(Fig. 575.)
DOUBLE PLATE ELECTRICAL MACHINE, MADE FOR THE UNIVERSITY OF  IISSISSIPPI, BY RITCMlIE.See ~ 837.




PRINCIPLE'S
OF
PHYSICS,
OR
NATURAL PHILOSOPHY;
DESIGNED FOR THE
lee Qlf fGlU^ee  and j^Jfls.
B?
BENJAMIN SILLIMAN, JR., M.A., M..D.,
PROFESSOR OF GENERAL AND APPLIED CHEMISTRY IN YALE COLLEGE.
SECOND EDITION,
REVISED AND REWRITTEN..{~ti Stlb  lUnbrb an^ b Itueni2-itoj ]lustrattons.
PHILADELPHIA:
PUBLISHED BY THEODORE BLISS & CO.
1865.




Entered, according to Act of Congress, in the year 1860, by
H. C. PECK & THEO. BLISS,
in the Clerk's Office of the District Court of the Eastern District of Pennsylvania.
MEARS a DUSENBERY, STEREOTYPERS.                           0. SHERMAN & SON, PRINTERS.




PREFACE TO THE SECOND EDITION.
MANY important changes have been made in the present edition,
designed to adapt the work more fully to the wants of the higher
seminaries, where mathematical demonstrations are required of the
classes in Natural Philosophy. With this view, the two first Parts
have been almost wholly rewritten, and upon a different plan of
arrangement.  Some subjects which were perhaps too fully treated
in the first edition,-as, for example, Crystallography,-have been
reduced, while others have been expanded to meet the just proportions of a harmonious treatment. These remarks apply also to Part
Third (the Physics of Imponderable Agents), and especially to
Optics and Heat.  In the latter chapter some topics have been
omitted which are more appropriately treated in Chemistry.
The mathematical demonstrations, while they are designed to be
as simple as possible consistent with exactness, are believed to be
as full and rigorous as are demanded in institutions where only
geometric and algebraic methods are used. Analytical methods
have not been introduced, as the book was not designed for the
comparatively limited number of colleges where the higher mathematics are employed in teaching Physics.
The questions at the foot of the pages in the first edition, have
been omitted, to gain space for a considerable number of practical
problems (mostly original,) designed to exercise the student in the
application of the principles and formulae found in the text.  Toaid in the solution of these, and to assist the teacher in the construction of additional problems, numerous physical TABLES have
been added in the APPENDIX.
The plan of using two kinds Af type, resorted to in the first
1 *                                          (5)




vi           PREFACE TO THE SECOND EDITION.
edition, has been continued with more particularity in this. The
book is thus adapted to the use of the general reader, and to students who seek only a knowledge of general principles.
These changes and additions, the author believes, entitle this
edition more fully to the encomiums bestowed on the first by many
of the ablest physicists and most experienced teachers in this
country. By the liberality of the publishers, numerous additions
have been made to the wood-cuts, while new designs, in numerous
cases, replace those of less beauty in the first edition.
The design has been, in this edition, to give to all the departments of physical science a just proportion of space, in harmony
with the general scope of the book. The subject of Mechanics
and Machines (upon which so many excellent special treatises
exist) has, therefore, been condensed into a smaller proportionate
space than it usually occupies in American treatises on Natural
Philosophy; while such fundamental subjects as Motion, Force,
Gravitation, Elasticity, Tenacity, and Strength of Materials, are
considered at more length.
The author has freely availed himself of all the sources of infor
mation within his reach. A list of the works chiefly used in the
preparation of this edition is appended-to which should be added
the chief foreign journals, and transactions of learned societieswhich have been resorted to for the original memoirs quoted on a
great variety of topics. He is also particularly indebted for good
counsel to many scientific and personal friends, the influence of
whose criticisms on the first edition they will find frequently in
the present.  More than to all others is he indebted to Dr. M. C.
WHITE, of New Haven, for his constant attention, both in the
preparation of new matter and in the revision of the press.
He also takes pleasure in again acknowledging his obligations
to Prof. C. H. PORTER, of Albany.
For a final revision of the sheets, and the detection of a number
of errors which had escaped previous proof-readers, the author
is indebted to Mr. ARTHUR W. WRIGHT, Assistant Librarian of
Yale College.
Fuller references have been added, especially to American authorities; and the author hopes no apology is required for the frequent
references to tht American Journal of Science, which is supposed




PREFACE TO THE SECOND EDITION.                  Vii
to be a work accessible to all American teachers, while the European journals are rarely so; and references to these would, therefore, be of little practical use to the great majority of readers of
such a treatise as this.
As no table of errata is given (all errors thus far discovered
being corrected), the author will esteem it a great favor if any
person using the book will communicate to him direct any errors
of fact or figures which may be discovered.
NEW HAVEN, October 15, 1860.
LIST OF THE PRINCIPAL WORKS USED IN PREPARING THIS EDITION.
COOKE. Chemical Physics. Boston, 1860.
DAGUIN.  Traite de Physique, tom. I., II., and III.  Paris and
Toulouse, 1855-1859.
DE LA RIVE. Treatise on Electricity, 3 volumes. London, 18531858.
GANOT. Trait6 de Physique. Paris, 1859.
GOODWIN. A Collection of Problems and Examples. Cambridge,
England, 1851.
JAMIN. Cours de Physique, tom. I. and II. Paris, 1858-1859.
KAHL. Mathematische Aufgaben aus der Physik. Leipzig, 1857.
MILLER. Chemical Physics. London, 1855.
MULLER. Lehrbuch der Physik und Meteorologie. Braunschweig,
1857.
POTTER. An Elementary Treatise on Optics, 2 Parts. London,
1851.
POTTER. An Elementary Treatise on Mechanics. London, 1855.
POTTER. Physical Optics. London, 1856.
WERNICKE. Lehrbuch der Mechanik. Braunschweig, 1858.








FROM PREFACE TO THE FIRST EDITION.
THIS hand-book has been prepared with a view to give a fair exposition of the present condition of the several departments of Physics. *
*   *   *   *   *   Accuracy of statement, fullness of illustration,
conciseness of expression, and a record of the latest and most reliable
progress of science in these departments, have been the leading objects
in its preparation.
Only those who have attempted to harmonize and present in due
proportion the whole of so vast a subject as this, in a compendious
form, can fully appreciate the labor and difficulties which attend it.
Without claiming for the present volume any credit more than
belongs to a faithful digest and compilation from the best authorities
in modern science, it is hoped that it will be found suited to the wants
of a large class of both teachers and students. No pains have been
wanting to secure accuracy both in fact and mechanical execution.
The publishers have spared no expense to illustrate the book with a
profusion of wood cuts. Many of these are original designs, or are
reduced from larger drawings by photography-and others have been
selected with care from the best standard authors. * * * * * *
Whenever it was possible, reference has been had to original memoirs
in Journals and Transactions, and in this way many errors current in
works of inferior authority have been corrected. With but few exceptions, references to foreign memoirs have been omitted in the text, as
their insertion could profit only a very small number of readers, and
might seem pedantic. Not so with respect to names of discoverers of
important principles and phenomena. A great number of'names of
these will be found in the text, in their proper places, and not unfrequently the dates of birth, or death, or both, are given.
Every teacher'must have observed that an abstract principle is
often fixed in the memory by the power of associated ideas, when it is
connected with a date or item of personal interest, as the attention is
(9)




X             PREFACE TO THE FIRST EDITION.
awakened by the dramatic far more than by the didactic. Hence it
has been thought judicious to introduce numerous important dates in
the history of science.
*      -*     *      *      *      *      *      *
It gives me great pleasure to acknowledge many obligations to Prof.
CHARLES H. PORTER, M. A., M. D., of Albany (some years my assistant),
for his constant and most important assistance in the compilation and
editing of this book. Preoccupied as my own time has been, I should
not at times have found it possible to proceed without his valuable
assistance and excellent judgment. Dr. M. C. WHITE, of this town, has
also rendered me important aid, especially in OPTICS, and in the revision of the press.
* HAEN CONN. Oct. 15                    858.
NEW HAVEN, CONN., Oct. 15, 1858.




CONTENTS.
PART FIRST.
PHYSICS OF SOLIDS AND FLUIDS.
CHAPTER I.
INTRODUCTION.
Matter-Observation and experiment, 1-Law, theory, and hypothesis-Inductive philosophy-Force, 2-The properties of matter are general, or specificThe changes in matter are physical, or chemical, 3-Physical and chemical
properties of matter-Physics and chemistry-Vitality, 4-Light, heat, and
electricity, 5.
CHAPTER II.
GENERAL PRINCIPLES.
~ 1. Definitions and General Properties of Matter-I. ESSENTIAL
PROPERTIES-The essential properties of matter-Magnitude or extension, 5
-Impenetrability-The three states of matter-II. ENGLISH AND FRENCH
SYSTEMS OF MEASURES-Units of measure, 6-English units of length-The
French system of measures, T-III. ACCESSORY PROPERTIES OF MATTERDivisibility, 8-Minute division in the animal and vegetable kingdoms, 9Atoms, molecules-'Compressibility, 10-Expansibility-Physical pores, 11Sensible pores-Mobility, 12-Inertia-Action and reaction, 13.
# 2. Of Motion and Force-I. MOTION-Varieties of motion, 13-Time
and velocity-Uniform  motion-Variable motion, 14-Motion uniformly
varied, 15-Compound motion, 16-Parallelogram  of velocities-II. OF
FORCES-Definition of force-Forces are definite quantities-Weight-Unit
of force —Dynamometers, 17-Equilibrium-Statical and dynamical forcesDirection of force, 19-Measure of forces-Mass-Propositions in regard to
forces, 20 —Momentum, 21-III. COMPOSITION OF FORCES-System of forces
(xi)




xii                            CONTENTS.
-Components and resultant-The parallelogram of forces, 22-Examples of
the composition of motion and force-Parallel forces-Resultant of unequal
parallel forces, 25-Resultant of two parallel forces acting in opposite directions-Couples, 26-Two forces not parallel and applied to different point!The resolution of forces-Example of the resolution of force, 27-IV. CURVILINEAR MOTION-CENTRAL FORCES-Of curvilinear motion-Centrifugal and
centripetal forces, 28-Examples of the action of centrifugal force-Experimental demonstration of the effects of centrifugal force, 29-The centrifugal
drying machine for laundries, 31-Analysis of the motion produced by central
forces, 32-Bohnenberger's apparatus-Parallelogram  of rotations, 33-The
gyroscope, or rotascope, 35-Problems on weights and measures-Problems
on motion, 37.
CHAPTER III.
GRAVITATION.
Q 1. Direction and Centre of Gravity-Definition-Law of universal
gravitation, 38-Direction of terrestrial attraction-Centre of gravity, 39Point of application of terrestrial attraction, 40-Centre of gravity-Corollaries, 41-Centre of gravity of regular figures, 42-Centre of gravity lying
without the body —Equilibrium of solids supported by an axis-Equilibrium
of solids placed upon a horizontal surface, 43-Centre of gravity in bodies of
unequal density in different parts-Equilibrium of bodies supported in more
than one point, 44.
@ 2. Laws of Falling Bodies-Gravity is a source of motion-The laws
of falling bodies are five, 45-Whole space described by a falling body, 47Verification of the laws of falling bodies-Atwood's apparatus, 48-Morin's
apparatus-Application of the laws of falling bodies, 50-Descent of bodies
on inclined planes, 51-Descent of bodies on curves-Brachystochrone, or
curve of swiftest descent-Action and reaction of a falling body, 52.
{ 3. Measure of the Intensity of Gravity-I. PENDULUM-The pendulum
-Properties of the simple pendulum, 53-Isochronism of the pendulum, 54Formulae for the pendulum-Propositions respecting the simple pendulum, 55
-The physical or compound pendulum-Centre of oscillation, 56-Application
of the pendulum to the measurement of time, 57-Cycloidal pendulum-Physical
demonstration of the rotation of the earth by means of the pendulum, 58-The
pendulum applied to the study of gravity, 59 —Use of the pendulum for measuring the force of gravity-Value of g in these experiments, 60-Seconds pendulum-II. MODIFICATIONS OF TERRESTRIAL GRAVITY AND THEIR CAUSES.-The
intensity of gravity varies with the latitude, 61-Influence of the earth's figure
upon gravity, 62-Exact dimensions of the earth-Sensible weight varies in
different localities-Effect of the earth's rotation on gravity, 64-Demonstration, 65-Variation of gravity above the earth and below its surface-Below
the earth's surface, 66.
{ 4. Mass and Weight-Mass-Weight-Density-Specific weight, 67French system of weights, 68-English and American system of weightsEstimation of the density of the earth by experiment, 69-The inference, 71.
a 5. Motion  of Projectiles-Projectiles, 71-The ballistic pendulumProblems-Falling bodies, 73-Descent of bodies on inclined planes-Central
forces-Pendulum and Gravity, 74-Flight ef Projeetiles, 75.




CONTENTS.                              Xiii
CHAPTER IV.
THEORY OF MACHINERY.
~1. Machines-Principle of-virtual velocities, 75-Machine, power, weight
— Equilibrium  of machines, 76-Utility of machines-Relation of power
to weight, 77-Adaptation of the power to the weight in machinery —Vis
viva, or living force, 78 —Illustrations of vis viva-Impact and its resultsImpact considered with reference to momentum, 80-Impact considered with
reference to vis viva, 81-Pressure produced by impact —Destructive effects
of impact, 82.
2. Mechanical Powers-The lever, 83-Conditions of equilibrium in the
lever-Compound levers-Application of the lever, 84-The scale beam-The
steelyard, 85-Examples of compound levers, 86-Roberval's counter platform
balance, 87-The wheel and axle, 88-Trains of wheel-work, 89 —Analysis of
a train of wheel-work, 90-The pulley-Fixed pulley-Movable pulley-Compound pulleys, 91-The inclined plane-Application of the power parallel to the
length of the inclined plane, 93-Application of the power parallel to the
base of the inclined plane, 94-Application of the power in some direction
not parallel to any side of the plane-The wedge-Application of the wedge,
95-The screw, 96-Mechanical efficiency and applications of the screw-The
endless screw, 97.
3. Strength and Power-Animal strength-Strength of men-Horsepower machines, 98-Table of the comparative strength of men and other
animals-Steam-power, 99-Perpetual motion, 100.
4. Impediments to  Motion-Passive resistances-Sliding frictionStarting friction-Friction during motion, 101-Coulomb's apparatus for
determining starting friction-Results of Coulomb's experiments on starting
friction, 102-Rolling friction-Coulomb's apparatus for determining rolling
friction-Results of Coulomb's experiments on rolling friction, 104-Mr.
Babbage's experiment-Advantages derived from friction-Rigidity of ropesResistances of fluids, 105-Actual and theoretical velocities-Ballistic curve,
106-PROBLEMS-Vis viva-The lever-Wheel and axle, 107-The pulleyInclined plane-The screw-Resistance, 108.
2




xiv                            CONTENTS.
PART SECOND.
THE THREE STATES OF MATTER.
CHAPTER  I.
MOLECULAR FORCES.
Cohesion and repulsion-Repulsion, 109-Examples of cohesion among solids,
10-Cohesion in liquids and between liquid gases and solids, 111-Between
gases and solids, 112.
CHAPTER II.
OF SOLIDS.-MOLECULAR FORCES ACTING BETWEEN PARTICLES OF LIKE KINDS.
1. Properties of Solids-The characteristic properties of solids-Structure of solids, 113.
2. Crystallography-Conditions of crystallization, 114-AmorphismCrystalline forms-Definitions, 115-Systems of crystals, 118-Modified forms,
120-Compound crystals, 121 —Cleavage-Determination of crystalline forms,
122.
3. Elasticity-Elasticity of solids, 122-Elasticity of tension and compression, 123-Coefficient of elasticity, 124-Elasticity of flexure, 125 —Applications-M. Bourdon's metallic barometer, 127-The Aneroid barometerElasticity of torsion, 128-Coulomb's laws of torsion, 129 —Torsion of rigid
bars-Limit of elasticity, 130-Change of density produced by tension, 131.
4. Strength of Materials-Laws of tenacity, 131-Johnson's resultsTenacity of vegetable and animal substances-Resistance to pressure in
columns, 132-The lateral or transverse strength of materials, 133-Practical
applications, 134-General estimate of the strength of beams-The Britannia
Tubular Bridge, 136-The Victoria Tubular Bridge-Limits of magnitude, 137.
5. Properties of Solids depending on a permanent displacement of their Molecules-Malleability-Ductility-Hardness, 138Brittleness-Hardening, Temper, Annealing, 139-Colors of tempered steelTempering by a bath-Temper of glass —Prince Rupert's Drops, 140-Tempering copper and bronze —Hammering, 141-Changes of structure affecting
the mechanical properties of metals, 142.
6. Collision of Solid Bodies-Motion communicated by collision, 142
-Direct impact of elastic bodies-Modulus of elasticity, 143-Velocity of
elastic bodies after direct impact, 144-Scholiim, 145-Transmission of shock
through a series of elastic balls-Experimental illustration of elasticity



CONTENTS.                               XV
PROBLEMS-Elasticity of tension-Elasticity of flexure-Tenacity-Transverse
strength, 146-Impact of elastic bodies, 147.
CHAPTER  III.
OF FLUIDS.-r-HYDRODYNAMICS.
1. Hydrostatics-I. DISTINGUISHING PROPERTIES OF LIQUIDS-Definitions
- Fluids-Hydrodynamics-Mechanical condition of liquids-Elasticity of
liquids-Compressibility, 148-Elasticity-Consequences, 150-II. TRANSMISSION OF PRESSURE IN LIQUIDS —Liquids transmit pressure equally in all
directions, 151-The Bramah hydrostatic press, 152-Uses in the arts —Pressure of a liquid on the bottom of a vessel, 153-Upward pressure, 154-Pressure on the sides of a vessel-Pascal's experiment with a cask, 155-The water
bellows, or hydrostatic paradox-Total pressure on the walls, 156-Total pressure on the bottom and sides of a vessel, 157-The centre of pressure, 158Pressures vary as the specific gravities of liquids-III. EQUILIBRIUM OF
LIQUIDS-The conditions of equilibrium  in liquids, 159-Equilibrium  of
liquids when freed from the influence of gravity-The experiment of Plateau
-Equilibrium of a liquid in communicating vessels, 160-Equilibrium  of
liquids of different densities in communicating vessels-Demonstration-The
spirit level, 161-Artesian wells —IV. BUOYANCY OF LIQUIDS-Theorem  of
Archimedes, 162-Another demonstration of Archimedes' principle-Floating
bodies, 16 —Examples-Equilibrium  of floating bodies, 165-Neutral equilibrium —Unstable equilibrium, 166-Stable equilibrium-The metacentre, 167
-V. DETERMINATION OF SPECIFIC GRAVITY-The problem stated-MethodsSpecific gravity by the hydrostatic balance, 168-Examples, 169, 170-Specific gravity bottles, 170 —Example-Specific gravities by hydrometers or
areometers-Nicholson's hydrometer or areometer, 171 —Gay Lussac's and
Beaume's hydrometers, 172.
~ 2. Hydraulics-I. MOTION OF LIQUIDS —Definition —Pressure of liquids
upon the containing vessel, 173 —Appearance of the surface during a discharge
-Theoretical and actual flow, 174-Reaction of the escaping vein-Barker's
mill, 175 —Flow —Theorem  of Torricelli-Deductions from  the Torricellian
theorem, 176-Demonstration of the theorem of Torricelli, 177-The inch of
water-Constitution of liquid veins, 178-Escape of liquids through short
tubes-Escape of liquids through long tubes —Formulee, 180-Jets of waterPressure exerted by liquids in motion, 181-Velocity of rivers and streamsStream  measurers, 182-II. WATER-POWER AND WATER-WHEELS-Waterwheels-The overshot wheel-The undershot wheel, 183 —The breast-wheelBoyden's American turbine, 184.
*MOLECULAR FORCES ACTING BETWEEN PARTICLES OF UNLIKE KINDS..T. CAPILLARITY-Observation-Definition, 187-General facts in capillarity,
188-Form of the surface-Cause of the curve of liquid surfaces by the
contact of solids, 189-Experimental illustrations, 190-Influence of the
curve on capillary phenomena, 191-Law of the elevation and depression
of liquids in capillary tubes, 192 —Depression of mercury in capillary tubes
-Ascent of liquids in capillary tubes, 193-Laws of the equilibrium  of
liquids between parallel or inclined laminae, 194-Movement of drops of
liquid in conical tubes or between laminae-Attraction and repulsion of
light floating bodies, 195-Escape of liquids from  capillary tubes-Flow




xvi                            CONTENTS.
of liquids from capillary tubes-II. OS.rOSE OR OSMOTIC FORCE —Oslose, exosmose, endosmose, 196-Endosmometer-Necessary conditions-Materials for
septum, 197-Direction of the current —Organic solutions-Inorganic solutions-Endosmose of gases-Theories of endosmose, 198 —PROBLEMS ON HYDRODYNAMICS-Elasticity of liquids-Hydrostatic pressure, 199 —Buoyancy
of liquids-Floating bodies, 200-Motion of liquids-Capillarity, 201.
CHAPTER  IV.
OF ELASTIC FLUIDS, OR GASES.
Pneumatics-I. DISTINGUISHING PROPERTIES OF GASES-Definitions-Pneumatics-Gases-Vapors-Tension-Expansion of gases, 202-Mechanical condition of gases-II. PROPERTIES COMMON TO BOTH LIQUIDS AND GASES-Gases
transmit pressure equally in all directions, 203-The atmosphere, 204-Atmospheric pressure, 205-Buoyancy of air, 206 —Impenetrability of air-Inertia
of air-III. BAROMETERS AND BALLOONS-Torricellian vacuum-Measure of
atmospheric pressure, 207-Pascal's experiments, 208-Construction of barometers-Apparatus illustrating the principle of the barometer, 209-Height
of the barometric column at different elevations-Cistern barometer-Fortin's
barometer, 210-The syphon barometer, 211 —Wheel barometer-Causes of
error-Correction for capillarity, 212-Correction for temperature-Variations of the barometric height, 213 —Variations observed in barometers are
of two kinds-Relation between barometric changes and the weather, 214
-Rules by which coming changes are indicated —Measure of heights by
the barometer, 215-Balloons, 216-Construction and filling of balloons,
217-Parachute-IV. COMPRESSIBILITY  OF GASES-Mariotte's law, 218Experimental verification of Mariotte's law, 219-Experiments of Despretz
-Experiments of Regnault, 220-Results obtained by Regnault-General
conclusions on the compressibility of gases, 221-V. INSTRUMENTS DEPENDING
ON THE PROPERTIES OF GASE —Manometers-Manometer with free air-Manometer with compressed air, 222-Bellows-Bellows with a continuous blast,
223 —Furnace blowers-Escape of compressed gases, 224-Pneumatic inkbottle-The syphon, 225-Intermittent syphon-Tantalus' vase —Intermittent
springs, 226-Intermittent fountain —Air-pump, 227-Degree of exhaustion
-Compressing machine-Water-pumps —Suction-pumps, 229-Suction and
lifting pump-Forcing-pump, 230-Rotary pump-Fire-engine, 231 —Hiero's
fountain —Hydraulic ram, 232-Chain-pump —Archimedes' screw, 233-PROBLEMS ON PNEUIMATICS —Atmospheric pressure, 23 —Barometer and balloons
-Mariotte's law, 235.
CHAPTER  V.
OF UNDULATIONS.
1. Theory of Undulations-Origin of undulations-Progressive undulations, 236-Mechanical illustration of undulations-Stationary undulations
-Isochronous vibrations-Phases of undulations, 237-Nodal points, 238., 2. Undulations of Solids-Solid bodies-Forms of vibration, 238 —
Vibration of cords-Laws of the vibration of cords, 239-Vibrations of rods
-Paths of vibration, 240-Vibration of elastic plates —Nodal lines-Determination of the position of the nodal lines, 241-Laws of the vibration of planes




CONTENTS.                            Xvii
-Method of delineating nodal lines-Nodal figures, 242-Vibration of membranes, 243.
3. Undulations of Liquids-Production of waves-Progressive undulations in liquids, 244-Stationary waves, 245 —Depth to which waves extend —
Reflection of waves-Waves propagated from the foci of an ellipse-Waves
propagated from the focus of a parabola, 246-Circular waves reflected from
a plane, 247-Combination of waves-Interference in an ellipse-Undulations
of the waters of the globe, 248.
4. Undulations of Elastic Fluids-Waves of condensation and rarefaction-Undulations of a sphere of air, 249-Mechanical illustration-Velocity and intensity of aerial waves, 250-Interference of waves of air-Intensity
of waves of air expanding freely-PROBLEMS ON THE LAWS OF VIBRATIONS,
251.
CHAPTER VI.
ACOUSTICS.
1. Production  and  Propagation of Sound-Acoustics —SoundSound a sensation —Key-note of nature-Noise-Musical sounds, 252-All
bodies producing sound are in vibration, 253-Sound propagated by waves
-Co-existence of sound-waves-Sound is not propagated in a vacuum,
254-Sound is propagated in all elastic bodies-Hearing-Time is required
for the transmission of sound-The velocity of all sounds is the same, 255Velocity of sound in air, 256 —Velocity of sound in different gases and vapors
-Calculation of distances by sound-Velocity of sounds in liquids-Velocity
of sounds in solids, 257-Interference of sound-Acoustic shadow, 258-Distance to which sound may be propagated, 259-Reflection of sound-Echo, 260
-Repeated echoes-Change of tone by echo, 261-Whispering galleriesRefraction of sound, 262-The speaking-trumpet, 263-Ear-trumpet-The
siren, 264-Savart's toothed wheel-Music halls, 266.
~ 2. Physical Theory of Music-Qualities of musical sounds-Tone or
pitch-Intensity or loudness-Quality-Unison-Melody —Harmony, 267Musical scale-Gamut, 268-The sonometer or monochord-Relative number
of vibrations corresponding to each note, 269-Absolute number of vibrations
corresponding to each note, 270-Length of sonorous waves-Interval, 271Compound chords-Perfect concord-A new musical scale, 272-Transposition
-Temperament, 274-Beating-Diapason, tuning-fork, 275-Sensibility of
the ear, 276.
3. Vibration of Air contained in Tubes-Sonorous tubes-Mode
of vibrating, 276-Mouth-pipes —Reed-pipes, 277-Gas jet-Musical instruments, 278-Vibration of air in tubes-Laws of Bernoulli-Demonstration,
279-Construction of musical instruments, 280-Vibrating dams, 281.
4. Vocal and Auditory Apparatus-I. OF VOICE AND SPEECH-Voice
and speech —The vocal apparatus of man, 281-The larynx —The glottis, 282
-Mechanism of the voice-Range of the human voice, 283 —Ventriloquism,
stuttering, &c., 284-Production of sounds by inferior animals-Birds-Insects
— II. THE EAR —HEARING-Auditory apparatus of man-The external ear,
285-The middle ear, tympanum, or tympanic cavity, 286-The internal ear,
287-Functions of the different parts of the ear —Natural diapason, 288 —
Organs of hearing in the lower animals —PROBLEMS IN ACOUSTICS-Velocity
of sound, 289-Physical theory of Music, 290.
2;




Xviii                           CONTENTS.
PART THIRD.
PHYSICS OF IMPONDERABLE AGENTS.
LIGHT, HEAT, AND ELECTRICITY.
CHAPTER I.
LIGHT, OR OPTICS.
1. General Properties of Light-Optics-Light-Nature of light —
Theories, 291-Sources of light-Phosphorescence, 292-Relation of different
bodies to light-Rays, pencils, and beams of light-Visible bodies emit light
from every point, 293-Propagation of light in a homogeneous medium-Velocity of light-Foucault's apparatus for measuring the velocity of light, 294
-Fizeau's method —Results-No theory of light is entirely satisfactoryProperties of light, 296-Amount of light reflected at different angles of incidence, 298 —Internal reflection-Total reflection, 299-Irregular reflectionDiffused light-Umbra and penumbra, 300-Images produced by light transmitted through small apertures-Intensity of light at different distancesPhotometers, 301-Bunsen's photometer-Rlumford's photometer-Silliman's
photometer, 302.
p 2. Catoptrics, or Reflection by Regular Surfaces-I. MIRRORS
AND SPECULA-Mirrors-Specula are metallic reflectors-Forms of mirrorsII. REFLECTION AT PLANE SURFACES-Reflection by plane mirrors, 303Images formed by plane mirrors, 304-Images multiplied by two surfaces of
a glass mirror-Images formed by light reflected by two plane mirrors, 305Multiplicity of images seen by means of inclined mirrors-Deviation of light
reflected by two mirrors, 306-Kaleidoscope, 307-Hadley's sextant —III.
REFLECTION AT CURVED SURFACES-Concave and convex spherical mirrors,
308-Foci of concave mirrors for parallel rays —Foci of diverging rays, 309Converging rays-Virtual focus-Secondary axes-Oblique pencils-Rule for
conjugate foci of concave mirrors-Convex spherical mirrors, 311-Images
formed by concave mirrors, 312 —-Virtual images-Formation of images by
convex mirrors, 313-General rule for constructing images formed by mirrors
Spherical aberration of mirrors-Caustics, 314.
~ 3. Dioptrics, or Refraction at Regular Surfaces-I. DEFINITIONS —
Prisms and lenses, 314-II. REFRACTION AT PLANE SURFACES-Refraction by
prisms, 315-Method of determining the index of refraction, 316-Plane glass
-Light passing through parallel strata of different media, 317-Pencils of
light refracted at plane surfaces, 318-Pencils of light transmitted through
plane glass-III. REFRACTION AT CURVED SURFACES-Principles determining
the foci of lenses, 320-Small pencils of light refracted at a spherical surface,
321 —Refraction at a concave surface, 322-Action of a double convex lens
upon small pencils of light, 323-Conclusions deduced-Anaiysis,"324-Action




CONTENTS.                                xix
of a double concave lens upon small pencils of light-Conclusions deduced
from analysis, 326 —Rules for determining the foci of lenses-Combined lenses,
327-Oblique pencils —The optical centre of a lens, 328 —Images formed by
lenses-Spherical aberration of lenses, 329-Accurate estimate of spherical
aberration, 330-Aberration of sphericity; distortion of images, 331.
~ 4. Chromatics-Analysis of light-Spectrum-Primary colors-Recompo,
sition of white light-Analysis of colors by absorption, 332-Complementary
colors-Properties of the solar spectrum, 333-Fraunhofer's dark lines in the
solar spectrum, 334-Lines in light from different sources, 335-Fixed lines
in the spectra from various colored flames-Intensity of luminous, calorific,
and chemical rays-Refraction and dispersion of the solar spectrum-Kalychromatics, 336-Chromatic  aberration-Achromatism, 337-Formulas for
achromatism, 338.
@ 5. Vision-Structure of the human eye, 339 —Action of the eye upon light,
340-Inversion of the image formed in the eye-Optic axis-Optic angleVisual angle, 341-The brightness of the ocular image-Conditions of distinct
vision-Background, 342-Sufficiency of illumination-Distance of distinct
vision —Visual rays nearly parallel, 343-Adaptation of the eye to different
distances-Appreciation of distance and magnitude-Aerial perspective, 344
-Single vision with two eyes-Double vision-Binocular vision, 345-Nearsightedness-Long-sightedness, 346-Duration of the impression upon the
retina-Optical toys-Thaumatrope-Time required to produce visual impressions-Appreciation of colors —Color blindness, 347-Chevreul's classification
of colors, and chromatic diagram, 348-Examples-The study of colors, 349.
{ 6. Optical Instruments-Magnifying  glasses, 349-The magnifying
power of a lens, 350-The simple microscope-Raspail's dissecting microscope-The compound microscope, 351-The telescope-The telescope used by
Galileo, 352-The opera-glass-Night-glasses-The astronomical telescope —
-Eye-pieces-The positive eye-piece-The negative eye-piece, 353-The terrestrial eye-piece-Reflecting telescopes-Sir William Herschel's telescope, 354
-Lord Rosse's telescope-Achromatic telescopes, 355-Equatorial mountings
for telescopes, 356-The Cambridge telescope with equatorial mountings, 357The visual power of telescopes, 358-Achromatic object-glasses for microscopes
-Lister's aplanatic foci, and compound objectives, 359-Aberration of glass
cover corrected-The compound achromatic microscope, 361-Solid eye-piece
-Visual power of the achromatic microscope, 362-The mechanical arrangement of the microscope, 363-The magic lantern-The solar microscope, 364
-The camera obscura-Wollaston's camera lucida, 365-Photography —Railway illumination, 366-The Fresnel lens-Sea-lights, 367-Revolving lights,
368-The telestereoscope, 369-The stereoscope, 370-The stereomonoscope,
372.
7. Physical Optics-I. INTERFERENCE, DIFFRACTION, FLUORESCENCE, &C.
Interference of light, 373-Facts at variance with theory-Interference colors
of thin plates, 374-Newton's rings-Length of luminous waves or vibrations,
375-Diffraction, 376-Fluorescence-Epipolic dispersion-Phosphorescence,
377-Colors of grooved plates-II. OPTICAL PHENOMENA OF THE ATMCrSPHERE
-The rainbow, 378-A secondary rainbow, 380-Spurious rainbow-Fogbows-Halos-Coronas-Parhelia-Atmospheric  refraction-Looming-The
mirage, 381-III. POLARIZATION OF LIGHT-Direction of luminous vibrations
-Transmission of luminous vibrations, 382-Change produced by polarization
of light —Resolution of vibrations, 783-Light polarized by absorption —-I'o



XX                             CONTENTS.
larization by reflection, 384-Polarization by metallic reflection-Polarization
by refraction-Polarization by successive refractions, 385-Partial polarization-Double refraction, 386-Positive and negative crystals-Polarization by
double refraction-Nicol's single image prism, 387-Polarizing instruments
-Colored polarization, 388-Rotary polarization-Arago's chromatic polariscope, 389 —Colored rings in crystals-Polarization by heat, and by compression, 390-Magnetic rotary polarization-Atmospheric polarization of light —
The eye a polariscope, 391-The practical applications of polarized lightPROBLEMS IN OPTICS-Velocity and intensity of light, 392-Reflection of light
-Refraction of light, 393-Optical Instruments-Polarization of light, 394.
CHAPTER II.
HEAT.
Q 1. Nature of Heat-Heat-Its nature-Temperature-Heat and cold, 395
-Action of heat on matter, 396.
# 2. Measurement of Temperature~I. THERMOMETERS-Thermometer
-Construction of mercurial thermometers-Thermometer tubes, 396-Filling
the tube with mercury-Standard points in the thermometer-Graduation, 397
-Freezing point-Boiling point, 398-Different thermometric scales-Fahrenheit's scale-Centigrade scale, 399 —Reaumur's scale-Comparison and
conversion of thermometric scales-House thermometers, 400-Tests of a good
thermometer-Sensibility of thermometers-Displacement of the zero point,
401-Limits of the mercurial thermometer-Spirit thermometers-Other liquid
thermometers, 402-Defects inherent in mercurial thermometers, 403-Standard thermometer, 405-II. SELF-REGISTERING THERMOMETERS-Maximum and
minimum thermometers, 406 —Rutherford's maximum and minimum thermometer-Negretti and  Zambra's maximum  thermometer, 407-Walferdin's
maximum thermometer-Metastatic thermometer, 408-III. METALLIC THERMOMIETERS AND PYROMETERS-Breguet's metallic thermometer-Saxton's deepsea metallic thermometer, 409-Saxton's reflecting pyrometer-Wedgewood's
pyrometer-Daniell's pyrometer, 410-Draper's pyrometer —Estimation of very
high temperatures-IV. THERMOSCOPEs-Thermoscopes-Air thermometers,
411-Leslie's differential thermometer-Howard's differential thermometerRumford's thermoscope-Thermo-multiplier, 412.
# 3. Expansion-I. EXPANSION OF SOLIDS-Linear expansion-Pyrometers
-Cubical expansion, 413-Relation between cubical and linear expansionExpansion of crystals-Coefficient of expansion, 414-The capacity of hollow
vessels is increased by the expansion of their walls-The amount of expansion
in solids, 415-The ratio of expansion increases with the temperature-Amount
of force exerted by expansion, 416 —Common phenomena produced by the
expansion of solids, 417-Fire regulators-Unequal expansion of solids, 418
-Compensating pendulums —Harrison's gridiron compensating pendulumGraham's compensating pendulum, 419-Mr. Henri Roberts' compensating
pendulum-Martin's compensating pendulum-Compensating balance wheels
of watches and chronometers, 420-II. EXPANSION OF LIQUIDS-General statement-Apparent and absolute expansion, 421-Correction of the observed
height of the barometer for temperature-Apparent expansion of mercury,
422-Amount of expansion of liquids, 423-Expansion of liquids above their
boiling points-Curves of expansion of liquids — The amount of force exerted




CONTENTS.                               xxi
in the expansion of liquids, 424-Expansion of water —M'aximum density of
water, 425-Effects of the unequal expansion of water-Maximum density of
different aqueous solutions, 426-The volume of water at different temperatures-III. EXPANSION OF GASES —General statement-Gay Lussac's laws
for the expansion of gases by heat-Result of Regnault's experiments upon
the expansion of gases, 427-Formulae for computing changes of volume in
gases, 428 —Formulae expressing general relation between volume, temperature, and pressure-Relation between expansibility and compressibilityDensity of gases, 429.
Q 4. Communication of Heat —I. CONDUCTION-Modes in which heat is
communicated-Conduction of heat, 430-Determination of the conductibility
of solids, 431-Conductibility of metals, &c. —Conductibility of crystalsConductibility of wood, 432-Vibrations produced by conduction of heatConductibility of liquids-Conductibility of gases, 433-Relative conductibility of solids, liquids, and gases-Examples and illustrations of the different
conductibility of solids-Examples drawn from  the animal and vegetable
kingdoms, 434-The conducting power of substances in a pulverized or fibrous
state-Clothing, 435-II. CONvECTION —Convection —Convection in liquidsCurrents in the ocean, 436-III. RADIATION-Radiation of heat-Radiant
heat is but partially absorbed by the media through which it passes, 437Intensity of radiant heat-Law of cooling by radiation, 438-Universal radiation of heat-Apparent radiation of cold, 439.
$ 5. Action of different Bodies upon Heat-I. SURFACE ACTIONReflection of heat-Conjugate mirrors-Determination of reflective power, 440
-Absorptive power-Emissive or radiating power, 441-Causes which modify
the emissive, absorbent, and reflective powers of bodies —Applications of the
powers of reflection, absorption, and radiation, 442 —II. DIATHERMANCYTransmission of radiant heat-Melloni's apparatus, 443-Influence of the
substance of screens, 444-Influence of the material and nature of the source
-Other causes which modify the diathermanic power of bodies, 445-Thermochrosy-Applications of the diathermancy of bodies-Refraction of heat, 446
-Polarization of heat, 447.
@ 6. Calorimetry-Calorimetry-Unit of heat, 447-Specific heat-Method
of mixture-Method by fusion of ice, 448-The method of cooling-Specific
heat affected by change of state-Specific heat of gases, 449-Specific heat of
gases under a constant volume, 450 —Specific heat determined by the laws of
acoustics, 451 —Relation between the specific heat and atomic weight of elements and compounds, 452.
Q 7. Liquefaction and Solidification-Latent heat, 452 —Liquefaction
and congelation  are always gradual —Freezing mixtures, 453-Laws of
fusion and latent heat of fusion —Peculiarities in the fusion of certain solids,
-Refractory bodies-Solution-Saturation, 454-Laws of solidification-Elevation of temperature during solidification —Change of volume during solidification, and its effects, 455 —Freezing of water —Absolute zero, 456.
1 8. Vaporization  and Condensation-Vaporization, 456-Formation
of vapors in a vacuum, 457-Saturated space or maximum tension of vapors
-Dalton's law of the tension of vapors-The tension of vapors in communicating vessels unequally heated-Temperature and limits of vaporization, 458
-Circumstances influencing evaporation-Dew-point —Ebullition, 459 —Circumstances influencing tfie boiling point, 460-The culinary paradox-Frank



Xxii                           CONTENT3.
lin's pulse glass-Useful applications in the arts-Measurement of heights by
the boiling point-Hypsometer, 461 —igh pressure steam-Production of
cold by evaporation, 462-Twining's ice machine-Latent heat of steam, 463
-Latent and sensible heat of steam at different temperatures —Mechanical
force developed during evaporation, 464-Liquefaction-Distillation-Distilling apparatus-Physical identity of gases and vapors —Theory of the liquefaction and solidification of gases, 465 —Methods of reducing gases to liquids
-Later researches of Faraday-Thilorier's and Bianchi's apparatus for condensation of gases, 466-Properties of liquid and solid gases-Latour's law,
467 —Density of vapors, 468.
9. Spheroidal condition  of Liquids —Spheroidal state-Illustration
of the spheroidal state-Noticeable phenomena connected with the spheroidal
state, 468-Spheroidal state produced upon the surface of liquids-A liquid
in a spheroidal state is not in contact with the heated surface beneath, 469A repulsive action is exerted between the spheroid and the heated surfaceThe causes which produce the spheroidal form, 470-Freezing water and
mercury in red-hot crucibles-Remarkable phenomena connected with the
spheroidal state-Explosions produced by the spheroidal state, 471.-Steam
boiler explosions-Familiar illustrations of the spheroidal state, 472.
10. The Steam-Engine-IIistorical-The  eolipile-First steamboatSavary's engine, 473-Papin's steam cylinder-Neweomen's engine, 474-The
atmospheric engine —Watt's improvements in the steam-engine, 475 —The low
pressure or condensing engine, 476-The high pressure engine-The cut off,
477-Steam boilers-Mechanical power of steam —Iorse-power, 478-Evaporating power and value of fuel, 479.
11. Ventilation and Warming —I. VENTILATION-Currents in air and
gases, 480-Draught in chimneys, 481-Reversed draughts and smoky chimneys
— Products of respiration and combustion, and necessity for ventilation, 482
— The quantity of vapor given off by the body —The quantity of air required
for good ventilation-Products of gas illumination, 483-The actual ventilation of buildings is a practical problem-Stone's ventilating shaft, 484-Cold
currents produced by ice-Refrigerators-Cowls-Emerson's ventilators, 485
-The supply of fresh air in dwellings-II. WARnING —The artificial temperatures demanded in cold climates-The open fire, 486 —Hot air furnaces, 487
-Heating by hot water-Perkins' high pressure hot water apparatus, 488
-Gold's steam  heaters-The radiators, 489-The boiler of Gold's steam
heater, 490.
12. Sources of Heat-Sources of heat-I. MECHANICAL SOURCES OF HEAT
-Friction, 490-Quantity of heat produced by friction-Circumstances which
vary the quantity of heat developed by friction-Illustrations and application
of the heat developed by friction, 491-Compression-Percussion —Capillarity,
492 —II. PHrYSICAL SOURCES OF HEAT-The sun-Quantity of heat emitted.by
the sun-Extremes of natural temperature, 493-Terrestrial radiation —Origin
of terrestrial heat-Atmospheric electricity, 494-III. CHEMICAL SOURCES OF
HEAT —Chemical combination-Combustion-On the cause of the heat generated by combustion-The amount of heat developed by chemical action, 495
-The pyrometrical heating effect of a substance, 496 —Relative value of fuel
-Combinations in the humid way —Animal heat; warm and cold-blooded
animals, 497-The cause of animal heat-Temperature of vegetables, 498.
13. Correlation of Physical Forces —I. MECHANICAL EQUIVALENT OF




CONTENTS.                             XXiii
HEAT-Relations of heat and force, 498 —Unit of measurement, the foot-pound
-Determination of the mechanical equivalent of heat-Results of Joule's
experiments, 499 —Conclusions deduced from Joule's experiments.-II. DYNAMICAL THEORY OF HEAT-The dynamicl theory of heat-Motions of the
molecules-Changes in the state or volume of bodies, 500-III. ANALOGY OF
LIGHT AND HEAT-Vibrations producing heat and light-Impressions of light
and heat, 501-Bodies become luminous by incandescence, 502-Heat and light
produced by chemical and mechanical action-Dilatation and change of state,
503-Change of state produced by heat-Quality of heat changed by absorption and radiation, 504-Difference between quantity and intensity of heatConclusion, 505-PROBLEMS ON  HEAT-Thermometers, 506-ExpansionSpecific heat, 507-Tension of vapors-Ventilation and warming, 508.
CHAPTER III.
ELECTRICITY.
General statement.....509
1. Magnetic  Electricity-I. PROPERTIES OF MAGNETS-LodestoneNatural magnets-Artificial magnets, 509-Magnetic needles-Distribution
of the magnetic force —Polarity, 510-Magnetic phantom-Magnetic curvesMagnetic figures, 511-Anomalous magnets-Attraction and repulsion-Magnetism  by contact, 512-Magnetism  in bodies not ferruginous-II. MAGNETIC INDUCTION OR INFLUENCE-Induction, 513-Theoretical considerations
-Theory of two fluids, 514-Coercitive force-III. TERRESTRIAL MAGNETISM
— Magnetic needle-Directive tendency, 515-The mariner's compass, 516The astatic needle-Magnetic meridian —Declination or variation, 517-Variation chart-Isogonal lines, 518-Daily variations of the magnetic needle-The
annual variation-Dip or inclination, 520-The action of the earth's magnetism
-Dipping needle, 521 —Inclination map, or isoclinal lines, 522-Magnetic
intensity, 523-Isodynamic lines, 524-The inductive power of the rarth's
magnetism-System  of simultaneous magnetic observations, 525-Lines of
magnetic force-Atmospheric magnetism, 526-Notions of the origin of the
earth's magnetism-IV. PRODUCTION OF MAGNETS-Artificial magnets, 527The circumstances affecting the value of magnets-Magnets by touch, 528Iorse-shoe magnets, 529-Magnets by electro-magnetism —Compound magnets, 530-Magnetism of steel by the sun's rays-To deprive a magnet of its
power, 531.
2. Statical or Frictional Electricity-I. ELECTRICAL PHENOMENA —
Definitions, 531-The chief sources of electrical excitement-Electrical effects
-Attraction and repulsion, 532-Vitreous and resinous, or positive and negative electricities-Electroscopes, 533 —Conductors of electricity-Good conductors —Bad conductors-Insulation, 534 —The earth is the great common
reservpir-Theories of electricity, or electrical hypothesis-Franklin's singlefluid hypothesis, 535-The hypothesis of Symmer, or Du Fay, 536-Electrical
tension-Electrical currents are either momentary or permanent —Path and
velocity of electric currents, 537-II. LAWS OF ELECTRICAL FORCES AND DISTRIBUTION OF ELECTRICITY UPON THE SURFACE OF BODIES-Coulomb's lawsTorsion electrometer, 538 —Demonstration of the first law —Demonstration of
the second law-Sir Wm. S. Harris-Proof-plane, 539-Electricity resides




