depends not only on its existing condition, but also on its previous state. The magnetisation is greater in the descending than in the ascending period 3 N 2 Fig. 914 gi6 Dynamical Electricity [907- for the same value of the magnetising force. This is due to residual mag- netisation ; there is a retardation ox lag of the magnetisation in respect of the magnetising force, to which Prof. Ewing has applied the term hysteresis. The hysteresis is greater the wider the difference in the two curves. Hys- teresis is diminished if the body is submitted to vibrations during the pro- cess of magnetisation. When a soft iron bar is submitted to magnetisations and demagnetisations in rapid succession, its temperature rises. The energy lost in each cycle is transformed into heat. The loss may attain 15,000 ergs per cubic centi- metre of soft iron for each complete cycle, and the term hysteresis is used to express this loss as well as to represent generally the phenomenon of magnetic retardation. One erg represents -asSxio"' calories (506), and since the density of iron is yS, and its specific heat o-ii (464), the calorific capacity of a cubic centimetre is 0-858. So that, taking the above number, we have 0-0004° as the rise in temperature for each complete cycle. The coercive Jorce of the magnetic substance is expressed numerically by the length CO or J CB. 908. Vibratory motion and sounds produced by currents. — When a rod of soft iron is magnetised by a strong electric current, it gives a very distinct sound, which, however, is only produced at the moment of closing or opening the circuit. This phenomenon arises from a sudden motion of the molecules of iron due to magnetisation or demagnetisation. When the circuit is broken and closed at very short intervals, De la Rive observed that, whatever be the shape or magnitude of the iron bars, two sounds may always be distinguished ; one, which is musical, corresponds to that which the rod would give by vibrating transversely ; the other, which consists of a series of harsh sounds, corresponding to the interruptions of the current, was compared by De la Rive to the noise of rain falling on a metal roof. The most marked sound is that obtained by stretching, on a sounding-board, pieces of soft iron wire, well annealed, from i to 2 mm. in diameter and l to 2 yards long. These wires, being placed in the axis of a long magnetising coil traversed by powerful cun-ents, send forth a number of sounds, which produce a surprising effect, and much resemble that of a number of church bells heard at a distance. Rods of zinc, copper, or brass give no note even with strong currents. Wertheim also obtained the same sounds by passing a discontinuous current through the wires themselves. The musical sound is then stronger and more sonorous in general than in the previous experiment. The hy- pothesis of a molecular movement in the iron wires at the moment of their magnetisation and demagnetisation is confirmed by the researches of Wertheim, who found that their elasticity is then diminished. 909. Reis's telephone. — The essential features of this instrument (fig. 915) are a sort of box, B, one side of which is closed by a membrane, C, while there is a mouthpiece. A, in another side. On the membrane is a piece of thin metal-foil C, which is connected with a wire leading to one pole of the battery G, the other pole of which is put to earth. Just above the foil, and almost touching it, is a metal point D, which is connected by the line wire (912) with one end of a coil of insulated wire surrounding an iron rod, the other end of the wire being put to earth. -911] Electric Clocks 917 When the mouthpiece is spoken or sung into, the sounds set the mem- brane in vibration ; this coming into contact with the point D causes a rapid Fig. 915 succession of currents to pass into the line and through the electromagnet in which the corresponding sounds are produced. 910. Electric bell. — One form of this instrument is represented in fig. 916. On a wooden board arranged vertically is fixed an electromagnet, E ; the line wire is connected with the bind- ing screw, /;/, with which '.is also connected one end of the wire of the electromagnet ; the other end is connected with a spring, t, to which is attached the armature, a ; this again, is pressed against by a spring, C, which in turn is connected with the binding" screw n, from which the wire leads to earth. Whenever the current passes, which is effected by a small contact-maker called a push, the. armature a is attracted, carrying with it a hammer, P, which strikes against the bell T and makes it sound. The moment this takes place, contact is broken between the armature a and the spring C, and the current being stopped the electromagnet does not act ; the spring c, however, in virtue of its elasticity, brings the armature in con- tact with the spring C, the current again passes, and so on as long as the current con- tinues to pass. 911. Electric clocks. — Electric clocks are clockwork machines, in which an electromagnet is both the motor and the regulator, by means of an electric current regularly interrupted, in a manner resembling that described in the preceding paragraph. Fig. 917 represents the face of such a clock, and fig. 918 the mechanism which works the needles. An electromagnet, B, attracts an armature of soft iron, P, movable on a pivot, a. The armature P transmits its oscillating motion to a lever, s, which by means of a ratchet, n, turns the wheel A. This, by the pinion, D, turns the wheel C which bv a series of wheels and pinions moves the hands. The Fig. 916 9i8 Dynamical Electricity [911- small one marks the hours, the large one the minutes ; but as the latter does not move regularly, but by sudden starts from second to second, it follows that it may also be used to indicate the seconds. It is obvious that the regularity of the motion of the hands depends on the regularity of the oscillations of the piece P. This is tested by connecting the clock in series with a standard, which itself has been previously regulated by a seconds pendulum. At each oscillation of the pendulum there is an arrangement by which the circuit is opened and closed, and thus the armature P beats seconds exactly. To illustrate the use of these clocks, suppose that on the railway from London to Birmingham each station has an electric clock, and that from the London station a conducting wire connects all the clocks on the line to Birmingham. When the current passes in this wire all the clocks will simul- taneously indicate the same hour, the same minute, and the same second ; for electricity takes an inappreciable time to go from Londonito Birmingham. Fig. gi7 Fig. 918 912. Electric telegraphs. — These are apparatus by which signals can be transmitted to considerable distances by means of voltaic currents propa- gated in metallic wires. Towards the end of the eighteenth century, and at the beginning of the nineteenth, many philosophers proposed to correspond at a distance by means of the effects produced by electric machines when pro- pagated in insulated conducting wires. In 181 1, Soemmering invented a telegraph, in which he used the decomposition of water for giving signals. In 1820, at a time when the electromagnet was unknown. Ampere proposed to correspond by means of magnetic needles, above which a current was sent, as many wires and needles being used as letters were required. In 1834, Gauss and Weber constructed an electromagnetic telegraph, in which a voltaic current transmitted by a wire acted on a magnetised bar, the oscillations of which under its influence were observed by a telescope. They succeeded in thus sending signals from the Observatory to the Physical Cabinet in -912] Electric Telegraphs 919 Gottingen, a distance of a mile and a quarter, and to them belongs the honour of having first demonstrated experimentally the possibility of electrical com- munication at a considerable distance. In 1837, Steinheil in Munich, and Wheatstone in London, constructed tele- graphs in which several wires each acted on a single needle ; the current in the first case being produced by an electro- magnetic machine, and in the second by a constant battery. Every electric telegraph consists essentially of three parts : i, a circuit consisting of a metallic connection be- tween two places, and a battery or its equivalent for producing the current ; 2, a transmitter for sending the signals from the one station ; and, 3, an indicator for receiving them at the other station. The mode of transmitting and receiving electric signals can be greatly varied, and we shall limit ourselves to a description of the three principal methods. On the larger circuits dynamos or accumulators or combinations of the two are used ; on smaller ones, where there is constant work, some form of Daniell's battery is used, and for other circuits Leclanch^'s cell is in extended use. In France, Daniell's battery is used for telegraphic purposes. The connection between two stations is made by means of copper or galvanised iron wire suspended by porcelain supports (fig. 919), which insulate the wire and protect it against the rain ; they are attached to posts or against the sides of buildings. In England and other moist climates special attention is required to be paid to the perfection of the insulation. In towns, wires covered with gutta-percha are placed in tubes laid in the ground. Submarine cables, where great strength is required combined with lightness and high conducting power, are formed on the general type of one of the Atlantic cables, a longitudinal view of which is given in fig. 920, while fig. 921 represents a cross section. In the centre is the core, which is the Fig. 921 conductor ; it consists of seven copper wires, each i mm. in diameter, twisted in a spiral strand and covered with several layers of gutta-percha, separated from each other by a coating of Chattertoris compound — a mixture of tar, resin, and gutta-percha. This forms the insulator ^xiy^ex, and it should have great resistance to the passage of electricity, combined with low specific inductive capacity (783). Round the insulator is a coating of hemp, and on 920 Dynamical Electricity [912- the outside is wound spirally a protecting sheath of steel wire, spun round with hemp. At the station which sends the despatch, the line is connected with the positive pole of a battery, the current passes by the Une to the other station, and if there were a second return line, it would traverse it in the opposite direction to return to the negative pole. In 1837, Steinheil made the very im- portant discovery that the earth might be used for the return conductor, thereby saving the expense of the second line. For this purpose the end of the conductor at the one station, and the negative pole of the battery at the other, are connected with large copper plates, which are sunk to some depth Fig. 922 Fig. 923 in the ground. The action is then the same as if the earth acted as a return wire. The earth is, indeed, far superior to a return wire ; for the added resistance of such a wire would be considerable, whereas the resist- ance of the earth beyond a short distance is absolutely nil. The earth really dissipates the electricity, and maintains the earth plates at the same potential as the earth, so that there is practically no fall of potential between two earth plates connected with a circuit through which a current is flowing. 913. Wheatstone and Cooke's single-needle telegraph. — This con- sists essentially of a vertical galvanometer (840) with a single needle, the arrangement of which is seen in fig. 923, while fig. 922 gives a front view -914] Morsels Telegraph 921 of the case in which the apparatus is placed, and shows an index parallel to the needle. A (fig. 923) is the galvanometer coil consisting of about 400 feet of fine copper wire, wound on two bobbins. The signs are made by transmitting the current in different directions through the galvanometer, by which the needle is deflected either to the right or left, according to the will of the operator. The instrument by which this is effected is a commutator or key^ worked by a handle seen in front of fig. 922. When the handle is turned to the right the positive pole, and when it is to the left the negative pole, of the battery is put in connection with the line. If the handle is vertical, as shown, the battery is disconnected from the line. Another form of sending apparatus, called a tapper, is similar to the commutator shown in fig. 924. There are two horizontal strips of springy brass, each of which is fixed at one ex- tremity to the top of an ebonite pillar, where binding-screws are attached to them. At their other ends they are provided with ebonite pressure knobs, whereby »ach may be pressed into con- tact with the metal piece below, to which a binding-screw is also attached. Two other ebonite pillars are connected across the top by a brass bridge with a binding- screw at one end. The brass springs are in contact with this bridge unless one or other of the knobs is depressed. All metallic contacts are tipped with platinum. Of the two binding-screws at the left of the figure one is earthed, the other connected through the galvanometer to line ; the other two, one in the middle, the other (low down) on the right, are connected to the poles of a battery. If neither knob is depressed the battery is not in action, and a current from the line, after traversing the galvanometer, passes from one strip through the bridge to the other and so to earth. By pressing the right- or left-hand knob, a positive or negative current may be sent into the line, the strip which is depressed being for the time disconnected from the bridge. The instrument illustrated in the figure is provided also with ebonite cams (not required for telegraphic pur- poses), for keeping either pole of the battery permanently connected with the circuit. The signs are given by differently combined deflections of the needle as represented in the alphabet on the dial (fig. 922). \denotes a deflection of the upper end of the needle to the left, and / a deflection to the right ; I, for instance, is indicated by two deflections to the left, and M by two to the right. D is expressed by right-left-left, and C by right-left-right-left, &c. These signs are somewhat complicated, and require great practice : usually not more than 12 to 20 words can be sent in a minute. The single- needle telegraph was formerly sometimes replaced by the double-needle one, which is constructed on the same principle, but there are two needles and two wires instead of one. 914. Morse's telegraph. — The telegraph just described leaves no trace of the despatches sent, and if any errors have been made in copying the 922 Dynamical Electricity [914- signals there is no means of remedying them. These objections are met in the case of the writing telegraphs, in which the signs themselves are printed on a strip of paper at the time at which they are transmitted. Of the numerous printing and writing telegraphs which have been devised, that of Morse, first brought into use in North America, is best known. It has been almost universally adopted on the Continent, and in England has nearly superseded the needle telegraph. In this instrument there are three distinct parts : the receiver, the sender, and the relay ; figs. 925, 926, 927, and 928 represent these apparatus. Receiver. — We will first describe the receiver (figs. 925 and 926), leaving out of sight for the moment the accessory pieces, G and P, placed on the right of the figure. The current which enters the indicator by the wire, C, passes into an electromagnet, E, which when the circuit is closed attracts an armature of soft iron, A, fixed near the end of a horizontal lever movable '^^mmimt MI|MBV«fBM*He Fig. 925 about an axis, I ; when the circuit is open the lever is raised by a spring. By means of two screws, m and n, the extent of movement of the lever is regulated. At the other end of the lever there is a blunt point which writes the signals. For this purpose a long band of strong paper, hp, rolled round a drum, R, passes between two copper rollers with rough surfaces, u and /, and turning in contrary directions. Drawn in the direction of the arrow, the band of paper becomes rolled on a second drum, Q, which is turned by hand. A clockwork motion placed in the box, BD, works the rollers, between which the band of paper passes. The paper being thus set in motion, whenever the electromagnet works, the point strikes the paper, and, without perforating it, produces an inden- tation the shape of which depends on the time during which the point is in contact with the paper. If it only strikes it instantaneously it makes a dot -914] Morse's Telegraph 923 ( — ) or short stroke ; but if the contact has any duration, a dash ( — ) of corre- sponding length is produced. Hence, by varying the length of contact of the transmitting key at one station, the operator produces a combination of dots and dashes at another station, and it is only necessary to give a definite meaning to these combinations. In order to make an indentation a considerable pressure is required, which necessitates the employment of a strong current, and the newer instruments (fig. 926) are based on the "y «■; I \ use of ink- writers. The paper band passes close to, but not touch- ing, a metal disc with a fine edge, c, which turns against a small ink- roller, a, all being rotated by the same mechanism. When the armature A is attracted, the bent plate at the other end of the lever presses the paper against the Fig. 926 1 "■ ~ F= "1 Printing. Single Needle. Printing. Single | Needle, i A J N A B As. III I! AA p Jls D Ax Q IIJ E _ N R vA F uA S W^ G /A T / H WW U vv/ I -- w V ssJ J J// W Jl E u X ^^ — — . — I.J L .L Y Ml — II Z /Av disc, which is inked by contact with the ink-roller, and thus produces a mark on the paper, which is either short or long according to the duration 924 Dynamical Electricity [914- of the contact. The signs are thus more legible, and are produced by far weaker currents. The same telegraphic alphabet is now universally used wherever tele- graphic communication exists ; and the signals for the single-needle instru- ment (fig. 922) as well as those used for printing have been modified, so that they now correspond to each other. Thus a beat of the top of the needle to the left \ is equivalent to a dot : and a beat to the right /to a dash. The table on the preceding page gives the alphabet. The_/?3g- signals used in military operations are similarly used. A swing of the flag from its upright vertical position to the right or left has the same meaning as the corresponding motion of the top end of the needle. So, too, long or short obscurations of the limelight used in signalling by night, or of the heliograph (533), correspond to dashes and dots. Morse key. — This consists of a small mahogany base, which acts as support for a metal lever ab (fig. 927), movable about a horizontal axis which passes through its middle. The end a of this lever is always pressed upwards by a spring beneath, so that it is only by pressing with the finger on the knob B that the lever strikes the platinum contact x. Round the base are three binding screws, one connected with the wire P, which comes from the positive pole of the battery ; the second connected with L, the line wire ; and the third with the wire >B A, which passes to the indicator ; for of course two places in communi- cation are each provided with an indicator and communicator. These details known, there are two cases to be considered, i. When a Fig. 927 message is to be received, the contact b is down, and a current arriving by the line wire passes into the lever of the key and thence by the contact b to the indicator. 2. A message is to be transmitted ; in this case the knob B is pressed so that the lever comes in contact with the contact piece x, thereby establishing connection between the battery wire P and the line L, and cutting out the local indicator. According to the length of time during which B is pressed, a dot or dash is produced in the receiver to which the current proceeds. Relay. — In describing the receiver we have assumed that the current of the line coming by the wire C (fig. 926) entered directly into the electro- magnet, and worked the armature A, producing a despatch ; but when the circuit consists of many miles of wire, the current may be too weak to act upon the electromagnet with sufficient force to print a despatch. Hence it is necessary to have recourse to a relay — that is, to an auxiliary electromagnet which is still traversed by the current of the line, but which serves to intro- duce into the recording apparatus the current of a local battery of from four to ten cells placed at the station, and which is only used to print the signals transmitted by the wire. -914] Morses Telegraph 92s Fig. 928 shows the relay. The current entering the relay by the binding screw, L, passes into an electromagnet, E, whence it passes into the earth by the binding screw T. Now, each time that the current of the line passes into the relay, the electromagnet attracts an armature, A, fixed at the bottom of a vertical lever, p, which oscillates about a horizontal axis. At each oscillation the top of the lever p strikes against a button n, and at this moment the current of the local battery, which enters by the binding screw c, ascends the column m, passes into the lever ^, descends by the rod o, which transmits it to the screw Z : thence it enters the electromagnet of the indicator, and returns to the local battery from which it started. Then, when the circuit of the line is open, the electromagnet of the relay does not act, and the lever ^, drawn by a spring r, leaves the button «, as shown in the drawing, and the local current no longer passes. Thus Fig. 928 the relay transmits to the indicator exactly the same phases of passage and intermittence as those effected by the manipulator in the station which sends the despatch. With a general battery of 25 Daniell cells the current is usually strong enough at upwards of 90 miles from its starting-point to work a relay. For a longer distance a new current must be taken, as will be seen in the paragraph on the change of current [vide infra). The three principal pieces of the Morse apparatus being thus known, the following is the actual path of the current. The current of the line coming by the wire L (fig. 925) passes at first to the piece P intended to serve as lightning-conductor, when, from the influence of atmospheric electricity in time of storm, the conducting wires become so highly charged with electricity as to give dangerous sparks. This apparatus consists of two copper discs, d and/ provided with teeth on the sides opposite each other, but not touching. The disc d is connected with the earth by a metal plate at the back of the stand which supports this lightning-conductor, while the disc / is in the circuit. The current coming- by the line L enters the lightning-conductor by the binding screw fixed at the lower part of the stand on the left ; then rises to a commutator, n, which conducts it to a button, c, whence it reaches the disc _/" by a metal plate at 926 Dynamical Electricity ' [914- the back. of the stand ; in case a lightning discharge should pass along the wire, it would now act inductively on the disc d, and emerge by the points without danger to those about the apparatus. Moreover, from the discyj the current passes into a very fine wire insulated on a tube, e. As the wire is melted when the discharge is too strong, it acts as a safety catch (859) ; the electricity does not pass into the apparatus, which still further removes any danger. Lastly, the current proceeds from the foot of the support to a screw on the right, which conducts it to a small galvanometer, G, serving to indicate by the deflection of the needle whether the current passes. From this galvanometer the current passes to a key (fig. 927), which it enters at L, emerging at A to go to the relay (fig. 928). Entering this at L, it works the electromagnet, and establishes the communication necessary for the passage of the current of the local battery, as has been said in speaking of the relay. Change ofairrent. — To complete this description of the Morse apparatus, it must be observed that in general the current Avhich arrives at L, after having traversed several miles, has not sufficient force to register the despatch, or to' proceed to a new distant point. Hence in each telegraphic station a new current must be taken, that of 'Oa.'^ postal battery, which consists of 20 to 30 Daniell cells, and is not identical with the local battery. This new current enters at P (fig. 925), reaches a binding screw which conducts it to the column H (fig. 926), and thence only proceeds further when the armature A sinks. A small contact placed under the lever then touches the button n ; the current proceeds from the column H to the metallic mass BD (fig. 925), whence by a binding screw and a wire, not represented in the figure, it reaches, lastly, the wire of the line, which sends it to the following station, and so on from one point to another. 915. The sounder. — The sound produced when the armature of the electro- magnet in a Morse instrument is attracted by the passage of the current is so distinct and [clear that many telegraph operators have been in the habit of reading the messages by the sounds thus produced. When necessary their reading could be checked by comparison with the signs produced on the paper. Based on this fact a form of instrument invented in America has come into use for the purpose of reading by sound. The sounder, as it is called, is essentially a small electromagnet on an ebonite base, resembling the relay in fig. 928. The armature is attached to one end of a lever, and is kept at a certain distance from the electromagnet by a spring. When the current passes, the armature is attracted against the electromagnet with a sharp click, and when the current ceases it is withdrawn by the spring. Hence the interval between the sounds is of longer or shorter duration according to the will of the sender, and thus in effect a series of short or long intervals which represent short and long sounds can be produced which correspond to the dots and dashes of the Morse alphabet. Such instruments are simple, easily adjusted, and portable, not occupying more space than an ordinary field-glass. They are coming into extended use, especially for military telegraph work. 916. Induction in telegraph cables. — In the earliest experiments on the use of insulated subterranean wires for telegraphic communication it was -916] Induction in Telegraph Cables 927 found that difficulties occurred in their use which were not experienced with overhead wires. This did not arise from defective insulation, for the better the insulation the greater the difficulty. It was suspected by Siemens and others that the retardation was due to statical induction taking place be- tween the inner wire through the insulator and the external moisture ; and Faraday proved that this was the case by the following experiments among others. A length of about 100 miles of guttapercha-covered copper wire was immersed in water, the ends being led into the observing-room. When the pole of a battery containing a large number of cells was momen- tarily connected with one end of the wire, the other end being insulated, and a person simultaneously touched the wire and the earth contact, he obtained a violent shock. When the wire, after being in momentary contact with the battery, was placed in connection with a galvanometer, a considerable deflection was observed ; there was a feebler one 3 or 4 minutes after, and even as long as 20 or 30 minutes afterwards. When the insulated galvanometer was permanently connected with one end of the wire, and then the free end of the galvanometer wire joined to the pole of the battery, a rush of electricity through the galvanometer into the wire was perceived. The deflection speedily diminished and the needle ultimately came to rest at zero. When the galvanometer was detached from the battery and put to earth, the electricity flowed as rapidly out of the wire, and the needle was momentarily deflected in the opposite direction. These phenomena are not difficult to explain. The wire with its thin insulating coating of gutta-percha becomes statically charged with electricity from the battery like a Leyden jar. The coating of gutta-percha through which the inductive action takes place is only fj of an inch in thickness, and the extent of the coatings (copper wire on the one side, and water on the other side of the dielectric gutta-percha) is very great. The surface of the copper wire amounts to 8,300 square feet and that of the outside coating is four times as much. The potential can only be as great as that of the battery, but, from the enormous surface, the capacity, and therefore the quantity (760), is very great. Thus the wires, after being detached from the battery, showed all the actions of a powerful electric battery. These effects take place, but to a less extent, with wires in air ; the external coating is here the earth, which is so distant that induction and charge are very small, more especially in the long lines. Hence the difficulty in submarine telegraphy. The electricity which enters the insulating wire must first charge the large Leyden jar which it constitutes, and only after this has happened can the current reach the distant end of the circuit. The current begins later at the distant end, and ceases later. The electricity is not projected like the bullet from a gun, but rather like a quantity of water flowing from a large reservoir into a canal in connection with large basins which it has to fill as well as itself If the electric currents follow too rapidly, an uninterrupted current will appear at the other end, which indicates small differences in strength, but not with sufficient clearness differences in duration or direction. Hence in submarine wires the signals must be slower than in air wires to obtain clear indications. The retardation is directly as the length and the self-induction (967) of the 928 Dynamical Electricity [916- line. By the use of alternating currents sent by a special form of key — that is, of currents which are alternately positive and negative (985) — these disturbing influences may be materially lessened, and communication be accelerated and made more certain, but they can never be entirely obviated. The first submarine telegraph cable (figs. 920, 921) was laid between Dover and Cape Grisnez in 1 851, and this was followed during the next ten years by the laying of submarine cables of greater length, which were short, however, in comparison with more recent developments. The successful telegraphic bridging of the Atlantic was effected in 1866, after three un- successful attempts in 1857, 1858, and 1865. At the present day there are about 200,000 miles of submarine telegraph cable. The greatest under- taking of the kind hitherto attempted is the Pacific cable now being con- structed between Vancouver and Australia, vid Fanning Island, Fiji, and Norfolk Island. 917. Siphon recorder. — Lord Kelvin indented an extremely ingenious instrument called the siphon recorder, by which the very feeble signals transmitted through long lengths of submarine cable are observed and also recorded. In principle it is a suspended coil galvanometer (896). It must be noted, however, that suspended coil galvanometers for ordinary electric work have only comparatively recently come into use. A light rectangular coil of fine wire j- (fig. 929), connected with the line wire by the screws p and q, hangs by a bifilar suspension between the two poles of a powerful electromagnet AB, so that its plane is parallel to the lines of force between the poles. The space inside the coil is occupied by a mass of soft iron f, by which the strength of the field is greatly increased. When a current is passed this coil tends to place itself perpendicular to the lines of force, and is deflected either to the right or the left according to the direction of the current ; its movements are almost dead-beat (963), as the damping is considerable. A very light capillary tube c dips with its short end in a reservoir of ink, while the other end is in front of a paper ribbon which is moved along at a uniform rate like the ribbon in a Morse's recorder. By the action of a light tapper the ink spurts out in a continuous series of fine drops against the paper, marking on it a straight line so long as no current passes in the coil. The siphon is, however, connected by a system of silk threads with the coil, and according as this is deflected to the right or the left the end of the siphon is deflected too, and traces a wavy line (fig. 930) on the paper, which represents deflections right or left of the central line, that are, in short, the Morse signals (914). Fig. 929 -918] Duplex Telegraphy 929 918. Duplex telegraphy. — By this is meant a system of telegraphy by which messages may be simultaneously sent in opposite directions on one Fig. 930 and the same wire, whereby the working capacity of a line is practically doubled. Several plans have been devised for accomplishing this very important improvement ; no more can here be attempted than to give a general account of the principle of the method in one or two cases. Let m (fig. 931) represent the electromagnet of a Morse's instrument which is wound round with two equal coils in opposite directions ; these coils are represented by the full and dotted lines, and one of them, which may be called the line coil, is joined to the line LL', which connects the two stations. The other coil, that represented by the dotted line, which may be called the equating coil, is in connection with the earth at E by means of an adjustable re- sistance, or arti- ficial line,"^. By this means the resistance of the branch flRE may be made equal to that of the branch alAJa . The battery b has one pole to earth at E, and the other pole. Fig. 931 by means of a Morse key, c, can be connected at a, where the two oppositely wound coils bifurcate. The back contact of the key is also connected with earth. The station at B is arranged in a similar manner, as is represented by corresponding dashed letters. Now when B depresses his key and sends a current into the line, inasmuch as the electromagnet of his instrument is wound w th equal coils in opposite directions, the armature is not attracted, for the core s not magnetised be- cause the currents in the two coils counteract one another. Tlius, although a cun-ent passes from B, there is no indication of it mhis own instrument — a condition essential in all systems of duplex telegraphy. 30 930 Dynamical Electricity [918- But with regard to the effect on A, there are two cases, according as he is or is not sending a message at the same time. If A's key is not down, then the current will circulate round the core of the electromagnet and will reach the earth by the path LacE ; the core will therefore become magnetised, the armature attracted, and a signal produced in the ordinary way. If, however, at the moment at which B has his key down, A also depresses his, then it will be seen that, as the batteries bb' are exactly alike, their electromotive forces neutralise one another, and no current passes in the line alAJa' : it is, as it were, blocked. But though no current passes in the line coil, a current does pass at each station to earth, through the equating coil, which, being no longer counterbalanced by any opposite current in the line coil, magnetises the core of the electromagnet, which thus attracts the armature and produces a signal. We have here supposed that A and B both send, for instance, the same •currents to line : the final effect is not different if they send opposite currents at the same time. For then the current in the line LL' is doubled. More electricity flows to line from each station through the line coil being no longer balanced by the equating coil ; the current of the line coil preponderates and then works the electromagnet. Hence each station, so to speak, produces the signal which the other one wishes to send. Another method is based on the principle of Wheatstone's bridge (923). At each station is a battery P (fig. 932), one pole of which is to earth while the other is connected with the key M. The wire from M bifurcates at A into the two branches AB and AC, between B and C is connected the galvanometer or the receiving instrument. The branch AB goes to line and AC to earth. There are exactly corresponding parts at the other station. Now, from the principle of the ^_^_ bridge, the resistances AB and AC may Xbe adjusted in such a manner that the J"^ J ! . "^"^ .... ' potentials at the points B and C are equal t-^;A^NA^^^-.^~.-^^^v.^w^^^^^.W\^\&^^^^ ^^^^^ ^^^ ^^^ j^ depressed and the current '''S- 93^ sent ; accordingly, no current passes in the bridge, and the galvanometer is at rest ; but the current from A passing to line bifurcates at B', a portion traversing the galvanometer and going to earth ; hence a signal is received at that station. Other methods of duplex telegraphy are based on the principle of leakage ; but for these, as well as for cpadruplex telegraphy, special manuals must be consulted. The present speed of transatlantic telegraphy is about twenty words a minute, and there are twelve duplexed cables having, therefore, a carrying capacity of 500 words a minute. 919. Bain's electrochemical telegraph. — If a strip of paper is soaked in a solution of potassium ferrocyanide and is placed on a metal surface connected with the negative pole of a battery, on touching the paper with a steel pointer connected with the positive pole, a blue mark due to the forma- tion of Prussian blue will be formed about the iron, so long as the current -921] Telautograph 93 1 passes. The first telegraph based on this principle was invented by Bain. The alphabet is the same as Morse's, but the despatch is first composed at the departure station on a long strip of ordinary paper. The paper is per- forated successively by small round and elongated holes, which correspond respectively to the dots and marks. The strip so prepared is interposed between a small metal wheel and a metal spring, both forming part of the circuit. The wheel, in turning", carries with it the paper strip, all parts of which pass successively between the wheel and the plate. If the strip were not perforated, it would, not being a conductor, constantly offer a resistance to the passage of a current ; but, in consequence of the holes, every time one of them passes, there is contact between the wheel and the plate. Thus the current works the relay of the station to which it is sent, and traces in blue, on a paper disc, impregnated with potassium ferrocyanide, the same series of points and marks as those on the perforated paper. 920. Earth currents. — In long telegraph circuits Jmore or less powerful currents are produced, even when the battery is not at work. This arises from a difference of potential being established in the earth at the two places between which the communication is established. These currents are some- times in one direction and sometimes in another, and are at times so powerful and irregular as quite to interfere with the working of the lines. Lines running NE and SW are most frequently affected ; lines running NW and SE are less so, and the currents are far weaker. Their strength often amounts to as much as 40 milliamperes (849), which is a stronger current than is required for working ordinary telegraph instruments. These currents do not seem to be due to atmospheric electricity, but they are certainly intimately connected with magnetic storms. 921. Writing telegraphs. Telautograph. — Many systems have been devised for transmitting by electricity the actual handwriting of the person who sends the message. The following gives a general idea of the principle of that invented by Mr. Cowper : — Two line wires are required, which are severally connected at the re- ceiving station with two galvanometers, whose coils are at right angles to each other. At the sending station is a vertical pencil with two light rods, jointed to it at right angles to each other. One of these contact rods guides a contact piece which is connected by a wire with one pole of a battery, the other pole of which is to earth. This contact piece slides over the edges of a series of contact plates insulated from each other, between each of which and the next a special resistance is interposed, and the last of the contact plates is connected with one line wire. The other contact piece slides over a second series of such plates connected with the other line wire. Let us consider one contact piece alone ; as it moves over the contact plates in one direction or the other, it brings less or more resistance into the circuit, and thereby alters the strength of the current. The effect of this is that the needle of the corresponding galvanometer is less or more deflected. Now the end of this needle is connected by a light thread with a receiving pen, which is a capillary tube full of ink. An oscillation of the needle would produce an up and down motion of the pen, and if simultaneously a band of paper passed under the pen, being moved regularly by clockwork, there would be produced on it a series of up and down strokes. A corresponding 302 932 Dynamical Electricity [921— effect would be produced by the action of the needle of the other galvano- meter, except that its strokes would be backwards and forwards instead of up and down. Now the action of the writing pen is that it varies simultaneously the strengths of the two currents, and they produce a motion of the receiving pen which is compounded of the two movements described above, and which is an exact reproduction, on a smaller scale, of the original motion. The following line is a facsimile. Fig- 933 Both the paper written in pencil at the sending station and that written in ink at the receiving station move along as the writing proceeds, and the messages have only to be cut off from time to time. Experiments made with this instrument show that it will write through resistances equal to 36 miles of telegraph wire. In Mr. Foster Ritchie's Telautograph two wires also are needed to con- nect the tiansmitting and receiving instruments ; these are connected as a single loop earthed at each end, thus providing three distinct circuits, since currents can be sent through either of the wires to return by earth, or can be sent by one wire to return by the other. The pencil with which the operator writes is connected to two sets of levers which actuate the sliding contacts of two rheostats (857) ; these rheostats are connected one in series with each of the two lines. As the resistances are varied by the motion of the sliding-contacts corresponding to the motion of the pencil, the currents in the two lines will vary. These currents pass through and deflect the moving coils of two d'Arsonval galvanometers (896) in the receiving instrument, which are connected by two sets of levers to the receiving pen. Thus the position of the pen is controlled b)- the deflections of the two galvanometers,, which are in their turn dependent on the position of the transmitting pencil. The pen will, therefore, exactly follow in its motions the movements of the pencil, and will consequently repeat on the paper at the receiving end the words written on that at the transmitting end. There is an ingenious arrangement by which the receiving pen only makes marks on the paper when the transmitting pencil is pressed down on the writing-table. The- message can be written at the ordinary speed of handwriting. There is no difficulty in writing, in spite of the pencil being attached to the rheostats, and having to move them. Moreover, as long as the paper is not shifted the writer can go back and make alterations and additions with perfect accuracy. -923] Resistance 933 CHAPTER VIII ELECTRIC MEASUREMENTS 922. Current. — Several types of instruments for measuring current have already been described. In some of these the relation between the indication of the instrument and the current flowing through it follows a known law, as in the tangent and sine galvanometers and Siemens electro- dynamometer. In others, for example in most ammeters, there is no simple connection between current and deflection, and the scale has to be graduated empirically. In reflecting galvanometers the maximum angular motion of the needle which can be observed does not exceed five or six degrees, and the movement of the spot of light may be taken as directly proportional to the current producing it. 923. Resistance. — -The most convenient method of ascertaining experi- mentally the ratio between the resistance of two conductors is by a method known as that of Wkeatstone' s bridge, the general principle of \\'hich may be thus stated : — Suppose two points, A and C (fig. 934), to be connected to the positive and negative poles respectively of a voltaic cell, and these points to be joined by Fig- 934 two wires, ABC, AB'C. The current arriving at A flows through the two branches |in strengths inversely proportional to their resistances (853). The potential of any point B in ABC is intermediate between those of A and C, and there must be some point B' in the lower branch, which has the same potential as B, and if these points are joined by a wire, no current will flow through it. If B' is moved a little towards C, B will be at a higher potential than B', and the needle of a galvanometer inserted at G, between B and B', will be deflected, say, to the right ; contrariwise, if B' move towards A, the deflection- will be to the left, B' being now at a higher potential than B. If the galvanometer needle is not deflected, B and B' are at the same potential, and this being so, it may be proved that r -.r' =s -.s' , where r, r', s, s', are the resistances respectively of AB, BC, AB', B'C. 934 Dynamical Electricity [923- Hence r = r^, and if r is a standard resistance, and the ratio of s' to J is known, the value of the unknown resistance / is determined. To prove the relation just given, let MN, NO, MN' and N'O' (fig. 935) be taken in the same straight line, proportional respectively to the several resistances r, /, s, s' ; and let MP be drawn at right angles to O'MO of a length proportional to the difference of potential between the points A and C. Then the straight lines PO and PO' represent the slope (or rate of Fig- 93s fall) of potential from A to C along the twojbranches respectively. If NQ is drawn perpendicular to MO, meeting PO in Q, NQ represents the difference of potential between B and C ; and the point N' (corresponding to B' in the previous figure), where the potential is the same as at N, will be found by drawing QQ' parallel to OO', and letting fall from Q' the perpendicular Q'N' upon O'M. The geometry of the figiare gives obviously. r NQ _N'Q' and , MP j + i-' MP' and therefore since NQ = N'Q' r r A convenient form of Wheatstone's bridge, and one well adapted for purposes of instruction, is that represented in fig. 936. It is called the metre wire bridge. It consists of a long mahogany board, on which is fixed Fig. 936 a thick copper band, which practically offers no resistance. To the ends of this band is soldered a straight platinum or German-sliver wire, near which is a scale divided into 100 parts. At c and d are breaks in the copper -923] Resistance 935 band, provided with binding screws, in which are introduced the resistances to be compared, O and x. The wires, from a cell of small E.M.F., so as not to introduce heating effects, are connected with the binding screws b and b'. Another wire connects the binding screw g and one terminal of a sensitive galvanometer, the other terminal of which is connected with a sliding spring contact-key g, so constructed that when the knob is depressed a knife-edge makes contact with the wire. The resist- ances to be compared having been introduced at c and d, the position on the metre wire is found by trial, at which, when the key is de- pressed, the needle of the galvanometer is not deflected. When this is found, for in- stance, at 34, the resistance of O : the resistance oix as 34 •• 66. Another form of Wheat- stone's bridge, known as the Post Office Pattern, is illus- trated in fig. 937 ; fig. 938 gives a plan of the instru- ment. AC and AD are two resistances each of 10 or 100 ^^' '3'' or 1,000 ohms, which correspond to the two parts of the straight wire in the rnetre bridge ; from D to B is a set of standard coils, R, the individual resistances ranging from i to 4,000, and the total resistance being about 10,000 ohms. The box is provided with two contact keys, K, K, that on the right for the battery circuit, that on the left for the galvano- meter circuit. K on the right, when depressed, connects to- gether the two points A, A by means of a wire under- neath the ebonite top of the box, indicated in fig. 938 by a dotted line. Similarly the left-hand key connects D and D together. The battery is introduced between A and B, the galvanometer between C and D, while the coil, whose resistance is to be measured, is connected by wires to the terminals C and B. The letters a, b, x, R in fig. 938, representing corresponding resistances, it will be seen that the bridge is balanced — that is, no current flows through the galvanometer, when .ar/R = ajb. To determine the value of the unknown resistance, x, we proceed as Fig. 938 93^ Dynamical Electricity [923- follows: — (l) Unplug lo and lo in the branches a and ^,that is, make a = d= lo, and leave all the rest of the plugs in their places, so that R = o. Now press the keys K, K, first the battery key on the right, then the galvanometer key on the left. The needle will be deflected, say, to the right. Now unplug a large resistance, or ' infinity,' in R ; the needle will be deflected to the left. Gradually reduce the resistance in R, and suppose that, when R = 23 the deflection is to the right, |and when R = 24 it is to the left. Then the unknown resistance is something between 23 and 24 ; and so long as «/5= 10/10 we cannot approximate closer to the real value of x, since the smallest resistance in the box is i ohm. (2) Let a = 10, 6= 100 ; then ^■/R= 10/100 and x= R/io, and therefore R must be something between 230 and 240. Suppose we find that the needle moves to the right when R = 245, and to the left when R = 246 ; it follows that X is between 24-5 and 24'6 ohms. (3) Make 6=i,cxx>, « being still 10; then .r = R/ioo, and R must be between 2,450 and 2,460. If there is practically no deflection on depressing the keys when R is 2,457, «•= 24-57 ohms. It will thus be seen that we can by this arrangement measure a resistance whose value does not exceed 100 ohms to the hundredth of an ohm. If the resistance to be determined is very large, say 200,000 ohms, we can measure it (though with no great accuracy) by making a =1,000 and ^=10, so that ;tr= looR, and R will be 2,000 ohms. This bridge, in fact, enables us to measure a resistance whose value is anything between •oi ohm and 1,000,000 ohms. But for very high or very low resistances other methods of determination are generally employed. 924. Resistance of a galvanometer. — The resistance of a galvanometer may be determined by Wheatstone's bridge in the ordinary way, introducing it in the place of x in fig. 936 or fig. 938. A modification of the bridge method, due to Lord Kelvin, enables the resistance to be measured by means of the deflection of the instrument itself Thus let the galvanometer whose resistance G is required be inserted at the gap d of the Wheatstone's bridge (fig. 936), O being a known resistance. Join ^a-' by a simple wire and let the other connections be as before. The galvanometer needle will be deflected, and the deflection will generally alter when K is depressed. Now let K be moved until a position has been found for it, such that the deflection is the same whether K is depressed or not. We then have G : O = the ratio in which K divides the wire. 925. Difference of potential. — The difference of potential between two points may be measured by the quadrant electrometer, or the electrostatic voltmeter (798). Large differences of potential may also be measured by Cardew's voltmeter (867), or other hot-wire instrument. The voltmeter, however, in most common use is essentially a sensitive galvanometer, having either a high resistance of its own, or an independent high resistance in series with it. Suppose, for example, it is desired to determine the difference of potential, e, between the ends A, B, of a coil through which a current is flowing. Connect A and B to the terminals of the galvanometer, sd that between A and B we have a divided circuit. If R is the resistance of the galvanometer (or galvanometer and associated high resistance coil), and r the resistance of the coil AB, the current flowing through the -927] Internal Resistance of a Cell 93,7 galvanometer is-^- of that flowing through the coil (853), and if R is very R large in comparison with r, we shall make no appreciable error in assuming that the presence of the galvanometer does not affect the value of r, the D.P. that we wish to measure. Then « = fR, where c is the current flowing through the galvanometer, and is directly read off if the galvanometer is a direct-reading voltmeter, or, if an ordinary galvanometer, is obtained by multiplying the deflection by the reduction factor (841). The Weston voltmeter is constructed on the same principle as the ammeter already described (898). It has a resistance often or fifteen thousand ohms. The electromotive force of a cell, that is, the D.P. between its poles on oj>en circuit, may be measured by connecting' it in circuit with a voltmeter. It is true that in this case the circuit is not open, but if the resistance of the voltmeter is large in comparison with that of the cell, the D.P. between the poles is practically the same whether the circuit is open or closed. This will be made evident by an examination of fig. 835, for if r/R is very small, HD is practically equal to MA. 926. Determination of resistance by measuring C and e. — There are many instances in which the resistance of a conductor cannot be conveniently •determined by Wheatstone's bridge. In these cases the method of measurement usually adopted is to connect the resistance to be measured in circuit with a suitable battery and an ammeter, and to note the current, C, at the same time that the D.P., e, between the ends of the conductor, is measured by a voltmeter. The resistance required is then e\Q. This method would be adopted for the measurement of the resistance of a short length of thick wire or cable. A powerful current is passed through the cable, and the D.P. between its ends measured by a sensitive voltmeter. Since e - CR, and R is assumed to be very small, it is necessary for C to be large in order that a measurable value of e may be obtained The resistance of the carbon filament of a glow lamp cannot be measured by Wheatstone's bridge when the lamp is glowing, but is easily determined by the above method. For example, if C, the current flowing through the lamp, is '5 ampere, and - are immediately available for electric effects. They are usually charged by shunt wound dynamos (991), whereby about 75 per cent, of the energy is available. An accumulator of a given size can only consume in each interval of time a de- finite quantityof gas for its formation by oxidation and reduction. If more gas is developed it escapes uselessly. The charging current must be neither too strong nor too weak. For each accu- mulator there is a special rate of charge and of discharge, which is most advan- tageous. Fig. 961 represents the course ot charging an accumulator in an actual experiment in which the charging was contmued for 22 hours. In the first hour or so the E.M.F. rose rapidly until it was about 2'o8 volts, when it was almost stationary for about 10 hours when 220 ampere-hours had been put in, and the E.M.F. was 2-13 volts ; from this point the E.M.F. rose more rapidly, until it reached 2-53 volts at the end of 21 hours. The maximum usually obtained is 2 '5 volts, at which the liquid becomes milky owing to a Fig. 960 958 Dynamical Electricity [947- disengagement of gas in the body of the Hquid itself, which indicates that the charge is complete. A charged accumulator gradually loses its charge by leakage, and the efficiency of an accumulator depends on the power of retaining its charge. In this respect great improvement has been made by attention to a number of minute points ; the durability now extends to years, whereas it was formerly measured by months or weeks. The capacity of an accumulator, which must not be confounded with electrostatic capacity (760), is measured in terms of ampere-hours. A cell whose capacity is 100 ampere hours would furnish a current of i ampere for 100 hours, 2 amperes for 50 hours, and so on. The capacity depends, of course, on the number and size of the plates — that is, on the weight of lead used. Of perhaps greater importance in judging of an accumulator is the efficiency, by which is meant the ratio of the energy it gives out during discharge to that which it absorbs during charge. The energy stored up in an accumulator is measured by the potential at the terminals during the VOLTB £.5S £.50 E.4.5 £*as 3.85 S.SO i ^ H / \ : / ; ! J : 1 f i : / : 1 / : ; 4» X ; '. ^ L-1 : < 1— — " ; •Mi na L_ HCU 9^ 5 6 7 S 9 10 11 12 13 14 15 16 17 La 19 20 21 22 Fig. 961 charging, multiplied by the strength of the current and by the time. The product gives the energy in volt-ampere-seconds. In like manner the energy given out in the discharge is the potential into the current ' strength into the time of discharge. The whole charge which can be imparted to an accumulator cannot be advantageously utilised, for the accumulator is injured if this is done, and in practice the charge is only allowed to run down until the potential is lo per cent, less than at starting. Thus a given accumulator was charged for iO'l6 hours with a current of 5 amperes, the average potential being 2-15 volts ; hence the energy stored is lo-i6 X 2-15 X 5 = 109 watt-hours. In the discharge, which lasted 7-35 hours, the average potential was i-88, and the current 6-5 amperes, repre- senting therefore 90 watt-hours ; the ratio of the two is o'826 — that is, the efficiency of the accumulator is 82 '6 per cent. ; a number which is now required for a good accumulator. It cannot be said that the reactions which take place during the charge and discharge of an accumulator are thoroughly understood ; they are undoubtedly more complicated than has been represented above, in which no account has been taken of the sulphuric acid. During the charge, the -948] Nobili's Rings 959 strength of the dilute sulphuric acid, and therewith its conductivity, gradually diminish, while during the discharge both increase. Hence a determination of the specific gravity of the solution at any time is a convenient practical method of measuring the state of the charge. This is effected by flat densi- meters (i2g) which float between the plates. The density may vary between 1-12 and i'22, representing respectively about i6 and 30 per cent, of sul- phuric acid, SHjO^. As an example, one cell of the Electric Power Storage Company had an internal resistance of O'ooi2 ohm at the beginning, and 0-0028 at the end, and weighed 50 kilos. In such a cell 880 watt-hours could be accumu- lated, and 680 watt-hours, or about 79 per cent., obtained in the discharge. Thus each kilo, represents 13-6 watt-hours of available energy, or 5^ of a horse-power ; that is, it could yield -^ H.P. for an hour, or i H.P. for fi minute. In accumulators which are to be used to work motors, as in tram- cars, electric boats, &c., the capacity is of first importance, while with stationary accumulators, as in electric lighting, the efficiency is the chief point. Many instructive comparisons may be made between a secondary bat- tery and a charged Leyden jar. Thus, for instance, when the poles of a secondary battery have been connected until no current passes, and are then disconnected for a while, a current in the same direction as the first is obtained on again connecting them ; this is the residual discharge. The capacity of a secondary battery depends on the area of the electrodes, on their nature, and on that of the interposed liquid, but not on the distance between them. The energy of the Leyden jar is stored in that state of mechanical strain which is called polarisation of the dielectric ; in the secondary battery the energy consists in the products which are stored up on the surface of the electrodes in a state ranging from chemical combination to mechanical adherence or simple juxtaposition. A dry battery (829) which has become inactive maybe used as a secondary battery. When a current is passed through it, in a direction contrary to that which the active battery would itself yield, it regains its activity. 