Xxiv                           CONTENTS.
only on the outer surfaces of excited bodies, 540-Distribution of electricityThe power of points 541-The loss of electricity in excited bodies-'IIT. INDUCTION OF ELECTRICITY-Electrical influence or induction, 542-The laws of
induction —Induction is an act of contiguous particles, 543-The attractions
and repulsions of light bodies, 544 —Electrometers-Cavallo's, Volta's, and
Bennett's-IV. ELECTRICAL MACHINES —The electrophorus, 545-The cylinder
electrical machine, 546-Amalgam-Ramsden's plate machine, 547-The American plate electrical machine-Large electrical machine-Ritchie's double
plate machine, 548 —The Tylerian machine, 549-Care and management of
electrical machines —Electricity from steam, 550-Other sources of electrical
excitement, 551-Theory of the electrical machine-Experimental illustrations
of electrical attractions and repulsions-The insulating stool, 552-Henly's
electroscope-Electrical bells-Volta's hail-storm —The electrical wheel —By
a candle flame, 553-V. ACCUMULATED ELECTRICITY AND ITS EFFECTS-Disguised or latent electricity-The condenser of 1Epinus, 554 —The discharge of
the condenser-Volta's condensing electroscope, 556-Dr. Hare's single goldleaf electrometer —The Leyden jar, 557-Electricity in the Leyden jar resides
on the glass, 558-The electric lattery-Discharge in cascade, 559-The universal discharger —The electric spark, 560-Kinnersley's thermometer-The
color of the electrical spark —The electrical discharge in a vacuum, 561-Difference between the positive and negative spark-The diamond jar —Scintillating tube and magic squares, 562-Effects of the electric discharge-Physiological effects, 563-Inflammation of combustibles-Chemical union effected
by electricity, 564-Volta's electrical lamp-The mechanical effects of the
electrical discharge, 565-The chemical effects —Ozone-VI. ATMOSPHERIC
ELECTRICITY —Franklin's kite, 566-Free electricity in the atmosphere, 567.
3. Dynamical Electricity-I. GALVANISM  AND VOLTAISM-Discovery
of galvanism, 568-The galvanic fluid-Origin of Volta's discovery-Contact
theory, 569 —Volta's pile, or the Voltaic battery, 570-Distinction between
voltaism and galvanism, 571-Quantity and intensity —Simple voltaic couple,
572-Electro-positive and electro-negative-Amalgamation, 573-II. BATTERIES WITH ONE FLUID-Voltaic batteries —Trough batteries —Hare's calorimotor, 574-The deflagrators of Dr. Hare-Smee's battery, 575-The sulphate of
copper battery-III. DRY PILES-Dry piles of Zamboni and De Luc, 576 —Bohnenberger's electroscope-IV. BATTERIES WITH TWO FLUIDS-Daniell's constantbattery, 577-Grove's nitric acid battery, 578-Carbon battery, 579-Other
forms of voltaic battery-V. POLARITY, RETARDING POWER, AND NOMENCLATURE OF THE VOLTAIC PILE-Polarity of the compound circuit, 580-Grouping
the elements of a pile-Electrical retarding power of the battery —Ohm's law,
581-Formulae of electric piles, 582-Intensity given by many couples, 583Effect of increasing the number of couples in a battery-Effect of enlarging
the plates of a battery, 584-Effect of enlarging the couples and increasing
their number-Faraday's nomenclature, 585-VI. THE EFFECTS OF THE VOLTAIC PILE-1. Physical effects-The voltaic spark and arch, 586 —Regulators
of the electric light, 587-Dubosq's photo-electric lantern-Properties of the
electric light, 588 —Heat of the voltaic arch-Deflagration, 589 —Measurement
of the heat of the voltaic current-2. Chemical effects of the pile —Historical,
590-Electrolysis cf water-Voltameter, 591-Laws of electrolysis-Electrolysis of salts, 592-Electro-metallurgy-The electrotype, 593-Crystallization
from the action of feeble currents, 594-Examples-Deposit of metallic oxyds
and Nobili's rings, 595-3. Physiological effects of the pile-The physiological




CONTENTS.                              XXV
effects of the voltaic pile-The magnetic effects of the pile-VII. THEORY OF
THE PILE-Three views, 596-Volta's contact theory, 597-The chemical
theory-Laws of the disengagement of electricity by 8hemical action-The
quantity of electricity required to produce chemical action, 598-Polarization
and transfer of the elements of a liquid-Chemical affinity and molecular
attraction distinguished-Peschel's molecular theory of the pile, 599.
4. Electro-Dynamics —I. ELECTRO-MAGNETISM-General laws, 600(Ersted's discovery, 601-The electric magnetic current moves at right angles
to the course of the conjunctive wire-Galvanometers or multipliers, 602The tangents or sine compass galvanometer-Rheostat, 604-Ampere's electromagnetic discoveries and theory-Mutual action of electric currents, 605De La Rive's floating current-Roget's oscillating spiral-Helix, solenoid, or
electro-dynamic spiral, 606-Directive action of the earth-Magnetizing by
the helix, 608-Arago's original experiment-Electro-magnets, 609-Page's
revolving electro-magnet, 610-Power of electro-magnets, 611-Vibrations and
musical tones from induced magnetism-Electro-magnetic motions and mechanical power, 612-Conversion of magnetism into heat-II. DIAMAGNETISM
-Action of magnetism  on light, 614 —Diamagnetism, 615-III. ELECTRIC
TELEGRAPH-Historical, 616-The earth circuit, 618-Varieties of electro-telegraphic communication-The electro-mechanical form-The electro-chemical
telegraphs-Morse's recording telegraph, 619-House's electro-printing telegraph, 620-The electro-chemical telegraph, 621-Autograph telegraphic messages-Submarine telegraphs-The Atlantic cable, 622-Electrical clocks and
astronomical records-Fire-alarm, 623.
5. Electro-dynamic Induction-I. INDUCED CURRENTS-Currents induced from other currents-Volta-electric induction, 623-Induced currents
of different orders, 625-Extra-current, or the induction of a current on itself
— Page's vibrating armature and electrotome, 626-Induced currents from the
earth's magnetism-Conversion of dynamic into static electricity-The induction coil, 627-Effects of the induction coil-The luminous effects, 629-The
chemical effects-Light of these currents in a vacuum-Gassiot's cascade in
vacuo, 630-Rotation of the electric light about a magnet-Applications, 631
— II. MAGNETO-ELECTRICITY —Currents induced by magnets, 632-Clark's
magneto-electric apparatus, 633-Identity of electricity from whatever source,
634.
6. Other Sources of Electrical Excitement-Universality of electrical excitement, 634-I. THERMO-ELECTRICITY-Thermo-electricity, 635Thermo-electric motions-Cold produced by electrical currents-Melloni's
thermo-multiplier-II. ANIMAL ELECTRICITY-The galvanic current, 636Eleitrioal animals-Electricity of plants, 638.
3




XXVi                           CONTENTS.
APPENDIX.
CHAPTER I.
METEOROLOGY.
1. Climatology-Climates, seasons-Influence of the sun, 639-Meteorological observations-Mean temperature, 640-Variations of temperature in
latitude-Variations of temperature in altitude, 641-Limit of perpetual snow
-Isothermal lines, 642.
a 2. Aerial Phenomena-General consideration of winds-Propagation of
winds-Anemoscopes, 643-Anemometers-The velocity of winds-Formula,
644-Regular winds-Periodical winds, 545-Variable winds-General direction of winds in the higher latitudes, 646-Physical properties of winds
-Hot winds-Hurricanes, or cyclones, 647-Tornadoes or whirlwindsWater-spouts, 649-General laws of storms, 650.
@ 3. Aqueous Phenomena-Humidity of the air-Absolute humidityRelative humidity, 651-Hygrometers-Saussure's hygrometer-Daniell's hygrometer-August's psychrometer or hygrometer of evaporation, 652-Fogs
or mists-Dew-Cause of dew-Circumstances influencing the production of
dew, 653-Substances upon which dew falls-Frost, 654-Clouds-Classification of clouds, 655-Rain, 656-Distribution of rain-Days of rain, 657Annual depth of rain-Snow-Colored snow, 658 —ail, 659.
- 4. Electrical Phenomena-Free electricity of air-Thunder-storms, 659
-The geographical distribution of thunder-storms-The origin of thunderclouds-Thunder, 660-Lightning-Classes of lightning-Zigzag or chain
lightning-Sheet lightning-Heat lightning-Ball lightning, 661-Volcanic
lightning-Return stroke-Lightning-rods, 662-Protective power-Aurora
borealis-Appearance of auroras-Remarkable auroras, 663-Height of auroras, 664-Frequency of auroras-Geographical distribution of auroras, 665
-Magnetic disturbances during auroral displays-Effect of the aurora on
telegraphic wires, 666-Reversal of polarity in the auroral current-PROBLEMfS
ON ELECTRICITY, 667.
Addenda-Note to ~ 369: Uniform musical pitch-Note to % 343: The velocity of all sounds not the same-Note to ~ 392: Sounds produced by insects,
668.
CHAPTER II.
PHYSICAL TABLES.
TABLE I.-Measures and weights (Cooke)..... PAGE 669
II.-For converting French decimal measures and weights into
English measures and weights (Gmelin).... 672
III.-Expansion of solids.......    674
IV.-Expansion of liquids...... 675




CONTENTS.                            XXVii
TABLE V.-Expansion of gases (Regnault)...    PAGE 676
VI.-Radiating power according to Provostaye, Desains, and Melloni 676
VII.-Conducting power of metals and building materials..    677
VIII.-Absorptive power of different bodies (Provostaye & Desains)   678
IX.-Absorptive power for heat from different sources (Melloni)   678
-X.-Diathermancy of different liquids (Melloni)... 679
XI.-Specific heat (Regnault and others)....    679
XII.-Freezing mixtures........      680
XIII.-Diathermancy of different solids (Melloni)...    681
XIV.-Tension of vapors at equal distances above and below the
boiling point of their respective liquids... 681
XV.-Melting points and latent heat of fusion of different bodies  682
XVI.-Boiling point of water under different pressures (Regnault)    682
XVII.-Boiling points of liquids (Kopp & Pierre)..            683
XVIII.-Boiling point of water at different places and their elevation
above the sea.                                       683
XIX.-Boiling point of water at different atmospheric pressures (Regnault).........    684
XX.-Liquefaction and solidification of gases (Faraday).. 684
XXI.-Aqueous vapor in a cubic foot of saturated air at different
temperatures (Guyot,condensed)..685
XXII.-Latent and sensible heat of steam (Regnault)...      686
XXIII.-Specific gravity of solids and liquids...       686
XXIV.-Volume and density of water (Kopp).                        687
XXV.-Comparison of the degrees of Baum6's hydrometer, with the
real specific gravity..                                 688
XXVI.-Tension, volume, and density of aqueous vapor (Regnault,
Peclet).........     689
ANSWERS TO PROBLEMS...  691
INDEX...........    699








PART FIRST.
PHYSICS OF SOLIDS AND FLUIDS.
CHAPTER I.
INTRODUCTION.
1. Matter.-Matter is that which occupies space, and is the object
of sense. Our knowledge of the material world is founded upon experience, or the evidence of our senses; and the conviction that the same
causes will always produce the same effects.
A definite and limited portion of matter, whether it be a particle of
dust or a planet, is called a body. The different kinds of matter, as
water, marble, gold, or diamond, are called substances. Numberless as
are the various substances known to man, they are all composed of
a limited number of simple bodies called elements.
2. Observation and experiment.-By observation we become
acquainted with those changes, in the condition and relations of bodies,
which occur spontaneously in the ordinary course of nature; but the
knowledge thus acquired is limited when compared with the results
of experiment. By the use of proper apparatus we can repeat natural
phenomena under varied conditions; and, among all the attendant
circumstances, we can determine what are accidental, and what are
essential to any given effect.
Phenomena.-A phenomenon, in the sense in which this word is
used in science, is any event taking place in the ordinary course of
nature. Thus the changes of the seasons, the fall of rain or dew, the
burning of a fire, and the death of an animal, are more truly phenomena of nature than those more rare or alarming events to which in a
vulgar sanse this word is usually confined.
8 *                                              (1)




2               PHYSICS OF SOLIDS AND FLUIDS.
3. Law, Theory, and Hypothesis.-In conducting an experiment,
we are taught to trace with certainty the connection between different
phenomena; to classify effects of the same kind and refer them to their
common cause; in fine, to deduce from many experiments the governing principle, or law of nature, in obedience to which they are produced,
and to unite both facts and principles into a theory, or comprehensive
view of the whole subject. Such theories are a fruitful source of new
experiments and new discoveries.
The terms law, theory, and hypothesis are often used interchangeably,
and are all designed to express the various degrees of perfection attained
in any department of human knowledge, towards the understanding of
the thoughts of God as expressed in the phenomena of the physical
world. An hypothesis is a guess or assumption, designed to aid further
investigation, and bears the same relation to a theory or law as the
scaffolding bears to the perfect building. A theory is the most perfect
expression of physical truth, and is deduced from both laws and prin..
ciples that have been established on independent testimony.
That a theory should rise to the highest expression of the laws of
nature, it must account not only for all known phenomena falling
under it, but for all possible cases with their irregularities and variations. Thus the law of gravitation, as developed by Newton from
terrestrial phenomena, has been found strictly universal in its application; not only meeting all known facts in celestial mechanics, but,
outstripping observation, it has foretold events which have been subsequently confirmed, or which it still requires centuries of years to
verify.
4. Inductive Philosophy.-When individual experience is enlarged by the experience of other inquirers and other times, and the
combined knowledge of many is so arranged as to be comprehended by
one, the system becomes a science or philosophy of nature. Because.
its principles are founded upon a comparison and analysis of facts, a
system of this kind is also called Inductive Philosophy.
Inductive philosophy is of modern origin. Galileo (born in 1564) was the
first to commence a course of experimental researches; and Bacon (born in
1561), in his immortal work, Novum Organum, showed that this was the only
road to an accurate knowledge of nature. The ancients were ignorant of the
principles and methods of inductive science. Their explanations of natural
phenomena were based on assumed causes; they are therefore confused and
contradictory, and often in direct opposition to experience.
5. Force.-From the axiom that every event must have a cause,
the mind naturally passes to the recognition of certain powers orforces
in nature adequate to account for the observed phenomena. Thus we




INTRODUCTION.                            3
refer the fall of bodies to the earth to the force of gravitation —the
strength of materials to the force of cohesive attraction-the directive
power of the compass-needle to the earth's magnetism-the evaporation
of water to the action of heat-the combustion of a fire to the action
of oxygen on the elements of the fuel, or to the force of chemical
affinity.
Man exercising his volition walks, or strikes a blow-examples of the
mysterious connection between spirit and matter, of the conscious exercise of mechanical force. By the use of a lever or screw he transmits
or multiplies his force at will-by experiment he learns that he can
also, by suitable appliances, call into action, where he pleases, certain
other forces, otherwise dormant, which he calls chemical, or physical,
according as they do, or do not, involve an essential change in the
nature of the materials employed. Both his consciousness and experience inform him that all these manifestations of force result from the
voluntary but mysterious action of mind upon matter. IHe is thus led
to the unavoidable conclusion that those great phenomena of nature,
over which he has no control, must have their origin also in the volitions
of a SUPREME RULER. FORCE and WILL thus become related terms, and
we are compelled to regard the forces of nature, as they are usually
styled, as only the outward and visible manifestations of the mind of
GoD.
In Physics the term force is often used for the unknown cause of a
known effect.
6. The properties of matter are general, or specific.-The
attentive consideration of any sort of matter will show us the existence of two sorts of properties in it-namely, general properties
and specific properties. Gold, for example, occupies space and possesses weight, but so also does all matter, whether solid, liquid, or
gaseous; these properties are general. But gold has a peculiar color
and lustre, is unchangeable by the action of causes which destroy the
identity of nearly all other sorts of matter, has a definite and peculiar
crystalline form, and weighs about nineteen times as much as a like
bulk of water. These are qualities peculiar to gold, and by which we
always recognize it. They are its specific properties.
7. The changes in matter are physical, or chemical.-Water
is changed by heat to steam  or vapor, by loss of heat (cold) it is
reduced to a solid. By the ceaseless action of these natural causes, it
perpetually changes its place and condition. It returns to the earth,
from its distillation in the great alembic of the atmosphere, as dew,
mist, rain, hail, or snow, and by gravity seeks to gain a place of rest
in the great ooean. But in all its changes of state and position it is




4              PHYSICS OF SOLIDS AND FLUIDS.
still the same substance. A bar of iron, by contact with a lodestone,
acquires new properties, which we call magnetic, but its color, form,
and weight remain unchanged. A glass tube or plate of resin rubbed
by dry silk or fur becomes electrical, in virtue of which property it
will attract or repel light bodies. These changes, which do not destroy
the specific identity of the substance, are termed physical changes.
But in a damp atmosphere the iron bar is soon covered with rust,
from the action of oxygen (one of the gases of the air) upon the iron.
The same change follows the action of water alone. In this latter case
the water is decomposed, and with great activity if a dilute acid is
present. The oxygen of the water combines with the iron, while the
hydrogen escapes as a gas, and thus the specific identity of both substances is destroyed. Such changes, destructive of specific identity, are
called chemical changes.
8. Physical and chemical-properties of matter.-The changes
of matter just noticed correspond to its physical and chemical properties. Gold possesses certain specific properties, depending solely on its
physical qualities; its density, lustre, color, form, malleability, and its
high point of fusion, are all qualities of gold which can never be lost
without an essential change of its nature, and are therefore termed
physical properties. Exposed however to the action of chlorine and
certain other agents, gold loses its specific identity, and becomes, as it
were, a new substance, while the same change passes equally upon the
agent by whose efficiency the transmutation is effected. Such changes
of matter, involving an essential loss of specific identity, depend on the
chemical properties of matter.
9. Physics and Chemistry.-It is plain that the distinctions
just pointed out are fundamental, in the nature of things, and that out
of them spring two entirely distinct, although nearly related, branches
of human knowledge, namely, PHYSICS and CHEMISTRY; the former is
more frequently called, in this country, Natural Philosophy; a term
too comprehensive in its general significance for an exact definition.
Now as all substances possess both physical and chemical properties,
it is plain that a thorough knowledge of either branch involves some
familiarity with the other. But the natural order of knowledge consists in obtaining first a familiarity with the general properties and
laws of matter, and subsequently the specific properties. Physical
knowledge therefore naturally precedes chemical.
10. Vitality, or the principle of life, is recognized as a distinct
force in nature, controlling both physical and chemical forces; by its
action inanimate or unorganized matter is transformed into animate
and organized existences. Thus, out of air, water, and a few mineral




GENERAL PROPERTIES OF MATTER.                   5
substances, all living forms, both animal and vegetable, are built up
by the chemistry of life. After a life of definite duration, they die,
and their structures dissolve again into the inanimate bodies out of
which they grew. They are subject to the general laws of matter, but
these laws are often modified, and sometimes directly opposed by the
action of that unknown power which we call the principle of life. The
description of organized bodies constitutes the science of Natural
Iistory.
11. Light, Heat, and Electricity are terms employed to distinguish certain phenomena, or forces in nature, connected with, or
growing out of the changes of matter, physical or chemical, or both.
They are supposed by most physicists to be dependent on the existence
of certain hypothetical fluids, or on the vibrations of an assumed
ethereal medium. As these fluids, or forces, are without weight or
other sensible properties of ordinary matter, they are termed, by many
writers, the imponderable agents, or simply imponderables. What
the spirit is to the animal body these mysterious agents are to lifeless
matter.
CHAPTER II.
GENERAL PRINCIPLES.
& 1. Definitions and General Properties of Matter.
I. ESSENTIAL PROPERTIES.
12. The essential properties of matter are (1) magnitude, or
extension, (2) impenetrability. We cannot conceive of matter without magnitude, and it is equally clear that the space occupied by any
given particle of matter cannot, at the same time, be occupied by any
other particle.
All the other general properties of matter, however universal they
may be, have been made known to us by observation and experiment,
and are not essential to the fundamental notion of the existence of
matter. The accessory or non-essential properties of matter are, 1,
Divisibility, 2, Compressibility, 3, Expansibility, 4, Porosity, 5, Mobility, and, 6, Inertia.
13. Magnitude or extension.-Extension is the property which




6               PHYSICS OF SOLIDS AND FLUIDS.
every body possesses of occupying a portion of space. The amount of
space so occupied by a body is called its volume.
Every body has three dimensions, length, breadth, and thickness,
the external boundaries of which are surfaces and lines. The exact
measurement of these three dimensions is the foundation of all exact
knowledge in experimental science, and demands the adoption of certain arbitrary units of comparison.
14. Impenetrability.-The power of a body to exclude all other
bodies from the space occupied by itself is called impenetrability.  This
property is possessed by all forms of matter. Air may be compressed
indefinitely, perhaps, but the mechanical force required for its compression is at once the evidence and the measure of its impenetrability.
A stone dropped into the water displaces its own bulk of the fluid,
but does not penetrate its particles. A nail driven into a board only
displaces certain particles of the wood, whose resistance or elasticity
imparts to the nail its power of adhesion.
The union of these two properties, extension and impenetrability
gives exactness to our fundamental notion of matter. Neither alone
will suffice to produce a body. The image in a mirror is not a body,
for behind the mirror, where the image appears, is the wall, or perhaps
another body. The shadow of any object in the sunlight has extension, but, as it is not impenetrable, it is not a body.
15. The three states of matter.-Matter is presented to our
senses in three unlike physical states, viz., solid, liquid, and gaseous.
The last two states are more comprehensively called fluids. These
three physical conditions of matter represent the opposite action of the
forces of attraction and repulsion. But as these interesting relations,
and the physical laws governing them, are fully discussed under their
appropriate heads, it is needless to do more than refer to thbem here.
(146.)
II. ENGLISH AND FRENCH SYSTEMS OF MEASURES.
16. Units of measure.-In order to determine with accuracy
the volume of solids and the area of surfaces or the length of lines,
some arbitrary unit of extension must be adopted. Of the three
geometric degrees of extension the unit of length is the only one which
need be arbitrary, since by squaring it we may measure surfaces, and
by cubing it we can measure solids. In early times the weight of
grains of wheat, ("thirty-two of which, from  the midst of the ear,
were, A. D. 1266, declared to be equal to an English penny, called a
sterling,") or the length of "barley corns" (three to an inch) gave the
rude basis of legal units of weight and measure in England, and, long
after, by adoption in the United States.




GENERAL PROPERTIES OF MATTER. 
17. English units of length.-The yard is the English unit of
length, adopted both in Great Britain and America. It appears to
have had its origin about A. D. 1120, in the reign of Henry the First,
" who ordered that the ulna, or ancient ell (which corresponds to the
modern yard) should be made of the exact length of his own arm, and
that the other measures of length should be based upon it." The yard
is divided into thirty-six inches.
In 1824 it was enacted by the English Parliament, that if at any
time the standard yard should be lost, defaced, or otherwise injured, it
should be restored by making a new standard yard, bearing the same
proportion to a pendulum vibrating seconds of mean time in the latitude of London, in a vacuum and at the level of the sea, as 36 inches
bears to 39.1393 inches, the latter being the length of the pendulum
vibrating seconds at London.
In 1834 the Parliament House was destroyed by fire, and with it the
standard yard. The measurement of the seconds' pendulum, as given
above, was subsequently found to be incorrect, and the commissioners
appointed to consider the steps to be taken to restore the lost standard,
recommended the construction of four standard yards from the best
authenticated copies of the old standard. These duplicates (a copy of
which exists in the U. S. Mint) are the basis of English and American
standards of length.
The subdivisions and multiples of the yard are given in Table I., at
the end of this volume.
Nearly all the English units of surface are squares whose sides are
equal to the units of length. The square and cubic inch are the units
most frequently employed for scientific purposes.
The measures of capacity are related to those of length, by the determination that a gallon contains 277.274 cubic inches. (1 101.)
Where volume can be calculated from linear measurements, it is
usual to estimate it in cubic yards, cubic feet, or cubic inches. In this
way earth-work and masonry are measured.
18. The French system  of measures originated with the great
revolution in France, when all regard for ancient institutions was
repudiated. A commission of the members of the Academy of Sciences
was appointed, who developed a decimal system, which was at once
adopted. They proposed that the ten-millionth part of the quadrant
of a meridian of the globe should be assumed as the basis of a new
metrical system. This was called a metre, and subdivisions and multiples of this unit were made on the decimal system. The metre is
equivalent to 39.37079 English inches, or 39.36850535 American
inches. Later determinations have shown that the length of the




8               PHYSICS OF SOLIDS AND FLUIDS,
standard metre is not precisely the one ten-millionth part of a quad.
rant. Thus it appears that the metre of France is a standard of
measure not less arbitrary than the English yard.
The French metre is subdivided into tenths, called decimetres; hundredths, or centimetres; and thousandths, or millimetres.* The names
of the multiples are as follows: the decametre, ten metres; the hectometre, one hundred metres; and the kilometre, one thousand metres.
This last length is equal to about two-thirds of an English mile, and
it is the ordinary road-measure in France.
The French units of surface are squares, whose sides are equal to
the units of length. The common French measure of land is the
square decimetre, which is called an are.
The measures of capacity are connected with those of length by
means of the litre, which is a cubic decimetre, (or a cube measuring
3.937 English inches on the side). It is equal to 1.765 Imperial pints,
or somewhat more than 1i English pints. (See Table I.)
The cubic metre is the measure of bulky articles, and has received
the name of stere. The stere, as well as the litre, and the are, have
decimal multiples and subdivisions, named like those of the metre.
The connection of the system of weights with those of capacity and length is
explained in ~ 100.
III. ACCESSORY PROPERTIES OF MATTER.
19. Divisibility.-By mechanical means matter may be reduced to
an extreme degree of comminution. By chemical means, and the processes of life, this subdivision is carried very much farther. A few
illustrations of each of these kinds of divisibility will suffice.
Gold is beaten into leaves so thin that one million of leaves measure
less than an inch in thickness. A bar of silver may be gilded, and
then drawn into wire so fine that the gold, covering a foot of such
thread, weighs less than  1gI of a grain. An inch of this wire, containing    I -   of a grain, may be divided into 100 equal parts distinctly visible, and each containing?,zoio    of a grain of gold.
Under a microscope magnifying 500 times, each of these minute pieces
may be again subdivided 500 times, each subdivision having to the eye
the same apparent magnitude as before, and the gold on each, with
its original lustre, color, and chemical properties unchanged, represents 3,Giru-i, Pl, U part of the original quantity.
Dr. Wollaston, by a very ingenious device, obtained platinum wire
for the micrometers of telescopes, measuring only 3,   of an inch in
diameter. Though platinum is nearly the heaviest of known bodies, a
* The smaller measures are named by Latin, the larger by Greek numbers.




GENERAL PROPERTIES OF MATTER.                     9
mile of such wire would weigh only a grain, and 150 strands of it
would together form a thread only as thick as a filament of raw silk.
A grain of copper dissolved in nitric acid, to which is afterwards
added water of ammonia, will give a decided blue color to 392 cubic
inches of water. Now each cubic inch of the water may be divided
into a million particles, each distinctly visible under the microscope,
and therefore the grain of copper must have been divided into 392
million parts.
One hundred cubic inches of a solution of common salt will be rendered milky by a cube of silver, 0'001 of an inch on each side, dissolved
in nitric acid, and the magnitude of each particle of silver thus repre.
sents the one-hundred billionth part of an inch in size. To aid the
student in forming an adequate conception of so vast a number as a
billion, it may be added that to count a billion from a clock beating
seconds, would require 31,688 years continuous counting, day and
night.
Minute division in the animal and vegetable kingdoms.-The
blood of animals is not a uniform red liquid, as it appears to the naked
eye, but consists of a transparent colorless fluid, in which float an innumerable multitude of red corpuscles, which, in animals that suckle their
young, are flat circular discs, doubly concave, like the spectacle glasses
of near-sighted persons. In man, the diameter of these corpuscles is
the 3500th of an inch, and in the musk-deer, only the 12,000th of an
inch, and therefore a drop of human blood, such as would remain suspended from the point of a cambric needle, will contain about 3,000,000
of corpuscles, and about 120,000.000 might float in a similar drop drawn
from the musk-deer.
But these instances of the divisibility of matter are far surpassed
by the minuteness of animalcules, for whose natural history we are
indebted chiefly to the researches of the renowned Prussian naturalist,
Ehrenberg. He has shown that there are many species of these creatures, so small that millions together would not equal the bulk of a
grain of sand, and thousands might swim at once through the eye of a
needle. These infinitesimal animals are as well adapted to life as the
largest beasts, and their motions display all the phenomena of life,
sense, and instinct. Their actions are not fortuitous, but are evidently
governed by choice, and directed to gratify their appetites and avoid
the dangers of their miniature world. The stagnant waters of the
earth (and sometimes the atmosphere) everywhere are populous with
them, to an extent beyond the power of the imagination to conceive
their numbers. Their silicious skeletons are found in a fossil state,
forming the entire mass of rocky strata, many feet in thickness and
4




10              PHYSICS OF SOLIDS AND FLUIDS.
hundreds of square miles in extent. The polishing-slate near Bilin,
in Bohemia, contains in every cubic inch about 41,000 millions of these
animals. Since a cubic inch of this slate weighs 220 grains, there must
be in a single grain 187 millions of skeletons, and one of them would,
therefore, weigh about the one 187-millionth of a grain. The city of
Richmond, Va., has been shown by Prof. Bailey to rest on a similar
deposit of silicious animalcules of exquisite form. It is impossible to
form a conception of the minute dimensions of these organic structures,
and yet each separate organ of every animalcule is a compound of
several organic substances, each in its turn comprising numberless
atoms of carbon, oxygen, and hydrogen. It is plain from these examples that the actual magnitude of the ultimate molecules of any body
is something completely beyond the reach equally of our senses to perceive, or of our intellects to comprehend.
20. Atoms, Molecules.-The ultimate constitution of matter has
divided the opinions of philosophers from the earliest period of science.
Two hypotheses have prevailed; the one, that matter is composed of
irregular particles without fixed size or weight, and divisible without
limit; the other, that "matter is formed of solid, massy, impenetrable,
movable particles, so hard as never to wear or break in pieces" (Newton), and which, being wholly indivisible, have a certain definite size,
figure, and weight, which they retain unchangeably through all their
various combinations. These ultimate and unchangeable particles are
called atoms (meaning that which cannot be subdivided).
While there is no mathematical objection to the assumption that
matter is infinitely divisible (since no mass can be conceived of, so small
that it cannot be mentally subdivided), physics and more particularly
chemistry have shown, from the mutual relations of bodies, that their
constituent particles possess definite and limited magnitudes.
The term molecude (a little mass) is more commonly applied to what,
in chemistry, are sometimes called divisible atoms; i. e., to a group of
two or more atoms, e. g., the molecule of water is composed of at least
two atoms, one of hydrogen and one of oxygen, forming together a
chemical compound. The phenomena of crystallization show us that
molecules possess different properties at different points of their surfaces. While their form is unknown, it is assumed that they touch
each other not at all, or only at a few points, leaving spaces between
them which bear a large ratio to their own bulk. From this fact result
the two general properties of compressibility and expansibility, which
are next to be considered.
21. Compressibility.-Diminution of volume in solids, by mechanical means, and by loss of heat, is a fact long familiar to all who are




GENERAL PROPERTIES OF MATTER.                        11
conversant with constructions. Even columns of stone, and arches, supporting heavy loads, are found to diminish sensibly from their original
dimensions by pressure alone.  Metals are compressed by coining. In
liquids it was long believed there was no compressibility, but in reality
liquids possess this property to a greater extent than solids.
1        Saxton's modification of Perkins's original apparatus serves to
$,    demonstrate the compressibility of water. A strong metallic vessel, C, fig. 1, is filled with water, and closed by a close fitting
screw plug, B, fig. 2; and a perfectly polished cylindrical piston of
steel, A, passes water-tight through the steel collar, P. When the
vessel is thus prepared, it is placed in a larger vessel capable of
enduring great pressure, which is also filled with water.
Pressure to any extent desired is then applied by means  2
of a hydraulic press. It is evident that if the water     l
undergoes diminution of volume when subjected to pressure, the piston A must be forced into the cylinder to a
corresponding extent. The index T having been placed at A
0 of the scale S, if it is found, after the experiment, above
that point, as in fig. 2, it is evidence of a corresponding
descent of the piston, due to compression of the water
contained in the cylinder C. On removing the pressure T
the elasticity of the water restores the original bulk.
Water is found, by this experiment, to yield about fifty
millionths of its volume for each atmosphere of pressure,
i. e., for a pressure of fifteen pounds to a square inch.  B
In air and all gases we see the property of com-    p
pressibility very apparent.  The air syringe is an
instrument in which a portion of air is compressed
before a solid piston, with the evolution of so much heat as to set fire
to tinder.
The return of gases and liquids to their original bulk on removal of
the condensing force is due to a property termed elasticity.  This
quality exists in many solids, if not in all, and its consideration will
be resumed hereafter.
22. Expansibility.-The expansion and contraction of all bodies
by heat and cold is a fact sufficiently familiar. Upon it is based the
construction of all instruments for reading changes of temperature, for
a description of which the reader is referred to the chapter on heat.
23. Physical pores.-The facts connected with the compressibility
of matter, and its change of form  by heat, indicate clearly  that
the atoms of matter (assumed to be unchangeable) are not in contact.
The spaces existing between them are called physical pores, on the
existence of which depends the property of porosity. Many chemical
phenomena illustrate the existence of this property. If equal measures
of alcohol and water, or of water and sulphuric acid are mixed, the




12              PHYSICS OF SOLIDS AND FLUIDS.
bulk of the resulting liquid is sensibly less than the sum of the two
liquids before they were mingled. This shrinkage can result only from
the insinuation of the particles of one substance among the pores of
the other.
The gre.at amount of heat developed, during these experiments, is a
significant fact. These molecular or physical pores of bodies are no
more sensible to our organs than the atoms themselves, and are permeable only to light, heat, and electricity..24. Sensible pores.-It is important to distinguish the molecular
porosity just described from those sensible openings which give to certain substances the property generally known as porosity. The pores
of organic bodies, as of wood, skin, and tissues, are only capillary
openings, or canals, for the passage of fluids. Nearly all animal and
vegetable substances present these sensible pores. The familiar pneumatic experiment-the mercurial rain-is an illustration of the porosity
of wood. Many minerals and rocks are porous. Common chalk and
clay are familiar examples. Hydrophane is a kind of agate, opaque
when dry, but translucent when wet from absorption of water. Even
gold, and other metals, under great pressure, as in the experiments of
the Florentine academicians in 1661, are found to exude water.
25. Mobility.-We constantly see bodies changing their place by
motion, while others remain in a state of rest. The capacity of change
of place, or of being set in motion, constitutes what is called mobility.
We recognize motion only by comparing the body moving with some
other body at rest. If that rest is real then the motion is absolute, but if
it is only apparent then the motion is only relative. Thus, on board ship,
or on a rail car, the passenger appears to change his place in reference
to objects about him. But all these objects are equally in motion with
himself.
All motion on the earth's surface is relative, because the globe itself
is impelled by a double movement-of revolution on its own axis, and
of translation about the sun.
Rest is also absolute or relative. Absolute when the body occupies
really the same point in space-relative when it preserves the same
apparent distance from  surrounding objects regarded as fixed, but
which are not in reality so. A ship sailing six miles an hour against
a current of the same velocity appears to persons on her deck to be
advancing with reference to the surrounding waves; but, viewed from
the shore, or by comparison with objects on shore, she appears at rest.
Absolute rest is of course unknown on the earth, since every terrestrial
object partakes of the double motion already noticed, and it is doubtful
if any part of the universe is in absolute rest, seeing that the stn




MOTION  AND  FORCE.                           13
itself with the whole solar system is carried around with a rapid motion
of translation in space about a central sun.
26. Inertia.-No particle of matter possesses within  itself the
power of changing its existing state of motion or rest. Matter has no
spontaneous power either of rest or motion, but is equally susceptible
to each, according as it may be acted on by an external cause. If a
body is at rest, a force is necessary to put it in motion; and conversely,
it capnot change from motion to rest without the agency of some force.
A body once put in motion will continue that motion in an unchanging direction with unchanging velocity until its course is arrested by
external causes.  This passive property of matter is called inertia.
Descartes first gave definite expression to this law in his " Principles."
When we are told that a body at rest will for ever remain so, unless it receives
an impulse from some external power, the mind at once assents to a statement
which embodies the results of our constant experience. But it requires some
reflection in one who for the first time considers the subject, to admit that
bodies in motion will continue to move for ever, unless arrested by external
forces. Casual, observation seems to contradict the assertion. On the earth's
surface we know of no motion which does not require force to maintain as well
as produce it.
We may observe, however, that all such moving bodies meet with constant
obstruction from friction, and the resistance of the air; and that as one or both
of these are diminished, the motion becomes prolonged and continuous.
The familiar apparatus called the wind-mill in vacuo is a good illustration of
the tendency to continued motion due to inertia-the usual causes of arrest of
motion being here greatly diminished.
The planets furnish the only example of constant motion. These celestial
bodies, removed from all the casual resistances and obstructions which disturb
our experiments at the earth's surface, roll on in their appointed orbits with
faultless regularity, and preserve unchanged the direction and velocity of the
motion which they received at their creation.
27. Action and reaction.-It follows as a necessary consequence
of the inertia of matter, that when a body, M, in motion strikes
another body, M', at rest, the action of M  in imparting motion to
AM  is exactly equaled by the power of M' to destroy motion in M.
Hence the law that action and reaction are always equal and opposite.
It is here assumed that the bodies impinging are entirely devoid of
elasticity, and so related that after collision they shall move on as
one body. It is also true for elastic bodies. See ] 181.
1 2. Of Motion and Force.
I. MOTION.
28. Varieties of motion.-We distinguish the following varieties
in the motion of a body.
4*




14              PHYSICS OF SOLIDS AND FLUIDS.
a-A motion of translation, or direct motion, in which all the points
of a body move parallel to each other.
b-A motion of rotation, as of a wheel on an axis, where the different parts of a body move at the same time in different directions.
Oscillation or vibration, as in a pendulum, is only a particular case of
rotation.
c-A combination of translation and rotation, as in the motions of
the earth.
The direction of motion is represented by a straight line drawn from
the point where motion commences, to the point towards which the
body is propelled. The direction is rectilinear, when it is constantly
the same, and curvilinear, when it varies every moment.
29. Time and velocity.-As all the phenomena of nature may
be referred to motion, so the succession of natural phenomena gives
us the idea of duration, or time. Day and night, months, and the
order of the seasons, are nature's units of time; but in physics the
invariable unit of time is the duration of a single oscillation of a pendulum, called a seconds' pendulum, the time of oscillation being a
second.  The length of such a pendulum  at London is 39-14056
English inches. The distance passed over by a moving body, in a
unit of time, is its velocity, represented by V in physical formulae.
This symbol obviously involves both time and velocity.
30. Uniform  motion.-A  body moving over equal spaces in
equal times is said to have uniform motion. It follows from  the
property of inertia that a body in motion, if left to itself, will continue
its motion uniformly both in time and direction.
PROPOSITION I. The distance PASSED over, in uniform velocity, is proportioned to the time. This follows directly from the definition of
velocity. Denoting by D the distance passed over, and by T the number of seconds, we have
X D             D
D= VX T,  V -           and T-.
The first expression is called the formula for uniform motion, and
the two others serve to calculate the velocity, the distance and time
being known; or the time, the distance and velocity being given.
It follows that if we represent T by one of the longer sides (A B) of
a parallelogram, A B C D, fig. 3, and V by one of          3
the shorter sides (B C) of the same parallelogram, <            D
then the area of the parallelogram A B C D represents
the distance passed over by a moving body in the number of seconds denoted by T.                                    A
31. Variable motion. —In varying motion the distances passed




MOTION AND FORCE.                       15
over in successive seconds are unequal. In this case, the velocity at
any given instant, is the relation between the distance traversed and
the time, considering the time infinitely small; or the distance that
would be traversed in a unit of time, supposing the motion at the given
instant to be continued uniform for the unit of time.
32. Motion uniformly varied.-When the velocity of a body
increases by a constant quantity in a given time, it is said to be uniformly accelerated. The increase of velocity in a second is called its
acceleration, which will be represented by v. Uniformly retarded
motion is where the velocity of the body diminishes by a uniform
quantity in each second of time.
PROPOSITION II. The change of velocity in uniformly varying motion,
at the end of any given time, is proportional to that time.
Let u be the initial velocity, that is, the velocity at the instant from
which the time is computed, v the acceleration and V the velocity at
the end of t seconds, then V== u + vt. The sign - corresponds to the
case of uniformly accelerated motion, and the sign - to that of uniformly retarded motion. In the last case the velocity becomes null
when u - vt, that is at the end of a number of seconds represented
by. The above formula in fact involves this proposition. If we
then make u = 0, that is, if it be assumed that the motion starts
from a state of repose, we shall have at the end of the time t, V= vt.
This is what we announced in stating that the velocity acquired, at the
end of a given time, is proportional to that time.
PROPOSITION III. In uniformly accelerated motion the distances passed
over, by a body starting from a state of rest, are proportional to the
squares of the times employed.
Representing the time by the line A B, fig. 4, and the velocity at
the end of the given time by the line B C,         4
divide the time A B into minute equal                      n
parts, A-i, 1-2, 2-3, 3-4 --       -             e
The velocities acquired during the times     b  ^           I
represented by A 1, A 2, A 3, A 4, will be a 
represented by the lengths of the several    l  
lines, I a, 2 b, 3 c, 4 d, -     which A    1   2   3   4'
are proportioned to these times. Suppose, however, that during each
minute portion of time A-i, 1-2, 2-3, 3-4 - - -, the velocity is constant, and equal to that attained at the end of each interval; the motion
being uniform, the distances passed over during these several subdivisions of time will be represented (30) by the areas of the parallelograms 1 a', 2 b', 3 c', --     —, and the distance passed over at the
end of the time A B, by the sum of these parallelograms. This sum




16               PHYSICS OF SOLIDS AND FLUIDS.
differs from the area of the triangle A B C by all that passes the line
A C. It is evident that if the time A B had been divided into a larger
number (say double) of equal parts, the sum  of the parallelograms
would have been less in excess of the triangle. The diminution is
indicated by the areas shaded in the figure. In proportion therefore
as the subdivisions of the time A B are more numerous, the sum  of
the parallelograms will differ less from the area of the triangle A B C.
Finally, when the number of divisions becomes infinite, that is, when
the velocity varies in a uniform  manner, the distance passed over
during the time A B will be represented by the surface of the triangle
A B C.
But that area   - A B X B C.  Substituting A          B — =, B C -  V,
and recalling the value of V= vt, we have for the distance passed
over D        A B X B C or D - =    vt2, a formula involving the pro)po
sition stated above.   This elegant demonstration is due to Galileo, who
discovered the laws of uniformly varying motion.
COROLLARIES. 1st. The last formula shows that the distance passed
over, in uniformly accelerated motion, by a body which starts fr'om  a
state of repose, is equal to the distance it would pass over withl a, uniform mean velocity.  2d. It follows also, from the same formula, if we
represent by a the distance through which a body moves in the first
second, we can easily find the following values for the distances it will
move through during each succeeding second, and also the whole distance it will have passed through at the end of each second.
Times,            1       2      3      4       5      n
Successive distances,   a     3a      5a     7a     9a   (2n -l)a
Whole distances,       a      4a     9a    16a   25a    b2a.
The coefficients in the last series are as the squares of the times, while
those in the second series are as the odd numbers, and are deduced
from  the last series by subtracting from each of its terms the one
next preceding it.  3d. The distance passed over during a given time,
in uniformly accelerated motion, is equal to one half the distance which
would be traversed during the same time by a uniform  motion, with
the velocity acquired at the end of the given time; that is, the velocity
at the end of the time t is equal to vt, and the distance which it
traverses during the time t is Ivt2, according to the formula.  4th.
To determine the velocity acquired in terms of the distance passed
over, it is necessary to eliminate t from  the equations V=- vt and
D-     vt2, which gives V= 1/2 v D.
The velocity is said to be due to the distance, (D,) an expression
which should not be literally interpreted.
33. Compound motion.-A body moving along a right line may
- -~  --- - -----' ——`-~-'  ^-""`~J?'"'i




MOTION AND FORCE.                        17
partake of two or more motions, in which case its path will be the
resultant of the combination of these motions. Such a motion is called
a compound motion. Daily observation confirms this statement, which
will be sufficiently illustrated when we consider the results of compoundforces.
34. Parallelogram of velocities.-The composition and resolution of
velocities will be more readily explained and illustrated when considering the
forces in which motion has its origin, as they follow the same laws.
II. OF FORCES,
35. Definition of force.-Byforce, as used in mechanics, we mean
any cause producing, or modifying, motion. All known forces, under
this definition, have their origin in three causes; namely, 1st, gravitation, or the mutual attraction of bodies for each other; 2d, the
unknown cause of the phenomena of light, heat, and electricity; and
3d, life, or the mysterious agency producing the motions of animals.
The study of forces and their effects constitutes the science of
mechanics.
36. Forces are definite quantities.-As we readily conceive of
one force as greater than another, so we understand that forces are
equal when, operating in opposite directions, they mutually balance
each and produce equilibrium. The same may be true of the action
of two, three, or more equal forces, forming, by their union, double,
triple, or any higher combination of force.
To determine a force with precision we must consider three things:
est, the point of application; 2d, the direction; 3d, the intensity, or
energy with which the force acts.
It is usual to represent forces, like other magnitudes, by lines of
definite lengths. Any line may be chosen as the unit of force. The
direction of a line will then represent the direction of the force, starting
from the point of application; and its length will represent the magnitude, or intensity, of the force, expressed by the number of times that
it contains the unit of force. A force is therefore defined in each of
its three elements by a line, being thus brought within the limits
of number, geometry, and mathematical analysis.
37. Weight; Unit of Force; Dynamometers.-Where a body
is left free to the action of gravity, but is held immovably by some
obstacle, the pressure or tension which it exerts on the point of support
is called its weight. It is important to distinguish carefully between
the words weight and gravity. The latter signifies the general cause
which produces the fall of all bodies to the earth, while the former




18              PHYSICS OF SOLIDS AND FLUIDS.
means only the result of the action of that general cause in the case
of a particular body.
-The common unit of force is the pound avoirdupois.
The weight of a body may be rendered\ sensible by the use of an
instrument called a dynamometer, or measurer of force.
One of the most simple of these is represented in fig. 5; it  5
consists of a steel spring, a C b. The metallic arc a d is fixed
near the end of the limb C a, and passes freely through an     illl
opening in the other limb. The graduated arc b e, is fixed, in    \
like manner, in the limb C b. The amount of the force exerted at the points e and d, determines the degree to which
the two limbs will approach, and is represented on the graduated arc in pounds and ounces, the graduation of the arc
being the result of actual trial, by hanging known weights 
upon the hook, and observing the positions marked by the
index.
Many forms of dynamometer exist, of which the spring balance, or
Le Roy's dynamometer, is the most familiar.
Le Roy's dynamometer, or spring balance, fig. 6, consists of a steel
spring, coiled within a cylin-                    6
drical tube. The end n of the
spring is attached to a rod of
metal, graduated in pounds and ounces, which is drawn out more, as
the applied force, b, is greater.
Reynier's dynamometer, fig. 7, consists of a steel spring, man b,
of which the part a and b ap-                     7
proach each other, when a force
is exerted at the points m and n.
An arc graduated in lbs. is attached to the spring at the point
a, and carries a needle, r o,
worked by a lever, c. The position of this needle upon the arc, 
indicates the amount of the force    =
exerted. If it is wished to de- 
termine the strength or force
exerted by any animal or machine, as the strength exerted by a horse
in drawing a plow through the ground, it is only necessary to attach
one end of the instrument, as n, to the plow, and have the horse
attached to the other end, m. The degree which is marked by the
pointer, when the horse moves, represents in lbs. the force exerted.
Another dynamometer is often used, similar in construction to the