948. Nobili's rings. — When a drop of copper acetate is placed on a silver plate, and the silver is touched in the middle of the drop with a piece of zinc, there are formed around the point of contact a series of copper rings alternately dark and light. These are Nobili's coloured rings. They may be obtained in beautiful iridescent colours by the following process : A solu- tion of lead oxide in potash is obtained by boiling finely powdered litharge in a solution of potash. -In this solution is immersed a polished plate of silver or of German silver, which is connected with the positive electrode of a battery of 10 volts. With the negative pole is connected a fine platinum wire fused in glass, so that only its point projects ; and this is placed in the liquid at a small distance from the plate. Around this point lead peroxide is separated on the plate in very thin concentric layers, the thickness of which decreases from the middle. They show the same series of colours as Newton's coloured rings in transmitted light (664). The lead peroxide owes its origin to a secondary decomposition ; by the passage of the current some lead oxide is decomposed into metallic lead, which is deposited at 96o Dynamical Electricity [948- the negative pole, and oxygen which is liberated at the positive ; and this oxygen combines with some lead oxide to form peroxide, which is deposited on the positive pole as the decomposition proceeds. This process is used for the metallic coloration of objects of domestic use and ornamenta- tion. The effects are also well seen if a solution of copper sulphate is placed on a silver plate, which is touched with a zinc rod, the point of fl'hich is in the solution ; for then a current is formed by these metals and the liquid. 949. Arbor Saturni, or lead tree. Arbor Dianas. — When in a solu- tion of a salt is immersed a metal which is more oxidisable than the metal of the salt, the latter is precipitated by the former, while the immersed metal is substituted, equivalent for equivalent, for the metal of the salt. This pre- cipitation of one metal by another is attributable partly to the difference in their affinities, and partly to the action of a current which is set up as soon as a portion of the less oxidisable metal has been deposited. The action is promoted by the presence of a slight excess of acid in the solu- tion. A remarkable instance of the precipitation of one metal by another is the Arbor Saturni. This name is given to a series of brilliant ramified crystallisations obtained by zinc in solutions of lead acetate, A glass flask is filled with a clear solution of this salt, and the vessel closed with a cork, to which is fixed a piece of zinc in contact with so ne copper wire. The flask, being closed, is left to itself. The copper wire at once begins to be covered with a moss-like growth of metallic lead, out of which brilliant crystallised laminae of the same metal continue to form ; the whole pheno- menon has great resemblance to the grow.th of vegetation, from which indeed the old alchemical name is derived. For the same reason the name Arbor Diana has been given to the metallic deposit produced in a similar manner by mercury in a solution of silver nitrate. If a rod of zinc is dipped in an acid solution of stannous chloride, crystallised tin is formed upon it ; the experiment is rendered more beautiful by dipping the platinum electrodes of a battery in the solution ; if the poles are reversed, the crystallised lamina disappear at one pole to reappear at the other. 950. Electrocapillary phenomena. — If a drop of mercury be placed in dilute sulphuric acid containing a trace of chromic acid, and the end of a bright iron wire be so fixed that it dips in the acid and just touches the edge of the mercury, the latter begins a series of regular vibrations which may last for hours. The explanation of this phenomenon, which was first ob- served by Kiihne, is as follows : — When the iron first touches the mercury, an iron-mercury couple is formed, in consequence of which the siu-face of the mercury is polarised by the deposition of an invisible layer of hydrogen ; this polarisation (820) increases the surface-tension of the mercury (137), it becomes rounder, and contact with the iron is broken ; the chromic acid present depolarises the mercury, its original shape is restored, the couple is again formed, and the process repeats itself continuously. Lippmann was led by the observation of this phenomenon to a series of interesting experimental results, which have demonstrated a relation -950] Electrocapillary Phenomena g6i between capillary and electric phenomena. Of these results the most important is the construction of a capillary electrometer. A glass tube, A (fig. 962), is drawn out to a fine point, and is filled with mercury : its lower end dips in a glass vessel, B, containing mercury at the bottom and dilute sulphuric acid at the top. Platinum wires are fused in the tubes A and B, and terminate in the binding screws a and i respectively. At the beginning of the experiment, the position of the mercury in the drawn-out tube is such that the pressure due to the surface-tension at the surface of separa- tion of the mercury in the tube and the liquid is sufficient to coun- terbalance the pres- sure of the column of mercury, A. This position is observed by means of a micro- scope, the focus of which is at the fiducial mark on the glass at which the mercury stops. If now a differ- ence of potential be established between a and 6, b being at the higher potential, the surface-tension of the mercury in the capil- lary tube is increased, the mercury ascends, and in order that the meniscus may be brought to its former position the pressure on A must be increased. This increase is most simply effected by means of a thick India rubber tube or bag, T, con- nected with the top of A, and with a manometer, H, and capable of more or less compression by means of a screw, E. The, difference in level of the two legs of the manometer is thus a measure of the increase of the- surface-tension, and therewith of the difference of potential. Lippmann found that, b being at the higher potential, the capillary surface continues to rise until the D.P. is about "9 volt, beyond which it descends, indi- cating a diminution in the apparent surface tension. Up to "6 volt the curve giving the relation between the D.P. and the pressure which must be applied to bring back the mercury to the fiducial mark is a straight line, showing that D.P. is proportional to pressure. If a is at a higher potential than b, the mercury surface moves downwards, whatever the D.P. This apparatus is much used in physiological work ; the electromotive force applied to it should not exceed o-6 volt, but it can estimate the one-thousandth part 3Q Fig. 962 962 Dynamical Electricity [950- of this quantity, and, as its electric capacity is very small, it shows rapid changes of potential, which ordinary electrometers cannot do. For very small electromotive forces, the pressure is kept constant, and the displace- ment of the meniscus is measured by the microscope. In practical use as an electrometer b is always at a higher potential than a. Dewar suggested a modified form of the capillary electrometer in which a fine horizontal tube of about i mm. diameter contained mercury with a drop of acid at the centre. The ends of the tube are fitted into lateral tubulures in glass bottles containing mercury. A difference of potential of •003 volt causes the drop of acid to move in the direction of the current along the tube. 951. Electric endosmose.- — By electric endosmose is meant the passage of matter with the current through a porous diaphragm. The phenomenon is observed in the following experiment, due to Porret : — Having divided a glass vessel into two compartments by a porous diaphragm, he poured water into the two compartments to the same height, and immersed two platinum electrodes in connection with a battery of 80 cells. As the water became decomposed, part of the liquid was carried in the direction of the current through the diaphragm, from the positive to the negative compartment, where the level rose above that in the other compartment. A solution of copper sulphate is best for these experiments, because then the disturbing influence of the disengagement of gas at the negative electrode is avoided. A porous vessel is necessary, for otherwise the transport by the liquid would be at once hydrostatically equalised. The converse of these phenomena, that is, the production of electric currents, when a liquid is forced through a diaphragm by mechanical means, has also been observed. Such currents, which were discovered by Quincke, are called diaphragm currents. A porous diaphragm, ^, is fixed in a glass tube (fig. 963), in which are also fused two platinum wires terminating in platinum electrodes, a and b ; on forcing a liquid through the diaphragm the existence of a current is evidenced by a galvanometer with which the wires are connected, the direction of the current being that of the flow of the liquid. The difference of potential due to this flow is proportional to the pressure. According to Zollner, all circulatory motions in liquids, especially when they take place in partial contact with sohds, are accompanied by electric currents, which have gene- rally the same direction as that in which the liquid ~a, ^. ~i flows. And he regards earth Fig. 963 currents as analogous to dia- phragm currents ; there are currents m the liquid mass in the interior of the earth, and these currents commg m contact with the solidified masses produce electric currents. Wertheim found that the elasticity of metal wires is diminished by the current, and not by the heat alone, but by the electricity ; he has also found that the cohesion is diminished by the passage of a current. 952. Calculation of E.M.F. of polarisation.— Supposing the electric current to flow through dilute sulphuric acid between platinum electrodes -953] Electrometallurgy 963 without any polarisation, the electric energy; absorbed in the liquid and con- verted into heat would be C'-R/, C being the current and R the resistance between the electrodes. But in the actual case, some of the energy of the current is employed in decomposing the water and separating hydrogen from oxygen, giving rise to the back E.M.F., e. The energy so spent during the passage of a quantity Q of electricity is «Q ergs, if e and Q are measured in absolute units, or «Q x 10' ergs, if e is measured in volts and Q in coulombs, since i ■volt= 10' C.G.S. units of E.M.F., and i coulomb =10-^ C.G.S. units of current. Now we know that when i gramme of hydrogen is burnt in oxygen to form 9 grammes of water, 34,000 calories of heat are produced, and since i calorie is equivalent to 4-2 x 10' ergs (860), it follows that the combustion of i gramme of hydrogen yields 34,000 x 4-2 x 10' ergs. If we assume that to separate i gramme of hydrogen from water the same quantity of energy is required as is afforded by the union of I gramme with oxygen to form the water, then, since the electrolysis of 9 grammes of water (yielding i gramme of hydrogen) requires 96,340 coulombs (940), it follows that « X 10' X Q = g X 10' X 96,340 = 34,000 X 4-2 X 10', therefore e = 4x— 3^ 963-4 = 1-482 volt. This agrees with the E.M.F. of polarisation as measured directly. If lead electrodes are used the chemical changes are not so simple, and, as we have seen, the back E.M.F. may rise to 2^ volts. 953. Electrometallurgy. — The decomposition of salts by the battery has received a most important application in electrometallurgy, or galvano- plastics, or the art of precipitating certain metals from their solutions by the action of an electric current. The processes are twofold ; in the one, electro- typing or galvanoplastics proper, a mould is used, on which a metal, usually copper, is more or less thickly deposited ; the deposit can afterwards be de- tached, and gives a copy of the original object ; in the other, which is known as electroplating, a thin coherent coating of metal — gold or silver, for instance — is deposited on objects and remains adherent to them. The art was dis- covered independently by Spencer in England and by Jacobi in St. Petersburg. In order to obtain a galvanoplastic reproduction of a metal or any other object, a mould must first be made, on which the layer of metal is deposited by the electric current. For this purpose several substances are in use, and one or another is preferred according to circumstances. For medals and similar objects which can be submitted to pressure, gutta-percha may be used with advan- tage. The gutta-percha is softened in hot water, pressed against the object to be copied and allowed to cool, when it can be detached without difficulty. For the reproduction of engraved wood blocks or type, wax moulds are now commonly used. They are prepared by pouring into a narrow flat pan a suitable mixture of wax, tallow, and Venice turpentine, which is allowed to set, and is then carefully brushed over with very finely powdered graphite. While this composition is still somewhat soft, the wood block or type is pressed upon it either by a screw press or, still better, by hydraulic pressure. If plaster-of- Paris moulds are to be made use of, it is essential that they be 3 Q 2 964 Dynamical Electricity [953- first thoroughly saturated with wax or tallow, so as to become impervious to water. In all cases, whether the moulds be of gutta-percha or wax, or any other non-conducting substance, it is of the highest importance that the surface be brushed over very carefully with graphite, and so made a good conductor. The conducting surface thus prepared must also be in metallic contact with a tt'ire or a strip of copper by which it is connected with the negative pole of the battery. Sometimes the moulds are made of a fusible alloy (343), which may consist of 5 parts of lead, 8 of bismuth, and 3 of tin. Some of the melted alloy is poured into a shallow box, and just as it begins to solidify, the medal is placed horizontally on it in a fixed position. When the alloy has become cool, a slight shock is sufficient to detach the medal. A copper wire is then bound round the edge of the mould, by which it can be connected with the negative pole of the battery, and then the edge and the back are covered with a thin non-conducting layer of wax, so that the deposit is formed only on the mould itself. The most suitable arrangement for producing an electro-deposit of copper consists of a trouglr of glass, slate, or wood, lined with India rubber or coated with marine glue (fig. 964). This contains an acid solution of copper sulphate, and across it are stretched cop- per rods, B and D, connected re- spectively with the negative and positive poles of a battery. By their copper conductors the moulds, m, are suspended in the liquid from the negative rod B, whilst a sheet of copper, C, presenting a surface about equal to that of the moulds to be covered, is suspended from the positive rod D, at the distance of about two inches, directly opposite to them. The copper plate suspended from the positive pole not only acts as an electrode, but keeps the solution in a state of concentration, for the acid liberated at the anode dissolves the copper, and reproduces a quantity of copper sulphate equal to that decomposed by the current. The battery employed for the electric deposition of metals ought to be one of great constancy. Batteries such as Daniell's and Smee's, formerly used, have in large establishments been supplanted by accumulators, or by dynamo machines (988), which furnish the electricity at one quarter the expense, and which are specially constructed to furnish currents of small E.M.F. The density oi z. current (941) is its strength divided by the surface of the electrodes, or the number of amperes per square centimetre, and a statement Fig. 964 -954] Electrogilding 965 of this density in conjunction with a knowledge of the composition and strength of the bath is a succinct way of defining the conditions of electric deposition. The density at the electrodes has a great influence on the form in which the ions are separated out ; thus with a moderate density silver separates in a crystallised form, and at a greater one in the form of a black powder. An important industrial application is made of electrolysis in the refining; of copper. The metal is extracted by the ordinary metallurgical processes so as to yield plates containing 95 per cent, of pure copper. These plates are then used as positive electrodes in a bath of copper sulphate, and the metal is deposited in a state of perfect purity on thin sheets of pure copper, which form the negative electrode, while the impurities fall to the bottom. As the electrodes are practically identical, there is no polarisation (820), and the work of the current is solely employed in overcoming the resistance of the baths. The application of electrolysis to the extraction of metals was of limited use until the powerful currents of dynamos became available. In mountainous countries, where water-power can be had, it may in many cases be practicable to deal in situ with the extraction of metals from their ores. 954. Electrogilding. — The old method of gilding was by means of mercury. It was effected by an amalgam of gold and mercury, which was applied on the metal to be gilded. The objects thus covered were heated in a furnace, the mercury volatilised, and the gold remained in a very thin layer on the objects. The same process was used for silvering ; but they were expensive and unhealthy methods, and have now been entirely replaced by electrogilding and electrosilvering. Electrogilding only differs from the process described in the previous paragraph in that the layer is thinner and adheres more firmly. Brugnatelli, a pupil of Volta, appears to have been the first, in 1803, to observe that a body could be gilded by means of the battery and an alkaline solution of gold ; but De la Rive was the first who' really used the battery in gilding. The methods both of gilding and silver- ing owe their present high state of perfection principally to the improve- ments of Elkington, Ruolz, and others. The pieces to be gilded have to undergo three processes before gilding. The first consists in heating them so as to remove the fatty matter which has adhered to them in previous processes. As the objects to be gilded are usually of what is called gilding metal or red brass, which is a special kind of brass rich in copper, and their surface during the operation of heating becomes covered with a layer of cupric or cuprous oxide, this is removed by the second operation. For this purpose the objects, while still hot, are immersed in very dilute nitric acid, where they remain until the oxide is removed, They are then rubbed with a hard brush, washed in distilled water, and dried in gently heated sawdust. To i"emove all spots they must undergo the third process, which consists in rapidly immersing them in ordinary nitric acid, and then in a mixture of nitric acid, bay salt, and soot. When thus prepared, the objects are attached to the negative pole of r^ battery of 3 or 4 volts. They are then immersed in a bath of gold as previously described. They remain in the bath for a time, which depends on the thickness of the desired deposit. There is a great difference in the 966 Dynamical Electricity [954- composition of the baths. ' That most in use consists cf i part of gold chloride and lo parts of potassium cyanide, dissolved in 200 parts of water. In order to keep the bath in a state of concentration, a piece of gold fur- nishes the positive electrode, which dissolves in proportion as the gold dis- solved in the bath is deposited on the objects attached to the negative pole. The density of the current should not exceed 1/125, that is, -008 ampere per square centimetre of the surface of the kathode. The method which has just been described can also be used for gilding silver, bronze, German silver, &c. But other metals, such as iron, steel, zinc, tin, and lead, are very difficult to gild well. To obtain a good coating, they must first be covered with a layer of copper, by means of the battery and a bath of copper sulphate ; the copper with which they are coated is then gilded as in the previous case. The tint of the deposit is modified by adding solutions of copper or of silver to the gold bath ; the former gives a reddish and the latter a greenish tint. 955. Electrosilvering. — What has been said about gilding applies exactly to the process of electrosilvering. The difference is in the composition of the bath, which consists of 2 parts of silver cyanide and 2 parts of potas- sium cyanide, dissolved in 250 parts of water. The positive electrode con- sists of a plate of silver, which prevents the bath from becoming poorer ; its surface should be equal to the total surface of the objects to be silvered ; the pieces to be silvered, which must be well cleaned, are attached to the negative pole. It may here be observed that these processes succeed best with hot solutions, and when the baths are old. The density of the current should be about 1/300. Knowing the weight of any given metal which is transported by unit of electricity (940), it is easy to calculate the weight deposited in a given time by a current of known strength. Thus the current just specified would deposit I '34 gramme of silver per square decimetre in an hour. A deposit of one ounce of silver on a square foot of surface gives a good coating ; its thickness, jj^ inch or 0-03 mm., is about half that of thin writing paper. 956. Electric deposition of iron, nickel, cobalt, and platinum. — One of the most valuable applications of the electric deposition of metals is to what is called the steeling {acierage) of engraved copper, plates. The bath required for this purpose is obtained by suspending a large sheet of iron, connected with the positive pole of a battery, in a trough filled with a satu- rated solution of sal-ammoniac ; whilst a thin strip of iron, also immersed, is connected with the negative pole. By this means iron from the large plate is dissolved in the sal-ammoniac, while hydrogen is given off on the surface of the small one. When the bath has thus taken up a sufficient quantity of iron, an engraved copper plate is substituted for the small negative strip. A bright deposit of iron begins to form on it at once and the plate assumes the colour of a polished steel plate. The deposit thus obtained in the course of half an hour is exceedingly thin, and an impression of the plate thus covered does not seem different from one obtained from the original copper plate ; it possesses, however, an extraordinary degree of hardness, so that a \ ery large number of impressions can be taken from such a plate before the thin coating of iron is worn off. When, however, this is the case, the film -956] Electric Deposition of Iron, Nickel, &c. 967 of iron is dissolved off by dilute nitric acid, and the plate is again covered with the deposit of iron. An indefinite number of perfect impressions may, by this means, be obtained from one copper plate, without altering the original sharp condition of the engraving. The covering of metals by a deposit of nickel has of late come into use. The process is essentially the same as that just described. The bath used for the purpose can, however, be made more directly by mixing, in suitable proportions, salts of nickel with those of ammonia. The anode consists of a plate of pure nickel. A special difficulty is met with in the electric deposition of nickel, owing to the tendency of this metal to deposit in an un- even manner, and then to become detached. This difficulty is overcome by frequently removing the articles from the bath and submitting them to a polishing process. Objects coated with nickel show a highly polished surface of the charac- teristic bright colour of this metal ; the surface layer is moreover very hard and durable, and is little affected either by the atmosphere or even by sulphu- retted hydrogen. A deposit of 2 grammes of nickel on the square decimetre represents a coating 0-023 rn™- i" thickness. The deposit of cobalt has a brighter tint than that of nickel. Professor Silvanus Thompson uses a bath of cobalt sulphate or chloride, to which magnesium sulphate is added. To obtain a deposit of platinum, the hydrate of this metal is dissolved in syrupy phosphoric acid, and this solution diluted with water so that it contains i-2 to r; per cent, of the hydrate. An anode of platinum or of carbon is used, and the strength of the bath is kept constant by the addition of the hydrate. Objects made of iron, nickel, and zinc must previously be coated with copper. 968 Dynamical Electricity [957- CH AFTER X ELECTRO-MAGNETIC INDUCTION 957. Induction by currents. — We have already seen (762) that by in- duction is meant the action which electrified bodies exert at a distance on bodies in the natural state. Hitherto we have had to deal only with electro- static induction ; we shall now see that current electricity produces analogous effects. Faraday discovered this class of phenomena in 1832, and he gave the name of currents of induction or indteced currents to instantaneous currents developed in conductors lOsffl under the influence of metal- lic conductors traversed by electric currents, or by the influence of powerful mag- nets, or even by the mag- netic action of the earth ; and the currents which give rise to them he called in- ducing currents. A closed circuit, AB (fig. 965), contains a galvanometer G. A second circuit, CD, Fig. 965 parallel to the first for a great part of the length, is connected with a battery, and can be closed or broken or reversed at pleasure. The moment the circuit is closed a momentary current is produced in ABG, proceeding in the opposite direction — that is, from B to A. When the circuit is broken a momentary current is produced in the same direction as in CD — that is, from A to B. The inductive action of a current at the moment of opening or closing may be more conveniently shown by means of two coils A and B (fig. 966) of which B consists of a great length of fine wire, and A is a coil of shorter and thicker wire, and of such dimensions that it can be placed inside B. For distinction A is called the primary, B the secondary coil. A is con- nected with a battery and B with a galvanometer. If A is placed inside B, the following phenomena are observed :— i. At the moment of closing the primary circuit A, the galvanometer, by the deflection of the needle, indicates the passage in B of a current, inverse to that in A, that is, in the contrary direction ; this is only instan- -959] Induction by Magnets 969 taneous, for the needle immediately reverts to zero, and remains so as long as the inducing current passes through A. ii. At the moment at which the battery circuit is broken, there is again Fig. 966 produced in B an induced current instantaneous like the first, but direct, that is, in the same direction as the inducing current. 958. Production of induced currents by continuous ones. — Induced currents are also produced when the primary coil traversed by a current is approached to or removed from the secondary. The coil A (fig. 966) being traversed by a current, if it is suddenly placed in the coil B, the galvanometer indicates by the direction of its deflection the flow through it of an 'inverse current ; this is only instantaneous ; the needle rapidly returns to zero, and remains so as long as the small bobbin is in the large one. If it is rapidly withdrawn, the galvanometer shows that the wire is traversed by a direct current. If, instead of rapidly introducing or replacing the primary coil, this is done slowly, the galvanometer deflection is relatively small, and smaller, the slower the motion. If, instead of varying the distance of the inducing current, its strength is varied — that is, either increased by bringing additional battery power into the circuit, or diminished by increasing the resistance — an induced current is produced in the secondary wire, which is inverse if the intensity of the inducing current increases, and direct if it diminishes. 959. Induction by magnets. — It has been seen (707) that the influence of a current magnetises a steel bar ; in like manner a magnet can produce induced currents in metal circuits. Faraday showed this by means of a coil of wire, like that represented in fig. 967. The terminals being connected 970 Dynamical Electricity [959- with a galvanometer, a bar magnet is suddenly inserted in the bobbin, and the following phenomena are observed : — i. At the moment at which the magnet is introduced, the galvanometer indicates in the wire the existence of a current, the direction of which is opposed to that which circulates round the magnet, considering the latter as a solenoid on Ampere's theory (894). ii. When the magnet is withdrawn, the needle of the galvanometer, which has returned to zero, indicates the passage of a direct current. Care must be taken that the galvanometer is sufficiently far away for the bar magnet to have no direct action upon it. The inductive action of magnets may also be illustrated by the following experiment : a bar of soft iron is placed in the above bobbin and a strong magnet suddenly brought in contact with it ; the needle of the galvanometer Fig. 967 is deflected, but returns to zero when the magnet is stationary, and is de- flected in the opposite direction when it is removed. The induction is here produced by the magnetisation of the soft iron bar in the interior of the bobbin under the influence of the magnet. The same inductive effects are produced in the wires of a horseshoe electromagnet, if a strong magnet is made to rotate rapidly in front of the extremities of the wire in such a manner that its poles act successively by influence on the two branches of the electromagnet ; or also by forming two coils round a horseshoe magnet, and passing a plate of soft iron rapidly in front of the poles of the magnet ; the soft iron becoming magnetic reacts by influence on the magnet, and induced currents are produced in the wire alternately in different directions. 960. General principles of induction. — All cases of induction may be most conveniently explained by reference to the lines of force in the field due to a magnet or closed circuit. When the number of lines passing through any circuit or part of a circuit is altered, there is an induced -960] Maxwell's Rule 971 E.M.F. set up which produces a current if the circuit is closed. If the number of Unes of force passing through the circuit is increased the current is in one direction ; if diminished, in the opposite direction. Mere motion of a conductor in a magnetic field will not give rise to any induced E.M.F. unless there is a change in the number of enclosed lines. Referring to fig. 966, when the coil A is in the position shown and the battery circuit is suddenly completed, the coil becomes a magnet and some of its lines of force pass' through B ; hence an induced E.M.F. is set up in B, and as the secondary current is complete this E.M.F. produces a sudden flow of electricity through the circuit, which deflects the galvanometer needle. When A is thrust into B the number of lines passing through B is increased, and the needle, which has come to rest, is again deflected and in the same direction as before. If A is removed, or the circuit broken, the lines of force will diminish or disappear, and the throw of the galvanometer needle will be in the opposite direction. Should A contain an iron core, the induced currents are much more powerful, on account of the high permeability of iron, and the consequent large increase in the number of lines of force due to the current in A. With regard to the experiment illustrated in fig. 967, it is clear that the effect due to the approach and withdrawal of the bar magnet must be of exactly the same character as that exhibited with the Fig. 968 solenoidal coil in fig. 966. The induced electromotive force, and con- sequently the throw of the galvanometer needle, depends in all cases upon the rate of change of the enclosed lines of force. Various rules have been given for realising the direction of the induced E.M.F. Maxwell's rule is a convenient one to remember in dealing with a ring or coil ; it is as follows : — If when a corkscrew is used the direction of turning is called right-handed with regard to the direction in which the point moves, then if the direction of the lines of force through a coil corresponds to that of the point of the corkscrew, the induced E.M.F. is right-handed if the lines are diminishing in number and left-handed if increasing. Both figures (fig. 968) give the direction of the induced E.M.F. and current in the ring when the enclosed lines of force are diminishing. If a ring is moving parallel to itself in a uniform magnetic field, whether at right angles or parallel to the field, there is no alteration in the number of lines of force enclosed, and no current is produced in the ring. In the case of a straight wire forming part of a closed circuit and moving in such a way as to cut the lines of force in the field, Fleming's rule is useful. It is as follows : — Suppose the forefinger and thumb of the right hand are in the same plane at right angles to each other, and the middle 972 Dynamical Electricity [960- finger is at right angles to both ; then if the thumb represents the direc- tion of the motion, and the forefinger that of the lines of force, the middle finger will represent the direction of the electromotive force. Another rule is the following : — Imagine a person identified with the wire and looking in the direction from which the lines of force are proceeding, so that they pass through him from front to back ; if he moves to his right the induced current will be from head to foot. 961. Lenz's Law. — The direction in which the induced current flows was given by Lenz in a form which is known as Lenz's law, and is as follows : — -When a current is induced in a conductor due to the motion in its neighbourhood of a magnet or of a coil carrying a current, its direction is such that the electro-dynamic action of the induced current on the magnet or on the current in the coil is such as to oppose the motion. Thus (fig. 965) when CD carrying a current is made to approach AB, an inverse current is produced in the latter and opposite parallel currents repel each other. When JJUJA'K[}ln.. Fig. 969 CD is withdrawn from AB, a direct current is induced, and parallel currents in the same direction attract each other. In each case the electro-dynamic action between the currents tends to stop the motion which gave rise to the induced current. In fig. 967, if a north pole is thrust into a coil the direction of the induced current will be such as to give north polarity to the near end of the coil ; that is, it will be anti-clockwise. If the primary and secondary coils A and B (fig. 966) are relatively at rest, but the current in A is started, or its strength increased, the effect on B is the same as if A were moved up to its present position from a considerable distance ; and, conversely, if the current in A is diminished or stopped, the effect on B is the same as if A were removed. 962. Inductive action of the Leyden discharge. — Fig. 969 represents an apparatus devised by Matteucci, for showing the development of induced currents by the discharge of a Leyden jar. It consists of two glass plates about 12 inches in diameter, fixed vertically on the two supports A and B. On the anterior face of the plate A are coiled about 30 yards of thick copper wire C. The two ends of this wire pass through the plate, one in the centre, the other near the edge, terminating in -963] Inductive Action of Magnets on Bodies in Motion 973 two binding screws, like those represented in m and n on the plate B. To these binding screws are attached two copper wires, c and d, through which the inducing current is passed. On the face of the plate B, which is towards A, is enrolled a spiral of finer copper wire than the wire C. Its ends terminate in the binding screws m and n, on which are fixed two wires, h and i, intended to transmit the induced current. The two wires on the glass plates are not only covered with silk, but each convolution is insulated from the next one by a thick layer of shellac varnish. In order to show the production of the induced current by the discharge of a Leyden jar, one end of the wire C is connectediwith the outer coating, and the other end with the knob of the Leyden jar, as shown in the figure. When the spark passes, the electricity traversing the wire C acts by induc- Fig. 970 tion on the wire on the plate B, and produces an instantaneous current in this wire. A person holding two brass handles connected with the wire z and h receives a shbck, the intensity of which is greater in proportion as the plates A and B are nearer. The experiment may also be made by simply twisting together two lengths of a few feet of guttapercha-covered copper wire. The ends of one length being held in the hand, an electric discharge is passed through the other length. 963. Inductive action of magnets on bodies in motion. — Arago was the first to observe, in 1824, that the number of oscillations which a magnetised needle makes under the influence of the earth's magnetism, before it comes to rest, is very much lessened by the proximity of certain metallic masses, and especially of copper. This observation led Arago in 1825 to the discovery of an equally unexpected fact — that of the rotative action which a plate of copper in motion exercises on a magnet. This phenomenon may be shown by means of the apparatus represented in' fig. 970. It consists of a copper disc, M, movable about a vertical axis. On this axis is a small pulley, B, round which is coiled an endless cord, passing also round the pulley A. ' When' this is turned by the hand, the disc M may 974 Dynamical Electricity [963- be rotated with great rapidity. Above the disc is a glass plate, on which is a small pivot supporting a magnetic needle, ab. If the disc is rotated with a slow and uniform velocity, the needle is deflected in the direction of the motion, and stops at an angle of from 20° to 30° with the direction of the magnetic meridian, according to the velocity of the rotation of the disc. But if this velocity increases, the needle is ultimately deflected more than 90° ; it is then carried along, describes an entire revolution, and follows the motion of the disc as long as it lasts. Babbage and Herschell modified Arago's experiment by causing a horse- shoe magnet placed vertically to rotate below a copper disc suspended on silk threads without torsion ; the disc rotated in the same direction as the magnets. The effect decreases with the distance of the disc, and varies with its nature. The maximum effect is produced with metals : with wood, glass, water, &c., it disappears. Lastly, the effect is enfeebled if there are non-conducting breaks in the disc, especially in the direction of the radii ; but it is increased again if these breaks are soldered with any metal. Faraday made a number of experiments on the phenomena presented by the motion of conductors in a magnetic field, and was the first to give an adequate explanation of them. They depend on the circumstance that in a magnetic field currents are induced in a solid mass of metal in motion. In Arago's experiment the magnet induces currents in the disc when the latter is rotated ; and, conversely, in Babbage's experiment, when the magnet is rotated while the disc is primarily at rest. Now these induced currents, by their electrodynamic action, tend to destroy the motion which gave rise to them ; they are simple illustrations of Lenz's law ; they act in the same way as friction would do. For instance, let AB (fig. 971) be a needle oscillating over a copper disc, and suppose that in one of its oscillations it goes in the direction of the arrows from N to M. In approaching M it develops induced currents in the copper in such a direction as, by their action on the pole A, to stop the motion which gave rise to them. If A is a north pole, the currents in the neighbourhood of M circulate anti-clockwise, while near N, which it is leaving, they have a contrary direction. Tracing the currents due to the south pole B in the same way, it will be seen that in the half of the copper disc to the left the currents induced by the motion of the needle have a clockwise, and ^* 97' in the right half an opposite direction, and their effect on both sides of the needle tends to stop it. The damping effect depends upon the strength of the induced currents, and therefore on the conductance of the plate. If a radial slit is made in the plate the circulation of the induced currents is impaired, and the effect diminished. The damping effect of the copper bowl of a compass on the needle is explained by the electrodynamic action between the needle and the currents it induces in the copper as it moves. If in Arago's experiment the disc is moving from N to M (fig. 971), N approaches A and repels it, while M, moving away, attracts it ; hence the needle moves in the same direction as the disc. Faraday suspended a cube of copper to a twisted thread, which was Fig. 972 -964] Heat developed by the Motion of a Conductor 975 placed between the poles of an electromagnet (fig. 11 16). When the cube was left to itself it began to spin with great velocity, but stopped the moment a strong current was passed through the electromagnet. In fig. 972 MM are the coils wound on the two limbs of an electromagnet, and N and S are soft iron pole pieces. IfFara- day's cube, in- stead of being solid, is made up of a number of thin square plates of copper separated by varnished paper (fig. 972), and has two hooks attached, so that it can be suspended between the poles of the electromagnet with the plates either vertical or horizontal, it will be found that the magnetic field has no action when the suspension is by the hook a, for then, as the cube spins, the plates, being horizontal, do not cut the lines of force. But if the plates are vertical, the motion of the cube is at once arrested when the current is switched on. In fig. 972 C is a copper ring with a saw-cut at the bottom, which can be filled in with a copper wedge, D. If C is spun between the poles of the electromagnet, the magnetic field has no effect on it unless the wedge is introduced, for otherwise there can be no induced current in the ring ; the sides of the gap merely become, alternately, positively and negatively charged. We are now in a position to explain the deadbeat action of a suspended coil galvanometer (897). If the coil is wound on an aluminium frame, we have a complete metallic circuit in a strong magnetic field, and any motion of the frame must cause the development of induced currents, which tend to stop its motion. It must be remembered that the damping force depends upon the strength of the induced current, and this varies inversely as the resistance of the circuit ; and as aluminium is a very good conductor, the damping action is considerable. Sometimes the suspended coil is wound on a paper or pasteboard frame ; in these cases there will be no electro- magnetic damping if the circuit of the coil is open, and the damping will be a maximum when the galvanometer is short-circuited. 964. Heat developed by the motion of a conductor in a magnetic field. — We have seen in Arago's experiment that a rotating copper disc acts at a distance on a magnetic needle, communicating to it a rotatory motion, and thatacubeof copper, rotating with great velocity, is suddenly stopped by the influence of the field between the poles of a strong magnet. It is clear that, in order to prevent the rotation of the needle or of the copper, a certain mechanical force must be expended in overcoming the resistance which arises from the inductive action of the magnet. 976 Dynamical Electricity [964- This was shown in a remarkable experiment made by Foucault by means of the apparatus- represented in fig. 973. It consists of a powerful electro- magnet fixed horizontally on a table, and provided with soft iron pole- pieces, A and B. A copper disc, D, 3 inches in diameter and a quarter of an inch thick, partly projects between the pieces A and B, and can be rotated by means of a handle and a series of toothed wheels with a velocity of 1 50 to 200 turns in a second. So long as the electric circuit of the electromagnet, is broken, very little resistance is experienced in turning the handle, and when once it has begun to rotate rapidly, and is left to itself, the rotation continues in virtue of the acquired velocity. But when the current is made to pass, the disc stops almost instantaneously ; and if the handle is turned considerable resistance is felt. If, in spite of thisj the rotation is continued, the energy spent is transformed into heat, and the disc becomes heated to a remarkable extent. In an experiment made by Foucault the temperature of the disc rose from 10° to 61°, the current being produced by three Bunsen cells ; with six the resistance was such that the rotation could not long be continued. The *'<**;"'*. Fig. 973 currents thus produced in solid conductors and converted into heat are often spoken of as Foucault or eddy currents. Such currents are of constant occurrence in magneto- and dynamo- electric machines, and weaken their efficiency, because some part of the work expended is required for their production and maintenance ; and also because, being converted into heat, they increase the internal resistance of the machine. These effects are got rid of or greatly diminished by forming the arma- ture cores of insulated iron wires or thin plates parallel to the axis ; they are thus at right angles to the direction in which Foucault currents tend to form. This does not, however, prevent the heating effects due to hysteresis (907). -965] Electromotive Force in Absolute Measure 977 965. Electromotive force in absolute measure. — In fig. 974, let H repre- sent the direction of the lines of force in a uniform magnetic field, andj^let the conductor AB be moved at right angles to the field and parallel to itself ; experiment then shows that an E.M.F. is set up the direction of which is from B to A. If the conductor AB is free, electrostatic charges are produced at the ends, positive at A and negative at B, which tend to neutralise each other, and are maintained by the E.M.F. which had produced them, and which counterbalances this tendency. Suppose the ends of the conductor AB joined by a wire which is outside the field, and therefore not subject to induction. This would be the case, for instance, if AB is moved at right angles to the line joining the poles of a rH B B' C. C' ■" / 1/ 1 a' Fig. 974 Fig. 975 powerful horseshoe magnet, while the ends are connected by wires with a galvanometer at a distance ; a current is then'produced as long as the motion continues, the direction of which is BAA'B'. If in the above case / is the length of the conductor, v the velocity with which it is moved across the lines of force, and H the intensity of the field, the electromotive force « = H/t/. For unit field, and a velocity of i cm. per second, the E.M.F. per centimetre of conductor moved is i C.G.S. unit. Hence the unit electromotive force on the C.G.S. system is defined as that produced in a straight wire i centimetre long when moving with a velocity of i cm. per second in a direction at right angles to its own length and to the lines of force in a uniform magnetic field of unit intensity. Suppose, for instance, we have two parallel horizontal metal rails AB, A'B' (fig. 975), with a bar CC laid across, the ends AA' being connected with a galvanometer. The direction of the field represented by the arrow H is from front to back. If the bar CC is a metre long and moves at right angles to its own length and to the direction of the field with a uniform velocity of 20 metres per second, then, since the vertical intensity of the earth's field is 0-444 (736), the induced E.M.F. will be loo x 0-444 >< 2000 = 8-88 x 10* C.G.S. units = 8-88 x lo"* volts, sincej): volt = 10" abs. units, and if the |total resistance of the circuit is i ohm, the current C = -000888 ampere or 888 micro-amperes. 3 R 978 Dynamical Electricity [966- An illustration of a method of producing a steady current by the motion of a conductor in a magnetic field is afforded by Faraday's disc, fig. 976. It is a disc of metal rotated about a metallic axis passing through its centre and perpendicular to its plane. Suppose two brushes, one B, pressing against the axis, and the other A, against the edge of the disc, are connected by a wire, and suppose the disc be made to rotate uniformly in a uniform magnetic field H, whose direction is perpendicular to the disc. Any radius of the disc cuts, in each revolution SH lines of force, where S is the area of the disc. Hence if T is the time of one revolution, — - is equal to the number of lines cut per second, and therefore equal SM to the electromotive force, and the induced current is C = =;=, -where R is TR the total resistance in the circuit. We have already seen (891) that if a ciirrent is passed through the disc from axis to circumference as shown in fig. 887, the disc rotates in a direc- tion opposite to that of the arrow. 966. Induction by the action of the earth. — Faraday discovered that terrestrial magnetism can develop induced currents in conductors in motion. He first proved this by placing a solenoidal coil (such as A, fig. 966) with its length parallel to the dipping-needle ; on turning this helix 180° about an axis perpendicular to its length in its middle, he observed that at each turn a galvanometer connected with the two ends of the helix was deflected. The apparatus depicted in fig. 977, and known as Delezemte's circle, serves well for showing the currents produced by the inductive action of the earth. It consists of a wooden ring, RS, about a foot in diameter, fixed to an axis ■oa, about which it can be turned by means of a handle, M. The axis oa is itself fixed in a frame PQ, movable about a horizontal axis. By pointers fixed to these two axes the inclination towards the horizon of the frame PQ, and therefore of the axis oa, is indicated on a dial, b, while a second dial, c, gives the angular displacement of the ring. This ring has a groove in which is coiled a great length of insulated copper wire. The two ends of the wire are joined up with brass plates on the insulated axis, whence by means of springs and binding screws they are connected with a galvanometer. If the plane of the coil RS, being originally at right angles to the lines of the earth's magnetic field, that is, to the direction of the dip needle, is then suddenly turned through any angle, the needle of the galvanometer shows the passage of a momentary current. At first the coil is full of lines of force, the flux being «AY, where Y denotes the earth's total magnetic force, A the area (in sq. cm.) of one turn of wire, and n the number of turns. When the coil has been rotated through 90°, the magnetic flux has been diminished to zero ; hence by Maxwell's rule (960) as we look down upon the coil in fig. 977 a direct or right-handed current has been developed in it. As the rotation is con- tinued from 90° to 180° the induced current in the wire has the same direc- tion as before, for although as we look down it appears to be reversed it -967] Self-induction. Extra Current 979 must be remembered that the coil itself is reversed in position, the part marked S being now on the right and that marked R on the left. Thus, the ■current in the coil is throughout the rotation from 0° to 180° in the same direction, say, positive. Similarly from 180° to 360° the current is in the opposite direction, or negative. Placing now the coil in the position in which its plane is perpendicular to the dip needle, turn it rapidly through 180°, so rapidly that the operation is completed before the needle of the galvanometer has sensibly moved. The rush of electricity through the galvanometer acts like the discharge of a condenser, and causes a throw of the needle proportional to the mean value of the induced E.M.F., and therefore proportional to Y, the total force of the earth's magnetism. If the axis of rotation, oa, is vertical, only the horizontal component of the earth's magnetism can act, and if then the coil is sharply turned from Fig. 977 0° to 180°, and we use a reflecting galvanometer instead of that shown in the figure, the throw of the needle, as measured by the excursion of the spot of light, is a measure of the horizontal component H. Similarly, if the axis is horizontal and in the magnetic meridian, only the vertical com- ponent V acts, and is thus measured by the deflection. Hence, from two such sets of observations we may determine the magnetic ■dip in any place, for tan i = — , where i is the inclination or dip (733). The arrangement a on the frame is made to act as a commutator (986) adjusting the opposed currents so that they are in the same direction. Hence when the coil RS is rapidly rotated with uniform velocity the gal- vanometer indicates a steady unidirectional current. 967. Self-induction. Extra current. — If a closed circuit traversed by a voltaic current is broken, a scarcely perceptible spark is obtained if the wire joining the two poles is short. Further, if the observer himself forms part of the circuit by holding a pole in each hand, no shock is S R 2 98o Dynamical Electricity [967- perceived unless the current is very strong. If, on the contrary, the wire is. long, and especially if it makes a great number of turns so as to form a coil with very close folds, and still more if a soft iron bar is inserted in the coil, the spark, which is inappreciable when the circuit is closed, acquires a great intensity when it is opened, and an observer who forms part of the circuit receives a shock which is the stronger the greater the number of turns. Faraday, who discovered these phenomena, showed that they were effects- of induction ; not only does a current act inductively on a neighbouring circuit, but each winding acts inductively on the next windings of its own circuit, both on making and on breaking the circuit, by a process which is called self-induction or inductance. On making the circuit, each winding induces in the neighbouring ones a current in the opposite direction to its own — that is, an inverse current. This, which Faraday called the extras Fig. 978 current on making or the inverse extra current, diminishes the intensity of the principal current ; the effect is that the current on making does not at once attain its full strength ; starting at zero its intensity gradually rises, and only reaches that strength after a time which, though short, is appre- ciable, more especially when an electromagnet with a great number of coils forms part of the circuit. When the circuit is broken each winding acts inductively on those near it, producing a current in the same direction as its own, and forming, as it were, a prolongation of it, but of far higher electromotive force ; since the electromotive force depends upon the rapidity with which the lines of force are removed from the circuit, and this may be very great. To show the existence of this current on breaking, Faraday arranged the experiment as seen in fig. 978. Two wires from the poles E E' of a battery are connected with the terminals D and F of an electromagnet B. On the path of the wires at the points A and C are two other wires, which are con- nected with a galvanometer, G. Hence the current from the pole E branches at A into two currents, one of which traverses the galvanometer, the other the electromagnet, and both join the negative pole E'. -968] Co-efficients of Self- and Mutual-induction 981 The needle of the galvanometer, being then deflected from G to a' by the current which goes from A to C, is brought back to zero, and kept there by a stop which prevents it from turning in the direction Ga', but leaves it free in the opposite direction. On breaking contact at E, it is seen that the moment the circuit is open the needle is deflected in the direction Ga ; showing a current contrary to that which passed during the existence of the battery current — that is, the current from C to A. But the battery circuit being broken, the only remaining one is the circuit AFBDCA ; and since in the part CA the current goes from C to A, it must traverse the entire circuit in the direction AFBDC — that is, the same as the principal current. This is the extra current on opening, or direct extra current, or self-induction current. Faraday pointed out the analogy of the effects of self-induction to those of the inertia of liquids, as in the hydraulic ram, for instance. A flow ■of water in a pipe can neither be suddenly established nor suddenly stopped, and if so stopped a shock is produced due to the energy of the fluid in motion (152). But while the effects of the hydraulic ram are lessened by the bends in a pipe, the extra current is far more marked in a •coil than in a straight wire of the same length. To observe the direct extra current the conductor on which its effect is to be tried may be introduced into the circuit, by being connected in any suitable manner with the binding screws A and C (fig. 978) in the place of the galvanometer. It can thus be shown that the direct extra current gives violent shocks and bright sparks, decomposes water, melts platinum wires, and magnetises steel needles. The shock due to self-induction may be tried by attaching wires con- nected with the poles of a single Grove or storage cell to two files, which are held in the hands. On moving the point of one file over the teeth of the other, a series of shocks is obtained, due to the alternate opening and closing of the circuit. In this experiment the hands should be moistened with water to diminish the resistance of the skin. 968. Co-efficients of self- and mutual-induction. — The co-efficient, L, of self-induction or inductance of a circuit is defined as being numerically equal to the number of lines of force enclosed by the circuit when the latter is traversed by unit current. Thus, LC denotes the number of enclosed lines when the current is C ; L is a constant'iso long as the form and arrange- ment of the circuit remain the same, and so long as it contains no iron. The rate of change of LC with time is equal to the electromotive force, of self-induction. Suppose the current in a circuit to be gradually diminish- ing ; then the number of enclosed lines is diminishing also, and an E.M.F. of self-induction is set up which opposes the weakening of the current, and is equal to the rate of disappearance of the lines of force. On the other hand, if the current is rising, the E.M.F. of self-induction, which is equal to the rate at which the lines of force increase, opposes the rise. If the change in the current is i ampere per second, and the induced E.M.F. is "i volt, then L, the co-eificient of self-induction, is unity and is called a henry. Suppose there are two neighbouring circuits, such as the two coils shown in fig. 966 ; each of them when traversed by a current will be penetrated by a magnetic flux, some of the lines of which will traverse the other circuit. 