MOTION AND FORCE.                        19
last, only that the force is exerted at the points a and b, fig. 7, which
are made to approach by a contrivance similar to that shown in fig. 5.
It is evident that, in this last arrangement, the force is applied in the
most favorable position for producing the maximum effect in collapsing
the spring; while in Reynier's dynamometer, the force is applied where
only the minimum effect is produced, and the instrument is therefore
generally employed for determining only very considerable forces.
38. Equilibrium.-When all the forces acting on a body are mutually counterbalanced, or neutralized, they, and the body on which
they act, are said be in equilibrium. The word repose and equilibrium
are to be carefully distinguished, however, as signifying different conditions of a body. Repose implies simply a state of rest, without
involving any idea of motion. Equilibrium signifies the state of a body
which, submitted to action of any number of forces, is still in the same
condition as if these forces did not act. By the definition of inertia
(26) a body may be in motion without being submitted to the action
of any force, and it may even continue its motion undisturbed, although
it becomes subject to forces producing equilibrium, since such forces
mutually neutralize each other. Equilibrium does not therefore include
the idea of immobility, and thus the words repose and equilibrium have
significations essentially unlike.
Equilibrium may exist without any point of support or apparent
resistance. A balloon in the air, or a fish in the water, are examples,
but the balloon and fish are balanced by counteracting forces hereafter
explained. What are familiarly known as examples of stable or unstable equilibrium are only special cases of the action of the force of
gravity, to be explained in their proper place.
39. Statical and Dynamical forces.-Statics is the science of
equilibrium. It considers the relations existing between the three
conditions (36), which are involved in the case of every force, in order
that equilibrium may result. Archimedes was the author of this portion
of mechanical science.
Dynamics considers the motions which forces produce. The foundations of this part of mechanical science were laid by Galileo in the
early part of the seventeenth century.
Hydrostatics and Hydrodynamics are the principles of statics and
dynamics applied to the phenomena of rest and motion in fluids.
The distinction between statics and dynamics is so far artificial that
the same force may, according to circumstances, produce either pressure or motion, without any change in the nature of the force.
40. Direction of force.-It is self-evident that the direction in
which a force is applied must determine the direction in which the




20              PHYSICS OF SOLIDS AND FLUIDS.
body receiving the force will move, if motion results, or of the resulting pressure, if the body is not free to move.
Moreover, the action of a force upon a body is independent of its state
of rest or motion. Daily experience and observation confirm this statement, which is also susceptible of experimental proof.
It follows: 1st. That if two or more forces act upon a body at the same
time, each of these forces produces the same effect as if it acted alone,
since the effect which each produces is not dependent upon any motion
which the others are capable of producing in the same body.
2d. Therefore, a body under the influence of a force, constant both
in direction and intensity, moves with a constantly accelerated velocity;
for as In each second the variation of velocity, v, is the same, in t
seconds it will be = vt; i. e., at the end of 2 seconds it will be 2v, of
3 seconds 3v, and so on. In other words, it is proportional to the time.
Reciprocally, 3d. A body moving in a right line with a uniform acceleration is actuated by a force of constant intensity acting in the direction
of its motion.
41. Measure of forces.  Mass.-In mechanics forces are usually
measured by their effects rather than by weight. The effects of a force
depend, other things being equal, on the mass of the body acted on.
The mass of a body is the quantity of matter the body contains, and
is proportional, in the same substance, to the number of its molecules.
Masses are equal when, after receiving for an equal time the impulse of
an equal and constant force, they acquire equal velocities.
Since we know forces only by their effects, that is by the amount of
motion or pressure they produce, let us look for a just measure of any
given force in the amount of motion which it causes. The following
four propositions will render this subject clear.
42. Propositions in regard to forces.-PROPOSITION I. Two constant forces are to each other as the masses to which in equal times they
impart equal velocities.
Consider, for example, n equal forces f,f,f, parallel to each other, acting upon
n equal masses wn,, mn. These masses receive equal velocities, and consequently preserve the same relative positions, and we readily conceive of them,
therefore, as bound together to form one mass equal to n X n. This compound
mass (n X n), in order that it may possess the same velocity, v, which any
single mass, nm, receives fromf, must be acted on by the force n X.f.
PROPOSITION II. Two constant forces are to each other as the velocities
which they impress, during the same time, upon two equal masses.
Suppose two forces F and F" to be commensurable, and let I be their common
measure, so that F  - nl and F' -  n'l.  Represent also by u the velocity
which the force I imparts at the end of a given time to the common mass. The




MOTION  AND FORCE.                           2)
force nl will impart to this mass the velocity V- nu, since each force equal
to I acts as if it were alone; in like manner the force n'l wi1l impart the velocity V   — n'u to the same mass. Thence follows this proportion,
nl: n'l =nu: n'u, or F: F' -_  V: V' which was to be proved.
If the forces compared are not commensurable, we must take I infinitely small.
PROPOSITION III. Two constant forces are to each other as the products
of the masses by the velocities which they impart to these masses in the
same time.
Let F F' be two forces acting on the two masses M M', and imparting to them,
at the end of the same time, the velocities Vand V'; also considerf another force
able to impart to the mass M, in the same time, the velocity V'; comparing the
forces F and/, which in the given time impart to equal masses iM unequal velocities V and V', it follows from Proposition II. that F:f = V: V'.
Comparing the forcesfand F', which impart to unequal masses JMand M' equal
velocities V' and V', it follows from Proposition I. that:-/f: F' =  M: M'.
Multiplying the two propositions term by term we have F: F' == MV:'' V',
which was to be proved,
From these principles it follows, that the measure of any force is
obtained by selecting some unit of force to serve as a term of comparison for all other forces; such a force acting on a unit of mass, during
one second (the unit of time), should impart to it a velocity or acceleration of one foot, one yard, one metre, or any other arbitrary measure,
as one foot per second, which latter measure we adopt.
By proposition second we can then find the relation that any force F, acting
on a mass of matter during one second, will bear to the unit of force. For if
F' is the unit of force in the proportion F: F' - I  V: M' V', then, by the definition, both Ml and VI are equal to unity, and we have F =- MV. That is,
according to the definition, F contains the unit of force as many times as there
are units in the product of the number AM into the number V. Assume, for
example, that the mass moved is equal to six units of mass, and the acceleration
v in a unit of time is equal to ten feet, then the intensity of the force is equal
to sixty, i. e., sixty times the unit of force. Hence we deduce the following:PROPOSITION IV. The measure of a force is the product of the mass
moved by the acceleration, or velocity, imparted in a unit of time.*
43. Momentum.-The momentum of a moving body is its amount
of motion, or its tendency to continue in motion. The momentum of
a body is equal to its mass multiplied by its velocity. When a force
acts upon a body, free to move, it produces its effect as soon as motion
is diffused among all the molecules, and the force is then transferred
into the substance of the moving body. In consequence of the inertia
* In all the propositions relating to velocity as a measure of force, there is
supposed to be no resistance to motion; the force acting only to overcome the
inertia of the body.
5




22               PHYSICS OF SOLIDS AND FLUIDS.
of matter (26), if the moving body should meet no resistance, it would
continue to move with the same velocity, and in the same direction,
for ever.
The expression Mv represents the intensity of the force which has
set the body in motion, and MT represents the amount of force that is
at any time accumulated and retained by the inertia of the moving
body. In either case the moving body is supposed to encounter no
resistance from any other object.
It is a fundamental principle in mechanics that the same force acting upon
different bodies in similar circumstances imparts velocities in the inverse ratio
of their quantities of matter. If the same force, in the absence of resistance,
successively projected balls whose masses were as the numbers 1, 2, 3, &c., it
would impart to them the velocities 1, i, i, &c., so that a mass ten times
greater would acquire a velocity of only  1. The product of each of these
masses into its velocity is the same, for 1 X 1 - 1, 2 X    1= 1, &c.
When a moving body encounters resistance, depending not only upon inertia,
but also upon other properties of matter, the effects produced depend upon the
rapidity with which the force, expressed by momentum, is brought to act upon
the opposing body. This class of effects is, therefore, proportioned to momentum, multiplied by velocity. This product MV2 is called vis viva, the application of which to practical mechanics will be explained hereafter (111). By the
principle that action and reaction are equal (27), we know that when a musket
is discharged the force of the explosion reacts upon the musket with the same
intensity as it projects the ball. According to the principles of momentum, the
weight of the gun, multiplied by the velocity of the recoil, must be equal to
the weight of the ball, multiplied by the velocity of its projection, yet the recoil
of the gun is received by the sportsmen with perfect impunity, while the moving
ball deals death or destruction to opposing objects.
III. COMPOSITION OF FORCES.
44. System  of forces. Components and resultant.-Whatever
may be the number and direction of forces acting upon one point, they
can impart motion or pressure in only one direction. We therefore
assume, that there is a single force which can produce the same action
as the system of forces, and may replace them. This is called the
resultant, and the forces to whose effect it is equivalent, are termed the
components.  The components and resultant may be interchanged
without changing the condition of the body acted on, or the mechanical
effect of the forces themselves.
A force is therefore mechanically equivalent to the sum of its components. On the other hand, any number of forces are mechanically
equivalent to their resultant.  As we know forces only by their effects
in producing motion or pressure, any forces which produce equal
motions or pressures are equal. We shall proceed to illustrate this
proposition in a few particular cases.
45. The parallelogram  of forces.-It has already been stated that




MOTION AND FORCE.                        23
forces may be represented by lines, both in direction and intensity;
also, that two forces acting on the same or equal masses of matter,
are to each other as their velocities, or F: F/ = V': V". The same
principles will therefore apply to the combinations of forces that apply
to the combinations of velocities or of motions.
When several forces act on a body, they may be arranged in three
ways, according to their direction. The forces may act,
1. All in one direction;
2. In exactly opposite directions; or
3. At some angle.
In the first case, the resultant is the sum of all the forces, and the
direction is unaltered. In the second, the resultant is the difference
of the forces, and takes the direction of the greater. If opposite forces
are equal, the resultant is nothing, and no motion is produced. In the
third case, a resultant is found to two forces, whether equal or unequal,
by the parallelogram of forces, according to the following law. By
any number of forces acting together for a given time, a body is brought
to the same place as if each of the forces, or one equal and parallel to it,
had acted on the body separately and successively for an equal time.
Suppose two forces, at right angles to each other, act simultaneously
on the point a, fig. 8, one in the direction a x,      8
and the other in the direction a y. Let one  l
force be such that, in a given time, as a second,             o l
it will move the point from a to b, while the...
other will, in the same time, move it from a to           
c, then by the joint action of both forces it will  ^ 
be impelled to r in the same time. The first      / 
force, by its separate action, would impel the  a          6
body to b in one second, and if it were then to cease, the second force,
or one equal and parallel to it, would impel the body to r in the same
time; or the body might be carried from a to c, and from c to r; in
either case the result is the same.
If a b = X, a c=  Y, and a r = R, then R =  /.X2 + Y2. If we call
the angle rab= -a   c)s. a=,  and sin. a= 
Again, suppose the forces act at an oblique angle; let the point P,
fig. 9, be acted on by two forces in the directions P A and P B. On
P A, measure P a, containing as many units of length as the force A
contains units of force; and on P B take P b in the same manner.
Complete the  parallelogram  P a c b; the diagonal P c will represent the direction of a single force C, equivalent to the combined effect




24              PIYSICS OF SOLIDS AND FLUIDS.
of A  and B, and P c will bontain as many units in length as C contains units of force.
In the same manner a result-                   9
ant may be found for three or                                 A.
any number of motive forces, by
compounding them, two by two,
successively.
In the triangle P a c, fig. 9, the
sides a P and a c =-P b are known,
and also the angle P a c, which is  H.......
th e         su pplement..na,................:...............
the supplement of the angle a P b,..
formed by the directions of the
forces. We may therefore calculate
the side P c, that is, the intensity 
of the resultant, and the angle
a P c, which determines its direc-                            B
tion.
Let the point a, fig. 10, be subjected to the forces whose magnitudes
and directions are represented by the lines a b, a C, and a d. We first
take any two which lie in                      10
the same plane, as a b and
aC, and find their result-,
ant a X; and compounding             /'       _...
this with the third force a d,   ar    _'  i
we find ay, which will re-        /!.      /
present the magnitude and        /  -''~     ~, 
direction of the general re-    /,.j       _- /./
sultant of all three forces.   /'-'I/__
The resultant of any num-   g 
ber of forces can therefore
be determined by geometrical construction, or calculated from  well
known geometrical principles.
This system of compounding forces is called the parallelogram of
forces, and applies equally to the combination of velocities or motions.
In order that the body may move in the straight line a r (fig. 8), the
two forces must act in the same manner. They may be instantaneous impulses, which will cause uniform motion; or both may act continuously
and uniformly, so as to produce a uniformly accelerated motion; or,
both forces may act with a constantly varying intensity, increasing or
diminishing at the same rate, and the body will still move in a straight
line. But if one force is instantaneous and the other constant, or one
constant and the other variable, or both varying by different laws, then
the body will move in a curve; but in every case it will reach the point




MOTION AND FORCE.                        25
r in the same time that it would have passed from a to b, or from a to c,
by the separate action of either force.
If the three forces a b, a C, and a d, all pass through the same point,
we may construct a parallelopipedon, as shown in fig. 10, and a y, the
diagonal of the parallelopipedon, will represent the direction and intensity of the resultant force. This method of compounding forces is called
the parallelopipedon of forces.
Examples of the composition of motion and force are of
constant and familiar occurrence.
A man in swimming, impels himself in a direction perpendicular to his feet
and hands, and if the forces are equal on each side, he will move in a resultant
line, passing through the centre of his body. Another instance is the flight of
birds. While flying, their wings perform symmetrical movements, and strike
against the air with equal force.
In the case of flying birds, the resistance of the air is perpendicular
to the surface of the wings, and                11
may be represented, fig. 11, by
C A and D A, at right angles to
their surface. Neither of these           /
pressures tends to impel the bird.
straight forward, but it moves in  -...E *
their resultant; for if the wings 
are equally extended, and act with  B   -
equal force, the lines C A and D A
make equal angles with A B, passing through the centre of the bird,       \D
and hence their diagonal, or A G,
the diagonal of equal parts of
them, will coincide with A B, and the bird will fly directly forward.
46. Parallel forces. Resultant of unequal parallel forces.Two forces, acting side by side, produce the same effect as if they were
in the same straight line. Two horses drawing a cart is an example.
Hence the resultant of two parallel forces acting in the same direction
is equal to their sum, and is parallel to them, and when they are equal,
is applied midway between them.
If the parallel forces are unequal, the point of application of the
resultant may be found by the following experiment. Let A B, fig. 12,
a bar of uniform thickness and density, be balanced on its centre C.
We may suppose the bar to be divided into two, A D and D B, of
unequal lengths, which might also be balanced on their centres E
and F. Now we have two parallel and unequal forces-the weight
of A D and the weight of D B-whose resultant is not midway
6*




26             PHYSICS OF SOLIDS AND FLUIDS.
between their points of application, E and F, but passes through C,
which is nearer E than F in the exact ratio that the force at E exceeds
that at F; for the weights                 12
of the two bars are as their   A
lengths, and C E measures                       D 
half the length DB, and 
C F half the length of AD;
so that CE is to C F in-                   U
versely as the weight at E is
to the weight at F. The truth of this conclusion may be tested by suspending at E and F two additional weights which have the same ratio
to each other as A D to D B, and the equilibrium will be undisturbed.
Hence the resultant of two parallel but unequal forces is equal to
their sum, and its distances from them are inversely as their intensities.
Thus, in fig. 13, if any two parallel            13
forces act at A and A', and their intensities are expressed by A B and A' B',  A'..,B
then their resultant will be repre-    \ 
sented by P R, provided it acts at P,
a point so situated that P A': P A=        ~~..
A B: A'B'. The same will be true          -     -.   >B 
whatever be the common direction of..  
the forces; if the positions of A B and               c 
A' B' are changed to A C and A' C',
then P R must move to P R', and equilibrium equally obtains.
47. Resultant of two parallel forces acting in opposite directions.-The resultant of two parallel forces, which     14
act in opposite directions, is found by the same construction as before, but it is equal to the difference
of the intensities of its components, and takes the
direction of the greater. Its point of application,   2
fig. 14, is in the prolongation of the line A B, at the  A
point C, situated so that C B and C A are in the inverse ratio of the forces Q and P. The point C will  o
be further removed as the difference between the        p
forces P and Q are diminished, so that if the forces
were equal, the resultant would be nothing, and situated at an infinite
distance.
The general resultant of aty number of parallel forces may be found
by compounding them, successively, two by two, in the methods already
prescribed.
48. Couples.-Whenever a body is solicited by two forces which




MOTION AND FORCE.                        27
are equal, parallel, and acting in opposite directions, it is impossible to
replace them, or produce equilibrium by a single force. Such a system of forces is called a couple, and its tendency is to produce revolu
tion around an axis. In this case, the value of the resultant is evidently
equal to zero, and the point of application is also at an infinite distance
from the points of application of the two equal components.
49. Two forces not parallel and applied to different points
may have a resultant, if they lie in the same plane. It is found by
extending the lines of direction until they intersect. But if the forces
are not parallel, and lie in different planes, then the directions, though
infinitely prolonged, will never intersect, and they cannot have any
single resultant, or be in equilibrium by any single force.
50. The resolution of forces is the converse of their composition.
Since two or more forces can be replaced by a single force, so, commonly, we may substitute two or more forces for one; and since an
infinite number of systems may have the same resultant, conversely,
one force may be replaced in innumerable ways by a system of several
forces. But if one of two required components is given in magnitude
and direction, there can be but one solution, and the problem  is
definite.
When a force acts upon a body at any other than a right tngle, a
part of its effect is lost. By resolving such an oblique force into two,
one parallel, and the other perpendicular           15
to the body, the latter component will re- M
present the actual force produced. Let a b,
fig. 15, represent a force acting under the
angle a b c against the surface M N. Resolve a b into a c perpendicular to M  N,
and a d parallel with it; then a c will be
the absolute effect of the force, and a b-                      a
a c is the loss. 
Example of the resolution of force.-The sailing of a boat in a
direction different from the wind is a most familiar illustration of these
principles. For example: the wind blows in the direction v a, fig. 16,
oblique to the sail, and to the course of the boat, and its force is
resolved into two components, one acting in the direction ca, impelling
the boat on its course in the line of least resistance, the other in the
direction b a, acting to carry the boat laterally on in the line of greatest
resistance. As the model of the boat allows it to advance freely through
the water in the direction c a, while it offers great resistance to lateral
motion, the force of the wind resolved in the direction b a produces
little effect upon the motion of the boat, she being held to her course




28              PHYSICS OF SOLIDS AND FLUIDS.
by the rudder. A skillful sailor can, by thus availing himself of the
principles of resolution of force, sail his vessel on a course within five
16
or six points* of being directly opposed to the wind which impels it.
IV. CURVILINEAR MOTION  CENTRAL FORCES.
51. Of curvilinear motion.-It has been shown that a body acted
upon by two forces will move in a direction which is the resultant of
the two forces. If one of two forces acting upon a body is a continuous force, acting in a direction tending to turn the body out of the
course it receives from the other, the resultant will not be a straight
line, but a curve, having its concavity turned towards the direction of
the continuous force. If at any instant the continuous force ceases to
act, the body will continue to move in the direction in which it was
moving when the constant force ceased to act. This direction will be a
tangent to the curve at that point.
52. Centrifugal and centripetal forces.-Let us consider a material point moving with a uniform velocity in the circumference of a
circle. The resultant of the forces acting on the particle will, therefore, by the necessity of the case, pass through the circumference of
the circle. In this case the force which prevents the moving particle
from  darting off in a tangent to the circle is called the centripetal, or
centre-seeking, force. This force at every instant arrests the tendency
of the particle to fly away from the centre. The tendency of the particle to fly away from the centre is called the centrifugal, or centreflying, force. These two forces are, together, termed central forces.
They are necessarily antagonistic to each other at every instant of curvilinear motion.
* A circle is divided into four quadrants, and each quadrant into eight points,
according to the phraseology of seamen.




MOTION AND FORCE.                            29
To understand the antagonism of central forces, take m c, fig. 17, an infinitely small arc of the circumference, and making           17
with the direction c' m a, of the preceding element
c' n, an infinitely small angle a m c. Join the extremi-..f....
ties of the element m c with the centre of the circle by. 
the radii mn C, c C, and draw b c parallel to m a. Since
n c is considered infinitely small, a c and mb are
parallel to each other, and m a c b is a parallelogram.
Therefore it follows by the parallelogram of forces,
that while the body was moving over the arc mc it
would in the same time have passed over the space
m a, in virtue of the velocity acquired in passing
over c' m, if no other force intervened; while by reason
of the central force acting from m to c, it would have
passed over the space m b, had it not been for the
original impulse c' m. This is the centripetal force,
and, compounded with the original impulse, c' m, the        C
particle follows the resultant m c.
Draw now a d parallel to m c, forming the second parallelogram m c a d. The
velocity of the particle following the diagonal m a may be decomposed into the
two components; one m c in the path of the circular motion, and the second
m d following the radius. This quantity (m d) represents the centrifugal force,
and as m I -= a c =- n b, it follows that at each instant of the circular motion
the centripetal and centrifugal forces exactly counterbalance each other, and
that the sole resulting motion is in the are m c. If at any instant the centripetal force ceases to act, m a, the resultant of the forces m c, in d, will throw the
particle in the path of the line c' mn a tangent to m. The term centrifugal force
must not be understood to mean a force which would cause the body to fly
directly from the centre, since as we have seen it must in that case move also
in the tangent.
Examples of the action of centrifugal force.-A stone flies from
a sling with a velocity equal to the force acquired by its revolution at
the moment when, by releasing one of the strings from the finger, it
flies off in a line tangent to the point of release. The water flies from
a grindstone, or mud from a carriage wheel, whenever the centrifugal
force due to the velocity of revolution is sufficient to overcome the force
of adhesion. The rapidity of revolution may be sufficient in a grindstone to overcome the cohesion of the particles of the stone, when it
bursts with a loud explosion, carrying death and destruction in its path.
A pail filled with water may be whirled with such velocity that the
centrifugal force overcomes the force of gravity, and the liquid is not
spilled.
53. Experimental demonstration of the effects of centrifugal
force.-The effects of centrifugal force may be illustrated by the apparatus represented in fig. 18. A wire is stretched upon a frame a b, connected with an upright shaft, which is made to revolve rapidly by means
of a cord, as shown in the figure. Two perforated balls, united by a string,




30              PHYSICS OF SOLIDS AND FLUIDS.
slide freely upon the horizontal wire. If the two sliding balls are of equal
weight, and are placed at equal distances from the axis of rotation, still
18
b
united by the string, they will retain the same position with any velocity of rotation which may be given to the apparatus; but if one of the
balls is more distant from the axis than the other, it will draw the
other along with it, and both balls will strike the support on the same
side, provided the distance between the balls is less than half the line
a b. If the two balls, united as before, and placed at equal distances
from the axis, have unequal masses, the heavier ball will draw the
other towards its own side of the apparatus. Two unequal balls,
united in the same manner, will remain at rest, if their distances from
the axis, on opposite sides, are in the inverse ratio of their masses.
Admitting that the centrifugal force is proportional to the mass of the
body, these experiments prove that the centrifugal force is proportional
to the radius of the circle described, when the times of revolution are
the same.
To demonstrate the effects of centrifugal force in liquids, the apparatus shown in the upper part of fig. 19 is attached by screws to the
coupling at the top of the re-                 19
volving shaft shown in fig. 18. B y
Two flasks with long necks are
placed obliquely, communica-  lIIl                      ll
ting with a reservoir filled with             l.
liquid placed at the middle of
the bar which supports them.
As the apparatus is rapidly revolved, the liquid rises into the flasks, and again descends when the
motion is arrested. If the vase, fig. 20, containing water, is attached to
the machine, and made to revolve, the surface of the water becomes
concave, the water rising by the sides of the glass, the surface becoming more deeply concave as the motion becomes more rapid. The piece
of apparatus shown at the bottom of fig. 19 carries two inclined tubes,
one enclosing water and a metallic ball, the other water and a ball of




MOTION AND FORCE.                        31
wood floating on its surface. As the rotation becomes rapid, the water
rises to the top of the tubes, the ball of wood then descends, and takes
a position on the inferior surface of the liquid, while the  20
metallic ball advances through the liquid, and rises to       
the most elevated extremity of the tube which contains it,
the liquid itself rising to the exterior end of the tube.
The different effect upon the two balls results from the
fact that the metal has a greater mass than an equal
volume of the liquid, while the contrary is true of the
wood; the centrifugal force being in proportion to the
mass, the tendency is to carry the denser substance to the
greater distance from the axis of rotation.
If a tube contains different liquids incapable of acting chemically
upon each other, they will place themselves, during rapid rotation, in
such an order that the denser fluid will be more distant from the axis,
the outward tendency being directly proportional to the mass of matter
in a given volume. These effects do not take place till, by the rapidity
of revolution, the centrifugal force becomes greater than the force of
gravity. The common circular or fan blowing machine is an example
of the action of centrifugal force on bodies in a gaseous condition.
A centrifugal pump has been devised acting in this manner. The fanblower is also used as a ventilator, drawing its supply of air from the
space to be ventilated, to supply that thrown out by the tangential
opening.
The centrifugal drying machine for laundries consists of a
very large upright cylinder, having a smaller cylinder within it. The
circular chamber between the two cylinders is closed by covers, by opening which the linen to be dried can be introduced. The bottom of this
chamber is pierced with holes like a sieve, through which the water
expressed from the linen can flow off. A rapid rotation being given to
this cylinder, the linen, by the effect of centrifugal force, is urged
against the exterior surface of the cylinder, and is there squeezed with
a force which increases with the rapidity of rotation, by the effect of
which the water is pressed out of it, and escapes through the holes in
the bottom. A rotation of 25 turns per second, or 1500 per minute, is
given to these drying cylinders, by which the linen, however moist it
may be, is rendered so nearly dry that a few minutes' exposure in the
air renders it perfectly so. In large linen manufactories this machine
produces a great saving of labor in the laundry department.
In the motion of the heavenly bodies we find. the most wonderful examples
of the action of central forces, acting as they do to prevent the moon from fall



22               PPHYSICS OF SOLIDS AND  FLUIDS.
ing upon the —earth, and the planets into the sun.  The action of centrifugal
force will be further considered in connection with terrestrial gravity.
54. Analysis of the  motion  produced  by  central forces. —
Let a body placed at a, fig. 21, receive an impulse which would carry it to d in
one second, or any small portion of a second, and         21
let it be attracted towards c by a constant force
which would move it to b in the same time that the.........
first impulse would carry it to d, then by the prin-..
ciples of the composition of forces it will be found     /.
at4he end of the given time at e, and if the attrac-        /' 
tive force should then cease it would continue to 
move in the direction em. If the attractive force.  /.
continues, the body will be found at g at the end     /.of the second period. As the central force is continually acting, the body will diverge more and........
more from the direction of the first force, and will  
describe a curve.  As the attractive force acts 
always towards the central point c, the body  
will revolve around that point. If the relation of 
the two forces is such that ce, cg, &c., are each 
equal to c a, the curve of revolution will be a                   /
circle. In most other cases the curve of revolution
will be an ellipse.                                          /
If the curve described is a circle, and we assume   — "
the arc a e to be very small, it will not sensibly differ from a straight line, and
according to well known geometrical principles we shall have
ab: ae -  ae a o.
aea
ab=a o
That is, the centrifigal and centripetal forces of a body describing a circle
with uniform velocity are directly proportional to the square of the velocity, and
inversely as the diameter of the circle.
The relation of these forces may be expressed differently. Considering a e
as the space described in one second, it will be the velocity of the body; but in
curvilinear, just as in rectilinear movement, the velocity is equal to the distance
divided by the time, i. e., equal to the circumference of the circle divided by the
time of revolution. Let R represent the radius of the circle, T the time of
revolution, v the velocity, and 77 the ratio of the circumference to the diameter.*
27rR
and we shall have a e =-  v - -. Substituting this value of a e in the previous equation, and considering that a o =  2R, we shall have
47r2R2   27r2R
ab =
2r     -  2 T2'
Therefore the attractive force would generate in one second a velocity
* The ratio of the circumference of a circle to its diameter is 3-14159, and
this number is usually represented by the Greek letter 7Z in mathematical formula.




MOTION AND FORCE.                            33
47r2R
expressed by twice a b, the distance passed over, equal to -.  The angular
velocity per second is expressed by the actual velocity, divided by the radius;
calling this angular velocity V, we have
47V2R:.  =       V 2.R.
The centrifugal or (which is the same thing) the centripetal force varies directly
as the radius of the circle of revolution multiplied by the square of the angular
velocity. Also if two bodies move in different circles and in different times, their
centrifugal anld centripetal forces trill be directly as the radii of their circles, and
incersely as the squares of the times of revolution.
It is also evident that the centrifugal force is proportional to the mass of the
body.
55. Bohnenbejger's apparatus.-In consequence of the operation
of the law of inertia, moving bodies preserve their planes of motion.
This is true as well of planes of rotation as of planes in a rectilinear
direction. By means of Bohnenberger's apparatus             22
we may illustrate the tendency of rotating bodies
to preserve their plane of rotation, and the invaria-           A
bility of the axis of the earth during its revolution.   A
Bohnenberger's apparatus consists of three rings, 
A A A, fig. 22, placed one within the other; the
two inner ones are movable, and connected by
pins at right angles to each other, in the same
way as the gimbals that support a compass.  In
the smallest ring there is a heavy metallic ball   n'.i.!!!i;'!
B supported on an axis, which also carries a little pulley c.  The ball
is set in rapid rotation by winding a small cord around c, and suddenly
pulling it off. The axis of the ball will continue in the same direction, no matter how the position of the rings may be altered; and the
ring which supports it will resist a considerable pressure tending to
displace it.
56. Parallelogram  of rotations.-It has been shown (48) that
rotary motion is produced by two equal parallel forces acting in opposite directions. If two new equal parallel forces act upon the same
body, tending to produce rotation about another axis situated in the
same plane, the compound resultant will tend to produce rotation about
a third axis, situated in the same plane, between the directions of the
other two.
Let the irregular body shown in fig. 23, while rotating about the axis
A X be suddenly acted upon by forces tending to produce rotation about
the axis AY.  Suppose the parts of the body lying between A X and
A Y to be impelled in opposite directions by the two rotary forces.
6




34             PHYSICS OF SOLIDS AND FLUIDS.
Take any point, as P, and drawing from P perpendiculars upon the
two axis, let PC = y and P B - x, also let         23
v represent the angular velocity about the
axis A X, and v' the angular velocity about 
the axis AY, then will vx -  vy express         /
the resultant force exerted upon the point
P. Now since, if the point P were taken 
in the axis AX, we should have vx = 0, and
if P were taken in A Y we should have v'y      ~1      I
0, it is evident that P may be so taken
that vx - v'y = 0, or vx -= vy. Lay off on A X a distance A E, such
that A E: A C   v: v', construct the parallelogram A C D E, and draw
the diagonal A D; then A E: A    = D C: DE = v:   =y: x. But
every point on the line AD X' will have the same relation to the axis
A X and A Y. Hence every point in this line will remain at rest, and
A X' becomes the resultant axis of rotation, in virtue of the forces previously tending to produce rotation about the two component axes.
To determine the velocity of rotation about the resultant axis A X',
take any point, as C, on the axis A Y. At this point v'y = 0, and the
point C has no tendency to move except that given by the moment vx
about the axis A X. Draw the perpendiculars C R and C Q upon A X
and A X' respectively. Represent C R by r, and C Q by r", and denote
the angular velocity about A X' by v". Now as the distance passed
over by the point C during any instant depends only on the moment
vx, it will be the same whether the rotation takes place about A X or
A X'; hence vr _= v"r",.. v" =. The triangles A CD and A C 
r
are equal, being each one-half the parellelogram A CD E, hence A D X
vr
CQ == A E X C R, and A DXr" = vr, hence A D    -. Comparing
this equation with the value of v" found above, we find that v" = AD.
From the above reasoning it appears that,Where a body is acted upon by two systems of forces, tending to produce rotations about two separate axes, lying in the same plane, the
resultant motion will be rotation about a new axis, represented in direction by the diagonal of a parallelogram, the sides of which will be represented by the component axes of rotation, and the magnitudes of the sides
by the forces tending to produce rotation about those axes.  The velocity
of rotation about the new axis represented in direction by the diagonal
of the parallelogram, will be measured by the length of the diagonal.
From the same principles it follows that, If a body is acted upon by three
systems of forces, tending to produce rotation about three different axes, all




MOTION AND FORCE.                            35
passing through the same point, the resultant motion will be rotation about a
new axis, represented in direction by the diagonal of a parallelopipedon formed
on the original axes as adjacent edges, with the magnitude of those edges corresponding to the respective forces acting about those axes, and the velocity of the
new rotation will be represented by the length of the diagonal of the parallelopipedon.
In describing rotary motions it is customary to speak of the'motion
as right-handed or positive, or as left-handed or negative.
Let A X, A Y, A Z, fig. 24, be three rectangular axes, passing through the
point A, which is called the origin of co-ordinates. Distances measured from A
towards either X, Y, or Z, are called positive, and distances measured in the
opposite directions are called negative. If a body revolves about either of these
axes, or about any axis drawn through A, in             24
such a direction as to appear, to an eye placed...-........z
beyond it, and looking towards A, to move in'...     /
the same direction as the hands of a watch,
when we look at the dial, such motion is
called right-handed, or positive rotation. If  
rotation takes place in the opposite direction,  A                Bi X
it is called left-handed, or negative. If a body.....
revolves in the directions shown in either part                  -  \.
of fig. 24, the rotation is called right-handed,  
or positive. If the three axes, A X, A Y, A Z, 
vere brought towards each other till they co-   Y
incide, these rotations would all coincide in
direction.
57. The gyroscope, or rotascope, is an instrument exhibiting some
remarkable results of the combination of rotary motions, and which
also shows, as in Bohnenberger's apparatus, the tendency of rotating
bodies to preserve their plane of rotation. A common form of the
rotascope, fig. 25, con-                        25
sists of a metal ring, A B,...............
inside of which is placed......
a  metallic  disk, C  D,  
loaded at its edge, and  
which  turns  independ-.
ently of the ring, upon   *,.
the axis.  Motion is com- 
municated by means of a.
cord, wound around the
axis of the disk and suddenly drawn off. If, when
the disk is rotating rapidly, it be placed on the steel pin F, supported on the column G, it seems
indifferent to gravity, and instead of dropping it begins to revolve in a
horizontal orbit, H I, about the vertical axis F G, in a direction corresponding with the movement of the lower part of the disk. This hori



36             PHYSICS OF SOLIDS AND FLUIDS.
zontal revolution gradually increases in velocity, and the free end of
the disk, in some circumstances, vibrates upward and downward, in
spiral curves. When the rotation of the disk is considerably diminished
by friction, gravity gradually prevails over the supporting power, and
at length the disk falls, in a descending spiral curve.
To explain the movement of the gyroscope, let the axis Y A Y',
fig. 24, correspond to the standard. A       24 (bis.)
being the point where one end of the...-..-....
axis of the revolving disk is supported.'....
Let A X correspond to the horizontal
-axis around which the disk of the
gyroscope revolves, and let Z A Z' be  A..s
another horizontal axis, at right angles..
with A X and A Y. Let a right-.
handed rotation be given to the disk of 
the gyroscope about the axis A X, as    Y
indicated by the arrows. While the
force of gravity causes the free end of the axis to descend, there will
also be commenced a right-handed rotation about the axis A Z. Both
these rotations nay be supposed to have constant velocities for an infinitely short interval of time. Let v denote the angular velocity about
A X, and v' the angular velocity about A Z. Lay off on A X a distance
A B = v, and on A Z a distance A C = v', complete the parallelogram
A B D C; then the diagonal, A D, will represent the resultant axis of
rotation, and the length of this diagonal will represent the velocity of
rotation about the new axis. As the disk can only rotate about the new
axis by moving towards D, there will thus be commenced a new movement of rotation, which we may call a horizontal revolution about the
perpendicular axis. This will be a right-handed rotation about A Y.
We now have to consider rotation about three axes, all passing
through the axis A. To construct the position of the resultant axis
for the second instant, lay off on A Z, considered as perpendicular to
A D and to A Y, a distance to represent the angular velocity due to
gravity, and on A Y the angular velocity in the orbit, acquired in
passing from the position A X to A D; A D represents the velocity
with which the disk rotates. Construct a parallelopipedon on these
three lines, and draw its diagonal through A. This diagonal will evidently give a direction that will continue the horizontal revolution
already commenced, and also an upward tendency in opposition to
gravity. The same process of construction might be continued for
every instant the rotation continues. It is evident that the horizontal
rotation would continually increase in velocity, and the tendency to




MOTION  AND FORCE.                            37
lift the end of the axis of the disk would also increase, were it not continually counteracted by the action of gravity. As the velocity of the
rotation of the disk is continually retarded by friction, the lifting power
exerted against gravity diminishes until the disk gradually descends
with a spiral revolution, and the instrument is brought to rest.
If the disk of the gyroscope were made to rotate in the opposite direction, or left-handed, the motion around the axis Z A Z', caused by
gravity, would also be left-handed when considered from  the point Z/,
and the resultant A D/ would lie on the opposite side of A X. This
would also give a left-handed rotation about the perpendicular A Y,
and the resultants would all be found in the solid angle A X, A Y,
A Z/, and again the tendency would be to counteract the depressing
force of gravity.  Thus we should have the rotating disk supported,
as experience shows it is, in whichever direction it is caused to rotate.
If the weight of the gyroscope were counterbalanced (as it is frequently constructed) by an equal weight on the opposite side of the vertical axis, it can
readily be seen that it would have no horizontal rotation. If the counterbalancing weight were so great as to raise the disk upward, the horizontal
revolution would be performed in the opposite direction.
Problems on Weights and Measures.
1. (a.) I-ow many English yards are contained in 135 French kilometres?
(b.) Reduce 2-5934 centimetres to English inches. (c.) What part of an English
inch is 1 millimetre? (d.) Reduce 3 centimetres to inches.
2. (a.) Reduce 4 feet 7 inches to French measure. (b.) Reduce 225 rods to
French measure of length.  (c.) Reduce 13 miles to French kilometres.
(d.) Reduce 5 yards to French metres.
3. (a.) Reduce 3 pints to litres and cubic centimetres. (b.) Reduce 5 litres
to English  measure.  (c.) Reduce 7 gallons to litres and decimal parts.
(d.) Reduce 7 cubic centimetres to English pints.
4. Reduce, by means of the Table II.,-(a.) 25 inches to decimal parts of a
metre. (b.) 139 centimetres to American inches. (c.) 75 feet to metres. (d.) 5
kilometres to American yards.
5. Reduce, by means of the table at the end of the book,-(a.) 7~ pints to
cubic centimetres. (b.) 10 gallons to cubic centimetres. (c.) 735 cubic centimetres to gallons.
Problems on Motion.
6. A body passes uniformly over a distance of 200 yards in 1 hour and 6
minutes: what is the numerical value of its velocity, according to the usual
conventions concerning the units of space and time?
7. A body is observed to describe uniformly a feet in n seconds; supposing
the unit of time to be 1 minute, what must be the unit of distance in order that
the numerical value of the body's velocity may be 1?
8. A man walks with a velocity represented by 2, and he finds that he walks
7 miles in 2 hours; if I foot be the unit of length, what is the unit of time?
9. A particle is moving with such a velocity, and in such a direction, that
6*




38               PHYSICS OF SOLIDS AND FLUIDS
the resolved parts of its velocity in the directions of two lines perpendicular to
each other, are respectively 3 and 4; determine the direction and velocity of
the particle's motion.
10. A is a more powerful and a heavier man than B; the greatest weights
which they can lift are as 8: 7, and their own weights are as 7: 6. Which is
likely to be the faster runner of the two?
11. Supposing a body acted upon by a force capable of causing an acceleration of 3 feet per second: What will be its velocity, and the distance passed
over, at the end of 1 minute?
12. What velocity will be acquired by a body moving 100 feet, under the influence of a force capable of causing an acceleration of 2 feet per second?
13. If a body starting with an initial velocity of 125 per second is found to
come to rest after the end of 5 seconds, what is the amount of retardation, and
what distance has the body passed over?
14. If a body weighing 100 pounds moves with a velocity of a mile in 7
seconds, what must be the weight of a body moving 3 feet per second, to have
the same momentum as the former?
15. If a ship weighing 2000 tons strikes a pier with a velocity of 6 inches per
second, what velocity must be given to a 64 pound shot, in order that it may
strike an obstacle with the same momentum?
16. Uniform force is defined as that which generates equal velocities in equal
times; would it be correct to define it as that which generates equal velocities
while the body moves through equal spaces?
CHAPTER III.
GRAVITATION.
] 1. Direction and Centre of Gravity.
58. Definition.-The fall of unsupported bodies to the earth, and
the pressure exerted by bodies at rest on the earth's surface, is due to
the force of gravity. The amount of this force seen in the downward
pressure of any body is called its weight.  Weight is due to the earth's
attraction for the body weighed. This is only a particular case of a
general force in nature, by reason of which all bodies in the universe
attract each other, thereby maintaining the order and stability of the
heavenly bodies.
59. Law  of universal gravitation.-The law  of gravitation  is
stated as follows: Every particle of matter attracts every other particle
in the DIRECT ratio of its mass, and in the INVERSE ratio of the square
of its distance.
Let Mand M' represent two masses, D and D' the distances.  Take
G and g the absolute gravities of the two masses at a given distance,




GRAVITATION                           39
and g: GW, the ratio of the force of gravity at distances D and D', then
G: g=  M: M,
g: G = D'2: D', compounding these proportions we have
G: G- =MD'2: MilD2, hence  G: G::: -        2.
Or the fprce of gravity of different bodies, at different distances, is
directly as the masses and inversely as the squares of the distances.
This law was discovered in 1666, by Sir Isaac Newton. Reflecting
on the power which causes the fall of bodies to the earth, and bearing
in mind that this power is sensibly the same on the highest mountain
as in the deepest valleys, he conceived that it might extend far beyond
this earth, and even exert its influence through all space. He assumed,
in conformity to the relation already discovered by Kepler, between
the times of revolution of the planets and their distances from the sun,
that this force must diminish in the inverse ratio of the square of the
distance. His first results were unsatisfactory, because (as afterwards
appeared) he used in his calculations an erroneous value of the earth's
radius. But in June, 1682, he received Picard's new measurement of
the arc of the meridian in France, from which it appeared that the
radius of the globe was nearly one seventeenth greater than had been
previously supposed. Armed with these new data, Newton resumed
his calculations, and in 1687 published his great work, the " Principia,"
in which he develops the consequences of his great discovery of the
laws of gravitation.
60. Direction of terrestrial attraction. Centre of gravity.As the direction of a force is the direction of the motion or pressure
caused by it, (40), it follows that a body falling under the influence of
gravity moves on a line, which would pass, if extended, through a
point sensibly near the centre of the globe. This point   26
in the globe is called its centre of gravity. Therefore 
the direction of the force of gravitation is in the line
uniting the centre of gravity of the earth with that of
the attractive body. The plumb line, fig. 26, gives this
direction. Here a mass of lead is suspended by a string,
and when it is at rest, it is evident without a mathematical demonstration, that the direction of the pressure,
and hence that of the force of gravitation, coincides
with that of the plumb line. This direction is called
the vertical, and a direction perpendicular to it is called
the horizontal.  Such is the surface of a liquid at rest.
It is plain, on the slightest reflection, that as the
plumb line coincides at every point of the earth's surface very nearly




40               PHYSICS OF SOLIDS AND FLUIDS.
to the radius of the same points, that several plumb lines placed near
each other, are sensibly parallel to each other (but are not mathematically so), because the distances between them are almost insensible
compared to the length of a radius of the earth.  The convergence is
only one minute to a geographical mile.
The rotation of the earth does not affect the direction of a falling body,
because it had, before it fell, the same velocity as the earth itself. Thus a bullet
dropped from the mast-head of a ship, sailing never so rapidly, falls to the deck
on precisely the same spot as if the ship were motionless-in virtue of the principle of the composition of motion, (45). Nevertheless, if bodies fall from a
very great height, there is an easterly deviation, as Newton announced, because
at the point of departure, on a circumference sensibly larger than at the surface
of the earth, the body has a horizontal velocity sensibly greater than the latter.
For a height of 550 feet, calculation indicates a deviation of 0-108 inch, and
experiment gave Reich in the deep mines of Freyberg 0'110 inch.
61. Point of application of terrestrial attraction.-As every
particle of a body is equally attracted by the earth, there must be as
many points of application for this force as there are particles of matter
in the body. IIence from the principle (46) for finding the resultant
of a system of parallel forces, it follows that if a body be supported by
a flexible cord from a fixed point, it cannot remain at rest unless the
resultant of all the parallel forces which gravity exerts on it passes
through the point of support.
It is thus possible to determine experimentally the position of the
resultant of the system of parallel forces which gravity exerts upon
a body.
27          For example, in fig. 27,              28
the chair is held by a string
attached to one arm, and the
resultant of the forces ex-               7 - 
/^A U)^   erted by gravity is in the
line A B, in which the chair
comes to rest.  But if the
chair is supported from  another point, as in fig. 28, it 
will come to rest in a new
position, and the resultant
will now be found also in a 
new position, namely in the 
line CD, and so for every 
new point of suspension we
can  by cxpcriment demonstrate a  different position  for the  ro
sultant.