982 Dynamical Electricity [968— When the currents in the two circuits are equal, the number ofUnes offeree due to either which pass through the other is the same. This number of lines, when each current is i ampere, is called the co-efficient of mutual induction, or the mutual inductance of the two circuits, and is denoted by M. "M, like L, the co-efficient of self-induction, is expressed in henrys. The mutual inductance of the circuits is i henry if an E.M.F. of i volt in one of them results from a variation of the strength of the current in the- Other at the rate of i ampere per second. In the case of a coil of wire of many turns the co-efficient of self-induc- tion varies as the square of the number of turns. A striking experiment on self-induction is to introduce a coil of wire into the circuit of an alternate current dynamo machine (985) feeding incandes- cent lamps, and, when the current is flowing, to insert suddenly a thick iron bar into, the coil. The self-induction is at once greater, and more lines of force pass through the coil. The current has to supply the energy necessary for this increase, and for a time falls in strength ; this is seen by the diminished light in the lamps. 969. Growth of a current and energ^y of the circuit. — When a circuit is completed the current does not instantaneously attain its full and final value, since the E.M.F. of the battery is opposed by that due to the self-induction of the circuit. If C ( = ^ ) is the final value of the current, the actual current at any time, /, after the circuit is completed, will depend upon the time and also upon the self-induction. Mathematical analysis shows that it is equal toC (i— e'l'V where e is the base of Napierian logarithms, _R , or 271828 ; so that C = e l is the amount by which the current falls short of its full value at any time, t. This last expression is equal to zero only when t is infinite, but it diminishes as a rule with great rapidity, and becomes sensibly equal to zero for a comparatively small value of t. When t = the value of the current is C (i — f-^), or -634 x C. The quantity R. L/R is called the time-constant of the circuit ; it is the time which must elapse from the moment of completing the circuit before the current attains to a value '634 (or nearly two-thirds) of its full strength. The time-constant is small if the inductance of the circuit is small in comparison with its resistance. On the other hand, in a circuit like that of a transformer, when the inductance is high and the resistance relatively small, the time-constant may be 5 or 10 seconds, or more. Since L/R = a time, and R is of the nature of a velocity, L = R^ is a length. If R = the C.G.S. unit of resistance, viz. a velocity of i centi- metre per second, and t = \ second, L is equal to i centimetre, and this is the C.G.S. unit of self-induction. But if R = i ohm = 10^ cm. /sec, L = 10" centimetres. Professors Ayrton and Perry proposed to call this unit a secohm, since it may be regarded as the product of a second and an ohm. Since 10^ cm. is the length of a quadrant of a great circle of the earth. Principal Lodge proposed to call the practical unit of self-induction a quadrant (or briefly, a quad). Neither of these suggestions has been -970] Resistance in Absolute Measure 983 adopted ; by international agreement the practical unit of self-induction is called a henry, after Professor Henry, of Princetown, New Jersey. Ohm's law is not applicable during the variable state which exists immediately after the completion of the circuit, for, until the current has attained its full value, only a part of the energy derived from the battery appears in the form of heat in the circuit. The remainder has been spent in establishing the magnetic field surrounding and penetrating the circuit, and remains in the form of potential energy in the field. It may be proved that this energy is equal to ^LC. Hence, if E is the E.M.F. of the battery and Q the quantity of electricity which has passed through the circuit during any time /, EQ --= C^R^ + ^LC-, C'R^ being that part of the energj- which is exhibited in the form of heat in accordance with Joule's law, and which increases with the time. The remainder, ^LC, depends only on the self-induction and the value of the current, and is independent of time when C has become constant ; in other words, energy is not required to maintain the magnetic field when it has once been established. When the circuit is broken the energy expressed by ^LC^ is given back to it, and causes the direct extra current and the brightness of the spark on breaking. 970. Resistance in absolute measure. — The first determination of the resistance of a conductor in absolute measure was made by a committee of the British Association in 1863. Before that time resistances were expressed in arbitrary units, such, for example, as the resistance of 100 yards of copper wire, or of i metre of platinum wire, of specified diameter. As there was no common standard, it was difficult to compare results obtained by different observers at different times or in different countries. Hence the desirability of finding a standard which should be the same at all times and places, and should be independent of the properties of any particular material. Now, for a steady current, we have by Ohm's law C = E/R, and to determine R in absolute measure we must have C and E in absolute measure. A current may be measured in absolute measure by a tangent galvanometer (837), when the strength of a magnetic field is known ; and an electromotive force may be determined by a method similar to that of article 965, but here, also, it is necessary to know the value of the magnetic field in which the conductor moves. In the British Association experiment C and E were measured, and the arrangement was such that the unknown magnetic fields were one and the same, and cancelled each other. The experiment consists in rotating a circular closed coil of wire, of resistance R, to be determined, about a vertical diameter. The current induced in the coil, due to cutting the horizontal lines of the earth's magnetic field, is an alternating one, its strength varying as the ordinate of a sine curve (59), but to an observer con- templating the rotating coil from the east or west side of it, the current, though varying in amount, will always be in the same direction. For instance, if the coil as seen from above is spinning right-handedly, the induced current ascends in that part of the coil which is towards the north. A compass needle suspended at the centre of the coil will be deflected Hr exactly as m the case of a tangent galvanometer. Hence C = — tan 6, in-n where H is the horizontal force, r the mean radius of the coil, n the number of turns, & the deflection of the needle, and C the mean current in absolute 984 Dynamical Electricity [970- measure. The mean current is equal to the mean electromotive force divided by the resistance. Now, as the coil turns from o° to 90'', the enclosed lines of force change by «AH, where A is the area of one turn ; in one revolution the change is 4«AH, and if T is the periodic time of revolution, the mean induced E.M.F. is 4«AH/T, and the current is 4«AH/TR. Equating the two expressions for the current, we have : Hr ^_.. n 4«AH tan 6 R TR 8«^A Fig. 979 r1 tan 6 In this expression rfi and tan 6 are mere numbers, h.\r is a length, and hence R is equal to a constant multiplied by a velocity. The resistance of the coil is, therefore, ex- pressed in terms of a velocity, and the unit resistance must be a resistance of i centi- metre per second. The practical unit is 10'' cm./sec. (850). 971. The Telephone. — To the number of instruments depending on induction may be added the telephone, an instrument devised for the transmission of articulate speech, which is equally remarkable for the sur- prising character of the results which it pro- duces, and for the simplicity of the means by which they are produced. Fig. 979 represents a perspective, and fig. 980 a section of Graham Bell's telephone. It consists essentially of a steel magnet, of about 4 inches in length by half an inch in diameter, enclosed in a wooden case. Round one end of this magnet is fitted a thin flat bobbin, BB, of fine insulated copper wire. For a magnet of this size a length of 250 metres of No. 38 wire, offering a re- sistance of 350 ohms, is well suited. The ends of this coil pass through longitudinal holes, LL, in the case, and are connected with the binding screws CC. In front of the magnet, and at a distance which can be regulated by a screw, but which is something less than a millimetre, is the essential feature of the instrument, a diaphragm, D, of soft iron, called the tympanum, not much thicker than a sheet of stout letter-paper. This diaphragm is screwed down by the mouth-piece E, which is similar to, though somewhat larger than, that of a stethoscope. Two such instruments are connected by wires. Each can be used either as sender or receiver, though in actual practice it is more convenient for each operator to have two telephones, one of which is held to the ear, while the other is used for speaking into ; the latter being larger and more powerful than the receiver. The action of the instrument depends on the production and variation -971] The Telephone 985 of electric currents, in the circuit consisting of the two instruments and the connecting wires, by variation of electromotive force, the resistance in the circuit being constant. Suppose the end of the magnet M, near the tympanum D, to be a north pole ; D, being in the field of M, is mag- netised, having south polarity at the centre and north polarity round the circumference. So long as D is at rest, the magnetic flux through the coil B is constant ; if D moves towards the magnet the flux increases, giving rise to an induced E.M.F. in the coil, which drives a current (say, negative) round the circuit ; similarly, when D returns, a positive curi-ent passes, due to the diminution in the number of lines of force enclosed by B, and when D oscillates in a periodic manner, a regular succession of positive and negative currents passes mto the line and to the receiving instrument at the other end. Here the field is alternately strengthened and weakened, causing the tympanum to vibrate in exact correspondence with that at the sending station. Suppose the simple note C, of 256 vibrations, to be sounded in front of the instru- ment ; the air particles oscillate, sound waves reach the tympanum, which is set in vibration owing to the successive increase and diminution of pressure on its front surface, and 256 current waves traverse the circuit. It might be supposed that a tympanum capable of vibrating 256 times a second would be unable to respond to a note of higher or lower pitch, but it is one of the most remarkable properties of this very simple instrument that the tym- panum can vibrate rapidly or slowly equally well. The variety of modes of vibration exhibited by a Chladni plate (284), depending on the places at which it is bowed and damped, helps us to understand this ; but the complexity of the motion of a telephone plate must be vastly greater than anything exhibited by a Chladni plate. For it must be remembered that the tones of the human voice are not simple, but each is compounded of a fundamental and a number of superposed har- monics, and as all the characteristics of the voice are faithfully reproduced at the distant instrument, it follows that each tympanum takes up all the component vibrations of a complex tone. Though the reproduction of the sound in the receiving instrument is perfect as far as articulation is concerned, it is considerably enfeebled, as might be expected. The sound has something of a metallic character, appearing as if heard through a long length of tubing, while it faithfully reproduces the characteristics of the person speaking. It does not result from a series of sharp and distinct makes and breaks, as the circuit is never broken, but there is a continuous rise and fall of current, corresponding in every gradation and inflection to the motion of the air agitated by the speaker. 986 Dynaiincal Electricity [971— The exact reproduction by one of the instruments of the note sounded into the other is illustrated by the following experiment : — Support two tele- phones horizontally, any distance apart ; connect them in circuit and remove from each its mouthpiece and tympanum, replacing them by steel tuning- forks of exactly the same frequency mounted on resonance boxes (251), If the tuning-forks are adjusted so that one prong of each is within about a millimetre of the end of the corresponding magnet, M, fig. 980, and one of them, A, is sounded by a violoncello bow, the second, B, will at once begin to vibrate. If, however, A is loaded with a little wax, and its frequency thereby slightly lowered, B will no longer respond. The vibration of B- can be seen, by placing in contact with its prong a small pellet of shellac,, suspended by a fine thread. As B is set in vibration the pellet is jerked off, and as it returns receives afiother impulse, and so on. If the forks are not exactly in unison the pellet remains quiescent. Various attempts have been made to improve the loudness of the sounds produced in the telephone, by varying the form of the various parts, and using more powerful magnets of horseshoe and circular forms ; Ader's telephone, which is largely used in France, is constructed with a circular horseshoe magnet. The amplitude of the vibration of the disc is extremely small ; according to Bosscha it must be about the ^ of the wave-length of yellow light (651). This extreme delicacy of the telephone is its drawback to speaking through ordinary telegraph circuits. The currents in adjacent wires, the vibration of the posts and of the insulators, or the passage of a cart over the streets, acts by induction on the telephone circuit, and overpowers its indications. When a telephone circuit was placed at a distance of 20 metres from a well-insulated line, through which signals were sent by means of a battery of a few cells, sounds were distinctly heard in the telephone. Speaking under such circumstances is like speaking in a storm. The powerful currents used for systems of electric lighting produce such a roar in an adjacent telephone circuit that it is impossible to speak through the telephone. The only effective way of diminishing the inductive action of adjacent systems is to have two insulated wires close to each other, forming a loop circuit. They are thus at the same distance from the inducing cir- cuit, and, as one of the wires is used for going and the other for returning, the similar influences must be in opposite directions, and therefore neu- tralise each other. Iron wires present a special difficulty in telephoning through long dis- tances. Telephone currents are alternating ones, and the self-induction of the circuit modifies both their strength and their character. This self- induction is more pronounced the longer the circuit, and with iron it is 300 times as strong as with copper. Hence for long distances a loop circuit of copper or bronze wire is used, and with such circuits it is possible to telephone through very long distances. In America, New York and Chicago, 930 miles apart, are in telephonic communication ; the greatest distance in Europe is from London to Marseilles, viA Paris. Telephones have been constructed in which the thin iron plate is re- placed by a thicker one, or by an unmagnetic one ; or if the telephone is held close to the ear, the plate can be dispensed with altogether. In the -972] The Microphone 987 latter two cases the sounds are perceived only when the spiral surrounding" the magnet can vibrate with it. A telephone may be constructed with a rod of soft iron instead of a magnet ; when the rod is held in the line of dip, and the mouthpiece is sung into, the sounds are reproduced. From its extreme sensitiveness, being perhaps the most delicate galvano- scope we possess, the telephone has become of great service in scientific research. It may be used instead of a galvanometer in a Wheatstone's bridge, in which case the cell is replaced by an intermittent source or by the secon- dary of a very small induction coil. The resistances in the arms of the bridge are modified until the sound heard in the telephone disappears or is reduced to a minimum. The method is useful for the measurement of liquid resistances, as, with an alternating source, there is practically no polarisation. Dolbear has constructed a telephone in which the electrostatic action of currents is used. It consists of two circular flat discs of metal rigidly fixed to each other in an insulated case of ebonite. One of the discs is in metallic connection with the line wire, in which are a battery and an induction coil ; in this way, while one disc is electrified positively, the other is negatively electrified by induction, and if the current is varied by speaking through a transmitter in the circuit their varying effects are faithfully reproduced, and reappear as sound vibrations on the receiver. 972. The microphone. — When the wires of an electric circuit, in which is interposed a telephone, are broken, and rest loosely on each other, sounds produced near the point of contact are reproduced and magnified in the telephone. The microphone, invented by Prof. Hughes, depends on this fact ; its arrangement may be greatly varied ; one of the simplest and most • convenient forms is that represented in fig. 981. A piece of thin wood is fitted vertically on a base of the same material ; two small rods of gas carbon CC, about \ of an inch thick, are fixed horizontally in the upright ; by means of binding screws, they are in metallic con- nection with the wires of a circuit in which are a small battery and a telephone ; and in each of them is a cavity. A third piece, D, of the same material, and- about one inch long, is pointed at each end, one of which rests in the lower cavity, ^^ JT 1 ^'^ ^"JS'-'n JSiyOTfr^ while the other pivots loosely in the upper one. When a watch is placed on the base B, its ticking is heard in the telephone with surprising '^' ' ' loudness ; the walking of a fly on the base suggests the stamping of a horse ; the scratching of a quill, the rustling of silk, the beating of the pulse, are perceived in the telephone at a distance of a hundred miles from the source of sound ; while a drop of water falling on the base has a loud crashing sound. To obtain the best results with a particular instrument, the position of the carbon must be carefully adjusted by trial ; and indeed 988 Dynamical Electricity [972- the form of the instrument itself must be variously modified for the special object in view ; in some cases great sensitiveness is required, in others great range. In order to eliminate as far as possible the effect of accidental vibrations due to the supports, the base should rest on pieces of vulcanised tubing, or on wadding. When a small disturbance is made either in the air close to the micro- phone or on its support, the contact between D and the upper and lower socket is varied, and consequently the electric resistance of the contacts, and possibly of the carbon D itself, in consequence of the slight increase or diminution of pressure upon it, alters, and the resulting variations in current cause sounds to be heard in the telephone. The form of the original microphone has been variously modified. It is desirable to increase the number of contacts, so as to avoid scratching noises. The Ader microphone consists of ten carbon rods laid in two sets of five each on three cross-pieces, also of carbon, fixed to the same piece of wood. Good results are also obtained by using small fragments or filaments of carbon. In modern telephone circuits the microphone in some form is generally employed as a sending instrument, the ordinary Bell telephone as a receiver. The usual method is to arrange a small induction coil, about the size of an ordinary cotton reel, with a primary of thick, and a longer secondary of thin, wire. The primary circuit includes battery and microphone transmitter One end of the secondary is put to earth and the other to a Bell telephone receiver and thence to the telephone line. A person holding the telephone to his ear will receive any message coming from the distant station, the cur- rents passing through the telephone and to earth. The message to be transmitted is spoken to a thin wooden sounding-board on the back of which a. number of microphone contacts, like that of fig. 981, are arranged in parallel. The changes of resistance of the carbons give rise to variations of current in the primary circuit of the induction coil, and every such change causes a corresponding induced current in the secondary which travels to the other station. Another form of transmitter consists of granulated carbon par- tially filling the space between two parallel carbon discs connected in the primary circuit. The impact of sound waves on one of the carbon discs (placed immediately behind the mouthpiece of a transmitter) alters the con- tact of the granules, and so produces the necessary changes of current. 973. The telegraphone. — This is an apparatus invented by Poulsen for recording magnetically on a steel wire a speech spoken into a telephone, the speech being recoverable from the wire after any interval of time. It is a magnetic phonograph (293). The principle of the apparatus is as follows : — A tiny horseshoe electromagnet, connected in circuit with a telephone, is made to travel with uniform velocity over a stretched steel wire, the wire lying between the two poles of the electromagnet. During the motion any words spoken into the telephone are recorded as a series of magnetic fields on the wire. To reproduce the record the magnet is connected to a tele- phone receiver and is again made to travel along the wire ; as the now magnetised wire passes between its poles it sets up currents which reproduce the recorded speech in the receiver. The record can be left on the wire and used over and over again. If it is desired to wipe out the record a steady current is passed through the magnet coils as it travels from end to end of -974] Hughes's Induction Balance 989 the recording wire ; this destroys the existing record and leaves the wire ready to receive a fresh one. In the actual instrument the steel wire is- wound spirally on a drum which can be rotated by a motor. 974. Hughes's induction balance. — The principle of this apparatus may be thus stated : — ^Suppose we have two exactly equal primary induction coils, A and A', and near them two secondary coils, B and t^lJ Bn-. .'^M -,-^ g iL B', also exactly equal, H p ' ''"' ^i r " " • W and connected up with a galvanometer, so that the coils act upon it in opposite directions. If now the current of a battery is sent through the primary coils, joined in series, the inductive effects on each of the secondary coils will be the same, and, as their action on the galvano- meter is opposed, no deflection of the needle will be produced. If, however, a piece of iron is introduced into the core of one of the secon- dary coils, the equality in the induction effects will be destroyed, and the needle of the galvano- meter at once deflected. This principle was first applied by Babbage, Herschel, and in a special apparatus by Dove Fig. 982 but the microphone and the telephone have led the inventor of the former to the invention of an apparatus which has opened out new possibilities, and has placed in the hands of the physicist an elegant and powerful engine of research, which in certain departments of investigation promises to be of great service. The form of instrument as devised by Professor Hughes is represented in fig. 982, where the essential parts are drawn to scale, though the relative distances of the parts are not so ; a and a' are the two primary coils, each of which consists of 100 metres of fine copper wire wound on a flat boxwood spool; b and b' are two secondary coils, all four coils being, in intention at least, exactly alike. The two primary coils are joined in series with a bat- tery of three or four volts, in which circuit a microphone, m, is also inserted ;. the ticking of a small clock on the table acts as make and break. The secondary coils are joined up with a telephone in such a manner that their action upon it is opposed. Now, whatever care be taken in winding the wire on the coils, it is not possible to get at the outset an exact balance. Hence, while the distance 990 Dynamical Electricity [974- between a and b is fixed, that between a' and V is not so, but can be slightly modified by means of a micrometer, screw, and thus, connection with the battery circuit having been made, a balance is obtained by slightly varying the adjustment, and the accomplishment of this is known by there being silence in the telephone. But if now any metal whatever is intro- duced into one of the secondary coils, a sound is at once heard. This arrangement is so far a simple, differential one, and furnishes as yet no means of measuring the forces brought into play, and for this purpose Hughes uses what is called a sonomder or audiometer. This consists of three similar coils, c, d, and e, placed vertically on a horizontal graduated rule along which d can be moved. By means of a switch, S, the primary coils c and e can be put in communication with the battery and microphone circuit quite independently of the balance, and it is so arranged that the ends of the coils c and e facing each other are of the same polarity ; the third coil, d, the secondary one, is connected with the telephone circuit. If these primary coils c and e were quite equal, then, when connected up with the battery circuit, no sound would be heard in the telephone, when the secondary d is exactly midway between them. But as the coil is moved from this position either towards c or e a sound is heard, due to the prepon- derance of one or the other. In practice the coils are so arranged that a balance is obtained when the secondary circuit is near one of the coils, c, for instance ; this represents a zero of sound, and as the coil d is moved nearer to ^ a sound of gradually increasing intensity is heard ; distances measured off along this line represent values of sound on an arbitrary scale. Suppose now that a balance has been obtained in the induction balance, and that the coil d in the sonometer is at zero ; no sound is then heard in the telephone when the current is switched either in one or the other circuit. But if the balance is disturbed by placing a piece of metal in the core of b, a definite continuous sound is heard. The current is then switched into the sonometer, and the secondary coil e is moved until the ear perceives the-fiame sound in both circuits. The distance then along which the coil d has been moved is thus an arbitrary measure of the effect produced. Although by the switch the transition from one circuit to the other can be effected with great rapidity, and -the ear can appreciate minute ■differences, this has not the value of a null method. Hughes has still further improved the balance by the following device, in which the sono- meter is dispensed with : — A graduated strip of zinc about 200 mm. in length by 25 mm. wide, and tapering from a thickness of 4 mm. at one end to a fine edge at the other, is made use of. The metal to be tested is placed in a plane between a and b on the left of the plate, and the strip is moved along the top of b' until a balance is obtained. The instrument is of surprising delicacy ; a milligramme of copper or a fine iron wire introduced into one of the coils which has been balanced can be loudly heard, and appreciated by direct measurement. If two shillings ■fresh from the Mint are balanced, rubbing one of them or breathing on it at once disturbs the balance. A false coin balanced against a genuine one is at once detected. The instrument furnishes a means of testing the deli- cacy of hearing ; such a piece of wire as the above, or a fine spiral of copper, furnishes a kind of test object for this purpose. -976] Inductormm. Ruhmkorff's Coil 991 CHAPTER XI PASSAGE OF ELECTRICITY THROUGH GASES 975. Inductorium. Ruhmkorff's coil. — Induced currents of high potential, and capable of producing many striking effects, are furnished by apparatus known as inductoriums, or induction coils. These present considerable variety in their construction, but all consist essentially of a hollow cylinder in which is a bar of soft iron, or bundle of iron wires, with two helices coiled round it, one connected with the poles of a battery, the circuit of which is alternately opened and closed by a self-acting arrangement, and the other serving for the development of the induced current. By means of these apparatus, and with a current of three or four amperes, physical, chemical. Fig. 983 and physiological effects are produced equal to and even transcending those obtainable with electric machines and the most powerful Leyden batteries. Of all the forms those constructed by Ruhmkorff are the most powerful Fig. 983 is a x-epresentation of one, the coil of which is about 35 cm. ip length. The primary wire is of copper, and is about 2 mm. in diameter, and 40 or 50 metres in teigth. It is coiled directly on a cylinder of cardboard, which forms the nucleus of the apparatus, and is enclosed in an insulating cylinder of ebonite. On this is tCoiled the secondary wire, which is also of copper, and is about 5 mm. in diameter. A matter of great importance in regard to these apparatus is the insulation. The wires are not merely insulated by being in the first case covered with silk, but each individual coil is separated from the rest by a layer of melted shellac. In the more recent induction coils, the secondary wire is wound in sections separated from each other by annular sheets of ebonite. The length of the secondary 992 Dynamical Electricity [975- wire varies greatly ; in the largest size hitherto made, that of the late Mr. Spottiswoode, it is as much as 280 miles, while the primary was 1,164 yards. With these great lengths the wire is thinner, about \ mm. The thinner and longer the wire the higher the potential of the induced electricity. The following is the working of the apparatus : — The current arriving by the wire P at a binding screw, rt, passes thence to the commutator C, to be afterwards described (fig. 986), from which by the binding screw b it enters the primary wire, and having traversed this, it emerges by the wire j (fig. 984). Following the direction of the arrows, it will be seen that the current ascends in the pillar i, reaches an oscillating piece of iron, o, called the hammer, descends by the anvil h, and passes into a copper plate, K, which takes it to the commutator C. It goes from there to the binding- screw c, and finally to the negative pole of the battery by the wire N. The current in the primary wire only acts inductively on the second- ary wire (957), when it is interrupted. The necessary interruption is effected by means of the oscillating hammer o (fig. 984). In the centre of the bobbin is a bundle of soft iron wires, forming together a cylinder a little longer than the bobbin, and thus projecting at the end as seen at A. When the current passes in the primary, the hammer, o, is attracted ; but immedi- ately, there being no contact between and h, the circuit is broken, the magnetisation ceases, and the hammer falls ; the current again passing, the same series of phe- nomena recommences, so that thehammer oscillates with great rapidity. A more effective current in- terrupter or make and break is shown in fig. 985. A is the soft iron hammer attached to the top of a stiff brass spring B, the tension of which can be regu- lated by a screw G. It is tipped with platinum at d. D is a brass upright with a brass screw passing through it, also tipped Fig. 984 3^^ the head E and clamped by the nut F. The primary current passes from the commutator to D, thence across the contact ab, down the spring B, and into the primary wire. As soon as the circuit is complete, A is attracted to the left by the magnetised core (not -976] Condenser 993 shown in the figure) and contact at ab is broken. The rapidity of oscillation of the vibrator and the sharpness of the break can be regulated to some extent by the screw-head G. 976. Condenser. — As the current passes thus intermittently in the primary wire of the coil, induced electromotive forces, alternately direct and inverse, are produced in the secondary wire. As the secondary wire is carefully insulated and of great length, and as the inteiTupter breaks the primary circuit with considerable sharpness, the induced electromotive force is capable of producing very powerful effects. Fizeau increased the electromotive force still more by connecting the terminals of a condenser to the two sides of the make and break. This condenser consists of sheets of tinfoil placed over each other and insulated by larger sheets of stout paper soaked in paraffin or resin (93 1 ). The whole being placed in a box at the base of the apparatus, one of the coatings is connected with one side and the other coating with the other side of the make and break in the primary circuit — that is, one coating is connected to o, the other to h (fig. 984), or one to C and the other to D (fig. 985). The capacity of the condenser sh,ould bear a relation to the self- induction of the primary circuit and the rapidity of the contact-breaker. To understand the effect of the condenser, it must be observed that at each break of the primary circuit a direct extra current is produced in it, the E.M.F. of which is sufficient to produce a large spark between the platinum terminals a and b (fig. 985), When the condenser is connected, the electric charges, instead of producing so strong a spark, pass into the condenser, but rebounding, traverse the circuit and give rise to a current through the primary contrary to that of the battery, which instantly demagnetises the soft iron core. Hence the E.M.F. induced in the secondary, which depends upon the rapidity with which the lines of force disappear, is much greater than it would be without the condenser, and the injurious effect of the spark between a and ^ is to a large extent prevented. The com/nutator serves to break contact or send the primary current in either direction. It is seen on the right of fig. 983, and fig. 986 shows a section. The ebonite cylinder. A, has brass plates, CC, on opposite sides. Against these press two elastic brass springs, joined to two binding screws, a, and c, with which are also connected the poles of the battery. The current arriving at a rises in C ; thence by a screw, y, it reaches the binding screw b and the primary winding ; then returning by the plate K, which is connected with the hammer, the current goes to C by the screw .r, descends to c, and rejoins the battery by the wire N. If, by means of the pj „, milled head, the key is turned 180 degrees, it is easy to see that exactly the opposite takes place : the current reaches the hammer by the plate K and emerges at b. If, lastly, it is only turned through 90 degrees, the elastic springs rest on the ebonite A instead of on the plate CC, and the circuit is broken. The two wires ft-om the apparatus at o and o' (fig. 983) are the two ends of 3 S 994 Dynamical Electricity [976— the secondary coil. They are connected with the thicker wires P P', so that the current can be sent in any desired direction. With large coils the hammer cannot be used, for the surfaces become so much heated as to melt. But Foucault invented a mercury contact-breaker which is free from this inconvenience, and which is an important improvement. Very powerful discharges were obtained by Spottiswoode from his coil by disconnecting the contact-breaker and sending into it the alternate currents of a powerful magneto-machine. Another form of current breaker is WehneW s eledrolyticinterruptor. It consists of an anode of stout platinum wire, projecting about a quarter of an inch from a glass tube into which it is fused, and a lead plate for kathode, the two being immersed in sulphuric acid (i of acid to 5 of water). When a current passes from a source of 20 to 100 volts the platinum glows intermittently, and the circuit is made and broken with great rapidity. A long thick spark shaped thus A is produced between the terminals of the secondary, whose frequency depends upon the size of the platinum anode, the volts applied, and the self-induction in the primary. The explanation of the action is to be found partly at least in the spheroidal state (390) intermittently assumed by the liquid in the neighbourhood of the hot platinum. 577. Effects produced by RuhmkorfFs coil. — The high potential of the electricity of induction coils has long been known, and many luminous and heating effects have been obtained by their means. But it is only since the improvements which Ruhmkorff introduced into his coil that it has been possible to obtain the large electromotive forces now common. Induced electromotive forces are produced in the secondary coil at each opening and closing of the primary. But these E.M.F.s are of very unequal intensity. When the primary circuit is closed, the E.M.F. of the battery is opposed by that due to self-induction, and the current (and with it the magnetic field) rises only gradually to its full value. But on breaking the primary circuit, owing to the action of the condenser, these same lines of force are removed with great rapidity. Hence the E.M.F. on 'break' is high and of short duration, while that on ' make ' is relatively feeble and of much longer duration. If the terminals of the secondary are brought within a millimetre of each other, and the ' make and break ' viforked by hand, it is found that a bright spark passes on break, but none at all on make. But if a galvanometer is placed in the circuit of the secondary, the opposite throws of the needle are the same on making and on breaking the primarj', showing that the quantity of electricity passing through the instrument is the same in the two cases ; hence, when the interrupter is working automatically, the needle, being equally urged in opposite directions in rapid succession, suffers no permanent deflection. A striking distance of i mm. (805) corresponds to an electromotive force of 5,490 volts ; and the striking distance of i inch, which is furnished by even a small machine, represents a potential of over 70,000 volts. 'VoB. physiological ^ik.c\s, of Ruhmkorff 's coil are very powerful ; in fact, shocks are so violent that many experimenters have been suddenly pro- strated by them. A rabbit may be killed with two Bunsen cells, and a somewhat larger number would kill a man. -977] Effects produced by Ruhnikorff's Coil 995 Fir. 987 The heating effects are also easily observed : an air thermometer is heated by the alternating currents ; if a very fine iron wire is interposed between the two ends P and P' of the secondary, this wire is immediately melted, and burns with a bright light. A curious phenomenon may here be observed, namely, that when each of the wires P and P' terminates in a \ery fine iron wire, and these two are brought near each other, the wire corresponding to the negative pole alone melts, showing that its temperature is higher. The chemical effects are very varied ; thus, according to the shape and distance of the platinum electrodes immersed in water, and to the degree of acidulation of the water, either luminous effects may be produced in water without decomposition, or the water may be de- composed and the mixed gases disengaged at the two electrodes, or the decomposition may take place, and the mixed gases separate either at a single pole or at both poles. Gases may also be decomposed or combined by the continued action of the spark from the coil. If the terminals of a small Ruhmkorff coil are connected to two platinum wires passing through an hermetically sealed tube containing air, their ends being separated by a small gap, as shown in fig. 987, moist nitrogen and oxygen combine to form nitrous acid. The luminous effects of Ruhmkorff's coil are also very remarkable, and vary according as they take place in air, in vapour, or in very rarefied gases. In air the coil produces a very bright loud spark, which, with the large coil made for the late W. Spottiswoode, has a length of 42 inches. In vacuo the effects are also remarkable. The experiment is made by connecting the two wires of the coil P and P' with the two rods of the electric ^%% (805) used for producing in vacuo the luminous effects of the electric machine. Exhaustion having been produced up to i or 2 mm. by a Fluess Pump (205), a beautiful luminous trail is produced from one knob to the other, which is virtually constant, and has the same intensity as that obtained with a powerful electric machine when the plate is rapidly turned. This experiment is shown in figs. 991 and 992. Fig. 990 represents a remarkable deviation which light undergoes when the hand is presented to the t.gg. The positive pole shows the greater brilliancy ; its light is of a fiery red, while that of the negati\e pole is of a feeble violet colour ; moreover, the latter extends along all the length of the negative rod, which is not the case with the positive pole. The coil also produces mechanical effects so powerful that, with the . largest apparatus, glass plates two inches thick have been perforated. This result, however, is not obtained by a single discharge, but by several succes- sive discharges. The experiment is arranged as shown in fig. 988. The two ends of the secondary wire are connected with the binding screws a and b ; by means of a copper wire, the terminal a is connected with the lower part of an apparatus for piercing glass like that already described (fig. 793) ; the other terminal is 3 S2 996 Dynamical Electricity [977- attached to the other conductor by a wire d. The latter is insulated in a large glass tube r, filled with shellac, which is run in while in a state of fusion. Between the two conductors is the glass to be perforated, V. When this presents too great a resistance, there is danger lest the spark pass in the coil itself, perforating the insulating layers which separate the wires, and then Fig. 988 the coil is destroyed. To avoid this, two wires, e and c, connect the poles of the coil with two metallic rods whose distance from each other can be regii» lated. If then the spark cannot penetrate through the glass, it strikes across, and the coil is not injured. The coil can also be used to charge Leyden jars. With a large coil giving sparks of 6 to 8 inches, and with 6 large Bunsen cells, Ruhmkorff Fig. 989 chai"ged batteries of 6 jars each, having about 3 scjuare yards of coated surface. The experiment with a single Leyden jar (fig. 989) is made as follows : — The coatings of the latter are in connection with the poles of the coil by the wires d and /, and these same poles are also connected, by means of the wires e and c, with the two horizontal rods of a universal discharger -979] Geisslei'-'s Tubes 997 (fig. 772). The jar is then being constantly charged by the wires z and d, sometimes in one direction and sometimes in another, and as constantly discharged by the wires e and c ; the discharges from iu to w taking place as sparks two or three inches in length, very luminous, and producing a deafen- ing sound. The discharges of the jar take place in one direction only, since the D.P. between ;// and n at ' make' of primary is insufficient to produce a spark. 978. Stratification of the electric light. — Quet observed, in studying the electric light which Ruhmkorff's coil gives in a vacuum, that if some of the vapour of turpentine, wood spirit, alcohol, or carbon bisulphide, &c., is introduced into the vessel before exhaustion, the aspect of' the light is Fig. 990 Fig. 992 totally modified. It appears then like a series of alternately bright and dark zones, forming a pile of electric light between the two electrodes (fig. 991). In this experiment it follows, from the discontinuity of the current of induction, that the light is not continuous, but consists of a series of dis- charges which are nearer each other in proportion as the hammer A (fig. 985) oscillates more rapidly. The light of the positive pole is most frequently red, and that of the negative pole violet. The tint varies, however, with the vapour or gas in the globe. 979. Geissler's tubes. — The brilliancy and beauty of the stratification of the electric light are most remarkable when the discharge of the 998 Dynamical Electricity [979- Ruhmkorff coil takes place in glass lubes containing a highly rarefied vapour or gas. These phenomena, which were originally investigated by Gassiot, are produced by means of sealed glass tubes first constructed by Geissler, of Bonn, and generally known as Geissler' s tubes (589). The tubes are filled with different gases or vapours, and are then exhausted, so that the pressure does not exceed half a millimetre. At the ends of the tubes two platinum wires are fused into the glass. When the two platinum wires are connected with the ends of a Ruhm- korff coil, magnificent lustrous strise, separated by dark bands, are pro- duced throughout the tube. These striae vary in shape, colour, and lustre with the degree of the vacuum, the nature of the gas or vapour, and the dimensions of the tube. The phenomenon has occasionally a still more brilliant aspect from the fluorescence which the electric discharge excites in the glass. Fig. 993 shows the striae in carbonic acid under a quarter of a millimetre pressure ; the colour is greenish, and the striae have not the same form as in hydrogen. In nitrogen the light is orange yellow. Fig. 993 Pliicker found that the light in a Geissler's tube did not depend on the substance of the electrodes, but on the nature of the gas or vapour in the tube. He found that the lights furnished by hydrogen, nitrogen, carbonic oxide, &c., give different spectra when they are decomposed by a prism. 980. De la Rue and Miiller's experiments. — These physicists made a very extensive and elaborate series of experiments on the stratification of the electric light by means of the currents produced by their battery (826). They employed for some of these experiments as many as 14,400 cells, which is a battery of the highest electromotive force ever put together. It is impossible to attempt to describe here more than a few of the results obtained. All the strata start from the positive pole. For a definite pressure an aureole is formed at the positi^•e pole ; with a diminished pressure this detaches itself, is succeeded by others, and so on. One of the most curious results is the definite and stationary character of the striae for given conditions : they are remarkably permanent, and seem almost as if they could be manipulated ; a single stratum may be seen fall- ing down a tube like a feather in a \acuum, or like a drop of water. -981] ■ Kathode Rays 999 The length of the spark between two terminals varies with the square of the number of cells ; thus while i,ooo cells give a spark of 0-0051 inch under ordinary atmospheric pressure, 11,000 cells give a spark of 0-62 inch. With an increase of exhaustion the potential necessary to cause a discharge to pass diminishes to a certain pressure which represents an exhaustion of least resistance ; from this it again increases, and the strata thicken and diminish in number until a point is reached at which no discharge takes place, however high be the potential. A change in the current often produces an entire change in the colour of the stratification ; thus in hydrogen the change is from blue to pink, due to rise ox fall of current. If the discharge is irregular and the strata indistinct, an alteration in the strength of the current makes the strata distinct and steady. Even when the strata are apparently quite steady and permanent, a pulsation may be detected in, the current by means of the telephone. The colour of the discharge in one and the same gas greatly depends on the degree of rarefaction. The least resistance to the discharge in hydrogen, and when its brilliancy is greatest, is at a pressure of 0'642 mm. or 845 M ( M is a very convenient symbol for the millionth of an atmosphere). When the rarefaction has attained 0-002 mm. or 3 M, the discharge only just passes even with a potential of 11,330 volts ; while with an exhaustion of 0-000055 mm., the nearest approach to a perfect vacuum ever attained, not only is there no discharge due to the large battery employed, but the i-inch spark of an induction coil does not pass. At a given pressure, air offers a greater resistance than hydrogen ; a spark which passes in hydrogen across a distance of 5 '6 mm. will strike across a distance of only 3 jnm. in air. In air at a pressure of 62 mm., which corresponds to an atmospheric height of 12-4 miles, the electric discharge has the carmine tint so often seen in the display of the aurora borealis (1044) ; at a pressure of 1-5 mm., corresponding to a height of 30-96 miles, it is salmon-coloured ; and at a pressure of 0-8 mm., representing a height of 33-96 miles, it is of a pale white. Under a pressure of 0-379 mm. the discharge has the greatest brilliancy. This represents a height of 37-67 miles, and would be visible at a distance of 585 miles : it is probably the upper limit of the height, though on the other hand it is pos- sible that the discharge may sometimes take place at a height of a few thousand feet. 981. Kathode rays. — The phenomena of the electric discharge in highly rarefied gases have been examined by Hittorf and by Sir W. Crookes ; the most complete and remarkable experiments are those due to the latter. When the wires from a Ruhmkorff coil or from an influence machine are connected up with a vacuum tube, a discharge passes ; if the air has been rarefied to about -^^^ of an atmosphere, the negative pole is surrounded by a faint bluish light, the glow light, while fron) the positive electrode, the anode, a peach-blossom coloured stream of light passes, filling the greater part of the tube, being separated from the glow light of the anode by a dark space. The stream of light appears continuous, but when viewed in a rotating mirror it is seen to be stratified, that is, made up of alternate dark and bright spaces. This stream of light from the anode has the character of a movable conductor, and is attracted or repelled by a magnet. 1000 Dynamical Electricity [981- As the rarefaction proceeds the glow hght of the kathode and the dark space extend continually farther towards the anode, the positive light receding in the same measure ; this goes on with increasing rarefaction until the positive light wholly disap- pears, and the rays from the kathode entirely fill the tube. Such rays are known as kath- ode rays and have many strik- ing peculiarities. The light is faint, but when it strikes against the glass at the opposite end of the tube it ex- cites the bright- est fluorescence, with ■ a colour which is affected by the nature of the glass. The rays proceed from the kathode in straight lines, and do not follow any bends in the tubes. This rectilinear propagation is well illustrated by the following experiment of Crookes. In fig. 994, A, the negative pole of the induction coil is connected with the electrode a;, which is made of aluminium, and forms a slightly con- cave-mirror. If the exhaustion is not more than 2 mm. pressure, and the positive pole is connected successively with the electrodes b, c, d, the dis- charge takes place in curved lines as shown in the figure. But when the rarefaction is exceedingly great, about a millionth of an atmosphere, the appearance is that presented in fig. 994, B. With whatever elec- trode the positive pole is connected, the rays proceed from the anode in straight lines, cross in the centre of curvature of the mirror, and, strik- ing against the opposite side, excite there the most brilliant fluorescence. The phenomena occur as if par- ticles were shot from the negative electrode at right angles to the svirface. Thus in fig. 995 the kathode D is a small slightly convex mirror of aluminium, while c is a cross of aluminium Fig. 994 Fig. 995 -981] Kathode Rays lOOI or mica which is so fastened by a small joint that it can be raised or lowered. When the discharge passes the kathode rays proceed in straight lines and impinging on the glass make the whole of it fluorescent except that portion corresponding to the cross, which thus throws a shadow. If now the cross c is lowered, the part which was previously in shadow is now more brightly luminous than the rest, so that a bright cross stands out on a less bright ground. The kathode rays can also produce mechanical effects favouring the \iew of the material character of these radiations. A Geissler's tube (fig. 996) is constructed with a pair of glass rails in it, on which rolls the axis of a light wheel, on the spokes of which are mica vanes. If now the discharge is directed against the top . of the vanes, the wheel moves along towards the anode. The experiment represented in fig. 997 shows the very great heat which kathode rays can produce ; a is the negative electrode in the form of a concave mirror, b a strip of platinum Fig. 996 Fis;, 997 foil, with a sufficiently powerful induction coil the platinum can be made white-hot or even melted. Some of the most beautiful of these experiments are those made by directing the discharge on various precious stones. In these circumstances diamond emits a splendid green fluorescence, ruby a brilliant red, emerald a carmine, and so forth. The electric discharge does not pass through a vacuum, as is shown by the following experiment : — A small tube containing caustic potash is fused to a Geissler's tube connected with a Sprengel pump. By continual exhaustion while the caustic potash is being heated, as complete a vacuum as possible is made and the tube sealed. The last minute trace of aqueous vapour is absorbed by the caustic potash as it cools. In this complete vacuum the discharge, however strong, no longer passes ; the vacuum acts as a complete non-conductor. If, however, the caustic potash is gently heated, a trace of aqueous vapour is given off, and a green fluorescent light flashes along the tube ; as the heating is continued and the vapour becomes denser we get the stratification, until ultimately the electricity passes along the tube in the form of a narrow I002 Dynamical Electricity [981- purple line. If the tube is allowed again to cool, the phenomena reproduce themselves in the reverse order. The phenomena here described are regarded by Crookes as due to an ultra-gaseous state, which he calls radiant matter. In gas under the ordinary pressure the average free path of a molecule of air is o-oooi mm. ; as the gas is more rarefied the length of the path increases, so that with the high degrees of exhaustion which Crookes employs in his later experi- ments — as much as the one twenty-millionth of an atmosphere — the length of the mean path is so much increased that its dimensions are comparable with those of the vessel, and along with this increase the number of inter- molecular shocks diminishes in a corresponding ratio. It is to this con- dition, in which the molecules move forward with their own motion, and, striking against the sides, give rise to the fluorescence, that Crookes accounts for the effects produced. It was shown by Perrin that the kathode rays carry negative electricity with them, and J. J. Thomson found that when the rays are deflected by a magnet the negative electrification follows the path of the deflected rays. Crookes' theory of the construction of the kathode rays is the best explanation yet offered of the observed phenomena, and is generally adopted in this country. Many physicists, however, chiefly on the Continent, regard the kathode rays as waves on the ether, that is, of the nature of light, relying on the fact that they can pass through a thin layer of solid material. This hypothesis would explain the fluorescent effects and the motion of the wheel in fig. 996, but seems inconsistent with the observed fact that the rays are deflected in a magnetic field, carrying their negative electrification with them. 982. Lenard rays. — It was found by Lenard that the effects of the radiation from the kathode in a highly exhausted tube can be perceived outside the tube. He made a small aperture in the end of a tube opposite the kathodes, and closed it by thin aluminium foil. When this tube was exhausted to about the one-millionth of an atmosphere, the kathode rays passed through the window of aluminium into the air, causing a faint bluish light which had no fixed boundary but did not extend to more than 5 cm. In these circumstances each point of the aluminium window becomes a new source of rays, which start from it in Straight lines in all directions, and are photographically active. Air behaves to these kathode rays like a turbid medium. Lenard regards these rays as a phenomenon of the ether, and not as due to the existence of ordinary matter in the tube. 983. Rbntgen rays. — Rontgen surrounded a tube, in which kathode rays were formed, by an envelope of black cardboard, and observed that a screen coated with barium platinocyanide, brought near the envelope, became highly fluorescent, whether the coated or uncoated side of the screen was presented. The effect was produced even at a distance of two metres. This effect is due to what have been called X or Rontgen rays, and must be considered as originating in that portion of the tube which fluoresces in consequence of its being struck by the kathode rays ; and from this surface the X rays spread in all directions. They are not identical with the kathode rays, though produced by them. Unlike the kathode rays, they are not deflected by a magnet ; they pass -984] Becquerel Rays 1003 readily through paper, ^vood, leather, and ebonite. Different metals trans- mit them in very \'arious proportions ; for example, an aluminium plate 3-5 mm. thick ; zinc, o-i mm. ; lead, 0-05 mm. ; and platinum o-oi8 mm. were all about equally transparent. When passed through prisms of aluminium or ebonite they are not refracted, nor are they concentrated by a lens ; they do not seem to be reflected regularly. They act on ordinary sensitive dry plates even when in a closed slide, and even also when this is wrapped in black paper. To protect such a plate from the action of the rays, the slide must be wrapped in lead foil. If the hand is held over a sensitive plate contained in a slide, and exposed to the rays, the plate on development shows an image of the skeleton of the hand, for the rays pass with more difficulty through the bones than through the soft parts of the hand. A number of important applications to surgery have already been made. The form of tube which has been found best for producing these rays is shown in fig. gg8. A and K are the anode and kathode respectively, K being a disc of aluminium rendered con- cave, with its centre of curvature at the centre of the platinum plate A, which is inclined at 45° to the axis of the tube. When the tube is sufficiently exhausted kathode rays proceeding from K are con- centrated on a small area of A, and from Fig. 998 this Rontgen rays proceed in straight lines, chiefly in the direction of the arrow. Such a tube is called a focus- One of the most remarkable properties of Rontgen rays is their power of rendering air a conductor of electricity. If the focus-tube and induction coil are placed inside a metal box, in which an opening is made in front of the focus-tube, and the opening closed by a thin aluminium window, the Rontgen rays can only escape through the window. When a charged electroscope is placed in front of the window and the coil is excited, the leaves at once collapse, even when the electroscope is some distance away, the charge escaping through the conducting air. The air appears to retain its conductivity for some time, for though the electroscope,'when placed on one side out of the line of discharge of the rays, is unaffected when the coil is turned on, the leaves at once collapse when the Rontgenised air is blown by a bellows on the cap. Positive and negative electricity are discharged with equal facility. Wlien knobs connected to the two coatings of a charged Leyden jar are at such a distance apart that no discharge occurs, sparks will at once pass between the knobs when the jar is placed in the path of the rays. Non-conductors, as well as conductors, are acted on ; a rod of excited sealing-wax or glass at once loses its charge when held near the focus- tube. 984. Becquerel rays. — Becquerel found that metallic uranium, as well as its salts, both in the solid and liquid condition, emits radiation very similar in its properties to Rontgen radiation. This Becquerel radiation can pass through substances opaque to ordinary light, and affect a photographic plate ; it also renders air through which it passes a conductor of electricity. I004 Dynamical Electricity [SSI- Uranium compounds appear to emit this radiation with unimpaired energy for months, though kept in the dark. Uranium radiation, though it has many properties in common with Rontgen radiation, is quite distinct from it, for it can be reflected, refracted, and polarised, and is certainly a form of light. Rontgen rays differ from ordinary light in that they are not refracted when passing from one medium to another, and they cannot be polarised or made to exhibit interference phenomena. Ultra-violet light has the power, also, under certain conditions, of rendering air a conductor of electricity. A freshly cleaned plate of zinc, when charged with negative electricity, loses its charge when ultra- violet light falls upon it. Ultra-\iolet light is produced by burning magnesium, or by the electric arc (better with zinc in place of one of the carbons) ; solar light is not rich in ultra-violet rays. Elster and Geitel showed that the more electropositive metals — potassium, sodium, and rubidium — lose a negative charge under the influence of ordinary daylight. -985] Alternate Cun'cnts * 1005 CHAPTER XII. MAGNETO- AND DYNAMO-ELECTRIC MACHINES 985. Alternate currents.^We have seen that when a coil such as that represented in fig. 976 is rotated in a magnetic field, induced currents are developed in it. When the terminals of the coil are connected to a galvano- meter and the circuit then closed, the current produced follows the same variations as the E.M.F., since the resistance is constant, or it would do so if there were no such thing as self-induction. The eflfect of self-induction is to cause the current to lag behind the electromotive force. Self-induction opposes any change in the current, retarding both its rise and fall, and is a maximum when the current is zero, and zero when the current is a maximum. It thus comes about that the current reaches its maximum a little after the E.M.F. has passed its maximum, the /a^ being constant throughout the cycle. Such currents are called alternate or alternating currents, and are, when their changes follow the sine law, further known as si7tusoidal currents. Suppose the field to be horizontal and the coil to rotate uniformly about a horizontal axis perpendicular to the lines of force. The E.M.F. at any moment is equal to the rate at which the lines of force are being cut, or what comes to the same thing, the E.M.F. is equal to the rate of variation of the enclosed lines of force. Now when the coil is vertical, although the number of lines enclosed is a maximum, they are (at the moment of verticality) undergoing no variation ; hence the E.M.F, is zero. On the other hand, when the coil is horizontal it encloses (at the moment) no lines ; just before this position is reached the lines are passing through in one direction, just after it is left they pass through in the opposite direction, and it is easy to show that the rate of charge is greater in this position than in any other. Thus, as the coil rotates the induced E.M.F. increases from zero to a maximum in the first quadrant, and falls to zero again in the second quadrant ; as the coil turns through the third and fourth quadrants the same changes occur, but with reversed sign. These changes are represented graphically by the sine curve XY of fig. 45, and the E.M.F. at any moment is proportional to the sine of the angle the coil has turned through from the vertical. If ^ represents the E.M.F. when the coil has turned through an angle 8, and E the maximum E.M.F., e='E. sm. 6 = Esin//(59), if p is the uniform angular velocity with which the coil is rotating, and t the time measured from the zero position. It might be thought that the maximum value of the current would be iOo6 * Dynamical Electricity [985- equal to the maximum value of the E.M.F. divided by the resistance of the circuit, in accordance with Ohm's law. But this is not so ; self-induction, by continually opposing any change in the current, gives rise to what is ■equivalent to an extra resistance, which is compounded with the true or ohmic resistance, the combination being called the impedance. The impedance of a circuit may be shown to be equal to v^R'^+^-L-, where R is the ohmic resistance, L the inductance, and^ the angular velocity of the rotating coil ; p = 2TrJi where ?z is the number of revolutions per second. The E.M.F. and current vary from o to a maximum ; the mean or average value of either may be shown to be equal to -, or -637 of its maximum. If E is the maximum TT value of the impressed 'E..M..7 ., that is, the E.M.F. applied to the circuit, and <^ the angle by which the current lags behind the E.M.F., we shall have C = — ■ and tan d) = ?- ; ^R2+/2L= R , 1 r .. average value of E.M.F. also, average value of current = 5_ ^ impedance Alternate currents are usually measured by some form of electrodynamo- meter (896), since an ordinary suspended-needle or suspended-coil galvano- meter would be useless for the purpose. The angle through which the torsion head of the electrodynamometer must be moved to bring the movable coil to its initial position varies as the square of the current, and therefore is the same for a given current whether it is positive or negative. If the current is sinu- soidal, the instrument indicates the mean value of its square, and the square root of the angle through which the torsion head has been turned is pro- pcrtional, not to the mean current, but to the square root of the mean value of its square, called the square root of mean square. This is the effective current, and is equal to the continuous current which would give the same instrumental reading. 986. Mag'neto-electric machine. — After the discovery of magneto- electric induction, several attempts were made to produce an uninterrupted series of sparks by rotating a coil in a magnetic field. Apparatus for this purpose were devised by Pixii and Ritchie, and subsecjuently by Saxton, Ettinghausen, and Clarke. Fig. 999 represents that invented by Clarke. It consists of a powerful horseshoe magnetic battery, A, fixed against a vertical wooden support. In front of this is an electromagnet, BB', whose soft iron cores are con- nected by the iron yoke V, while a similar plate of brass joins the pole-ends of the cores and forms a support for the rotating spindle. This spindle ter- minates at one end in a commutator qo, and at the other in a pulley connected by an endless band to the driving wheel. The wire of the electromagnet is, of course, wound in opposite directions on the two bobbins B and B' ; one of its free ends is joined through the spindle to the brass ferrule o, and the other to a ferrule q which is insulated from the axis. The springs b and c carry off the induced current ; they are always in connection with the ends of the wire if they press respectively against the brass rings o and q. The spring a is only used when it is ■desired to effect a sharp break in the circuit. -986] Magneto-electric Machine 1007 When the electromagnet turns, its two branches become alternately magnetised in opposite directions under the influence of the magnet A. Suppose in the position shown in the figure, B is opposite the north pole of the magnetic battery A, the lines of force leaving this pole pass through the air-gap, the core of B, the yoke V, the core of B', and the air-gap to the south pole of A, and then through the magnet A to the starting-point, so completing the magnetic circuit. The electromagnet in this position con- tains more lines of force than in any other ; as soon as it begins to move, say, anti-clockwise, the number of lines diminishes, and when it has turned through 90°, so that the yoke V is vertical, no lines pass through it. When this position is passed the number of lines begins to increase, but in the opposite direction, and reaches a maximum when another quarter turn has Fig. 999 been made. But a httle consideration will show that the direction of the electromotive force in the wire on the bobbins is the same throughout this half-turn, its amount being zero in the t\\o horizontal positions, and a maxi- mum in the vertical. During the second half of the revolution exactly the same changes recur, but the sign of the induced E.M.F. is reversed. If the circuit is completed by joining the springs b and c by a conductor, we have alternating currents produced in it which are approximately sinusoidal. A galvanometer included in the circuit will show little or no deflection, since the flow of electricity through it is as much in one direction as in the opposite. ioo8 Dynamical Electricity For physiological effects copper spirals are fixed at in and n, and the experimenter, holding the handles p and p' in his moistened hands, feels a sharp shock at each half-revolution, the intensity of which depends on the velocity of rotation. The muscles contract with such force that they cease to obey the will, and the hands can with difficulty be detached. With an apparatus of large dimensions a continuance of the shock is unendurable. By the use of a ticjo-part commutator the current may be rectified — that is, the direction may be changed at every half-revolution, so that, although the current is not constant, it has always the same direction. It consists of a brass ferrule on the insulated axis, split diametrically, so as to be reduced to two half-cylinders insulated from each other, and from the axis of rotation (fig. I coo). The two parts of the commutator are connected to the two ends of the wire forming the electromagnet. It will be seen from fig. looo that, as the coils rotate, each spring touches one part of the commutator during- half the revolution, and the other part during the second half ; and the gaps are so placed on the axis that the change of contact of the springs from the one to the other takes place at the moment when the direction of the current is changing, that is, when V is horizontal. Fig. looo shows the arrangement for the decomposition of water. The principle of Clarke's machine was subsequently utilised in large magneto-electric machines for the production of the electric light, the machines of NoUet and de Meritens being well-known examples. In these the single magnetic battery and pair of coils of Clarke's machine were replaced by a considerable number of batteries arranged on a circular or cylindrical frame, with a corresponding number of coils with iron cores. In modern machines permanent steel magnets are dispensed with, and the necessary magnetic fields are produced by electromagnets, called the field magnets, actuated from some independent source, either a battery or more generally a direct-current dynamo. Fig. looi is a diagrammatic picture giving the arrangement of the field magnets and rotating; coils, called the armature, in a type of alternating- current machine adopted by Siemens. The magnetic field is produced by two sets of cylindrical electromagnets, whose cores are securely fixed to two circular cast-iron frames. Three pairs of coils are shown in the figure, and the coils are connected in such a way that the exciting current makes the ends of the cores which face each other of opposite polarity, as well as those which are side by side on the same ring. Thus, the lines of force from any N pole pass to the S pole opposite, as well as to SS poles on either side of N. The armature coils, shown in the figure as circular turns of wire, are in reality pear-shaped coils wound over wooden cores, and arranged on the circumference of a wheel which is mounted on the shaft and can be rotated at any desired speed. The coils in rotating cut through a succession of strong magnetic fields, alternating in direction. Since in any adjacent pair of coils the fields are opposite, the coils must be wound as shown in the figure, in order that the currents induced in neighbouring coils may be in the same direction. Suppose the direction of rotation of the armature coils (fig. looi) is anti- clockwise, then the coils are just leaving the pole-pieces. In each coil the -987] Siemens' s Armature 1009 number of enclosed lines is diminishing, and, therefore, applying the rule of article 960, it will be found that the dii-ection of the induced current is that shown in the figure. The E.M.F. increases until each coil reaches a position midway between the pole-pieces, the number of enclosed lines being then a minimum ; when the coil has reached the next pole-piece the E.M.F. is zero. The number of alternations is equal to the number of coils on either frame, and the change of sign takes place when the armature coils are just over the pole ends of the field magnet. Fig. looi {From Slingo aitd Brooker's ' Electrical Engineering*) The induced E.M.F. varies, as we have seen, with the ordinate of a sine curve ; its average value, since it depends upon the rate at which the armature coils cut the lines of force due to the field magnets, must vary with the number of lines emanating from each field pole, and with the number of alternations per second, and this latter factor is equal to the number of revolutions per second multiplied by the number of pairs of poles. If, then, N is the number of lines emanating from each pole,/ the number of pairs of poles, and V the number of revolutions per second, the average E.M.F. is proportional to N/V. 987. Siemens's armature. — Werner Siemens devised a cylindrical arma- ture for magneto-electric machines, in which the insulated wire is wound lengthwise on the core, instead of transversely, as is usually the case. It consists of a soft iron rod or cylinder, AB (fig. 1002), from one foot to three feet in length. A deep groove is cut in this cylinder and on the ends, in which is coiled the insulated wire, as shown in section in fig. 1003. To 3T lOIO Dynamical Electricity [987- the two ends of the cylinder, brass discs, E and D, are secured. With E is connected a commutator C, consisting of a steel sleeve cut obliquely into two parts which are insulated from each other and from the axis of rotation, and connected respectively with the two ends of the wire. On the other disc is a pulley, fi, round which passes a cord, so that the bobbin revolves very rapidly on the two pivots. If the coil is made to rotate rapidly between the opposite poles of magnetised masses, then as the segments A and B become alternately magnetised and demagnetised, their induction produces in the wire a series of currents alternately positive and negative, as in Clarke's apparatus (986). Fig. 1002 When these currents are collected in a commutator which adjusts them — that is, sends all the positive currents on one spring and all the negative on another — these springs become the positive and negative terminals of a direct-current machine. The magnetic field in which the armature rotates may be produced by an electromagnet as well as by permanent steel magnets. Fig. 1003 shows a section of such an arrangement ; AA are the iron plates or cases on which the wire is wound, and CC the iron pole-pieces separated by non-magnetic metal, OO. 988. Dynamo-electric machines. — A «| ' { 7tMi^^\l(f'Btt^ great advance was made by the discovery \\ ''"'^"'"^ ipffj™ °^ ^^ principle of the reaction of a cur- l/i'V^S^^P/'^lBP^ "^^^^ °^ itself — a discovery made by Dr. Werner Siemens and Sir C. Wheatstone independently of each other, and almost simultaneously. When an armature is rotating between the poles of a horse- shoe electromagnet through the coils of which no current passes, since there is no magnetic field there will be no induced E.M.F. in the armature. But iron which has once been magnetised almost always retains some trace of residual magnetism, and consequently there will generally be a magnetic field — possibly very feeble — between the poles of an electromagnet. The dynamo principle consists in connecting the armature circuit and the field-magnet circuit, so that any current developed in the armature may pass, wholly or in part, through the field-magnet coils. The result will be that any current induced in the armature, due to the slight residual magnetism of the field magnets, will also pass through the field-magnet coils and strengthen the field, thereby increasing the induced current, which again reacts on the field, and so on. Thus a trace of Fig. 1003 -989] Gramme Ring lOII residual magnetism is sufficient to start the apparatus, and the current then goes on increasing as the rotation is continued, and is indeed only limited by the limit to the magnetisation of the iron, by the heating of the wires and the bearings, and by the difficulty of properly insulating the coils when such powerful currents are used. Apparatus which transform mechanical energy into the energy of electric currents, or conversely, are known as dynamo-electric machines, or briefly dynamos. The name was originally restricted to self-exciting machines — that is, to those in which no permanent magnets, or extraneous means of excitement, were employed. It is now used without limitation for electric generators or motors. Dynamo machines are called dynamo-electric generators when they convert mechanical into electric energy, and dynamo-electric motors when they are arranged to produce mechanical power at the expense of an electric current. 989. Gramme ring. — We have seen how, by the use of a two-part com- mutator, the alternate currents developed by the rotation of a coil of wire in Fig. 1004 a magnetic field may be rectified. But though the current is thus rendered unidirectional, it is of very varying strength, changing from zero to a maximum, and again to zero, twice over in each i-evolution. By the applica- tion of a principle discovered by Pacinotti in 1862, and subsequently and independently by Gramme, it is possible to attain from a revolving coil a practically continuous and steady current. One form of armature in which the principle is embodied is known as a Gramme ring. The principle of the Gramme ring will be understood from the following explanation : — Let N and S (fig. 1004) be the poles of the field magnets, and we will suppose the field to be uniform, as represented by uniformly 3TI IOI2 Dynamical Electricity [989- spaced lines drawn from N to S. A is a wooden ring wound with an endless wire, capable of turning about an axis through its centre at right angles to the plane of the paper, with uniform angular velocity. Further, let us suppose the wire to be bare copper wire, the successive turns being close together, but not touching, and sufificiently insulated from each other by the wood on which they are wound ; for simplicity, only i6 turns are represented in the figure. Each convolution as it rotates will have an electromotive force induced in it, the magnitude of which depends on its position in the field ; in the turns near o° and i8o° it will be very small, and in those near 90° and 270° it will be a maximum, since there the lines of force are cut most rapidly. With a right-handed rotation of the armature the direction of the E.M.F., and therefore of the currents in the successive turns, will be as indicated in the figure. It will be seen that there results a current flowing downwards from Q to P through the right-hand half of the armature, and an equal current also flowing downwards on the left-hand side. These are opposed to each other and hence there is no resultant current. But if P and Q are springs pressing against the wire at 0° and 180°, and are connected to an external circuit, the two currents unite into a single current which flows out into the external circuit at P and returns to the armature at Q. This current is practically continuous, the fluctuations from perfect steadiness becoming smaller and smaller as the number of coils on the ring is increased. Since the induced E.M.F. depends upon the rate of cutting lines of force, it is clear that a very great advantage will be gained by winding the wire on an iron core, since under given conditions the magnetic flux is very much greater through an iron than through a non-magnetic core. The wire is insulated, and the springs or brushes for carrying off the current, instead of touching the periphery of the ring, are arranged to rub against a series of metal strips, called commutator seg- ments, arranged on the rotating shaft and connected to the successive turns or coils on the ring. Fig. 1005 shows the arrangement of a real Gramme ring. The core ;s not solid, but con- sists of a coil of a number of turns of varnished soft iron wire, and conse- quently the changes in its magnetisa- tion which take place are far more rapid, and the heating effect due to these rapid changes is less than would the wire is continuous, and the two Fig. 1005 rmg be the case if it were one solid ends are soldered together. On this core are wound the coils B, C, D, &c. ; they are connected to the copper commutator segments, mn, to each of which are soldered the wires of two successive coils, so as to form a continuous whole. The com- mutator segments are insulated from each other by mica, and are fixed on -990] Displacement of the Brushes. Angle of Lead 1013 a wooden block o, mounted on the axis of rotation. The commutator seg- ments form a sheath about this axis, and two flat brushes of copper wire are in contact with the upper and lower parts of this sheath, and receive the currents which originate in the coils. Fig. 1006 shows a small hand machine fitted with a Gramme ring armature, the field being excited by a set of Jamin's permanent magnets. The points of contact of the brushes, it will be seen, are on a line at right angles to the mag- netic field. 990. Displacement of the brushes. Angle of lead. — Fig. 1007 represents the direction of the hnes of force in the simple case of a Gramme ring when rotated on open circuit. It will be seen how they almost entirely pass through the ring. The line AB is then the posi- Fig. 1006 tion in which, the brushes should be placed in accordance with the explana- tion given. A A B j B Fig. 1008 When the armature is rotated on closed circuit and the brushes are in the position corresponding to the ends of AB, sparks pass between the brushes B Fig. 1007 IOI4 Dynamical Electricity [990- and the contact pieces, which would speedily destroy them. It is found that by displacing the brushes in the direction of the motion a position is found, varying with the strength of the current, in which the sparking disappears. This is attributable to the fact that the total field is now the resultant of the original field and that due to the magnetisation of the core of the armature by the current flowing through it. The effect of the composition of the two fields is a displacement of the original lines of force (fig. 1008), and the points in which the induced electromotive force is null are moved into the position A'B'. The angle through which the line of brushes must be displaced so as' to prevent sparking is called the angle of lead. 991. Classification of dynamo machines. — ^The principal types of dynamo machines are depicted in figs. 1009-1012, originally due to Prof. Sylvanus Thompson. The field magnet is repre- sented as a horseshoe with long limbs, on which the exciting wire is wound, and an iron yoke. The iron pole-pieces are curved so as to embrace as closely as possible the rotating armature. The latter is not shown in the figures, but the commutator, with its segments and contact brushes, is indicated. Fig. 1009 represents a machine in which the current from a battery or separate machine excites the field magnets, and this type is known as the separately excited machine. In a separately excited, as in a magneto machine, the E.M.F. is pro- portional to the speed of the revolution, and for a given speed, E being constant, the current varies inversely as the resistance. Fig. loio represents the original form of the dynamo ; the current from the armature passes directly from one brush into the wire of the field magnet, from thence into the external circuit, returning to the armature by the other brush ; such macljines are said to be series wound. There is no D.P. between the terminals of a series wound dynamo on open circuit. When the terminals are joined by a resistance, or in technical language when a load is applied, the machine quickly excites, and the E.M.F. rises to its proper value for that load. As the resistance increases the current falls, both directly and also in consequence of the diminished E.M.F. caused by the weakening of the field ; and when the resistance exceeds a certain limit the machine does not excite. On the other hand, when the external resistance decreases, there is a limit to the increase of the current due to saturation of the field magnets and other causes. Series wound dynamos are not used for charging accumulator cells, since there is always a danger that, on a temporary break in the circuit or slackening of the speed of running, the back E.M.F. of the cells may overpower that of the machine, reverse its magnetism, and drive it backwards. A third type is that represented in fig. loii, and is known as the shunt wouitd dynamo ; the current through the armature divides at B, one portion Fig, 1009 -992] Drum Armature 1015 passes through the long and thin wire of the field magnet, and the other through the external circuit — -for instance, an electroplating bath. Thus, the external circuit and the shunt coils are in parallel and share the current produced in the armature. The shunt coils have a high resistance as compared with the field-magnet coils of a series dynamo. When the machine is on open circuit, the armature and shunt are in series with each other, and under these conditions the D.P. at the terminals is a maximum for a given speed. When the poles are joined by a resistance which is gradually diminished from a high value, the D.P. diminishes and the current increases up to a certain limit, after which it again diminishes and tends to vanish when the load is very large. Near the limiting value a change in the external resistance produces only a slight effect on the current, for increase of resistance throws more current into the shunt coils and therefore strengthens the field and with it the E.M.F. The compound wound dynamo is represented in fig. 1012. There are two field-magnet coils, one of, low resistance, the other of relatively high resistance, connected respectively in series with, and in shunt with, the external circuit. The coils may be wound in such a way that the machine may give either constant pressure or constant current whatever the load. A constant pressure machine is used for feeding glow lamps in parallel. If a number of these lamps are removed, the resistance in the external circuit is increased, and the current would be lessened, partly from Ohm's law, and partly from the weaker magnetisation whereby the difference of potential would be less, and possibly to such an extent that the lamps would not glow ; but with the compound winding a greater proportion of the current now passes through the shunt wire, and thus the field is strengthened. By a suitable choice of the resistances, and the relative number of turns of the wires, the increase of the magnetisation can be made so great that the diminution in the difference of potential is thereby compensated. 992. Drum armature. Siemens' dynamo-electric machines. — There is another type of armature used in direct-current machines, known as a drum armature. The core is a cylinder or drum formed of a number of thin iron- discs or washers insulated from each other, and on this the wire is wound longitudinally, crossing over at the ends, each turn being shifted slightly on the drum with regard to the preceding one. The wire forms a closed circuit, and, as in the ring armature, the ends of each turn or group of turns are brought to commutator segments ranged on the axis of rotation. The principal difficulty in winding drum armatures is to carry over the wire at the ends of the drum in such a way that the end faces may not be blocked up with wire and insulating material, and ventilation prevented, and many ingenious plans have been devised for overcoming this diffi- culty. Fig. 1012 Fig. 1013 cut all the lines of force which pass through the armature core. 1016 Dynamical ElectHcity [992- Fig. loi 3 represents the essential features of one of the small-sized vertical machmes made by Siemens & Co., a characteristic of which is the drum armature. The poles of the field magnets MM', MM' are joined together, north to north and south to south, by massive pieces of soft iron, bent so as to almost completely encircle the armature ; the front pieces, N, form the north pole of the com- bined field magnet, and similar pieces behind form the south pole, and the lines of force run horizontally from front to back. D is the armature, and C the .commutator segments on which rest two pairs of brushes, the plane of commutation being nearly vertical. One advantage of the drum armature is that all the turns of wire on the drum Drum armatures are^now much more used than ring armatures, especially in slow- speed dynamos. The resistance from brush to brash, as in the case of the Gramme ring, is only one-quarter of the actual resistance of the wire on the armature. 993. Motors. — An electric motor is a machine for converting electric into mechanical energy. Any dynamo-generator may serve as a motor ; that is, if a current from a battery or other source is allowed to pass through its armature and field magnets, the armature will rotate. In the case of a series wound machine, fig. loio, the direction of rotation is opposite to that in which the armature must be driven in order to produce a current in the same direction. This will be clear from a consideration of fig. 1008, for as in the generator the south pole, S', of the armature is urged away from the north pole and towards the south pole of the field magnet, work being done against magnetic forces, so in the machine used as a motor the direction of the current being the same, S' will be attracted towards N, and the direc- tion of rotation will be reversed. If the machine is shunt wound, on the contrary, and a battery is inserted in the external circuit to produce a current in the same direction as that due to the action of the machine as a generator, the armature will rotate in the same direction as before, since the polarity of the field magnets is reversed. If a battery or dynamo is connected up with an ammeter and a motor whose armature is prevented from turning, the current, C, is equal to E =^, where E is the applied E.M.F., and R the resistance of the circuit. When the armature is allowed to rotate, the cuiTent, as indicated by the ammeter, falls, owing to the back E.M.F. set up in the motor, and the diminution of current is greater, the greater the speed ; for the armature -994] Transformers 1017 cannot rotate without developing an electromotive force, and the direction of this must, by Lenz's law, be such as to tend to stop the motion. Let e denote this back E.M.F. for a given speed, then C= ~ . The power supplied from the source - CE watts, of which an amount equal to C-R is absorbed in heat in the circuit ; the remainder, which from the above equa- tion is equal to C«, represents the power absorbed by the motor and con- verted into mechanical power. The efficiency of the motor = -— or — , and CE E is greater the more nearly this fraction is equal to unity ; that is, the smaller the current. The maximum amount of energy in a given time will be obtained from the motor when Q,e or ?i — — ^■' is a maximum. Now, since the sum of the two factors e and E — ^ is constant, their product will be a E maximum when they are equal to each other, or when E — ^ = ^, or « = - Thus, the maximum efficiency of a motor must be distinguished from its maximum rate of working. 994. Transformers. — Ruhmkorff's coil, as we have seen, is an arrange- ment by means of which we can transform electricity of low into electricity of high potential. There is no creation of electricity ; the energy produced in the secondary circuit is produced at the cost of that in the primary. The apparatus acts, in short, as a transformer or converter, and it is reversible, for if we connect the long thin wire with a source of electricity yielding alter- nating discharges at high potential, we get alternating discharges in the short thick wire, of low potential but of much greater strength. The functions of the wires are reversed in this case ; the thin long wire is the primary and the short thick wire the secondary. This modification of the principle of Ruhmkorff's coil is of great practical importance in the transmission of electric energy. One of the chief types of transformer, represented in fig. 1014, consists of 3. closed iron ring, or preferably a bundle of soft iron wires or strips, so as to hinder the formation of Foucault currents (964). In either case the magnetic circuit is closed, the primary wire AB is coiled on this, and over it the secondary, ab, both carefully insulated ; or the two sets are coiled separately in individual sections, as shown in the figure. In another type, represented in fig. loi 5, the primary and secondary wires are wound together and form the core, while on this is coiled in a con- tinuous circuit at right angles iron wire or strips, coated on the surface with iron oxide, which, being an insulator, tends to prevent the formation of Foucault currents. It is of great importance that the insulation of transformers be good, more especially when, as in recent times, it is requisite to transform potentials ■of 30,000 to 40,000 volts, or even more. In such cases the whole transformer is placed in oil, which penetrates the pores and insulates admirably. The chief requirement in any transformer is that it shall effect the trans- formation of electric energy without great loss. In the ideal case the transformed electric energy would be equal to the original, which, however, is impossible ; for in the first case heat, according to Joule's law, is produced ioi8 Dynamical Electricity [994- both in the primary and the secondary wire, and this is lost as far as useful effect is concerned. Then, further, some energy is consumed in Foucault currents, and, moreover, the magnetisation and demagnetisation of the iron core or envelope represent a loss of energy, which is spoken of as the loss by hysteresis (907). Owing to all these causes, the power in the secondary wire is always less than that in the primary, and the ratio of the two is called the efficiency. In the most improved modern forms an efficiency of 96 per cent, is attained. The efficiency is greater when the transformer works under a full load. The magnetisation then oscillates within narrower limits, and the losses due to hytteresis are smaller. In the transmission of power from one place to another, transformers play an important part. Suppose a source of power available of 50,000 watts, for example, and that this is to be transmitted in the form of ^^^/JWiliiiMii^^^Kk Fig. 1014 Fig. 1015 electric power to a certain distance, there to be utilised. Since a watt represents the product of two factors, a volt and an ampere, we may vary these factors, which make up the total, in any way we like. We may transmit it in the form of a strong current of low electromotive force, or of a weak current with very high electromotive force. Thus, for instance^ we can transmit the above quantity as a current of 500 amperes under a pressure of 100 volts. But for this purpose the resistance of the conductor through which the current passes must be small, which necessitates that it have a large section and consist of very good conducting material — that is, of copper. The energy could however, also be transmitted in the form of a weak cur- rent, say of 10 amperes, under a pressure of 5,000 volts ; the conductor required for this purpose might be very much thinner, and therefore far less costly. By increasing the number of coils of a dynamo machine, and the speed of rotation, currents may be produced of very high electromotive force.. But in practice it is found that a certain speed of rotation cannot be -994] Transformers 1019 exceeded, and, moreover, the difficulty of insulation in the machines them- selves is greatly increased ; the electricity is apt to discharge in the body of the machine itself, and thus destroy the insulation. In practice it is not safe to go beyond 2,000 volts. Here comes in the great utility of transformers. Suppose the gene- rator to produce a strong electric current of low potential which is then passed into a suitable transformer and, on the principle CE = C'E', is converted into a small current of high electromotive force. This weak current is then transmitted along a thin wire to the place where it is to be utilised, where it again enters a transformer, and is changed into a current of the desired strength. The first great progress made in this direction was at the Electric Exhibition of 1891, at Frankfort-on-the-Main, in which mechanical power was transmitted from Lauffen-on-the-Neckar through a distance of no miles with a loss of 28 per cent. The water-power available at Lauffen worked a turbine producing 300 horse-power ; this generated an enormous current of 4,000 amperes and 55 volts, or 220,000 watts ; by means of copper rods over an inch in diameter this current was passed into a trans- former, where it was changed into a current of 8 amperes at 27,000 volts. This small current was transmitted through copper wires -/j of an inch in diameter, to Frankfort, where it again entered a transformer, in which its electromotive force was transformed down to 100 volts. The chief practical difficulty in the transmission of power economically seems now to be one of insulation. I020 Dynamical Electricity [995- CHAPTER XIII DIAMAGNETISM 995. Diamagnetism. — Coulomb observed, in 1802, that magnets act upon all bodies in a more or less marked degree : this action was at first attributed to the presence of ferruginous particles. Brugmann also found that certain bodies — for instance, bars of bismuth — when suspended between the poles of a powerful magnet, do not set axially between the poles, that is, in the line joining the poles, but eguatorialfy, or at right angles to that line. In other words, while a magnetic substance such as iron sets along the lines of force of the magnetic field, a bar of bismuth sets at right angles to the field. This phenomenon was explained by the assumption that the bodies were transversely magnetic. Faraday made the important discovery in 1845 that all solids and liquids which he examined are either attracted or repelled by a powerful electromagnet. The bodies which are attracted are called mag- netic or paramagnetic, and those which are repelled are diamagnetic bodies. Among the metals, iron, nickel, cobalt, manganese, platinum, cerium, osmium, and palladium are paramagnetic ; while bismuth, antimony, zinc, tin, mercury, lead, silver, copper, gold, and arsenic are diamagnetic, bismuth being the most so and arsenic the least. The three metals iron, nickel, and cobalt exhibit the magnetic property in so marked a degree as compared with other paramagnetic substances that they are generally classed by themselves and called ferromagnetic C701). Diamagnetic effects were first observed by Faraday in a particular kind of glass called Faraday's heavy glass ; they can be exhibited only by means of very powerful magnets. In experimenting on the diamagnetic effects exhibited by solids, liquids, and gases, pole-pieces of soft iron, S and Q (figs. 1016-1018), of different shapes, are screwed on the magnets. i. Diamagnetism of solids. If a small rectangular bar is suspended between the poles of an electromagnet, it sets eguatorialfy, or at right angles to the lines of force, if it is a diamagnetic substance, such as bismuth, anti- mony, or copper ; but axially, or in the direction of the lines of force, if it is a magnetic substance, such as iron, nickel, or cobalt. Besides the sub- stances enumerated above, the following are diamagnetic : rock crystal, alum, glass, phosphorus, iodine, sulphur, sugar, bread ; and the following are mag- netic : many kinds of paper and sealing-wax, fluorspar, graphite, charcoal, &c. ii. Diamagnetism of liquids. To experiment with liquids, very thin glass tubes filled with the substance are suspended between the poles instead of the cube m, in the figure 1017. If the liquids are magnetic, such as solutions of iron or cobalt, the tubes set axially ; if diamagnetic, like water, blood, milk, alcohol, ether, oil of turpentine, and most saline solutions, the tubes set equatorially. The attraction or repulsion of a magnetic substance is affected -995] Diamagnetism I02I by the magnetic quality of the medium which surrounds it. For example, a thin glass bulb containing a solution of ferric chloride is attracted when suspended in a vessel containing a weaker solution, and repelled if the vessel contain a stronger solution of ferric chloride. Thus a paramagnetic sub- stance may appear to be repelled by a magnet, just as a balloon filled with hydrogen appears to be repelled by the earth, the explanation in each case being that the medium displaced is more powerfully attracted than the body which displaces it. A diamagnetic substance surrounded by a magnetic or neutral substance sets equatorially. According to its composition glass is sometimes magnetic and sometimes diamagnetic, and as glass tubes are used for containing the Fig. 1016 Fig. J017 Fig. iot8 liquids in these investigations, its deportment must first be determined, and then taken into account in the experiment. The behaviour of liquids in a magnetic field may also be observed by Pliicker's method. A solution of a para- or diamagnetic liquid is placed on a watch-glass between the two poles, S and Q, of a powerful electro- magnet. When the current passes, the form of the surface is altered as represented in fig. 1018 ; this continues as long as the current passes, and is produced to different extents with all magnetic liquids. The changes in the aspects of the liquids are, however, so small as to require careful scrutiny to detect their existence. A method of magnifying these changes so as to render them visible to large audiences was devised by Professor Barrett. A source of light is placed above the watch-glass containing a drop of the solution to be tried. Below the watch-glass, and between the legs of the magnet, is placed a mirror at an angle of 45°. By this means the beam of light passing through the watch-glass is reflected at right angles on to a screen, where an image of the drop is focused by a lens. If now a drop of diamagnetic liquid, such as water, or, better, sulphuric acid, be placed on the watch-glass, as soon as the current passes, the drop retreats from the two poles, and gathers itself up into a little heap, as at A (fig. 1018). So doing, it forms a double convex lens, by which the light is brought to a short focus below the drop, an effect instantly seen on the screen. When the current is interrupted the drop falls, and the light returns to its former appearance. A paramagnetic liquid, such as a solution of ferric chloride, has exactly the opposite effect. The drop becomes flattened, and instead of assuming a plano-convex shape, it becomes nearly concavo-convex, as at B. The light is dispersed, and the effect shows itself on the screen. Instead of a mirror and I022 Dynamical Electricity [995- lens, a sheet of white paper may be placed in an indined position under the watch-glass, and the effects are somewhat varied, but equally well pro- nounced. ii. Diamagnetism of gases. Bancalari observed that the flame of a candle placed between the two poles in Faraday's apparatus was strongly repelled (fig. 1016). All flames present the same phenomenon to different extents, resinous flames or smoke being most powerfully affected. The magnetic deportment of gases may be exhibited for lecture purposes by inflating soap bubbles with them between the poles of the electromagnet, and projecting on them either the lime or the electric light. Faraday experimented on the magnetic nature of gases. He allowed gas mixed with a small quantity of a visible gas or vapour, so as to render it perceptible, to ascend between the two poles of a magnet, and observed their deflections from the vertical line in the axial or equatorial direction ; in this way he found that oxygen was least, nitrogen more, and hydrogen most diamagnetic. With iodine vapour, produced by placing a little iodine on a hot plate between the two poles, the repulsion is strongly marked. Becquerel found that oxygen is the most strongly paramagnetic of all gases, and that a cubic yard of this gas condensed would act on a magnetic needle like 5"5 grains of iron. This magnetism of gases may be shown by suspending a glass globe to the pan of a balance, above the pole of a powerful magnet ; this globe, after being exhausted, is exactly counterpoised, and having been filled with a given gas, the weight is ascertained which is required to detach it. With oxygen the attraction is appreciable, and is five times as much as with air under the same pressure. Faraday found that oxygen, although paramagnetic under ordinary circumstances, became diamagnetic when the temperature was much raised. Liquid oxygen is highly pai"amagnetic. Dewar found that when some of this contained in an open glass vessel was brought near the pole of a powerful electromagnet, it flew towards it and remained adherent until all was evapo- rated. In the crystallised bodies which do not belong to the regular system, the directions in which the magnetism or diamagnetism of a body is most easily excited are generally related to the crystallographic axis of the substance. The optic axis of the uniaxial crystals sets either axially or equatorially when a crystal is suspended between the poles of an electromagnet. Faraday assumed from this the existence of a magneto-crystalline force, but it appears probable from Knoblauch's researches that the action arises from an unequal density in different directions, inasmuch as unequal pressure in different directions produces the same result. According to Pldcker, for a given magnetising force, the specific magne- tisms developed in equal weights of the undermentioned substances are repre- sented by the following numbers, those bodies with the minus signs prefixed being diamagnetic : — Iron 1,000,000 Nickel oxide 287 Cobalt 1, 009,000 Water . • -25 Nickel . 465,800 Bismuth -23-6 Iron oxide 759 Phosphorus . -13-1 -996] Diainagnetisin 1023 If a sphere of iron is placed in a uniform magnetic field, lines of force are drawn into the substance of the sphere so that the number of lines through it is greater than the number that previously passed through the space Fig, 1019 which it occupies (fig. 1019). Its magnetic susceptibility (722) is positive, and its magnetic permeability greater than unity. If, however, the substance of the sphere is diamagnetic — for instance, a ball of bismuth — the lines of force in the field are apparently repelled, so that fewer lines pass through it than would have been the case had it been a neutral substance (fig. 1020). Its susceptibility is negative and its permeability less than unity. A rod of iron places itself axially in a magnetic field, because in that position the number of lines of force or induction passing through it is a maximum ; a rod of bismuth similarly places itself equalorially to render the number of lines of induction a minimum. Paramagnetic substances move into the strongest parts of a variable field, diamagnetic substances into the weakest. I024 Dynamical Electricity [996- CHAPTER XIV CONNECTION BETWEEN ELECTRITY AND LIGHT 996. Optical effects of powerful magnets. — Faraday discovered, in 1845, that a powerful magnetic field exercises an action on the propagation of light in substances exposed to its action thus if a polarised ray traverses them in the direction of the lines of force, the plane of polarisation is rotated either to the right or to the left according to the direction of the magnetisation. Fig. 1020 represents Faraday's apparatus, as constructed by Ruhmkorff. It consists of two powerful electromagnets, M and N, fixed on itwo iron supports, O O', which can be moved on an iron base, K. The current from a battery of 20 volts passes by the wire A to the commutator, H, the coil M, and then to the coil N, by the wire g, descends in the wire z, passes again to the commutatoi", and emerges at B. The two cylinders of soft iron, which are in the axis of the coils, are perforated by cylindrical holes, to allow the light to pass. At b and a there are two Nicol prisms, b serving as polariser and a as analyser. By means of a limb this latter can be rotated about a horizontal axis, the angle being read off on a gradu- ated circle, P. The two prisms being then placed so that their principal sections are perpendicular to each other, the prism a completely extinguishes the light -997] Kerr's Electro-optical Experiments 1025 transmitted through the prism b. If at c, on the axis of the two coils, a slab is placed with parallel faces, of heavy or flint glass, monochromatic light is still extinguished so long as the current does not pass ; but when the connections are made, the- light reappears, and in order, to extinguish it the analyser must be turned through an angle which can be read off on the limb, and which measures the rotation. By reversing the direction of the current the rotation is reversed. If the source of light is not monochro- matic, and if the analyser is turned to left or right, according to the direc- tion of the current, the light passes through the different tints of the spectrum, as is the case with plates of quartz cut perpendicularly to the axis (690). Becquerel showed that a large number of other substances besides heavy glass rotate the plane of polarisation under the influence of powerful magnets. The direction of the rotation for a given substance is the same as that of the current which pro- duces the given mag- netic field, and is independent of the direction in which the rays of light pass. Hence if the ray is • reflected on itself and traverses the substance a second time in the opposite direction, the rotation is doubled. By thus increasing the path of the ray by successive reflections (fig. 1022), the rotation may be increased in the same proportion. The rotation of the plane of polarisation between two points is propor- tional to the distance between the two points and to the intensity of the magnetic field. This is known as Verdefs law. The angle, expressed in circular measure, through which the plane of polarisation is rotated, when unit magnetic field acts upon a plate i cm. thick of a given material, is called Verdefs constant for that material. For different rays it is nearly as the inverse square of the wave length. For the ray D and at 0° it is 0'04o' for bisulphide of carbon and o'Oi3' for water. It diminishes with rise of temperature. By means of Faraday's apparatus it has been found that thin layers of iron, cobalt, and nickel, so fine as to be transparent, exert a powerful rota- tion of the plane of polarisation for transmitted light. The rotation for the central rays of the spectrum in iron is 32,000 times that in glass of the same thickness. In all diamagnetic substances the rotation is in the direction of the magnetising current ; in paramagnetic substances it is in the opposite direction. 997. Kerr's electro-optical experiments. — Dr. Kerr has discovered a remarkable relationship between electricity and light. He finds that when certain dielectrics are subjected to electric strain, they become doubly refracting (673). The general arrangement of the experiments is as follows : — A cell, P (fig. 1023), is suitably constructed of stout glass plates, in which is placed the liquid under examination ; its dimensions are 4 inches in length by I inch in width, and about \ of an inch in thickness. Two copper plates placed horizontally, and kept at a distance of about ^ of an inch, can be 3U I026 Dynamical Electricity [997- connected with the electrodes of a Holtz machine (fig. 744), or, what is more convenient, with the opposite coatings of a Leyden jar, which in turn is charged by such a machine. B is the mirror of a hehostat, by which a beam of Hght may be sent in any direction. M and N are two Nicol prisms (674) ; C is a compensator, while D is a condensing lens. Of the two Nicol prisms, ]\I serves as polariser, and N as analyser ^> -4 s- (670) ; at the outset they are arranged so that their principal sections are at right angles to each other, and make an angle of 45° with the vertical. Thus the light polarised by the prism M is extinguished by the analyser N, so that the field between them is quite dark, and remains so even when the cell is filled with liquid ; the cell is so aj'ranged that the observer looks through the slit of dielectric which is between the conductors in the cell. If now the plates are oppositely charged, the field at once becomes clear. Of all dielectrics hitherto examined, carbon bisulphide is that which best exhibits the phenomenon. A fraction of a turn of a Holtz machine is at once sufficient to produce light in the field, which disappears immediately the plates are discharged. As the machine is worked and the potential rises, the light between the conductors gradually increases in brightness until a pure and brilliant white is obtained ; with further increase of potential a fine progression of chromatic effects is obtained ; the luminous band between the conductors changes first from white to a straw colour, which deepens gradually to a rich yellow ; it then passes through orange to a deep brown, next to a pure and dense red, through purple and violet to a rich and full blue, and then to green. All the colours are beautifully dense and pure, and as fine as anything seen in experiments with crystals in the polari- scope. The phenomenon generally ceases at the green of the second order with a discharge of electric sparks. The action of carbon bisulphide under electric strain is similar to that of rapidly cooled glass or glass stretched in a direction parallel to the lines of force ; it is an action of the same kind as that of & uniaxial crystal (677) ; in this respect carbon bisul- phide occupies a place among dielectrics similar to that of Iceland spar among crystals. In order to measure the effect produced, a compensator, C, is placed behind the cell ; the plates are connected with Lord Kelvin's quadrant electrometer in such a manner that the potential can be directly measured, and then compared simultaneously with the difference of the path of the extraordinary and ordinary ray in the dielectric. Kerr arrived thus at the law : ' The strength of the electro-optical action of a given dielectric, that -999] Influence of Light on Conductivity. Photophone 1027 is, the difference in the path of the ordinary and extraordinary rays, for unit thickness of the dielectric, varies directly as the square of the resultant electrical force.' Kerr also found that when a pencil of plane polarised light is reflected from the polished surface of either pole of an electromagnet of iron, it undergoes a rotation in the direction contrary to that of the mag- netising current. This result is also obtained when it is reflected from the sides of the electromagnet when the magnet is excited. 998. Zeeman effect. — Another connection between light and magnetism was discovered by Zeeman in 1897, who found that the spectrum lines of an incandescent vapour are modified when the vapour is subjected to a power- ful magnetic field. Suppose the spark giving the incandescent vapour to have the position c in fig. 102 1, and to be examined in a direction at right angles to the lines of force. It is found that each spectrum line is tripled, and the separation between the constituents of a triplet is proportional to the strength of the magnetic field. Using a polariscope in combination with the spectroscope, it is found that the outer lines are polarised in a plane parallel to the lines of force, and the central line in a plane perpendicular to the lines. If the radiant vapour is viewed in a direction parallel to the magnetic field, which can be done with the arrangement illustrated in fig. 102 1, the central line of the triplet vanishes, while the outer ones are circularly polarised — the shorter waves (those nearer the violet end of the spectrum) in the direction of the magnetising current, and the longer waves in the opposite sense. Further investigation has shown that the phenomena are much more complicated than was at first supposed ; different spectrum lines are found to behave in different ways in the magnetic field, some appearing as quartets, while others are resolved into sextets or more complicated forms. 999. Influence of light on conductivity. Photophone. — The metalloid selenium has under ordinary conditions a high resistance, but if a specimen of this substance is raised to the melting temperature and slowly cooled, it becomes a moderately good conductor. Its resistance in this state is changed, to a marked extent, when light falls upon it. This was shown by the following experiment : — A thin strip of selenium, about 38 mm. long by 13 mm. broad, was provided at the ends with conducting wires and placed in a box with a draw-lid. The selenium, having been carefully balanced in a Wheatstone's bridge, was exposed to diffused light by withdrawing the lid when the resistance at once fell in the ratio of 1 1 to 9. On exposure to the various spectrum colours, after having been been in the dark, it was found to be most affected by the red, but the maximum action was just outside the red, where the resistance fell in the ratio of 3 to 2. Momentary exposure to the light of a gas-lamp, or even to that of a candle, caused a diminution of resistance. Exposure to full sunlight diminished the resistance by one-half. The effect produced on exposure to light is immediate, while recurrence to the normal state takes place more slowly. A vessel of hot water placed near the strip produced no effect, and hence the phenomenon cannot be due to heat, but there appear to be certain rays which have the power of producing a molecular change in the selenium by which its conductivity is increased. If the two electrodes of a Ruhmkorff coil are connected with a Geissler tube, suitably exhausted, so that a discharge just does not pass when the 3 U 2 I028 Dynamical Electricity [999- apparatus is in the dark, it passes at once when the tube is exposed to ultra- violet rays. It has also been noticed that the length of a spark between two dis- charging spheres is modified when ultra-violet light — for example, that radiated by another spark in the neighbourhood — falls upon the spheres. On the property which selenium has of changing its resistance, due to the incidence of light upon it, is based the action of an apparatus invented by Mr. A. Graham Bell, and called by him a photophone, by which articu- late speech can be transmitted to a considerable distance by the simple agency of a beam of light. Its performance depends not only upon the action of light on crystallised selenium, but also on the fact that a thin plate of glass bulges — becomes alternately convex and concave — when sound waves fall upon it. A plate of microscope glass, silvered in front, is fitted into a mouthpiece like that of a telephone, the silvered face being outside. This is the trans- mitter. A powerful beam of solar, or electric, light is directed by a large min'or on the transmitter, and, after reflection, is rendered parallel by means of a suitable lens. It then falls upon a parabolic mirror in a direction parallel to the axes, and accordingly converges after reflection to the focus, where a selenium cell is fixed. The latter is constructed as follows : — Two fine copper wires are wound side by side, and as close together as possible, without touching, on a small strip of mica, there being 20 or 30 turns. The free ends of the wire are connected to a circuit containing battery and telephone. The spaces between the successive turns are now filled with melted selenium, which is carefully annealed and then rendered sensitive to the action of light. When the parallel beam of light is concentrated on the selenium cell, the latter will have a definite resistance and no sound will be heard in the telephone. But if the transmitter is spoken into, the microscope glass vibrates, changes its curvature, and so causes the beam, which falls on the parabolic mirror, to be alternately diverging and converging. The result is that the quantity of light falling on the selenium cell, and hence its resistance, changes in correspondence with the words spoken into the transmitter. 