GRAVITATION.                          41
62. Centre of gravity.-As there is in every solid body a point
about which, when it is suspended, its molecules are equally distributed in every direction, all the attractions exerted upon them may
be replaced by a single resultant force applied at this point. But
whatever position the body may assume, the resultant of its parallel
forces of gravity will always pass through the same point. This common point, of intersection of the resultants of gravity in any body, i~
called the centre of gravity. As we may find the resultants experi
mentally, so also is the centre of gravity of any solid    29
easily found. If any irregular solid is suspended, as in
fig. 29, its centre of gravity will lie in the line c d, prolonged through its axis. It will alst lie in the line a b, 
by which the body is a second time suspended, and being
found in both lines, it must necessarily be at their inter- 
section. A correct conception of the important relations ac.. —----
of the centre of gravity lies at the foundation of the
whole science of mechanics, and  especially of equilibrium.
63. Corollaries.-(1.) The centre of gravity must be regarded as
the point of application of the resultant of the forces which gravity
exerts upon the molecules of any body. This is proved by the fact
that the point of application is any point on the line of the resultant,
and that the centre of gravity is a point common to all the resultants.
(2.) When the centre of gravity is supported, the body remains at
rest. Conceive the irregular mass, fig. 29, to be sustained on an axis
passing through ab or cd, the body will remain at rest in whatever
position of revolution it may be, on either of these axes, since the whole
intensity of the forces of gravity is expended in pressure against the
points of support.
(3.) The sum of all the attractions exerted by any mass of matter
may be conceived as proceeding from its centre of gravity. Newton
has demonstrated that a particle of matter placed without a hollow
sphere is attracted in precisely the same manner as if the whole mass
of the sphere were collected at its centre, and constituted a single particle there. The same must be true of solid spheres, since they may be
regarded as made up of a great number of hollow spheres, having the
same centre.
The principle that action and reaction are equal and opposite (27),
applies perfectly to the mutual attractions of the masses of matter.
Hence follows the somewhat startling inference that the earth must
rise to meet a falling body. This is unquestionably true, but since the
mass of the earth is almost infinitely greater than that of any body




42               PHYSICS OF SOLIDS AND FLUIDS.
falling on its surface, its motion must likewise be almost infinitely
small, since the velocity v', acquired by the earth at the end of one
second is as much less than the velocity v, acquired by the falling
body, as the mass of the body (m) is less than the mass of the earth
(M), or V: v - m: lt.
64. Centre of gravity of regular figures.-In case of solids which
have a regular figure, and uniform density, it is not necessary to resort
to experiment.  In such bodies, the centre of gravity coincides with
the centre of figure, and to find it is a question purely geometrical.
The truth of this assertion may be shown, if we suppose a plane or
line to be divided into two equal and similar parts, so that its molecules are arranged two by two, with respect to the dividing line. Take
any two molecules similarly situated, on opposite sides of the division,
their attractions will be equal and opposite; and so also of every other
pair; therefore, the resultant of the system must be at the point of
division, and the centre of gravity is there also.
The centre of gravity of a circle, or sphere, is at the centre of each;
of a parallelogram or parallelopiped, at the intersection of the diagonals;
and of a cylinder at the middle point of its axis. To find the centre
of gravity of a triangle, fig. 30, draw a line A D, from the vertex to
the middle point of the base; it will                 30
divide equally all the lines, as m n, drawn 
parallel to the base.  If the triangle is
placed so that the line A D  may be 
exactly over the edge of the prism  P Q,    In
each one of the rows of molecules composing the figure, as m n, will be in 
equilibrium on the edge of the prism,  l-. —"  
since it is supported at its centre.  The 
same will be true when they are united,                 Q
and the triangle will not tend more to one side than another; hence its
centre of gravity must be in the line A D, and for a like reason, also
in the line BE (situated similarly to A D), and therefore at their intersection G. It may be shown geometrically that the point, thus found
divides the line joining the summit and the middle of the base, into
two parts, of which the one nearest the vertex is double that nearest
the base.
SUPPORT OF A TRIANGULAR MASS AT ITS ANGLES.-If it were required to support a triangular block of marble at its angles, we may find what part of the
weight will be sustained by each support, by applying the foregoing principles.
The weight of the block, fig. 31, which we will suppose to be 45 lbs., is a force
applied to its centre of gravity, g. We have stated that the distance b g is twice




GRAVITATION.                             43
the distance g d, and hence we may resolve the vertical force of 45 lbs., acting
at g, into.two others; one of 15 lbs. at b, and the        31
other of 30 lbs. at d; but the last force, since it acts       b
at the middle point of a c, may also be resolved into          \
two others of 15 lbs. each, acting the one at a, and   \
the other at c. Hence the weight of the triangle is                   a
equivalent to three equal forces acting vertically at     d
its angles; and the three points of support sustain 15              1
equal pressures, whatever may be the form of the         3a
triangle.                                                   45
65. Centre of gravity lying without the body.-The  centre
of gravity is not, necessarily, in the body itself,        32
but may be in some adjoining space.  This is
evidently true of the solid ring, fig. 32, and
generally of any hollow  vessel, of whatever
form.
Of a compound body, the centre of gravity is
easily found by composition of forces, when the
weights and centres of gravity of the parts are
known.
66. Equilibrium  of solids supported by an axis.-A solid is in
equilibrium when its centre of gravity is supported. This is according
to. 63. But this condition may be fulfilled in different ways, according
to the method of support. If a disk of uniform density, fig. 33, is supported by an axis, passing through the centre a,             33
which is also its centre of gravity, it will be in
that sort of equilibrium which is called indifferent,   /-~.
because it has no tendency to revolve, either to the  /;
right or left, but remains at rest in all positions...........
If the axis passes through b, the disk will be in \ v.           g
stable equilibrium; for if it is turned about its  \
axis, the centre of gravity will move in the arc m n,
and being no longer vertically below the axis, it will not be directly
supported by it, but tends always to return to its former position. If
the axis is at c, the equilibrium is unstable; for, if the centre of gravity
is in the least removed from a position vertically above the axis, it
cannot return, but it will describe a semicircle in its descent, until it
comes to rest exactly below the point of support.
In general terms, therefore, a body attached to an axis may be in
stable, unstable, or indifferent equilibrium, according as its centre of
gravity is below, above, or upon the axis.
67. Equilibrium  of solids placed upon a horizontal surface.In bodies placed upon a horizontal surface, the centre of gravity, as in




44              PHYSICS OF SOLIDS AND FLUIDS.
those which are suspended, tends to descend, and if the bodies are free
to move, they will rest in one of the positions of equilibrium just
named. If rays are drawn from the centre of gravity to every part of
the surface, some of these rays will be oblique, and some perpendicular,
or normal to the surface, whatever may be the external form of the
body; and among the normal rays, there is generally a longest and a
shortest ray. If the body rests upon the plane, at the extremity of one
of the normal rays, its centre of gravity is evidently in the vertical line,
drawn through the point of contact, and the body is in equilibrium.
But if it rests at the extremity of an oblique ray, the centre of gravity
is not supported, since it is not in the vertical of the point of contact,
and the body falls.
If the normal ray at the point of contact is neither longest nor
shortest, but simply equal to the'adjacent rays, the equilibrium is indifferent.  Such is the case with a sphere, placed on a level plane; it
rests in every position, for its centre of gravity can-   34
not fall lower than it is. But this position cannot
be assumed by a body not strictly spherical. For
example, if an egg rests at the extremity of a longest
descending ray, a, as in fig. 34, it will be in unstable'equilibrium, since motion to either side tends to'/J)
lower the centre of gravity, and enable it to fall; but
if it rests at the extremity of a shortest ray, a', it 
will be in stable equilibrium, since any motion side-     w
ways must raise the centre of gravity, and it will, therefore, fall back
to its original position.
68. Centre of gravity in bodies of unequal density in different parts.-If the density of a body is unequal in different parts,
its centre of gravity will be external to its centre of magnitude, and
the body can come to rest in only                 35
two positions, when the centre of            b
gravity is at the highest, and at the
lowest place in the vertical of the   /
point of contact. If a cylinder of         e ---
this description were placed upon an 
inclined plane, as in fig. 35, it would
be in equilibrium when its centre of 
gravity was at either e or a; if at e,
and the cylinder were moved a little to the right, the centre of gravity
would fall through the arc e a, but at the same time the cylinder itself
would perform the apparent contradiction of ascending the plane.
69. Equilibrium of bodies supported in more than one point.



GRAVITATION.                           45
When a body is supported by two points, the vertical, from  its centre
of gravity, ought to fall on the centre of the line which connects them.
If a body has four points of support, as a common table, the vertical
should fall upon the intersection of their diagonals.
In carriages, if the vertical falls in a different manner, the load is improperly
distributed, and the carriage will be liable to upset, in passing over an uneven
road.
A body resting on a base more or less extended, will be in equilibrium
only when the vertical from the centre of gravity falls within the area
of the base; and the body will stand firmer in proportion as the centre
of gravity lies lower, and the base is broader. A pyramid is, therefore,
the most stable of all structures.
The singular feats exhibited by chile*is  toys,-and by rope-dancers, depend
on the facility with which the centre of gravity is shifted.
6 2. Laws of Falling Bodies.
70. Gravity is a source of motion.-In discussing the laws of
motion, we have already cited gravitation as a source of uniformly
accelerated motion. We have now to consider the laws of falling bodies,
and in doing so we shall have occasion to recapitulate some of the
ground already passed over.
71. The laws of falling bodies are five, as follows:
THE FIRST LAW Is —-The velocity of a falling body is independent of its
mass.
Galileo (born 1564), who first demonstrated the laws of falling
bodies, at Pisa, argued that if the molecules of a body were separated
from each other, each molecule would fall with the same velocity, since
each is solicited by the same force; and if we conceive these molecules
reunited into a mass, each particle still acts alone, and hence it is of no
importance whether the particles are many or few. The velocity of the
mass will be that of one of its particles-and, consequently, is independent of the mass.
THE SECOND LAW Is-The velocity of a falling body is independent of
the nature of the body.  Experiment alone can confirm this law, which
at its first statement appears to be contradicted by common observation.
For example: a gold coin falls swiftly, and in a straight line, but a piece
of paper descends in a devious course, and with a slow, hesitating motion.
The popular explanation is, that the coin is heavy and the paper light; but
this cannot be the true reason, since, when the gold is beaten out into thin
leaves, its weight remains the same, but the time of its fall is very much,rolonged.
7




46              PHYSICS OF SOLIDS AND FLUIDS.
The differences in the time and manner of falling are caused so ely
by the resistance of the air; which resistance varies,    36
according to the shape and volume of the body, and
not according to its mass, or the number of particles 
contained in it. This conclusion is established by the
guinea and feather experiment, first devised by Newton, who used a glass tube 10 feet long, arranged as
in fig. 36, with a stopcock for removing the air by an airpump. Bodies of unlike density, as a coin and piece of
paper, within the tube will, when it is suddenly inverted,
be seen to fall with equal rapidity, and strike the bottom
together; but after admitting the air, the one will descend
swiftly, and the other will be retarded, just as it happens    l
when they fall under ordinary circumstances. A piece
of stiff paper, cut to the exact size of a coin and placed on
it, will fall with it, if care is taken to drop the two quite
horizontally, and without disturbing the position of the
paper on the coin. This simple experiment illustrates the
law as well as the vacuum  tube, the resistance of the air
being all met by the coin. Thus, when no resistance
modifies the effects of gravity, it attracts all bodies with
the same energy, and gives them the same velocity, whatever may be their weight, and whatever the kind of matter of which they are composed.
THE THIRD LAW Is-The velocity acquired by a body
falling freely from a state of rest is proportional to the
times, and follows the order of the natural numbers 1, 2, 3,
&c. This is the case of a uniformly accelerated motion, (32).
THE FOURTH LAW Is-The whole spaces passed over by a
falling body, starting from a state of rest, are proportional
to the squares of the times employed in falling-while the
spaces fallen through in successive times'increase as the
odd numbers. 1, 3, 5, 7, &c. The velocity of a body when
it begins to fall, is nothing; but from that moment it regularly increases. Let us represent the velocity acquired at the end of the
1st second by g; then the average velocity during the same time will be,
0+g
2 -   YS
the arithmetical mean between 0, the starting velocity, and v, the final
velocity. A body moving at this rate, will traverse the same space in




GRAVITATION.                          47
one second which it would have fallen in one second; let this space
= s; then the space being equal to the product of the velocity and the
time, Jg X 1 = s, or g = 2s; that is, the final velocity acquired by a
body falling one second, is double the space through which it has fallen.
It has been ascertained that in latitude 45~ this space is about 16 
feet, (16-08538 feet, see 90) and g = 321 feet.
In the 2d second, the body starts with a velocity of g = 321 feet, and
acquires, at the close, the velocity of 2g = 641 feet. The space fallen
during the same time is 481 feet; viz. 321 feet by the velocity acquired
during the first second, and 161- feet by the gradual action of gravity
in this second only. Or as before, the space described by the body
during the 2d second, is equal to the space it would have fallen with
the mean velocity between its initial and final velocities; i. e. with the
velocity
g + 2g   3g
2       2
the space, therefore, = 3 X 16i.  = 481 feet.
In the same way we find that the velocity acquired at the end of the
3d second, will be 3g= 961 feet; and in the same time the body will
have fallen, with the mean velocity,
2g+ 3g    5g
2        2
through a space of 5s = 5 X 16l  = 80 5 feet.
A falling body, therefore, descends, in the 2d second of its fall,
through three times, and in the 3d second, through five times the space
fallen in the first second. Or in the words of the 4th law, the spaces
increase as the odd numbers.
Whole space described by a falling body.-We have seen that
the time of falling, and the final velocity, increase in the same ratio; and
that the average velocity of any fall, is exactly half the final velocity,
and the whole distance fallen is the same as if the body had moved at
a uniform rate, with a mean velocity; hence, any increase in the time
of falling is attended by a corresponding increase of the average
velocity during the whole fall. But the whole space described in any
fall is jointly proportional to the time, and the average velocity; if,
therefore, the time is doubled, the body falls not only twice as long, but
also twice as fast, and it must descend through four times the distance.
Again, if a body falls three times as long as another, it also falls with
three times the average velocity, and descends, altogether, through
nine times the distance. The tines being represented by the order of
the natural numbers, 1, 2, 3, &c., the spaces are represented by their
squares, 1, 4, 9, 16, &c.




48              PHYSICS OF SOLIDS AND FLUIDS.
THE FIFTH LAW IS-A body falling freely from a state of rest acquires,
during any given time, a velocity which would, in the same time, carry it
over twice the space already traversed.
We have seen that a body falling for any time, acquires a final velocity which is double the average velocity of the fall; if, therefore, the
action of gravity were suspended at the end of any given time, and the
body continued to move with its acquired velocity, it would, in the
same time, traverse twice the distance it had already fallen. For
instance, the space fallen through in three seconds is 1441 feet, and
the final velocity is 961 feet; now a body falling uniformly, for three
seconds, with this velocity, would pass through a space of 3 X 96 =
289 -_ 2 X 1441 feet.
TABLE EXPRESSING THE LAWS OF FALLING BODIES. —The following table
expresses the 2d, 3d, and 4th laws: (See 32.)
Times,                   1, 2, 3,  4,  5.
The final velocities,    2, 4, 6,  8, 10.
The space for each time, 1, 3, 5,  7,  9.
The whole spaces,        1, 4, 9, 16, 25.
Let D = the distance, t == the time, V= the final velocity, and g -
the velocity acquired during the first second, then from the foregoing
laws we may deduce the following equations, by which practical questions are readily solved.
(1.) V= gt, whence (2.) t  -.
9
(3.) D =  gt2, whence (4)t =   D
g
By substituting in (3) the value of t (2)
v2    V2
D- g X  2
2X =g
And substituting (4) in (1),
V — g   2     J -- 2gD.
72. Verification of the laws of falling bodies; Atwood's Apparatus.-It is evident that the third and fourth laws of falling bodies
cannot be verified by direct experiment; both because the results of
such a trial would be disturbed by the resistance of the air, and',ecause the velocity of the fall is too great to be followed by the eye.
ut there are mechanical contrivances by which the intensity of the
force of gravity may be diminished, without changing its nature. We
can cause a falling body to descend so slowly that the resistance of the




GRAVITATION.                               49
air becomes imperceptible, and all the circumstances of the fall may then
be observed with entire precision.  Galileo               37
used an inclined plane to verify his laws, 
but a far more exact form of apparatus is
now in use for this purpose, called, from the
name of its inventor, Atwood's apparatus
This apparatus, fig. 37, is composed of a ver- 
tical column, about eight feet in height, surmounted by a large wheel, moving with the
least possible friction, and upon which is suspended a fine silk cord, carrying equal weights, 
B B', at its extremities. A scale of feet and
inches is marked on the standard, parallel to the
path of one of the weights, to measure the spaces
through which it falls, and the corresponding               i2
times are shown by the seconds pendulum. To
insure the simultaneousness of the fall with the 
beat of the pendulum, the weight is set in mo- 
tion by the fall of the tablet H, which is released
by the action of an electro-magnet, G, (seen on
a large scale in fig. 38), acting as will presently
be explained. The weights B and B' being
equal, the force of gravity has no effect upon             i
them, and they remain at rest in any position.
But let one of them, as B, be increased by a
small additional weight, B", and the equilibrium  will be immediately disturbed. The
weight of B" being the only disturbing force, 
the motion produced is of the same kind as the            I    c
motion of a body falling freely, but the rate of
acceleration and the space fallen through, are
each as much less as the mass of B" is less than
the combined masses of B" + 2 B.                      3    j
The form and relation of B and B" are more 
clearly shown in the enlarged scale of fig. 38.
For example; let B" be a quarter of an ounce,
and the weights B and B' be each 24 ounces,
or 96 quarter ounces. The whole mass to be
moved, by the action of gravity upon B" only,
is 193 times the weight of B", and therefore the
velocity imparted, and the space fallen through,  l 
must be 193 times less than the velocity and
space of B" falling freely.
In the apparatus here figured, the beats of
the seconds pendulum  are announced by the
bell, whose hammer, I, is struck by the electromagnet, G, as neatly constructed by Ritchie.
A point, E, on the pendulum rod, just touches a drop of mercury as it passes
the vertical line, and thus completes for an instant the circuit of a voltaic
battery, whose terminal wires are shown at the base of fig. 37.
7*




50                PIYSICS OF SOLIDS AND  FLUIDS.
The electro-magnet then acts, and its armature, G' I', moves to the poles
of G, thus releasing, first the tablet H, and with it     38
the weight B, and next announcing the successive 
seconds upon the bell, at each swing of the pendulum.  No clock-movement is required to secure 
the accurate beats of the seconds pendulum during 
the short period of a single experiment. Now B,
with B" attached to it, will fall from the tablet 11,  
at the instant the first sound of the bell is heard,
following the first swing of the pendulum. At the        
instant of the next ring, the weight will be seen to
have fallen exactly 1 inch; during the second beat,
through three inches more; during the third beat, 
through 5 inches; during the fourth beat, through 7
inches, &c., according to the fourth law.
In the same experiment it appears, that the whole 
space fallen through at the end of the 1st second, is
1 inch; at the end of the 2d second, 4 inches; at
the end of the 3d second, 9 inches; at the end of the 
4th second, 16 inches, &c., according to the first 
clause of the 4th law.
To demonstrate the 3d and 5th laws, it is necessary to arrest the accelerating force at a given mo-   B3i
ment. This is accomplished by giving to B" the
form  of a slender bar, as shown in fig. 38, long
enough to be caught by the sliding stage C, while B continues its course with
a uniform velocity, from the time it ceases to be acted on by the gravity
of B". The velocity at the end of any second is determined by the space
traversed during the next second. If the stage C is fixed at the distance
of one inch from  the top of the scale, B" will be detached at the end of
the first second, and B will descend uniformly through two inches during
each succeeding second. If the ring is fixed at the fourth division, the bar will
strike at the end of two seconds, and B will pass on at the rate of four inches
per second. By the use of this simple and ingenious apparatus, a most satisfactory experimental demonstration of the truth of Galileo's laws of falling
bodies is obtained.
Morin's Apparatus.-Another apparatus for the verification of these
laws has been contrived by Morin, a French physicist, in which the velocity of
the falling body is not retarded, and the error from atmospheric resistance is
made inconsiderable by the use of a large weight. The falling body carries a
crayon which marks a line on a rapidly revolving vertical cylinder, covered with
paper, and divided by vertical and horizontal lines, representing respectively
time and distance. The line drawn by the crayon carried by the falling body is
a portion of a parabola, a curve whose distance from each division on its vertical axis is as the ratio of the squares of the successive divisions on that line.
73. Application of the laws of falling bodies.-The laws of
falling bodies apply equally to every motion produced by a uniform
force or pressure.
In every such motion, the velocities are proportional to the times elapsed
since the motion began; the final velocity is twice the average velocity; the




GRAVITATION.                               51
spaces described in equal successive times, increase as the odd numbers; and
the whole spaces increase as the squares of the times in which they are described.
But in each instance the velocity acquired, and the space described in a given
time, will be different; and the rate of acceleration will never be so rapid as in
the case of a body falling freely, because in no other instance will the force be
so great in proportion to the quantity of matter moved.
74. Descent of bodies on  inclined  planes.-When a body is
placed upon an inclined plane, it descends, as just explained, with a
uniformly accelerated motion, but its velocity is less than that of a body
falling freely.  The weight of the body,                  39
or its gravitation, represented by the line a
e g, fig. 39, is resolved (50) into two
components, one of which, ef (or p g), is
perpendicular to the plane, and produces                       e
pressure only, and the other, ep (orfg),
is parallel to the plane, and is the cause
of the accelerated motion. The triangles
efg and a b c being similar, their corresponding sides are proportional, and 
we have                                     c
fg: eg =ac: ab;
that is, the rate of acceleration on an inclined plane, is to that of a body
falling freely as the height of the plane is to its length.
The final velocity depends on the height of the plane. In      40
fig. 40, let a c, the height of the plane, be i of its length a b; a
then, that part of the weight of the body which produces       d
motion, is i of the whole force, and the velocity acquired,. 
and the space traversed in one second, by the action of this
force, would be * of the velocity and space of a body falling
freely. Let the line a f represent 161- feet, and take a d,
equal to * of a f; then, a body starting from a would arrive
at d in one second, or, falling freely, it would reach f in the
same time.
Draw the horizontal line e d; the ratio of a e to a d is the  f
same as the ratio of a c to a b; that is, a e is equal to i of a d; and a d having
been taken equal to i of a f, a e is   of a f. Since the spaces increase as the
squares of the times, the body that would fall to f in one second would fall to
e in i of a second; and (3d law) the velocity acquired at e would be i of the
velocity acquired at f. But we have already seen, that the velocity acquired
by a body descending to d, is * of the velocity acquired by the same body
falling to f, in the same time; hence the velocity of a body descending the
inclined plane to d, is equal to that of a body falling freely to e; and generallyThe velocity acquired at any given point on an inclined plane, is
proportional to the vertical distance of that point below  the point of
departure.




52              PHYSICS OF SOLIDS AND FLUIDS.
From this it also follows that the average velocities are the same in
descending all planes of the same height; and, therefore, the times of
descent are proportional to their lengths.
75. Descent of bodies on curves.-It was shown by Galileo that
all bodies starting from a horizontal plane with equal initial velocities
arrive at the level of a second horizontal plane with equal velocities,
whatever kind of curve they may have passed over. This is a general
truth of which the statement at the close of the last paragraph is only
a particular case. From these principles it follows that the velocity
acquired in descending any regular curve is the same as would be
acquired in falling fieely by gravity through the same vertical height.
But the time of descending a curve, concave upwards, is less than is
required to descend an inclined plane between the same points, while
for descending a curve convex upwards a greater time is required.
76. Brachystochrone; or curve of swiftest descent.-it was
demonstrated by J. Bernoulli, and is confirmed by experiment, that
a body descending a cycloid, whose base is horizontal, reaches its
goal in less time than by any other path between the same points. The
cycloid is a plain curve, described by            41
a point on the circumference of a 7i
wheel, rolling on a level surface without slipping. The curve hd in the
triangle hkd, fig. 41, is part of a  
cycloid.
At first it would seem  that the                            d
straight line hd, being an inclined plane, would be the brachygtochrone, since it is shorter than the cycloid joining the same points,
but the latter descends very rapidly at first, and so the falling body
acquires near its starting point a much higher velocity than it would
on the inclined plane. This increased velocity it adds to each of its
subsequent movements, and though its velocity on arriving at d is no
greater than if it had passed down the inclined plane, it arrives there
in a shorter time than it could by any other path. Another curious
property of the cycloid is, that a body will descend from h to d in this
curve, in the same time it would descend to d fpm any intermediate
point in the cycloid.
77. Action and reaction of a falling body.-On arriving at the
bottom of a plane or curve, a body will have acquired (5th law) a velocity, such as would carry it, in the same time, over a distance equal to
twice the length of the descent, or cause it to ascend another similar
curve. The ascent of the body being opposed by the constant force of
gravity, will be retarded at a rate which exactly corresponds with its




GRAVITATION.                          53
previous acceleration. On the double curve A B C, fig. 42, the body
will have equal velocities at any                42
two points at the same level, as at
E and D; and the velocity being 
nothing when the body has arrived      C  
at C, it will descend again and..
mount to A, the point from which 
it first started.  This alternate                B
movement being caused by the constant force of gravity, would continue for ever, and furnish an instance of perpetual motion, were it not
for the resistance of the air and friction, by which the body is gradually
brought to rest at B.
The pendulum is an example of a body alternately ascending and descending
a very small circular curve.
Q 3. Measure of the Intensity of Gravity.
I. PENDULUM.
78. The pendulum.-Any body suspended by a flexible cord, or
wire, from a fixed point of support, is a pendulum. A plumb line is
a pendulum, and when it is at rest, as we have seen (60), it shows the
exact vertical, and indicates the direction of the force of gravity. But
if it is moved from the perpendicular into any other position, and left
to fall, the pendulum swings in a vertical plane, and rises on the other
side of the vertical to a height equal to that from which it had fallen.
The cause of these alternate movements is gravity, and the motion is
called an oscillation.
To aid in the study of the movements of the pendulum, mathematicians distinguish between the simple, or mathematical pendulum, and
the compound, or physical pendulum.
79. Properties of the simple pendulum.-The simple pendulum
consists, by mathematical conception, of a single heavy particle of
matter, suspended at the extremity of a line, without weight, inextensible, and perfectly flexible. Such an instrument is purely ideal, and
is conceived of only as a convenient means of investigating the laws of
the real, or physical pendulum.
Let C M, fig. 43, be a simple pendulum, in a vertical position, and
consequently in equilibrium. If it is moved to the position C m, the
weight m P, acting at the point m, is decomposed into two components,
m B acting in the direction C m, and consequently destroyed by the
resistance of the point of support, and m D perpendicular to C m,
which solicits the return of m to the position of equilibrium. This'ast




54             PHYSICS OF SOLIDS AND FLUIDS.
component is equal to g sin. a; calling g the accelerating force of gravity,
represented by m P, and a the angle m C M, or        43
D A m, which is the same thing.
It is plain that the component m D must
diminish with the angle a, that is in proportion
as the pendulum approaches the point of equilibrium C M. The accelerated velocity of its
fall is therefore not a case of uniform acceleration, since it becomes null when the pendulum
is vertical.
The pendulum does not however rest at M, 
but, in virtue of its acquired velocity (momen-  
tum), it rises through an equal ascending arc.
M n, with a retarded motion, since the component of gravity, tangent to the arc described, is
now turned in the opposite direction-so that this component diminishes
the velocity at each point of M n, by a quantity equal to the increase
of velocity acquired at the corresponding points of m M, and equidistant from M. Thus the acquired velocity is entirely destroyed when
the pendulum  has passed over the arc M n, equal to M m. At n it
rests for an inappreciable instant, after which it returns again to M,
mounts to m, and would thus continue moving for ever like the ball
rolling in a double curve (77), supposing it met no resistance from
friction and the air.
Each swing, from n to m, or m to n, is called an oscillation, and one
half the angle n C m, or one half the arc n m, which measures it, is
called the amplitude of the oscillation. The time occupied in describing the arc m n is the time or duration of an oscillation. The angle
of elongation n C M, or M C m, measures the deviation of the pendulum from the vertical.
80. Isochronism  of the pendulum.-From the last section it is
evident that the movements of the pendulum, on each side of the vertical, are made in equal times. But it is also true that the duration of
an oscillation is always the same, in the same locality, and provided
the angle of elongation, n C M, fig. 43, does not exceed 4~ or 5~.
Within this limit the time of oscillation is sensibly the same, and the
pendulum requires as much time to describe an arc of one-tenth of a
degree as one of ten degrees. The explanation of this curious and most
remarkable fact is to be found in the varying length of the component
D m, fig. 43, which increases with the angle of elongation. Hence,
the greater length of arc is exactly compensated by the greater velocity
with which the pendulum describes it. This is what is meant by the




GRAVITATION.                          55
isochronism of the pendulum-from two Greek words, meaning equal
times. This isochronism is not, however, absolute, unless the amplitude of the oscillation is infinitely small.
81. Formulae for the pendulum.-The property of isochronism,
and the other properties of the simple pendulum, when the amplitude
is infinitely small, are comprised in the formulaT=7r4T:
T representing the duration of an oscillation, 1 the length of the pendulum, 7r the relation between the circumference and diameter of a
circle (equal to 3'1416), and g the accelerating force of gravity.
If the amplitude of the oscillations is not infinitely small, the formula
becomes, for ordinary limits,
T=7rl (1-a).
where a is one-half the length of the arc n m, fig. 43. It requires the
aid of the higher mathematics to demonstrate these formulae fully, but
we may deduce from them the following important propositions:
82. Propositions respecting the simple pendulum.-lst. Oscillations of small amplitude are made in times sensibly equal. By substituting in the first formula I = 39-14056 inches, as determined by experiment, for the seconds pendulum at London, and let T== 1, we shall
find the accelerating force of gravity, g-32-175 feet. Substituting
these values of g and I in the second formula, and also a = 3'1416 - 90
= 0-0349, we shall have for the time of vibration when the elongation
is four degrees on each side of the vertical T-= 1000076, which differs
from the time of vibration, when the arc of vibration is infinitely small,
by only seventy-six millionths of a second.
2d. The duration of an oscillation in pendulums of different lengths,
is proportional to the square root of the length of the pendulum. This
law may be demonstrated experimentally by comparing pendulums of
different lengths. If the lengths are in the ratio of 1, 4, 9, then the
times of oscillation will be as 1, 2, 3, respectively. Let three such
pendulums, arranged as in fig. 44, commence to oscillate at the same
time; it will be found that the one-foot pendulum makes two oscillations for each oscillation of the four-foot pendulum, and three oscillations for each one made by the nine-foot pendulum. The time of
oscillation, and the length of the pendulum being known, we may
determine by this law. 1st, the length of a pendulum which would
oscillate in any proposed tine; and, 2dly, the time of oscillation of a
pendulum of any proposed length. For the times of oscillation are as




56              PHYSICS OF SOLIDS AND FLUIDS.
the square roots of the lengths, or, what is the same thing, the
lengths are as the squares of the times.                   44
Or mathematically, by substituting in the first equation
(81) C   -— \, which is a constant quantity at any given
place, the equation becomesT'= C / 1. For a pendulum of
any other length, as 1', we have T' = C1/ I' and comparing
the two
T: T' =/1'I:i/1':   and also
1:  - T2: T|'2.
3d. In a pendulum of invariable length the duration
is inversely proportional to the square root of the intensity of gravity. Hence,
1        1
T: T'"  _       \ -
where g' and g represent the intensity of gravitation at two
places.
83. The physical or compound pendulum:-Centre of oscillation.-The simple pendulum, as already
remarked, is only an intellectual conception, and cannot      9
be realized in experiment. Practically, we employ for the physical
pendulum  a heavy body, suspended by an inflexible rod from a fixed
point. The axis of suspension is usually a knife        45
edge of steel, resting on polished agate planes, or
hard steel. In the physical pendulum the rod has          c
weight as well as the ball; and nearly all the material points of both rod and ball are placed at
different distances from the point of suspension.
Let us examine the oscillations of any two of these 
material points, m and ni, fig. 45. If they were      f,.in- -^.
suspended by separate threads, then, according to
the 3d law, m would oscillate more rapidly than 
n; but if they are suspended by the same inflex- 
ible wire, they must move together, and make    -
their oscillations in the same time. The first *-..  -I
accelerates the second, and the second retards the,  i
first, so that their common velocity is intermediate between the velocity
of either of them, oscillating alone. Such a compensation takes place
in every oscillating body, and between the particles which are nearer
and those more remote from the point of suspension, there is always a
point so situated that it is neither accelerated nor retarded, but oscillates exactly as if it were suspended alone, at the end of a thread,




GRAVITATION.                            57
without weight. This remarkable point is called the centre of oscillation; and its distance from the point of suspension is the length of the
pendulum.  This is equal to the length of a simple pendulum which
would oscillate in the same time as the physical pendulum.
The position of the centre of oscillation depends upon the form, magnitude, and density of the several parts of the pendulum, and the position of its axis. If the rod of the pendulum is thick in proportion to
the ball, its centre of oscillation will be higher than in a contrary
arrangement. It is always below the centre of gravity, although whatever raises or lowers the centre of gravity will change the centre of
oscillation in the same direction. Whatever may be the positions of the
point of suspension, and the centre of oscillation, they are always interchangeable; i. e., if the pendulum is suspended by its centre of oscillation, these two points exchange their functions, and the oscillations are
made in the same time as before. It is by an experiment of this kind,
that the centre of oscillation, and consequently the length of a pendulum, is determined. This remarkable property of the compound pendulum was first demonstrated by Huyghens.
84. Application of the pendulum  to  the measurement of
time.-Galileo, to whom we owe the discovery of so many important
physical laws, discovered also the properties of the pendulum. When a
choir boy in the great Cathedral of Pisa (from whose bell tower-the
leaning tower of Pisa-he. demonstrated long afterward the laws of
falling bodies), and not yet eighteen years of age, his attention was
arrested by the great regularity of the movements of a lamp suspended
by a chain from the ceiling of the cathedral. This observation led him
to the discovery in question. Although Galileo attempted to employ
the pendulum to measure time, it was the great Dutch philosopher,
Christian V. Huyghens, to whom we are indebted for the invention
(in 1656) of the clock escapement, by means of which the pendulum is
made to perform its proper function as a time-keeper.* This apparatus
is seen in fig. 46.
An oblique-toothed wheel, R, called a rachet wheel, is moved by a weight and
cord. This motion is controlled by a piece, a b, called the anchor escapement,
placed above the wheel so as to oscillate on its axis of suspension, o o', at right
angles to the wheel. The oscillatory motion is imparted to the anchor a b by
the pendulum c P, which is made to communicate with the axis o o' by the
crotchet of. If the pendulum is vertical the apparatus is at rest, for then the
* " The Arabian astronomers, and more especially En-Junis, at the close of
the tenth century and during the brilliant epoch of the Abbassidian Califs, first
employed these vibrations" (of the pendulum) " for the determination of time."
(IHumboldt's Cosmos, Vol. 5, p. 19.)
8




58                PHYSICS OF SOLIDS AND  FLUIDS.
pallet b of the escapement holds the wheel by the point of one of its teeth.
If, however, the pendulum is then moved to                46
the left, the wheel is released and moves for-   C
ward by force of the weight, until the other
point of the escapement a again arrests its
motion; but the return swing of the pendulum          lO
in its turn disengages a, and the wheel R revolves the space of another tooth, when it is
again caught on b, and so on. The motion of
the wheel R is thus made up of small equal
advances, succeeding each other regularly with
the oscillations of the pendulum. The points
of the teeth on the rachet wheel, and also the 
points of the escapement anchor, are carefully
formed to offer the least possible friction and f  
resistance to motion.    1 
The pendulum  and escapement of a clock
are so arranged as to prevent the clock from
running down, except by the regular and
measured velocity indicated by the movement
of the pendulum  and escapement. On the
other hand, the escapement is so constructed 
that the rachet wheel imparts to it a slight
pressure at every swing of the pendulum, sufficient to counteract the retarding force of friction to which the pendulum is subject. The
train of wheel-work, of which the clock is p
composed, serves to record the vibrations of
the pendulum, and indicate at once to the ob-    /
server the progress of time.
85. Cycloidal pendulum.-Owing to the resistance of the air, and
to friction, a pendulum unconnected with other machinery has the
amplitude of its vibrations gradually diminished, and vibrations varying greatly in amplitude, vary very sensibly in the time in which they
are performed. To make vibrations of different amplitude absolutely
isochronous, Huyghens conceived the idea of making the pendulum
describe a cycloid, which, it will be remembered, is the curve of swiftest
descent (76). The vibrations of such a pendulum would, in theory, be
absolutely isochronous; but the mechanical difficulties in the way of
adapting the pendulum to motion in this curve forbid its adoption.
A long, heavy pendulum vibrating in a very small circular arc, is found in
practice the most perfect, and is for this reason generally used in astronomical
clocks. The sources of error in the clock arising from inequalities of temperature will be considered in the chapter on heat.
86. Physical demonstration of the rotation of the earth by
means of the pendulum.-Mr. Leon Foucault, in 1851, executed the
first physical demonstration that had been made of the rotation of the




GRAVITATION.                          59
earth upon its axis. This remarkable and most interesting experiment
consists in suspending a heavy ball to a long and flexible wire, and
allowing the whole to vibrate freely, in the manner of a pendulum.
Under these circumstances it will be found, in these latitudes, that the
plane of vibration gradually changes its position, turning slowly from
east to west, or with the motion of the hands of a watch.
The connection between the motion of the pendulum  plane and the
earth's rotation, may be easily understood. A pendulum set in motion
will continue in the same plane of vibration, however the point of suspension may be rotated. This may be proved by holding in the fingers
a pendulum, made of a simple ball and string, and causing it to vibrate.
Upon twirling the string between the fingers, the ball will rotate on its
axis, without, however, affecting at all the direction of its vibrations.
The reason for this is obvious; the swinging pendulum, when about to
return (after an outward oscillation) from its point of rest, is made to
move from that point by gravity alone, and can, therefore, fall in but
one direction.
If a pendulum were oscillating at either of the poles of the earth, the
plane of revolution, as it would not change with the revolution of the
earth, would mark this revolution, by seeming to revolve in a contrary
direction, and in 24 hours it would make apparently the whole circuit
of 360 degrees. But, at the equator, the plane of vibration is carried
forward by the revolution of the earth, and so undergoes no change
with reference to the meridians. Between the equator and the poles,
the time required for the pendulum to make 360~, varies according to
the latitude, being greater the further from the poles.
The observed rate of motion of the plane of vibration nearly coincides
with that indicated by calculation. Thus, at New Haven (N. lat. 41~
18-'), the calculated motion, per hour, was 9'928~, the observed motion
was 9-97~. (C. S. Lyman.)
The greatest length of the pendulum wire hitherto employed was that
of 220 feet, in the Pantheon at Paris. At Bunker Hill Monument it
was 210 feet long; at New Haven 71 feet. The weight of the ball employed (usually lead), has varied from 2 to 90 pounds. The longer the
wire, and the heavier the ball of the pendulum, the greater will be the
probability of accurate results, for when the mass of the body ig great,
and its motion slow, the resistance of the air will have but comparatively little effect on the direction of the vibration.
87. The pendulum  applied to the study of gravity.-By the
pendulum we ascertain more accurately than by any other method the
truth of the first law of falling bodies; viz., that gravity acts equally
upon matter of every description (71). Newton, and more recently




60             PHYSICS OF SOLIDS AND FLUIDS.
Bessel, verified this law, by using a pendulum having a hollow ball,
which was filled, successively, with various substances-metals, ivory,
meteoric stones, wool, feathers, liquids, &c.-that could not be otherwise
submitted to trial. This experiment affords the most precise and unmistakable evidence that gravity (g) acts on all bodies in the same manner.
Since A is a constant quantity, the formula for the pendulum shows
that if T and I do not vary, g remains also constant.
88. Use of the pendulum for measuring the force of gravity.The value of the term g for any place may be easily obtained mathematically (the length of a pendulum which oscillates in a given time
(T) being known), by transposing the formula for the pendulum (81);
thus we have for the intensity sought1C2l
g   — =,  and assuming Tequal unity, then I is
the length of a seconds pendulum, and we have
g -- 21.
Experimentally, we may determine the intensity of gravity at any
place, by counting with exactness the number of oscillations made at
the place of observation in a given time, by a pendulum whose length
is known, and then dividing the time by the number of oscillations.
Any error in observing the time of a single oscillation is thus greatly
diminished, by subdivision, and by a sufficient number of repetitions
this error may be reduced to a quantity too small for consideration.
It was thus that Borda and Cassini, in 1790, measured with great
accuracy, the intensity of gravity at the Observatory in Paris, using a
pendulum composed of a platinum ball, suspended by a fine platinum
wire, upon knife edges of steel, resting on agate planes. The whole
was about four metres long, and its oscillations were counted, not
directly, but by means of an ingenious comparison with the motions of a
clock pendulum, placed a few metres behind, marking by a telescope
the occurrence of a coincidence in the vertical position of the two pendulums, and then observing the number of seconds before a coincidence
occurred again. The pendulums were inclosed in glass cases, to avoid
currents of air.
89. Value of g in these experiments.-After carefully eliminating the errors of experiment due to the influence of the air (the con
sideration of which would lead us too far into the refinements of this
subject for our limited space), Borda and Cassini found for the intensity
of gravity at Paris g = 98088 metres, equal to 32-1798 feet. This
value has been confirmed by Arago, Biot, and others, and slightly corrected by Bessel, by considering the loss of weight in air due to the
motion of the pendulum, giving the quantity g = 9-8096 metres.




GRAVITATION.                               61
Seconds pendulum.-On  the other hand, when we know  the
accelerating force of gravity, g, at any given place, it is easy to calculate the length of the simple pendulum vibrating seconds, assuming the
oscillations to be infinitely small.  Thus in the formula for the pendulum  (81), making T-=  I, and using for g the value determined for
the place, we have I = at Paris 0-993866 metre = 39-127 inches, and
corrections being made for the interference of the air, this quantity, as
determined by Bessel, is 0-993781 metre- 39-12367 inches.
II. MODIFICATIONS OF TERRESTRIAL GRAVITY AND THEIR CAUSES.
90. The intensity of gravity varies with  the latitude.-Very
numerous observations made with the pendulum, on different parts of
the earth's surface, have shown that the force of gravity is by no means
the same at all places, and particularly that it increases in going from
the equator toward either pole. This result is observed in the increasing length of the pendulum vibrating seconds, since by ~ 88, g is proportional to 1, the pendulum must be longer, as the force of gravity is
greater, to preserve the same time in oscillation.  The value of g for
any latitude is obtained with approximate accuracy by the formula
g     32-17076 (1-0-00259, cos. 2A), in which A is the latitude of the
place, and 32.17076 feet the value of g at latitude 45~. By substituting
for A, successively 0~ and 90~, we obtain at the equator g = 32-0874377
feet, and at the poles g = 32-254083 feet.
The following table of the variation in the length of the seconds pendulum, with
the latitude, is condensed from a large list in Saigey. (Physique du Globe,
p. 132, t. 2.)
Length of seconds
Places observed.        Latitudoes  pendulum in Ameri- Names of observers.
can inches.*
Spitzbergen,....   79~ 49' 58" N.   39-2161492        Sabine.
Greenland,....   74~ 32' 19" "    39-204339                "
St. Petersburg,...  59~ 56' 31" "       39-1704818     Lutk6.
Paris,.....         48  50' 14 "    39-1299322        Biot.
New York,....40~ 42' 43" "            39-1023743     Sabine.
Jamaica, W. I.,...  17~ 56' 07"."     39-0362352        ~
St. Thomas, W. I.,..   0~ 24' 41" "    39-0216688          "
Maranham,....   2  31' 35" S.    39-0126141          Foster.
Rio Janeiro,...    22~ 55' 22" "    39-0452899  Basil Hall.
Cape of Good Hope,.33~ 55' 56" "    39-0795405          Fallows.
Cape Horn,..         55~ 51' 20'"      39-1567028      Foster.
N. Shetland,...    62~ 56' 11'"      39-1807176   "
* In reducing Saigey's table of lengt~ of the seconds pendulum at different
localities, to American inches, the French metre has been taken at 39-36850535
inches, as adopted by the United States Coast Survey.
8*




62              PHYSICS OF SOLIDS AND FLUIDS.
Numerous observations on the U. S. Coast Survey, and elsewhere,
show that the value of g is by no means rigorously the same at all'
points on the same parallel; a discrepancy to be explained only by
supposing an inherent difference in the constitution of the earth's crust
at different places.
The variation of gravity with change of latitude is due to two causes.
1st. To the flattening of the earth at its poles. 2d. To the centrifugal
force created by the revolution of the earth upon its axis. The last
cause also, beyond doubt, induced the flattening of the poles in the
earlier history of our planet.
91. Influence of the earth's figure upon gravity.-Until 1666
the perfect sphericity of the earth had not been questioned, although in
the preceding century the flattening of the planet Jupiter at the poles
had been observed. Subsequently (in 1672), Richer, sent by the
Academy of Paris to Cayenne, remarked that his pendulum no longer
beat seconds at the latter place, until it was shortened a line and a quarter from its length at Paris. This observation at once indicated a less
force of gravity at Cayenne than at Paris, and suggested doubts respecting the sphericity of the earth. Huyghens attributed this diminution
of the force of gravity to centrifugal force, and conceived that the earth
must be bulged out at the equator.
Huyghens and Newton, assuming that the earth had bdome solid
from an originally fluid mass, whose particles attracted each other,
subject to the laws of hydrostatics and of the centrifugal force, arrived
at the conclusion, from mathematical calculation, that the earth's figure
was that of an oblate spheroid, whose polar diameter was about 26
miles less than its equatorial. Laplace            47
reached almost the same conclusion, by
calculating the effect of the equatorial
mass on the motions of the moon. The 
effect of the centrifugal force upon a 
yielding mass, may be shown by the ap-    fv —- -
paratus, fig. 47. Two circles of wire, or.-'.
flexible metallic ribbons, are attached
below to an axis, and above to a sliding    \   
ring, and being rapidly rotated by the'
whirling table, the circles flatten in the..
direction of the axis, and bulge at the
equator, as shown by the dotted lines.
But it was only by the actual measurement of an arc of meridian
that the exact figure of the earth became known. This important geodesic operation was undertaken, by La Condamine and others, in 1736




GRAVITATION.                             63
in Peru, by order of the French government, and way less accurately
performed by Picard in France, in 1669.  This operation led to the
conclusion (since demonstrated by numerous similar measurements),
that the successive arcs on the same meridian, comprised between two
verticals forming an angle of 1~, become larger and larger as we advance toward the poles. Consequently, the equatorial radius is greater
than the polar, and the plumb line will point to the centre of the earth
only in one of those radii.
The astronomers Mason and Dixon, who, in 1764-6, established the
boundaries between Pennsylvania, Delaware, and Maryland, afterwards,
in 1768, re-measured a line of 538,067 feet, with great accuracy, very near
the meridian, for the purpose of determining the value of an are. Fourfifths of this (434,011-e46) was one unbroken line, without triangulation,
on a vast level plain. They used rods of fir, frequently compared with a
standard brass measure at a fixed temperature. They found the length
of a degree of latitude to be 36S,763 English feet. (Phil. Trans. 1768.)
The general results may be illustrated by the following diagram.
Let the line A P, fig. 48, represent a quad-        48
rant of a meridian, of which 0 P is the polar,
and 0 A the equatorial radius. Let us take
stations on this meridian, one degree distant
from each other, commencing from the equator, and from each station prolong the direc- 
tion of the plumb line until it intersects the
plumb line similarly produced from the pre- 
vious station; a b c are three such points, and          /
it is plain that the intersections of the plumb
lines from each of the ninety verticals on the
quadrant, would together evolve the curve  o
a b cp, and the same if the stations were in-                        A
finite. Objects on different parts of the earth's 
surface are not attracted to a common centre
of gravity.  The centre of gravity for any
point, A, B, C, P, on the quadrant, A P, must lie in the corresponding points,
a, b, c, p, where the respective normals cut the evolute a p. At A, for example,
the attraction of gravity acts as if it originated at a, for B at b, for C at c, &c.
But the intensity of gravity is greater at B than at A, at C than at B, and so on.
The revolution of the evolute ap on its axis Op will evidently generate a
surface (called a locus), in which will be found the centres of gravity for all
points on the upper hemisphere, and a similar surface may be produced for all
points on the lower hemisphere by the revolution of the curve ap'.
Evidently, therefore, a body placed at the equator will be very differently affected by the force of gravity, from what it would if placed at
the poles.  The amount of flattening at the poles is about 3   of the
equatorial radius, or, accurately, 3-.4; that is, the polar radius is so
much shorter than the equatorial-exactly 21'319 kilometres, equai
13-246483 miles; or in the diameter nearly 26~ miles (26-492966).  In