1000. Absolute electric units. Dimensions. — Assuming the centimetre, gramme, and second as units respectively of length, mass, and time, it has been shown (63) how the units of force, work, &c., may be derived from them. We may now proceed to the further derivation of electric units and determine their dimensions, that is, their relation to the fundamental units, and there are two ways in which this may be done. We may start with the law of repulsion between two similar charges of electricity, and build up a system on this basis ; this system is called the electrostatic system. Or we may take as our starting-point the repulsion between two magnetic poles, the system so derived being called the electro-magnetic system. Each of these systems is absolute.,vi^^i}ae. sense that in both the various units are derived in the simplest possible manner from the centimetre, gramme, and second. The electrostatic system is, perhaps, the simpler of the two, but that based on magnetic action is more convenient, and best lends itself to —1000] Absolute Electric Units. Dimensions. 1029 the practical determination of the more important standards, such as those of E.M.F. and resistance. We shall distinguish the electrostatic units by small, and the electro- magnetic units by the corresponding capital letters, a square bracket indicating that the dimensions of the particular quantity are referred to. ELECTROSTATIC SYSTEM. Quantity of electricity, q. — Coulomb's law states that the repulsion between two equal charges of q units, separated by a distance r, in air, is F = ir, (753)- If the charges are placed, not in air but in a medium whose specific inductive capacity is k, the force in action between them is given by F = -9- The dimensions of k are not known, but as we have no right to Kr- assume that the specific inductive capacity of a substance is independent -of length, mass, and time, we must retain the symbol k in the equations to represent its unknown dimensions. Hence q = Y^^r, and since [F] = MLT ~ ^ (63) Potential, ^.— SinceJW (work) = eq, and [W] = ML=T "" " [«] = ML-'T~' -^ M^L^T"' K* = M*L*T~' K ~ i Capacity, c. — Since quantity = capacity x difference of potential (760), ^= ?, Thus the capacity of a conductor depends on length and specific induc- tive capacity only. It has been shown that, in air, the capacity of a sphere is equal to its radius. Current, i. — The strength of a current is the quantity of electricity passing per unit time, -or i = " :. [z^M^L^T"'*^. Resistance, r.— By Ohm's law, r= -, :. [r] = M^L*T~'(c~*-^ M^L^T~'(c*=L~'Tac~\ ELECTROMAGNETIC SYSTEM. In this system the action between two magnetic poles is the starting- point. By Coulomb's law (719) F= — , if the poles, each of strength m, are separated by a distance, r, in air. If, however, the medium has a magnetic I030 Dynamical Electricity [1000- permeability u, the force is — ^ The symbol u must be retained, as we do- not, know the dimensions of magnetic pei-meabihty. Magnetic pole, m. — From the formula Y = nf-\^r'- we have [7;z] = mMt~V^- Magnetic field, H. — Unit magnetic field is that in which unit pole is- acted on by unit force, or H = , m Magnetic induction ax flux density, B. — Since B = ^H (721), Electric current, I. — The force F on a pole m placed at the centre- of a circle of radius r, due to a current I, flowing through a length r, of the- circumference = wzlr/r-. Hence the dimensions of a current are given by [I] = MLT~^L^ M^L^T^V* = MMT-V~i Quantity of electricity, Q. — Since Q = \t. Electromotive force. Difference of potential, E. — Since work, W, = EQ,, [E] = ML=T~'-^ M^L^/x~* = M^L^T~V*- Resistance, R. — By Ohm's law, R = . .-. [R] = M^L^T~Vi -^ M^L^T~V-' = LT~V- Capacity, C. — Since Q = EC, In article 737 the dimensions of magnetic pole, magnetic field, and magnetic flux were given on the assumption that the force F, between two- poles = —-—. The reader Avill have no difficulty in modifying them, by _^ 777 777 • ■ taking F = , so as to a\oid the assumption that the magnetic permeabflity of the medium is equal to unity. 1001. Relation of electrostatic to electromagnetic units. — Since the dimensions of any physical quantity must be the same whatever system of units is employed in specifying it, it follows that the dimensions of q, e, c, &.C., are the same respecti\ely as those of Q, E, C, &c. Now, as we have seen,, [{r] = M^L^T~* K^,and [Q] = M^L^^i"^, and therefore -1002] Electromagnetic Theory of Light 103 1 That is, —- is of the nature of a velocity ; call it v. The same result is arrived at if we equate the dimensions, on the two systems, of any of the other magnitudes. Thus, although we know nothing as to the dimensions of either k or fi, we see that the reciprocal of the square root of their product is a velocity. This velocity can be determined by measuring a given quantity of electricity, or a given difference of potential, or the capacity of a given condenser, both electrostatically and electromagnetically. For example, if Pj is the numerical value of a certain definite quantity of electricity measured on the electrostatic system, and P„ the numerical value of the same quantity measured on the electromagnetic system, we must have P.{(gr.)* (cm.)S(sec.)-' k^} = P„ {(gr.)*(cm.)V-*} P, /cm. \ ~i -i Pm Vsec. / Thus, the ratio of P^ to P,„ (which ratio has the dimensions of a velocity) is equal to v. Let a condenser be constructed of brass plates separated by air ; its capacity is — - (799), and if it is charged and the difference of poten- 47rrt tial, V, between its coatings is measured by an absolute electrometer (797), AV its charge, expressed in electrostatic measure, is — - = P^. If the condenser 4Jr« is then discharged through a ballistic galvanometer (843) of known constants, WT /9 the charge (electromagnetic) = P„ = — ^sin-- The ratio P«/P„, is found ttG 2 to be about 3 x 10^" = v, from which it follows that the unit in terms of which P, is measured is that in which P,„ is measured ; or that the 3 X 10'" electromagnetic unit of quantity is 3 x 10'" times the electrostatic unit. Similarly, it has been found that the electrostatic unit of electromotive force or potential is 3 x 10'" electromagnetic units, &c. The relations between the units may be formulated as follows : I electromagnetic unit of quantity = v electrostatic units I „ „. current =v „ „ I „ „ capacity =v'^ „ „ V „ units of E.M.F. =1 „ unit w' „ „ resistance =1 „ „ The first determination oft/ was made in 1856 by Weber and Kohlrausch who measured a quantity of electricity, and found z/ = 3-107 x 10'". Since that time many determinations of v have been made, amongst others by Lord Kelvin, Clerk Maxwell, Ayrton and Perry, Rowland, and J. J. Thomson. The mean value of the various results obtained is very nearly 3 x 10*°. This number agrees very closely with that which has been experimentally found for the velocity of light — 186,400 miles per second(5i8). 1002. Electromagnetic theory of light. — When two conducting plates, separated by a dielectric, such as the coatings of a Leyden jar, are connected to the poles of a battery, the plates become oppositely charged. The positive and negative charges strive to unite, and would do so were the medium 1032 Dynamical Electricity [1002- between them a conductor. Although no current in the ordinary sense passes, we have seen that the dielectric is profoundly modified by the presence of the charges on the plates. According to Faraday it is polarised (766), and Dr. Kerr's experiments (797) showed that it is strained, as a solid is strained by the application of mechanical stress. The experiment of the dissected Leyden jar (787) showed that the electrification of the charged jar resided in the glass, and that the metal coatings merely served the purpose of distributing the charge over the surface of the glass. Using the phraseology of Clerk Maxwell, we say that when connection of the plates with the battery is made, a displacement of electricity takes place in the dielectric, or that there is a displacement current through the dielectric, positive electricity tending to move in the direction of the electromotive force, the result being that if the positive plate has a charge Q, an equal quantity, Q, passes through each section of the dielectric drawn parallel to the plate. This displacement of electricity from point to point is resisted- by the electric elasticity of the dielectric, so that for a given applied electromotive force the displacement (and therefore the charge Q) is least in the case of that dielectric whose electric elasticity is greatest, just as, for a given applied mechanical pressure, the deformation of an elastic solid is inversely proportional to the elasticity of the solid. But we know that when a condenser is charged, the charge for a given applied E.M.F. is proportional to the specific inductive capacity of the dielectric (783). Hence the electric elasticity of a medium is inversely proportional to its specific inductive capacity ; its reciprocal is sometimes called the pliability of the medium, so that pliability = i//c, when k is the specific inductive capacity. If the plates are alternately charged in opposite directions, the electric displacement alternates, and as it is always resisted by the electric elasticity of the dielectric, it follows that if the alternations follow each other with sufficient rapidity, they will give rise to waves in the surrounding medium, just as the to-and-fro motions of air particles give rise to sound waves in air. Now a disturbance, when producedat any point in an elastic medium, spreads with a velocity= A / J (231), where e is the elasticity and d the density of the medium. If we imagine a medium whose elasticity is i/k, k being its dielectric constant, and whose density is ^, the magnetic permeability of the medium, the velocity of wave motion through it will be . / —, which is V !>■< equal to v, the velocity of light. Clerk Maxwell, discarding the idea of action at a distance, adopted the views of Faraday as to the part played by the media surrounding conductors on electric phenomena ; these views he represented in mathematical forms, and so rendered them capable of theoretical development. Maxwell's theory led him to the conclusion that electric and magnetic forces are propagated from one place to another by a medium which occupies all space, with a velocity i/VK/i, where k is the specific inductive capacity, and ji the magnetic permeability of the medium. Now this is the velocity of light through what we call the luminiferous ether, and as it seems unnecessary to fill all space with two different ethers through which luminous and electric disturbances -1002J Electromagnetic Theory of Light 1033 respectively travel with equal velocities, we are led to the conclusion that the same medium transmits both, and further, that luminous and electric disturbances are the same in kind ; in other words, that light is an electro- magnetic phenomenon. This is Maxwell's electromagnetic theory of light. One consequence of the theory is that the specific inductive capacity of a medium should be equal to the square of its refractive index. For consider two media, say air and glass : let Kj and /Xj be the sp. ind. cap. and permeability of air, and V the velocity of propagation through it, and let K.,, /i„, V^ have the same meanings in reference to glass ; also let n be the refractive index of glass ; that is, the ratio of the velocity of light in air to the velocity in glass. Then, n = v^- = ^ / }HH. But the magnetic permea- bility of air and glass are practically the same, and if we call the sp. ind. capacity of air unity, k^ = k = the specific inductive capacity of glass with air taken as the standard, and then n = ^k or k = n'': This is known as Maxwell's law. Since the refractive index of a substance varies with the wave length of the radiation, it is clear that if we wish to test Maxwell's law by experi- mentally determining k and ?z, the experiments ought to be maije under like conditions with regard to wave length, and unless this is done we cannot expect very close agreement. The following substances, for which k and n were determined in the ordinary way at the temperature of the atmosphere, obey the law very fairly : — Substance K \ H- Paraffin Petroleum oil . . Turpentine Benzine ... . . Carbon bisulphide . Sulphur . . . . Resin 2-29 2-07 2-23 2-38 267 473 2-55 2 -02 2-075 2-128 2-26 2-67 4-89 2-37 Exceptions are much mofe numerous than accordances, but it has been shown by Fleming and Dewar, in the case of many substances, that the specific inductive capacity varies enormously with temperature, and that if it is determined at a very low temperature, the agreement between k and rfi is much closer than at ordinary temperatures. The following are examples, taken from Fleming's Cantor lectures : — Water . Ethyl alcohol Amyl „ Ethylic ether Olive oil . K at 15° C. /cat 185° C. M- 3°„ 2-4-2-9 1-78 (D line) 25-8 3-11 1-83 16 2-14 1-95 • 1 4-25 2-31 1-81 1 3-16 2-i8 2-13 I034 Dynamical Electricity [1002- In the case of water it has been found that n^ measured electrically for waves about 6 metres long, is 8-9, hence jfi = 79-2, and is therefore equal to k at ordinary temperatures. Faraday was unable to detect any difference in the dielectric constants of various gases. Boltzmann has shown, however, that there are differences among them, and that for them there is a very close agreement between •Jk and n, as is seen from the following table : — Vacuum Air Carbon dioxide Hydrogen . Ethylene K v« n i-ooooo 1-00059 1-00095 1-00026 I-00I3I I-oooooo 1-000295 1-000473 I -0001 32 1-000656. I-OOOOOO I -000294 I -000449 I-OOOI28 . 1-000678 1003. Hertz's experiments. — The theoretical previsions of what is known as the ' Faraday-Maxwell ' theory received a striking confirmation in a most remarkable and beautiful series of experiments by the late Professor Hertz, of which we can only give an outline of some of the principal results. In order to demonstrate that light is essentially an electromagnetic phenomenon, it would be necessary to produce, with a vibratory motion of purely electromagnetic origin, the same class of phenomena as can be produced with ordinary light, such, more especially, as interference and refraction. Hertz devised an apparatus which he calls a vibrator or oscillator or radiator for obtaining by continuous but very rapid electric oscillations true rays of electric energy. Two spheres or plates of metal, AA' (fig. 1024), are provided with straight metal rods with small knobs at the end, the distance,. C, of which can be adjusted. The rods are in connection with the terminals of a Ruhmkorff coil B, which charges the two spheres to different poten- tials, and a spark passes at C. This spark, by heating the air, forms, as it were, a path for the subsequent oscillations (800), and the vibrator now discharges itself independently, as if it were detached from the coil, forming between the discharges of the Ruhmkorff a series of oscillations of ex- treme rapidity. Theory shows that the period, /, of the oscillations in ACA' = 27rv/LC, where C is the capacity of the two plates or spheres A, A', and L the self-induction of the rod and spark- gap connecting them, both expressed in electro- magnetic units. In considering the electric oscillations in ACA', we may leave the induction coil out of consideration, regarding it merely as a device for charging A and A' up to a certain difference of potential. If the small knobs at C are a little less than i centimetre apart, the difference of potential between A and A' will rise to about 36,000 volts (805) before a spark occurs. When a spark passes electric oscillations are set up in the con- ductor ACA' (800), each part of it becoming alternately positively and negatively charged, and thus waves are produced in the surrounding -1003] Hertz's Experiments I03S space. Hertz succeeded in measuring the length of these waves and also their velocity, which he showed to be the same as that of light, thus confirm- ing Maxwell's theory. In one of Hertz's experiments A and A' were spheres 1 5 cm. in radius, and the connecting wire was i metre long, with a spark gap of i centimetre in the middle. The wave length of the radiated waves was found to be 4-8 metres, which gives, as the period of the oscilla- tion, since vt=\, 1-6 hundred-millionths of a second. The oscillations diminish rapidly in amplitude ; indeed, after ten or twelve to-and-fro swings they come to an end. Thus the whole series is completed in the one five-millionth part of a second, and for the rest of the interval between one spark and another there is no radiation. Let us next consider how electric radiation may be detected. If we have a vibrating tuning-fork producing sound waves and we approach to it a body tuned in unison with the fork, the body in question begins to vibrate also ; such bodies, as we have seen, are called resonators (255). In order to investigate the distribution of electric waves in the region about a vibrator. Hertz used what he called an electric resonator. This consists (fig. 1025) of a wire ring, one end terminating in a point and the other in a small knob, which by a micrometric arrangement, not shown in the figure, may be kept at any desired distance. The dimensions of the frame are adjusted — tuned as it were — so that its oscillations synchronise with those of the vibrator. If now the resonator is placed with its axis parallel to the axis of the vibrator — positions are found in which a floA\- of minute sparks passes between the ends of the resonator ; their quantity and strength diminish as the distance from the vibrator increases, but are perceptible at even 50 or 60 feet. These waves are transverse to the direction of propa- gation, as appears from the fact that when in a given position the resonator is giving sparks, it ceases to do so when turned at right angles. When the vibrator works well the whole room is pervaded by electric waves, and by varying the position and distance of the resonator in reference to the vibrator, it is possible to plot out the exact form of the wave motion in the field. These electric waves pass through ordinary conductors, such as a door, or a wall, but are reflected from a conducting surface. If the vibrator is placed at a suitable distance in front of a large sheet of metal, the waves are reflected from the wall, and interfering with incident rays give rise to stationary waves made up of nodes and loops at regular intervals, quite analogous to the corresponding acous- tical phenomenon. This may be demonstrated by means of the resonator, which gives no spark if placed at a node, but does so if in a loop. If the metal is a perfect conductor, there is formed a node at the reflecting surface and others at equal distances. This is analo- [^ gous to the case of a stopped pipe. ^ If the vibrator is placed in front of a tall cj-lindrical metal reflector with a parabolic section (fig. 1026), the effects produced are 1036 Dynamical Electricity [1003- more pronounced, and can be perceived at a greater distance than before. A mass of electric rays parallel to the focal line is formed, and the ex- periment of the conjugate mirrors (425) may be repeated. An insulating screen placed between the two mirrors does not stop the action, but a con- ducting screen does. The electric rays undergo refraction on passing from one medium to another. This Hertz demonstrated by means of a huge prism of pitch, weighing about half a ton, 5 feet in height, with a refracting angle of 30°, and with a face of over a square yard. When the rays, rendered parallel by the mirror, fell on this, they were deflected towards the base, and by means of the resonator the position of minimum deviation could be obtained, and thus the refractive index was found to be i "69 ; the optical refractive index is between 1-5 and r6. By allowing electric rays to fall on a plane reflecting surface, part are absorbed and part reflected, and it is readily shown that the angle of reflec- tion, as with light and heat, is equal to the angle of incidence (522). If the electric rays concentrated by a mirror fall on a grating formed of parallel copper wires, it is found that when the grating is in the direction of the rays — that is, when the wires are parallel to the focal line of the mirror —they are stopped, but are transmitted when the wires are turned at right angles to the direction. This is a phenomenon of polarisation ; the grating acts in regard to the rays like a tourmaline in respect of plane polarised light (672). In another experiment Hertz reproduced the phenomena of diffraction (661). Hertz's experiments have been reproduced by many observers, and with 9 t c. Fig. 1027 other resonators and modifications in the way of experimenting. Dragoumis found that Geissler's tubes were well fitted for this purpose. Lecher's method of investigation is convenient. The vibrator is formed of two metal plates, ab (fig. 1027), connected with the terminals of a Ruhmkorff coil as in fig. 1023, opposite which are two similar ones, a'b' \ from these pass wires, st s'f, 40 or 50 feet in length and about 6 inches apart, parallel from j to /, which are tightly stretched by means of strings. In this arrangement a and d are the plates of two condensers which discharge with oscillations when the induction coil is set in action. The -1003] Hertz's Experiments 1037 potentials of the plates a' and V are therefore raised and lowered with great frequency ; hence the wires connected to them are subjected to rapidly \arying electromotive force, and if they are properly adjusted as to length and distance apart, stationary waves are produced in them due to high frequency oscillating currents. At the free ends of the wire will be loops — that is, there will be maximum changes of potential there, but no currents. If a Geissler tube g, with or without electrodes, is placed across the ends of the wires, it becomes luminous ; and if a metal wire, .1.- x\ is placed across the wires the luminosity may cease, but by moving the cross wire backwards or forwards, positions are found for which the luminosity reappears. This happens when the two separate circuits, a'sxs'b, xgx', are in resonance with each other. If a portion of each of the wires is cut off the resonance is disturbed, the tube is dark, and to restore the luminosity the bridge xx' must be moved nearer to F ; the amount of the displacement is half the length of the pieces thus cut off. If a sheet of tinfoil is attached to each end, the capacity is increased, the period of the vibration is increased, the wave length is greater, and to keep the tubes luminous the cross wire must be moved nearer the ends//'. This leads to a method of determining the electric wave-length. In certain ex- periments «ith a period of vibration of the one ten-millionth of a second, the distance of two consecutive nodes, or half a wave length, was found to be 14 m., so that from the formula (226) this gives for the velocity of electric waves 280,000 kilometres per second — -that is, approximately the same as that of light (518). The velocity is the same whatever be the nature of the wires used, from which it follows that the transmission is effected by the medium between the wires and not by the wire itself. The positions of the nodes on either of the wires st, s'i' may be found by encircling the wire by an insulated coil of fine platinum wire which is included in one arm of a Wheatstone's bridge (923). The resistance of the wire is increased when its temperature is raised. When the coil is situated at a current-node on the wire its resistance is not altered, but it increases and rises to a maximum as the coil is shifted to a point half-way between twa nodes. At the two sides of a node the oscillatory currents are always in opposite directions, and so there is practically no current and no develop- ment of heat ; at a loop the currents have their maximum intensity, and the wire is heated to the greatest extent. Thus the platinum-wire coil acts as a bolometer (932). A thermoelectric junction of iron and nickel is frequently used instead of the platinum-wire coil. The circular wire resonator of Hertz presents many difficulties in its use. The sparks are always small and cannot generally be seen except in a dark room. A much more sensitive detecter or receiver is that which was called by Lodge a coherer, and is based on an experiment made , by Branly, in which a circuit was formed including a Daniell cell, a glass tube containing metal filings, and a galvanometer. No current passed through the circuit since the filings are a non-conductor. When, however, the spark of an electric machine or a Leyden jar was produced in the neighbourhood of the tube, the needle of the galvanometer was powerfully deflected. The current ceased to pass when the tube containing the filings was gently 1038 Dynamical Electricity [1003- tapped, but did so when a spark was again produced, and so on. Thus the incidence of electric waves enormously diminishes the resistance of the filings ; in the original condition they are separated by thin air films, and the effect of the electric radiation is to set up rapidly alternating electro- motive force through the filings, bringing them into electric contact and ■causing them to cohere. The theory of Maxwell and the experiments of Hertz have led to a fundamental change in our views as to the way in which the electric ■current is transmitted. It has hitherto been considered that when the circuit is closed the wire itself is the agency by which the current is trans- mitted. We must for the future consider that the surrounding medium, the ether, transmits the electric energy, and that this energy enters the wire from the outside ; it is there destroyed as electro-magnetic energy, but is converted into heat, which heat travels by radiation from layer to layer like changes of temperature in a conductor. The less the rapidity with which the electric forces change their direction in the medium, the more com- pletely does heat penetrate the wire ; when the change takes place many million times in a second the interior of the wire is not affected by the current. This is analogous to the case of a body which is subject to excessively rapid .alternations of heat and cold. 1004. Wireless telegraphy. — Hertz's experiments were made about the year 1888 ; in 1896 Mr. Marconi brought over to England a system of signal- ling between two stations by means of electric waves and without the interven- tion of conductors of any kind. Since that time great advances have been made, and the distances signalled through increased from a few miles to 200 miles (from the Isle of Wight to Cornwall). Quite recently Mr. Marconi has announced the successful transmission of signals from Cornwall to Newfoundland. The transmitter in Marconi's system consists of a Ruhmkorff induction •coil, capable of giving a lo-inch spark in air. The terminals of the secondary are provided with polished brass balls about 2 cm. in diameter, and kept at about I centimetre apart (fig. 1028), but the spark gap is increased as the distance to be signalled over is greater. One of the terminals is earthed, while the other is connected with an insulated vertical conducting wire whose length is from 100 to 200 feet. This last is the essential part of the transmitter. The primary circuit of the Ruhmkorff includes a battery of about 10 volts, which is applied by a special form of key for a longer or shorter time, corresponding to the dots and dashes to be sent. When the key is depressed sparks pass between the terminal balls of the secondary. Each spark gives rise to electric oscillations in the aerial wire, which are transmitted in all directions through the ether and fall upon a ■similar aerial wire at the receiving station. In the simplest form of the receiving appa,ratus the aerial wire (fig. 1029) is connected to earth through a coherer, and the terminals of the coherer are joined by a circuit containing cell and galvanometer or relay (914). The circuit of the galvanometer is not dosed because the coherer is not a conductor ; but when Hertz waves impinge upon the receiving wire oscillations are set up in it which, traversing the coherer, render it a conductor, and the galvanometer needle is deflected. Many forms of coherer have been tried ; that employed by Marconi, which is -1004] Wireless Telegraphy 1039 at least as sensitive as any other, consists of a mixture of grains of nickel and silver contained in a small exhausted glass tube between silver electrodes very close together. When by the impact of Hertz waves the metallic powder is rendered conductive, a slight mechanical tap is necessary to restore it to its former non-conducting state. A ' tapper ' is consequently a neces- sary part of the receiving apparatus. In fig. 1028, A is the aerial conductor, S the spark balls in the secondai-y of the induction coil, K a signalling key in the primary, which can be depressed for an interval of time corresponding to a dot or a dash. Of the spark balls one is connected with the vertical conductor, the other is I A' Fig. 1029 Fig. 1028 •earthed. Fig. 1029 shows the receiver in its simplest form. The aerial wire A' is like that at the sending station — that is, the same aerial wire is used both for sending and for receiving ; it is connected to earth through the coherer C. R is a relay (914) which sets in action a circuit containing a battery of 8 or 10 dry cells and a recording instrument, M. These cells also work — -by an electromagnet similar to that of an electric bell (910) — the 'tapper,' which is close to C, but is not shown in the figure. When the transmitting key is depressed for an interval of time correspond- ing to a dot, several sparks pass at S, giving rise to electric oscillations in the vertical conductor, A. The waves radiated from it fall on A' and set up • oscillations in it whereby C becomes a conductor, and completes the circuit 1 040 Dynamical Electricity [1004- CR for a dot-intei-val of time, so that the Morse instrument at M records a dot. Similarly a longer depression of the transmitting key gives rise to a dash. It is found that with an oscillator such as that described, the oscillations are damped out very rapidly, all the energy being radiated in a few strong swings. The radiation is intense, but it lasts a very short time. The periodic time of vibration, /, = 27rA/LC where L is the inductance and C the capacity of the vibrating system. The receiving system will absorb the incident radiation to the greatest extent when its natural period of oscillation corresponds to that of the transmitter — that is, when the transmitting and receiving circuits are in tune with each other. Hence recent experiments have been directed (i) to diminution of damping, in other words, to the Fig, 1030 maintenance of the oscillations in the transmitter ; and (2) to the accurate tuning of the two circuits, so as to make the product LC the same for both. In connection with the question of tuning we may gain some help by considering some analogous acoustic phenomena. When a loud noise is made in the neighbourhood of a piano, from the wires of which the dampers have been removed, every wire is set in vibration, quite independently of wave length. This corresponds to a transmitter with intense but brief oscillations ; all receivers in the neighbourhood, if they are sufficiently sensitive, will be affected, whatever their natural period. But if a note of feeble intensity, but of definite pitch, is sounded in the room where the piano is, that string only will respond which is in unison with the note ; the rest will be unaffected. This corresponds to the transmitter with less intense -1004] Wireless Telegraphy 1041 I but more prolonged oscillations : a receiver in tune with it will respond ; others not in tune will not respond. Resonance depends upon the accumu- lated effects of properly timed impulses. They may be small but they must be maintained. If the electromotive impulses acting upon a receiving cir- cuit die away very quickly, resonant effects cannot be produced. Tuning has now been so far perfected that signals passed between the Isle of Wight and Poole (Dorsetshire) are not interfered with by those transmitted from Ports- mouth to Portland, though the two lines of communication cross each other at a small angle. For the purposes of wireless telegraphy it is desirable to have a more rapid and regular make and break for the induction coil than that with which the instrument is ordinarily provided (975), and several forms of mechanical break have been devised. Fig. 1030 shows a form in which the number of ' breaks ' per second, and also the duration of each ' make,' can be greatly varied. A is a glass cylinder, with a stout ebonite lid B, through the centre of which passes a spindle which can be put into rapid rotation by means of a motor M, driven by a battery of 5 or 6 volts. The spindle has attached to it near the top a portion of a cylinder provided with a number of equidistant blades, and at the bottom an arrangement which rotates inside a fixed flat cylindrical box, seen at the bottom of the glass cylinder. This box communicates with a vertical tube, in which a small orifice is made on the side facing the blades. By means of the knob S at the top of the tube the orifice can be raised or lowered, so that the mercury expelled from it may strike the blades at any distance from their tips. The lower part of the glass vessel contains mer- cury, to the height of about 1 1 inches, and the rest is filled with paraffin oil; When the spindle is set in rotation, mercui-y, which enters the flat cylinder by an aperture on the top, is forced up the lateral tube S, and is driven out of the small orifice in a hori- zontal sti-eam against the revolv- ing blades. If this apparatus is inserted between the battery (10 volts) and the primary of the induction coil, and the cylin- der with its blades rotated by the motor, the circuit is made and bioken by the mercurj' meeting the blades or passing through the spaces between them. The mercury can be made to impinge upon the broad or the narrow parts of the blades at pleasure, thus altering the duration of the ' make.' 3X Fig. 1031 1042 Dynamical Electricity [1004- The success recently attained in transmitting signals through great distances is partly due to the use of a specially constructed transformer (994) in the receiving circuit. Instead of connecting the vertical receiving wire in series with the coherer, as in fig. 1029, it is connected in series with the primary, P, of this transformer (fig. 1031), the secondary, S, of which is in series with the coherer C, cell B, and relay R. A condenser, K, is inserted between a and b. By this arrangement the voltage of the received oscillations is increased in the ratio of about 10 to i, and the resistance of the coherer more easily broken down. Tuning is effected by varying the self-induction of the aerial wire, and the capacity of the con- denser K, and in other ways, the object being to make LC the same for the transmitting and the receiving apparatus. 1005. Penetration of rapidly alternating currents and oscillatory currents into a conductor. — If we consider a conducting wire as made up of a number of parallel conducting filaments, an alternating current passing through any particular filament will be impeded by the induction due to currents in the neighbouring filaments, and their effect will be most felt in the axis of the wire. Consequently the currents will be stronger nearer the circumference than in the middle. If the alternations are sufficiently rapid the current will be practically confined to the skin of the conductor, the skin being defined as the thickness in which the strength of the current falls to i/e or -37 of its value at the surface. \i 71, the frequency of the alternations, = 100, the thickness of the skin is '5 mm. for iron, and 6'5 mm. for copper. But if n = 10", as in the oscillatory discharge of a Leyden jar or Hertz vibrator, the thickness of the skin is -005 mm. for iron, and "07 mm. for copper. Hence, since a lightning discharge is oscillatory, a lightning conductor of com- paratively thin copper ribbon or stranded iron wire is as serviceable as a massive rod, and cheaper. -1006] Physiological Actions 1043 CHAPTER XV PHYSIOLOGICAL ACTION OF THE CURRENT. ANIMAL ELECTRICITY 1006. Physiological actions. — Under this name are included the effects produced by a battery current on living organisms or tissues. When the electrodes of a battery of many cells are held in the two hands a violent shock is felt, especially if the hands are moistened with acidulated water, which increases the conductivity. The violence of the shock increases with the number of elements used, and with a large number — as 200 Bunsen's ■cells, giving an electromotive force of 360 volts — is even dangerous. The power of contracting upon the application of a voltaic current seems to be a very general property oi protoplasm^the: physical basis of both animal and vegetable life ; if, for example, a current of moderate strength is passed through such a simple form of protoplasm as an amoeba, it imme- diately withdraws its processes, ceases its changes of form, and contracts into a rounded ball — soon, however, resuming its activity upon the cessation of the current. Essentially similar effects of the current have been observed in the protoplasm of young vegetable cells. If a frog's fresh muscle (which will retain its vitality for a considerable time after removal from the body of the animal) is introduced into a galvanic circuit, no apparent effect will be observed during the steady passage of the current, but every opening or closure of the circuit will cause a muscular contraction, as will also any sudden and considerable alteration in the strength of the current. By very rapidly interrupting the current the muscle can be thrown into a state of uninterrupted contraction, or physiolo- gical tetanus, each new contraction occurring before the previous one has passed off. Other things being equal, the amount of shortening exhibited l3y the muscles increases, up to a certain limit, with the intensity of the current. These phenomena entirely disappear with the life of the muscle ; hence the experiments are somewhat more difficult with warm-blooded animals, the vitality of whose muscles, after exposure or removal from the body, is maintained with more difficulty ; but the results of careful experi- ment are exactly the same here as in the case of the frog. The influence of an electric current upon living nerves is very remark- able ; as a general rule, it may be stated that its effect is to throw the nerve into a state of activity, whatever its special function may be : thus, if the nerve be one going to a muscle, the latter will be caused to contract ; if it be one of common sensation, pain will be produced ; if one of special sense, the sensation of a flash of light, or of a taste, &c., will be produced, accord- ing to the nerve irritated. These effects do not manifest themselves during the even passage of the current, but only when the circuit is either opened or 3x2 I044 Dynamical Electricity [1006- closed or both. Of course the continuity of the nerve with the organ where its activity manifests itself must be maintained intact. The changes set up by the current in the different nerve-trunks are probably similar, the various- sensations, &c., produced depending on the different terminal organs with which the nerves are connected. If .a powerful electric current is passed thi'ough the body of a recently killed animal, violent movements are produced, as the muscles ordinarily retain their vitality for a considerable time after general systematic death: by this means, also, life has been re-established in animals which were appa- rently dead — a properly applied current stimulating the respiratory muscles- to contract. Professor Burdon Sanderson has ascertained that the movement which causes the Dionaa inuscipula (Venus's fly-trap), one of those which are called carnivorous plants, to close its hairy leaves and thereby entrap in- sects which alight upon it, is accompanied by an electrical current in a manner analogous to that manifested in muscular contraction. The manner in which the irritation is caused seems immaterial. 1007. Muscular currents. — The existence of electric currents in living muscle was first indicated by Galvani, but his researches fell into oblivion after the discovery of the voltaic pile, which was supposed to explain all the phenomena. Since then, Nobili, Matteucci, Du Bois Reymond, and others,, have shown that electric currents do exist in living muscles and nerves. For investigating these currents it is necessary to have a delicate gal- vanometer, and also electrodes which will not become polarised or give a current of their own, and which will not in any way alter the muscle when placed in contact with it ; the electrodes which satisfy these conditions best are those of Du Bois Reymond, as modified by Donders. Each consists of a glass tube, one end of which is narrowed and stopped by a plug of paste made by moistening china-clay with a solution of common salt ; the tube is then partially filled with a saturated solution of zinc sulphate ; and into this dips the end of a piece of thoroughly amalgamated zinc wire, the other end of which is connected by a copper wire with the galvanometer ; the moistened china-clay is a conducting medium which is perfectly neutral to the muscle, and amalgamated zinc in solution of zinc sulphate does not become polarised. The ordinary galvanometer has been superseded in many physiological investigations by the capillary electrometer of Lippmann (95°)- 1008. Currents of muscle at rest. — If a living irritable muscle is removed from a recently killed frog, and the clay of one electrode is placed in con- tact with its surface, and of the other with its tendon, the galvanometer will indicate a current from the former to the latter ; showing, therefore, that the surface of the muscle is positive with respect to the tendon. By varying the position of the electrodes, and making various artificial sections, it is found — 1. That any longitudinal section is positive to any transverse section. 2. That any point of a longitudinal section nearer the middle of the muscle is positive to any other point of the same section farther from the centre. —1010] Currents in Active Muscle 1045 3. In any artificial transverse section any point nearer the periphery is positive to one nearer the centre. 4. The current obtained between two points in a longitudinal or in . a transverse section is always much more feeble than that obtained between two different sections. 5. No current is obtained if two points of the same section equidistant from its centre are taken. 6. To obtain these currents it is not necessary to employ a whole muscle, •or a considerable part of one, but the smallest fragment that can be experi- mented with is sufficient. To explain the existence and relations of these muscular currents, it may be supposed that each muscle is made up of regularly disposed electromotor •elements, which may be regarded as cylinders whose axes are parallel to that •of the muscle, and whose sides are charged with positive and their ends with negative electricity ; and, further, that all are suspended and enveloped in a conducting medium. In such a case it is clear that throughout most of the muscle the positive electricities of the opposed surfaces would neutralise one another, as would also the negative charges of the ends of the •cylinders ; so that, so long as the muscle was intact, only the charges at its sides and ends would be left to manifest themselves by the production of •electromotive phenomena ; the whole muscle being enveloped in a conducting stratum, a current would constantly be passing from the longitudinal to the transverse section, and, a part of this being led off by the wire circuit, would manifest itself in the galvanometer. A perfectly fresh muscle, very carefully removed, with the least possible contact with foreign matters, sometimes gives almost no current between its different natural sections, and the current always becomes more marked after the muscle has been exposed a short time ; nevertheless, the phenomena are vital, for the currents disappear completely with the life of the muscle, sometimes becoming first irregular or even reversed in direction. 1009. Rheoscopic frog. Contraction without metals. — The existence of the muscular currents can be manifested without a galvanometer, by using another muscle as a galvanoscope. Thus, if the nerve of one living muscle of a frog is dropped suddenly on another living muscle, so as to come in contact with its longitudinal and transverse sections, a contraction of the first muscle will occur, due to the stimulation of its nerve by the passage through it of the electric current derived from the surface of the second. 1010. Currents in active muscle. — When a muscle is made to contract there occurs a sudden diminution of its natural electric current, as indicated by the galvanometer. This is so instantaneous that, in the case of a single muscular contraction, it does not overcome the inertia of the needle of the galvanometer ; but if the contractions are made to succeed one another very rapidly— that is, if the muscle is teta?iised — then the needle swings steadily back towards zero from the position in \\hich the current of the resting muscle had kept it, often gaining such momentum in the swing as to pass beyond the zero point, but soon reverting to some point between zero and its original position. The negative variation in the case of a simple muscular contraction can, however, be made manifest by using another muscle as a rheoscope ; if the 1046 Dynamical Electricity [1010- nerve of this second muscle is laid over the first muscle in such a position that the muscular current passes through it, and the first muscle is then made to- contract, the sudden alteration in its strength of the current stimulates the nerve laid on it, and so causes a contraction of the muscle to which the latter belongs. The same phenomenon can be demonstrated in the muscles of warm- blooded animals ; but with less ease, on account of the difficulty of keeping them alive after they are laid bare or removed from the body. Experiments made by placing electrodes outside the skin, or passing them through it, are inexact and unsatisfactory. loii. Electric currents in nerve. — The same electric indications can be obtained from nerves as from muscles — at least, as far as their smaller size will permit ; the currents are more feeble than the muscular ones, but can be demonstrated by the galvanometer in a similar way. Negative varia- tion has been proved to occur in active nerve as in active muscle. The effect of a constant current passed through one part of a nerve on the amount of the normal nerve-current, measured at another part, has already been described. 1012. Electric fish. — Electric fish are those fish which have the re- markable property of giving, when touched, shocks like those of the Leyden jar. Of these fish there are several species, the best known of which are the torpedo, the gymnotus, and the silurus. The torpedo, which is very common in the Mediterranean, was carefully studied by Becquerel and Breschet in France; and by Matteucci in Italy. The gymnotus was investigated by Humboldt and Bonpland in South America, and in England by Faraday, who had the opportunity of examining live specimens. The shock which they give serves as a means both of offence and of defence. It is purely voluntary, and becomes gradually weaker as it is repeated and as these animals lose their vitality, for the electric action soon exliausts them materially. According to Faraday, the shock which the gymnotus gives is equal to that of a battery of 1 5 jars exposing a coating of 25 square feet, which explains how it is that horses frequently give way under the repeated attacks of the gymnotus. Numerous experiments show that these shocks are due to ordinary electricity. For if, touching with one hand the back of the animal, the belly is touched with the other, or with a metal rod, a violent shock is felt in the wrists and arms ; while no shock is felt if the animal is touched with an insulating body. Further, when the back is connected with one end of a galvanometer wire and the belly with the other, at each discharge the needle is deflected, but immediately returns to zero, which shows that there is an instantaneous current ; and, moreover, the direction of the needle shows that the current goes externally from the back to the belly of the fish. Lastly, if the current of a torpedo be jjassed through a helix in the centre of which is a small steel bai', the latter is magnetised by the passage of a discharge. By means of the galvanometer, Matteucci established the following facts : — I. When a torpedo is lively, it can give a shock in any part of its body, but as its vitality diminishes, the parts at which it can give a shock are nearer the organ which is the seat of the development of electricity. 2. Any -1013] Application of Electricity to Medicine 1047 point of the back is always positive as compared with the correspond- ing point of the belly. 3. Of any two points at different distances from the electric organ, the nearer always plays the part of a positive pole, and the farther that of a negative pole. With the belly the reverse is the case. The organ where the electricity is produced in the torpedo is double, and formed of two parts symmetrically situated on two sides of the head and attached to the skull-bone by the internal face. Each part consists of nearly parallel lamelte of connective tissue enclosing small chambers, in which lie the so-called electric plates, each of which has a final nerve ramification distributed on one of its faces. The face, on which the nerve ends, is turned the same way in all the plates, and when the discharge takes place is alway negative to the other. Matteucci investigated the influence of the brain on the discharge. For this purpose he laid bare the brain of a living torpedo, and found that the first three lobes could be irritated without the discharge being produced, and that when they were removed the animal still possessed the faculty of giving a shock. The fourth lobe, on the contrary, could not be irritated without an immediate production of the discharge ; but if it was removed, all dis- engagement of electricity disappeared, even if the other lobes remained untouched. Hence it would appear that the primary source of the electricity elaborated is the fourth lobe, whence it is transmitted by means of the nerves to the two organs described above, which act as multipliers. In the silurus the head appears also to be the seat of the electricity ; but in the gymnotus it is found in the tail. 1013. Application of electricity to medicine. — The first applications of electricity to medicine date from the discovery of the Leyden jar. Nollet and Boze appear to have been the first who thought of the application, and soon the spark and electric friction became a universal panacea ; but it must be admitted that the results of subsequent trials did not come up to the hopes of the early experimentalists. After the discovery of dynamic electricity Galvani proposed its applica- tion to medicine ; since which time many physicists and physiologists have been engaged upon this subject, and yet there is still much uncertainty as to the real effects of electricity, the cases in which it is to be applied, and the best mode of applying it. Practical men prefer the use of currents to that of statical electricity, and, except in a few cases, discontinuous to continuous currents. There is, finally, a choice between the currents of the battery and induction currents ; further, the effects of the latter differ, according as induction currents of the first or second order are used. In fact, since induction currents, although very intense, have a very feeble chemical action, it follows that when they traverse the organs they do not produce the chemical effects of the current of the battery, and hence do not tend to produce the same disorganisation. Further, in electrifying the muscles of the face, induction currents are to be preferred, for these currents only act feebly on the retina, while the currents of the battery act energeti- cally on this organ, and may affect it dangerously. There is a difference in the action of induced currents of different orders ; for while the primary induced current causes lively muscular actions, but has little action on the 1048 Dynamical Electricity [1013- cutaneous sensibility, the secondary induced current, on the contrary, in- creases the cutaneous sensibility to such a point that its use ought not to be prescribed to persons whose skin is very irritable. Hence electric currents should not be applied in therapeutics without a thorough knowledge of their various pi-operties. They ought to be used with great prudence, for their continued action may produce serious acci- dents. Matteucci says : ' In commencing, a feeble current must always be used. This precaution now seems to me the more important as I did not think it so before seeing a paralytic person seized with almost tetanic con- vulsions under the action of a current formed of a single element. Take care not to continue the application too long, especially if the current is energetic. Rather apply a frequently interrupted current than a continuous one, especially if it be strong ; but after twenty or thirty shocks, at most, let the patient take a few moments' rest.' Of late years, however, feeble continuous currents have come more into use. -1015] Meteorograph 1049 ELEMENTARY OUTLINES METEOROLOGY AND CLIMATOLOGY METEOROLOGY 1014. Meteorology. — The phenomena which are produced in the atmo- sphere are called meteors \ and meteorology is that part of physics which is concerned with the study of these phenomena. A distinction is made between aerial meteors, such as winds, hurricanes, and whirlwinds ; aqueous meteors, comprising fogs, clouds, rain, dew, snow, and hail ; and luminous meteors, as lightning, the rainbow, and the aurora borealis. 1015. Meteorograph. — The importance of being able to make continuous observations of various meteorological phenomena has led to the construc- tion of various forms of automatic arrangements for this purpose, of which that of Osier in England may be mentioned. One of the most compre- hensive and complete is Secchi's meteorograph, which consists of a base of masonry about 2 feet high (fig. 1032); on this are fixed four columns about 2^ yards high, which support a table on which is a clockwork regulating the whole of the movements. The phenomena are registered on two sheets which move downwards on two opposite sides, their motion being regulated by the clockwork. One of them occupies ten days in so doing, and on it are registered the direction and velocity of the wind, the temperature of the air, the height of the barometer, and the occurrence of rain ; on the second, which only takes two days, the barometric height and the occurrence of rain are repeated, but on a much larger scale ; this gives moreover the moisture of the air. Direction of the wind. — The four principal directions of the wind are re- gistered by means of four pencils fixed at the top of thin brass rods, a, b, c, d (fig. 1032), which are provided at the bottom ends with soft iron keepers attracted by two electromagnets, E E', for west and north, and by two other electromagnets lower down for south and east. These four electro- magnets, as .well as all the others on the apparatus, are worked by a single battery of twenty-four cells. The passage of the current in one or another loso Meteorology [1015- of these electromagnets is regulated by means of a vane (fig. 1032) consisting of two plates at an angle of thirty degrees with each other, b}~ Fig. 1032 which greater steadiness is obtained than with a single plate. In the rod of the \ane is a small brass plate, o ; this part is in the centre of four metal -1015] Meteorograph 105 1 sectors, insulated from each other, and each provided with a binding-screw^ by which connection is estabhshed with the binding-screw K, and the elec- tromagnets E E'. The battery current reaches the rod of the vane by the wire a, and passes thence to the sUding contact o, which leads it to the electromagnet for the north, for instance. If the current passed constantly in this electromagnet, the pencil on the rod d would be stationary ; but from the electro- magnet E' the current passes into a second electromagnet, «, over the clockwork, and is thereby alternately opened and closed, as will be seen when we speak of the velocity of the wind. Hence the armature of the rod d, alternately free and attracted, oscillates ; and its pencil, which is always pressed against the paper AD by the elasticity of the rod, traces on it a series of parallel dashes as the paper descends, and so long as the wind is in the north. If the wind changes then to west, for in- stance, the rod a oscillates, and its pencil traces a different series of marks. The rate of displacement of the paper being known, we get the direction of the prevalent wind at a given moment. Velocity of the wind. — This is indi- cated by a Robinson's anemojneter, and is registered in two ways : by two counters which mark in decametres and kilometres the distance travelled by the wind ; and by a pencil which traces on a table a curve, the ordinates of which are proportional to the velocity of th^ wind. Robinson, who originally devised this form of anemometer (fig. 1034), proved that its velocity is proportional to that of the wind ; in this apparatus the length of the arms is so calculated that each re- volution corresponds to a velocity of ten metres. The anemometer is placed at a considerable distance from the meteoro- graph, and is connected with it by a copper wire, «^, which passes to the electro- magnet, «, of the counter. On its rod there is, moreover, an excentric, which at each turn touches a metal contact in connec- tion with the wire d. The battery current reaches the anemometer by a wire a, the circuit is closed once at each rotation, and the current passes to the electromagnet «, which move the Fig. 1034 I OS 2 Meteorology [1016- needle of the dial through one division. There are fifty such divisions, which represent as many turns of the vane, and therefore so many multiples of ten metres. The lower dial marks the kilometres. The curve of velocities is traced on the sheet by a pencil, i, fixed to a horizontal rod. This is joined at its two ends to two guide-rods, o and y, which keep it horizontal. The pencil and the rod are moved laterally by a chain which passes over two pulleys, r' and r, and is then coiled over a pulley placed on the shaft of the counter, but connected with it merely by a ratchet- wheel ; and moved thus by the counter and the chain, the pencil traces evei-y hour on the sheet a line the length of which is proportioned to the velocity of the windi From hour to hour an excentric moved by clockwork detaches, from the shaft of the counter, the pulley on which is coiled the chain, and this pulley becoming out of gear, a weight, p, connected with the pencil z', restores this to its starting-point. All the lines, V, traced succes- sively by the pencil, start as ordinates from the same straight line, and their ends give the curve of velocities. The counters on the right and left are worked by electromagnets, mm', and are intended to denote the velocity of special winds ; for instance, those of the north and south, by connecting their electromagnets with the north and south sectors of the vane (fig. 1033). Temperature of the air.