61               PHYSICS OF SOLIDS AND FLUIDS.
an exact model of the earth 15 inches diameter, it would be represented by ~  of an inch; a quantity too small to be detected by the eye
or hand.
92. Exact dimensions of the earth.-According to the latest calculations the exact dimensions of the earth, as given by Kohler, when
reduced to American standard measures, are as follows:
Volume of the earth, 259,756,014,917 cubic miles.
Surface of the earth,  196,881,077     square miles.
Length of a quadrant, 6213-99609       miles.
Mean radius (lat. 45~), 3955-94978
Equatorial radius,    3962-57302 
Polar radius,          3949-32654 
Difference between the last two dimensions 13-24648 miles.
The equatorial swelling, or that portion of the earth which lies outside of
a perfect sphere, whose circumference is described by the polar radius,
is 1T part of the whole volume of the earth. Two verticals include an
angle of I1  when they are 101-7 feet distant from each other, and they
will inclose a sector of 1' when they are distant from each other 1-15
miles.
93. Sensible weight varies in different localities.-The same
body is sensibly lighter at the equator than at the poles of the earth, in the
ratio of 194 to 195. This difference cannot be detected by the balance, because
the thing weighed is counterpoised by an equal            49
standard weight, under the same circumstances;                 c
and if both are removed to another station, their 
weight, if changed, will be changed equally, and a 
body and its counterpoise once adjusted, will continue to balance each other wherever they are carried. It is not in this sense that 194 lbs. at the
equator will weigh 195 lbs. at the poles; but if we 
conceive a body, y, suspended by a cord, imagined a
without weight, passing over a pulley at the equator, 
as in the annexed figure, 49, and connected by
other pulleys, all without friction, with x, another
equal weight, at the poles; then, although the
weights would counterpoise each other in a balance, they would not in this
situation, but the polar weight would preponderate, and y would require to be
increased by T- th part, to restore the equilibrium.
The above phenomena are readily demonstrated by the spring-balance, or
dynamometer (37.)
94. Effect of the  earth's rotation  on  gravity.-Newton and
others have determined, by calculation, that the increase of weight,
due to the spheroidal form of the earth, is g, when a body is transported from the equator to the poles; yet the difference of weight is
found experimentally to amount to the much more considerable quan



GRAVITATION.                              65
tity of  6a  part of the total weight of the body.  This large difference
is accounted for by the centrifugal force, which is nothing at the poles,
and regularly increases towards the equator, where it is greatest, and
in the same ratio diminishes the weight of bodies on the earth's surface. The earth revolves once in 24 hours, but if it revolved seventeen
times more rapidly than it now does, or in lh. 24m. 25s., the centrifugal
force would balance the force of gravity, and bodies at the equator would
have no sensible weight.  If the velocity of revolution was farther
increased the oceans would be thrown off like water from a grindstone,
and all loose materials would fall into space.
Demonstration.-By the laws of centrifugal force it follows that the observed weight of any substance on the earth's surface is the difference between the
earth's attraction and the centrifugal force developed by the revolution of the
47C2R
earth. By? 54 the centrifugal force at the equator -=  G =    2; R being the
equatorial radius, and T a diurnal revolution. If G represent the attraction of
the earth, and g the weight of a body at the equator, then ( 1 ) g = G-   ~-.
Let m, fig. 50, be a material particle taken on any parallel, and represent A m,
the radius of this parallel, by r, the centrifugal        50
force at this point, mf= c =   T —. But as this H
force does not act in the direction of gravity, de-  
compose it into two others, one of which, m b,
being at right angles to gravity, has no effect                     E
upon it, and the other m a acting directly against 
gravity. Let m 0 E, the latitude of the place,
which is equal to a mf, be designated by L, then in
the right-angled triangle a mf, m a is equal to
mf X cosine of a mf = c cos. L. In the triangle
A m 0, A m =  r = R cos. L. It follows that the vertical component m a 
4^2R
T - cos.2 L. The force of gravity at m is then,
4n2R
(2) g =    -    - cos. L.
The diminution of gravity due to the centrifugal force is therefore proportional to the square of the cosine of the latitude. At the pole, where L -  90~,
g =  G. At the equator L = 0, and g is found by the formula. In the first
formula (1) the value of the second term of the equation being very small in
relation to the first, gives very nearly g =  G (1-,,  by placing G as a
common factor, and replacing it in the denominator of the second term by g.
Taking for the mean radius of the earth R = 20,887,413 feet, and g = 32-1798
feet, and T-  86,164 seconds (the time of a revolution of the earth on its axis),
4wnv 2 v               1
we find for the value of -     very nearly -.If, therefore, the earth
g ]u           289   172'




66              PHYSICS OF SOLIDS AND FLUIDS.
revolved 17 times faster than it does at present, making T seventeen times
smaller, the second term in the parenthesis would become unity, and the value
of g would be zero, or bodies at the equator would have no weight.. The expression (1) enables us to calculate the attractive force at the equator, assuming as
a starting point the value g = 32-09025 feet as the value of gravity as indicated
by the pendulum. We then find the attractive force at the equator G = 32-20147
feet, and the centrifugal force at the equator = 0-111216 feet.
95. Variation of gravity above the earth and below its surface.-By the law of gravitation it follows that as we rise above the
earth the force of gravity must diminish.  This diminution is sufficient
to be appreciable at any considerable distance above the level of the
sea; therefore, to compare the results of experiments relating to the
force of gravity at different situations on the earth's surface, it is necessary to reduce all observations to a common standard-the sea level..
Representing by g' the intensity of gravity at any elevation h, and
the earth's radius by R, neglecting the variation of the centrifugal
force, we have
g: g' = (R +  h)2: R2; hence g = g(R.R2
The mean distance of the moon from the earth's centre is about
sixty times the equatorial radius of the earth, and it completes its orbit
(assumed to be circular) in 27'322 days. As, therefore, the intensity
of the earth's attraction at the moon equals the centrifugal force (as is
evident from physical astronomy), this force can be calculated by substituting for R sixty times the earth's radius, in the formula for centrifugal force. Substituting for T the time of a lunar revolution expressed
4r2 X 60R
in seconds, we find for the earth's attraction on the moon g =   2
= 0.00679 feet, which is about 3600 times less than the attraction of
the earth for bodies on its surface at the equator (assuming for bodies
as distant as the moon that the attraction of the earth is concentrated
at its centre). This agrees with the law of gravitation, the square of
60 being 3600.
Below the earth's surface, assuming the earth to be a sphere, the
force of gravity is proportional to the distance of the particle from its
centre. It is plain that the force of attraction at any point beneath
the surface is diminished by whatever part of the earth is above the
particle, and the resultant force is the difference between the two components. Could a body be placed in empty space at the centre of the
earth, it would be sustained there without any material support by the
equal and opposite attractions. It can also be demonstrated mathematically that, if the earth were a hollow sphere of uniform density,
a material particle would remain at rest at any point within it. It




GRAVITATION.                          67
follows from this that:-The attraction of the earth, for a particle of
matter below its surface, is directly proportional to its distance from the
centre of the earth.
1 4. Mass and Weight.
96. Mass.-The mass of a body is the quantity of matter which it
contains; and since the absolute weight of a mass of matter is the sum
of the attraction of gravitation upon all its molecules, it follows that, in
the same place, the masses of bodies are to each other as their weights.
Calling the mass M and the weight W, and the force of gravity g, for
any given body, then W= Mg. We have already seen (41) that the
masses of bodies may be compared by the forces required to impart to
them equal velocities.  Since gravity acts equally on matter of whatever description, this comparison may also be made by comparing their
weights when otherwise under the same conditions.
97. Weight.-The term weight as used above, and always in scientific language, means the pressure exerted by a given mass, due to the
force of gravity. This varies, as we have seen, with the force of gravity,
and is not the same for the same mass at all parts of the earth's surfacQ (93). The weight of any given kind of matter varies also with its
mass. A mass of two, three, or ten times a given unit weighs two,
three, or ten times as much as that unit at the same place, and hence
we are very prone to confound the weight of a substance with its mass.
On the surface of the earth this confusion of terms can lead, as we have
seen (93), to an error of only about one two-hundredth part of the
whole (-,  ). That is, a mass of iron weighing 1000 lbs. on the equator
would weigh 1005 lbs. at the pole. Such a mass of iron would weigh
only 500 lbs. at a distance of 2000 miles below the surface of the earth,
or 1650 miles above the earth, and only 160 lbs. on the moon, while it
would weigh about 2600 lbs. on the planet Jupiter, and 28,000 lbs. if
placed on the sun.
98. Density.-The density of a body is the mass comprised under a
unit of volume, or M==  <X D, where the mass, M, of a body is equal
to its volume, V, multiplied by its density, D;
M
transferring, we have  V   D.
This may be otherwise stated, thus —st, the mass is proportional to
the volume; 2d, for an equal volume the mass is proportional to the
density; and, 3d, the density of the same mass is inversely proportional
to the volume it occupies.
99. Specific weight is the weight contained in a unit of volume; this
is also often called specific gravity. Representing specific weight by w,




68             PHYSICS OF SOLIDS AND FLUIDS.
and absolute weight by W, we have W'= VX w, hence, 1st, the weight
is proportional to the volume; 2d, for an equal volume the absolute
weight is proportional to the specific weight; and, 3d, for equal abso
lute weights the specific weight is inversely as the volume.
By the first formula we have w =Dg, whence w is the weight of the
unit of volume, and D its mass. Replacing w by this value in the last
formula, it becomes W= VX D X g.
Specific weight differs therefore from density exactly as weight
differs from mass. Both weight and gravity vary with the latitude,
and the unit accepted as a standard varies also, but when the same
standards are employed, the numbers expressing the weights remain
unchanged, and no sensible error results. The terms density and
specific gravity have thus been used interchangeably for each other,
although, speaking strictly, involving different quantities. The balance
is the common instrument used to determine weights. It will be
described under the lever, of which it is one form.
100. French system  of weights.-As in measures (16), so in
weights it is indispensable to assume some arbitrary standard unit.
The French have assumed as their unit of weight, the pressure exerted
by one cubic centimetre of pure water at its maximum density (39~.2
Fahrenheit), in a vacuum, and at the latitude of Paris. This unit is
called a gramme, and it weighs (nearly) 15-433 grains English. The
gramme is multiplied and divided decimally, and these multiples and
subdivisions are named on the same plan with the parts of a metre:
Thus we have,
1 Kilogramme = 1000 grammes,      1 Gramme    = 1-000 gramme,
1 Hectogramme -  100    "         1 Decigramme = 0-100    "
1 Decagramme -   10    "          1 Centigramme = 0-010    "
1 Gramme             I "          1 Milligramme - 0-001    "
The kilogramme is the commercial unit of weight, and is rather less
than 21 lbs. avoirdupois, being 15,432'42 English grains.
The French unit is of course a gramme only at Paris, and at higher
or lower latitudes weighs (according to the principles before explained)
more or less than a gramme. But this leads to no practical inconvenience, so long as a set of exact measurements made in one latitude are
not brought into rigorous comparison with those made by the same
standard in another latitude. The general acceptance of the French
system  among scientific men, and its special fitness for scientific
research, owing to the very simple relation which exists between it and
the system  of measures already described, would seem  to render the
universal adoption of a decimal system of weights and measures for
the United States one of the great desiderata still to be accomplished
for our common country.




GRAVITATION.                          69
101. English and American system of weights.-In England,
as in the United States, two distinct units of weight are in common use,
leading to constant confusion, both of terms and quantities. These
units, the Troy pound and the Avoirdupois pound, are entirely arbitrary.
They are represented by certain masses of brass, declared by law to be
the legal standards of the above names. These pounds are related to
each other in the ratio of 144 to 175, and, excepting the grains,
none of their subdivisions are alike.'The troy pound contains 5760
grains divided among 12 ounces, and the avoirdupois pound contains
7000 grains divided among 16 ounces. The legal standard of weight
in the United States is the troypound, copied by Capt, Kater in 1827
from the English Imperial Troy pound, for the U. S. Mint at Philadelphia, where it now is. The avoirdupois pound is, however, the unit
of weight in actual use in most commercial transactions. Kater's copy
of the troy pound is a standard at 62~ of Fahrenheit's thermometer and
30 inches of the barometer. A cubic inch of distilled water weighs in
the air at 62~ Fahrenheit and 30 inches barometric pressure 252'456
grains.
The English standard of weight is connected with that of measure by
the parliamentary enactment, that277'274 cubic inches shall constitute
the Imperial gallon of 70,000 grains, or ten pounds of pure water at
62~ F. and 30 inches barometric pressure.
The American standard gallon contains at 39~'83 F. (the maximum
density of water adopted by Hassler) 58,372 grains of pure water at 30
inches barometric pressure. Tables for the comparison and reduction
of the French, English, and American units will be found at the end
of this volume.
102. Estimation of the density of the earth.by experiment. —
In the vicinity of a mountain a plumb-line is not truly perpendicular,
but is drawn to one side by the lateral attraction of the mountain. The
amount of this deviation is measured by observations on the zenith distances of a star, at two stations on opposite sides of the mountain, and
on the same meridian. This deviation was first noticed near Mount
Chimborazo in 1738, by the French Academicians engaged in measuring
a meridian arc in Peru, where the deviation was 7"'5. In 1774, Maskelyne found a deviation of 5"'83, caused by the lateral attraction of
Schehallien, an isolated mountain in Scotland. Hutton spent three
years in ascertaining the mean attraction of one thousand stations on
this mountain; a labor rewarded by the Royal. Society of London.
Estimating the mean density of the rocks of Schehallien at 2'5 to 3 ",
as determined by Playfair, the mean density of the earth was determined to be over five times the density of water. The accurate inves.
9




70               PHYSICS OF SOLIDS AND FLUIDS.
tigation of this problem was one of the highest importance in astronomy,
since it furnished the means of determining the mean density of the
earth, by comparing its attraction with the attraction of a part of its
mass, whose density could be ascertained by direct experiment.
This problem is solved with much greater precision, by the famous
experiment of Cavendish, in which the earth's attraction is compared
with that of a mass of lead.
Cavendish's determinations of the density of the earth were made, in 1798,
by means of an apparatus suggested by the Rev. John Michell.
" Michell's apparatus was a delicate torsion balance, consisting of a light
wooden arm, suspended in a horizontal position, by a slender wire 60 inches
long, and having a leaden ball, about 2 inches in diameter, hung at either extremity.  Two heavy spherical masses of metal were then brought near to the
balls, so that their attractions conspired in drawing the arm aside. The deviation of the arm was observed; and the force necessary to produce a given deviation of the arm, being calculated from its time of vibration, it was found what
portion of the weight of either ball was equal to the attraction of the mass of
metal placed near it. From the known weight of the mass of metal, the distance of the centres of the mass, and of the ball, and the ascertained attraction,
it is easy to determine the attraction of an equal spherical mass of water, upon
a particle as heavy as' the ball placed on its surface. Now the attraction of this
sphere will have to that of the earth the same ratio as their densities; and as
the attraction of the earth is equal to the weight of the ball, it follows, that as
the calculated attraction is to the weight of the ball, so is the density of watei
to the earth's density, which is thus determined." ( Wilson's Life of Cavenldish.)
A comparison of about two thousand experiments with an improved
form  of this delicate apparatus, conducted by Mr. Francis Bailey, in
1842, determined the mean density of the earth to be 5 6604 times that
of water. It is worthy of remark that Newton, whose guesses were
often worth more than the researches of less sagacious men, had conjectured the earth's density to be between 5 and 6 times the density
of water.
The calculation is conducted thus. Let L be half the length of the horizontal
arm of wood. G the attraction of the masses of lead, and t the time of an
oscillation-neglecting the effect of torsion-Then, according to the theory of
the pendulum (81),
Take I for the length of a simple pendulum oscillating in the same time (t) by
gravity, and we have
t     or L:   = l:g, and: L =- g: G.
Calling the attraction of the unit of mass upon the unit of mass at the unit of
distance a; the mass of each sphere of lead m; d the distance from the centre
of this sphere to that of the attracted sphere when in the position of equilibrium;




GRAVITATION.                            71
and, lastly, M the mass and R the mean radius of the earth, and we have,
according to the laws of attraction,
am       aM
G —-- gd2, -2
By substituting these values of G and g in the last proportion, it becomes
I: L - d2M: R2m, or
I: m -   1R2: Ld2,
which fixes the ratio between the mass of the earth (M) and that of one of the
masses of lead (m), as given by the balance. The volume of the earth being
represented by V, and its mean density by D, we have by (98) M-=VX D,
from which, M and V being known, D is deduced.
The inference, unavoidable, from these facts is, that the interior
parts of the earth must be much more dense than the superficial crust.
Granite and other rocks on the earth's surface have an average density
of about 2'5. This remarkable fact may be explained, partly by
remembering that the interior parts of the earth sustain the enormous
pressure of the surface portions, and partly by the hypothesis of primitive fluidity, which authorizes the belief that the more dense portions
of the planet would seek the lowest place, and the lighter parts the
surface.; 5. Motion of Projectiles.
103. Projectiles are bodies thrown into the air by some momentary
force.  They are therefore subject to two forces, one the projectile
force, which is momentary, the other the constant force of gravity.
When a body is projected vertically upward, it rises with a uniformly
retarded motion, the action of gravity diminishing the velocity of ascent,
at every instant, until the projectile force is expended, when the body
commences to descend, and passing every point in its downward path
at the same rate as in its upward flight, it acquires at the end of its
fall a velocity equal to that with which it was projected.
In the same manner when a body is projected vertically downwards
its path is the same as that of a body falling freely, but the space
traversed, and also the velocity, are resultants of the sum of the two
forces. These are simple cases under the laws of uniformly accelerated
or retarded motion already considered (32).
If the direction of the projectile is not perpendicular, then the path
of the projectile must be a curve (51).
Thus, if a cannon-ball is shot in the direction a b (fig. 51), with a velocity
which would carry it through the space a I in one second, then, by the laws of
inertia, it would continue in this line, passing through equal spaces in equal
times. If it was acted upon by gravity alone, it would move in the vertical
a c, through the spaces I' II' III', in corresponding seconds. But, while it is




72                PHYSICS  OF SOLIDS AND  FLUIDS.
projected in the direction a b, it is subject also to the action of gravity, and,
like any other body, must fall through the                51
vertical space of 16 yl feet during the 1st
second; at the end of that time, therefore, it
will be found at e, instead of at I. In the
same manner, at the end of the 2d and 3d
seconds, it will be at f and g, instead of II
and III; and at the end of four seconds the
body will arrive at A, the result by the parallelogram of forces being exactly the same as
if it had been first carried by the projectile 
force in the line a b during four seconds, and/             /     \ h
then allowed to fall during four seconds by   I   
the action of gravity over b h =  a e. Since
the action of the projectile force is only mo-  / 
mentary, while the effect of gravity is constantly increasing, the body will not describe
the diagonals of the parallelograms, a e, a, a 
ic., but a curve, which in mathematics is
called a parabola, indicated by the dotted'ine connecting a efg and h.
By a similar construction, we find the path    c
of a body projected horizontally, or obliquely downwards, in which cases the
projectile will describe one-half of a parabola. In every case the path of the
projectile is a complete or partial parabola, whose axis is in the direction of
gravity; and its vertical distance below the line of projection at any given
moment, is always equal to the space it would have fallen freely during the time
since it was projected.
By the principle of parallelogram of velocities, it is evident that in the time
the body would describe the curve a efg h, it would, without the action of
gravity, describe the line a b =  vt, v being the velocity of projection, and t the
time of flight. Let a be the angle of elevation b a h, v' the vertical velocity,
and v" the horizontal velocity, then v' =  v sin. a, and v" =  v cos. a. The vertical velocity would evidently be spent in one-half the time of flight, and an
equal descending velocity would be acquired at the time of striking the point h,
2v sin. a
hence, v' =  v sin. a =  ~gt, and t -      =  the time of flight. The hori9
zontal range will equal the horizontal velocity v" multiplied by the time of
2v sin. a   2v2 sin. a cos. a   v2 sin. 2a
flight' v cos. a X  -                           ----
g             g               g
This value of the horizontal range                      52
ah is evidently the greatest for any   F...
value of v, when sin. 2a =  1, or a - 
45~; and, for elevations equally above.. c
and  below  45~, the horizontal range                  -
will be equally diminished; that is,  —.....
the horizontal range will be the same'                                   D
for an elevation of 40~ as for 50~, and
the same for an elevation of 30~ as for
60~.  Fig. 52 shows the form of the curves described by projectiles at




GRAVITATION.                             73
angular elevations of 0~, 15~, 45~, 60~, and 90~ (A B, A C, AD, A E,
A F). The dotted lines show the angles of projection, and the smooth
lines, with corresponding letters, show the paths described by the
projectiles. The effect upon the flight of projectiles produced by
resistance of the air, will be considered hereafter.
104. The ballistic pendulum  is an instrument employed to measure the velocity of projectiles.  A                 53
heavy mass of wood and iron, shown
at b, fig. 53, is suspended at C, on a
shaft three or four yards in length 
over a graduated arc B E D.  The
ball, fired in  the direction N N,                g 
strikes the ballistic pendulum at A,
and, penetrating the heavy mass,
imparts to it a velocity which is 
determined by comparison of the
arc E D  described by the pendulum, and the time in which the.. -...
whole mass is found to vibrate.  S - Nis supposed to be the centre of
gravity, M  the centre of oscillation, 
C G the arm of impact, and M H the 
perpendicular height through which the pendulum rises. From these
data the velocity of the ball at the moment of impact can be calculated.
Problems.-Falling Bodies.
17. If a stone is dropped into a well, and it is seen to strike the water at the
end of 3 seconds, what is the depth of the well?
18. A body is projected upward with a velocity which will carry it to the
height of 64 feet 4 inches; after how long a time will it be descending with
half the original velocity?
19. Find the velocity with which a body must be projected upwards from the
foot of a tower, so as to meet half way another body let fall at the same time
from the top of the tower.
20. A balloon is ascending vertically with a given velocity, and a body is let
fall from it, which reaches the ground in t seconds: find the height of the balloon
at the moment of the body leaving it.
21. A body is observed to fall the last a feet of its descent from rest in t
seconds: find the height from which it fell.
22. A body has fallen through the distance of half a mile; what was the
distance described in the last second?
23. A body is projected upwards with a velocity of 64k feet in a second; how
far will it ascend before it begins to return?
9*




74                PHYSICS OF SOLIDS AND FLUIDS.
24. A stone dropped from a bridge strikes the water in 2~ seconds; what is
the height of the bridge? Also if the stone be projected downwards with a
velocity of 3 feet per second, in what time will it strike the water?
25. A stone thrown horizontally from the summit of a high cliff is seen to
strike the ground at the end of 5 seconds; what is the height of the cliff above
the point where the stone falls?
26. A body is projected vertically upwards, and the time between its leaving a
given point and returning to it again is given; find the velocity of projection
and the whole time of motion.
27. From what elevation must a body weighing 500 pounds fall, to strik
with the same momentum as a body weighing 900 pounds falling from an elevt
tion of 64A feet?
Descent of Bodies on Inclined Planes.*
28. What time will be required for a body to descend an inclined plane whost
length is 200 feet, and whose elevation is 64A feet.
29. What velocity will be acquired by a body descending a plane inclined at
an angle of 30~, the perpendicular height being 1451 feet?
30. If a railway train, with a speed of 30 miles per hour, arrives at a
descending grade of 60 feet to the mile, and has no force applied to check its
speed, what will be its velocity after running 3 miles on the grade?
31. If a train, moving at the rate of 25 miles an hour, arrives at a grade of
50 feet per mile, 2 miles in length, and no more steam is applied than before
arriving at the grade, what will be the velocity of the train after ascending the
grade?
Central Forces.
32. Find the force with which a body weighing 8 lbs. would stretch a string,
3 feet long, retaining it in a circle, when the body makes 3 revolutions per
second.
33. What must be the weight of a body revolving 7 times per second in a
circle 10 feet in diameter, in order that the centrifugal force of the revolving
body may be equivalent to a weight of 1000 lbs.?
34. How many times must the revolution of the earth be increased to have
the weight of bodies at the equator diminished one-half, calling the radius of
the earth 4000 miles?
35. What must be the number'of revolutions per second of a body weighing
17 lbs., revolving in a circle whose radius is 5 feet, that its centrifugal force may
be the same as that of a body weighing 25 lbs., revolving 9 times per second in
a circle whose radius is 3 feet?
Pendulum and Gravity.
36. What is the time of vibration at Paris of a simple pendulum whose length
is 3 metres?
37. What is the force of gravity in a deep mine where the length of the
seconds pendulum is found to be 38 inches?
38. What is the time of vibration of a simple pendulum 30 inches in length,
where the accelerating force of gravity is 32 feet per second?
39. What is the time of vibration of a simple pendulum at Paris, the length
of the pendulum being one metre, and the amplitude of vibration being a    9~?
* In these problems the retarding force of friction is not to be considered.




THEORY  OF MACIHNERY.                            75
40. What is the accelerating force of gravity at New York? at Boston? at
New Orleans? at Cape Horn? at Stockholm?
41. If the force of gravity at the earth's surface be regarded as unity, what
will be the force of gravity at a distance below the surface equal to one-tenth
part of the earth's radius?
Flight of Projectiles.*
42. What distance will a ball be thrown on a horizontal plane, if it is fired
from a cannon with a velocity 700 feet per second at an angular elevation of 33~?
43. What is the greatest distance to which a ball can be thrown on a horizontal plane, if it leaves the mouth of the cannon with a velocity of 1000 feet
per second?
44. If a ball leaves the cannon at an elevation of 30~, with a velocity of 800
feet per second, in what time will it strike the horizontal plane?
45. At what angle of elevation must a ball be fired that, with an initial velocity of 600 feet per second, it may strike a horizontal plane at a distance of two
miles?
46. If a ball discharged from the mouth of a cannon, at an elevation of 35~,
strikes the horizontal plane at a distance of three miles, what was its original
velocity?
CHAPTER IV.
THEORY OF MACHINERY., 1. Machines.
105. Principle of virtual velocities.-It was shown in l   46, that
when  a body, having  a fixed                        54
point of support, is acted on by,....
two parallel forces in the same,    -............ —-'
direction, the forces will be in  ".....   -P..
equilibrium, if they are to each''..
other inversely as their distances
from  the supporting point.  Thus in fig. 54, if an inflexible rod, supported at C, is acted on by two forces, W  and P, such that
W: P=  P: CW,
then they will be in equilibrium. But as in every proportion the product of the first and last terms is equal to the product of the second
and third; so instead of saying that the forces are inversely as their
distances, the same thing is expressed by W  X C W  --- P  X C P. The
~ In these problems no account is supposed to be taken of the resistance of
the air.




76              PHYSICS OF SOLIDS AND FLUIDS.
principle may be otherwise illustrated thus:-Let the bar W P be made
to oscillate gently about the point of support C. It is plain that the
spaces described by the ends of the bar will be proportional to their
distances from the axis; for the angles at the axis being equal, the
arcs af and b h are directly proportional to their radii C W and C P.
Hence
W: P = bh: af;
That is, two forces are in equilibrium when they are to each other
inversely as the spaces which they describe. The arcs being described
in the same time, represent the velocities, and the principle is usually
thus stated: forces in equilibrium must be to each other inversely as their
velocities. The products, therefore, of the forces multiplied by their
respective velocities, are equal:
W X af = P X bh.
These products are called the moments of the forces, and when these
momenta are equal the forces are in equilibrium. If the movement is
doubled, halved, or raised in any proportion, the efficacy of the force is
similarly varied. Any arrangement by which two forces are brought
into this relation to each other, constitutes a machine.
106. Machine, Power, Weight.-In extension of the statement
last made, a machine is any arrangement of parts in an apparatus, by
which force may be transmitted from one point to another, usually with
some modification of its intensity or direction, and with reference to the
performance of mechanical work.
The moving force in a machine is called the power; the place where
it is applied is the point of application; and the line in which this point
tends to move is the direction of the power. The resistance to be overcome is called the weight, and the part of the machine immediately
applied to the resistance is the working point.
The moving powers and the resistances in mechanics are both
extremely various; but of whatever kind they may be, they can
always be expressed by equivalent weights, i. e., such as being applied
to the machine would produce the same effects.
107. Equilibrium of machines.-When the power and weight are
equal, the machine is in equilibrium, and it may be at rest, or, as is
usually the case, in a state of uniform motion. If a machine in this
case is put into uniform motion, it must, by force of inertia, continue
to move indefinitely; for the power and weight being equal, neither of
these forces can stop or modify the motion, without some extraneous
force, which is contrary to the supposition.
Thus, if an engine draws a railway train with uniform velocity, the power




THEORY (F MACHINERY.                           77
of the engine is in equilibrium with the resistance of the train. At starting,
the power is greater than the resistance, and the motion of the train is consequently accelerated, until the resistance becomes equal to the power, when
equilibrium is again established. If any part of the power is now withdrawn,
the power becomes less than the resistance, and the motion is consequently
retarded until the train is brought to rest.
The mechanical energy, or moving force of the power, is found by
multiplying its equivalent weight by the space through which it moves,
or its velocity; and the value of the resistance is estimated in the same
manner.  As we have just seen, the relation between these moments
determines the state of the machine.
108. Utility of machines.-It is sometimes said, in illustration of
the usefulness of machines, that a great weight may be supported or
raised by an insignificant power; but such statements, if literally
understood, are obviously untrue.  No machine, however ingenious its
construction, can create any force, and therefore the working point can
exert no more force than is transmitted to it from the source of power.
Every machine has certain fixed points, which are arranged to support
any required part of the weight, while the remainder of the weight,
and that part only, is directly sustained by the power. This remainder
cannot be greater than the power.
109. Relation of power to weight.-But if the weight is not only
supported, but raised through a given space, then the power must move
through a space as much greater than the weight moves through, as the
weight itself is greater than the power; in other words, the power and
weight must be inversely as their velocities. This inverse proportion
is expressed when it is said, that power is always gained at the expense
of time.
To raise 1000 lbs. to a height of one foot by a single effort, would require a
force equivalent to 1000 lbs.; but the same thing may be accomplished by a
power of 1 lb. acting for 1000 times successively, through a space of one foot.
If a man by exerting his entire strength could lift 200 lbs. to a certain height,
in one minute, no machine whatever can enable him to lift 2000 lbs. to the same
height in the same time. He may divide the weight into ten parts, and lift each
part separately; or by the intervention of a machine he may raise the whole
mass together, requiring, however, ten minutes for the task.
On the other hand, it is often the object of a machine to move a small
resistance by a great power.
In a watch, the moving force of the mainspring is very much greater than
the resistance of the hands, revolving about the dial. In a locomotive engine,
each full stroke of the piston moves the train through a space equal to the
circumference of the driving wheel; if the length of stroke is cne foot, and the
circumference of the wheel 12 feet, then the velocity of the piston will be to the
velocity of the train, as 2 to 12; consequently the power acting on the piston is
greater than the resistance of the train, in the proportion of 12 to 2.




78             PHYSICS OF SOLIDS AND FLUIDS.
110. Adaptation of the power to the weight in machinery. —
The use of machines is to adapt the power to the weight. If the intensity, direction, and velocity of the power, were the same as the intensity
and direction of the resistance, and the velocity required to be given to
it, then the power might be directly applied to the resistance, without
the intervention of a machine. But if a small power is required to
move a great resistance; or, if a power acting in one direction, is
required to impart motion in another; or, to impart a velocity greater
or less than its own, then it is necessary to employ a machine which
will modify the effect of the power in the required manner. Besides
these, the motion of the power may differ from the motion required in
the resistance in a great variety of ways.
The power may have a reciprocating motion, as in the locomotive engine, and
be required to produce a continuous motion in a straight line, as in moving a
train upon a railway. Or, the power may have a rectilinear motion, as a stream,
and be employed to produce the circular motion of the stones in a grist-mill, or
the reciprocating motion of a saw, in a saw-mill.
In every class of machines, the relations existing between the power
and the resistance, depend solely on the construction of the machine;
but even a general account of the ingenious contrivances by which the
moving force is regulated, modified, and adapted to the varying conditions and requirements of the resistance, would lead us far beyond the
limits and design of this work.
111. Vis viva, or living force, is the power of a moving body to
overcome resistance, or the measure of work which can be performed
before the body is brought to a state of rest. The vis viva of a
body is represented by MVa, or the mass of the body multiplied by the
square of its velocity.
When a body is projected vertically upwards, the height to which it
will ascend is proportional to the square of its velocity. If Wrepresent
the weight of the body, and h the height to which it is elevated by a
given impulse, the amount of work performed will be represented by
V2
Wh, but W= Mg and h =  g -, substituting these values of Wand h,
we have the work performed = i MV2. Hence the work which can be
performed by the accumulated power of a moving body is equal to onehalf the mass multiplied by the square of the velocity.
Take the case of a pile-driver, in which a heavy mass of iron is elevated to a height of 30 or 40 feet, and is then suddenly allowed to fall;
the resistance overcome in raising the driver is exactly proportional to
the elevation to which it is raised, and the accumulated power of the
stroke increases in the same ratio; hence it is evident that the vis




THEORY OF MACHINERY.                       79
viva, or power of overcoming resistance, must be truly represented by
MV2.
Again, in the case of a railway train moving with a velocity V, the greatest velocity attainable by a given power of steam; let v be the acceleration of velocity imparted to the train by the locomotive during the first
second of its action, and Mthe mass of the moving train, including the
locomotive. If the movement of the train were not retarded by friction,
or some other opposing force, we should have V= vt, or the velocity, V,
would go on constantly increasing; but such we know is not the case,
for the train soon attains a maximum velocity, when the entire force
of the locomotive is every instant expended in overcoming friction, and
the train moves on with a momentum expressed by MV, but its vis viva
is expressed by MV2. If the force of steam were suddenly discontinued, the power of the moving train to ascend a grade, to overcome
any obstacle, or to deal destruction to itself, or to any object with
which it comes in collision, would still be proportional to vis viva or
MV2. Now suppose the velocity of the train to be doubled, so that
V = 2 V. It is evident that in any given interval of time the train
will pass over twice as many points of resistance as before, and as it
passes each point at twice the previous velocity, it will encounter at
every point twice as much resistance to motion as before. Hence to
impart to the train a double velocity, a fourfold force is required; and
the power of the train to overcome resistance will be proportional to
its vis viva, MV,2. This will be the true measure of the force which
has imparted the velocity V', and which is now constantly expended
in overcoming the resistance encountered by the moving train. The
same principles determine the power expended, or work actually performed (resistance included), by any kind of machinery.
It may be necessary to explain more fully the distinction between
momentum and vis viva, so that it may be readily understood when the
one or the other is to be taken as the measure of force.
Momentum, MV, expresses the relation of force to inertia, or the
amount of motion in a moving body. Vis viva, MV2, is the measure
of twice the amount of work which a moving body can perform before
it is brought to rest. Vis viva is the measure of force required to
maintain a constant motion, MV, against the resistance caused by the
positive properties of bodies, as attraction, cohesion, repulsion. Momentum is the measure of the force required, without regard to time, to set
a body in motion with a velocity V, when no other body interferes with
its motion, as in the case of a body falling freely in a vacuum. In the
case of the railway train, the mass of the train multiplied by its velocity is the measure of useful work performed in a unit of time, but it




80               PHYSICS OF SOLIDS AND FLUIDS.
is not the measure of resistance overcome, or actual work performed,
or of the force which has been expended in performing that work. The
latter is measured by one-half the vis viva, or  ~ MV2.
Illustrations of vis viva.-Suppose a battering-ram weighing 4000 lbs.
to be impelled with a velocity of 30 feet per second, its vis viva, MV2 =- 4000 X
30 x 30 = 3,600,000; yet a cannon ball weighing 64 lbs., flying with a velocity
of 1000 feet per second, will have a power of dealing destruction more than
seventeen times as great, for its vis viva equals 64,000,000. Calculations of this
sort explain the origin of the terribly destructive power of the engines of
modern warfare.
A railway train moving 50 miles an hour will possess more than six times
the vis viva that it would have when going twenty miles an hour; and, therefore, it will possess more than six times the power of dealing destruction, either
to itself or to an obstacle, at the former than at the latter rate. Thus the well
known relation between speed and amount of damage, in case of accident, is
readily accounted for, as also the enormous comparative cost of fuel, and wear
and tear of trains of high speed.
The destructive power of hurricanes, which move fom 60 to 100 miles an
hour, is readily understood when we know that the power of dealing destruction
increases in proportion to the square of the velocity.
112. Impact and its results. —When a body in motion encounters
another, the velocity and momentum of both undergo certain changes,
which depend on the elasticity of the bodies, and other physical circumstances.
Impact considered with reference to momentum.-a-When
a body in motion strikes another at rest, it can continue to move
only by pushing this body before it, and it must impart so much
momentum  that, after impact, both may move with a common velocity. If the masses of the two bodies are equal, it is evident that,
after impact, the momentum will be equally divided between them, and
their velocity will be one-half of the velocity of the moving body
before collision.  If the mass at rest is double the mass in motion, the
common velocity will be one-third; and generally, when a moving body
communicates motion to a body at rest, the velocity of the two united
will be to that of the moving body as the mass of the latter is to the
sum of the masses of both.
If a musket ball, whose weight is lT lb., and its velocity 1300 feet a second,
strikes a suspended cannon ball weighing 48 lbs., it will put it in motion, and
their common velocity will be to that of the bullet as 1) is to 48 - L, or as 1
is to 961; the velocity of the two is therefore 1 3o0o0, or about 1I feet a second.
b-Bodies moving in the same direction may impinge, if their velocities are different. If an inelastic body overtakes another, the first
will accelerate the second, and the second will retard the first, until
theyhave acquired a common velocity, when they will move on together.




THEORY OF MACHINERY.                          81
Since the bodies move in the same direction, there can be no increase
or diminution of the total momentum by impact, but only a re-distribution. If they are equal in mass, their velocity, after impact, will be
half the sum of their previous velocities.
If before impact, A had a velocity of 6, and B a velocity of 4, then theil
common velocity will be 5.
The two bodies may have unequal masses as well as velocities.
If the mass of A is 8, and its velocity 17, its momentum will be 136. If B
has a mass of 6, and velocity of 10, its momentum will be 60. The sum 196
is the total momentum  of the united masses after impact; and this sum
divided by the sum of the masses gives 14, the common velocity.
c-If two equal bodies, moving with equal velocities in opposite
directions, impinge on each other, their moments being equal, will be
mutually destroyed, and the bodies will remain at rest. The force of
the shock, in this case, is equal to that which either would sustain, if,
while at rest, it were struck by the other with a double velocity.  If
the moments of the bodies are unequal, then, after impact, they will
move together in the direction of the greater, and their joint momentum
will be equal to the difference of their previous moments, and their
velocity will be found by dividing that difference by the sum of the
masses.
d-These laws may be shown experimentally by suspending two balls
at the centre of a graduated arc, and producing impact according to
the conditions described.
If two bodies moving in different lines impinge on each other, then,
after contact, they will move together in the diagonal of that parallelogram whose sides represent their previous moments and directions.
From these principles it follows that, if two inelastic bodies, 1r and N, moving
in the same direction, with velocities V and V', come in contact, their common
MV+ NV'
velocity after impact will be expressed by the formula V" -=     ~N.
Ml +- N
When the bodies move in opposite directions, the velocity of the body having
the greater momentum is to be taken as positive, and the other negative; the
resultant velocity will be in the direction of the body which previously had the
greater momentum.
Impact considered with reference to vis viva.-When a body
in motion strikes another body at rest, which is free to move, the two
MiV
bodies have a common velocity, V" =  M-          The vis viva after imM2 V2
pact will be expressed by (M  +- N) V"/2 =   +           Suppose the
M+ N'
second body N to be a certain number of times, (represented by a,)
10




82               PHYSICS OF SOLIDS AND FLUIDS.
greater than the first body M, then N   a M. The vis viva of the comA1  2 r      2 2V2     MV2
bined mass after impact will then become M-+ N-      (1 +    - 1   
M+ N-_ M{1 +a)  14-I0+
Hence:
When a moving body strikes a body at rest, and the two move onl together,
the vis viva of the combined mass is as many times less than the vis viva
of the first body before impact as the combined mass is greater than the
first.
This principle shows how a man may receive the most violent strokes of a
sledge-hammer, upon an anvil laid upon his chest, without the slightest injury,
when, if only a light board were interposed between his person and the descending hammer, the stroke would be instantly fatal to life. The interposition of
any heavy body wards off the force of a blow on the same principles.
Pressure produced by impact.-Beaufoy determined that a body
of 1 lb. weight, with a velocity of 1 foot in a second, strikes with a pressure equal to Q05003 lb. To find the pressure produced by the impact
of any projectile, we have the general formula,
Pressure = 0-5003 MV2.
If the body descends vertically, the weight of the body itself must of
course be added to the direct effects of impact.
Destructive effects of impact.-The motion communicated to very
large or immovable bodies, by an impact of small ones, is not lost,
but becomes insensible from its enormous diffusion. Motion can be
destroyed only by motion; friction and resistance disperse, but do not
destroy it. An impact can act directly upon only a few of the molecules of the body to which it imparts motion.
The power which projects a bullet acts on only one-half its surface.
The motion must, therefore, be diffused from the parts struck to all
the other parts of the body, before it can begin to move; and this diffusion requires time, which may be short indeed, but is not infinitely
so. It happens, therefore, that a movable body, if struck by another
moving with great velocity, may be penetrated or broken at the point
of impact, without being itself put in motion. The part of the body
which receives the blow is set in motion with such velocity that its particles are rent asunder before motion can be communicated to the mass
of the body. Such effects appear incredible to persons unacquainted
with the inertia of matter and its consequences.
A rifle ball may be fired through a pane of glass suspended by a thread,
without shattering the glass, or even causing it to vibrate. A door half open
may be perforated by a cannon ball without being shut by it. A soft missile,
like tallow, or a light one, like a feather, will act with the force of lead, if sufficient velocity is given to it. Firing a tallow candle through a board is a well



THEORY OF MACHINERY.                         83
known feat of showmen. In ricochet firing, a cannon ball, shot at an elevation
of from 3~ to 6~, rebounds from the surface of water, just as every boy has
made flat stones skip from point to point on its surface.
2 2. Mechanical Powers.
113. The lever.-A lever is any inflexible rod, fig. 55, resting on a
point, F, called the fulcrum, and around which any two forces tend to
turn it. Levers may be either straight, or bent; simple, or compound.
It is usual to divide levers into three classes, according to the position
of the fulcrum in relation to the power and weight.
55                                 56
Fig. 55 is a lever of the first class, where the fulcrum is between the
power and the weight. In the second class, fig. 56, the weight is between the fulcrum and the power. In                  57
the third class, fig. 57, the power is;,
applied between the fulcrum  and the
weight.  
The arms of a lever are the lines on 
each side of the fulcrum, at right angles
to the direction of the power and weight. 
In the three figures just given, the levers being horizontal and the
forces vertical, the arms of the lever             58
are evidently, in each case, the por-                       R
tions into which it is divided.  If,                        \
however, the lever is bent or is in-              -           \
dined to the direction of either, or         F,                 A
both, of the forces, then the arms are    -I 
the perpendiculars between the fulcrum  and directions of the forces.  
Thus in fig. 58 the power acting in
the direction B  P, the moment of the power is not expressed by
P X A F, but by P X B F. The distance from the fulcrum is called
the leverage.




81              PHYSICS OF SOLIDS AND FLUIDS.
114. Conditions of equilibrium in the lever.-These conditions
are: 1st, The lines of direction of the two forces must be in the same
plane with the fulcrum; 2d, The two forces must tend to turn the lever
in opposite directions; 3d, Whatever may be the class of the lever the
weight and power will be in equilibrium when they are inversely as
their distances from the fulcrum. Thus in either of the three figures
above
P:W=FW:FP or PXFP=WXFW.
Consequently the moment of the power, or its tendency to turn the
lever will be augmented, either by increasing the power itself or its
distance from the fulcrum.
The pressure on the fulcrum, when the power and weight are in
equilibrium, is found by applying the principle of the composition of
forces (46). In a lever of the first class, the resultant of the power
and weight is a single force, equal to their sum, and passing through
the fulcrum; consequently, the pressure will be equal to the sum of the
power and weight. In a lever of the second or third class the resultant
is equal to the difference of the power and the weight.
Compound levers.-When a small force is required to sustain a
considerable weight, and it is not convenient to use a very long lever, a
combination of levers, or a compound lever is employed. When such
a system is in equilibrium, the power, multiplied by the continued product of the alternate arms of the levers, commencing from the power,
is equal to the weight multiplied by the continued product of the alternate arms, commencing from the weight. For example, the system
represented in fig. 59, consisting of three levers of the first class, will be
59
.          F 
P
in equilibrium when
P X A F X B F X C F" = W X D F" X C F' X B F.
If the long arms are 6, 4, and 5 feet, and each of the short arms 1 foot,
then 1 lb. at A will sustain 120 lbs. at D; but if a simple lever had
been used, the long arm being increased simply by adding these quantities, we should have gained a power of only 6 + 4 + 5 = 15 to 1.
115. Application of the lever.-Machines and utensils in daily
use offer us familiar examples of the three classes of levers.




THEORY OF MACHINERY.                          85
Of the first class we name the crowbar and poker, when used to raise
the load on their points. Scis-                  60
sors, snuffers, and pincers are
pairs of levers of this class,
the point C, fig. 60, which connects them being the fulcrum. 
The power is applied at the
handles, and the resistance is the object between the blades.
Another example of the bent lever is seen in the ordinary truck, fig. 61, used
for moving heavy goods a short distance. In this machine, the axis of the
wheels, F, is the fulcrum, against which the foot is placed, while the weight at R
is raised off the ground by the hand, applied at P.
61                                  62
The scale beam, or balance, is one of the most useful applications of
the first class of levers. The beam is a lever poised at its centre on a
knife-edge of steel, a, fig. 62. From its ends A B are suspended the
scale pans C E. The centre of gravity, m, is placed below the fulcrum,
a, to secure a horizontal position of the beam when in equilibrium.  If
it coincided with the fulcrum the balance would rest equally well n all
positions, and if it were above the fulcrum the beam would be upset by
a slight disturbance.
The steelyard is a lever of the                  63
first class, with unequal arms. The6 7 e_ 
mass, Q, to be weighed, is attached 
to the short arm, A, fig. 63, and it    J                      IG
is counterpoised  by  a  constant
weight, G, shifted upon the longer 
arm, marked with notches to indicate pounds and ounces, until equilibrium is obtained. It is evident
that a pound weight at G  will
balance as many pounds at Q as the distance G C is greater than A C.
10*




86               PHYSICS OF SOLIDS AND FLUIDS.
Levers of the second class occur less frequently. A pair of nutcrackers, with the fulcrum at the                   64
joint C, fig. 64, is a double lever c
of this class.  An oar is another
example; the water is the ful- 
crum, the boat is the weight, and
the hand the power. A door moving on its hinges, and a wheelbarrow,
are other examples of levers of the second class.
In levers of the third class, the power being nearer the fulcrum, is
always greater than the weight.  On account                65
of this mechanical disadvantage, it is used           w.... —.. -
only when considerable velocity is required,   "'\
or the resistance is small.  Fig. 65 represents \/
such a lever, W  F, moving on a hinge as a fulcrum; it is plain that the power P  moves
through a small arc, and the weight through a
large one, and since they are described in the 
same time, the velocity of the power is less 
than that of the weight.                                         F
The common fire-tongs, sugar-tongs, and sheep-shears, are double levers of
this class. The most striking illustrations of this class of levers are seen in the
animal kingdom. The compact form and beautiful symmetry of animals depend
on the fact that their limbs are                 66
such levers. The socket of the
bone, a, fig. 66, is the fulcrum;
a strong muscle, b c, attached
near the socket is the power,
and the weight of the limb and
whatever resistance tw may oppose to motion, is the weight.
The tore-arm  and hand are
raised through a space of one
foot, by the contraction of a
muscle applied near the elbow,
moving through less than Ila that space. The muscle, therefore, exerts 12 times
the force with which the hand moves. The muscular system is the exact inversion of the system of rigging a ship. The yards are moved through small
spaces with great force, by hauling in a great length of rope with small force;
but the limbs are moved through great spaces with comparatively little force,
by the contraction of muscles through small spaces with very great force.
Examples of compound levers are familiar in the various platform
scales, such as Fairbanks' and others. However various in form, they
all depend upon the principles already explained.
The principle of the construction of the weighirg machine is illustrated in
fig. 67. It consists of a wooden platform, placed over a pit made in a loca



THEORY OF MACHINERY.                           87
tion convenient for driving heavy loads upon it, and is so arranged as to move
freely up and down without touching the walls of the pit. The platform rests
upon four levers, A F, B F, C F, and D F, all converging toward the centre F,
and each moving on a fulcrum at A, B, C, D, securely fixed in each corner of
the pit. The platform rests
on its feet, a' c' d', which
rest on steel points, a b c d.
The four levers are supported at the point F, under the centre of the platform, by a long lever, G E,
resting on a steel fulcrum            i       iii         i
at E, while its longer arm
at G is connected with a              a 
rod, which is carried up                                               c
and attached to the shorter
arm of the steelyard, and   C              ~
is counterpoised by the
weight P, which, by its           \position on the longer arm, 
indicates at once the weight                              \
of the load placed upon
the platform.
As the four levers A, B, C, D, are perfectly equal and similar, and all act
upon the same fulcrum F, the effect of the weight placed upon any part of the
platform is the same as if it were concentrated at either of the points a, b, c, d.
In order therefore to ascertain the conditions of equilibrium, we need only
consider one of these levers, as A F. Suppose the distance from A to F to be
10 times as great as from A to a, a force of 1 lb. at F would balance 10 lbs. at a,
or on any part of the platform. So, also, if the distance from E to G be 10
times greater than the distance from the fulcrum E to F, a force of 1 lb., applied so as to raise up the end of the lever G, would counterpoise a weight of
10 lbs. on F, therefore, 1 lb. tending to raise G, would balance 100 lbs. on the
platform. If the poise, P, is placed 5 times as far from the fulcrum of the steelyard as the attachment of the rod connected with G, ththf 2 lbs. at P will balance
10 lbs. at G, or 100 lbs. at F, or 1000 lbs. on the platform. If the weight of P
and the graduation of the steelyard are arranged on these principles, the weight
of the heaviest loads on the platform may be determined with great facility.
Weigh-locks on canals, and many other applications of the compound lever,
are arranged on the same principles.
Roberval's counter platform  balance.-The exterior appearance
of this balance is shown in fig. 68, and its interior arrangement in
fig. 69. The equilibrium of this system of levers is, like that of fig. 67,
independent of the position of the load on the pans, and the mechanism
is such that the pans move on a vertical stem with no deflection from a
horizontal plane.
Each pan is supported by a system of three levers, A B, C D, E F, fig. 69.
The lever D C, which supports the pan P, rises and falls equally at both ends
with the motions of the beam A B, C being attached to the end of the beam B,




88               PHYSICS OF SOLIDS AND FLUIDS.
and D being attached at E to the lever E F; E H being equal to G B, while F
is securely attached to the base, E and B rise and fall equally, and D C is always
68
69
_n _
V1 \ 3_ I                                C
horizontal in every position of the beam A B. Since the lever D C preserves its
horizontal position, the stem a supporting the pan P, moves vertically, whatevermay be the position of the load on the pan. The indices n m are in the
same horizontal line when the pans are in equilibrium. This system is named
from the inventor, Mr. Roberval of Paris, and dates from about A. D. 1660.
116. The wheel and axle.-The common lever is chiefly employed
to raise weights through small                   70
spaces, by a succession of short 
intermitting efforts. After the
weight has been raised it must  
be supported in its new position, until the lever can be
again adjusted, to repeat the
action. The wheel and axle is
a modification  of the lever,
which corrects this defect; and,
since it converts the intermitting action of the lever into a
continuous motion, it is sometimes called the perpetual lever.
This machine consists of a cylinder called the axle, turning on a




THEORY OF MACHINERY.                        89
centre, and connected with a wheel of much greater diameter. The
power is applied to the circumference of the wheel, and the weight is
attached to a rope, wound around the axle in a contrary direction.
Instead of the whole wheel, the power may be applied to a handle
named a winch, or to one or more spokes in-            71
serted in the axle. When the axle is horizontal
the machine is called a windlass, fig. 70, when
it is vertical it forms the capstan, fig. 71, used
on shipboard, chiefly to raise the anchor. The
head of the capstan is pierced with holes, in
each of which a lever can be placed, so that
many men can work at the same time, exerting
a great force, as is often necessary in raising an
anchor, while the recoil of the weight is arrested by a catch at the
bottom.
The law of equilibrium is the same as            72
in the lever. Draw from  the centre, or
fulcrum c, fig. 72, the straight lines c b
and c a, or c a', to the points on which                       \
the weight and power act; a c b, or a' c b,  
is evidently a lever of the first class, in 
which the short arm c b is the radius of 
the axle, and c a or c a', the long arm, a 
is the radius of the wheel. Hence,    P                 W
P
P Xac=  WXcb.
Or,
P: W= cb: a c.
That is to say, the wheel and axle are in equilibrium, when the
power is to the weight as the radius of the axle is to the radius of the
wheel.
In one revolution of the machine, the power moves through a space
equal to the circumference of the wheel, and the weight moves through
a space equal to the circumference of the axle; hence the power and
weight are inversely as their velocities, or the spaces they describe.
117. Trains of wheel-work.-The efficiency of this machine is
augmented by diminishing the thickness of the axle, or by increasing
the diameter of the wheel. But if a very great power is required,
either the axle would become too small to sustain the weight, or the
wheel must be made inconveniently large. In this case a combination
of wheels and axles may be employed. Such a system corresponds to
the compound lever, and has the same law of equilibrium. The power




90               PHYSICS OF SOLIDS AND FLUIDS.
being applied to the first wheel transmits its effect to the first axle,
this acts on the second wheel, which transfers the effect to the second
axle, &c., until the force, transmitted through the series in this order,
arrives at the last axle, where it encounters the resistance. In equilibrium, the power multiplied into the continued product of the radii
of all the wheels, is equal to the weight multiplied into the continued
product of all the axles.
Trains of wheel-work are connected by an endless band, or by cogs
raised on the surfaces of the wheels and axles. Cogs on the wheel are
called teeth, and those on the axle are called leaves; the axle itself is
named a shaft. The number of teeth on the wheels, and leaves on the
pinions is proportional to their circumferences, and also to their radii.
Hence, the number of teeth and leaves is substituted for the radii of the
wheels and axles, and the law of equilibrium is stated as follows:
The power multiplied into the product of the number of teeth of all the
wheels, is equal to the weight multiplied into the product of the number
of leaves in all the pinions.
Analysis of a train of wheel-work.-A system of wheels is represented in fig. 73.  If the number                   73
of leaves in b, the pinion of the first
wheel, is one-sixth of the number of
teeth on the second wheel, e, the wheel
will be turned once by every six turns
of the pinion.  Let the second pinion,
c, have the same relation to the third
wheel, f; then the first wheel will revolve 36 times while the third revolves
once; and the radius of a, the wheel
to which the power is applied, being 3
times the radius of d, the axle which
ssutains the weight, the velocity of the
power is 3 X 36 = 108 times the velocity of the weight.  Or,                   P1im1                     P
P: WI — 1:108.
Combinations of wheel-work are employed either to concentrate or to diffuse
force; either to set heavy loads in motion by means of a small power, or to produce a high velocity by exerting a considerable power. In the first case, the
power is applied to the first wheel of the series, and is transmitted in the order
already described. In the second instance, this arrangement must be reversed;
the power must exert itself on the shaft, d, in order to produce rapid revolution of the last wheel. The crane for hoisting goods is an example of the first
kind; the watch is an instance of the second.




THEORY OF MACHINERY.                        91
118. The pulley.-Fixed pulley.-The usual form of this machine
is a small wheel, turning on its axis, and having      74
a groove on its edge, to admit a flexible rope or_  
chain. In the simple fixed pulley, fig. 74, there
is no mechanical advantage, except that which
may arise from  changing the direction of the
power. Whatever force is exerted at P, is transmitted, without increase or diminution (except   b             a
from friction and the rigidity of the rope), to the
resistance at the other end of the cord. From the
axis C, draw C a and C b, radii of. the wheel, at
right angles to the direction of the forces; a C b
represents a lever of the first class, with equal    r
arms; hence, in equilibrium, the power and
weight must be equal, and they describe equal spaces.
119. Movable pulley.-When the block or frame is not fixed, the
pulley is said to be movable. The weight is           75
suspended from the axis of the movable pul- -
ley, and the cord is fastened at one end, and   D
passing over a fixed pulley, is acted on by the
power at the other. In this arrangement,
fig. 75, it is plain that the weight is supported
equally by the power and the beam at D. For
the pulley acts as a lever of the second class,
whose arms are to each other as 1:2; the
fulcrum is at b, b c is the leverage of the
weight, and b a the leverage of the power.
The diameter b a is twice the radius b c, therefore equilibrium will obtain when the power 
is equal to one-half of the weight: i. e.,        f      a
P: W==bc: ba: 2, 2
therefore,
W
PTo raise the weight one foot, each side of the cord must be shortened
one foot, and the power, consequently, passes over two feet. The
space traversed by the power is twice the space described by the
weight.
120. Compound pulleys.-Sometimes compound pulleys are used,
each consisting of a block which contains two or more single pulleys,
generally placed side by side, in separate mortices of the block. Such
an arrangement is shown in fig. 76. The weight is attached to the




92              PHYSICS OF. SOLIDS AND FLUIDS.
movable block, and the fixed one only serves to give the power the
required direction. It is easily seen that the power      76
required at P is just the same as would be required at
any point between A and B. The weight is divided
equally among the pulleys of the movable block, and,
of course, among the cords passing around them; and   B 
as the power required to sustain a given weight is 
diminished one-half by a single movable pulley, it        
follows that such a system  will be in equilibrium 
when the power is equal to the weight divided by the
number of cords, or by twice the number of movable       \ 
pulleys.
W'
P: W==l:2n, or, P=  2-~.
In this system, as in the single movable pulley, the
space through which the weight is raised, is as much
less than the space.through which the power descends,
as the weight is greater than the power.
P: W= velocity of weight: velocity of power.      W
If the power is moved through 6 feet, fig. 76, each division of the cord
in which the movable block hangs will be shortened one foot, and the
weight raised one foot.
Another system of pulleys is represented in          77
fig. 77. In this arrangement each pulley hangsc 
by a separate cord, one end of which is attached   " 
to a fixed support, and the other. to the adjacent
pulley. The effect of the power is rapidly aug-      I 
mented, being doubled by each movable pulley 
added to the system. The numbers placed near         2 
the cords show what part of the weight is sustained by each, and by each pulley.  Such a        4 i
system, however, is of little practical use, on     ) 
account of its limited range. In the common      8  B
block system, fig. 76 (in practice the pulleys or    8
sheaves of each block are placed side by side,
to save room, here they are separated for sake
of clearness), the motion may continue until 
the movable block touches the fixed one; but
in this only till D and E come together, at
which time A will have been raised only i of that distance.
P: W=1:2" or P=.




THEORY OF MACHINERY.                         93
121. The inclined plane.-This mechanical power is commonly
used, whenever heavy loads, especially such as may be rolled, are to
be raised a moderate height. In this way casks are moved in and out
of cellars, and loaded upon carts. The common dray is itself aninclined
plane (as is clearly seen by inspecting fig. 78). Suppose a cask weigh78
ing 500 lbs. is to be raised 4 feet by means of a plank 12 feet long; it
is plain, that while the cask ascends only four feet, the power must
exert itself through 12 feet, and hence, 12: 4 = 500: 1661, the force
necessary to roll the cask.
In mechanics, the inclined plane is a hard, smooth surface, inclined
obliquely to the resistance.  The length of the plane is RS, fig. 79,
S T its height, and R T its base. The power may be applied,
a-In a direction parallel to the length;
b-Or parallel to the base;
c-Or in any other direction.
In each case the conditions of equilibrium may be derived from those
of the lever.
122. Application of the power parallel to the length of the
inclined plane.-When a body is placed upon an inclined plane, fig
79, its weight, which is the                   79
resistance to be overcome,
acts in the direction of the 
force of gravity, namely in
the perpendicular ba. Let
the power, P, act, by means
of the cord, in the direction
a c, parallel to the inclined X 
plane R S, then from  the. 
point a draw a d at right                                       /
angles with the inclined  -
plane, and  complete the                                        P
parallelogrm  a c b d. The force of gravity will be resolved into two
11




94             PHYSICS OF SOLIDS AND FLUIDS.
other forces; one represented by b c causing pressure on the inclined
plane; the other, represented by c a, tending to cause motion down the
inclined plane. This latter force is to be balanced by the power ap
plied to move the body. The body will therefore be sustained when
P: W= ac: ab;
and since the triangles a b c and R S T are similar,
P: W-= ST: RS;
Or
w    ST
m        R So
This may be illustrated by an apparatus constructed like that shown
in the figure.
If the direction of the power is parallel to the inclined plane, equilibrium will obtain, when the power is to the weight as the height of
the plane is to its length. While the weight is raised through a space
equal to the vertical height of the plane, the power must move through
a space equal to its length. If the length of a plane is 10 feet, and its
height 2 feet, P must move 10 feet, while W is raised 2 feet; hence the
power and weight are inversely as their velocities.
123. Application of the power parallel to the base of the
inclined plane.-In the second case,               80
let the power act in the direction of a P,
fig. 80, parallel to B C, the base of the
plane; and draw, the lines b a and b c P1  a
perpendicular to the direction of the
power and weight: then a b c is a 
bent lever, having its fulcrum at b, and
equilibrium will take place when     _                       C
P: W    bc: ab;           B
and, the triangles a b c and A B C being similar,
P: W- AB: BC;
Or
AB
P= WXB
B C'
If the direction of the power is parallel to the base of the plane,
equilibrium will obtain when the power is to the weight as the height
of the plane is to its base.
In this case the space described by the power is to the space described
by the weight as the base of the plane is to its height.




THEORY  OF MACINERY.                            95
124. Application of the power in some direction not parallel
to any side of the plane.-Lastly, let the power act in some direction not parallel to any side of the plane; for example: in the direction
a P, fig. 81, draw the lines b c and b a perpendicular to the directions
of the two forces; then, as before,
P: W= bc: ab.
But as the triangles a b c and A B C are not similar, the proportion
between the arms of the lever cannot                     81
be expressed by the sides of the plane.
It follows from what has been said, that
the effect of a given power is greater, as the A
height of the plane is diminished or its  
length increased; and that the effect is P 
greatest when its direction is parallel to 
the length of the plane, for, if the power
acts in any other direction, a part of its
force is expended, either in increasing the               W 
pressure of the body on the plane, or in lifting the weight directly.
125. The wedge.-Instead of lifting a load by moving it along an
inclined plane, the same result may be obtained by               82
moving the plane under the load.  When used in this            B d A
manner, the inclined plane is called a wedge.  It is
customary, however, to join two planes base to base.
In fig. 82, AB is called the back of the wedge, AC 
and B C its sides, and dC its length.  The power is
applied to the back of the wedge, so as to drive it  
between two bodies, and overcome their resistance.                
The resistance may act at right angles to the length or to
the sides of the wedge. In the first case it resembles an inclined plane, when
the power is parallel to the base; and hence the forces will be-in equilibrium
when the power is to the resistance as the back of the wedge is to its length.
In the second case it is similar to a plane when the power is parallel to the
length; and therefore in equilibrium when the power is to the resistance as
the back of the wedge to its side.
The power is supposed to move through a space equal to the length of the
wedge, while the resistance yields to the extent of its breadth.
126. Application of the wedge.-As a mechanical power, the wedge
is used only where great force is to be exerted in a limited space. In oil-mills,
the seeds from which vegetable oils are obtained are sometimes compressed
with enormous force by means of a wedge. It is everywhere employed to split
masses of stone and timber. The edges of all cutting tools, as saws, knives,
chisels, razors, shears, &cc., and the points of piercing instruments, as awls, nails,
pins, needles, &c., are modified wedges. Chisels intended to cut wood, have
their edge at an angle of about 300; for cutting brass, from 50~ to 60~; and for
iron, about 80~ to 90~. The softer or more yielding the substance to be divided




96               PIYSICS OF SOLIDS AND FLUIDS.
the more acute the wedge may be constructed. In general, tools which are
urged by pressure,. admit of being sharper than those which are driven by a
blow.
The theory of the wedge gives but very little aid in estimating its effects, as
it takes no account of friction, which so largely modifies the results, and the
proportion between pressure and a blow cannot be defined.
127. The screw.-This machine has the same relation to the ordinary inclined plane that a spiral staircase has to a straight one. This
relation is shown in fig. 83, the dotted line K L         83
marking the continuation of the spiral. The             il lll 
position of the different parts of an iiclined
plane upon a screw is shown in fig. 84. a b c d efg,
is the spiral course of the inclined plane upon the
screw, and a c' e' g' are points in the straight
inclined plane corresponding to similar letters on
the threads of the screw, as would be seen by 
winding the plane around the cylinder. The
thread of a screw projects from  the surface of the cylinder, and is
designed to fit into a spiral groove, cut in the interior of a block called
the nut; a lever is also                      84
fixed in the head of the   
cylinder to which the........ 
power is applied. The 
combination  of these c........
parts forms the mecha- a
nical power technically
called thee screw.
In working the screw, the resistance acts on the inclined face of the
thread, and the power parallel to the base of the screw. This corresponds to the case in which the direction of the power is parallel to
the base of the inclined plane. Equilibrium will, therefore, take place
when the power is to the resistance as the distance between the threads
of the screw is to the circumference described by the power.
P: W-= h: 2Rrt, and P     WX —;
2Rmc'
h being the distance between the threads, R the radius of the screw, or
of the length of the lever attached to it, and tr the ratio of the circumference of a circle to its radius.
During each revolution the power describes a circle, whose circumference depends on the length of the lever, but the end of the screw
advances only the distance between two threads; thus in this, as in all
cases of the use of machines, what is gained in power is lost in velocity.




THEORY OF MACHINERY.                       97
128. Mechanical efficiency and applications of the screw. —
The mechanical efficiency of the screw             85
is augmented, either by increasing the
length of the lever, or by lessening the
distance between the threads. If the
threads of a screw are i of an inch
apart, and the power describes a circle 
of 5 feet (120 half-inches) circumference, a power of I lb. will balance a
resistance of 120 lbs.; if the threads
are i inch apart, I lb. will balance 240
lbs., the efficiency being doubled.
Fine screws are therefore more powerful than coarse ones. The applications
of this most useful mechanical power
are too numerous to mention, but no
more frequent or important example of its use can be named than is
seen in its use in presses of nearly all kinds. A good illustration of
which is seen in the copying press, fig. 85.
129. The endless screw  is a contrivance by which a slow motion
is imparted to a wheel, as shown in fig.           S6
86. The threads of the screw act upon 
the cogs of the wheel, and serve to move
the weight Q, attached to the axis ML.
If we call the radius of the circle described by the winch D B =  r, and let 
h = the distance between the threads of
the screw, we shall have the power of the
2~r
screw =  -. Let R = MF, and
R' = M L, and the power of the wheel and axle will =-,.
Then W: P = 2wr X R: h X R;
2XrR
W-PX
hR'
Therefore the weight is to the power as the circumference of the
circle described by the winch D, multiplied by the radius of the wheel,
is to the distance between the threads of the screw multiplied by the
radius of the axis.
1 1 *




98              PIYSICS OF SOLIDS AND FLUIDS.
Q 3. Strength and Power.
130. Animal strength.-The mechanical effect produced by men
and animals is subject to extreme variation, according to the various
circumstances under which it is applied. The effect produced is determined by multiplying the load (or weight) by the speed. There is
always a certain relation between the elements, which will give the
maximum effect; for the load may be so great that it will require all
the strength of the animal to support it, and then he cannot move; or,
again, the animal may have a speed of motion so great, that he cannot
carry any load, however small.
131. Strength of men.-It has been found that the strength of a
man may be exerted, for a short time, most advantageously in raising a
weight when it is placed between his legs. The greatest weight that
can be raised in this manner, varies from 450 to 600 lbs.; its average
amount does not however exceed 250 lbs.
The greatest mechanical effect from muscular force is obtained when
the animal acts simply by raising his weight to a given height, and
then is lowered by simple gravity, as upon a moving platform, the
animal actually resting during the descent. In other words, the animal
affords a convenient mode of raising a given weight (his own) to a
certain height. Thus, if two baskets are arranged at each end of a
rope hung over a pulley, and a weight to be raised is placed in one of
the baskets, one or more men, whose weight is greater than that of the
load to be raised, can, by getting into the empty basket, raise the
weight as often as may be required. It has been found by experiment
that, in this way, a man working eight hours can produce an effect
equivalent to 2,000,000 lbs. raised one foot; while at a windlass an
effect of only 1,250,000 lbs. is produced, and at a pile engine, only
750,000 lbs. In the tread-mill, the daily effect of men of the average
strength is 1,875,000 lbs. raised one foot. Spade labor is one of the
most disadvantageous forms in which human labor can be applied; the
force exerted being always much greater than the weight of the earth
raised. The muscular effect of the two hands of a man is about (50 k)
1101 lbs., and for a female about two-thirds of this quantity.
132. Horse-power machines.-One of the most advantageous
methods of applying the strength of animals, is by machines constructed upon the principle of the tread-mill. In practice, however, it
has been found more convenient to apply horse-power to machinery by
means of a large beveled or toothed wheel, fixed horizontally on a
strong vertical axis, as in fig. 87. The horses are attached to projecting arms of this wheel, and as they move in their circular path, they




THEORY OF MACHINERY.                             99
push against their collars, and make the wheel revolve. This beveled
wheel acts on a beveled pinion attached to a horizontal shaft, in connection with the machinery to                       87
be set in motion. The maximum
effect which a horse can exert
in drawing is 900 lbs., but when
he works  continuously, it is
much less. In the machine just
mentioned, a horse of average
strength produces as much effect
as seven men of average strength
working at a windlass. Accord- 
ing to  experiments  made by
Predgold, it appears that the
average load which a single horse can draw, at the rate of 20 miles per
day, in a cart weighing 7 cwt., is one ton of 1800 lbs.
133. Table of the comparative strength  of men and other
animals.-The following estimates of the relative strength of man and
other animals, have been given by the authorities whose names are
indicated, Coulomb's estimate of the labor of a man being in each case
taken as the unit.
Carrying loads on the back, on a level road:
Horse, according to Brunacci,    4'8
t         " i    Wessemann,  6-1
Mule,        "     Brunacci,    7'6
In drawing loads, on a level road, with a wheeled vehicle:
Man with a wheelbarrow, according to Coulomb,    10'0
Horses in four-wheeled wagon,  "        "        175'0
"   in two-wheeled cart, according to Brunacci, 243-0
Mule,       "         "          "         "    233-0
Ox,         "          "         "         "    122-0
Hassenfratz gives the following comparative estimate:
In carrying loads on a level road.  In drawing loads on a lev:l road.
Man,........  1-0  Man,......                               1-0
Horse,.......   8-0  Horse,.......  7'0
Mule,........  8-0  Mule,........ 70
Ass,........           4'0  Ass,......                  2-0
Camel,.....    31-0  Ox,..... 4 to 7-0
Dromedary,.....    25-0  Dog,......                       0-6
Elephant,...... 147-0  Reindeer,......                   0-2
Dog,....                   1.0............
Reindeer,......  3-0............
134. Steam-power.-Water is converted into steam by the applica,
tion of heat. Steam is an elastic, condensible vapor,, capable of exert



100             PHYSICS OF SOLIDS AND FLUIDS.
ing great force. During the conversion of a cubic inch of water into
steam a mechanical force is exerted, which may be stated, in round
numbers, as equivalent to a ton weight raised one foot high. The
water is merely the medium by which the mechanical effects of heat
are evolved. The real moving power is the combustible, the coal or
wood, consumed in the evaporation of the water.
The maximum  effects from  a given weight of coal, in evaporating
water, and consequent mechanical effect, have been obtained in Cornwall, England, where a bushel of coal, weighing 84 lbs., has produced
a mechanical effect equivalent to 120,000,000 lbs. raised one foot.
Probably 100,000,000, is the maximum mechanical effect attainable, in
regular work, by the consumption of a bushel of coal.
As the maximum effect produced by man is 2,000,000, and that of a
horse 10,000,000, it follows, that one bushel of coal consumed daily
may perform the work of 50 men or 10 horses.
In the chapter on heat and the steam-engine, this subject will be
more fully considered. It is introduced here only for the sake of the
convenient standards of force it gives us.
The dynamometer, already described (37), is employed to measure the
efficiency of any given mechanical power.
135. Perpetual motion.-Many visionary persons have convinced
themselves of the possibility of constructing a machine to work con
tinuously, with no new access of power. That such a machine is im
possible, in the nature of things, is             88
clear from the fact that no combination of parts in a machine can create
power. A machine can only transmit
force, subject to the various losses
incident to friction and other resistances.
Fig. 88 shows one of the numerous
forms of apparatus contrived in the
vain effort to elude the laws of nature 
and produce a perpetual motion. The
eight balls are hinged on points, in
such a way that those on the falling
side are held farther from the axis than those on the rising side. Not
only does experiment show that such a machine will not work, but it
is plain that the sum of the resistances (aside from friction, &c.)
must equal the sum of the powers.
Nature, in cataracts, in the revolution of the earth and other heavenly
bodies, furnishes us examples of perpetual motion. But in mechanics




THEORY OF MACHINERY.                      101
this term  implies the assumed capacity of a machine to continue the
performance of its work by some renewing force-as of a clock which
should wind itself up in proportion as by gravity it runs down-a
thing plainly impossible.
# 4. Impediments to Motion.
136. Passive resistances. —Besides those resistances which a machine is designed to overcome, there are certain others which arise
during the movement of the machine, and oppose its useful action by
destroying more or less of the moving power. These forces are designated by the general name of passive resistances, or impediments to
motion.
Several kinds are distinguished:
1st.-When we attempt to cause one body to slide over another, a
resistance is experienced, so that it is necessary to use a certain degree
of force to commence the sliding, and also to continue the motion after
it has been begun. This is the resistance called sliding friction, or
simply friction.
2d.-When a cylindrical body is rolled on a plane surface, the movement is opposed by a force called the rolling friction. It is seen, for
example, in the rolling of carriage wheels on the ground.
3d.-The ropes and chains which enter into the composition of some
machines, are supposed, in theory, to be perfectly flexible, but as they
are not so, a considerable loss of power is caused by their stiffness, or
imperfect flexibility.
4th.-The movements of all machines take place either in air or
water, and the particles of these fluids which come in contact with the
machine, are continually set in motion, which can only happen at the
expense of the moving power. This is called the resistance offluids.
137. Sliding friction.-If the surfaces of bodies were perfectly hard
and smooth, they would slide upon each other without any resistance.
But the most highly polished surfaces are, really (as they appear under
the microscope), full of minute projections and cavities, which fit in
each other when two surfaces are brought into contact. The force
required to overcome the roughness and consequent adhesion of surfaces is the measure of friction. This quantity, divided by the weight
of the body, forms a fraction which is called the co-efficient of the
friction.
138. Starting friction-Friction during motion.-The amount
of force necessary to commence the motion of two bodies, sliding on each
other, is, in most cases, greater than the force required to continue the
movement uniformly after it has been begun; hence this resistance is




102            PHYSICS OF SOLIDS AND FLUIDS.
distinguished into two kinds, starting friction, and friction (luring
motion. They are also called statical and dynamical friction. Whewell
proposes to name the former striction, reserving the word friction for
the latter. However named, the laws of each can be determined only
by experiment.
Coulomb's apparatus for determining starting friction.-Different observers are by no means agreed in respect to all the laws of
friction; we shall here follow the results obtained in 1781, by the
celebrated French philosopher and mathematician, Coulomb. In 1831,
Morin, by command of the French government, repeated and enlarged
the experiments of Coulomb, usually verifying his general conclusions.
The principal apparatus used by Coulomb is represented in fig. 89.
89
It consists of a horizontal table; a box, A, to receive the weights used
to produce the different pressures; a pan, D, on which were placed the
weights to drag the box along the table by means of a cord passing
over a pulley. The box was mounted on slides, of the same substance
on which the experiment was to be made, and corresponding slips of
the same, or a different substance, were placed under the sliders on
the table. The amount of the weight required to be placed in D, to
move the box from a state of rest, is the measure of starting friction;
and the weight necessary to continue the movements uniformly, is the
measure of friction during motion.
Results of Coulomb's experiments on starting friction.Without detailing the experiments, it will be sufficient to state their
general results embraced in the following laws:
Friction during movement is,
lst.-Proportional to the pressure exerted upon the sliding surfaces
2d.-Independent of the extent of the surfaces in contact.
3d.-Independent of the velocity of the movement.
4th.-Greater between surfaces of the same than surfaces of different
materials




THEORY OF MACHINERY.                          103
5th.-Greatest between rough surfaces, and is diminished by polishing, and usually by the use of suitable unguents.
Friction at starting is,
lst.-Proportional to pressure.
2d.-Independent of extent of surface.
3d.-Generally increased by polishing the surfaces.
The friction at starting, and during the movement, are the same,
when the sliding surfaces are hard, like the metals; but if the bodies
are compressible, like wood, the starting friction is much the greatest.
When at least one of the surfaces is compressible, the resistance is not
always the same, but varies according to the time the surfaces have
been in contact. If wood slides on wood, the starting friction attains
its greatest intensity in two or three minutes; but if the sliding surfaces are wood and metals, the greatest intensity is not reached for a
much longer time, several hours, and sometimes several days. But after
a certain time has elapsed, the starting friction is no longer augmented
by lengthening the time of contact.
It appears strange at first, and contrary to our previous ideas, that
the friction at starting, and during movement, should not be increased
by enlarging the surfaces in contact, and vice versa. The explanation is
this.  Friction is proportional to pressure; if, therefore, two bodies
have the same weight, and one has twice the surface of the other, the
weight, being equally distributed on each surface, will be twice as
great on each point of the surface of the first body as on each point of
the second, and consequently the friction at each point of the first is
twice the friction at each point of the second, and the whole friction
must be the same for each body. This law, however, does not hold good
in extreme cases.
With the same pressure, the friction varies exceedingly according to
the nature of the surfaces in contact. The following table shows the
ratio of friction in several cases, the pressure being 100.
Ratio of friction to pressure.    i
Surfaces in contact.
At starting.  In motion.
Wood upon wood,.........                     0'50           0-36
i"  ",    "   with coating of soap,.  0'36                 0'14
it  t"    "    "    "    of tallow,.        0'19           0-07     i
"I   "  metals,.........                    0'60           0-42,,,,,,   with coating of tallow,         0-12           008 
Leather bands on wood,.......                0'63           0-45
"        wet,.........7                               0 33
Metals on metals,..                018            018
it"    "    "   with coating of olive oil,   0-12           0-07
K. _ _ _ _ __       __ _       _ _ _ _ _ - -   _ _ _ _ _ _




104             PHYSICS OF SOLIDS AND FLUIDS.
139. Rolling friction.-The resistance experienced in rolling a
cylinder along a plane surface is distinct in character from the friction
produced in sliding the cylinder, and very much less in amount. In
wood rolling on wood the proportion of resistance to pressure is from
16 to 1000, or 6 to 1000, while the sliding friction in the same case would
be as 5 to 10, or 36 to 100, according to the kind of sliding friction. The
resistance of rolling friction arises from a slight change of form produced in the body, and the surface on which it moves, and corresponding to the amount of pressure. The cylinder is flattened, and the plane
depressed, so that the moving force is exerted in continually nloving
the body up a very minute inclined plane.
Coulomb's apparatus for determining rolling friction.-The
apparatus employed by Coulomb, consisted of two bars, horizontal and
parallel, with a space between them, fig. 90.  A cylinder of the same,
or a different substance, was placed                  90
transversely across the bars, and loaded
with any required pressure by hanging
strings upon it, carrying equal weights
at their extremities.  Another string,
wound several times around the middle
of the cylinder, carried a pan c to receive the weight necessary to produce
motion. It is evident that this weight                      1
acted always at the extremity of the
radius of the cylinder as a lever.
Results  of  Coulomb's  experiments on rolling friction. —From the 
experiments were derived the following
laws:
The friction of rolling bodies is,
1st.-Proportional to pressure.
2d. —Independent of velocity, of the diameter of the cylinder, and of
the extent of the surfaces in contact.
3d. Greater when the substances are the same than when they are
different.
4th.-Not diminished by coatings of grease, but is so by the polish
of the surfaces.
If the force which produces the movement, instead Of being applied
always at the same arm of the lever, fig. 90, were applied horizontally
at the centre of the cylinder, or at the upper extremity of its vertical
diameter, it would be inversely proportional to the diameter.
The friction of the axle of a wheel, whether the axle itself turns, or




TIIEORY OF MACHINERY.                     105
the wheel on the axle, is somewhat less than sliding friction, but obeys
the same laws. The friction of axles may be reduced one-half or onequarter its original amount by the use of proper unguents.
140. Mr. Babbage's experiment.-Mr. Babbage cites an instructive experiment to illustrate the decrease of friction. A block of stone
weighing 1080 lbs. was drawn on the surface of a rock by a force of
758 lbs.; placed on a wooden sledge, it was drawn on a wooden floor by
a force of 606 lbs.; when both wooden surfaces were greased, 182 lbs.
was sufficient; and when the block was mounted on wooden rollers of
three inches diameter, a force of only 28 lbs. was required to move it.
141. Advantages derived from friction.-The advantages arising
from friction are vastly greater than the loss of power which it
occasions. Without this property of matter it would be equally impossible to make or use machines, for nothing could be nailed, or screwed,
or tied together, or grasped securely in the hand. From the difficulty
of walking on very smooth ice, we may infer how useless would be the
effort to move, if our feet met no resistance whatever.
142. Rigidity of ropes.-When ropes are used to transmit force,
their stiffness occasions a considerable loss of power, amounting, in
some combinations of pulleys, to two-thirds of the whole power. The
amount of the loss from this cause is modified by many external circumstances, such as the dampness of the cordage, its quality, and the
manner in which it is made. In general, the resistance of ropes is,
ist.-Proportional to the tension to which they are subjected.
2d.-It increases with the thickness, and is greatest in those that
have been strongly twisted.
3d.-It is inversely proportional to the diameter of the wheel or
cylinder around which the ropes are bent.
143. Resistances of fluids.-The resistance which a moving body
meets in air and water, is an effect of the transfer of motion from the
solid to the particles of the fluid. For the moving body must constantly
displace a part of the fluid equal to its own bulk, and the motion thus
communicated is so much loss of the motive power. When other circumstances are the same, the denser the medium the greater will be
the resistance which it offers. Newton demonstrated that if a spherical
body moves in a medium at rest, and whose density is the same as its
own, it will lose half of its motion before it has described a space equal
to twice its diameter. The resistance encountered by a body moving
in water is 800 times greater than if it were moving with the same
velocity in air; for water being 800 times more dense than air, the
body must displace and communicate its own motion to 800 times as
much matter in the same time.
12




106             PHYSICS OF SOLIDS AND FLUIDS.
The resistance also depends upon the extent and form of the surface
which is directly opposed to the resistance; i. e., at right angles to the
direction of the motion. A body with a pointed, wedge-shaped, or curved
surface, is less opposed than one whose surface is flat and broad.
The resistance increases as the square of the velocity; for if the
velocity is doubled, the loss of motion must be quadrupled, because
there is twice as much fluid to be moved in the same time, and it las
also to be moved twice as fast. Again, let the velocity be trebled, then
the body will meet three times as many particles of the fluid in the
same time, and communicate three times the velocity: therefore the
resistance is 3 X 3 - 9 3 32.
Bodies having the same figure and density overcome the resistance
of fluids more easily in proportion to their size. In cannon-balls, for
example, the extent of surface to which the resistance is proportional
increases as the square of the diameter, while the weight, or power to
overcome resistance, increases as the cube of the diameter. If twc
balls have diameters in the ratio of 2: 3, the resistances which they
will encounter at the same velocity of projection, will be in the ratio
of 4: 9, and their moving force in the ratio of 8: 27.
144. Actual and theoretical velocities.-In consequence of these
impediments to motion, the actual movements of bodies are materially
different from the theoretical motions explained in previous sections.
The motion of falling bodies is very far from being uniformly accelerated, nor do all bodies fall with equal rapidity, as theory requires,
- and as was seen to be true in the guinea and feather experiment. The
resistance of the air, which is very small at first, rapidly increases, and
after a certain time becomes equal to the force of gravity, when the
body will no longer be accelerated, but move uniformly through the
remainder of its descent. The descent of bodies on inclined planes
and curves deviates still more from uniformly accelerated motion, since
the effect of friction is added to the resistance of the air.
145. Ballistic curve.-A  still greater difference is observed between the actual and theoretical motions of pro-         91
jectiles (103). Instead of describing a parabola,
A E B, fig. 91, the projectile actually describes
the curve A C D, called the ballistic curve, which        c
never attains so great a vertical height, or so long  A.-B
a range as the corresponding  parabola, and
which, toward the end of its course, continually             D 
approaches the perpendicular, E F.  A  fourpound shot, which flies 6437 feet in the air, would traverse in a vacuum
a space of 23,226 feet.




THEORY  OF MACHINERY.                           107
As in the case of friction, the benefits resultirng from this state of things
overpay the disadvantages.  Fish could not swim, nor birds fly, were it not foi
the resistances of the media they inhabit. The paddle-wheels of a steamer
would not move it, nor its rudder guide its course, if they met no resistance to
their movements. And we can very well dispense with a perfect theory of projectiles, if thereby the rain is prevented from descending with the destructive
velocity of hail-stones.
Problems.-Vis Viva.
47. If a locomotive and train move 20 miles an hour, how much greater force
will be required to move a train weighing three times as much 25 miles an
hour?
48. If a locomotive weighing 30 tons will draw a train weighing 90 tons 15
miles an hour, at what velocity will it draw a train weighing 30 tons? The
weight of the locomotive is to be added to the train in both cases.
49. What will be the relat;ve destructive power of a hurricane moving 60
miles an hour, and another moving 90 miles an hour?
50. If a pile-driver weighing 1500 lbs. raised 20 feet strikes with a given force
to overcome resistance, to what height must it be raised to give a shock two and
a half times as great?
51. What is the comparative destructive power of a cannon-ball weighing 64
lbs. flying 1000 feet per second, and another ball weighing 200 lbs. flying 1500
feet per second?
The Lever.
52. Two weights, 3 and 4, balance on the extremities of a lever 4 feet long;
find the fulcrum.
53. Four weights, 1, 3, 7, 5, are placed at equal distances on a straight lover.
Determine the position of the fulcrum.
54. Two men carry a weight of 2 cwt. hung on a pole, the ends of which rest
on their shoulders; what part of the load is borne by each man, the weight
hanging 6 inches from the middle of the pole, the whole length of which is 4
feet?
55. A beam, 18 feet long, is supported at both ends; a weight of 18 cwt. is
suspended at 3 feet from one end, and a weight of 12 cwt. at 8 feet from the
other end; required the pressure at each point of support.
56. A uniform beam, 40 feet in length, the weight of which is 4 cwt., is supported by two props, A and B, 30 feet apart; a weight of 24 cwt. is then suspended on the beam at the distance of 10 feet from B, the beam projecting 8
feet over the prop A, and 2 feet over that at B; required the pressure on each
of the props.
57. On a lever 3 feet in length a weight of 500 lbs. is suspended at one end,
at 22 inches from its fulcrum; what weight at the other end will keep the lever
in equilibrium, the lever being assumed to be without weight?
Wheel and Axle.
58. A power of 10 lbs. on a wheel the diameter of which is 10 feet, balances
a weight of 300 lbs. on the axle; what is the diameter of the axle, the thickness
of the rope on the wheel being one inch, and that of the rope on the axle two
inches?




108L              PIYSICS OF SOLIDS AND FLUIDS.
59. A weight of 2240 lbs. is sustained by a rope of 2 inches in diameter, going
round an axle 4 inches in diameter; what weight must be suspended at the circumference of a wheel-radius 6 feet-by a rope of the same thickness, to obtain
equilibrium?
60. In a combination of wheels and axles there are given the radii of the
wheels, 20, 26, and 48 inches, and the radii of the pinions and axle, 4, 5, and 8
inches. If a power of 1 cwt. be applied to the circumference of the first wheel,
what weight will it be able to sustain at the circumference of the axle, or last
shaft?
61. The number of teeth in each of three successive wheels is 144, and the
number of teeth in each of the axles or pinions is 6; what weight will this machine support on the last shaft with a power of 2 cwt. on the first wheel?
The Pulley.
62. In a system of pulleys, such as is shown in fig. 76, the number of movable pulleys being 5; required the weight, the power being 500 lbs., and the
weight of the movable block and pulleys being 30 lbs.
63. What power at P, fig. 77, will be required to balance a weight, W, of 3
tons, the number and arrangement of the pulleys being as shown in the figure?
Inclined Plane.
64. What power acting as in fig. 79, will balance a weight of 300 lbs. on the
inclined plane, the length of the plane being 25 feet, and the vertical height
five feet?
65. On an inclined plane, whose base is 10 feet and height 3 feet, what power
acting parallel to the base will balance a weight of 2 tons?
66. What power is required to draw a train of cars, weighing 40 tons, up a
railway grade rising 1 foot in every 100 feet?
The Screw.
67. What weight can be raised by means of a screw having its threads one
inch apart, by a power of 150 lbs. acting at a distance of 6 feet from the axis
of the screw?
68. Supposing one-third of the power is lost in overcoming the friction of
the screw, what power will be required, acting 3 feet from the axis of the screw,
to raise 3 tons, the threads of the screw being 2 inches apart?
69. What power at the winch D, fig. 86, is required to raise a weight of 2 tons
at Q, if the radius of the axle is 6 inches, the radius of the wheel 3 feet, the
distance between the threads of the screw -. part of the circumference of the
wheel, and the length of the winch D B  = 2 feet?
Resistance.
70. If a mass of iron weighing 5 tons slides upon iron rails, what force is
required to start it, and how much to keep it moving afterwards?
71. If a steam vessel of 100 tons is moved through the water at 10 miles an
hour, by an engine of 300 horse-power, what is the power of an engine required
to propel another vessel, of the same model, of 2000 tons at the same speed?
72. If a ball, 6 inches in diameter, is discharged from a cannon at the
rate of one mile in 7 seconds, how much greater force would be required to
throw a ball of double the weight with the same velocity, taking into account
the resistance of the air and the dimensions of the balls?
73. If an engine of 500 horse-power propels a vessel of 1500 tons 12 miles an
hour, at what velocity will an engine of 600 horse-power propel a vessel of 2000
tons, built on the same model as the preceding?




PART SECOND.
THE THREE STATES OF MATTER.
CHAPTER I.
MOLECULAR FORCES.
146. Cohesion and Repulsion.-The three states of matter (15)the solid, liquid, and gaseous-exist, as is assumed, in virtue of certain forces inherent in the particles of matter, and called molecular
forces. These forces are either attractive or repulsive, drawing the particles of bodies toward. each other, or tending to separate them. In
solids the attractive force greatly overpowers the repulsive, and the
particles of matter become therefore relatively fixed at certain distances
from  each other-not being in actual contact, but having, as we have
seen (23), numerous pores between them. Heat may enlarge and cold
diminish these pores, and with  Ihem  the sensible magnitude of the
solid; but the integral particles of the solid cannot be separated without the exercise of some exterior and greater force. When the particles of a body are not separated too far, they return again, upon
the withdrawal of the constraining force, to their original position
(Elasticity). This species of attraction existing between particles of
the same kind is distinguished by the term cohesion, and when existing
between particles of an unlike kind, it is called adhesion.
Repulsion.-If we admit, as the phenomena of porosity demand
(23), that in spite of cohesive attraction, the particles of bodies do not
actually touch each other, it follows that there must exist in the molecules of matter a second and counterbalancing force opposed to cohesion,
12*                                             (109)




110              THE THREE STATES OF MATTER.
and-in solids-in equilibrium with it.  This force is called repulsion,
We shall presently revert to the evidence of its action on matter.
While the existence of these two molecular forces is in many cases
capable of direct proof, the exact mode of their action is chiefly conjectural. It is, however, certain that the attractive forces act only at insensible distances. In this respect the molecular forces are to be distinguished from gravitation,which acts at all distances. Chemical attraction
is also distinguished from the mechanical forces of cohesion and adhesion,
by the important fact that its exercise is invariably attended by the
loss of specific identity (7), and, of course, by the substitution of new
qualities in the compound for those characteristic of its constituents.
Since the force of gravity is proportional to the mass, and inversely as
the distance, if cohesion were merely the attraction of gravitation acting at
insensible distances, the particles of a body situated at the centre of gravity of
a large mass, should cohere more strongly than particles at a distance from the
centre of gravity, or than the same particles when the mass is reduced to fragments, but no such difference has been observed, we must therefore conclude
that gravity and cohesive attraction are essentially different forces.
147. Examples of cohesion among solids.-Cohesion, when once
destroyed by mechanical violence, is not usually brought into exercise
again by mere contact of the separated particles. Thus the broken
fragments of a glass vessel, or of a stone, do not reunite at ordinary
temperatures. Two hemispheres of tarnished lead will not adhere by
their flat surfaces by mere pres-                  92
sure, but if the coating of oxyd is^ 
first removed by a sharp knife,
and the two clean surfaces are
then  pressed together, with  a
slight wrenching  motion, they
will cohere strongly.  Arranged
as in fig. 92, two surfaces one
inch in diameter will sustain ten
pounds or more.  This is only
an example of welding at common temperatures, a process sufficiently familiar in hot iron. Wax,
dough, india rubber, and other
similar substances, offer examples
of a like nature, provided clean
surfaces  be  pressed  together.                                   i
Dust, or other foreign bodies,                                     1,. illl
prevent this union. Even polished glass plates, allowed to remain long




MOLECULAR FORCES.                       111
in contact, if perfectly clean, and under pressure, have been known to
cohere so strongly as to separate by fracture in any other direction
sooner than in the line of junction. Boyle demonstrated that this fact
is not accounted for by attributing the action to atmospheric pressure.
He suspended a pair of adhesion plates in the vacuum of an air-pump,
where, in the absence of atmospheric pressure, it required still a considerable weight to detach the surfaces.
Adhesion is distinguished from cohesion by the fact that while the
latter occurs between particles of a like kind, producing homogeneous
bodies, the former takes place between particles of unlike kinds, producing heterogeneous bodies. Glue binding together pieces of wood is
an example of adhesion. This species of mechanical attraction is,
however, seen in its most important relations in the curious phenomena
of capillarity, to be discussed hereafter.
The terms cohesion and adhesion are often used interchangeably,
and, when the distinctions here pointed out are borne in mind, no evil
will arise from this use of terms.
The force of cohesion among the particles of solids, when exerted
under favorable conditions, produces the regular forms of crystals, to
which we shall presently revert.
148. Cohesion in liquids and between liquid  gases and
solids.-The force of cohesion in liquids gives the spherical form to
drops of rain and dew, and rounds the drop of water suspended from
the end of a glass rod. If two drops of water or any other liquid
approach each other near enough, they unite to form a larger spherical
drop. A soap-bublle is only a large hollow sphere of water, whose
outer film of liquid assumes and preserves its spherical form in virtue
of cohesive attraction and the laws of liquid equi-      92b
librium. The soap, while it adds to the viscous condition of the water, really diminishes its cohesive        \
force, as was shown by Prof. Henry. The force of  
cohesion in water may be directly measured by sus-  
pending a counterpoised disk of glass or metal from
a scale pan, fig. 92b adjusted to allow the disk just to 
touch the surface of the water. The weight required
in the opposite pan, to separate the disk from the water, then becomes
the measure of cohesion among the particles of water forming the outer
circle of contact.
By this means Gay Lussac found that a disk of 4'362 inches in
diameter required 982 grains to separate it from water, while from
alcohol (density 0-819) and spirits of turpentine, 478'83 and 525
grains, respectively, produced separation; all being at the temperature




112             THE THREE STATES OF MATTER.
of 46~ Fahr. The thickness and material of the disk made no difference
in the result, showing that the force of cohesion was the only force to
be overcome, and that this force was exerted at a distance less than the
thickness of the film of liquid necessary to moisten the surface of the
disk. It is also evident that the weights obtained do not represent the
whole cohesive force in each case, since, from  the circumstances of the
trial, it can be only the outer circle of particles whose cohesion is overcome, and this being the largest circle, each succeeding row or line
of particles yields readily to the same force.
Between liquids and solids the force of adhesion is modified by the
phenomena of capillarity and surface attraction.
Between gases and solids cohesion is seen to exist when we
attempt to wet the polished surface of a steel blade, or a clean surface
of glass, with water. The liquid fails to wet the polished surface of the
metal, &c., owing to the film of air adhering to it, due to the attraction
of the solid for the air. If the blade is slightly heated, or its surface
is roughened mechanically or by acids, this film of air is removed, and
the blade is then wetted. (See Smee's battery: Electricity.)
Gases do not manifest cohesion among themselves, because the repulsive force overcomes it, but numerous examples of its exercise may be
quoted besides that just named.  The bubbles of gas escaping from
aerated water adhere to the sides of a glass vessel from this cause.
But above all is this seen in the power of recently ignited charcoal to absorb and retain gases. Owing to its numerous sensible pores, charcoal
presents a very large surface in a small space. The more compact the
wood the more numerous are these pores, and the more remarkable the
consequent absorption of gas.  Different gases are also very differently
absorbed by it, depending on their condensibility and solubility. Thus,
while only four or five volumes of common air are absorbed by charcoal,
thirty volumes of carbonic acid, and eighty or ninety volumes of ammonia or chlorohydric acid gas, are absorbed by charcoal recently
ignited. This curious and important property is easily illustrated over
the mercurial trough, by using glass cylinders, filled with the various
gases, to cover bits of charcoal placed on the mercury-the absorption
commencing at once and advancing gradually for some hours.
We will consider the action of molecular forces, first, between molecules of the same kind, and, second, when acting between molecules of
unlike, kinds, to which are referred the phenomena of capillarity.