—'X\i\% is indicated by the expansion and con- traction of a copper wire of 16 metres in length stretched backwards and forwards on a fir post 8 metres in length. The whole being placed on the outside — on the roof, for instance — the expansion and contraction are trans- mitted by a system of levers to a wire, v, which passes to the meteorograph, where it is jointed to a bent lever, /. This is jointed to a horizontal rod, .f, which supports a pencil, and at the other end is jointed to a guide-rod, x. Thus the pencil, sharing the oscillations of the whole system, traces the curve of the temperatures. Pressure of the atmosphere. — This is registered by the oscillations of a barometer, B, suspended at one end of a bent scale-beam, I F, playing on a knife-edge (fig. 1036). The arm F supports a counterpoise ; to the arm I is suspended the barometer B, which is wider at the top thfen at the bottom. A wooden flange or floater, Q, fixed to the lower part of the tube, plunges in a bath of mercury, so that the buoyancy of the liquid counterbalances part of the weight of the barometer. Owing to the large diameter of the barometric chamber, a very slight variation of level in this chamber makes the tube oscillate, and with it the scale-beam I F. To the axis of this is a triangle, ghk, jointed to a horizontal rod, which in turn is connected with a guide-rod, 2. In the middle of this rod is a pencil which, sharing in the oscillations of the triangle ^/^/i', traces the curve H of pressure. A bent lever at the bottom of the barometer tube keeps the latter in a vertical position. Rainfall. — This is registered between the direction of the winds and the curve H by a pencil at the end of a rod, u, which is worked by an electro- magnet, c. On the roof is a funnel which collects the rain, and a long tube leads the water to a small water-balance with the cups placed near the meteorograph (fig. 1035). To the axis of the scale-beam one pole of the battery is connected ; the left cup being full, tips up, and a contact, a, closes the circuit, and the current passes then to one of the binding-screws, -1015] Meteorograph 1053 C (fig. 1032), and hence to the electromagnet, e. Then the right cup, being' in turn full, tips in the opposite direction, and the contact b now transmits the current to the electromagnet. Thus, at each oscillation, this latter attracts its armature, and with it the rod u, which makes a mark by means of a pencil at the end. If the rain is abundant, the oscillations of the beam are rapid, and the marks, being very close together, give a deep shade ; if, on the contrary, the oscillations are slow, the marks are at a greater distance, and give a light shade. When the rain ceases the oscilla- tions cease also, and the pencil makes no mark. To complete this description of the first face of the meteorograph : S is the alarum-bell of the clock- M g|H^»' work ; 00 a cord supporting a weight which moves ^ ^ the works of the hour-hand ; LZ is a second cord that supports the weight which works the alarum ; the wheel U, placed below the clockwork, winds up the sheet AD when it is at the bottom of its course. The second sheet (fig. 1036) gives the barometric height and the rainfall like the first, but on a larger scale, since the motion of the sheet is five times as rapid. Its principal function is that of registering the moisture of the air. This is effected by means of the psychrometer (fig. 1037). T and T' are two thermo- pjg j^^j meters fixed on two plates. The muslin which covers the second is kept continually moist by water dropping on it. In each of the bulbs is fused a platinum >\ire ; the stems of the thermometers are open at the top, and in them are two platinum wires, m and «, suspended to a metal frame movable on four pulleys supported by a fixed piece, B. The frame A, in contact with the current of the battery, is suspended to a steel wire, L, which passes over a pulley to the meteorograph (fig. 1036). Here is a long triangular lever, W, which supports a small wheel, to which is fixed the wire L. The lever W, which turns about an axis,_/j is moved by a rod, a, by means of an excentric, which the clock works every quarter of an hour. At each oscillation the lever W transmits its motion to a small chariot, on which is an electromagnet, x, and at the same time to the steel wire L, which supports the frame A (fig. 1036). The chariot, moved towards the left by the rotation of the excentric, lets the frame sink. The moment the first platinum wire reaches the mercurial column of the dry- bulb thermometer, which is the highest, the circuit is closed, and the current passes into the electromagnet of the chariot. An armature at once causes a pencil to mark a point on the sheet which is the beginning of a line repre- senting the path of the dry-bulb thermometer. As the frame continues to descend, the second platinum wire touches the mercury of the wet bulb, and causes a current to flow in a relay, M, which opens the circuit of the electro- magnet, X. The pencil is then detached ; then, returning upon itself, the chariot reproduces the closing and opening of the circuit in the opposite direction, the pencil making another mark, which is the end of the line. There are thus formed two series of dots arranged in two curves, one of which represents the path of the dry, and the other the path of the wet, bulb. The horizontal distance of the t\vo points of these curves is proportional to -the IOS4 Meteorology [1015- difiference t-t^ of the temperatures indicated at the same moment by the thermometers (fig. 1037). ,S^ ' ^^=r^OQ r\ a M EJ M f 1! ^ 1 Fig. 1036 Quantity of rain. — The quantity of rain which falls in a given time IS registered on a disc of paper on a pulley, R. On the groove of this is coiled a chain to which is suspended a brass tube, P. This is fixed at the -1016] Direction and Velocity of Winds loss bottom to a float, which plunges in a reservoir placed in the base of the meteorograph. On passing out of the water-balance (fig. 1035) the water passes into this reservoir, and as its section is one-fourth that of the funnel, the height of water which falls is quadrupled ; it is measured on a scale, G, ■divided into millimetres. As the float rises, a weight, Z, moves the pulley in the contrary direction, and its rotation is proportional to the height of water which has fallen. A pencil moves at the same time from the centre to the circumference of the paper disc with a velocity of 5 mm, in 24 hours : hence the quantity of rain which falls every day is noted on a different place on the paper disc. 10 1 6. Direction and velocity of vyinds. — Winds are currents moving in the atmosphere with vari- able directions and velocities. There are eight principal directions in which they blow — north, north-east, east, south-east, south, south-west, west, and north-west. Mariners further divide each of the distances between those eight directions into four others, making in all 32 directions, which are called Jl>oints or rhumbs. A figure of 32 rhumbs on a circle, in the form of a star, is known as the mariner's card. Velocity is determined by means of the anemometer (fig. 1034), a small vane with fans, which the wind turns ; the velocity is deducted from the number of turns made in a given time. In our climate the mean velocity is from 18 to 20 feet in a second. With a velocity of less than 18 inches in a second no movement is perceptible, and smoke ascends straight ; with a velocity between i^ and 2 feet per second the wind is perceptible and pig. ,037 moves a pennant ; from 13 to 22 feet it is moderate, it stretches a flag and moves the leaves of trees ; with from 23 to 36 feet velocity it is fresh, and moves the branches of trees ; with 36 to 56 feet it is strong, and moves the larger branches and the smaller stems ; with a velocity of 56 to 90 feet it is a storm, and entire trees are moved ; and from 90 to 120 it is a hurricane. To measure the pressure of , the wind a plate is used, which by means of a vane is always kept in a direction facing the wind.' Behind the plate are one or mofe springs, which are the more pressed the greater is the pressure of the wind against the plate. Knowing the distance through which the plate is pressed, we can calculate the pressure which the wind exerts on the plate in question. With some degree of approximation, and for low velocities, the pressure may be taken as proportional to the square of the velocity. Thus, if the pressure on the square foot is 0-005 pound with a velocity of i'5 foot in a second, it is 0-02 pound with a velocity of 3 feet, and 0-123 with a velocity of 7-33 feet. 1056 Meteorology [1017- 1017. Causes of winds. — Winds are produced by a disturbance of the equilibrium in some part of the atmosphere : a disturbance always resulting- from a difference in temperature between adjacent countries. Thus, if the temperature of a certain extent of ground becomes higher, the air in contact with it becomes heated, expands and rises towards the higher regions of the atmosphere ; whence it flows, producing winds which blow from hot to cold countries. But at the same time the equilibrium is destroyed at the surface of the earth, for the barometric pressure on the colder adjacent parts is greater than on that which has been heated, and hence a current will be produced with a velocity dependent on the difference between these pressures : thus two distinct winds will be produced — an upper one setting outwards from the heated region, and a lower one setting inwards towards it. 1018. Regular, periodical, and variable -roinds. — According to the more or less constant directions in which winds blow, they may be classed as regular, periodical, and variable winds. i. Regular winds are those which blow all. the year through in a virtually constant direction. These winds, which are also known as the trade winds, are uninterruptedly observed far from the land in equatorial regions, blowing from the north-east to the south-west in the Northern Hemisphere, and from the south-east to the north-west in the Southern Hemisphere. They prevail on the two sides of the equator as far as 30° of latitude, and they' blow in the same direction as the apparent motion of the sun — that is, from east to west. The air above the equator being gradually heated, rises as the sun passes round from east to west, and its place is supplied by the colder air from the north or south. The direction of the wind, however, is modified by this fact,, that the velocity which this colder air has derived from the rotation of the earth — namely, the velocity of the surface of the earth at the point from which it started — is less than the velocity of the surface of the earth at the point at which it has now arrived : hence the currents acquire, in reference to the equator, the constant direction which characterises the trade winds. ii. Periodical winds are those which blow regularly in the same direction at the same seasons and at the same hours of the day : the monsoon, simoom, and the land and sea breeze are examples of this class. The name monsoon is given to winds which blow for six months in one direction and for six months in another. They are principally observed in the Red Sea and in the Arabian Gulf, in the Bay of Bengal and in the Chinese Sea. These winds blow towards the continents in summer, and in a contrary direction in winter. The simoom is a hot wind which blows over the deserts of Asia and Africa, and which is characterised by its high temperature and by the sands which it raises in the atmosphere and carries with it. During the prevalence of this wind the air is darkened, the skin feels dry, the respiration is accelerated, and a burning thirst is experienced. This wind is known under the name oi sirocco in Italy and Algiers, where it blows from the great desert of Sahara. In Egypt, where it prevails from the end of April to June, it is called katnsin. The natives of Africa, in order to protect themselves from the effects of the too rapid perspiration occasioned by this wind, cover themselves with fatty substances. A wind characteristic of Switzerland and known as the F'dhn originates as -1020] Law of the Rotation of Winds 1057 follows : a mass of air coming from the south-east being impelled over a mountain ridge becomes rarefied as it ascends ; the temperature falls, and it deposits its moisture on the other side as rain or snow. Being driven still forward into the valleys, the superincumbent pressure being greater, the air is condensed, and its temperature rises, and having parted with its moisture it appears as a wind which is at once hot and dry. One observation gave the temperature at 31-4° C, while it only contained 20 per cent, of moisture. The land and sea breeze is a wind which blows on the sea-coast, during the day from the sea towards the land, and during the night from the land to the sea. For during the day the land becomes more heated than the sea, in consequence of its lower specific heat and greater conductivity, and hence, as the superincumbent air becomes more heated than that upon the sea, it ascends and is replaced by a current of colder and denser air flowing from the sea towards the land. During the night the land cools more rapidly than the sea, and hence the same phenomenon is produced, but in a contrary direction. The sea breeze commences after sunrise, increases up to three o'clock in the afternoon, decreases towards evening, and is changed into a land breeze after sunset. These winds are only perceived at a slight distance from the shores. They are regular in the tropics, but less so in our climates ; traces of them are seen as far as the coasts of Greenland. The proximity of mountains, and also of forests, likewise gives rise to periodical daily breezes. iii. Variable winds are those which blow sometimes in one direction and sometimes in another, alternately, without being subject to any law In mean latitudes the direction of the winds is very variable ; towards the poles this irregularity increases, and under the arctic zone the winds frequently blow from several points of the horizon at once. On the other hand, in approach- ing the torrid zone they become more regular. The south-west wind prevails in England, in the north of France, and in Germany ; in the south of France the direction inclines towards the north, and in Spain and Italy the north wind predominates. 1019. Law of the rotation of winds. — Notwithstanding the great irregu- larity which characterises the direction of the winds in our latitude, it has been ascertained that the wind has a preponderating tendency to veer round according to the sun's motion — that is, to pass from north, through north- east-south-east to south, and so on round in the same direction from west to north ; that it often makes a complete circuit in that direction, or more than one in succession, occupying many days in doing so, but that it rarely veers, and very rarely or never makes a complete circuit in the opposite direction. This course of the winds is most regularly observed in winter. According to Leverrier, the displacement of the north-east by the south- west wind arises from the occurrence of a whirlwind formed upon the Gulf Stream. For a station in south latitude a contrary law of rotation prevails. This law, though more or less suspected for a long time, was first formally enunciated and explained by Dove, and is known as Dove's law of rotation of winds. 1020. Weather charts. — A considerable advance has been made in weather forecasts by the frequent and systematic publication of weather charts ; that is to say, maps in which the barometric pressure, the tempe- .^1 Y ios8 Meteorology [1020- rature, the force of the wind, &c., are expressed for considerable areas in an exact and comprehensive manner. A careful study of such maps renders possible a forecast of the weather for a day or more in advance. We can here do no more than explain the meaning of the principal terms in use. If lines are drawn through those places on the earth's surface where the corrected barometric height at a given time is the same, such lines are called isobarmmtric lines, or, more briefly, isobaric lines or isobars. Between any two points on the same isobar there is no difference of pressure. Isobars are usually drawn for a difference of 2"5 mm. or of ^ of an inch. If we take a horizontal line between two isobars, and at that point at which the pressure is greatest draw a perpendicular line on any suitable scale, which shall represent the difference in pressure between the two places, the line drawn from the top of this perpendicular to the lower isobar will form an angle with the horizontal, and the steepness of this angle is a measure of the fall in pressure between the two stations, and is called the barometric gradient. Gradients are usually expressed in England and America in hundredths of an inch of mercury for one degree of sixty nautical miles, and on the Continent in millimetres for the same distance. The closer are the isobars the steeper is the gradient, and the more powerful the wind ; and though no exact numerical relationship can be proved to exist between the steepness of the gradient and the force of the wind, it may be taken that a gradient of about 6 represents a strong breeze ; and a gradient of lo, or a difference in pressure oi ^ of an inch for 60 miles, is a stiff gale. The direction of the wind is from the place of higher pressure to that of lower, and in this respect the law of Buys Ballot may be mentioned, which has been found to hold in all cases of the Northern Hemisphere, where local configuration does not come into play. If we stand with our back to the wind, the line of lower pressure is on the left hand. For places in the Southern Hemisphere exactly the opposite law holds. If within any area the pressure is lower, the wind blows round that area, the place of lowest pressure being on the left of the observer, standing with his back to the wind. The direction of the wind is, in short, contrary to that of the hands of a watch. Such a circulation is called cyclonic ; it is that which is characteristic of the West Indian hurricanes, which are known as cyclones. Conversely, the wind blows round an area of higher pressure in the same direction as the hands of a watch ; and this circulation is called anti-cyclo7iic. Cyclonic systems are by far the most frequent, and are characterised by steep gradients ; the air in them tends to move in towards the centre, and thence to the upper regions of the atmosphere. They bring with them over the greater part of the region which they cover much moisture, an abundance of cloud, and heavy rain. An anti-cyclonic system has the opposite charac- teristics : the gradients are slight, the wind is light, and moves with the hands of a watch. The air is dry, so that there is but little cloud, and no rain. Cyclonic systems, from the dampness of the air, produce warm weather in winter, and cold wet weather in summer. Anti-cyclonic systems bring our hardest frosts in winter and greatest heat in summer, as there is but little moisture in the air to temper the extremes of climate. Both systems travel over the earth's surface — the cyclones rapidly, but the anti-cyclones more slowly. -1022] Clouds IOS9 1 02 1. Fogs and Mists. — When aqueous vapour rising from a vessel of boiling water diffuses in the colder air, it is condensed ; a sort of cloud is formed, consisting of a number of small particles of water, which remain apparently suspended in the air. These are usually spoken of as vapour, yet they are not so — at any rate, not in the physical sense of the word, for in reality they are condensed vapour. When this condensation of aqueous vapour is not occasioned by contact with cold solid bodies, but takes place throughout large spaces of the atmo- sphere, it constitutes fogs or mists, which, in fact, are essentially the same, the appearance seen over a vessel of hot water. A chief cause of fogs consists in the moist soil being at a higher tem- perature than the air. The vapours which then ascend condense and become visible. In all cases, however, the air must have reached its point of satura- tion before condensation takes place. Fogs may also be produced when a current of hot and moist air passes over a riyer at a lower temperature than its own ; for then, the air being cooled as soon as it is saturated, the excess of vapour present is condensed. The distinction between mists and fogs is one of degree rather than of kind. A fog is a very thick mist. By observations based on diffraction phenomena (660), the diameter of fog particles has been found to vary from 0-0154 to 0'052l mm. ; the longer the continuance of fine weather, the smaller are the particles ; before rams they increase rapidly. Dines, by direct microscopic measurement, found that the diameter of fog particles varied with the same fog from 0-015 to o'i27 mm. ; the larger occur in dense fogs, in lighter fogs they sink to 0-0033. Kamtz found from 0-014 to 0-035 ™ni- When water is coated with a layer of coal-tar, it is prevented from evaporating. Sir Edward Frankland ascribes the dry fog met with in London to the large quantities of coal-tar and paraffin vapour which are sent into the atmosphere, and which, condensing on the particles of fog, prevent their evaporation. Aitkin has shown that aqueous vapour never condenses unless some liquid or solid is present on which it is deposited. Particles of dust in the air are the nuclei for clouds and fogs. This he showed by passing steam into filtered air ; it remained quite clear, while a turbidity was produced under the same circumstances in unfiltered air. The density of the cloud was found to depend on the number of particles of dust in the air. A most abundant source of dust is the combustion of coal. The sulphur in the coal in burning also forms sulphurous acid, which though a gas, is found to act as a nucleus. 1022. Clouds.' — Clouds are masses of vapour condensed into little drops or particles of extreme minuteness, like fogs. There is no difference of kind between fogs and clouds. Fogs are clouds resting on the ground. To a person enveloped in it, a cloud on a mountain appears like a fog. They always result from the condensation of vapour which rises from the earth. The horizontal base of a cloud denotes a layer of air in which the ascending current of air has attained the dew-point. According to their appearance clouds were divided by Howard into four principal kinds : the nimbus, the stratus, the cumulus, and the cirrus. These four kinds are represented in 3 Y2 io6o Meteorology [1022- fig. 1038, and are designated respectively by one, two, three, and four birds on the wing. The cirrus consists of small whitish clouds, which have a fibrous or wispy appearance, and occupy the highest regions of the atmosphere. The name of mares' tails, by which they are generally known, well describes their appearance. From the low temperature of the spaces which they occupy, it is certain that cirrus clouds consist of frozen particles ; and hence it is that halos, coronas, and other optical appearances, produced by refrac- tion and reflection from ice-crystals, appear almost always in these clouds and their derivatives. Their appearance often precedes a change of weather. The cumulus are rounded spherical forms which look like mountains of cotton wool piled one on the other. They are more frequent in summer Fig. 1038 than in winter, and after being formed in the morning, they generally dis- appear towards evening. If, on the contrary, they become more numerous, and especially if surmounted by cirrus clouds, rain or storms may be expected. Any such cumulus is nothing more than an ascending current of air which makes its path visible by condensed aqueous vapour. Stratus clouds consist of very large and continuous horizontal sheets, which form chiefly at sunset and disappear at sunrise. They are frequent in autumn and unusual in spring-time, and are lower than the preceding. The nimbus, or rain clouds, which are sometimes classed as one of the fundamental varieties, are properly a combination of the three preceding kinds. They affect no particular form, and are solely distinguished by a uniform grey tint and by fringed edges. They are indicated on the right of the figure by the presence of one bird. -1023] Formation of Clouds 1061 The fundamental forms pass into one another 'in the most varied manner. Howard classed these transitional forms as cirro-cumulus, cirro-stratus, and cumulo-stratus, and it is often very difficult to tell, from the appearance of a cloud, which type it most resembles. The cirro-cumulus is most cha- racteristically known as a ' mackerel sky ; ' it consists of small roundish masses, disposed with more or less irregularity. It is frequent in summer, and attendant on warm and dry weather. Cirro-stratus appears to result from the subsidence of the fibres of cirrus to a horizontal position, which at the same time approach laterally. The form and relative position when seen in the distance frequently give the idea of shoals of fish. The tendency of cumulo-stratus is to spread, settle down into the nimbus, and finally fall as rain. The height of clouds varies greatly ; in the mean it is from 1,300 to 1,500 yards in winter, and from 3,300 to 4,3co yards in summer. But they often exist at greater heights ; Gay-Lussac in his balloon ascent, at a height of 7,630 yards, observed cirrus clouds above him, which appeared to be at a considerable height. In Ethiopia, D'Abbadie observed storm-clouds whose height was only 230 yards above the ground. In order to explain the suspension of clouds in the atmosphere, Halley first proposed the hypothesis of vesicular vapours. He supposed that clouds are formed of an infinity of extremelj minute \esicles, hollow, like soap- bubbles filled with air, which are hotter than the surrounding air, so that these vesicles float in the air like so many small balloons. Others assume that clouds and fogs consist of extremely minute droplets of water, which are retained in the atmosphere by the ascensional force of currents of hot air, just as light powders are raised by the wind. Ordinarily, clouds do not appear to descend, but this absence of downward motion is only apparent. In fact, clouds do usually fall slowly, but then the lower part is continually dissipated on coming in contact with the lower and more heated layers ; at the same time the upper part is always increasing from the condensation of new vapours, so that from these two actions clouds appear to retain the same height. 1023. Formation of clouds. — Many causes may concur in the formation of clouds. The usual cause of the formation of a cloud is the ascent, into higher regions of the atmosphere, of air laden with aqueous vapour ; it thereby expands, being under diminished pressure ; and in consequence of this expansion it is cooled, and this cooling produces a condensation of vapour. Hence it is that high mountains, stopping the currents of air and forcing them to rise, are an abundant source of rain. If the air is quite dry, its temperature would be one degree lower for every 300 metres. The case is different with moist air ; for when the air has ascended so high that its temperature has fallen to the dew-point, aqueous vapour is condensed, and in consequence of this heat is liberated ; when the dew-point is thus attained, and the air is saturated, the cooling due to the ascent and expansion of air is counteracted by this liberation of latent heat, so that the diminution of temperature with the height is considerably slower in the case of moist than of dry air. About one-half of the entire quantity of moisture in the air is contained in the first six or seven thousand feet upon the ground. The following calculation will give us the quantity of water separated io62 Meteorology [1023- in a given case : Suppose air at a temperature of 20° to be saturated with aqueous vapour at that temperature ; the pressure of the vapour will be I7'4 mm., and the weight contained in one cubic metre of air I7'i grammes. If the air has risen to a height of 3,500 metres, it has come under a pressure which is only \ of what it was : its temperature is 4°, and its volume about ij times what it originally was. As it remains saturated the pressure will be 6'i mm., and the quantity of vapour will be 6-4 grammes in a cubic metre — that is to say, 6-4 x i^ = 9-6 grammes in the whole mass of what was originally a cubic metre. The pressure of aqueous vapour has sunk during the ascent from I7'4 mm. to 6'i mm., and its weight from 17-1 grammes to 9'6 grammes ; that is, a weight of 7-5 grammes has been deposited from the mass of air which at the sea-level occupied a space of one cubic metre. These 7-5 grammes are in the form of the small droplets which constitute fogs or clouds. If the mass of air has risen to a height of 8,500 metres, where the pres- sure is only one-third that on the sea-level, the temperature is — 28°, and the space it occupies three times as great as at first. The pressure of aqueous vapour is 0-5 mm., and its weight o'6 gramme in a cubic metre. Hence there is now only i-8 gramme left of the entire quantity of aque- ous vapour originally present, and the remaining 15-3 grammes would be separated as water or ice. A similar calculation will show that at a height of 4,200 metres, where the temperature is zero and the pressure §, the quan- tity of water present in the original cubic metre is only 0-82 gramme, the rest being deposited. Thus, a mass of air which, at the sea-level, occupies a space of a cubic metre, and is saturated with aqueous vapour at 20°, and then contains 17- 1 grammes, will contain only 9-6 grammes at a height of 3,500 metres, 8-2 grammes at 4,200 metres, and i-8 gi'amme at 8,500 metres. Hence, while a mass of air rises from the sea-level to a height of 4,200 feet, 8-9 grammes of aqueous vapour are separated as cloud-particles ; at 8,500 metres, or about double the height, 6-4 grammes are separated in the form of ice. A hot moist current of air mixing with a colder current undergoes a cooling, which brings about a condensation of the vapour. Thus, the hot and moist winds of the south and south-west, mixing with the colder air of our latitudes, give rain. The winds of the north and north-east tend also, in mixing with our atmosphere, to condense the vapours ; but as these winds, owing to their low temperature, are very dry, the mixture rarely attains saturation, and generally gives no rain. The formation of clouds in this way is thus explained by Hutton. The pressure of aqueous vapour, and therewith the quantity present in a given space when saturated, diminishes according to a geometrical progression, while the temperature falls in arithmetical progression, and therefore the elasticity of the vapour present at any time is reduced by a fall of tempera- ture more rapidly than in direct proportion to the fall. Hence, if a current of warm air, saturated with aqueous vapour, meets a current of cold air also saturated, the air acquires the mean temperatitre of the two, but can retain only a portion of the vapour in the invisible condition, and a cloud or mist is formed. Thus, suppose a cubic metre of air at 10° C. mixes with a cubic metre of air at 20° C, and that they are respectively saturated with aqueous -1024] Rain 1063 Fig. 1039 Fig. 1040 vapour. By formula (407) it is easily calculated that the weight of water contained in the cubic metre of air at 10° C. is 9397 grammes, and in that at 20° C. is I7'IS3 grammes, or 26-559 grammes in all. When mixed they produce two cubic metres of air at 15° C. ; but as the weight of water required to saturate this is only 2xi2'8 = 25-6 grammes, the excess, 0-95 gramme, will be deposited in the form of mist or clouds. 1024. Rain. — When the individual water-particles become larger and heavier by the condensation of aqueous vapour, and when, finally, individual particles unite, they form regular drops, which fall as rain. The quantity of rain which falls annually in any given place, or the annual rainfall, is measured by means of a rain-gauge, or pluviometer. Ordinarily it consists of a cylindrical vessel, M (figs. 1039 and 1040), closed at the top by a funnel-shaped lid, in which there is a very small hole, through which the rain falls. At the bottom of the vessel is a glass tube, A, in which the water rises to the same height as inside the rain- ' gauge, and is measured by a scale on the side, as shown in the figures. The apparatus being placed in an exposed situation, if at the end of a month the height of water in the tube is two inches, for example, it shows that the water has attained this height in the vessel, and, conse- quently, that a layer of two inches in depth expresses the quantity of rain which this extent of surface has received. It has been noticed that the quantity of rain indicated by the rain-gauge is greater the nearer this instrument is to the ground. This has been ascribed to the fact that the raindrops, which are generally colder than the layers of air which they traverse, condense the vapour in these layers, and therefore constantly increase in volume. Hence more rain falls on the surface of the ground than at a certain height. But it has been objected that the excess of the quantity of rain which falls, over that at a certain height, is six or seven times that which could arise from condensation, even during the whole course of the raindrops from the clouds to the earth. The difference must therefore be ascribed to purely local causes, and it is now assumed that the difference arises from eddies produced in the air about the rain-gauge, which are more perceptible the higher it is above the ground : as these eddies dis- perse the drops which would otherwise fall into the instrument, they diminish the quantity of water which it receives. In any case it is clear that, if raindrops traverse moist air, they will, from their lower temperature, condense aqueous vapour and increase in volume. If, on the contrary, they traverse dry air, the drops tend to vaporise, and less rain falls than at a certain height ; it might even happen that the rain did not reach the earth. From measurements of the corona (1022), Delezenne determined the 1064 Meteorology [1024- diameter of the globules in the case of rain-clouds just about to fall, and in the case of the cloud from a low-pressure steam-engine (478). The former was found to vary from 0-0565 to 0-0226 mm., and the latter from 0-005 1 to 0-0042 mm. With the former, 5,500 droplets would be needed to make a drop of water a millimetre in diameter, and with the latter 50,000. According to the same author, there would be about 1 5 mgr. of globules in a cubic metre of a cloud which produced a rainfall of 10 mm. of water in an hour. With this number the mean distances of the particles with the above magnitudes are respectively 1-845, 0706, 0-167, a^"d 0-148 mm. Many local circumstances may affect the quantity of rain which falls in different countries ; but, other things being equal, most rain falls in hot cli- mates, for there the vaporisation is most abundant. The rainfall decreases, in fact, from the equator to the poles. At London it is 23-5 inches ; at Bordeaux it is 25-8 ; at Madeira it is 27-7 ; at Havannah it is 91-2; and at St. Domingo it is 107-6. The quantity varies with the season : in Paris, in winter, it is 4-2 inches ; in spring, 6-9 ; in summer, 6-3 ; and in autumn, 4-8 inches. The heaviest annual rainfall at any place on the globe is on the Khasi Hills, in Bengal, where it is 600 inches ; of which 500 inches fall in seven months. On July i, 1851, a rainfall of 25J inches on one day was observed at Cherrapoonjee. At Kurrachee, in the north-west of India, the rainfall is only 7 inches. The rainfall diminishes with the height of a station above the sea-level at the rate of 3 or 4 per cent, for each loo feet of altitude above the sea. The driest recorded place in England is Lincoln, where the mean rainfall is 20 inches ; and the wettest is Stye, at the head of Borrowdale, in Cumber- land, where it amounts to 165 inches. The greatest average amount of rain- fall in any one day, taking the means of all stations, is \\ inch ; though individual stations far exceed this amount, sometimes reaching 4 inches. An inch of rain on a square yard of surface expresses a fall of 46-74 pounds, or 4-67 gallons. On an acre it corresponds to 22,622 gallons, or 100-9935 tons. 100 tons per inch per acre is a ready way of remembering this. 1025. Waterspouts. — On hot summer days, and when the weather is otherwise calm, we often notice sand and dust carried forward in a column with a whirling motion. As storms come on, larger whirlwinds of this kind are formed, which carry with them leaves, straw, and even small branches. When they are of larger dimensions they form real whirlwinds. They are probably due to the contact of two winds blowing in the upper regions of the atmosphere. When they pass over land they form large conical-shaped masses of dust, which make them visible at a distance ; when they pass over rivers or the sea they present a curious phenomenon : the water is disturbed, and rises in the form of a cone, while the clouds are depressed in the form of an inverted cone ; the two cones then unite and form a continuous column from the sea to the clouds (fig. 1041). Even, however, on the high seas the water of these watersprouts is never salt, proving that they are formed of condensed vapour, and not of sea-water raised by aspiration. 1026. Influence of aqueous vapour on climate. — -Tyndall applied the property possessed by aqueous vapour of powerfully absorbing and radiating -1026] Influence of Aqueous Vapour on Climate 1065 heat to the explanation of some obscure points in meteorology. He esta- blished the fact that in a tube 4 feet long the atmospheric vapour on a day of average dryness absorbs 10 per cent, of obscure heat. With the earth warmed by the sun as a source, at the very least 10 per cent, of its heat is intercepted within 10 feet of the surface. The absorption and radiation of aqueous vapour is more than 16,000 times that possessed by dry air. The radiative power of aqueous vapour may be the main cause of the torrent-like rains that occur in the tropics, and also of the formation of cumulus clouds in our own latitudes. The same property probably causes the descent of very fine rain, called serein, which has more the characteristics of falling dew, as it appears a short time after sunset, when the sky is clear ; its production has therefore been attributed to the cold resulting from the Fig. 1041 radiation of the air. It is not the air, however, but the aqueous vapour in the air, which by its own radiation chills itself, so that it condenses into sdrein. The absorbent power of aqueous vapour is of even greater importance. Whenever the air is dry, terrestrial radiation at night is so rapid as to cause mtense cold. Thus, in the central parts of Asia, Africa, and Australia, the daily range of the thermometer is enormous ; in the interior of the last- named continent a difference in temperature of no less than 40° C. has been recorded within 24 hours. In India, and even in the Sahara, ice has been formed at night, owing to the copious radiation. But the heat which aqueous vapour absorbs most largely is of the kind emitted from sources of low temperature ; it is to a large extent transparent to the heat emitted from the sun, whilst it is almost opaque to the heat radiated from the earth. io66 Meteorology [1026- Consequently the solar rays penetrate our atmosphere with a loss, as estimated by Pouillet, of only 25 per cent., when directed vertically downwards, but after warming the earth they cannot retraverse the atmosphere. Through thus preventing the escape of terrestrial heat, the aqueous vapour in the air moderates the extreme chilling which is due to the unchecked radiation from the earth, and raises the temperature of that region over which it is spread. In Tyndall's words, ' aqueous vapour is a blanket more necessary to the vegetable life of England than clothing is to man. Remove for a single summer night the aqueous vapour from the air which overspreads this country, and every plant capable of being destroyed by a freezing tempera- ture would perish. The warmth of our fields and gardens would pour itself unrequited into space, and the sun would rise upon an island held fast in the iron grip of frost.' 1027. Tyndall's researches. — Tyndall found that the action of the sun or of the electric light decomposed certain highly rarefied vapours. He used a glass tube, which could be exhausted and then filled with air charged with the vapours of volatile liquids, by allowing the air to bubble through small Wolff bottles containing them. By mixing the air charged with vapour with differ- ent proportions of pure air, and by varying the degrees of exhaustion, it was possible to have a vapour under any degree of attenuation. The tube could also be filled with the vapour of a liquid alone. The tube having been filled with air charged with vapour of amyl nitrite, a somewhat convergent beam from the electric lamp was passed into the tube. For a moment the tube appeared optically empty, but suddenly a shower of liquid spherules was precipitated on the path of the beam, forming a luminous white cloud. The nature of the substance thus precipitated was not specially investigated. This effect was not due to any chemical action between the vapour and the air, for when either dry oxygen or dry hydrogen was used instead of air, or when the vapour was admitted alone, the effect was substantially the same. Nor was it due to any heating effect, for the beam had been previously sifted by passing through a solution of alum, and through the thick glass of the lens. The unsifted beam produced the same effect ; the obscure calorific rays did not seem to affect the result. The sun's light also effects the decomposition of amyl nitrite vapour ; and this decomposition was found to be mainly due to the more refrangible rays. When the electric hght, before entering the experimental tube, was made to pass through a layer of liquid amyl nitrite an eighth of an inch in thickness, the luminous effect was not appreciably diminished, but the chemical action was almost entirely stopped. Thus, that special constituent of the luminous radiation which effects the decom- position of the vapour is absorbed by the liquid. The decomposition of liquid amyl nitrite by light, if it take place at all, is far less rapid and distinct than that of the vapour. The absorption is the same, whether the nitrite is in the liquid or in the vaporous state, showing that it is not the act of the molecule as a whole, but that it is atomic ; that is, that it is to the atoms that the peculiar rate of vibration is transferred which brings about the decomposition of the body. It was also found that a vapour which when alone resists the action of light may, by being associated with another gas or vapour, exhibit a vigorous action. Thus, when the tube was filled with atmospheric air, mixed with —1027] Tyndall's Researches 1067 butyl nitrite vapour, the electric light produced very little effect ; but with half an atmosphere of this mixture, and half an atmosphere of air which had passed through hydrochloric acid, the action of the light was almost instan- taneous. In another case, mixed air and butyl nitrite vapour were passed into the tube so that the mixture was under a pressure of 2'5 mm. Air passed through aqueous hydfochloric acid was introduced until the pressure was 3 inches. The condensed beam passed through at first without change, but afterwards a superb blue cloud was formed. In cases where the vapours are under a sufficient degree of attenuation, whatever otherwise be their nature, the visible action commences with the formation of a blue cloud. The term ' cloud,' however, must not be understood in its ordinary sense ; the blue cloud is invisible in ordinary daylight, and to be seen must be surrounded by darkness, it alone being illuminated by a powerful beam of light. The blue cloud differs in many important particulars from the finest ordinary clouds, and may be considered to occupy an inter- mediate position between these clouds and true cloudless vapour. By graduating the quantity of vapour, the precipitation may be obtained of any required degree of fineness ; forming either particles distinguishable by the naked eye, or particles beyond the reach of the highest microscopic power. The case is similar to that of carbonic acid gas, which, diffused in the atmosphere, resists the decomposing action of solar light, but is decom- posed when in contact with the chlorophyll in the leaves of plants. When the blue cloud produced in these experiments was examined by any polarising arrangement, the light emitted laterally from the beam— that is, in the direction at right angles to its axis— was found to be perfectly polar- ised. This phenomenon was observed in its greatest perfection the more perfect the blue of the cloud. It is produced by any particles, provided they are sufficiently fine. This is quite analogous to the light of the blue sky. When this is examined by a Nicol prism, or any other analyser, it is found that the light emitted at right angles to the path of the sun's rays is polarised. The phenomena of the firmamental blue, and the polarisation of the sky-light, thus find definite explanations in these experiments. We need only assume the existence, in the higher regions of the atmosphere, of excessively fine particles of water ; for particles of any kind produce this effect. It is easy to conceive the existence of such particles in the higher regions, even on a hot summer's day. For the vapour must there be in a state of extreme attenuation ; and inasmuch as the oxygen and nitrogen of the atmo- sphere behave like a vacuum to "radiant heat, the extremely attenuated particles of aqueous vapour are practically in contact with the absolute cold of space. ' Suppose the atmosphere surrounded by an envelope impervious to light but with an aperture on the sunward side, through which a parallel beam of solar light could enter and traverse the atmosphere. Surrounded on all sides by air not directly illuminated, the track of such a beam would resemble that of the parallel beam of the electric light through an incipient cloud. The sunbeam would be blue, and it would discharge light laterally in the same condition as that discharged by the incipient cloud. The azure revealed by such a beam would be to all intents and purposes a blue cloud.' i.o68 Meteorology [1028- 1028. Dew. Hoarfrost. — Dew is aqueous vapour which has condensed on bodies during the night in the form of minute globules. It is occasioned by the chilHng which bodies near the surface of the earth experience in consequence of nocturnal radiation. Their temperature having then sunk several degrees below that of the air, it frequently happens, especially in hot seasons, that this temperature is below that at which the atmosphere is saturated. The layer of air which is immediately in contact with the chilled bodies, and which has virtually the same temperature, then deposits a por- tion of the vapour which it contains (400) ; just as when a bottle of cold water is brought into a warm room it becomes covered with moisture, owing to the condensation of aqueous vapour upon it. According to this theory, which was first propounded by Dr. Wells, all causes which promote the cooling of bodies increase the quantity of dew. These causes are the emissive power of bodies, the state of the sky, and the agitation of the air. Bodies which have a great radiating power more readily become cool, and therefore ought to condense more vapour. In fact there is generally no deposit of dew on metals, whose radiating power is very small, especially when they are polished ; while the ground, sand, glass, and plants, which have a great radiating power, become abundantly covered with dew. The state of the sky also exercises a great influence on the formation of dew. If the sky is cloudless, the planetary spaces send to the earth an in- appreciable quantity of heat, while the earth radiates very considerably, and therefore, becoming very much chilled, there is an abundant deposit of dew. But if there are clouds, as their temperature is far higher than that of the planetary spaces, they radiate in turn towards the earth, and as bodies on the surface of the earth experience only a feeble chilling, no deposit of dew takes place. Wind also influences the quantity of vapour deposited. A gentle breeze increases the deposition, since it renews the air; the contrary effect is produced by a strong wind, which heats the surface by contact, and thus does not allow the air time to become cooled. Finally the deposit of dew is more abundant according as the air is moister, for then it is nearer its point of saturation. Hoarfrost and rime are dew which has been deposited on bodies cooled below zero, and has become frozen. The flocculent form which the small crystals present of which rime is formed, shows that the vapour solidifies directly without passing through the liquid state. Hoarfrost, like dew, is formed on bodies which radiate most, such as the stalks and leaves of vege- tables, and is chiefly deposited on the parts turned towards the sky. We must distinguish between the dew formed in consequence of lowering of temperature by radiation, and the deposit formed by warm moist air passing over a cold wall ; in mild weather this deposit forms a liquid, and in severe weather a snow or icy coating. Unlike dew, a deposit of this kind is most abundantly found on good conductors, for they are the coldest. 1029. Snow. Sleet. — Snow is water solidified in stellate crystals, vari- ously modified, and floating in the atmosphere. These crystals arise from the congelation of the minute particles which constitute the clouds, when the temperature of the latter is below zero. They are more regular when formed in a calm atmosphere. Their form may be investigated when they are collected -1031] Ice. Regelation 1069 on a black surface and viewed through a strong lens. The regularity, and at the same time variety, of their forms are truly beautiful. Fig. 1042 shows some of these forms as seen through a microscope. Very roughly, a fall of one foot of snow may be taken as equal to an inch of rain. It snows most in countries near the poles, or lying high above the sea-level. By the limit of perpetual snow — or, briefly, snow-lme — is meant that height above the sea-level at which the snow does not melt, even in the hottest summers. It is lower nearer the poles than the equator : it does not depend solely on the latitude, but is influenced by many local circumstances. Sleet is also solidified water, and consists of small icy needles pressed together in a confused manner. Its formation is ascribed to the sudden congelation of the minute globules of the clouds in an agitated atmosphere. Fig. 1042 When the ground is cooled below zero after severe frost and a thaw sets in, the moist air passing over the ground deposits its moisture, which is converted into a continuous sheet of ice ; this is known as glazed frost (the French verglas) ; it may also occur when raindrops which have been cooled below zero in the higher regions of the air, and are accordingly in a state of superfusion (348), fall on the ground, which may even be above the freezing- point. 1030. Hail. — Hail is a mass of compact globules of ice of different sizes which fall in the atmosphere. In our climate hail falls principally during spring and summer, and at the hottest times of the day ; it rarely falls at night. The fall of hail is always preceded by a peculiar noise. Hail is generally the precursor of storms ; it rarely accompanies them, and follows them still more rarely. Hail falls from the size of a small pea to that of an ^^% or an orange, with a core of compressed snow which is sur- rounded by concentric layers of ice. While snowstorms may last for days, hailstorms do not last for more than a quarter of an hour. The formation of hailstones has never been altogether satisfactorily accounted for ; nor, more especially, their great size. 1031. Ice. Regelation. — Ice is an aggregation of snow-crystals, such as are shown in fig. 1042. The transparency of ice is due to the close contact I070 Meteorology [1031- of these crystals, which causes the individual particles to blend into an un- broken mass, and renders the -substance optically^ as well as mechanically, continuous. When large masses of ice slowly melt away, a crystalline form is sometimes seen by the gradual disintegration into rude hexagonal prisms ; a similar structure is frequently met with, but in greater perfection, in the ice-caves or glaciers of cold regions. An experiment of Tyndall shows the beautiful structure of ice. When a piece of ice is cut parallel to its planes of freezing, and the radiation from any source of light is permitted to pass through it, the disintegration of the substance proceeds in a remarkable way. By observing the plate of ice through a lens, numerous small crystals will be seen studding the interior of the block ; as the heat continues these crystals expand, and finally assume the shape of six-rayed stars of exquisite beauty. This is a kind of negative crystallisation, the crystals produced being composed of water ; they owe their formation to the molecular disturbance caused by the absorption of heat from the source. Nothing is easier than to reproduce this phenomenon, if care be taken in cutting the ice. The planes of freezing can be found by noting the direction of the bubbles in ice, which are either sparsely arranged in striae at right angles to the surface, or thickly collected in beds parallel to the surface of the water. A warm and smooth metal plate should be used to level and reduce the ice to a slab not exceed- ing half an inch in thickness. A still more important property of ice remains to be noticed. Faraday discovered that when two pieces of melting ice are pressed together they freeze into one at their points of contact. This curious phenomenon is now known under the name of Regelation. The cause of it has been the subject of much controversy ; Faraday's explanation is as follows : — The particles on the exterior of a block of ice are held by cohesion on one side only : when the temperature is at o° C, these exterior particles, being partly free, are the first to pass into the liquid state, and a film of water covers the solid. But the particles in the interior of the block are bounded on all sides by the solid ice, the force of cohesion is here a maximum, and hence the interior ice has no tendency to pass into a liquid, even when the whole mass is at o°. If the block is now split in halves, a liquid film instantly covers the fractured surfaces, for the force of cohesion on the fractured surfaces has been lessened by the act. By placing the halves together, so that their original position shall be regained, the liquid films on the two fractured surfaces again become bounded by ice on both sides. The film being excessively thin, the force of cohesion is able to act across it ; the consequence of this is, the liquid particles pass back into the solid state, and the block is reunited by regelation. A more satisfactory explanation is that which refers the phenomena to the lowering of the freezing-point of water by pressure (342). Two pieces of ice at 0° C. will not melt, if they are prevented from absorbing heat. When pressed together at 0°, since the melting-point is lowered, an incipient lique-. faction takes place at the surfaces of contact, and when the pressure is relaxed, the freezing-point rises and the two pieces are frozen together. The .formation of a snowball is explained in the same way. At temperatures below 0° C. a snowball cannot be made ; the snow is dry and the pressure -1033] Atmospheric Electricity 1071 of the hands is not sufficient to lower the melting-point necessary to produce regelation. The snow-bridges, also, which span wide chasms in the Alps and else- where, and over which men can walk in safety, owe their existence to the regelation of gradually accumulating particles of snow. We see an example of this formation of ice from pressure in the glazed appearance of the tracks in snow on roads over which heavy carts have passed. Bottomley has made a very instructive experiment which illustrates the effect of pressure on regelation. A block of ice is suspended on two supports, and a hempen string with heavy weights at each end is laid across it. After some time the string has slowly cut its way through, but the cut surfaces have reunited, and, excepting a few bubbles, show no trace of the operation. If a metallic wire is used instead of the string, the action is accelerated owing to the heat conducted along the wire from the outside. 1032. Glaciers. — Tyndall applied this regelating property of ice to an explanation of the formation and motion of glaciers, of which the following is a brief description : — In elevated regions, the snow-line (1029) marks the boundary of eternal snow, for above this the heat of summer is unable to melt the wintei-'s snow. By the heat of the sun and the consequent percola- tion of water melted from the surface, the lower portions of the snow-field are raised to 0° C. ; at the same time this part is closely pressed together by ihe weight of the snow above ; regelation therefore sets in, converting the loose snow into a coherent mass. By increasing pressure the intermingled air which renders snow opaque is ejected and the snow becomes transparent ; ice is then formed. Its own weight and the pressure from behind urge downwards the glacier which has thus been formed. In its descent the glacier behaves like a river, passing through narrow gorges with a certain velocity, and then spreading out and moving more slowly as its bed widens. Further, just as the central portions of a river move faster than the sides, so Forbes ascertained that the centre of a glacier moves more quickly than its margin, and from the same reason (the difference in the friction encountered) the surface moves more rapidly than the bottom. To explain these facts Forbes assumed ice to be a viscous body capable of flexure, and flowing like lava ; but as ice has not the properties of a viscous substance, the now generally accepted explanation of glacier motion is that supplied by the theory of regelation. According to this theory, the brittle ice of the glacier is crushed and broken through narrow channels, and partially melted owing to the increased pressure, and then, as it emerges from the gorge which confined it, the pressure is relieved and the liquefied portion again freezes and becomes united by virtue of regelation. By numerous experiments Tyndall artificially imitated, on a small scale, the moulding of glaciers by the crushing and subsequent regelation of ice. 1033. Atmospheric electricity. Franklin's experiment. — The most frequent luminous phenomena, and the most remarkable for their effects, are those produced by the free electricity in the atmosphere. The first physicists who observed the electric spark compared it to the gleam of lightning, and its crackling to the sound of thunder. But Franklin, by the I072 Meteorology [1033- aid of powerful Leyden batteries, first established a complete parallelism between lightning and electricity ; and indicated, in a memoir published in 1749, the experiments necessary to attract electricity from the clouds by means of pointed rods. The experiment was tried by Dalibard in France ; and Franklin, pending the erec- tion of a pointed rod on a spire in Philadelphia, had the happy idea of flying a kite, provided with a metal point, which could reach the higher regions of the atmosphere. In June, 1752, during stormy weather, he flew the kite in a field near Philadelphia. The kite was flown with ordinary packthread, at the end of which Franklin attached a key, and to the key a silk cord, in order to insulate the apparatus ; he then fixed the silk cord to a tree, and having presented his hand to the key, at first he obtained no spark. He was beginning to despair of success, when, rain having fallen, the cord became a good conductor, and a spark passed. Franklin, in his letters, describes his emotion on witnessing the success of the experiment as being so great that he could not refrain from tears. Franklin imagined that the kite drew from the cloud its electricity ; it is, in fact, a simple case of induction, and depends on the inductive action which the thunder-cloud exerts upon the kite and the cord. 1034. Apparatus to investigate the electricity of the atmosphere. — To observe the electric potential in fine weather, an apparatus may be used as devised by Saussure for this kind of investigation. It is an elec- troscope similar to that already described (748), but the rod to which the gold leaves are fixed is sur- mounted by a conductor 2 feet in length, and termin- ates in either a knob or a point (fig. 1043). To protect the apparatus against rain, it is covered with a metal shield 4 inches in diameter. The glass case is square instead of being round, and a divided scale on its inside face indicates the divergence of the gold leaves. This electroscope gives signs of atmospheric electricity only as long as it is raised in the atmosphere so that its pointed end is in layers of air of different electric potential from its own. To measure the potential of the atmosphere Saussure also used a copper ball, which he projected vertically with his hand. This ball was fixed to one end of a metal wire, the other end of which was attached to a ring, which could glide along the conductor of the electroscope. From the divergence of the gold leaves, the electric condition of the air at the height which the ball attained could be determined. Becquerel, in ex- periments made on the St. Bernard, improved Saussure's apparatus by substituting for the knob an arrow, which was projected into the atmosphere by means of a bow. A gilt silk thread, 88 yards long, was fixed with one end to the arrow, while the other end was attached to the stem of an electro- scope. Fig. 1043 -1034] Apparatus to investigate Atmospheric Electricity 1073 To observe the electricity of clouds, where the potential may be very considerable, use is made of a long bar terminating in a point. This bar, which is insulated with care, is fixed to the summit of a building, and its lower end is connected with an electrometer. Let the space round the point of the bar be at a positive potential, V. The bar, which we will suppose to be at zero potential, becomes charged by induction with negative at the point and positive at the lower end, so that the leaves of the electroscope diverge. Negative electricity is discharged from the point (780) until its potential is equal to that of the surrounding space. When equilibrium is established, the electroscope indicates the potential of the point and, therefore, of the space in its neighbourhood. If the potential of this space rises, the point discharges negative electricity and the leaves diverge wider ; if the potential falls the point discharges positive electricity, and the divergence diminishes. Fig. 1044 Thus the electroscope shows the changes in potential of the space round the point. In stormy weather the potential may be considerable, and as the bar can then give dangerous shocks, a metal ball must be placed near it which is well connected with the ground, and which is nearer the bar than the observer himself; so that if a discharge should ensue, it will strike the ball and not the observer. Richmann, of St. Petersburg, was killed in an experiment of this kind, by a discharge which struck him on the forehead. In modern arrangements, the sharp point has been replaced by a burning match or by dropping water. A roll of nitrate of lead paper, looking something like a thin cigarette, is attached to the conductor, and when lighted smoulders slowly, producing a smoke which rapidly dissipates electricity and raises the potential of the conductor to that of the surrounding space. A convenient instrument for investigating atmospheric electricity was introduced by Lord Kelvin, one form of which used in the Meteorological 3Z I074 Meteorology [1034- Observatory of Montsouris, is represented in fig. 1044. It consists of a large metal vessel, A, resting on three insulating glass legs fixed to the top of a tall column of cast iron. A sheet-metal mantle, B, protects the supports from the rain. The apparatus is arranged in the open, and can be filled with water from a pipe, C. The water issues through a long lateral jet in A, in a stream so fine that the volume of the water is not appreciably altered. An insulated wire, z, passing through the column, connects the vessel A with an electrometer placed indoors. This plan of collecting the atmo- spheric electricity is adopted in balloons, where a smouldering match is undesirable. The manner in which the electricity of the atmosphere is registered is seen from fig. 1045, which represents the form in use at the above observatory. Fig. 1045 In a light-tight, box is ^ band of sensitised photographic paper, stretched on the surface of a cylinder and moved by clockwork. In one side of the box is a long cylindrical glass lens, in front of which at E are two quadrant electrometers (796). Both of these are connected with the same collector of electricity, placed outside, and their sectors are charged by the same source of electricity, but one of them is ten times as sensitive as the other. Near one side of the box is a gas-burner with an opaque chimney. A, in two opposite sides of which are longitudinal slits, through which the light passes to two total reflection prisms (550),/ p', which are arranged so as to send two pencils of light on tbe mirrors, m m' , of the -1035] Ordinary Electricity of the Atmosphere 1075 electrometer. This is shown on a larger scale on the left of the figure : the two pencils fall upon the lens, L, which concentrates in a point the slices of light issuing from the chimney and reflected from the mirror. These follow the motion of the mirror, and thus impress on the sensitive paper the curves of electric potential of the air. There is also an arrangement by which an electromagnet puts the electrometers to earth for a few minutes at every hour, and thus discharges them. The mirrors revert then to their original position and commence a new trace. If we replace the electrometer with its mirror attached by a magneto- meter, we can easily see how the variations in the magnetic declination may be recorded (730). 1035. Ordinary electricity of the atmosphere. — By means of the dif- ferent apparatus which have been described, it has been found that the presence of electricity in the atmosphere is not confined to stormy weather, but that the atmosphere always contains free electricity, in the vast majority of cases positive, but occasionally negative. When the sky is unclouded the. potential is always positive, and it increases with the height above the ground. Its value is greatest in the highest and most isolated places. No trace of positive electricity is found in houses, streets, and under trees ; in towns, positive electricity is most perceptible in large open spaces, on quays, or on bridges. Lord Kelvin found in the Isle of Arran, at a height of 9 feet above the ground, a difference of potential equal to 200 to 400 Daniell cells, or from 216 to 432 volts. This represents a rise of potential of from 24 to 48 volts for each foot of ascent. This is subject to great varia- tion ; with winds from the north and north-east the potential was often six to ten times as much as the higher of these amounts. The change of potential is most rapid in cold dry weather, when the quantity of moisture in the air is at its lowest. Thus, at a temperature of - 8° to — 12° C, Exner found a change of 600 volts per metre in the direction of the vertical. With a vapour-pressure of 2-3 mm. the change was 325, with 6'8 it was 116, and with 1 2 '5 it was 68. Between 5 and 7.30 a.m. the positive electricity in the air is at a mini- mum ; it increases from 7 to 9.30 A.M., according to the season, and then attains its first maximum. It then decreases rapidly until from 2.30 to 4.30 P.M., and again increases till it reaches its second maximum, from 6.30 to 9.30 P.M. ; the remainder of the night the electricity decreases until sun- rise. Thus the greatest amount of electricity is observed when the baro- metric pressure is highest. These increasing and decreasing periods, which are observed all the year, are more perceptible when the sky is clearer and the weather more settled. The positive electricity of fine weather is much stronger in winter than in summer. It may, in short, be said that electricity of the air follows the opposite course to that of temperature and moisture. When the sky is clouded, the electricity is sometimes positive and some- times negative. According to Palmieri, the occurrence of negative electricity is a certain indication that within a distance of 40 miles it either rains, or snows, or hails. It often happens that the electricity changes its sign several times in the course of the day, owing to the passage of an electrified cloud. During storms, and when it rains or snows, the atmosphere may be 3 2 2 10/6 Meteorology [1035- positively electrified one day, and negatively the next, and the numbers of the two sets of days are virtually equal. During a thunderstorm the changes in potential and sign of electricity are so rapid that the photographic method of registration fails. From a long series of observations on the electricity of the atmosphere made in the early morning, Dellman found that the electricity increased with the density of the fog, but in a far more rapid ratio. The electricity of the ground was found by Peltier to be always negative, and this seems to be the cardinal fact in reference to atmospheric electricity ; it is so, however, to different extents, according to the hygrometric state and temperature of the air. The density is, moreover, exceedingly small, being calculated at O'ooo36 unit per square centimetre, from which it follows that the electric pressure (757) is 0-0000008 dyne per square centimetre, or less than the millionth of a milligramme-weight. Even if the pressure were ten times as great, it would be insufficient to raise the lightest bodies. 1036. Causes of atmospheric electricity. — Although many hypotheses have been propounded to explain the origin of atmospheric electricity, it must be confessed that our knowledge is in an unsatisfactory state. Volta first showed that the evaporation of water produced electricity. Pouillet subsequently showed that no electricity is produced by the evapo- ration of distilled water ; but that if an alkali or a salt is dissolved, even in small quantity, the vapour is positively and the solution is negatively electrified. The reverse is the case if the water contains acid. Hence it has been assumed, that as the waters which exist on the surface of the earth and on the sea always contain salt dissolved, the vapours disengaged ought to be positively and the earth negatively electrified. The development of electricity by evaporation may be observed by heating strongly a platinum dish, adding to it a small quantity of liquid, and placing it on the upper plate of the condensing electroscope (fig. 795), taking care to connect the lower plate with the ground. When the water of the capsule is evaporated, the connection with the ground is broken, and the upper plate raised. The gold leaves then diverge if the water contains salts, but remain quiescent if the water is pure. Reasoning from such experiments, Pouillet ascribed the development of electricity by evaporation to the separation of particles of water from the substances dissolved ; but Reich and Riess showed that the electricity disengaged during evaporation could be attributed to the friction which the particles of water carried away in the current of vapour exert against the sides of the vessel, just as in Armstrong's hydro-electric machine (771). By a series of experiments, Gaugain arrived at the same result. Sohncke recalls an experiment of Faraday which he has repeated, showing that the friction of minute particles of water against dry ice is an abundant source of electricity ; he ascribes atmospheric electricity to this origin, suggesting that in the upper regions particles of both water and ice may coexist. The ice particles become positively electrified, while those of water are negative. When these fall in rain, they carry with them their negative electricity. A similar theory has been propounded by Luvini. 1037. Electricity of clouds. — Clouds are in general electrified usually -1038] Lightning io77 positively, but sometimes negatively, and differ only m their higher or lower potential. The formation of positive clouds is by some ascribed to the vapour disengaged from the ground and condensed in the higher regions. Negative clouds are supposed to result from fogs, which, by their contact with the ground, become charged with negative electricity, which they retain on rising into the atmosphere ; or to have been separated from the ground by layers of moist air, and negatively electrified by induction from the positive clouds, which have repelled into the ground positive electricity. Thunder-clouds are sometimes as low as 700 to 1,000 feet ; but their usual height appears to be 3,000 to 6,000 feet. Whatever be the origin of atmospheric electricity, there can be no doubt that the invisible aqueous vapour is the carrier of it, and it is easy to explain the high potential of clouds from the condensation of this vapour. For suppose 1,000 vapour-particles, each of the same size and possessing the same charge of electricity, coalesce to form a single droplet, the diameter of such a droplet will be ten times that of the individual particles — that is, its capacity is ten times as great, since the capacity is equal to the radius (760) ; but the quantity of electricity will be 1,000 times as great as on the small one, and therefore the potential will be 100 times as great. Now the number of vapour-particles which go to form a single droplet is rather to be counted by billions ; hence, however small be the finite value which we assign to the potential of the electricity of the vapour- particles, that of the drops will be enormously greater, and sufficient to account for the high potential of clouds. 1038. Lightning;. — ^This, as is well known, is the dazzling light emitted by the electric spark when it shoots from clouds charged with electricity. In the lower regions of the atmosphere the light is white, but in the higher regions, where the air is more rarefied, it takes a somewhat reddish tint ; as does the spark of the electric machine in a rarefied medium (805). The flashes of lightning are often more than a mile, and sometimes extend to four or five miles, in length ; they generally pass through the atmosphere in an irregular direction — a phenomenon ascribed to the resist- ance offered by the air condensed by the passage of a strong discharge. The spark then diverges from a right line, and takes the direction of least resistance. In a vacuum, electricity passes in a straight line. We cannot, however, regard the length of a lightning flash as the direct striking distance between two conductors. Owing to the number of droplets met on its path, the discharge is rather to be compared with that of the luminous tubes and panes (781;). The experiments of Mascart on the rela- tion between the striking distance (805) and the potential required to pro- duce it show that the striking distance increases far more rapidly than the potential. Thus, while the potential required for a striking distance of i cm. is represented by 8-3, for 4 cm. it is 15-9, for 8 cm. 20-5, and for 15 cm. 23-3. From this it is possible that a lightning discharge is produced by a difference of potentials between two clouds which is not greatly out of proportion with those obtained by our electric machines. Several kinds of lightning flashes may be distinguished — i, the zigsag flashes, which move with extreme velocity in the form of a line of fire with sharp outlines, closely resembling the spark of an electric machine. The 1078 Meteorology [1038- recent investigation of the shape of lightning discharges by means of extra rapid photographic dry plates (622) has shown that the path of a dis- charge is not so sharply zigzag as is usually represented, but has more the shape of the course of a river as shown on a map, and with frequent branch- ings ; 2, the sheet flashes, which, instead of being linear, like the preceding, fill the entire horizon without having any distinct shape. This kind, which is most frequent, appears to be produced in the cloud itself, and to illuminate the mass. According to Kundt, the number of sheet discharges is to the zigzag discharges as 11:6; and from spectrum observations it would appear that the former are brush discharges between clouds, while the latter are true electric discharges between the clouds and the earth. Another kind, called heat lightning, is ascribed to distant lightning flashes which are below the horizon, but illuminate the higher strata of clouds, so that their bright- ness is visible at great distances ; they produce no sound, probably in con- sequence of the fact of their being so far oif that the rolling of thunder cannot reach the ear of the observer. There is, further, the very unusual phenomenon of globe lightning, or the flashes which appear in the form of globes of fire 18 inches in diameter. These, which are sometimes visible for as much as ten seconds, descend from the clouds to the earth with such slowness that the eye can follow them. They often rebound on reaching the ground ; at other times they burst and explode with a noise like that of the report of many cannon. No adequate explanation has been given of these, though Plante with a large battery of his cells has imitated the phenomena. The duration of the light of the first three kinds does not amount to the millionth of a second, as was determined by Wheatstone by means of his rotating wheel, which was turned so rapidly that the spokes were invisible : on illuminating it by the lightning flash, its duration was so short that whatever the velocity of rotation of the wheel, it appeared quite stationary i that is, its displacement is not perceptible during the time the lightning exists. The light produced by a lightning flash must be comparable to that of the sun in brightness, though it does not appear to us brighter than ordinary moon- light. But considering its excessively brief duration, and that the full effect of any light on the eye is only produced when its duration is at least the tenth of a second, it follows that a landscape continuously illuminated by the lightning flash would appear 100,000 times as bright as it actually appears to us during the flash. Here also may be mentioned the phenomenon known as St. Elmds fire, which occurs in a highly electric state of the atmosphere when the clouds are low. It is a sort of brush discharge (778), appearing like small flames issuing from prominent point-objects such as masts, tops of trees, lightning- conductors ; it has also been observed on the points of helmets and lances, alpenstocks ; it is of course most easily seen in the dark, and is accompanied by a slight rustling noise. On the sea during thunder-storms it is not un- common on mastheads and yardarms. 1039. Thunder. — Thunder is the violent report which succeeds lightning. The occurrence of lightning and thunder is practically simultaneous, but an interval of several seconds is generally observed between the perception of these two phenomena, which arises from the fact that sound travels at -1040] Effects of Lightning 1079 the rate of only about 1,100 feet in a second (230), while the passage of light is almost instantaneous. Hence an observer will hear the noise of thunder only five or six seconds, for instance, after the lightning, according as the distance of the thunder-cloud is five or six times 1,100 feet. The noise of thunder arises in some such manner as the crack of a whip or the report of a gun. The lightning discharge, whether by heating the air or by a purely mechanical action, such as is illustrated with Kinnersley's thermometer (fig. 794), causes it to expand with explosive violence, which is only possible by a compression of the surrounding air. This com- pressed air rushes in to fill the partial vacuum, forming itself, in turn, a partial vacuum, and thus, giving rise to alternate condensation and rarefaction, constitutes the wave-motion producing the sound. The depth of the note represents a great wave-length, and shows that the disturbance must have a great length. Near the place where the lightning strikes the sound is sharp and of short duration. At a greater distance a series of reports are heard in rapid succession. At a still greater distance the noise, feeble at first, changes into a prolonged rolling sound of varying intensity. If the lightning is at a greater distance than 14 or 15 miles, it is no longer heard, for sound is more imperfectly propagated through air than through solid bodies : hence there are lightning discharges without thunder ; these occur at times when the sky is cloudless. The rolling of thunder, the alternate rise and fall of the sound, occurs ordinarily with sheet lightning, less so with forked lightning, when the sound is short and crackling. Various causes contribute to produce the rolling ; one cause is the reflec- tion from the ground, from clouds, and even from layers of air of unequal density. Lightning, too, is not a single discharge, but a series of discharges, each of which gives rise to a particular sound, and which are variously reflected by objects which they meet on their path. If two waves reach the ear simultaneously they strengthen each other if they are in the same phase, but if in different ones they interfere partially or wholly and the sound sinks. Thus it may happen that the sound after sinking may rise again. This is the well-known phenomenon of beats (263). The phenomenon has finally been ascribed to the zigzags of lightning themselves, assuming that the air at each salient angle is at its greatest compression, which would produce the unequal intensity of the sound. The distance of the nearest point of a lightning flash is obtained in kilometres if we divide the time in seconds which elapses between the lightning flash and the beginning of the thunder by 3. This is evident since s = vt and v the velocity found is 330 metres or \ kilometre per second. 1040. Effects of iightning^. — The lightning discharge is the electric discharge which strikes between a thunder-cloud and the ground. The latter, by the induction of the electricity from the cloud, becomes charged with contrary electricity ; and when the tendency of the two electricities to com- bine exceeds the resistance of the air, the spark passes, which is often expressed by saying that ' a thunderbolt has fallen.' The discharge usually falls first on the nearest and best conducting objects, and, in fact, trees, elevated buildings, metals, are particularly struck io8o Meteorology [1040- by the discharge. Hence it is imprudent to stand under trees during a thunderstorm. The effects of lightning are very varied, and of the same kind as those of Leyden batteries (790), but of far greater power. The lightning discharge kills men and animals, ignites combustibles, melts metals, breaks bad con- ductors in pieces. When it penetrates the ground it melts the silicious substances on its path, and thus produces in the direction of the discharge those remarkable vitrified tubes cailed /uiguHies, some of which are as much as 12 yards in length ; in most cases there are found to be accumulations of water below such fulgurites. When it strikes bars of iron it magnetises them, and often inverts the poles of compass needles. The action of lightning on trees is very singular. When struck by it they are sometimes stripped of their bark, either wholly or partially, or the wood is often split into thin laths, or into a mass of fibres. Franklin ascribed this to the sudden evaporation of the water. After the passage of lightning a highly peculiar odour is frequently produced, like that perceived in a room in which an electric machine is being worked. This is due to the formation of ozone, a peculiar allotropic modification of oxygen. An electrified cloud forms with the earth below a condenser, the intervening mass of air being the dielectric. This mass of air is therefore in a state of strain, like the dielectric in a charged Leyden jar, and it is to this state of strain which precedes the actual discharge, rather than to the discharge itself, that is due the production of ozone. Heated air conducts better than cold air, probably only owing to its lesser density. Hence it is that large numbers of animals are often killed ,by a single discharge, as they crowd together in a storm, and a column of warm air rises from the group. 1041. Return shock. — This is a violent and sometimes fatal shock which men and animals experience, even when at a great distance from the place where the lightning discharge passes. It is caused by the inductive action which the thunder-cloud exerts on bodies placed within the sphere of its activity. These bodies are then, like the ground, charged with the opposite electricity to that of the cloud ; but when the latter is discharged by the recombination of its electricity with that of the ground, the induction ceases, and the bodies reverting rapidly from the electric state to the neutral state, the concussion in question is produced — the return or back shock. The return shock is always less violent than the direct one ; there is no instance of its having produced any inflammation, yet plenty of cases in which it has killed both men and animals ; in such cases no broken limbs, wounds, or burns are observed. The return shock may be imitated by placing a gold-leaf electroscope connected by a wire with the ground near an electric machine ; when the machine is worked, at each spark taken from the prime conductor the gold leaves of the electroscope suddenly diverge. It is stated that persons struck by. lightning often lose their lives only by a temporary injury to the nerves which control the act of respiration ; so that under favourable circumstances such persons might probably be saved if respiration could be restored by artificial means. -1042] Lightning- Conductor 1081 A 1042. Lightning-conductor. — This was invented by Franklin in i755- There are two principal parts in a lightning-conductor, the rod and the conductor. The rod (fig. 1046) is a pointed bar of iron, preferably galvanised, P, fixed vertically to a tube or rod of iron, which, by means of a collar a a, and tube g, is fitted on the roof of the edifice to be protected ; it is from 6 to 10 feet in height, and its basal section is about 2 or 3 inches in diameter. The con- ductor is best formed of a wire rope, C, attached to the rod by a metal collar, b. The section of the metallic conductor ought to be about half a square inch, and the individual wires 0-04 to o'o6 inch in diameter : they ought to be twisted in strands, like an ordinary cord. The conductor is usually led into a well, a pond, or other continuous mass of water, and to connect it better with the ground it should terminate in a plate called an earth plate, or if a strand of wires the separate wires should be spread out. This plate should be of the same metal as the conductor, so as to avoid the possibility of local galvanic action (819), by which one or the other metal would be eaten away and the continuity destroyed. If there is no well near, a hole is dug in the soil to the depth of 6 or 7 yards, or to where the earth is permanently damp ; where the ground is naturally dry it is advantageous to direct the rainfall from the roof towards where the plate is placed, and the ends of the conductor having been introduced, the hole is filled with powdered coke, which conducts very well. A good earth contact is obtained when it is possible to connect the wire conductors with large iron gas or water pipes. The action of a lightning-conductor is regarded as an illustration of the action of induction and of the property of points (780) ; when a storm cloud positively electrified, for instance, forms in the atmosphere, it acts inductively on the earth, producing a negative charge on bodies placed on the surface, the larger as these bodies are at a greater height. The density is then greatest on the highest bodies, which are therefore most exposed to the electric discharge ; but if these bodies are provided with metal points, like the rods of conductors, the negative electricity flows into the atmosphere, and neutralises the positive electricity of the cloud. Hence the action of the lightning-conductor is twofold ; not only does it tend to prevent the accumu- lation of electricity on the surface of the earth, but it also tends to restore the clouds to their natural state, both which concur in preventing lightning- discharges. The quantity of electricity is, however, sometimes so abundant that the lightning-conductor is inadequate to discharge the electricity accumulated, and the lightning strikes ; but the conductor receives the discharge, in consequence of the greater conductivity, and the edifice is preserved. A conductor, to be efficient, ought to satisfy the following conditions : — (i.) The rod ought to be so large as not to be melted if the discharge passes, (ii.) It ought to terminate in a point, or in several points, to give readier issue to the electricity disengaged by induction from the ground, (iii.) Copper io82 Meteorology [1042- was formerly preferred to iron owing- to its greater conductivity. But the lightning discharge is strictly analogous to the discharge of a Leyden jar, which according to circumstances may form either a continuous discharge like a steady current, or a series of oscillations (800). In the latter case the discharge is restricted to the surface owing to the effect of impedance (1005), which may have a greater influence than the ohmic resistance, so that the advantage of the greater conducting power of copper disappears. The con- ductor must be continuous from the point to the ground, and the connection between the rod and the ground must be as intimate as possible ; this is the most important of all, and the one point most frequently neglected in the older arrangements. A lightning-conductor with bad earth contact is not only useless but dangerous. In regard to this, it may be said that the best earth for contact is water. The continuity of the conductor may be tested by means of a voltaic cell and a portable form of galvanometer, (iv.) If the building which is provided with a lightning-conductor contains metallic surfaces of any extent, such as zinc roofs, metal gutters, or ironwork, these ought to be connected with the conductor, or, still better, have each a separate earth connection. If the last two conditions are not fulfilled, there is a great danger of lateral discharges — that is to say, that the discharge takes place between the conductor and the edifice, and then it increases the danger. The requirements above laid down are based on the older view of the protection of buildings. Another mode of protection is based on the screen- ing action of a closed conducting surface either continuous or formed of wire gauze. Such an enveloping conductor, as we have seen (765), protects a body inside it from external electric action, and probably does so also in the case of violent and sudden electric discharges. If a building could be surrounded by a wire cage which itself had good earth contact, this would be an efiScient protection. Accordingly, an alternative plan aims at provid- ing all the ridges, eaves and corners, and chimneys of a building with abun- dance of galvanised iron wire, preferably barbed, and with wire netting, all in metallic connection with each other and with the earth. Copper conductors with a surface of 50 sq. mm. have been known to be raised to nearly a red heat by a lightning discharge, and such as have a section of 5 sq. mm. have frequently been melted. An estimate based on this fact gives for the quantity of electricity passing in such a discharge values of not less than 50 nor more than 290 coulombs. 1043. Rainbow. — The rainbow is a luminous phenomenon which appears in the clouds opposite the sun when they are resolved into rain. It consists of seven concentric arcs, presenting successively the colours of the solar spectrum. Usually only a single bow is perceived, but there are sometimes two : a lower one, the colours of which are very bright ; and an external or secondary one, which is paler, and in which the order of the colours is reversed. In the interior rainbow the red is the highest colour ; in the other rainbow the violet is. It is seldom that three bows are seen ; theoretically a greater number may exist, but their colours become so faint that they can- not be perceived. The phenomenon of the rainbow is produced by decomposition of the white light of the sun when it passes into the drops, and by its reflection from their inside face. In fact, the same phenomenon is witnessed in dew- -1043] Rainbow 1083 drops and in jets of water — in short, wherever sunlight passes into drops of water under a certain angle. The appearance and the extent of the rainbow depend on the position of the observer, and on the height of the sun above the horizon ; hence only some of the rays refracted by the raindrops, and reflected in their concavity to the eye of the spectator, are adapted to produce the phenomenon. Those which do so are called effective rays. To explain this let us suppose n (fig. 1047) to be a drop of water, into which a solar ray S a penetrates. At a point of incidence, a, part of the light is reflected from the surface of the liquid ; another, entering it, is de- composed and traverses the drop in the direction a b. Arrived at b, part of the light emerges from the raindrop, the other part is reflected from the concave surface, and tends to emerge at g. At this point the light is again partially reflected ; the remainder emerges in a direction gO, which forms with the incident ray, S 3, an angle called the angle of deviation. It is such rays as gO^ proceeding from the side next the observer, which produce Fig. 1047 on the retina the sensation of colours, provided the light is sufiiciently intense. It can be shown mathematically that in the case of a series of rays which impinge on the same drop, and only undergo one reflection in the interior, the angle of deviation increases from the ray S"«, for which it is zero, up to a certain limit, beyond which it decreases, and that near this limit rays passing parallel into a drop of rain also emerge parallel. From this parallelism a beam of light is produced sufiiciently intense to impress the retina ; these are the rays which emerge parallel and are efficient. As the different colours which compose white light are unequally refran- gible, the maximum angle of deviation is not the same for all. For red rays the angle of deviation corresponding to the active rays is 42° 2', and for violet rays it is 40° 17'. Hence, for all drops placed so that rays proceeding from the sun to the drop make, with those proceeding from the drop to the eye, an angle of 42° 2', this organ will receive the sensation of red light ; this will be the case with all drops situated on the circumference of the base of a cone, the summit of which is the spectator's eye ; the axis of 1084 Meteorology [1043- this cone is parallel to the sun's rays, and the angle formed by the two opposed generating lines is 84° 4'. This explains the formation of the red band in the rainbow ; the angle of the cone in the case of the violet band is 80° 34'. The cones corresponding to each band have a common axis called the visual axis. As this right line is parallel to the rays of the sun, it follows that when this axis is on the horizon, the visual axis is itself horizontal, and the rainbow appears as a semicircle. If the sun rises, the visual axis sinks, and with it the rainbow. Lastly, when the sun is at a height of 42° 2', the arc disappears entirely below the horizon. Hence the rainbow is never seen except in the morning and evening. What has been said refers to the interior arc. The secondary bow is formed by rays which have undergone two reflections, as shown by the ray S' i d f e O, in the drop/. The angle S'lO formed by the emergent and incident rays is called the angle of deviation. The angle is no longer suscep- tible of a maximum, but of a minimum deviation, which varies for each kind of rays, and to which also efficient rays correspond. It is calculated that the minimum angle from violet rays is 54° 7', and for red rays only 50° 57' ; hence it is that the red bow is here on the inside, and the violet arc on the outside. There is a loss of light for every internal reflection in the drop of rain, and therefore the colours of the secondary bow are always feebler than those of the internal one. The secondary bow ceases to be visible when the sun is 54° above the horizon. The moon sometimes produces rainbows like the sun, but they are very pale. 1044. Aurora borealis. — The aurora borealis, or northern light, or more properly /o/ar aurora, is a remarkable luminous phenomenon which is fre- quently seen in the atmosphere in high latitudes. Fig. 1048 represents an aurora borealis observed at Bossekop, in Lapland, lat. 70', in the winter of 1838-39- Plate III. represents a very beautiful aurora observed by Lemstrom on the north coast of Norway. The radial divergence of the aurora and the convergence towards a corona is due to an effect of perspective. The work of this author {L'Aurore Bordale, Gauthier Villars, Paris) is a storehouse of information on this subject. A French scientific commission to the North observed 150 aurorse boreales in 200 days ; it appears that at the poles, nights without an aurora borealis are quite exceptional, so that it may be assumed that they take place every night, though with varying intensity. They are visible at a considerable distance from the poles, and over an immense area. Some- times the same aurora borealis has been seen at the same time at places so widely apart as Moscow, Warsaw, Rome, and Cadiz. The height of the aurora above the surface of the ground is probably lower than has generally been stated. Lemstrom holds that from 22 to 44 miles is a close approximation to the truth ; and it may be regarded as certain that even in more southern latitudes the aurora is often seen much lower — at a height of two or three miles, for instance. In polar countries certain forms of aurora, more especially those of weak flames, are seen to proceed from the ground on the tops of certain mountains. They are most frequent at the equinoxes, o S o -1044] Aurora Borealis io8s and least so at the solstices. The number differs in different years, attain- ing a maximum every ii years at the same time as the sun-spots, and like these a minimum which is about five or six years from the maximum. The years 1844, 1855, 1866, and 1877 were poor in the appearance of the aurora. There is, moreover, a period of about 60 years ; for the years 1728, 1780, and 1842 have been remarkable for the prevalence of the aurora. The last two periods are also remarkable for the occurrence of disturbances in the earth's magnetism. Numerous hypotheses have been devised to account for the aurora boreales. As they share the rotation of the earth, they must have an atmo- spheric origin. Their direction is not due north and south, but is always parallel to that of the dipping-needle, pointing to the magnetic pole ; this points to their intimate connection with the earth's magnetism. Magnetic Fig. 1048 storms (738), and the prevalence of strong earth currents, are usually coincident with the appearance of especially brilliant aurorse. It is probable that the attenuated air in the upper regions of the atmosphere is a fairly good conductor of electricity, and we know that when a conductor moves across the lines of force in a magnetic field, electro- motive force is set up, and electric discharge may follow. Thus it is probable that the aurora is an electric discharge due to variations in the magnetic field which exists in the space surrounding the earth. The spectrum of the aurora borealis has been .found to consist of several lines in the green, and of an indistinct line in the blue ; to which must be added a red line due to the red protuberances ; these lines are the same as those of nitrogen, greatly rarefied and at a low temperature ; one special line between the green and the yellow, and called the yellow line, is so characteristic of the aurora that it is visible even when the eye can discern io86 Meteorology [1044- no other trace of this light ; this line has not been produced in laboratory experiments. De la Rive held that auroras boreales were due to electric discharges which take place in polar regions between the positive electricity of the atmosphere and the negative electricity of the earth. The positively elec- trified aqueous vapours are supposed to be carried by the equatorial current in the higher regions of the atmosphere to the poles, where the neutralisa- tion takes place. These discharges produce luminous appearances of the same kind as are observed in Geissler's tubes ; and De la Rive showed by means of an apparatus specially devised for the purpose that the forms of the luminous phenomena are in accordance with this theory. By direct experiments Lemstrom has been able to imitate and reproduce a peculiar form of aurora observed in winter as a flame-like appearance on the tops of two mountains 800 and 1,100 metres in height, and to show that it is of electric origin. He erected on the summit of a hill a system of pointed rods extending over a surface of nearly 4,000 square feet ; each rod was carefully insulated from the earth by means of a Mascart's insulator (fig. 707), but was connected with the rest, and an insulated wire led down from this system into the valley, where it was connected with one ter- minal of a galvanometer, the other being put to earth. The existence of a positive current from the air to the earth was observed, and at the same time yellowish- white columns of light, reaching to a height of 120 metres, were observed to issue from the points. Observed with the spectroscope it gave the characteristic lines between D and E. Making similar experiments on even a larger scale in Lapland on a detached peak, he observed that the characteristic luminous phenomena were produced there, while the neighbouring peaks remained dark. The investigations of Exner relative to the fall of atmospheric electric potential lend a further support to the view that the aurora is due to elec- tricity. In the polar regions the rate of fall of potential is 13 times greater in summer, and 18 times greater in winter than at the equator. Hence an electric phenomenon, which depends on the magnitude of this fall of potential, must be more intense in winter and in high latitudes than in summer and in the torrid zones. The occurrence of irregular currents of electricity which manifest them- selves by abnormal disturbances of telegraphic communications is not in- frequent : such currents have received the name of earth currents. Sabine held that irregular magnetic disturbances are due to a peculiar action of the sun, and are probably independent of its radiant heat and light. It has also been ascertained that the aurora borealis, as well as earth currents, invariably accompanies these magnetic disturbances. According to the late Balfour Stewart, aurorse and earth currents are to be regarded as secondary phenomena due to small but rapid changes in the earth's magnetism : he likened the body of the earth to the magnetic core of a Ruhmkorff's coil (975) : the lower strata of the atmosphere forming the insulator, while the upper and rarer, and therefore electrically conducting, strata may be considered as the secondary coil. On this analogy the sun may perhaps be likened to the primary current which performs the part of producing changes in the magnetic state of the —1046] Temperature of the Air 1087 core. Now in RuhmkorfPs coil the energy of the secondary current is derived from that of the primary current. Thus, if the analogy be correct, the energy of the aurora borealis may in like manner come from the sun ; but until we know more of the connection between the sun and terrestrial magnetism, these ideas are to be accepted with some reserve. CLIMATOLOGY 1045. Mean temperature. — The mean daily temperature is that obtained by adding together 24 hourly observations, and dividing by 24. A very close approximation to the mean temperature is obtained by taking the mean of the highest and lowest temperatures of the day and of the night, which are determined by means of the maximum and minimum ther- mometers. These ought to be protected from the sun's rays, to be raised above the ground, and far from all objects which might influence them by their radiation. The temperature of a month is the mean of the temperature of 30 days, and the temperature of the year is the mean of those of 1 2 months. Finally, the temperature of a place is the mean of its annual temperatures for a great number of years. The mean temperature of London is 8'28° C, or 46'9° F. The temperatures in all cases are those of the air, and not those of the ground. 1046. Causes which modify the temperature of the air. — The principal causes which modify the temperature of the air are the latitude of a place, its height, the direction of the winds, and proximity of seas. Influence of the latitude. — The influence of the latitude arises from the greater or less obliquity of the solar rays, for as the quaritity of heat absorbed is greater the more perpendicular are the rays, the heat absorbed decreases from the equator to the poles, for the rays become more oblique. This loss is, however, in summer, in the temperate and arctic zones, partially compensated by the length of the days. Under the equator, where the length of the days is constant, the temperature is almost invariable ; in the latitude of London, and in more northerly countries, where the days are very unequal, the temperature varies greatly ; but in summer it sometimes rises almost as high as under the equator. The lowering of the temperature produced by the latitude is small; thus, in a latitude 115 miles north of Paris, the temperature is only 1° C. lower. Influence of height. — The height of a place above the sea-level has a much more considerable influence on the temperature than its latitude. The cooling on ascending in the atmosphere has been observed in balloon ascents, and a proof of it is seen in the perpetual snows which cover the highest mountains. It is due in part to the greater rarefaction of the air, which necessarily diminishes its absorbing power ; besides which the air is at a greater distance from the ground, which heats it by contact ; and finally, dry air is very diathermanous. The law of the diminution of temperature corresponding to greater heights in the atmosphere has not been made out, in consequence of the numerous disturbing causes which modify it, such as the prevalent winds, the hygrometric state, the time of day, the season of the year, &c. The io88 Meteorology [1046- difference between the temperatures of two places at unequal heights is not proportional to the difference of level, but for moderate heights an approxi- mation to the law may be made. As the mean of a series of very careful observations made during balloon ascents, a diminution of i° C. corresponded to an increase in height of 210 metres. It will thus be seen that at a certain height above the ground there must be a surface or layer where the temperature is uniformly zero. The height of this isothermal surface ( 1048) will vary materially with the time of the year, being lower in the cold months : it varies also with the time of day, rising rapidly about midday. In summer this height may be taken at from 3,400 to 3,700 metres above the sea-level. Direction of winds. — As winds share the temperature of the countries which they have traversed, their direction exercises great influence on the air in any place. In Paris, the hottest winds are the south ; then come the south-east, the south-west, the west, the east, the north-west, north, and lastly, the north-east, which is the coldest. The character of the wind changes with the seasons ; the east wind, which is cold in winter, is warm in summer. Proximity of the sea. — The neighbourhood of the sea tends to raise the temperature of the air, and to render it uniform. The average temperature of the sea in equatorial and polar countries is always higher than that of the atmosphere. With reference to the uniformity of the temperature, it has been found that in temperate regions — that is, from 25° to 50° of latitude — the difference between the highest and lowest temperature of a day does not exceed, on the sea, 2° to 3° ; while upon the continent the difference amounts to from 12° to 15°. In islands the uniformity of temperature is very per- ceptible. In continents, on the contrary, the winters for the same latitudes become colder, and the difference between the temperature of summer and winter becomes greater. 1047. Gulf Stream. — A similar influence to that of the winds is exerted by currents of warm water. To one of these, the Gulf Stream, the mildness of the climate in the north-west of Europe is mainly due. This great body of water, taking its origin in equatorial regions, flows through the Gulf of Mexico, whence it derives its name ; passing by the southern shores of North America, it makes its way in a north-westerly direction across the Atlantic, and finally washes the coast of Ireland and the north-west of Europe generally. Its temperature in the Gulf is about 28° C. ; and it is usually a little more than 5° C. higher than the rest of the ocean on which it floats, owing to its lower specific gravity. To its influence is due the milder climate of West Europe as compared with that of the opposite coast of America ; thus the river Hudson, in the latitude of Rome, is frozen over three months in the year. It also causes the polar regions to be separated from the coasts of Europe by a girdle of open sea ; and thus the harbour of Hammerfest is open the year round. Besides this influence in thus moderating climate, the Gulf Stream is an important help to navigators. 1048. Isothermal lines. — When on a map all the points, whose tempera- ture is known to be the same are joined, curves are obtained which Hum- boldt first noticed, and which he called isothermal lines. If the temperature of a place only varied with the obliquity of the sun's rays — that is, with the -1050] Distribution of Temperature on Surface of Globe 1089 latitude — isothermal lines would all be parallel to the equator ; but as the temperature is influenced by many local causes, especially by the height, the isothermal lines are always more or less curved. On the sea, however, they are almost parallel. Maps vii, viii, and ix represent these .lines for the Year, for January, and for July. A distinction is made between isothermal lines, isotheral lines, and iso- chimenal lines, where the mean general, the mean summer, and the mean winter temperatures are respectively constant. An isothermal zone is the space comprised between two isothermal lines. Kupffer also distinguishes isogeothermic lines where the mean temperature of the soil is constant. 1049. Climate.^ — By the climate of a place are understood the whole of the meteorological conditions to which the place is subjected ; its mean annual temperature, summer and winter temperatures, and the extremes within which these are comprised. Some writers distinguish seven classes of climates, according to their mean annual temperature : a hot climate from 30'^ to 25° C. ; a warm climate from 25° to 20° C. ; a mild climate from 20° to 15° C. ; a temperate climate from 15° to 10° C. ; a cold climate from 10° to 5° C. ; Sivery cold cliinate from 5° to zero C. ; and an arctic climate where the temperature is below zero. Those climates, again, are classed as constant climates where the dif- ference between the mean and summer and winter temperatures does not exceed 6° to 8° ; variable climates, where the difference amounts to from 16° to 20° ; and extreme climates, where the difference is greater than 30°. The climates of Paris and London are variable ; those of Pekin and New York are extreme. Island climates are generally little variable, as the temperature of the sea is nearly constant ; and hence the distinction between land and sea climates. Marine climates are characterised by the fact that the difference between the temperature of summer and winter is always less than in the case of continental climates. But the temperature is by no means the only character which influences climate ; there are, in addi- tion, the moisture of the air, the quantity and frequency of the rains, the number of storms, the direction and intensity of the winds, and the nature of the soil. 1050. Distribution of temperature on the surface of the globe. — The temperature of the air on the surface of the globe decreases from the equator to the poles ; but it is subject to perturbing causes so numerous and so purely local, that its decrease cannot be expressed by any law. It has hitherto not been possible to do more than obtain by numerous observations the mean temperature of each place, or the maximum and minimum tempera- tures, "f he following table gives a general idea of the distribution of heat in the Northern Hemisphere. Mean temperature at different latitudes Abyssinia . 31-0° C. Naples . . 167° c. Calcutta 28-5 Mexico . . i6-6 Jamaica 26-1 Marseilles 14-1 Senegal 24-6 Constantinople • 137 Cairo . 22-4 Pekin . . 127 Constantine . . 17-2 Paris . IO-8 4 A ogo Meteorology [1050 Brussels . IO-2° C. Moscow . 3-6° C. Strasburg 9-8 St. Petersburg 3-5 Geneva . • 97 St. Gothard -lO Boston . . 9-0 Greenland ■ -77 London 8-3 Melville Island -187 Stockholm . • 5-6 These are mean yearly temperatures. The highest temperature which has been observed on the surface of the globe is 47'4° at Esne, in Egypt, and the lowest is —75° in the Arctic Expedition of 1876; which gives a difference of 122° between the extreme temperatures obsei-ved on the surface of the globe. The highest temperature observed at Paris was 38-4° on July 8, 1793, and the lowest —23-5° on December 26, 1798. The highest observed at Greenwich was 35° C. in 1808, and the lowest —20" C. in 1838. No arctic voyagers have succeeded in reaching the poles, in consequence of the seaS round them being completely frozen, and hence the temperature there is not known. In our hemisphere the existence of a single glacialpole — that is, a place where there was the maximum cold — has been long assumed. But the bendings which the isothermal lines present in the Northern Hemisphere have shown that in this hemisphere there are two cold poles — one in Asia, to the north of Gulf Tamour ; and the other in America, north of Barrow's Straits, about 15° from the earth's north pole. The mean temperature of the first of these poles has been estimated at - 17°, and that of the second at — 19°. With respect to the southern hemispheres, the observations are not sufficiently numerous to decide whether there are one or two poles of greatest cold, or to determine their position. 105 1. Temperatures of lakes, seas, and springs. — In the tropics the temperature of the sea is generally the same as that of the air ; in polar regions the sea is always warmer than the atmosphere. The temperature of the sea in the torrid zone is always about 26° to 27° at the surface : it diminishes as the depth increases, and in temperate as well as in tropical regions the temperature of the sea at great depths is between 2-5° and 3-5°. The low temperature of the lower layers is caused by submarine currents which carry the cold water of the polar seas towards the equator. The variations in the temperature of lakes are more considerable ; their surface, which becomes frozen in winter, may become heated to 20° or 25° in summer. The temperature of the bottom, on the contrary, is virtually 4°, which is that of the maximum density of pure water. Springs, which arise from rain water which has penetrated into the crust of the globe to a greater or less depth, necessarily tend to assume the tempera- ture of the terrestrial layers which they traverse. Hence, when they reach the surface their temperature depends on the depth which they have attained. If this depth is that of the layer of invariable temperature, the springs have a tempeiature of 10° or 11° in this country, for this is the temperature of this layer, or about the mean annual temperature. If the springs are not very copious, their temperature is raised in summer and cooled in winter by that of the layers which they traverse in passing from the invariable layer to the o A O m 3 H o U3 -1052] Distribution of Land and Water 1091 surface. But if they come from below the layer of invariable temperature their temperature may considerably exceed the mean temperature of the place, and they are then called thermal springs. The following list gives the temperatures of some of them : — C. Wildbad . ■ 37'5 Vichy . 40 Bath . 46 Ems . . 46 Baden-Baden . . 67-5 Chaudes-Aigues . 88 Trincheras • 97 Great Geyser, in Iceland, at a depth of 66 feet . .124 From their high temperature they have the property of dissolving many mineral substances which they traverse in their passage, and hence form mineral waters. The temperature of mineral waters is not modified in general by the abundance of rain or of dryness ; but it is by earthquakes, after which they have sometimes been found to rise and at other times to sink. 1052. Distribution of land and water. — The distribution of water on the surface of the earth exercises great influence on climate. The area covered by water is considerably greater than that of the dry land ; and the distribution is unequal in the two hemispheres. The entire surface of the globe occupies about 200 millions of square miles, nearly three-fourths of which are covered by water ; that is, the extent of the water is nearly three times as great as that of the land. The surface of the sea in the Southern Hemisphere is to that in the Northern in about the ratio of 13 to 9. The depth of the open sea is very variable ; the lead generally reaches the bottom at about 300 to 450 yards ; in the ocean it is often 1,300 yards, and instances are known in which a bottom has not been reached at a depth of 4,500. It has been computed that the total mass of the water does not exceed that of a liquid layer surrounding the earth with a depth of about 1,100 yards. 