PROPERTIES OF SOLIDS.                     113
CHAPTER II.
OF SOLIDS.
MOLECULAR FORCES ACTING BETWEEN PARTICLES OF LIKE KINDS.
1. Properties of Solids.
149. The characteristic properties of solids, now to be considered, are, 1. Crystalline Form; 2. Elasticity; 3. Resistance to Fracture (including Strength of Materials); 4. Hardness, and 5. Those
properties dependent on a permanent change in the arrangement of the
molecules-as Ductility, Malleability, Temper, &c.
150. Structure of solids.-In solids the particles of matter are
held in fixed relation to each other by the molecular forces (146). The
relative disposition of the molecules, or of their groups, constitutes what
is called structure in solids. This structure may be either symmetrical
or regular, as in living beings and crystals, or amorphous, as in most
rocks and many other substances.
There exists in nature a plan, which cannot be mistaken, to combine
matter in complete and symmetrical wholes. The bodies of animals
consist, usually, of two equal, (or nearly equal), and similar sets of limbs
and organs, one on the right and one on the left side. The organs of
most flowering plants are similarly and regularly arranged in whorles of
three members, as in the lily, or of five, as in the rose, or in some other
simple numbers, and the same law is beautifully exemplified in the
arrangement of the leaves and branches of all plants and trees (phyllotaxy). In the animal and vegetable world, the laws which direct the
aggregation of matter are those of VITALITY, and it is observed that
most of the forms thus produced are bounded by curved lines and
surfaces.
In the inorganic or lifeless world different laws are in force, and in
the production of solids the atoms, under favorable circumstances,
arrange themselves in forms which are angular and bounded by plane
surfaces. The geometrical forms thus produced are analogous to the
more complicated results of vitality as seen in animal and vegetable life.
These forms are called CRYSTALS, and the laws governing the aggregation of matter into such forms, are called the laws of crystallization.
When solids are formed in a manner unfavorable to the regular
action of the molecular forces, the regular forms of crystals are not




114              THE THREE STATES OF MATTER.
produced, but a mass which has perhaps some traces of crystalline
structure (as in marble), or which is entirely amorphous(152), according
as the act of solidification has been more or less disturbed. Thus, in
granite we easily detect the crystalline structure of some of the constituents closely aggregated, while in slates and many mechanical
rocks no traces of crystalline structure can be seen.
# 2. Crystallography.
151. Conditions of crystallization.-In  order that crystals may
form, it is a necessary condition that the molecules of the body to be
crystallized should have freedom  of motion among themselves, and
ample time to arrange themselves in accordance with the force of crystallogenic attraction. These conditions may be met in either of the
following methods: 1. By solution; 2. By fusion; 3. By sublimation
or evaporation; or, 4. By electrical or chemical decomposition.
(a) By solution.-Many solids dissolve in water; thus most salts, as
common salt, Epsom  salts, saltpetre, borax, alum, &c., form  a clear
solution in water, in which all crystalline attractions are subordinated,
until by gradual evaporation, or by cooling from  a saturated hot solution, the several salts reappear, each in its own appropriate form.
Sulphur and phosphorus also, dissolved by heat in bisulphid of carbon,
crystallize by the cooling of the solution. Some substances are equally
soluble in cold or in hot water, and crystals are obtained from their
solutions only by evaporation, with or without the aid of heat.
Common salt is an example of such a substance; when      93
evaporated very gently, as by solar heat, perfect cubes
are formed; if rapidly, as by fire, a confused mass of
irregular crystalline grains result. Sometimes the floating crystals, as they grow in weight continually, but
slowly, sink, giving rise to the curious hopper-shaped      -^
forms seen in fig. 93. 
Alumina dissolves in melted boracic acid, and the solution, exposed
for a time to the highest heat of a porcelain furnace, loses the boracic
acid slowly by evaporation, and the alumina crystallizes as rubies or
sapphires.  Many other gems have thus been obtained, of microscopic
size, by M. Ebleman, by solution in boracic or phosphoric acids, or
their salts, at a high heat.
(b) Byfusion.-By melting sulphur, bismuth, and many other substances, in crucibles, and allowing them to cool very slowly; when a
crust has formed on the surface it is pierced, and the contents remaining fluid are turned out, the interior cavity is found lined with crystals
of the substance experimented on.
(c) By sublimation.-By heat many substances rise in vapor, and on




CRYSTALLOGRAPHY.                         115
cooling again, in a proper receptacle, assume their appropriate crystalline forms-camphor, sulphur, arsenious acid, iodine, arsenic, sal-ammoniac, &c., can be thus crystallized.
(d) By electrical or chemical decomposition.-By adding to a solution
of some substances some other dissolved body, which causes the first
to become insoluble, a crystalline powder often falls (this is true in
most cases of precipitation), due to the formation of a new compound,
of a less solubility than either of the substances employed. The crystals
of metals, e. g. of copper, gold, silver, &c., are easily formed by the
processes of electro-metallurgy.
152. Amorphism.-Amorphism  is that state of a solid in which
there is no trace of a crystalline structure; examples of such a state
are seen in common glass, gun-flint, wax, obsidian, sugar-candy, &c.
An amorphous body, having no planes of cleavage, is broken in one
direction as easily as in another. Bodies are generally more soluble,
less hard and dense, in the amorphous than in the crystalline state.
An amorphous body may be produced in a number of ways; for
example, by fusion, as in the case of glass; by evaporation of solutions, as those of the gums and glue in water; and by precipitation
from their solutions, as is the case with alumina and phosphate of lime.
The property of toughness, seen, as for example, in emery (amorphous corundum), and horn-stone (amorphous quartz), is much more highly developed in
the amorphous than in the crystalline varieties of these minerals.
153. Crystalline  forms.  Definitions.-The  crystalline  forms
assumed by the same substance are, with certain limitations, always
the same; depending on the nature of the substance, and are therefore
essential forms. The study of these forms and the laws of crystallogeny,
reveal to us all that we know of the ultimate forms of matter.
A crystal is a polyhedron, and the terms of solid geometry are used
in crystallography without change.
94        Replacement.-An edge or angle is           94&
replaced when cut off by one or more
secondary planes. Fig. 94, i i.
_IOlF    Truncation.-An edge or angle is  
truncated when the replacing plane is         O  i 2i0
equally inclined to the adjacent faces.
Fig. 94.
Bevelment.- An edge is beveled when replaced by two planes which
are respectively inclined at equal angles to the adjacent faces i 2 i 2, fig.
94b. Truncation and bevelment can only occur on edges formed by the
meeting of equal planes.




116             THE THREE STATES OF MATTER.
The axes of a crystal are imaginary lines passina through its centre,
and about which two or more faces are symmetrically arranged. They
connect either the centres of opposite faces, fig. 95, or edges, fig. 96, or
the apices of opposite solid angles, fig. 97, or of both edges and angles,
fig. 98.
95              96               97                98
25                                                 -R
Three axes are employed for the different systems in crystallography
(excepting the sixth, fig. 114), whose length may be equal, or only two
alike, or all unequal; they may also be at right angles to each other, or
oblique.
A prism is a column having any number of sides. In crystallography we have four and six-sided prisms, which may be either right
prisms, that is, erect; or oblique prisms, that is, inclined.
Four-sided prisms occur of a number of kinds; their bases may be
either square, rectangular, rhombic, or rhomboidal. If the base is a
square, or a rectangle, and the prism erect, the eight solid angles are
equal and rectangular; the edges are twelve, and may vary; for
example,
A cube is bounded by six equal sides (the lateral sides being equal
to the bases), and the twelve edges are all equal, fig. 95.
99                          100
i ^    ii,
A right square prism, fig. 99, has a square base and a height which
may be either greater or less than its breadth; its sides are equal
rectangles, the eight basal edges (four at each base) are equal to each
other, but differ from the four lateral edges.
A right rectangular prism, fig. 100, has a rectangular base, and sides
also rectangular, the opposites only equal; two edges at each base dif



CRYSTALLOGRAPHY.                         117
fer from the other two, while the lateral edges are also different; hence
there are three sets of edges, four in each set.
The base may also be a rhomb or rhomboid.
A right rhombic prism, fig. 101, has a varying height and a rhombic
base. Its plane angles are two obtuse and two acute, with correspond.
ing solid angles and lateral edges; the four lateral faces are rectangles,
and, like the basal edges, are equal.
101                  102                   103
An oblique rhombic prism, figs. 102, 103 (fig. 102 a front view, and
fig. 103 a side view); has a rhombic base and a varying height, the
lateral faces are rhomboids. The lateral edges, like the basal edges,
have two acute and two obtuse angles. When the height is equal to
the breadth the form is:
A rlwmbohedron, fig. 98, composed of six equal rhombic faces.
A right rhomboidal prism  has a rhomboidal base and a varying
height, only the two opposite sides and angles are equal, the lateral
rectangular faces correspond to the basal edges; the opposites only are
equal. This form is similar to fig. 101.
An oblique rhomboidal prism, fig. 104, has a rhomboidal base and a
varying height. The lateral faces are rhomboids. The edges of each
base are of four kinds; for two opposite are longer than the other two,
and of each pair, one.is obtuse and the other acute.  In this solid,
therefore, only diagonally opposite edges are similar, and only opposite
solid angles are equal.
104                  105                   106
An hexagonal prism, fig. 105, is an erect six-sided prism.
An octahedron has eight triangular faces; its form is like two four
sided pyramids united base to base. Three octahedrons are described.
18




118              THE THREE STATES OF MATTER.
The regular octahedron, fig. 106, has a square base and eight faces,
equilateral triangles; its solid angles are six, and equal, as also are its
twelve edges.  The plane angles are 60~, the interfacial angles are
109~ 28' 16"; this solid is symmetrical, like the cube.
The right square octahedron, fig. 107, has a square base, but a vertical height, greater or less than in the regular octahedron. Its faces
are equal isosceles triangles. Its basal edges are equal and similar,
but they differ in length from the eight equal pyramidal edges. The
vertical solid angles differ from the basal
The right rhombic octahedron, fig. 108, has a rhombic base and a
varying height; its faces are equal triangles; the basal edges are
equal; the plane angles of the base and the pyramidal edges are of
two kinds, two obtuse and two acute.
107                  108                     109
The rhombic dodecahedron, fig. 109, is bounded by twelve equal
rhombs; it has twenty-four similar edges, and fourteen solid angles;
they are of two kinds: Eight obtuse, formed by the meeting of three
obtuse plane angles, and six acute, formed by the meeting of four acute
plane angles.
154. Systems of crystals.-There are six systems of axes, producing the same number of systems of crystalline forms, by the symmetrical arrangement of planes about these axes. They are called the
monometric, dimetric, trimetric, monoclinic, triclinic, and hexagonal
systems.
(a) The monometric system  (from monos, one, and metron, measure),
includes the cube, fig. 95, the regular octahedron, fig. 106, and rhombic
dodecahedron, fig. 109. Each of these forms is perfectly symmetrical,
NOTE.-In studying this subject, the pupil will find it of the greatest assistance to his easy comprehension of the forms mentioned, to produce them with
a knife, from some soft substance like a turnip or a potato, which are more
easily managed than chalk or wood, and neater than clay. Sets of crystalline
forms and cards, with the outlines of the various forms prepared for cutting
up, are furnished cheaply by the German chemical dealers, for the use of
Bchools.




CRYSTALLOGRAPIIY.                         119
being equal in height, length, and breadth. Their axes are three in
number, of equal length, and at right angles to each other. In the
cube, the axes connect the centres of opposite faces, in the octahedron,
the apices of opposite solid angles, and in the dodecahedron, the apices
of opposite acute solid angles. The relation of the axes in these solids
to each other, may be understood by deriving one form from the other.
If in the cube (its faces are indicated by o) we truncate each of its
eight solid angles, fig. 110 is first produced, and as the truncation proceeds, fig. 111, and finally a perfect octahedron. It will be noticed that
the centres of o, the ends of the axes in the cube, correspond to the
apices of the solid angles in the octahedron, which are also the ends
of axes.
110                     111
(b) The dimetric system (from dis, two-fold, and metron, measure),
includes the square prism, fig. 99, and square octa-         112
hedron, fig. 107, bearing the same relation to each other
as the cube does to the regular octahedron.  In this 
system there are three axes, all at right angles to each.. 
other, but only the two lateral are equal, the third, or       j
vertical axis, being of varying length.  In the prism,  
the axes connect the centres of opposite faces, in the       ~:
octahedron the apices of opposite solid angles. If a square prism
has each of its solid angles truncated, we shall have first, fig. 112, and,
finally, the square octahedron is produced.
(c) The trimetric system (from tris, three-fold, and metron, measure),
includes the rectangular prism. fig. 100, the rhombic prism, fig. 101,
and the rhombic octahedron, fig. 108. Each of these forms has its
three axes at right angles to each other, and all are unequal in length.
In a rectangular prism (the base a rectangle), the axes connect the
centres of opposite faces. In the rhombic prism (base a rhomb), the
vertical axis connects the centres of the bases, the two lateral axes connect the centres of opposite edges. In the rhombic octahedron (base
a rhomb) the axes connect the apices of opposite solid angles.
(d) The monoclinic system (from monos, one, and klino, to incline),
includes the right rhomboidal prism, fig. 101, and the oblique rhombic




120              THE TIREE STATES OF MATTER.
prism, fig. 102.  In this system  the three axes are unequal, the two
lateral axes are at right angles with one another, the vertical is inclined
to one of the lateral axes and at right angles with           113
the other.  In the right rhomboidal prism  the axes
connect the centres of opposite faces. In the oblique /F 
rhombic prism the vertical axis connects the centres i  -
of the bases, and the two lateral axes, the centres of..
opposite lateral edges.  The truncation of the lateral 
edges of one prism finally produces the other.  The                 /
relation of these prisms to each other is seen in fig. 103.
(e) The triclinic system  (from  tris, three, and klino, to incline),
includes the oblique rhomboidal prism, fig. 104. All the axes are unequal and oblique, the vertical axis connects the centres of the bases;
the lateral axes connect the centres of the lateral edges.
(f) The hexagonal system  includes the hexagonal            114
prism, fig. 105, and rhombohedron, fig. 114.  In the
hexagonal prism, fig. 105, the vertical axis connects    A    -R
the centres of the bases, the three lateral axes connect
the centres of opposite lateral faces or edges, and cross 
each other at an angle of 60~, at right angles to the 
vertical axis.
In the rhombohedron, two diagonally opposite solid angles consist of three
equal obtuse or three equal acute plane angles; the diagonal connecting these
solid angles is called the vertical axis; placed with this axis in a vertical position, the rhombohedron is said to be in position, and looking from above, it
will be noticed that the lateral edges are at an equal distance from the vertical
axis; the three lateral axes connect the centres of the lateral edges intersecting
each other, as do the lateral axes of the hexagonal prism, at an angle of 60~.
Placing the rhombohedron in position, if we remove the six lateral edges, replacing them by planes parallel to the vertical axis, there is
produced a regular hexagonal prism, terminated by three-sided
pyramids. If their vertical solid angles are also removed the
regular hexagonal prism results. If we remove from an hex-        i
agonal prism three alternate basal edges, and at the other ex-    I
tremity also, three edges, alternating with the first, as shown  I  I
in fig. 115, and continue the removal until the original form  I.
is obliterated, a rhombohedron is produced; it also results by I.......
removing, in a corresponding manner, the alternate solid
angles from the hexagonal prism. When the plane angles forming the vertical
solid angles are obtuse, the rhombohedron is called obtuse, and if acute, the
solid is called an acute rhombohedron.
155. Modified forms.-If bodies in crystallizing assumed only the
fundamental forms, there would be but comparatively little variety
and beauty in crystalline solids; it is to the modification of the funda.
mental forms that we owe that endless variety of crystalline figures




CRYSTALLOGRAPHY.                         121
which we observe in nature, and that are produced in the laboratory.
These modified forms are called secondary or derivative forms, and are
produced by the replacing of the edges and angles of the fundamental
forms by planes, which are called secondary planes. The modifications of crystals take place according to two simple laws.
1st. All the similar parts of a crystal may be simultaneously and similarly modified. The forms thus resulting are called holohedral forms
(from holos, whole, and edra, face).
2d. Half the similar parts of a crystal may be simultaneously and
similarly modified.  The forms thus resulting are called hemihedral
forms (from hemisa, half, and edra, face).
[It is beyond the design of this elementary work to enter into more detail
concerning the different systems of crystallography, and of modified forms.
For further information the student is referred to Dana's Mineralogy, from
which, by permission, this chapter has been condensed.]
156. Compound crystals.-Sometimes we find two or more crystals
united regularly and symmetrically together. The form, if composed
of two individuals, is called a twin crystal. Fig. 116 is a simple crystal
116             117               118                119
^a~~A "'/ 1 
of gypsum; if it be bisected along the imaginary line a b, and the
right half be inverted and applied to the other half, it will form fig.
117. If an octahedron, as fig. 118, be bisected through the dotted line,
120                           121
and the upper half revolved half way around be then united to the
lower, it produces fig. 119. Both figs. 117 and 119 are twin crystals.
1l*




122             TIIE THREE STATES OF MATTER.
The imaginary axis, on which the revolution of half the crystal is
made, is termed the axis of revolution and the imaginary section, the
plane of revolution. Compound crystals, composed of more than two
individuals, are frequently observed, as in the case of the snow-flake, a
not unusual form of which is represented by fig. 120, composed of six
crystals meeting at a point, or of three crossing each other at an angle
of 60~. Fig. 121 represents a compound crystal of chrysoberyl.
157. Cleavage.-By the application of mechanical force to crystals
we observe that they often split in certain directions, leaving even and
polished surfaces. The production of such surfaces, in causing the
separation of the particles of the crystals, is called their cleavage; the
planes along which the separation takes place are called cleavage joints.
Cleavage is often obtained with great ease, as, for example, with mica,
which may be separated by means of the fingers into thin leaves.
Galena, also, cleaves easily, and as the three cleavage planes are at
right angles to each other, a cube results. Calc spar splits in three
oblique directions, and thus a rhombohedron is obtained; while in fluor
spar a cleavage of its solid angles produces an octahedron. The cleavage of many crystals is obtained with great difficulty, as, for example,
in quartz and tourmaline; in others no cleavage can be produced,
owing to the strong cohesion among the laminge. In some crystals but
one cleavage is visible, as with mica; several have two; others three,
as galena and calc spar; fluor spar has four, blende has six, while
others have even more. We obtain, by the cleavage of a crystal, some
one of the thirteen fundamental forms. Varieties of the same mineral
have the same cleavage. Cleavage occurs parallel to the faces of the
fundamental form, or along the diagonals; the facility of cleavage and
lustre of the surfaces is always the same, parallel to similar faces.
158. Determination of crystalline forms.-In order to determine
a crystal, it is essential to refer it to the system to which it belongs,
and to determine the simple forms of which it consists, with the relative lengths and inclination of the axis.
j 3. Elasticity.
159. Elasticity of solids.-Elasticity, already mentioned as one
of the properties of matter, has a peculiar importance in solids, because
it is itself a moving force, and serves to measure the intensity of
other forces. All bodies offer a resistance to compression and extension, which is due to elasticity. It is shown in the effort of a compressed spring, or a bent bow, to recover from  its forced state of
flexion.
Tension, flexure, and torsion are also at once evidence and measures




ELASTICITY.                          123
of the force of elasticity in solids; while in fluids compression is the only
evidence of its presence, and hence compressibility alone is a general
property of matter.
Every body has a limit of elasticity beyond which it cannot be carried without a permanent derangement of its particles, or fracture. A
perfectly elastic body is one which returns completely to its original
form when pressure is removed; and every body does this, each within
its own limit of elasticity. Hence every body may, in a restricted sense,
be said to be perfectly elastic.  The return of an elastic body to its
primitive position is usually made with several oscillations, called oscillations of elasticity. This is familiarly seen in the recoil of a bent blade
or spring of steel.
It is evident that in bending the steel its molecules are deranged from their
position of equilibrium by compression on one side and extension on the other,
and that it is the force with which they tend to replace themselves which produces the elasticity of the blade.
There is a similar, although less perceptible, change of figure in an ivory ball,
which, dropped upon a hard surface, will rebound nearly to the height from
which it fell. It does not immediately recover its spherical shape, but is for
several times, alternately, an oblate and prolate spheroid.
160. Elasticity of tension and compression.-By tension is to
be understood the action of a force exerted in the direction of the length,
of a wire, for example. The laws of elasticity of tension have been experimentally deduced, by suspending weights from the lower end of a
rod or wire, sustained at top by a firm support. The elongation occasioned by each addition of weight is measured by a telescope mounted
on a graduated bar, parallel to the wire (the apparatus is called a
cathetometer). If the limit of elasticity is not passed, the rod or wire
returns to its original length on removing the weights; but if the strain
is continued too long, or too great a tension is brought to bear, a permanent change of length results. When the limits of elasticity are not
passed, the following laws are developed by this mode of experiment.
1. For the same substance the elongation caused by each unit of tension
is the same, whatever may have been the original tension.  Thus, with a
wire loaded with ten or twenty pounds, the elongation for each successive pound is the same as for the first pound.
2. The elongation is proportional to the tension employed. This follows
from the first law, and signifies that if the rod or wire is elongated one
unit by one pound, it will be elongated ten units by ten pounds, &c.
3. The elongation with a given tension is proportional to the length of
the rod. That is to say, if a rod of a given length is elongated a unit
of length by a given tension, a rod two units long is elongated twice as
much by the same tension.




124             THE THREE STATES OF MATTER.
4. The elongation is inversely proportional to the area of the section of
the rod. That is, if of two rods of the same substance, of equal length,
and subject to the same tension, one has twice the area of the other, it
will be elongated only half as much.
Experiment has shown that in the case of the compression of a metallic
bar, or rod, in the direction of its length, by an endwise force, the bar
is shortened just as much as it would be lengthened if the same force
had been used to stretch it. Hence the laws for the elasticity of compression are quite the same with those for tension.
These laws may be demonstrated mathematically as well as experimentally, but it is not requisite here that we should do more than
enunciate and illustrate thlem.
161. Coefficient of elasticity.-From the laws of elasticity, of
tension, and compression, just enunciated, it follows that the elongation
(1) of a given rod is proportional to a constant quantity, C, depending
on the nature of the substance; secondly, to the weight, T, by which
it is stretched; thirdly, to its length, L; and, fourthly, that it is
inversely proportional to the area of its section, S: i. e.
l= C. W. L. -
hence,
WL               IS
I= C   -,  or  C —
8,             LW
Putting K= -I in these equations, they become
1 WL             LW
I   - K    S  or K-' —IS
If in the last equation we make I = L, and S = 1, it becomes K-  W.
The quantity K is called the coefficient of elasticity. In other words,
the coefficient of elasticity, in any homogeneous substance, is equal to
the weight required to double the length of a bar of that substance
having a given area, assuming such an elongation physically possible,
which it is not, unless in the case of caoutchouc.
We are indebted to Wertheim for most of our experimental knowledge
of this subject. The following table shows the mean coefficient of elasticity of a number of metals, as deduced by him, with various weights,
at different temperatures, from 1~ to 392~ Fahrenheit.




ELASTICITY.                             125,                  METALS.*y Ialue of K at the temperature ofMETALS.-                            ~
1~-140 F.  500 F.  590-680 F.  2120 F..3920 F.
Gold hammered,                 9,351    8,603
"  annealed,                                   5,585    5,408    5,482
Silver hammered,               7,800    7,411
"   annealed,                                  7,140    7,274    6,374
Palladium hammered,           10,659   10,289
Platinum hammered,            16,224   15,647
"    annealed,                              15,518   14,178   12,964
Copper hammered,             13,052   12,200
"    annealed,                                10,519    9,827    7,862
Iron-wire (ordinary),         17,743   18,613            19,995
I    annealed,                              20,794   21,877   17,700
Steel-wire annealed blue,     17,690   18,045            18,977
English steel-wire annealed,                    17,278   21,292   19,278
Cast-steel annealed,                            19,561   19,014   17,926
Berlin-brass hammered,         9,782    9,005
An inspection of this table shows that the coefficients of elasticity of
the metals, generally diminish as the temperature rises from 1~ to
392~ F. But for iron and steel, the coefficients augment up to 212~ F.,
and then diminish, until at 392~ F., they have the same tenacity as at
common temperatures.
Wertheim  has also determined by experiment that the coefficient of
elasticity in the metals is increased by all means which produce an
increase of density, and decreased by the contrary means.  He found,
also, that the passage of an electric current in a conductor momentarily
diminishes this coefficient, independent of the alteration 6f temperature
produced by the electricity. In alloys the coefficient is nearly the
mean of the coefficients of the several metals compounded, even when
there is a difference of bulk between the mass of the alloy and the sum
of its ingredients.
162. Elasticity  of flexure.-Let A B, fig. 122, be a rectangular
beam, fixed horizontally by one of its ends. If the free end of such a
beam is acted on by any force tending to bend it in the direction B D',
the bar will, in virtue of its elasticity, return again to its horizontal
position when the flexing force ceases to act, after performing a certain
number of oscillations.
The elasticity of flexure is due chiefly to the united effect of the
* The rods employed in these experiments had each a section of one square
millimetre, and the values of K are the weights, in kilogrammes, that would be
required to stretch the rods to double their original length. These values, in
general, greatly exceed the limit of elasticity.




126              THE THREE STATES OF MATTER.
elasticity of tension and compression. For the molecules on the upper
side of the curve are extended, while those on its under side are compressed, and the united effort of                    122
these two forces-which are equal —.
is to restore the beam  to its first 
position.  The  conversion  of  a 
straight line into a curve, as in this           _ _d           —.-:
case, is also accompanied by a dis-               b 
turbance in the equilibrium  of the molecules, independent of the
change due to their separation and compression; and such a change
develops elasticity.
The laws of elasticity of flexure are comprised in the following formulae:
WI3          Dabd3
(1.) a-  d  or   =        3
In which a is the arc I B', described by the flexure; W, is the flexing weight
acting in a perpendicular; b, the horizontal breadth of the bar; d, its thickness;
I, the length of the bar, and D, a constant quantity, depending on the nature of
the substance used. If in the above we make each of the quantities (a, b, d, and
1, equal unity, it follows that D =  W, or D, is a weight which will bend a given
bar one unit long, and of a given diameter (say one centimetre), through a unit
of arc (say one degree). This quantity, D, is called the coefficient of elasticity
of flexure, and in any case the value of a, b, d, and 1, being known experimentally, the value of D is readily ascertained by calculation.
If a beam is supported at its two extremities, A, B, fig. 123, and the weight is
applied in the middle, the formula becomes
16Dabd3
(2.) WT=     —, where a is the flexure and I the distance
from the supports.
123
[1                                            A
The following laws are deduced from the first formula:
The following laws are deduced from the first formula:
1. The displacement of the free end of the bar is proportional to the
load.
This is equally evident from the experiments of Coulomb and from
an analysis of the isochronism of the oscillations accompanying the
effort to restore the equilibrium.
2. The load requisite to produce a given.flexure zs proportional to the
breadth of the beam or bar.




ELASTICITY.                         127
This is evident if we consider a beam two or three times as broad,
composed of two or three separate beams, each requiring the same load
as the first bar to flex it through the same arc.
3. The load is also proportional to the cube of the depth or thickness of
the bar.
4. The load is in the inverse ratio of the cube of the length of the bar.
If the section of the beam is not a rectangle, with one side perpendicular to the direction of the flexing force, these laws cannot be
directly applied. It is assumed in all the cases that the bar returns to
its first position when left to itself; or, in other words, that the pressure
has not exceeded the limit of elasticity.
Applications.-Constant use is made of the elasticity of flexure.
The dynamometer of Reynier has already been named (37). Springs
of all kinds, for balances, carriages, time-pieces, bows, &c., employ this
agency. The aneroid barometer of Vidi, and the metallic manometer
and thermometer of Bourdon are familiar and most useful applications
of this force.
163. M. Bourdon's metallic barometer.-M. Bourdon, of Paris,
has applied  the principle of elas-             124
ticity of flexure to the construction
of a metallic barometer, which, with
great simplicity of construction, has
all the advantages of the aneroid.
The essential part of the instrument,
fig. 124, consists of a very, thin and
elastic brass tube, A, bent into the
form of an arc of a circle, whose cross
section is a flattened ellipse, with
its longer diameter perpendicular
to the plane of curvature. This tube,
exhausted of air, and hermetically
closed, is attached only at its centre,
so that the ends are free to move.
With a diminished atmospheric pressure, the ends separate from each other. If the atmospheric pressure
increases, the ends come nearer together. By means of the metallic
wires, a, b, and the spring, c, these movements of the ends of the tube
are communicated to a needle moving over a graduated plate.
The same principle Bourdon has applied to the construction of
manometers for locomotives and other steam-boilers, which are now
extensively used in all countries.




128              THEE THREE STATES OF MATTER.
164. The aneroid barometer.* —The construction of this instrument, invented by Vidi, of Paris, depends upon the elasticity of flexure.
Being of small size, and containing no                 126
mercury, it is very portable, and it gives
results sufficiently accurate for all ordinary
purposes. It consists of a circular copper
box, the cover of which is very thin, and
hermetically sealed, after the air is partly 
exhausted from its interior.  This chest is 
contained in an outer case, fig. 125, about
four inches il diameter, and which has a
dial-plate like that of a watch. Variations 
in the pressure of the atmosphere will           B'r RE,
cause the cover of the exhausted box to
move with the change of tension.  By
means of a combination of levers and springs, the movements of the
centre of this cover are communicated to a pointer which moves over
the graduated plate.
Fig. 126 shows the interior construction of this instrument. To the cover M
of the exhausted box, are attached two
uprights, S, which act upon a lever, P,            126
by means of a pin uniting them. This
lever, P, is attached to a bar, moving
freely on two pivots placed at its extremities. A lever, B, unites the bar, 
K, to the plate, A, pressing on two
springs, D. By means of a spring,
represented on the side of the figure, the
rod E, in connection with A, communicates movement to the bent lever, II,
causing a metallic wire to uncoil itslf 
from the axis, 0, of the pointer, thus 
transmitting to it the movement.
Excellent aneroid barometers are now made at Lebanon Spa, N. Y., by E.
Kendall, at a moderate cost.
The theory of the barometer and the mode of observing atmospheric
pressure with the aneroid barometer, is explained in the chapter on
gases.
165. Elasticity of torsion.-When a metallic rod or wire is twisted
by a force applied at one extremity,.while the other remains fixed, it
has a constant tendency to return to its first position, and if the force
e Aneroid is derived from the Greek alpha (a), privative, and ipEp, to flow
(a barometer without a fluid), in allusion to the absence of quicksilver.




OF SOLIDS.                            129
is withdrawn, when left to itself, the wire makes a number of oscillations before it comes to a state of rest.
We can easily see how torsion is developed from elasticity. Let a b, fig. 127,
be a metallic wire, made tense by a weight, W, and           127
twisted by a force applied at d, acting in a circle of
which d b is the radius. Let m n represent an enlarged 
view of a row of molecules on the surface of the wire        a
parallel to the axis. If the length of the wire remains
unchanged during torsion, and the line mn takes the              m l
position of the spiral  fn', it is evident that the distances
between the molecules in this line must be increased. The
elasticity of torsion, therefore, depends upon the force
with which the particles tend to preserve their respective
distances from each other. By the same force with which
the molecules on the surface of the wire tend to resist
separation, the molecules in the axis of the wire are compressed, and there is a tendency to diminish the length
of the wire. Torsion, therefore, tends to separate the
molecules on the surface of the wire, and to compress
those situated in the axis.                            d       b
The angle of torsion is the angular distance,  l'               r 
d b d', through which the movable end of the wire is 
rotated about its axis. The force of torsion is the power applied at the
extremity of a lever whose length is unity, placed perpendicular to
the axis of the wire, to produce the deviation indicated by the angle
of torsion; this force is called the coefficient of torsion.
166. Coulomb's laws of torsion.-For our knowledge of the laws
of torsion we are indebted to Coulomb, who has reduced these laws to
the following formula:
-W                  i2a2 W
(1)  t  _= 7ai2/; or, (2) f  -   2g
When a cylindrical weight, W, is suspended to a wire, as shown in
fig. 127, so that its axis corresponds with the axis of the wire, W is the
suspended weight, a its radius, g the accelerating force of gravity (71),
f the coefficient of torsion for the extended wire, and t the time of an
oscillation when the force of torsion is removed, and the wire is left
free to vibrate.  The following laws were deduced by Coulomb from
the preceding formula:
(1.) The force of torsion is proportional to the angle of torsion.
To prove this law, Coulomb caused the weight to oscillate around its axis by
the torsion of the wire, and found that the times of oscillation were the same
whatever their amplitude. This result corresponds with the formula in which
the time of oscillation is independent of the amplitude.
Based upon this law, Coulomb invented a very delicate torsion balance which
14




130              TIIE THREE STATES OF MATTER.
bears his name. This instrument will be described when speaking of its use in
electrical experiments (820).
(2.) The force of torsion remains the same whatever may be the tension
of the wire.
Experiments prove that the squares of the times of oscillation arc proportional
W
to the weights employed, whence it follows that -, in formula (2), is constant
whatever may be the value of W, therefore it is evident from the formula that
the coefficient of torsion, f, is constant, and that the force of torsion agrees
with the preceding law.
(3.) The coefficient of torsion is inversely proportional to the length of
the wire.
Experiments prove that the square of the time of oscillation is proportional to
the length of the wire, and the formula shows that f is inversely proportional
to t2, therefore it must also be inversely proportional to the length of the wire.
(4.) The coefficient of torsion is proportional to the fourth power of the
diameter of the wire.
According to experiment, the time of oscillation is inversely proportional to
the square of the diameter, and the formula shows that the coefficient of torsion
is inversely proportional to the square of the time of oscillation, hence the
coefficient of torsion is proportional to the fourth power of the diameter of the
wire.
167. Torsion of rigid bars.-Savart found by experiment that the
laws of Coulomb, which had been previously determined for flexible
wires of cylindrical form, were equally applicable to rigid bars of
brass, copper, glass, or wood, whether the sections were circular,
square, rectangular, or triangular, provided that comparisons were
made only between bars of the same form.
More recently Poisson has demonstrated these laws, in case of cylindrical
rods, by means of the calculus, and M. Cauchy has obtained the same result by
the calculus for bars having a rectangular section.
168. Limit of elasticity.-When a wire or rod has been stretched
by a weight which is very great in proportion to the diameter of the
wire or rod, the elongation and the diminution of diameter do not
entirely disappear when the tension is removed. The bar is then said
to have been forced, or to have been stretched beyond its limit of elasticity. Similar effects are seen when elasticity has been developed by
compression, flexion, or torsion.
These results are explained by supposing that the molecules composing the wire or rod have been forced into new relations with each
other, so that elasticity no longer acts on all the particles in the same
direction  as before, and therefore a permanent change of form  is




OF SOLIDS.                             131
developed. It follows, therefore, that after a rod or wire has thus been
forced, there should be a new state of elasticity similar to the first; and
such experiment shows to be the case.
If a degree of tension, sufficient to produce permanent elongation,
acts for a long time, a rod will be gradually drawn out into wire.
M. Vicat has observed a wire, placed where it was free from any sudden shock,
extended by a weight exceeding its limit of elasticity (equal to about one-third
what would be required to produce instantaneous rupture), and which continued
to be elongated for years without attaining its limit of extension.
Thin plates of glass or steel placed obliquely, or supported only at the ends,
will, after a time, contract a permanent curvature.
The limit of elasticity is rapidly diminished by heat.
At temperatures of 59~ F., 212~ F., and 392~ F., Wertheim found that the
limits of elasticity for copper varied as the numbers 3, 2, 1; and for platinum
as 14~, 13,. 11. Annealing diminishes the limits of elasticity, but Wertheim
found that a temperature of 392~ F. made no sensible difference in the elasticity
of those metals which had been previously annealed.
169. Change of density  produced  by  tension.-In  general,
metals that are forced by excessive tension increase in density by a
lateral approach of their molecules, but the contrary effect is produced
by tension in bars of iron or lead. Annealing restores the density of
metals which have been forced by tension.
# 4. Strength of Materials.
170. Laws of tenacity.-The absolute strength or tenacity of a
body is its power of resisting a force applied in the direction of its
length, and tending to draw it asunder. The following are the laws of
tenacity:
1st. The tenacity of a bar, or rod, or the resistance it is able to sustain,
is proportional to the area of its transverse section.
2d. The tenacity is independent of the length of the bars.
The resistance which a rod can sustain is evidently proportional to the
transverse section of the body, for the cohesion of two, three, or four times as
many particles must be destroyed, if the area of the section is increased two,
three, or four times. If a wire supports a certain weight, two such wires, or
one of double size of the same quality, will support a double weight. Tenacity
is not modified by length, except that the probability of casual defects increases
with the length. Tenacity is measured experimentally by securing one end of
the body to a fixed point, and hanging gradually increasing weights to the other,
until it is broken. The breaking weight measures the absolute strength. To
compare the strength of different bodies, we must assume a unit of area; the
one usually chosen is one square inch.
The following table gives the absolute strength of some of the mere




132                TIIE THREE STATES OF MATTER.
important bodies, expressed in pounds, for one square inch area of the
transverse section.
1st. METALS:-                         2d. WooDS:Sycamore,.9,630
Steel untempered,. 110,690-127,094 Brcha,..           9,
Birch,...... 12,225
"  tempered,   114,794-153,741 Elm,....           9,720-15,040
"  cast,... 134,256  Lac40
Iron, bar             53,182- 84,611 Oak10367-25,851
"  wire,..  58,730-112,905 Box..... 14,
cast,..    16,243-  19,464  Ash,......0-2,
~,.,   ~' _    Ash,  ~ ~    lYOV L3,480~-2,455
Silver, cast,..    40,997           Pn.                  1,
Copper,...  20,320-  37,380  i,                             -1,96
Brass,  "..    17,947-  19,472...      6,991-12,876
"   wire,..   47,114- 58,931                  3d. CORDS:
Gold,....    20,490- 65,237 Hemp twisted, i to 1 inch,.. 8,746
Tin, cast,...       4,736            "      "   1-3   ".. 6,800
Zinc,.....           2,820             "      "   3-5   ".. 5,345
Lead,.....            887-  1,824   "        "   5-7   ".. 4,860
Wrought metals are more tenacious than cast, and alloys are sometimes
stronger than either of their constituents. The strength of metals, as a rule,
diminishes as they are heated; and sudden, frequent, and extreme changes of
temperature always impair tenacity.
Johnson's results.-From an extensive series of carefully conducted
experiments, the late Professor Walter R. Johnson ascertained that, if
either bars or plates of malleable iron are subjected to a high degree of
tension, whilst heated to 550~ or 600~ F., and are then gradually cooled,
the maximum  tenacity of the iron is sensibly increased over fifteen
(15Y1y) per cent.  From. the maximum  thus obtained, the tenacity
gradually diminishes by heating, but the tenacity will remain greater
than before the first heating, unless the temperature is raised above
7000 F.  (Report to Franklin  Institute on strength of materials for
steam-boilers, 1837.)
The strength of cords is in proportion to the fineness of the strands, and also
to the fineness of the flax or hemp fibres of which the strands consist. They
are weakened by overtwisting. Damp hempen cords are stronger than dry ones,
twisted than spun, tarred than untarred, and unbleached than bleached. Silk
cords are three times stronger than those of flax.
Tenacity of vegetable and animal substances.-Woods are subject to great inequalities. Trees grown on mountains are much stronger than
those of the same kind from the plains.
Animal and vegetable substances, converted from the liquid to the solid state,
as gums, varnish, glue, &c., possess extraordinary strength. Rumford found that
a solid cylinder of paper, glued together, whose sectional area was one square
inch, would support 30,000 lbs.; and a similar cylinder of hempen strings, glued
together lengthwise, supported 92,000 lbs.-a tenacity greater than that observed
in iron.
171. Resistance to pressure in columns.-The resistance of a




OF SOLIDS.                            133
column to a vertical force which tends to crush it, depends on its form,
its sectional area, and its height. Of two columns of the same material, having the same form and equal heights, the one which has the
larger sectional area will be the stronger, but the exact ratio of increase
in strength is unknown.
According to Euler: When the base remains the same, the strength of a
column diminishes as"the square of the height; that is, when the height is
trebled, the strength is diminished nine times.
The resistance of a right prism is in the inverse ratio of the square of the
height, and directly as the width, and the square of the thickness.
A prism, whose base is a parallelogram, has less strength than one of the same
height and volume, whose base is a square; and the latter less than a cylinder
of equal height and volume.
A solid cylinder resists less than a hollow one of equal height and mass; and
lastly, a solid cylinder less than an equivalent cone. A column of one piece is
stronger than one composed of several.
Solids do not offer the same resistance in all positions: stones in the position
of their natural bed are stronger than when placed otherwise; and wood is
stronger in the direction of its fibres than across them.
The strength of rectangular columns is directly as the product of the longer
side of the section into the cube of the shorter side, and inversely as the square
of the height.
172. The lateral or transverse strength of materials is their
power to resist a breakingforce applied at right angles to their length.
Let a b c, fig. 128, be a beam secured at one end, and supporting at
the other extremity a weight, W,                   128
acting at right angles with its 
length.  It is evident that while       ab
the suspended weight tends to 
produce extension and rupture                                      c
at the upper surface, a, the par-  
tides at the opposite or under                                    d
surface, o, will be compressed.
Between these two points there will be a certain plane, m n, called the
neutral axis, where there is neither extension nor compression.
Suppose the power of the beam to resist compression is the same as
its power of resisting extension, then the neutral axis will divide the
transverse section into two equal parts, an area of compression and an
area of extension.  When the fibres on the surface a are extended to
their limit of tenacity, the fibres at o will be compressed with an equal
force, while no force is exerted on the neutral axis, therefore the entire
force required to be overcome to produce rupture is equal to one-half
the longitudinal tenacity of the beam. If t represents the absolute
tenacity of a unit of area (See Table, ~ 170), b the breadth of the beam,
14*




134              THE THREE STATES OF MATTER.
and d its depth, then the resistance to be overcome, R, = —=  tbd. The
effect of the breaking force tends to turn the section a o about the neutral
axis. The sum of all the extending forces,          128 a
H h, fig. 128 a, will be represented by the  Al a,                 e
area of the triangle a G a'. These forces    H
act at different distances from   the  neutral.........'"" {..................
axis, G, but their entire effect will be the   B 00
same as if they were all concentrated at
the centre of gravity of aGa', which is
at a distance from  G equal to ~ a G =
i a o =    d. The statical moment of the extending force will therefore be
~tbd X id = -tbd2.
The statical moment of the compressing force is also iRtbd2. Hence the
sum of the moments of the statical forces opposed to fracture is *tbda.
To overcome this moment of resistance, the weight, W, acts at the end
of the beam, the length of which we represent by l; then, since at the
moment of fracture the statical moment of the weight must equal the
statical moment of the resistance, we shall have
W  =   tbd', or, W== 
The lateral cohesion of the beam prevents the different laminae from sliding
on each other, and thus tends to prevent fracture, but this element of strength
is neglected in the preceding analysis.
To find the weight required to break a beam supported at one end,
we have the followingRULE: Multiply the absolute tenacity of a beam of the same dimensions,
by its depth, and divide the product by six times the length; the quotient is the weight suspended at the extremity required to break the beam.
Practical applications.-To apply this rule to practical purposes,
it is necessary to take into consideration the weight of the beam itself.
This weight may be considered as acting at its centre of gravity, consequently the strain produced by it will be only half as much as if it
acted at the extremity of the beam, we must therefore subtract from the
breaking weight one-half the weight of the beam. Calling the weight
of the beam w, the formula becomes,
tbd2   w
W= ---    2.
61    2If we would estimate the load which a beam can sustain without danger of
breaking, we must consider that beams, of whatever material they may be
constructed, are liable to be more or less imperfect. To afford security from
accident, it is customary to estimate the working load as only i, i, or, in some
cases, only I part what would be required to produce fracture.