4 A 2 PROBLEMS AND EXAMPLES IN PHYSICS I. EQUILIBRIUM 1. A body being placed successively in the two pans of a balance, requires i8o grammes to hold it in equilibrium in one pan, and i8i grammes in the other ; required the weight of the body to a milligramme. From the formula x = s/pf we have X = .v/iSo y i8i = 1808', 499. 2. What resistance does a nut ofter when placed in a pair of nutcrackers at a distance of | of an inch from the joint, if a force of S pounds applied at a distance of 4 inches from the joint is just sufficient to crack it ? Arts. 26J pounds. 3. What force is required to raise a cask weighing 6 cwt. into a cart o'8 metre high along a ladder 275 metres in length ? Ans. 195J pounds. 4. If a horse can move 30 cwt. along a level road, what can it move along a road the inclination of which is i in 80, the coefficient of friction on each road being ^ ? Ans. Qlls% cwt. 5. The piston of a force-pump has a diameter of 8 centimetres, and the arms of the lever by which it is worked are respectively 12 and 96 centimetres in length ; what force must be exerted at the longer arm if a pressure of I2'36 pounds on a square cen- timetre is to be applied? Ans. 77'6g pounds. II. GRAVITATION 6. A stone is thrown vertically downwards from a balloon with a velocity of 50 metres in a second. How soon will the velocity amount to 99 metres in a second, and through what distance will the stone have fallen ? To find the time requisite for the body to have acquired the velocity of 99 metres in a sceond, we have V = V * gt; in which V is the initial velocity, g the acceleration of gravity, which, with sufficient approximation, is equal to 9'8 (metre, second), and t the time. Substituting these values, we have t = 9^ ~ ^° = i?. = e seconds. 9-8 g-S For the space traversed we have s = Vt + igi^ = So X s + 4'9 X 25 =372-5 metres. 7. A projectile was thrown vertically upwards to a height of 5io"''22. Disregard- ing the resistance of the air, what was the initial velocity of the body ? The velocity is the same as that which the body would have acquired on falling from a height of 5io'22 metres. From the formula v = ^zgs we get V = /\/2 X 9-8 X siq'zz = \/ioooo = 100 metres. 1 8. A stone is thrown vertically upwards with an initial velocity of 100 metres. After what time would it return to. its original position? I094 Problems and Examples in Physics The time of rising and falling is the same, but the time of falling is - (from the g formula v=gt) or — — =io"2, which is half the time required ; therefore /=20"4 sec. 9» 9. A stone is thrown vertically upwards with an initial velocity of loo metres per second ; after x seconds a second stone is thrown with the same velocity. The second stone is rising 87 seconds before it meets the first. What interval separated the throws ? The rising stone will have the velocity v = V — gt, whence v = 100 — 9 '8 x 87. On the other hand, the falling stone, at the moment the stones meet, will have the velocity given by the equation v = gt', in which f is the time during which the stone falls before it meets the second one. This time is equal to 87 seconds + x — ^—. Hence Its velocity is , . . = 9-^ («-^ ^ ^ - P)- Equating the two values of v and reducing, we obtain x = ■i seconds, 10. A body moving with a uniformly accelerated motion traverses a space of 1000 metres in 10 seconds. What would be the space traversed during the eighteenth second if the motion continued in the same manner ? The formulae = J ^^ gives for the acceleration^ = 20 (metre, second). The space traversed during the eighteenth second vrill be equal to the difference of the space traversed in 18 seconds and that traversed at the end of the seventeenth. 20 X i82 20 X 17^ X — — '— — 350 metres. 2 2 11. A cannon-ball has been shot vertically upwards with a velocity of 250 metres in a second. After what mterval of time would its velocity have been reduced to 54 metres under the retarding influence of gravity, and what space would have been traversed by the ball at the end of this time ? If / be the time, then at the end of each second the initial velocity would be dimi- nished by g^'S. Hence we shall have 54 = 250 — t X 9"8, whence t = 20 seconds ; and for the space traversed Q-8 X 20^ = 250 X 20 — 2 = 3040 metres. 2 12. Required the time in which a body would fall through a height of 2000 metres, neglecting the resistance of the air. From .5 = 4 g^ and substituting the values, we have 2000 = <— fl, whence t = 20 '2 seconds. 2 13. A body falls in air from a height of 4000 metres. Required the time of its fall and its velocity when it strikes the ground. From the formula s = ^ gp we have for the time < = / — ; and, on the other hand, from the formula for velocity v = gtv/e have t = - = ?5?=20'4. _ vf 9'8 Hence - = / — , from which v = ^/2 sg, and substituting the values for s and g, V = 280 metres. 14. A stone is thrown into a pit 150 metres deep and reaches the bottom in 4 seconds. With what velocity was it thrown, and what velocity had it acquired on reaching the bottom ? Ans. The stone was thrown with a velocity of ly'g, and on reaching the bottom had acquired the velocity 57'!. 15. A stone is thrown downwards from a height of 150 metres with a velocity of to metres per second. How long will it require to fall ? Gravitation 1095 The distance through which the stone falls is equal to the sum of the distances through which it would fall in virtue of its initial impulse and of that which it would traverse under the influence of gravity alone ; that is, 150 = io< + " — Taking the positive value only wo get t = 4-61 seconds. 16. How far will a heavy body fall in vacuo during the time in which its velocity increases from,4o'2S feet per second to 88 '55 feet per second? Aks. ' Taking the value of ^ at 32'2, the body falls through 96 '6 feet. 17. Required 'the time of oscillation of a simple pendulum whose length is 0-9938, and in a place where the intensity of gravity is g'Si. From the general formula < = ir / -, in which t expresses the time of one oscillation, I the length of the pendulum, and g the intensity of gravity, we have t = 3-1416 V-^-^g3|4 = I second. 18. What is the intensity of gravity in a place in which the length of the seconds pendulum is o" -991? _ In this case < = t / — ; and also < = ir /_; and therefore , = -, from ■V ^' V ^' ^ g which g' = ^--. Substituting in this latter equation the values of g', /, and V, we have^' = 9-782. 19. In a place at which the length of the seconds pendulum is 0-99384, it is required to know the length of a pendulum which makes one oscillation in 5 seconds. In the present case, as g remains the same in the general formula, and t varies, the length / must vary also. We shall have, then, from which, reducing and introducing the values, we have /' = 52 X 0-99384 = 24-846. 20. A pendulum, the length of which is i"'9S, makes 61,682 oscillations in a day. Required the length of the seconds pendulum. Ans. 0-99385 metre. 21. A pendulum clock loses 5 seconds in a day. , By how much must it be shortened to keep correct time ? Let J = the number of seconds in one day, and s' the number indicated by the clock, then s Mf = n: n' = f: t = \/T' : \/l .-■ 86400 : 86395 = i : \/ill' = 1 : ij x .-. at= -9998843. Hence i— j;=o-oooiiS7 Am. 22. What is the normal acceleration of a body which traverses a circle of 4-2 metres diameter with a linear velocity of 3 metres per second ? Ans. 4-286 metres. 23. An iron ball falls from a height of 68 cm. on a horizontal iron plate, and rebounds to a height of 27 cm. Required the coefficient of elasticity of the iron. If an imperfectly elastic ball with the velocity v strikes against a plate, it rebounds with the velocity v, = — kv, from which, disregarding the sign, k = -'. Now we have the velocity w, = 'i/^gk, and v = ^2 ^A, from which A = 4i Substitut- ing the corresponding values, we get k = 063. ^ 24. Two inelastic bodies, weighing respectively 100 and 200 pounds, strike against each other with velocities of 50 and 20 feet ; what is their common velocity, after the impact? Ans. 30, or 3-3, according as they move in the same or in opposite directions before impact. 1096 Problems and Examples in Physics III. ON LIQUIDS AND GASES 25. The force with which a hydraulic press is worked is 20 pounds ; the arm of the lever on which this force acts is s times as long as that of the resistance ; lastly, the area of the large piston is 70 times that of the smaller one. Required the pressure transmitted to the large piston. Force on smaller piston = 20 x 5 = P ,, larger ,, = 70 P = 7000 pounds. 26. The force with which a hydraulic press is worked being 30 kilos, and the arm of the lever by which this force is applied being 10 times as long as that of the resist- ance, and the diameter of the small piston being two centimetres ; find the diameter of the large piston, in order that a force of 2000 kilos may act upon it. Ans. S'i64 centimetres. 27. One of the limbs of a U-shaped glass tube contains mercury, to a height of °"'S7S ; 'he other contains a different liquid to a height of o'°"42 ; the two columns being in equilibrium, required the density of the second liquid with reference to mer- cury and to water. Ans. d = o'4i6 and cC = S'66 ; d and d' being the densities compared to mercuiy and water respectively. 28. What force would be necessary to support a cubic decimetre of platinum in mercury at zero ? Density of mercury 13 '6 and that of platinum 21 5. From the formula P = VD the weight of a cubic decimetre of platinum is I X 21*5 = 2i*'*5 and that of a cubic decimetre of mercury is a x 13*6 = I3^"6. From the principle of Archimedes, the immersed platinum loses part of its weight equal to that of the mercury which it displaces. Its weight in the liquid is therefore 2i'S — I3'6 = 7'9, and this represents the force required. 29. Given a body A which weighs 7'ss grammes in air, 5-17 gr. in water, and 6"3S gr. in another liquid, B ; required from these data the density of the body A and that of the liquid B. The weight of the body A loses in water 7'S5 — S'i7 = 2 '38 grammes ; this repre- sents the weight of the displaced water. In the Uquid B it loses 7'ss — 6 •35 = i'2 gr. ; this is the weight of the same volume of the body B, as that of A and of the displaced water. The specific gravity of A is therefore 7SS _ 3-172, and that of B ?— = o'Sod. 238 ^ ' ' 238 ^ * 30. A cube of lead, the side of which is 4 cm., is to be supported in water by being attached to a sphere of cork. What must be the diameter of the latter, the specific gravity of cork being 0*24, and that of lead 11 '35 ? The volume of the lead is 64 cubic centimetres ; its weight in air is therefore 64 X ii'3S. and its weight in water 64 x ii'3S — 64 = 662-4 gr. If r be the radius of the sphere in centimetres, its volume in cubic centimetres will bet^"— , and its weight in grammes is 4^^ 024 Now, as the weight of the 3 3 displaced water is obviously i ir r* in grammes, there will be an upward buoyancy 3 represented by ^^^ - '^ '^ ^ '^ °'^4 = ''" ^ "^ °76 ^hich must be equal to the 3 3 3 weight of the lead; that is, t!!^ y- Q^ _ 662-5, from which '' = S'^'gas and the 3 diameter = 11 '85. 31. A cylindrical steel magnet 15 cm. in length and i -2 mm. in diameter is loaded at one end with a cylinder of platinum of the same diameter and of such a length that Liquids and Gases 1097 when the solid thus formed is in mercury, the free end of the steel projects lo ram. above the surface. Required the length of this platinum, specific gravity of steel being 7-8 and of platinum 21-5. The weight of the steej in gramraes will be 15 ir r' x 7'8 and of the platinum *"• r* X si^s. These are together equal to the weight of the displaced mercury, which is " r^ (14 + x) i3'6, from which x = g'ag cm. 32. A cylindrical silver wire o""oois in diameter weighs 3 '2875 grammes; it is to be covered with a layer of gold o"ooo2 in thickness. Required the weight of the gold, the specific gravity of silver being io'47 and that of gold ig'26. If r is the radius of the silver wire and Ji its radius when covered with gold, then r = o''075 and J! = o«-o95. The volume of the silver wire will be t r" I and its weight n r^ I X io'47, from which / = I7"76B. The volume of the layer of gold is 71 (^2 - y2) X 17768, and its weight TT (o'ogs' — o"o7S'') X 17768 x I9'26 = 3'6s6 nearly. 33. A kilogramme of copper is to be drawn into wire having a diameter of o"i6 centimetre. What length will it yield ? Specific gravity of copper 8-88. The wire produced represents a cylinder I cm. in length, the weight of which is jrtO I X 8'88, and this is equal to 1000 grammes. Hence i = se^'ooSs. 34. The specific gravity of cast copper being 879, and that of copper vrire being, 8-88, what change of volume does a kilogramme of cast copper undergo in being drawn into wire ? Ans. '°° . 86617 35. Determine the volumes of two liquids, the densities of which are respectively f3 and 07, and which produce a mixture of three volumes having the density o'g. If X and y be the volumes, then from P = VD, i"3* + o'j y = 3 x o'g and I + JI = 3, from which x = i and y = 2,. 36. The specific gravity of zinc being 7 and that of copper g, what weight of each metal must be taken to form 50 grammes of an alloy having the specific gravity 8 '2, it being assumed that the volume of the alloy is exactly the sum of the alloyed metals ? Let X = the weight of the zinc, and y that of the copper, then x ■*■ y = $0, and from the formula P = VD, which gives V = —, the volumes of the two metals and of the alloy are respectively -+-''= ^° . From these two equations we get x = 17 '07 7 g 8-2 andji = 32-93. 37. A platinum sphere 3 cni. in diameter, is suspended to the beam of a very accv)- rate balance, and is completely immersed in mercury. It is exactly counterbalanced by a copper cylinder of the same diameter completely immersed in water. Required the height of the cylinder. Specific gravity of mercury i3'6, of copper 8-8, and of platinum 21 '5. Ans. 2 '023 centimetres. 38. To balance an ingot of platinum 27 grammes of brass are placed in the other pan of the balance. What weight would have been necessary if the weighing had beeii effected in vacuo? The density of platinum is 21 '3, that of brass 8'3J and air under a pressure of 760 mm. and at the temperature 0° has — the density of water. 770 The weight of brass in air is not 27 grammes, but this weight minus the weight of a volume of air equal to its own. P ' P Since P = VD .■ . V = - and the weight of the air is — — - = ^7 ' D D V. 770 8-3 X 770' By similar considerations, if x is the weight of platinum in vacuo, its weight in air logS Problems and Examples in Physics will be * minus the weight of air displaced, that \%x — — , and this weight 21 '5 X 77° is equal to that of the true weight of the brass ; and we have X — ■ = 27 — (- ; from which x — 26"qg6. 2i"S X 770 8'3 X 770 39. A body loses in carbonic acid gas i'i5 gr. of its weight. What would be its loss of weight in air and in hydrogen respectively ? Since a Utre of air at 0° and 760 mm. weighs i 293 gramme, the same volume of carbonic acid weighs i'293 x i'524 = i -97 gramme. We shall, therefore, obtain the volume of carbonic acid corresponding to iT5gr. by dividing this number by f97, which gives o'5837 litre. This being then the volume of the body, it displaces that volume of air, and therefore its loss of weight in air is o'5837 x I"293 = °'7547 gramme, and in hydrogen o'5837 x i "293 x 0*069 = o'o52076. 40. Calculate the ascensional force of a spherical balloon of oiled silk which, when empty, weighs 62*5 kilos., and which is filled with impure hydrogen, the density of which is — that of air. The oiled silk weighs o"25o kilo, the square metre. 13 The surface of the balloon is 2 = 250 square metres. This surface being that of 0-25 a sphere, is equal to 4 ir R^, whence 4 n- .ff' = 250 and R = 4*459 ; therefore V = "'— — 3 = 371 -52 cubic metres. The weight of air displaced is 371 '52 x i'293 kilo. = 48o'37S kilos. ; the weight of the hydrogen is 36*88 kilos., and therefore the ascensional force is 480*375 - (36'88 + 62*5) = 380*995 kilo. 41. A balloon 4 metres in diameter is made of the same material and filled with the same hydrogen as above. How much hydrogen is required to fill it, and what weight can it support ? The volume is i ir ^' = 33*5 1 cubic metres, and the surface 4 ^i?' = 50*265 sqtiare 3 metres. The weight of the air displaced is 33*51 x 1*293 = 43*328 kilos., and that of the hydrogen is from the above data 3*333 kilos., while the weight of the material is 12*566 kilos. Hence the weight which the balloon can support is 43*328 - (12*566 + 3*333) = 27*429 kilos. 42. Under the receiver of an air-pump is placed a balance, to which are suspended two cubes; one of these is 3 centimetres in the side, and weighs 26*324gr. ; and the other is 5 centimetres in the side, and weighs 26*2597 grammes. When a partial vacuum is made these cubes just balance each other. What is the pressure? Ans. o'°*374. 43. A soap-bubble 8 centimetres in diameter was filled with a mixture of one volume of hydrogen gas and 15 volumes of air. The bubble just floated in the air ; required the thickness of the film. The weight of the volume of air displaced is 4 »■ /-5 x 0*001293 gramme, and that of the mixture of gases ^ t r^ x 0*001293 x ^ _ — zS. ; and the difference of 3 16 these will equal the weight of the soap-bubble. This weight is that of a spherical shell, which, since its thickness t is very small, is with sufficient accuracy 4 t r^ t s\n grammes, where s is the specific gravity = 1*1. Hence ^ TT r* ( *ooi293 — '001293 X _'?_?._?3\ _ ^^^at x 1*1. 3 \ 16 / Dividing each side by 4 ir r^, and putting >- = 4, we get 3 4 X *OQi293 (i - ^^°g^^ )=3-3<; Liquids and Gases 1099 or •001293 X "^ ' = 3*3 / : 4 whence / = '00009116629 cm. 44. In a vessel whose capacity is 3 litres, there are introduced 2 litres of hydrogen under the pressure of 5 atmospheres ; 3 litres of nitrogen under the pressure of half an atmosphere, and 4 litres of carbonic acid under the pressure of 4 atmospheres. What is the final pressure of the gas, the temperature being supposed constant during the experiment ? The pressure of the hydrogen, from Dalton's law, will be -, that of the nitro- 3 gen will remain unchanged, and that of the carbonic acid will be -i 3. Hence the 3 total pressure will be — + _ + _ = 9i atmospheres. 323 45. A vessel containing 10 litres of water is first exposed in contact with oxygen under a pressure of 78 cm. until the water is completely saturated. It is then placed in a confined space containing 100 litres of carbonic acid under a pressure of 72 cm. Required the volumes of the two gases when equilibrium is established. The coeffir cient of absorption of oxygen is 0-042, and that of carbonic acid unity. The volume of oxygen dissolved is 0-42. Being placed in carbonic acid it will act as if it alone occupied the space of the carbonic acid, and its pressure will bp 78 X — ^ — = 0*326 cm. 100*42 Similarly the 10 litres of water will dissolve ro litres of carbonic acid gas, the total volume of which will be' no, of which 100 are in the gaseous state and ro are dissolved. Its pressure is therefore 72 x ^^ = 65*454 cm. no Hence the total pressure when equilibrium is established is 0*326 T 65*454 = 6578 cm. ; and the volume of the oxygen dissolved reduced to the pressure 65*78 is o"'*42 X ° ^^ = o'"*oo2o8, and that of the carbonic acid 10 x ^ ^ 454 _ 0*95. 65*78 65*78 46. In a barometer which is immersed in a deep bath the mercury stands 743 mm. above the level of the bath. The tube is lowered until the barometric space, which contains air, is reduced to one-third, and the mercury is then at a height of 701 mm. Required the atmospheric pressure at the time of observation. Ans. =764"". 47. What is the pressure on the piston of a steam boiler of 8 decimetres diameter if the pressure in the boiler is 3 atmospheres? Ans. 10385*85 kilos. 48. What is the pressure of the atmosphere at that height at which an ascent of 21 metres corresponds to a diminution of i""" in the barometric height ? Ans. 378*9°"". 49. What would be the height of the atmosphere if its density were everywhere uniform? Ans. 7954*1 metres, or nearly 5 miles. 50. How high must we ascend at the sea-level to produce a depression of i mm. in the height of the barometer? Ans. Taking mercury as 10,500 times as heavy as air, the height will be 10*5 metres. 51. Mercury is poured into a barometer tube so that it contains 15 cc. of air under the ordinary atmospheric pressure. The tube is then inverted in a mercury bath and the air then occupies a space of 25 cc. ; the mercury occupying a height of 302 mni. What is the pressure of the atmosphere ? Let X be the amount of this pressure, the air in the upper part of the tube will have a pressure represented by -2_, and this, together with the height of the mercurial 25 column 302, will be the pressure exerted in the interior of the tube on the level of the IIOO Problems and Examples in Physics mercury in the bath, which is equal to the atmospheric pressure ; that is -2- + 302 = X, from which x = 755 mm. 52. What effort is necessary to support a cylindrical bell-jar full of mercury immersed in mercury ; its internal diameter being 6 centimetres, its height ol above the surface of the mercury (fig. i) 18 centimetres, and the pressure of the atmosphere o'77 centimetre? The bell-jar supports on the outside a pressure equal to that of a column of mercury the section of whose base is cd, and the height that of the barometer. This pressure is equal to IT J?* X o'77 X i3'6. The pressure on the inside i» that of the atmosphere less the weight of a column of mercury whose base is ct/ ^d] ^ ^ d r,^ d, ^' = §^- d 7-8' r, s/ r^ 89. A wire stretched by a weight of 13 kilos, sounds a certain note. What must be the stretching weight to produce the major third ? The major third having S the number of vibrations of the fundamental note, and as, 4 all other things being the same, the numbers of vibrations are directly as the square roots of the stretching weight, we shall have x = 2o-3i2 kilos. 90. The diameters of two wires of the same length and material are o'oois and O'oo38 m. ; and their stretching weights 400 and 1600 grammes respectively. Required the ratio of the numbers of their vibrations. Ans. n : n, = i'266 : i. 91. A brass wire i metre in length stretched by a weight of 2 kilogrammes, and a silver wire of the same diameter, but 3'i65 metres in length, give the same number of vibrations. What is the stretching weight in the latter case ? Since the number of vibrations is equal, we shall have - /^ = ' /^: rlW nd rl.S/ „ d, from which, replacing the numbers, we get jr = 25 kilos. 92. A brass and a silver wire of the same diameter are stretched by the weights of 2 and 25 kilogrammes respectively, and produce the same note. What are their lengths, the density of brass being 8 '39, and of silver ro'47 ? Ans. The length of the silver wire is 3-16 times that of the brass. 93. A copper wire 1*25 mm. in diameter and a platinum one of 0*75 mm. are stretched by equal weights. What is the ratio of their lengths, if, when the copper wire gives the note C, the platinum gives F on the diatonic scale? Ans. The length of the copper is to the length of the platinum = 1-264 ' i- 94. An organ pipe gives the note C at a temperature 0° ; at what temperature will it yield the major third of this note? Ans. 153° C. 95. A brass wire a metre in length, and stretched by a weight of a kilogramme, yields the same note as a silver wire of the same diameter but 2-5 metres in length and stretched by a weight of 7-5 kilogrammes. Required the specific gravity of the silver. Ans. io-o68. 96. How many beats are produced in a second by two notes, whose rates of vibra- tion are Respectively 340 and 354 ? Ans. 14. Heat iios V. ON HEAT 9?. Two mercurial thermometers are constructed of the same glass ; the intertial diameter of one of the bulbs is 7°"°'s and of its tube 2"s ; the bulb of the other is 6'2 in diameter and its tube 1-5. What is the ratio of the length of a degree of the first thermometer to a degree of the second? Let A and B be the two thermometers, D and D the diameters of the bulbs, and d and d! the diameters of the tubes. Let us imagine a third thermometer C with the same bulb as B and the same tube as A, and let /, /', and /" denote the length of a degree in each of the thermometers respectively. Since the stems of A and C have the equal diameters, the lengths / and i" are directly as the volumes of the tubes, or what is the same, as the cubes of their diameters ; and as B and C have the same buUc, the lengths /' and /" are inversely proportionate to the sections of the stems, or what amounts to the same, to the squares of their diameters. We have then I D^ , I" i" plane mirrors, 525 ; multiple, 526 ; magnitude of, 540 ; produced by small apertures, 515 ; virtual and real, 525 ; inversion of, 629 Imbibition, heat produced by, 489 Impedance, 985 Impenetrability, 7, 8 Imponderable matter, 6 Incandescent lamps, 865 Inclination, 733 ; compass, 734 Inclined plane, 46 ; motion on, 52 Index of refraction, 547 ; measurement of, in solids, 559 ; in liquids, 560 ; in gases, 561 Indicator, diagram, 480 ; Richards', 480 Indices, refractive, table of, 561 Induced currents, 957-969 ; general prin- ciples of, 960 Inductance, 967 Induction balance, 974 ; by the earth, 966 ; of a current on itself, 967 ; electrostatic, 762 ; in telegraph cables, 916; Faraday's theory of, 766; by Leyden discharge, 962 ; by magnets, 959 ; magnetic, 700 Inductive capacity, specific, 783 Inductorium, 975 Inertia, 7, 22 ; applications of, 23 Influence, magnetic, 700 ; electrostatic, 762 Ingenhaus's experiment, 410 Injector, Giffard's, 208 Insects, sounds produced by, 244 Insolation, 650 Instruments, optical, 596 ; polarising, 670 ; mouth, 272 ; reed, 273 ; stringed, 281 ; wind, 271 Insulating, bodies, 744 ; stool, 778 Insulators, 743 Intensity, of light, 519; of magnetisa- tion, 722 ; of reflected light, 529 ; of a musical note, 246 ; of radiant heat, 420 ; of sound, causes which in- fluence, 227 ; of terrestrial magnetism, 735 ; of terrestrial gravity, 84 Interference, of light, 659 ; of sound, 262 Intermittent, fountain, 213 ; springs, 215 ; siphon, 215 Interrupter of induction coil, 975 ; Wehnelt, 976 ; mercury, 1004 Intervals, musical, 247 Inversion, of images, 629 ; thermo- electric, 870 lonisation, 937 Ions, 943 Iris, 625 Iron ships, magnetism of, 740 Irradiation, 641 Irregular reflection, 528 Isobars, 1020 Isochimenal line, 1048 Isochronism, 56 Isoclinic lines, 733 Isodynamic lines, 735 Isogeothermic lines, 1048 Isogenic lines, 728 Isotheral lines, 1048 Isothermal, lines, 373, 412, 507, 1048 ; zone, 104S JAR, Harris's unit, 794; Leyden, 786-794 Jet, lateral, 143 ; height of, 144 ; form of, 149 Jew's harp, 273 Jolly's, spring balance, 87 ; determina- tion of gravity, 77 Joly's condensation method for specific heat, 461 Jordan's glycerine barometer, 178 Joule's, experiment on heat and work, 506 ; equivalent, 506 ; law, 860 ; elec- tromagnet, 901 Jupiter, 516 Jurin's laws of capillarity, 131 KALEIDOPHONE, 639 Kaleidoscope, 526 Kamsin, 1018 Kater's pendulum, 81 Kathode, 934 ; rays, 981 Kation, 934 Keepers, 709 Kelvin, Lord {see Thomson) Kerr's electro-optical experiments, 997 Keynote, 249 Kienmayer's amalgam, 769 Kilogrammetre, 62, 479 Kilowatt, 860 .Kinematograph, 639 Kinetic energy, 64, 506 Kinnersley's thermometer, 808 KirchhofFs laws, 855 Knife-edge, 73 Kbnig's, apparatus, 257 ; manometric flames, 290 Kundt's velocity of sound, 279 Index 1 1 27 (THE NUMBERS REFER TO THE ARTICLES) LABYRINTH of the ear, 261 Lactometer, 128 Lag, magnetic, 907 Lalande and Chaperon's cell, 826 Lambert's method, 581 Lamp, incandescent, 865 ; Dobereiner, 489 ; differential, 864 Land and water, distribution of, 1052 Lane's electrometer, 793 Langley's, observations on the spectrum, 436 ; bolometer, 932 Lantern, magic, 616 Laplace's baronietric formula, 179 Laryngoscope, 573 Larynx, 260 Latent heat, 344 ; of fusion, 467 ; of vapours, 375, 468 Lateral jet, 143 Latitude, magnetic, 733 ; influence of, on the temperature of the air, 1050 ; parallel of, 84 Lavoisier and Laplace's calorimeter, 455 ; method of determining linear expan- sion, 315 Lead angle of, 990 Lead tree, 949 Lechatellier's thermo-junction, S75 Lecher's method, 1003 Leclanche's cell, 828 Ledger lines, 252 Leidenfrost's phenomenon, 390 Lemniscate, 681 Lenard rays, 982 Lens, axis of, 562 ; optical centre, secondary axis of, 566 Lenses, 562-572 ; formulae for, 563 ; achromatic, 595 ; aplanatic, 570 ; combination of, 571; echelon, 619; images in double convex, 564 ; in double concave, 565 ; lighthouse, 619 Lenz's law, 961 Leslie's, cube, 427 ; experiment, 376 ; thermometer, 309 Level, water, 108 ; spirit, 109 Level surface, 69 Lever, 43 Leyden discharge, inductive action of, 962 Leyden jars, 786-794; potential and capacity of, 799 ; work by, 8oi Lichtenberg's figures, 788 Liebig's condenser, 380 Lift, hydraulic, 107 Ligament, suspensory, 625 Light, 510 ; diffraction of, 660 ; homo- geneous, 583 ; intensity of, 519 ; inter- ference of, 659 ; laws of reflection of. 522 ; oxyhydrogen, 618 ; polarisation of, 665 ; change of intensity with dis ■ tance, 519, 522 ; sources of, 648 ; theory of polarised light, 675 ; undu- latory theory of, 510, 651 ; velocity of, 516-518 Lighthouse lenses, 619 Lighting, electric, 864 Lightning, 1038 ; effects of, 1040 ; con- ductor, 1042 Limit, of elasticity, 20 ; of perceptible sounds, 244 Linde's, ice-machine, 503 ; apparatus, 387 Line, aclinic, 733 ; of coUimation, 606 isoclinic, 733 ; agonic, 728 ; isogonic, 728 ; isodynamic, 735 ; of sight, 606 Linear expansion, coefficients of, 317 Lines, of magnetic force, 699 ; of elec- tric force, 759 Lippmann's, capillary electrometer, 950 ; colour photography, 624 Liquefaction, of gases, 383 ; of vapours, 378 Liquids, 95 ; buoyancy of, 99 ; com- pressibiUty of, 96 ; conductivity of, 413; calculation of density of, 120; diffusion of, 140 ; diamagnetism of, 995 ; expansion of, 322 ; equilibrium of, 103 ; manner in which they are heated, 414 ; pressure on sides of vessel, loi ; refraction of, 560 ; rota- tory power of, 691 ; spheroidal fonn of, 16 ; spheroidal state of, 390 ; specific heat of, 463 ; volatile and fixed, 352 ; tensions of vapours of, 362 ; of mixed liquids, 363 Lissajous's experiments, 286-288 Local, action, 819 ; battery, 914 Locatelli's lamp, 432 Locomotives, 477 Lodestone, 694 Long sight, 643 Loops and nodes, 270 Loss of weight in air, correction for, 408 Loudness of a musical tone, 246 LuUin's experiment, 808 Luminiferous ether, 510 Luminous bodies, 511 ; heat, 440 ; meteors, 1014 ; paint, 649 ; pencil, 512; radiation, 437 ; ray, 5 1 2 MACHINE, Atwood's, 79 ; elec- tric, 768-776 Mackerel-sky, 1022 Macleod's gauge, 206 1128 Index (THE NUMBERS REFER TO THE ARTICLES) Magdeburg hemispheres, 162 Magic lantern, 616 Magnetic attraction and repulsion, 696 ; battery, 708 ; circuit, 902 ; curves, 700 ; declination, 727 ; dip, 733 ; ele- ments, 727 ; equator, 733 ; field, 699, 834, 836 ; flux density, 721 ; foci, 735 ; force, laws of, 717 ; force due to bar magnet, 723 ; induction, 700, 902 ; influence, 700 ; meridian, 726 ; needle, 694; observatories, 738; poles, 716, 733 ; reluctance, 902 ; saturation, 698 ; storms, 738 ; substances, 701 Magnetisation, 703 ; by the action of the earth, 739 ; by currents, 707, 904 ; curve, 904 ; intensity of, 904 ; by single, separate, and double touch, 704-706 Magnetism, 6, 694 ; earth's, 726 ; of iron ships, 740 ; Ampere's theory of, 894 ; remanent, 904 ; theory of, 698 ; ter- restrial, 726 ; distribution of free, 713; eff'ect of temperature on, 712 Magneto and dynamo-electric machines, 985-992 Magnetometer method, 904 Magnetomotive force, 902 Magnets, artificial and natural, 694 ; broken, 697 ; action of earth on, 726 ; Meyer's floating, 714 ; heat developed by, 964 ; north and south poles of, 695; portative force of, 710; satura- tion of, 698 ; effect of temperature, 712; induction by, 959; inductive action on moving bodies, 963 ; action on currents, 889 ; on solenoids, 893 ; optical effects of, 996 Magnification, 540, 569 ; linear and superficial measure of, 600 ; of a tele- scope, 606 Magnifying, glass, 597 ; power, 605 Magnitude, 9; apparent, of an object, 599 ; of images in mirrors, 540 Major, chord, 247 ; triads, 248 Malleabihty, 7, 91 Mance's, heliograph, 533 ; method, 927 Manganese, magnetic limit of, 711 Manhole, 473 Manometer, 96, 184 ; with compressed air, 185 ; Regnault's barometric, 187 Manometric flames, 290 Mares' tails, 1022 .Alarine, barometer, 169 ; engines, 473 Mariner's, card, 1016 ; compass, 732 Mariotte and Boyle's law, 181 Mariotte's tube, 181 Marloye's harp, 283 Mascart's insulator, 744 Maskelyne's experiment, 69 Mason's hygrometer, 404 Mass, measure of, 26 ; unit of, 26 Matter, 2 Matteucci's experiments, 7^6, 962 Matthiessen's thermometer, 309 Maximum and minimum thermometersj 3" Maximum current, conditions of, 847 Maxwell's electromagnetic theory of light 1002 ; colour discs, 581 ; rule, 960 law, 1002 Mayer's floating magnets, 714 Mean temperature, 1045 Measure of force, 29 ; of work, 61 Measure of magnification, 600 ; of mass, 26 ; of space, 25 ; of time, 24 ; of velocity, 28 Measurement of small angles by reflec- tion, 530 Mechanical, equivalent of heat, 506 ; effects of electric discharge, 808 Melloni's researches, 424 Melting point, influence of pressure on, 342 Membranes, semipermeable, 139; sensi- tive, 229 ; vibrations of, 285 Meniscus, 130; convex, 130; in baro- meter, 171 Mensbrugghe's experiment, 133 Mercury, frozen, 376, 384, 390 ; pendt.* lum, 321 ; coefficient of apparent expan- sion, 323 ; expansion of, 322 ; pump, 209 ; purification of, 169 Meridian, 25 ; geographical and mag- netic, 726 Metacentre, 114 Metal, Rose's and Wood's fusible, 341 Meteoric stones, 487 Meteorograph, 1015 Meteorology, 1014 Meteors, aerial, 1014 Metre wire bridge, 923 Metronome, 83 Meyer's method for vapour density, 393 Mho, 845 Microfarad, 931 Micrometer, 605 ; screw, 1 1 Microphone, 972 Microscope, simple, 597 ; Duboscq's, 618 ; compound, 601 ; field of, 604 ; focusing, 598 ; magnifying powers of, 600 ; photo-electric, 618 ; solar, 617 Microspectroscope, 591 Microvolt, 848 Migration of the ions, 943 Mill, Barker's, 150 Milliammeter, 898 Index 1 1 29 (THE NUMBERS REFER ^lilliampere, 849 Mineral waters, 1051 Minimum, thermometer, 311 ; deviation, 558 Minor chord, 248 Minotto's battery, 823 Mirage, 551 Mirrors, 523 ; applications of, 543 ; burn- ing. 425 ; concave, 424, 535, 537 ; conjugate, 425 ; convex, 536 ; para- bolic, 544; rotating, 530, 810; spherical, 534 Mists, 102 1 Mixture of gases, 189 ; of gases and liquids, 190 ; laws of, 388 Mixtures, freezing, 350 ; method of, 457 Mobile equilibrium, 421 Mobility, 7, 21 Modulus, Young's, 87 Moisture of the atmosphere, 406 Molecular forces, 3 ; sieve, 139 ; state of bodies, 4 ; state, relation of absorption to, 450 ; velocity, 296 Molecules, 3 Moment, of forces, 39 ; of magnet, 720 ; comparison of moments, 724 Momentum, 31 ilonochord, 267 ^Monochromatic light, 583 Monosyllabic echo, 237 Monsoon, 10 18 Montgolfier's, balloon, 197 ; ram, 152 Moon, light of, 521 Morin's apparatus, 80 Morren's mercury pump, 209 Morse's, telegraph, 914; key, 914 Moser's images, 194 >rotion, 21 ; on an inclined plane, 50 ; laws of, 32 ; in a circle, 55 ; resistance to, in a fluid, 50 ; uniformly accelerated rectilinear, 51 ; of a pendulum, 56 ; of projectile, 53 Motor, electric, 993 Multiple, echoes, 237 ; images formed by mirrors, 526, 549 Muscular currents, 1007 Musical, boxes, 283 ; comma, 248 ; inter- vals, 247 ; scale, 248 ; temperament, 250 ; note, properties of, 246 ; inten- sity, 246; notation, 252; pitch and timbre, 246 ; range, 252 Mutual induction, 968 Myopia, 643 NASCENT state, 17 Natterer's apparatus, 384 Natural magnets, 694 TO THE ARTICLES) Needle, declination, 728 ; dipping, 734 ; astatic, 839 ; magnetic, 696 ; thermo- electric, 87s Negative plate, 816 Negatives on glass, 621 Nerve-currents, loii Neumann's law, 465 Neutral region, 762 ; equilibrium, 72 ; temperature, 870 Newton's, disc, 578 ; law of cooling, 422 ; rings, 664, 665 ; theory of light, 579 Newtonian telescope, 611 Niaudet's cell, 826 Nicholson's hydrometer, 119 Nickel, electric deposition of, 956 Nicol's prism, 674 Nimbus, 1022 Nobert's lines, 605 Nobili's, rings, 948 ; thermo-electric pile, 873 Nocturnal radiation, 504 Nodal points, 270, 275, 659 Nodes and loops, 270 ; of an organ pipe, 275 ; explanation of, 277 Noises, 221 Nonconductors, 743 Norremberg's apparatus, 67 1 Northern light, 1044 Norwegian stove, 416 Notation, musical, 252 Notes, in music, 246 ; musical, of women and boys, 260 ; wave-length of, 253 Nut of a screw, 48 OBJECT-GLASS, 602, 606 Objective, 602 Oboe, 273 Obscure radiation, 437 ; rays, 43S ; transmutation of, 438 Observatories, magnetic, 738 Occlusion of gases, 195 Occultation, 516 Octave, 247 Oersted's experiment, 835 Ohm, 831 Ohmmeter, 928 Ohm's law, 845 ; prism, 659 Opaque bodies, 511 Opera-glasses, 608 Ophthalmoscope, 647 Optic axis, 630 ; axis of biaxial crystals, 658 ; angle, 630 ; nerve, 625 Optical, centre, 566 ; effects of magnets, 996 ; instruments, 596 Optometer, 632 Orbit of the eye, 625 II30 Index (THE NUMBERS REFER TO THE ARTICLES) Organ, 281 ; pipes, 275 ; nodes and loops of, 27s Orthochromatic plates, 622 Oscillating currents, 800, 1005 Oscillation, 57 ; axis of, 81 ; method of, 719, 753 Osmose, 139 Osmotic pressure, 139 Otto von Guericke's air-pump, 201 Otto's gas engine, 483 Overshot wheels, 151 Oxyhydrogen light, 618 Ozone, 809, 933, 1040 PACINOTTI'S ring, 989 Paddles of steam vessels, 151 Paint, luminous, 650 Pallet, 83 PandEean pipe, 282 Pane, fulminating, 785 Papin's digester, 374 Parabolic mirrors, 544 ; curve, 80, 143 Parachute, 199 Paradox, hydrostatic, 102 Parallel of latitude, 84 ; forces, 39 ; centre of, 39 Parallel rays, 512 Parallelogram of forces, 36 Paramagnetic bodies, 701 Pascal's law of equality of pressures, 97 ; experiments, 164 Passage tint, 692 Path, mean, of molecules, 296 Pedal, 281 Peltier's effect, 87 S Pendulum, 56 ; application to clocks, 83 ; ballistic, 83 ; compensation, 321 ; electric, 742 ; length of compound, 81 ; reversible, 81 ; verification of laws of, 82 Penetration of a telescope, 607 Pentane lamp, 520 Penumbra, 514 Percussion, heat due to, 486 Period of vibration, 56 Permanent, gases, 383 ; magnetism, 904 Permeability, magnetic, 721, 904 Persistence of impression on the retina, 639 Perspective, aerial, 631 Phantasmagoria, 618 Phase, 57, 287 Phenakistoscopc, 639 Phenomenon, 5 Phonautograph, 289 Phonograph, Edison's, 293 Phosphorescence, 649 Phosphorogenic rays, 584 Phosphoroscope, 650 Photo-electric microscope, 618 Photo-electricity, 751 Photogenic apparatus, 618 Photography, 620-624 Photometers, 520 Photophone, 999 Physical phenomena, 5 ; agents, 6 ; properties of gases, 154; shadow-,, Physiological effects, of the electric dis- charge, 802 ; of the current, 1006 ; of Ruhmkorffs coil, 977 Piano, 281 Pictet's researches, 386 Piezo-electricity, 75 1 Piezometer, 96 Pigment colours, 582 Pile, voltaic, 818 ; thermo-electric, 873 Pincette, tourmaline, 680 Pipes, organ, 272 Pisa, tower of, 70 Pistol, electric, 809 Piston, of air-pump, 201 ; rod, 474 Pitch, concert, 251 ; of a note, 246 ; a screw, 48 Plane, inclined, 46 ; mirrors, 523 Plant^'s secondary battery, 946 Plate electric machine, 768 Plates, 553 ; colours of thin, 664 ; vibra- tions of, 284 ; Chladni's, 284 ; photo- graphic dry, 622 Pliability, electric, 1002 Plumb line, 69 Pluviometer, 1024 Pneumatic syringe, 156, 486 Point, boiling, 366 Points, action of, 761, 780 ; nodal, 270 Poisseuille's apparatus, 147 Poisson's coefficient, 87 Polar aurora, 1044 Polarisation, of liquid, 944 ; E.M.F. of, 952 ; angle of, 668 ; current, 944 ; of electrodes, 820, 944 ; by double refrac- tion, 666 ; by reflection, 667 ; by single refraction, 669 ; elliptic and circular, 683 ; of heat, 693 ; of light, 666 ; of the electric medium, 766 ; rotatory, 687 ; elliptic, 686 Polarised light, theory of, 675 ; colours produced by the interference of, 676- 682 Polarising instruments, 670 Pole, glacial, 1050 Index 1131 (THE NUMBERS REFER TO THE ARTICLE^) Poles, of cell, 816 ; electric, 754 ; of the earth, 733 ; magnetic, 733 ; of a mag- net, 695, 716; unit, 720; mutual action of, 696 ; red and blue, 6g6 Polygon offerees, 7 Polyorama, 618 Polyprism, 555 Pores, 13 Porosity, 7, 13 ; application of, 15 Portative force, 710, 905 Positive plate, 816 Postal battery, 914 Potential difference, 757 ; measurement of, 925 Potential energy, 64 ; of electricity, 757, 763; of a Leyden jar, 799 Pound, avoirdupois, 26, 30 ; foot, 61 Poundal, 30 Power, 62 ; of a lens, 644 ; of a micro- scope, 604; of a machine, 860 Presbyopia, 643 Press, hydraulic, 107 Pressure, centre of, loi ; on a body in a liquid, III ; atmospheric, 163 ; amount of, on human body, 165 ; experiment illustrating, 211 ; influence on melting point, 342 ; heat produced by, 486 ; electric, 757 ; electricity produced by, 751 Pressiures, equality of, 97 ; vertical down- ward, 98 ; vertical upward, 99 ; in- dependent of form of vessel, 100 ; oil the sides of vessels, loi ; capillary, 134 ; of vapour, 354 Prevost's theory of exchanges, 421 Primary coil, 957, 975 Principle of Archimedes, 112 Prismatic compass, 732 Prisms, 554 ; right angled, 556, 616 ; double refracting, 673 ; Nicol's, 674 ; with variable angle, 555 Projectile, motion of, 53 Prony's brake, 480 Proof plane, 754 Propagation of light, 5 1 3 Protuberances, 590 Psychrometer, 404, 1015 Pulley, 44 ■, Pump, air, 201 ; condensing, 210; filter, 207 Pumping engine, 474 Pumps, different kinds of, 216 ; suction, 217 ; suction and force, 218 Punctum caecum, 625 Pupil of the eye, 625 Pyknometer, 120 Pyroelectricity, 751 Pyroheliometer, 487 Pyrometers, 312 ; electric, 875, 932 QUADRANT electrometer, 748, 796 Quadrantal error of compass, 740 Quality of musical note, 246 Quantity, electric, 752, 930 Quartz threads, 89 RADIANT heat, 417 ; detection and measurement of, 418 ; causes which modify the intensity of, 420 ; Melloni's researches on, 432 ; relation of gases and vapours to, 443 ; relation to sound, 451 Radiating power, 429 ; identity of ab- sorbing and radiating, 430 ; causes which modify, &c., 431 ; of gases, 446 Radiation, cold produced by, 504 ; of gases, 446 ; luminous, and obscure, 437 ; laws of, 437 ; solar, 487 Radiative power of vapours, 1026 Radiometer, 449 Radiomicrometer, 973 Railway, friction on centrifugal, 55 Rain, 1024 ; clouds, 1024 ; bow, 1043 ; fall, 1015, 1024, 1025 ; gauge, 1024 ; drop, velocity of, 50 Ram, hydraulic, 152 Ramsden's, electric machine, 768 ; eye- piece, 603 Raoult's researches, 346 Rarefaction, in air-pump, 202 ; by Spren- gel's pump, 206 Ray, incident, 546 ; luminous, 512; ordinary and extraordinary, 655 Rays, actinic, or Ritteric, 438 ; diver- gent and convergent, 513; of heat, 417, 434 ; invisible, 433 ; obscure, 438 ; path of, in eye, 628 ; phosphoro- genic, 584 ; polarised, 666 ; trans- mission of thermal, 439 Reaction and action, 42 Real image, S3S. 5^4 Reaumur scale, 304 Receiver of air-pump, 201 Recomposition of white light, 578 Reduction factor, 838 Reed instruments, 273 Refining of copper, electric, 853 Reflected light, intensity of, 529 Reflecting, power, 427 ; goniometer, 543; sextant, 531 ; stereoscope, 637 telescope, 609 1132 Index (THE NUMBERS REFER TO THE ARTICLES) Reflection, apparent, of cold, 428 ; laws of, 423 ; of heat, 423 ; from concave mirrors, 425 ; irregular, 528 ; in a vacuum, 427 ; of light, 522 ; total, 550 ; of sound, 236 Refracting, stereoscope, 638 ; telescope, 606 Refraction, 54S-559 ; double, 653 ; po- larisation by, 666, 669 ; explanation of single, 652 ; of sound, 238 ; con- stant of, 561 ; atomic, 561 ; molecular, 561 Refractive index, 547 ; determination of, 559 ; "f gases, 561 ; of liquids, 560 ; of solids, 561 ; indices of media of eye, 626 Refractory substances, 341 Refrangibility of light, alteration of, 593 Regelation, 1031 Regnault's, experiments, 229 ; determi- nation of density of gases, 334, 335 ; manometer, 187 ; methods of deter- mining the expansion of gases, 334 ; of specific heat, 459 ; of pressure cf aqueous vapour, 361 ; hygrometer, 402 Regulator of the electric light, 864 Regulus, 343 Reis's telephone, 909 Relay, 914 Reluctance, magnetic, 902 Remanent magnetism, 902 Replenisher, 774 Repulsion, laws of, magnetic, 718 ; elec- tric, 753 Residual, charge, 789 ; magnetism, 902 Residue, electric, 789 Resinous electricity, 745 Resistance, limiting angle of, 46 ; of a fluid, 50 ; of a conductor, 743, 850 ; specific, 845 ; influence of temperature on, 851 ; of a liquid, 852, 942; in parallel, 853 ; coils, 856 ; measure- ment of, 923 ; of galvanometer, 924 ; of a cell, 927 ; in absolute measure, 970 Resistivity, 850 liesonance, 255, 276 ; box, 251 ; globe, 256 Resonator, electric, 1003 Resultant of forces, 35-37 Retardation, magnetic, 907 Retina, 625 ; persistence of impression on, 639 Return shock, 1041 Reversible pendulum, 81 Reversibility of Holtz's machine, 775 Reversion spectroscope, 588 Rheoscopic frog, 1009 Rheostat, 857 Rhomb, Fresnel's, 685 Rhumbs, 732 Riess's thermometer, 806 Right ascension, 611 Rime, 1028 Rings, coloured, 680 ; Gravesande's, 298 ; in biaxial crystals, 681 ; Newton's, 664, 665 ; Nobili's, 948 Ritchie's, experiment, 430 ; telautograph, 921 Ritteric rays, 438 Robinson's anemometer, 1015 Rock salt, heat transmitted through, 440 Rods, vibrations of, 283 Roget's vibrating spiral, 881 Rbntgen rays, 983 Rose's fusible metal, 341 Rotary engine, 478 Rotating mirror, 517, 811 Rotation, electrodynamic and electro- magnetic, of liquids, 8go ; of winds, 1019 Rotation, of the earth, 84 ; of magnets by currents, 887 ; of currents by mag- nets, 886, 889 Rotatory polarisation, 687 ; of liquids, 691 ; coloration produced by, 689 ; due to magnetic field, 996 ■Rousseau's densimeter, 129 Roy and Ramsden's measurement of linear expansion, 316 Rubbers of an electric machine, 768 Ruhlmann's barometric and thermome- tric observations, 180 Ruhmkorfif's coil, 975 ; effects produced by, 977 Rumford's photometer, 520 Rutherford's thermometers, 311 SACCHARIMETER, 692 Safety, catch, 859 ; tube, 382 ; valve, 107, 374 Salimeters, 128 Salts, decomposition of, by current, 935 Saturation, degree of, 397 ; magnetic, 698, 904 ; of colours, 582 Saussure's hygrometer, 405 Savart's toothed wheel, 241 Scale of hardness, 92 Scales, in music, 248 ; chromatic, 250 ; of a thermometer, 304 Scattered heat, 428 ; light, 528 Scheiner's experiment, 632 Schiehallion experiment, 69 Index it33 (THE NUMBERS REFER TO THE ARTICLES) Scintillation of stars, 551 Sciopticon, 616 Sclerotica, 625 Scott's phonautograph, 289 Scraping sound, 283 Scratching sound, 283 Screen, magnetic, 721 Screw, II, 48 Search light, 543 Secchi's meteorograph, 1015 Secondary, axis of a lens, 566 ; batteries, 945 ; coil, 921 ; actions, 935 Seconds pendulum, 81 Secular magnetic variations, 728 Segments, ventral and nodal, 270, 275 Segner's water-wheel, 151 Selenite, 678 , Selenium, 999 I Self-induction, 967 ; coefficient of, 968 Semicircular error of compass, 740 | Semi-conductors, 743 Semipermeable membranes, 139 Semiprisni, 587 j Semitones, 249 | Senarmont's experiment, 412 Sensitive membrane, 229 Serein, 1026 > Series and parallel, 846 Series, thermo-electric, 869 ; dynamo, 991 Sextant, 53 1 Shadows, 514 Sharpness of sight, 633 Shock, electric, 800; return, 1041 Shooting stars, 487 Short sight, 643 Shunt, 854 ; dynamo, 991 Siemens', armature, 987 ; dynamo, 986, 992 ; electric thermometer, 995 ; elec- trodynamometer, 896 Sieve, molecular, 139 Sight, long and short, 643 Silent discharge, 809 Silurus, 1012 Silver voltameter, 941 Simoom, 1018 Simple, harmonic motion, 57 ; rigidity, 89; cell, 815 Sine galvanometer, 838 Sines, curve of, 59 Singing of liquids, 366 Sinuous currents, 883 Sinusoidal currents, 985 Siphon, 214 ; barometer, 169 ; recorder, 917; intermittent, 215 Siren, 242 Sirocco, 1018 Sixe's thermometer, 311 Size, estimation of, 631 Sky, 1027 Sleet, 1029 Slide valve, 476 Sling, 55 Smee's battery, 826 Snow, 1029 ; line, 1029 Soap-bubble, colours of, 664 Solar, constant, 487 ; microscope, 618 ; light, thermal analysis of, 434 ; radia- tion, 487 : spectrum, 576 ; properties of the, 584 ; dark lines of, 585 ; lime, 24 ; day, 24 Soldering, 18 Soleil's saccharimeter, 692 Solenoid, 893 Solidification, 346 ; change of volume on, 349 ; retardation of, 348 Solidity, 4, 7 Solids, conductivity of, 411 ; index of refraction in, ^tl ; diamagnetism of, 995 ; linear and cubical expansion of, 317 ; surface tension of, 96 Solids, formula: of expansion, 319 Solution, 345 ; ideal, 139 Sondhauss's experiments, 238 Sonometer, 267, 974 Sound, 222 ; cause of, 223 ; not propa- gated in vacuo, 224 ; propagated in all elastic bodies, 225 ; propagation of, in air, 226 ; causes which influence inten- sity of, 227 ; apparatus to strengthen, 228 ; interference of, 262 ; velocity of, in air, 230 ; in gases, 231 ; in liquids, 234 ; solids, 235 ; reflection of, 236 ; refraction of, 238 ; relation of radiant heat to, 451 ; transmission of, 228 ; waves, 229 Sound, Helmholtz's analj'sis of, 256 Sound, Konig's apparatus, 259 ; Kundt's, 279 Sounder, 915 Sounds, intensity of, 291 ; limit of percep- tible, 244 ; synthesis of, 258 ; percep- tions of, 261 ; produced by currents, 908 Space, measure of, 25 Spar, Iceland, 673 Spark, and brush discharge, 804 ; elec- tric, 778 ; duration and velocity of, 810, 811 Speaking, trumpet, 239 ; tubes, 228 Specific gravity, 27, 118-129 ; bottle, 120, 122; hydrometer, 119; of gases, 338; tables of, 121, 123 Specific heat, 453-466 ; of liquids, 462 ; of gases, 466 "34 Index (THE NUMBERS REFER TO THE ARTICLES) Specific inductive capacity, 783 Spectacles, 644 Spectral analysis, 586 ; colours and pig- ment, 582 Spectrometer, 559 Spectroscope, 587 ; direct vision, 588 ; experiments with, 589 ; uses of the, 591 Spectrum, 436 ; pure, 576 ; solar, 574 ; dark lines of, 585 ; diffraction, 662 ; properties of, 584 ; of aurora borealis, 1044 Specular reflection, 528 Spherical aberration, 542, 570 Spheroidal, form of liquids, 16 ; state, 390 Spherometer, 11, 539 Spiral, goi ; Roget's vibrating, 881 Spirit-level, log Spray producer, 208 Sprengel's air-pump, 206 Spring balance, 87 Springs, 1051 ; intermittent, 215 Stable equilibrium, 72 Standard cell, Daniell's, 821 ; L. Clark's, 827 Stars, declination of, 612 ; spectral analy- sis of, 590 Staubbach, 78 Stave, 251 Steam, heating by, 499 Steam-engines, 472 ; boiler, 473 ; horn, 242 ; pipe, 208 ; various kinds of, 478 ; work of, 479 Steeling, 956 Stereometer, 186 Stereoscopes, 636-638 Stethoscope, 240 Stills, 379 Stool, insulating, 778 Stopcock, doubly exhausting, 202 ; Gay Lussac's, 388 Storage batteries, 947 Storms, magnetic, 738 Stoves, 498 ; Norwegian, 416 Stratification of electric light, 978 Stratus, 1022 Strength, dielectric, 784 Striking distance, 805 Stringed instruments, 281 Strings, transverse vibration of, 266 Subdominant chords, 248 Substance, 2 Suction pump, 217 ; and force pump, 218 ; load which piston supports, 219 Sun, 521 ; thermal analysis of light of, 435. 590 Sun-spots, 738 Superfiision, 348 Surface, tension, 133-138 ; table of, 137 ; viscosity, 148 Susceptibility, magnetic, 722 Suspension, axis of, 73 ; Cardan's, 168 Suspensory ligament, 625 Swan lamps, 865 Swimming, 117 ; bladder of fishes, 116 Switch, 974 Symmer's theory of electricity, 746 Synthesis of sounds, 258 Syringe, pneumatic, 156, 486 TAMTAM metal, 93 Tangent galvanometer, 837 Tapper, 1004 Tears of wine, 134 Telautograph, 921 Telegraph, cables, 912; single needle, 913; Jlorse, 914; sounder, 915; writing, 921 ; Cowper's, 921 ; induction in, 916 ; electric, 912-921 ; electro- chemical, 919 Telegraphone, 973 Telegraphy, duplex, 918 ; without wires, ,1004 Telephone, 971 ; Reis's, 909; toy, 235 Telescopes, 606 ; astronomical, 606 ; terrestrial, 607 ; Galileo's, 608 ; Gre- gorian, 610 ; Herschelian, 612 ; New- tonian, 611 ; reflecting, 609; notable, 613 Telluric lines, 585 Temperament, musical, 250 Temperature, 299 ; correction for, in barometer, 172 ; critical, 373 ; deter- mined by specific heat, 463 Temperature, absolute zero of, 504, 508 ; influence of, on specific gravity, 123 ; influence of, on expansion, 319 ; mean, 1045 ; how modified, 1046 ; distribu- tion of, 1050 ; of lakes, seas, and springs, 1051 Temperatures, different remarkable, 313 Tempering, 93 Tenacity, 7, go Tension, electric, 756 ; surface, 133 Terrestrial, currents, 895, 920 ; heat, 488 ; magnetic couple, 726; magnetism, 726-736 ; telescope, 607 Terrestrial gravitation, 69, 84 Test objects, 605 Thaumatrope, 639 Theodolite, 10 Theory, 5 ; of induction, 766 Thermal analysis of sunlight, 434 ; unit 452, 493; springs, 1051 Index "35 (THE NUMBERS REFER TO THE ARTICLES) Thermal rays, transmission of, 439 ; unit, 452 Thermobarometer, 372 Thermo-dynamic efficiency, 481 Thermo-electric, series, 869 ; inversion, 870 ; battery, 872, 874 ; pile, S73 ; pyrometer, 875 ; diagram, 877 Thermo-electricity, 868 Thermometer, 300 ; mercury, construc- tion of, 302-304 ; displacement of zero, 305 ; alcohol, 307 ; differential air, 309; metallic, 310; maximum and minimum, 311 ; correction of readings, 329 ; weight, 324 ; air, 335 ; Kinnersley's, 808 ; electric, 875, 932 Thermoscope, 308 Thin plates, colours of, 664 Thomson effect, 879 Thomson's, electrometers, 796, 797 ; galvanometer, 841 ; apparatus for atmospheric electricity, 1034 ; water- dropping collector, 773 Thread of a screw, 48 Threads, fine, 89 Throw of a needle, 843 Thunder, 1039 Timbre, 246 Time, measure of, 24 ; mean solar, 24 ; constant, 969 Tint, 582 ; transition, 692 Tones, combinational, 264 ; differential, 264 Tonic, 248 Toothed wheel, 241, 518 Torpedo, 1012 Torricelli's experiment, 163; theorem, 142 ; vacuum, 170 Torsion, angle of, 89; balance, 89, 718, 753 ; moment of, 89 Total reflection, 550 Tourmaline, 672, 751 ; pincette, 680 Tourniquet, hydraulic, 150 Tower of Pisa, 70 Toy telephone, 235 Trachea, 260 Trajectory, 53 Transformation of energy, 66 Transformers, 994 Transit, 24 Transition tint, 692 Translucent bodies, 511 Transmission, of heat, 409 ; of light, 510, 553 ; of power by current, 994 ; of sound, 225 Transparency, 7, 511 Transpiration of gases, 193 Triad, harmonic, 248 Triangle, 283 Triangle of forces, 38 Trumpet, speaking, ear, 239 Tubes, Geissler's, 206, 979 ; safety, 382 j speaking, 228 Tuning-fork, 251, 283, 292 Turbines, 151 Twaddle's hydrometer, 125 Twilight, 528 Twinkling of stars, 551 Tympanum, 261 Tyndall's researches, 435, 451, 1027, 1032 ULTRAGASEOUS state, 981 Unannealed glass, colours pro- duced by, 682 Undershot wheels, 151 Undulation, length of, 226, 651 Undulatory theory, 294, 510, 651 Uniaxial crystals, 654 ; double refrac- tion in, 658 ; positive and negative, 657 Unit, Harris's, jar, 794 ; thermal, 452 Unit of length, area and volume, 24 ; heat, 452 ; of work, 62 Units, fundamental, 63 ; absolute elec- tric, 1000 Unstable equilibrium, 72 VACUUM, application of air-pump to formation of, 201 ; extent of, produced by air-pump, 202 ; Crookes's, 450, 981 ; fall of bodies in a, 78 ; formation of vapour in, 354 ; heat radiated in, 419 ; reflection in a, 428 ; Torricellian, 170 Valency, of an element, 940 Valve, safety, 107, 374 ; face, 476 ; slide, 476 Van der Waals' formula, 183 Vane, electric, 780 Van 't HofF's theory, 139, 937 Vaporisation, 353 ; latent heat of, 375, 469 Vapour, aqueous, pressure of, at va- rious temperatures, 354-364; forma- tion of, in closed tube, 373 ; latent heat of, 375 ; definition of, 373 Vapours, 352 ; absorption of heat by, 440 ; absorptive powers of, 445 ; density of, Gay- Lussac's method, 391 ; Hofmann's, 392 ; densities of, 394 ; Dumas's method, 393 ; elastic force of. M36 Index (THE NUMBERS REFER TO THE ARTICLES) 354 ; formation of, in vacuo, 355 ; saturated, 356 ; unsaturated, 357 ; pressure of, of different liquids, 362 ; of mixed liquids, 363 ; in communi- cating vessels, 364 Variations, magnetic, annual, 729 ; diur- nal, 729 ; barometric, 173 ; causes of, 174 ; relation of, to weather, 175 Velocities, composition of, 54 Velocity, 28 ; of efflux, 142 ; of electri- city, 811; of light, 516; graphic representation of changes of, 54 ; Kundt's method, 279 ; molecular, 296 ; of sound in air, 230 ; gases, 231, 232 ; in liquids, 234 ; in solids, 235 ; of winds, 1015 Vena contracta, 145 Ventral segment, 270, 275 Verdet's constant, 996 Vernier, 10 Vestibule of the ear, 261 Vibrating spiral, Roget's, 88 1 A'ibration, 223 ; amplitude of, 56 ; pro- duced by currents, 908 ; of tuning- forks, 283, 288 Vibrations, 266 ; of membranes, 285 measurement of number of, 241 number of, producing each note, 251 of musical pipe, 277 ; of rods, 283 of plates, 284 ; of strings, 265 Vierordt's quantitative spectrum analysis, 591 View, field of, 604 Vinometer, 381 A'^iolin, 281 Virtual and real images, 525, 537 Viscosity, 95, 147 ; of gases, 450 Vision, distance of distinct, 633 ; bino- cular, 635 Visual angle, 630 Vital fluid, 812 Vitreous, electricity, 745 ; fusion, 341 ; humour, 625 Vocal chords, 260 Volatile liquids, 352 Volt, 816, 831 Volta's, condensing electroscope, 795 ; electrophorus, 772 ; fimdamental ex- periment, 813 Voltaic, arc, 863 ; cell, 816 ; pile, battery, 818 ; induction, 957 Voltameter, water, 933, 941 ; silver, 941 ; copper, 941 Voltmeter, 925 ; electrostatic, 798 ; Car- dew, 867 Volume, unit of, 25 ; determination of, 113; change of, on solidification, 349 ; of a liquid and that of it vapour, relation between, 395 Volumometer, 186 Voss's electric machine, 775 WATER, barometer, 177 ; bellows, 208 ; decomposition of, 933 ; hammer, 78 ; hot, heating by, 501 ; level, 109 ; maximum density of, 331 ; spouts, 1025; wheels, 151 Water-dropping collector, 773 Watt, 860 ; wattmeter, 899 Waves, 226; length of, 226, 651, 663 ; plane, 652 ; of a note, 253 Weather, its influence on barometric va- riations, 175 ; glasses, 176 ; charts, 1020; forecasts, 1020 Wedge, 47 Wedgwood's pyrometer, 3 1 2 Wehnelt, interrupter, 976 Weighing, method of double, 77 Weight, 26 ; of bodies weighed in air, correction for loss of, 408 ; of gases, 157; thermometer, 325 Wells's theory of dew, 102S Wells, artesian, no Weston ammeter, 898 Wet-bulb hygrometer, 404 Wheatstone's, bridge, 923 ; method, 929 ; photometer, 520; rotating mirror, 8l0 ; and Cooke's telegraph, 913 Wheel and axle, 45 Wheel barometer, 176 Wheels, friction, 79 ; escapement, 83 ; water, 151 Whirl, electric, 780 Whispering galleries, 237 White light, decomposition of, 574 ; re- composition of, 578 Wiedemann and Franz's tables of con- ductivity, 410 Wimshurst's machine, 776 Winch, 46 Wind, chest, 273; instruments, 271, 282 Wind pipe, 260 Windhausen's ice machine, 503 Winds, causes of, 1017 ; direction and velocity of, 1015, 1016 ; law of rota- tion of, 1019 ; periodical, regular, and variable, 1018 Wine, alcoholic value of, 381 ; tears of, 134 Wireless telegraphy, 1004 Wollaston's, battery, 818 ; camera lucida, 615 ; cryophorus, 376 ; doublet, 597 Wood, conductivity of, 410 Wood's fusible metal, 341 Index (THE NUMBERS REFER TO THE ARTICLES) "37 Work, 60 ; measure of, 61 ; of an engine, 480 ; rate of, 48 1 ; unit of, 62 ; internal and external, of bodies, 296 Writing telegraphs, 921 YELLOW spot, 625 Yoke, 901 Young and Fresnel's experiment, 659 Young's modulus, 88 ZAMBONI'S pile, 829 Zeeman effect, 998 Zero, absolute, 504 ; pressure of aqueous vapour below, 358 ; displacement of, 305 Zigzag lightning, 1038 Zinc, amalgamated, 819 Zither, 281 Zoetrope, 639 >.* Zone, isothermal, 1048 PRINTED BY SPOTTISWOODE AND CO. 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