OF SOLIDS.                         135
For a cylindrical beam supported at one end, the breaking weight, diminished
by the weight of the beam itself, is
t7rr3   w
W= - - - -,  r  being the radius of the beam.
For a tube whose external and internal radii are r and r', the breaking weight
will be
twr3 T        - tr'3  w'  \   w/-' 
~ 4t: 41   2 )2                41 \   "        2
For a rectangular tube supported at one end,
t          \   whw'
W -_ 61  bdz —b'd'2  _ 2
- 2
If a rectangular beam is supported at the centre, and the weight is
divided into two parts, rest-                 129
ing upon opposite ends of the
beam, as shown A, fig. 129, we
must replace W, w, and I in the
preceding formula by jW, ~w, 
and ~l. Making these substi- 
tions, and reducing:
w    4tbd2o
61 -' )or,
The weight which a beamn                   2 C
can support when it rests upon 
its centre, and the weight is
equally divided at its extremi-        4w
ties, is four times as great as if the beam were supported only at one end,
and the weight was suspended from the other end.
One-half of the beam is included as a part of the breaking weight.
If the beam is supported at its two extremities, and the weight is
suspended at the centre, as shown at B, fig. 129, the breaking weight
will obviously be the same as the sum of the two weights in the pre
ceding case.
If the beam is secured at both extremities, as shown at D, fig. 129,
and the weight is placed at the centre, three fractures are to be produced simultaneously. To produce the fracture at the centre separately
will require the same weight as in the preceding case, and the fractures
at C and Ct will each require one-half as much more force, while onehalf of the weight of the beam is to be included. Therefore,
w   8tbd2
2-   6-1




136             THE THREE STATES OF MATTER.
General estimate of the strength of beanis —If the weight is
evenly distributed over the whole beam, it will support twice as much
as if the whole pressure were placed in the centre. If a rectangular
beam has two or three times the breadth of another, the depth and
length being the same, it will have two or three times the lateral
strength; and if the length is increased two or three times, other
things being equal, the power of suspension will become one-half
or one-third respectively. When the length and breadth remain the
same, the strength increases with the depth, but in a higher proportion. A beam having the same length and breadth as another, but
twice or three times the depth, will bear a four or nine times greater
weight. A thin board or beam is therefore much stronger when placed
on its edge than on its side; on this principle, the rafters and floor
timbers of buildings are made.
In round timber, the power of suspension is in proportion to the
cubes of the diameters, and inversely as the length; a cylinder whose
diameter is two or three times greater than that of another, will carry
a weight 8 or 27 times heavier. The lateral strength of square timber
is to that of the tree whence it is hewn as 10: 17 nearly.
The strongest rectangular beam that can be sawn from a piece of
round timber is one whose breadth is equal to the square root of onethird multiplied by the diameter, and its depth is equal to the square
root of two-thirds multiplied by the diameter.
A tube is the form which combines the least weight of materials
with the greatest lateral strength. Galileo was the first who remarked
that the bones of animals, the quills of birds, the stalks of plants which
bear a heavy weight of seed at their summit, and other similar hollow
cylinders, offer a much greater resistance than solid cylinders of the
some length, and constructed of the same quantity of matter.
A round tube whose external and internal diameters are to each
other as 10: 7 has (according to Tredgold) twice the lateral strength
of a solid cylinder containing the same amount of material.
A rectangular tube, whose height is considerably greater than the
breadth, will sustain a greater amount of lateral pressure than a hollow
cylinder of the same thickness, and containing the same amount of
material, because a much greater amount of material is placed at a
remote distance from the neutral axis. Hollow rectangular beams of
iron are used in architecture, and the same form of construction was
selected by Stephenson for the Britannia and Victoria Bridges.
The Britannia Tubular Bridge, across the Menai Straits, is an
immense rectangular iron tube, or corridor, 17 feet wide, 22 feet high
at the ends, 30 feet at the centre, and 1834 feet long, through whicl




OF SOLIDS.                          137
the English Western Railroad passes from Wales to the island of
Anglesea, 104 feet above high water mark. Two of the openings
between the piers are each 460 feet, and the other two each 230 feet.
The ordinary pressure of the railroad trains which pass this bridge
produces a depression of merely one-eighth of an inch, or less; discernible only by the aid of instruments.
The Victoria Tubular Bridge, for the passage of the Grand Trunk
Railway across the St. Lawrence, at Montreal, is 6600 feet, or a mile
and a quarter in length. It has 24 openings of 242 feet each, and a
centre span of 330 feet. The abutments are 36 feet, and the central
piers 60 feet above summer water. The breadth of these immense iron
tubes is 16 feet, the height at the ends of the bridge 19 feet, and at the
centre 21 feet 8 inches. The tubes are constructed of boiler iron,
varying from i to ~ an inch in thickness, strongly braced with lateral
irons placed at distances of from 3 to 6 feet. The cost of this stupendous bridge was $7,000,000.
173. Limits of magnitude.-The materials of all structures must
support their own weight, and therefore their available strength is the
excess only of their absolute strength above what is necessary to support themselves.
When all the dimensions of materials are increased, the absolute
strength augments as the square of the ratio of increase, but at the
same time, the weight of the materials augments as the cube of the
increase.
If the dimensions of a beam are doubled, it is four times stronger,
and eight times heavier; or if its magnitude is multiplied 4 times, its
strength will be multiplied 16 times, and its weight 64 times.
In cornsequence of unequal ratio in increase, the strength of a structure of any kind cannot be estimated from its model alone, which is
always much stronger in proportion to its size than the structure. In
enlarging a structure, a limit is soon reached at which it has no available strength, its total absolute strength being required to support
itself; and if this limit is passed, it will fall to pieces by its own weight.
All works, natural and artificial, have such limits of magnitude which
they cannot surpass while their materials remain the same.
In conformity to this principle, small animals are stronger than large ones,
and insects and animalculae are capable of feats of strength and agility, which
seem miraculous when translated into the proportions of man. The operation
of the same law may be seen by comparing the unwieldy movements of the
elephant with the lithe and active tiger, or the easy motion of song-birds, and
the arrowy swoop of the hawk, with the laborious and measured flight of the
swan, and the condor of the Andes. For the same reason, the gigantic saurians,
whose bones are mentined by geologists, had their home in the ocean, where,




138              THE THREE STATES OF MATTER.
in modern times, are found sea-weeds of interminable length, and animals,
whose ponderous mass would be incapable of motion, if they were not floated
buoyantly by the element they inhabit.
{ 5. Properties of Solids depending on a permanent displacement of their Molecules.
174. Malleability, or the property of being wrought under the
hammer, belongs to many of the metals in an eminent degree, and
upon it their utility in a great measure depends.
The following is the order of malleability of the principal metals,
when extended under the hammer; viz., lead, tin, gold, zinc, silver,
copper, platinum, iron.  This order represents the facility of extension
depending on relative hardness, but gold may be beaten thinner than
any other metal (compare ~ 19).
The property of extending into plates in the rolling-mill is somewhat
different from the facility of extending under the hammer, and is possessed by the metals in the following order; viz., gold, silver, copper, tin,
lead, zinc, platinum, iron. Malleability varies with the temperature.
Iron is most malleable when it first attains a white heat, and in that state
huge masses of it are taken from the furnace to be forged, the metal yielding
like wax to the pressure of the rolling-mill, or the blows of the hammer. Zinc
is most malleable at 300~ or 400~, and lead and copper when they are cold.
Glass, which is very brittle when cold, becomes malleable at a high temperature.
Gold may be hammered into leaves so thin that a million of them are less than an
inch thick. Metals lose their malleability by constant hammering, but recover
it again by being heated and slowly cooled-a process called annealing.
175. Ductility, or the property of being drawn into wire, must not
be confounded with malleability, for the same metals are not always
both ductile and malleable, or do not possess these properties to an
equal extent.  In general, ductility increases with the temperature.
The following is the order of ductility in the principal metals; viz.,
platinum, silver, iron, copper, gold, zinc, tin, lead.
Iron may be-drawn into the finest wire, but it cannot be rolled into plates of
proportional thinness.  Tin and lead possess these qualities in the reverse
order.
176. Hardness has no relation to density, or the number of particles
within a given space, but depends only on the nature of the particles,
their mutual arrangement, and cohesion.
The metals may be scratched by glass, which is far lighter than most of them,
and among metals, density is not connected with relative hardness. Alloys are
often harder than either of their constituents, and some metals, as steel, may
have their hardness modified by heat at pleasure.
The following table gives the scale of hardness used by mineralogists,
commencing with tale, the softest crystalline solid, and ending with




OF SOLIDS.                           139
diamond, which is esteemed the hardest, since it cuts all other bodies,
but cannot be cut by any but itself.
Deg.      Substance.     Deg.      Substance.
1       Tale.            6       Feldspar.
2       Gypsum.          7        Quartz.
3       Cale spar.       8       Topaz.
4       Fluor spar.      9        Sapphire.
5       Apatite.        10       Diamond.
The terms hard and soft are seen by an inspection of this table to
be entirely relative, since each succeeding body is harder than the one
preceding, and vice versa, the extremes only being respectively softer
and harder than all others.
We employ hardened steel to cut wood, and even iron; emery (the rough
sapphire) is required to cut and polish steel and glass. The diamond, set in a
staff of metal, is an efficient tool for cutting plates of glass into any required size.
Even the hardest rocks, as porphyry and jasper, are readily turned into any
required form in the lathe, by the use of a diamond properly set as a turning
tool.
177. Brittleness.-Bodies which are easily broken in pieces and
pulverized are said to be brittle. Such are hard bodies generally, and
also many highly elastic substances.
178. Hardening; Temper; Annealing.-When certain metals are
heated to redness or to a higher temperature, and then are suddenly
cooled, by plunging into cold water, oil, or mercury, they become hard,
brittle, and more elastic than before. This process is called hardening.
The effects of this method of hardening are most important in the case of
steel, since it is in virtue of this quality that its application to a great variety
of purposes depends.
When steel is raised to a high heat and slowly cooled, it becomes
soft, ductile, flexible, and much less elastic than before. This process
is called softening or annealing, although the latter term is more frequently employed to denote a similar process of removing the hardness
produced by hammering, and other mechanical means.
Softened steel may be hammered, rolled into sheets, drawn into wire,
or wrought into any form  required in the arts.  If hardness or great
elasticity is required, the steel is then heated to redness and plunged
into cold water, oil, mercury, or some other fluid, by which it is rapidly
cooled. If, as is generally the case, it is then too hard for the use to
which it is to be applied, a portion of the hardness is removed by what
is called drawing the temper, by heating to a lower temperature, and




140               THE THREE STATES OF MATTER.
allowing the article to cool gradually. The proportion of hardness
removed depends on the temperature to which the articles are heated.
This process of reheating and cooling, by which the degree of hardness
is modified to suit any special purpose, is called tempering.
Colors of tempered steel.-The workmen carefully observe the color
of the steel, as it is reheated, and determine, from the tint, when a degree of
heat is obtained sufficient to produce the temper desired. The tints which correspond approximately to the different temperatures are as follows:Light straw,  428~ F.    Violet yellow, 509~        Blue,     560~
Golden yellow, 446~       Purple violet, 530~      Deep blue, 603~
Orange yellow, 464~       Feeble blue,  550~        Sea-green, 626~
Dies used in coining require to be made of the hardest steel. Files have but
a very little of the hardness removed by tempering. Razors and fine cutlery
are reheated to a pale yellow; penknife blades to a light straw color; table
cutlery, where flexibility is required more than hardness, is reheated to violet;
watch-springs to a full blue; coach-springs to a deep blue.
Tempering by a bath.-In many manufactories the requisite heat for
tempering is obtained by immersing the hardened steel articles in a bath of
metallic alloys, mercury, or oil, the temperature of which can be exactly regulated by a thermometer. The articles to be tempered are placed in the bath,
which is then heated to the required temperature, and then allowed to cool
slowly. In this way a great number of articles of the same kind can be made
to assume a uniform temper at small expense.
It is a remarkable property of steel that when it is heated to a temperature
that allows it to begin to harden, by rapid cooling it receives its full degree of
hardness. It cannot be partially hardened at any lower temperature. A bar
of steel, heated at one end while the other remains cold, will be found, after
rapid cooling, hardened at one end, with a sharp line of demarkation between
the hard and soft parts. Where it has been heated to a temperature insufficient
for hardening, and is then rapidly cooled, it is sensibly softened.
Temper of glass.-Glass undergoes the same changes by tempering
as steel. It becomes, by rapid cooling, more brittle, harder, and less
dense. A specimen of glass, examined by Chevandier and Wertheim,
having a density of 2'513, acquired by annealing a density of 2-523.
For hardening glass it is sufficient to allow it to cool rapidly in the
open air, by moving it about. Glass-ware is annealed by passing it
slowly through a very long oven, called a " leer," the end where it
enters being nearly a red heat, and the other extremity nearly cold.
Without the process of annealing, glass utensils would be almost
worthless.
Prince Rupert's Drops.-A beautiful illustration of the properties of
unannealed glass may be seen in the scientific toy called Prince Rupert's Drops,
or Dutch Tears. They are made by dropping melted glass into water, by which
neans it is suddenly cooled and becomes very hard and brittle. They have a




OF SOLIDS.                            141
long oval form tapering to a point at one end, fig. 130. The body of these
glass drops will bear a smart stroke from a hammer without break-    130
ing, but if a portion of the smaller end is broken off the whole mass
will be broken into an alumost ipallplable powder, with a violent
shock. The Bologna vial is another similar example.
Tempering copper and bronze.-Most metals are acted
on l)y heat and cold in the same manner as steel, but to a
less extent.  Copper is a remarkable exception, since its
properties in this respect are exactly the reverse of those manifested
by steel. When copper is rapidly cooled it becomes soft and malleable,
t)ut when it is slowly cooled it becomes hard and brittle.
Bronze, which is an alloy of copper and tin, undergoes, by change
of temperature, the same changes as copper, but in a more remarkable
degree.
A recent fracture of bronze, which has been rapidly cooled, presents
a yellow color; but after it has been slowly cooled the color is a brilliant white, like pure tin. It is thus evident that hardening and annealing cause different arrangements of the particles of copper and tin of
which the bronze is composed.
179. Hammering.-By hammering, the molecules of many bodies
are brought nearer to each other, so that their density is increased.
By rolling, wire-drawing, extension, compression, bending, twisting,
or any mechanical means by which the limits of elasticity are passed,
changes are effected similar to those produced by hammering.
Lead yields under the hammer or rolling-mill without increasing its density,
but its density may be increased by compressing in dies, or in any situation
where it has no room to spread out under the action of the compressing force.
By such mechanical means the physical properties of solid bodies undergo
changes analogous to those produced by tempering. They become dense, tenacious, hard, brittle, and their limit of elasticity (168) is increased, although their
elastic force is unchanged, as was shown by Coulomb, from the fact that their
vibrations in either condition are accomplished in the same time.
Annealing restores the metals to the same condition as before they were submitted to mechanical force. Iron and platinum require to be frequently annealed
during the process of drawing into wire.
The ancients gave to the bronze plates of their armor the necessary hardness
by hammering.
When zinc and iron have been hardened by rolling, the tenacity and elasticity
are not the same in both directions of the plates, and rolling does not increase
the tenacity in so great a degree as drawing into wire. M. Navier found that a
rod of forged iron, having a section of one square millimetre, required to break
it a weight of 40 kilogrammes. When it had been rolled into thin plates, a
strip cut in the direction of its length, having the same sectional area, required
a weight of 41 kilogrammes to break it; but only 36 kilogrammes if cut in a
transverse direction.
Fine wire twisted into cables is used to support suspension bridges, because
15




142              THE THREE STATES OF MATTER.
such cables are much stronger than the same amount of iron in the form of rods
or coarse wire.
180. Changes of structure, affecting the mechanical properties of metals, take place spontaneously by the lapse of time, or more
rapidly by the influence of heat or vibrations.
These changes have been principally observed in iron.  When this
mnetal is recently forged it is very strong and flexible, and its fracture
is fibrous and of a dull color; but when it becomes old, or has been
subjected to frequent vibrations, or changes of temperature, it becomes
hard and brittle, and its fracture is coarsely granular, presenting many
brilliant facets. This change, often seen in the axles of railway carriages, is produced by vibration combined with the heat of friction,
especially in the severe weather of northern winters. These facts, well
known to engineers upon railroads, explain the necessity of running
trains at but moderate speed when the thermometer indicates a temperature near to zero.
Similar changes, diminishing the tenacity, take place in chains and anchors,
which have been for a long time imbedded in ice. Gay Lussac has observed bars
of iron, which became almost as brittle as glass by remaining for a long time
at a high temperature in an oven.
Some curious results produced by vibration were discovered  by
Savart, who, having caused strips of glass and bars of metal, drawn
into wire, to vibrate in the direction of their length, found that they
gave out at first very indistinct and confused sounds, but on continuing
the experiments for a long time this confusion gave place to clear and
distinct tones, which were obtained with ease.
Brass wire strained like the strings of a piano, where it is exposed
to atmospheric changes and constant vibration from currents of air, in
a few months loses its tenacity and becomes completely friable, showing in its cross fracture a radiated structure.
Annealing produces the same effect, in this respect, as vibration. Substances
cast in the form of plates do not resound well until after the lapse of several
days. Sulphur, cooled in the form of a disc, does not at first give out a clear
sound, but after a time it vibrates readily, and after the lapse of some months
the sound emitted is very much changed. This proves that there has been some
modification of structure.
Q 6. Collision of Solid Bodies.
181. Motion communicated by collision.- When two solid bodies
come into collision, the motion is redistributed through them, owhether one
or both bodies are.in motion.
1. If the bodies are soft and tenacious, or if the shock is not so




OF SOLIDS.                           143
great as to overcome the tenacity of one or both bodies, they acquire a
uniform  motion, and move in contact as one body, as stated under
impact, ~ 112.
2. If the bodies are hard and inelastic, and the collision takes place
at only a small portion of the surfaces, and if the shock is so great as to
overcome the tenacity of one or both bodies before motion is uniformly
distributed through the masses, they will be broken in pieces, and the
fragments scattered in different directions.
3. If the bodies are so elastic that motion may be distributed through
the mass before the limit of elasticity is passed, a reaction will take
place, and the elasticity will modify the distribution of motion.
182. Direct impact of elastic bodies.-When two elastic spherical bodies m and n', fig. 131, come into collision, while moving in the
same straight line, they will undergo compression or flattening, as shown
in the figure, and their centres will continue to approach each other
until they acquire a common velocity (112).  This velocity is represented by x -=     +, u and ut being the velocities before impact,
and x the common velocity of their centres of gravity at the instant of
greatest compression. If the limit of elasticity has       131
not been passed, the elasticity of the two bodies... n'
will now act as an internal force, causing their m
centres of gravity to recede from each other, until 
the bodies recover their original forms, when they.
separate, and the shock terminates.
183. Modulus of elasticity.-When two elastic bodies meet, the
force with which they are urged towards each other is called the force
of compression; the force of elasticity causing their centres to recede
during the second interval of the shock is called the force of restitution;
the ratio of these two forces is called the modulus of elasticity. When
this ratio is unity, or the force of restitution is equal to the force of
compression, the bodies are said to be perfectly elastic.  When this
ratio is zero, the bodies are said to be inelastic. For any value of this
ratio, between these extremes, the bodies are said to be imperfectly
elastic.
There are no bodies known that are perfectly elastic, or perfectly
inelastic; hence, in considering the collision of solid bodies, it is necessary to take into aocount the degree of elasticity which they possess.
The following table exhibits the degree of elasticity of several corn
mon substances, perfect elasticity being taken as unity.




144               THE THREE  STATES OF MATTER.
Substances.    Degree of elasticity.  Substances.   Degree of elasticity.
Glass,....           094        Bell metal,...          0'67
Hard-baked clay,          089        Cork,....            065
Ivory,...          0081       Brass,....               0-41
Limestone,..            079        Lead,....             020
Steel, hardened,.        0'79       Clay just yielding         01
Cast-iron,..            0-73  to the hand, 
Steel, soft,..         0-67
184. Velocity of elastic bodies after direct impact.-If two
imperfectly elastic bodies, m and m/, move in the same straight line
with velocities u and u/, u being greater than u/, the first body will
overtake and strike against the second with the same force as if the
second body were at rest, and the first body were moving with a velocity equal to u     u/.  The two bodies, being elastic, will suffer compression until they acquire a common velocity,
milt    m'u'
m       
The velocity lost by m at this instant will be u - x, and the velocity
gained by m/ will be x     u'
Let e be the modulus of elasticity, and v and v' the velocities of the two bodies
after they recover their original forms at the close of the second period of the
shock.
Since the forces of compression and restitution are in proportion to the velocities they generate or destroy, the velocity destroyed in mi by the force of
restitution will be e (u - x), and the velocity gained by m', by the force of restitution, will be e (x - u').
Hence the whole velocity lost by m will be (1 + e) (u - x), and the whole
velocity gained by sm' will be (1 +- e) (x - uI). The velocity of m after impact
will be
v =      (1 + e) (u -) =   — e( u — ).                   (a)
The velocity of m' after impact will be
v' =  u' +  (1 + e) (x -') =x -+ e(x - u').           (b)
Substituting the value of x in the formula (a) and (b), and reducing, we
obtain
mu  -- 1m''   m'e(u - ~u')
V..                                       (C)
m +- m'  -          + m'n
tm= u +- In'u'   me(u - 21'), =          -+.                      {d)
mn +-     m       + n-m'
If the two bodies move in opposite directions before impact, we must make
either u or u' negative in the preceding formula. If one of the bodies is at rest




OF SOLIDS.                            145
before impact, u' becomes zero. If e = 1, the formulae represent the conditions
of perfectly elastic bodies, and if e =  0, the formulae will apply to inelastic
bodies.
From the preceding formulae we may deduce the following general
conclusions:
1. If two bodies are pe)fectly elastic, their relative velocities befbre and
after impact are the same.
Making e = I in (a) and (b), and subtracting the latter from the former, we
have,v   v' - f t -  te.
2. If the bodies are perfectly elastic and equal, they will interchange
velocities by impact.
Making m =  m', and e =  1 in (c) and (d),
V=  (L + u') - i(u - u') = U'.
V' =       i(u + U') +  (u - U') - U.
3. By the impact of bodies, whether elastic or otherwise, no motion is
lost.
Multiplying (c) by m, and (d) by m', and adding and cancelling similar terms,
we have
mu -- m'v' --- mu -- m'i',
in which the first member of the equation is the sum of the momenta of the
two bodies after impact, and the second member the sum of their momenta before
impact.
4. The velocity which one body communicates to another at rest, when
perfectly elastic, is equal to twice the velocity of theformer, divided by one
plus the ratio of the masses of the two bodies.
In formula (d) let m'   rm, u' = 0, and e = 1, we shall then obtain
2u
1 1 ~
5. When a body in motion strikes another equal body at rest, both
bodies being perfectly elastic, the first body comes to a state of rest, and
the second flies off with the previous velocity of the first.
If the two masses are equal, r -: 1 in the last formula, and v' ==u.
Scholium.-If a series of perfectly elastic balls are arranged in a
line, and all are in contact before impact, except the first, which is
made to strike against the second, all the balls except the last will
remain in contact, and at rest, after impact, and the last will move off
with the velocity of the first.
15.*




146               THE THREE STATES OF MATTER.
185. Transmission of shock through a series of elastic balls.
Experimental illustration of elasticity.-If several equal ivory
balls are suspended, as shown in fig.                   132
132, when 1 is drawn back to a, and              M. 
let fall against 2, only the last in the  
series, 7, will move; this will start  
with the velocity which 1 had at the....  
instant of striking against 2, and it  
will fly off to the position b, at a dis-      1  2  3  4      6  7
tance equal to the limit to which the first had been drawn back; it will
then return striking against 6, which will again be set in motion, all
the others remaining at rest. This alternate movement of the extreme
balls of the series will continue until friction, and the resistance of the
air conspiring with the slightly imperfoct elasticity of the balls, at length
causes the action to cease.
Problems.-Elasticity of Tension.
74. A rectangular bar of iron whose transverse section is one square centimetre, and whose length is three feet, is suspended with its upper extremity
attached to a firm support: what weight must be suspended at its lower extremity
to cause a temporary elongation of one-fourth of an inch when the temperature
is 14~ F., 50~ F., 212~ F., 392~ F.?
This problem may be solved for rods of any of the metals mentioned in the
table (161).
75. A rectangular bar of hammered brass 2~ feet in length, suspended by its
upper extremity, supports a weight of 75 kilogrammes: how much will it be
temporarily elongated when the temperature is raised to 50~ F. 
Elasticity of Flexure.
76. If a beam 10 feet long, 3 inches wide, and 6 inches in depth, suffers a
certain amount of flexure when one end is firmly supported in a wall, what
weight will be required to give an equal flexure to another beam of the same
material, 15 feet long, 6 inches wide, and 9 inches in depth?
77. What weight suspended at the middle of the last-mentioned beam will be
~required to produce an equal amount of flexure when the beam is supported at
both ends?
Tenacity.
78. How many pounds weight, suspended by a steel wire hanging vertically,
will be required to break it when the wire is one-fourth of an inch in diameter?
Calculate for both tempered and untempered steel.
79. In a pendulum experiment, it is required to suspend a weight of 64 lbg.
by a copper wire. What must be the diameter of the wire, when, for the sake
of security, i is deducted from its strength as given by the table?
Transverse Strength.
80. If a beam of oak, 6 inches wide by 9 inches in depth, projects 20 feet




OF SOLIDS.                               147
from a wall in which it is secured, what weight suspended at the end, as in fig.
128, will be required to break it, no account being taken of the weight of the
beam itself?
81. What weight will be required to break a cylinder of cast iron 25 feet long,
having an external diameter of 2 feet, and an internal diameter of 20 inches, the
weight being supported at the extremity?
82. What weight, placed at the centre of the greater span of the Britannia
Tubular Bridge, would be required to break it, calling the breadth of the tube
17 feet, height 30 feet, calculating for a single thickness, } of an inch of plate
iron, and estimating the tenacity equal to a force of 60,000 lbs. to the square
inch?
83. Deducting from the weight found in the last problem, the weight of onehalf the length of tube spanning the greater opening, and estimating the working load as i the breaking weight, how heavy a train might safely cross the
Britannia Bridge?
84. How heavy a train may safely cross the Victoria Bridge (172), if the
thickness of the tube at the centre is ~ an inch, and if, disregarding the weight
of the tube itself, the train is limited to J the absolute tenacity of the structure?
85. What weight can be sustained at the middle of the strongest rectangular
beam that can be sawn from a birch log 2 feet in diameter, and 30 feet long,
reckoning the weight of the timber nine-tenths that of water?
Impact of Elastic Bodies.
86. Two glass spheres weighing 12 oz. and 7 oz. respectively, move in the
same direction with velocities of 8 feet and 5 feet in a second. Find the respective velocities of the two balls after impact, and their common velocity at the
instant of greatest condensation.
This problem may be varied by substituting for glass, balls made of each
substance whose degree of elasticity is given in the table (183).
87. A perfectly elastic body ni, moving with a velocity of 12, impinges on
another perfectly elastic body, m', moving in the opposite direction with a velocity of 5; by impact m loses one-third of its momentum. What are the relative
weights of the masses m and i'?
88. A body, m (=- 3m'), impinges on m' at rest.  The velocity of m after
impact is i of its velocity before impact. Required the value of e, the modulus
of elasticity.
89. Two bodies m and m', whose elasticity is i, moving in opposite directions
with velocities of 25 and 26 feet per second respectively, impinge directly upon
each other. Find the distance between them 41 seconds after impact.
90. A number of perfectly elastic balls are placed in a right line. The first is
made to start with a given velocity; determine the ratio of the balls so that its
momentum may be equally divided among the remainder.
91. An elastic ball falls from a height of 40 feet. How high will it rebound,
supposing that one-fifth of the final velocity is lost at the impact in consequence
of imperfect elasticity?
92. An ivory ball falls from an elevation of 100 feet. With what velocity must
another similar ball be projected upward in the same vertical line, that after
the two balls meet, the first ball may return to the same elevation from which
it fell?




148             TIHE THREE STATES OF MATTER.
CHAPTER III.
OF FLUIDS.
HYDRODYNAMICS.
Q 1. Hydrostatics.
I. DISTINGUISHING PROPERTIES OF LIQUIDS.
186. Definitions.-Fluids-Hydrodynamics.-Fluids are bodies
in which the attractive and repulsive forces (146) are, 1st, either in perfect equilibrium, producing liquids or inelastic fluids; or 2d, in which
the repulsive force holds sway, producing gases or elastic fluids..
Hydrodynamics treats of the peculiarities of state and motion among
fluid bodies, both liquids and gases (15). It is subdivided into hydrostatics, or fluids at rest, and hydraulics, or fluids in motion.
187. Mechanical condition of liquids.-Liquids, owing to the
slight cohesive attraction among their particles, possess no definite form,
but adapt themselves to the shape of the containing vessel. This is a
necessary consequence of the perfect freedom of motion among the particles of a liquid. Liquids vary very much, however, in the degree of
their fluidity, as between thin mobile liquids like alcohol or water, and
thick, viscous, bodies like oils and tar. In viscous bodies, the imperfect
fluidity is a consequence of the only partial ascendency of the repulsive
force, leaving still a notable amount of cohesion among the particles.
Heat serves to increase the repulsive force, and so converts viscous into
thin liquids.
Liquids and gases are conveniently distinguished as non-elastic and
elastic fluids, but this distinction is not absolute, since all liquids possess
some elasticity, more, usually, than belongs to the solid state of the same
bodies.
188. Elasticity of liquids.-Compressibility.-We have already,
in sec. 21, illustrated the compressibility of water. The researches
of Canton, in 1761, Oersted, in 1823, and others of later dates, have
proved that all liquids are slightly compressible.  The piezometer
(,tsto, to press, and tpepov, a measure) is an instrument designed to
measure the compressibility of liquids. Oersted's apparatus, fig. 133,
consists of a strong glass cylinder; twenty-four or twenty-five inches




OF FLUIDS.                            149
in height, mounted on a stand: the upper part is acturately closed by a
brass cap, through which passes the funnel tube, R, to supply the vessel
with water, and a cylinder, furnished with a piston, moving by the
screw P.  In the interior is a vessel A, containing the liquid to be
compressed, having a capillary tube at its upper part, which bends and
descends to the mercury 0, contained in the lower part of the vessel.
This capillary tube is subdivided into                  133
equal parts, and the number of these 
parts the vessel A  can contain, is accurately determined.  There is also in the 
interior of the cylinder, a tube of glass,
B, furnished with a graduated scale, C;
this tube is closed at its upper end, and
has its lower end immersed in the mer-                i
cury, 0.  This tube is called a mano-                 1i
meter (280), and is, when at rest, nearly             l
filled with air.                                        Ali
In order to experiment with this apparatus,         I
fill the vessel, A, with the liquid to be compressed, and by means of the funnel, R, fill
the cylinder with water, having previously            i.
placed mercury in its lower part. Turning
the screw, P, the piston descends; in conse- 
quence, the air in the tube, B, is compressed, 
and the mercury is elevated; the degree of
elevation shows the amount of pressure; at
the same time, the mercury rises in the capillary tube, and gives the measure of the conpression of the liquid in A.
Supposing each division of the capillary
tube held but a millionth part as much as 
the vessel A, then if the liquid to be compressed was water (at the pressure of one atmosphere), we should
observe the mercury to rise between 49 and 50 divisions.
There is one correction to be made in the observations obtained by
this instrument; it might be supposed that the capacity of A would be
invariable, the exterior and interior walls being compressed equally by
the liquid, but it is not so; the interior capacity of the vase undergoes
the same diminution as would a body of glass of the same form and
volume, submitted to the same pressure.  This diminution amounts
to about 33 ten millionths (T6,ag-6f), of the primitive volume, for
each atmosphere of pressure.
This quantity can be calculated in any case, as well for glass as for




l5ci              THE TIIHREE STATES OF MATTER.
copper and brass (the three mat(rials used in the improved piezometer
of Itegnault), from  the known elongation of rods of these substances
at the same tension, according to the laws of Wertheim  (160).  M.
GRASSI (Ann. de Chimie et Phys., 3" Sarie. Tom. XXXI., p. 437) has
lately revised the results of Oersted, Canton, and of Messrs. Colladon and
Sturm, on a great number of liquids, and at different temperatures.
The compressibility of water diminishes with increasing temperatures.
On the other hand, heat increases the compressibility of alcohol, ether,
chloroform, and wood spirit.
Salt or sulphuric acid diminishes the compressibility of water in proportion to the quantity dissolved, but for a given density these solutions obey the same order as pure water.
Grassi's principal results are given in the following table, the compressibility being parts in a million at a pressure of one atmosphere:
Pressure in atmosLiquids used.        Temperature.     Compressibility.    pheres employed.
Mercury,....                 32~ F.       0-000,002-95
Water.....              32           0-000,050-3
Do......             77           0000,045-6
Do....           128~           0'000,044-1
Ether,.....             32~           0-000,111-0        3-408
Do.....            57~           0000,140-0          1-580
Alcohol,.....             45           0000,082-8          2-302
Do.....                55~~         0-000,090-4         1-570
Wood spirit,                   56~          0-000,091.3
Chloroform,...                47           0-000,062-5
Do..54~                          0-000,064-8         1-309
It appears, that of all liquids tried, mercury has the least, and ether
the greatest, ratio of compressibility.  The pressures were carried to
the great extent of 220 atmospheres.
Elasticity.-It is hardly requisite to remark that the return of compressed liquids to their original bulk, on removal of pressure, is proof
of an elastic force in them equal to their ratio of compressibility.
Consequences.-It follows from what has been said,First. That the molecules of liquids, owing to the entire freedom  of
motion among themselves, are in equilibrium.
Second. That liquids possess perfect elasticity, and a slight degree of
compressibility.
Let us now farther consider the necessary consequences of these mechanical
conditions of liquids, both independent of gravity, and also with reference to
that force.




OF FLUIDS.                          151
II. TRANSMISSION OF PRESSURE IN LIQUIDS.
189. Liquids transmit pressure equally in all directions.Liquids transmit in all directions, and with the same intensity, the pressure exerted on any point of their mass.
This important theorem  was first clearly announced by B. Pascal.
Let fig. 134 be a vessel filled with a liquid, and furnished with a number of equal cylinders, in each of which is a well-fitting piston. The
vessel and liquid are both assumed to be without weight, consequently
none of the pistons have any tendency to move. If pressure is applied
to the piston A, it will be forced inwards, and the other pistons B, C, D,
and E, of equal area, will each be forced outwards with the same pressure, so that if the piston A was pressed inwards with a force of one pound,
it would be found necessary to apply a force          134
of one pound to each of the other pistons, 
in order to keep them  in their place. If
the area of B and C was two or three times         A.
that of A, then the pressure upon them
would be two or three times as great. We
cannot perfectly demonstrate, that liquids 
transmit pressure equally in all directions
(because we cannot obtain for experiment,
as would be necessary, liquids without
weigit, and pistons working without fric- 
tion), but that this pressure is exerted in all directions, is shown by the
simple apparatus, fig. 135, consisting of a cylinder, furnished with a
piston and terminated by a sphere; on this              135
sphere are placed small tubes, jutting out in
all directions; upon filling the sphere and
cylinder with water, and pressing upon the
piston, the water is forced out from each of the
jets with equal energy. This is a necessary
consequence of the mechanical constitution of
liquids (187).
Let A represent the area of any portion of
the inner surface of a vessel, and A' that of any
other portion of the same vessel, while P and
P' are the pressures exerted on these surfaces
respectively by any force of compression on    ~
the liquid, and we have
P: P'   A: A'.
It also follows that this expression represents correctly the pressure




152             THE THREE STATES OF MATTER.
exerted on any solid body plunged in the liquid, as well as for any part
of the sectional area of the liquid itself.  Hence:The entire pressure sustained by aly surface is proportional to its area,
"and thus," says Pascal in his Treatise on the Equilibrium of Fluids,
it appears that a vessel full of water is a new Principle in Mechanics,
and a new Machine which will multiply force to any degree we choose."
Pascal also referred the equilibrium of fluids to the principle of virtual
velocities which regulates the equilibrium of other machines (105).
190. The Bramah Hydrostatic Press.-This powerful appalilaus
depends upon the principle just announced.              136
Want of good workmanship alone prevented
Pascal from  realizing his conception of this
machine (in 1653), as was long afterwards
(A.D. 1796), done by Bramah, at London.
As the form of the vessel has no influence 
on the equal transmission of pressures, and  
the point of application of force may be 
situated at any convenient distance from the 
press, it is plain that the mechanician can use
this principle as circumstances demand. Thus, in fig. 136, the piston a
may be to the larger one b c as 1: 20, and hence a pressure of one pound
137... _._. —---- --  __                       __ _  
exerted on a will raise b c with a force of twenty pounds, and converely
any pressure exerted on b c will be diminished twenty fild at a.




OF FLUIDS.                              153
The main parts of the Bramah hydrostatic press, fig. 137, consist of a small
forcing-pump, A, in which is a piston worked by a lever. This pump communicates with a large and strong cylindrical reservoir, B, by a tube indicated by the
dotted lines in the figure. In this cylinder a water-tight piston moves, bearing
at its upper end a flat metallic plate, between which and the top of the frame,
D, the substance, M, to be compressed, is placed.
The cylinders are filled by means of the curved tube H, one end of which
rests in a vessel containing water, or oil, the other terminates in the barrel A,
and has a valve at its end opening upwards. This valve opens when the piston
is raised, thus drawing in water, and closes when the piston descends. By
working the piston, the barrels A and B are completely filled with water. The
orifice 0 is in connection with a stop-cock, by which the water can be drawn
off when the pressure is to be reduced.
If the cylinder B has an area of 200 square inches, and the small cylinder an
area of half a square inch, the pressure of the water on the piston above B, will
be 400 times that applied at the lever. But let the arms of the lever be to each
other as one to fifty, then when a force of fifty pounds is applied at the long
arm, the piston will descend with a force of 2500 pounds (50 X 50 = 2500),
and there will be exerted, theoretically, a force of 1,000,000 pounds upon the
piston in B (50 X  50 X 400 =  1,000,000), or, deducting one-fourth for the loss
occasioned by the different impediments to motion, a man would still be able to
exert a force of 750,000 pounds.
This enormous result is gained, of course, very slowly, in accordance
with the well-known relation of power to weight (109).
Uses in the arts.-The hydrostatic (often called 7ydclrulic) press is of
extensive use in the industrial arts. It is employed for compressing cloth, oilcake, paper, hay, gunpowder, candles, vermicelli, and for numerous other articles, to which the proper form or condition is imparted by severe pressure;
also for testing steam-boilers and chain cables. The tubes of the famous
Britannia tubular bridge over the straits of Menai (172) were raised to their
place by means of powerful hydraulic presses.
191. Pressure of a liquid  on  the bottom  of a vessel.-The
pressure exerted by a liquid on the horizontal base of a containing vessel,
is 1st, independent of the shape of the vessel, and 2d, is equal to the
weight of a columnn of this liquid, whose base is that of the vessel, and
whose height equals the depth of the liquid.
In a conical vessel, standing on its base and filled with liquid, conceive any number of horizontal planes, dividing the contents of the
vessel into a series of frustums, so thin that each frustum may be
considered a cylinder. It is evident that the pressure exerted by each
cylindrical mass on its own base is equal to its own weight. But by
the principle of Pascal each succeeding section will have to support
a pressure, as much greater than the weight of the superincumbent
masses as the area of its base is greater than the area of the base of
16




154             THE THREE STATES OF MATTER.
that preceding it.  Hence, the base of the conical vessel   138
will support a pressure equal to the weight of a column of A
water whose base and height are respectively those of the
vessel.
Evidently, from  this reasoning, if the conical vessel is inverted, or its form is in any way modified, the same law holds
good. 
The truth of this principle may be experimentally demonstrated by means of the apparatus in fig. 138. If this instrument is placed in a liquid, the piston C is forced in with a
pressure equal to the weight of a column of the liquid, whose
base has the area of the piston, and whose height is equal to
the depth of the liquid above the surface of the piston.
To demonstrate that the pressure is independent of the form of the
vessel, M. Haldat has contrived the apparatus, fig. 139. It consists of
a tube, A B c, bent twice at right angles. On A, may be placed the
vessels M and P, of equal height, but of different forms. The tube
A B c is filled with mercury, which rises to an equal height in A and c;
M is then placed on A, and filled with water; the mercury immediately
rises in c, to a certain point, as a. We then replace M by P, and fill
with water to the same height as                   139
before.  The mercury again rises
to the point a, as it did with the
vessel M; it is evident that the                            l
pressure transmitted to the mer-                          
cury in the direction A B, was the 
same in both cases, proving, most
conclusively, that the pressure does
not depend upon the quantity of
liquid, for the vessels MI and P differ 
greatly in capacity. The area of the
base formed by the surface  of the
mercury, and the vertical height formed by the column of water, were,
however, the same in both cases, and upon these, as before stated, the
pressure depends. In the case of a vessel having vertical walls, the pressure would be equal to the weight of the liquid the vessel contained.
192. Upward pressure.-Having shown that pressure in liquids is
exerted from above, downwards; it follows, from  the law of equality
of pressure, that a corresponding force is exerted from below, upwards.
This pressure is made very manifest by the buoyancy experienced when
we plunge the hand into a liquid of great density, as into mercury. In




OF FLUIDS.
order to demonstrate this upward pressure experimentally, a tube of
glass is taken, open at both ends, fig. 140, having at the lower end a
disk of glass, B, which is supported by means of a thread from its
centre: the whole is then placed in a vessel         140
of water and abandoned to itself; the disk
remains attached to the end of the cylinder,
owing to the upward pressure of the water.
If now the interior tube be carefully filled,
the disk will not fall until the level of the
water within the tube is nearly the same as
that in the outer vessel, proving that the
upward pressure is equal to the weight of
the interior column, and therefore that:- The    B
upward pressure, in any vessel, is equal to the  / l    - -
weight of a column of liquid having the same  
base as the cylinder, A, and whose height
equals the depth of the section below the suiface of the liquid.
193. Pressure on the sides of a vessel.- The            141
pressure of a liquid on any portion of a lateral wall, is
equal to the weight of a column of liquid, which has for
its base this portion of the wall, and for its height the
vertical distance frjom its centre of gravity to the swlface
of the liquid. Thus, in fig. 141, the pressure at the  c        D
height, C D, of the wall is, by g 191, equal to the weight  B
of the column A B, since the pressure of this is communicated laterally to all the particles lying on the
same horizontal plane.
This lateral pressure increases, of course, with the depth of liquid in
the vessel. Thus, in fig. 142, the column of liquid A C   142
pressing with a certain force on Z, the column E F.       A.
will press on G, with a force as much greater, as E F is
deeper than A C. This may be further illustrated by
plunging the apparatus, fig. 138, at various depths and
in a horizontal position, the piston will be forced in     C
with a pressure corresponding to the depth; also, if it
is placed in any position intermediate between the   p
horizontal and vertical, the piston will be similarly
pressed in, thus showing that pressure is exerted
equally in all directions.
194. Pascal's experiment with a cask.-Pascal made a striking
experiment at Rouen, in 1647, to illustrate the enormous pressure




1536              THE THREE STATES OF MATTER.
exerted by a lofty column of water contained in a small tube.  A
strong cask, filled with water and arranged as in fig. 143, was fitted
with a small tube about forty feet high.  When this tube was filled
with water, the effect of the pressure transmitted to all parts of the
cask was sufficient to burst the vessel.
143
144
T
195. The water bellows, or hydrostatic paradox.-This familar
experiment is only a modification (in form) of Pascal's cask.
The hydrostatic bellows, fig. 144, consists of two boards, B C, and E D, connected with leather or India-rubber cloth, A, in such a manner that the upper
board can rise and fall, like the common air bellows. The tube T E communicates with the interior of the apparatus. Supposing the tube to have a cross
section of one square inch, and the top of the bellows to have a surface of 100
square inches, one pound of water in the tube would lift 100 pounds on the bellows, the weight of the water acting with a pressure equal to one pound on each
square inch of the surface. The pressure is proportioned to the height of the
column of water; for if we use a smaller tube, for the same bulk of fluid, the
height of the column of water will be greater, and will raise a greater weight;
if the tube be larger, the column will not be so high, and will not raise so large
a weight.
196. Total pressure on the walls.-In the vessel ABC D  fg.




OF FLUIDS.                              157
145, divide the side AB into 10 equal parts. Supposing the pressure
at 1 to be one pound, then the pressure at 2 would be two pounds,
at 3 three pounds, &c., as the intensity of the pressure increases directly
with the depth. The average intensity of pressure would be found at
the 5th division (or a point midway between the 1st and 10th), and the
total pressure on the walls would be the same as if it sustained the
average intensity over the whole lateral surface, and therefore the total
pressure upon a wall of such a vessel, is equal to the weight of a column
of the liquid whose base is equal to the area of the side, and whose height
is equal to one-half of the depth of the liquid             145
in the vessel. This is true, whether the vessel  A                       D
be vertical or inclined in any direction.  In   
the case of a cubical vessel, this pressure on         _      -
one side would be equal to one-half the                 -       
weight of the liquid contained in the vessel.  "] 
Total pressure on the bottom  and sides of a vessel.-The
total pressure exercised on the bottom and sides of a vessel, is much
greater than the weight of the liquid contained in the vessel. In the
case of a cubical vessel, the pressure exerted on the bottom is equal to
the whole weight of the liquid (191), the pressure exerted on each side
being equal to half the weight of the liquid on the four sides, it is equal
to twice its weight, consequently, in a cubical vessel the entire pressure exerted on the bottom and sides is equal to three times the weight of
the contained liquid.
Table, showing the pressure in pounds, per square inch, and square foot, produced
by twater at various depths.
Depth in feet. Pressure per square inch. Pressure per square foot.
1           0-4328             62 3232
2           0-8656            124-6464
3           1-2984            186-9696
4           1-7312            249-2928
5           2-1640            311-6160
6           2-5968            373-9392
7           3-0296            436-2624
8           3-4624            498-5856
9           3-8952            560 9088
10           4-3280            623-2320
By aid of the above table, the pressure of water on any surface of a vessel
containitg it, can be determined. As, for example, the pressure of water on a
square foot, at the bottom of a vessel twenty-three feet in depth; at two feet,
the pressure is 124-6464; at twenty feet, ten times as much; =  1246-464; at
16*




158              THE THREE STATES OF MATTER.
three feet, 186-9696, and 1246-464 + 186-9696 - 1433-4336, the pressure of water
on a square foot of surface, at a depth of twenty-three feet.
That the pressure produced at great depths is really immense, can be shown
by confining a piece of wood at great depths in the sea. The pressure force:
the water into the pores, so that it will not be capable of floating afterwards.
A bottle, the body of which is square, if tightly corked and lowered into the
sea, will be broken by the pressure. If the body of the bottle is strong and
cylindrical, the cork will be forced in. Below a certain depth, divers cannot
penetrate, and the same may, perhaps, be true of fishes.
197. The centre of pressure upon any surface immersed in a
flui.d is the point of application of the resultant of all the pressures
acting upon it.
If the pressure of a fluid upon an immersed surface were the same
at all depths, the centre of pressure would be at the centre of gravity
of the surface. But as the pressure increases with the depth, the centre
of pressure will always be below the centre of gravity.
The centre of pressure in an immersed surface, or in the side of a
vessel containing a fluid, is a point to which aforce equal and opposite
to the resultant of all the pressures must be applied to keep the surface at
rest.
The position of this point, for various regular surfaces, has been
determined by the calculus.
The centre of pressure of a rectangular surface, vertically or obliquely
immersed, so as to have one side in the surface of the liquid, is in a line
joining the centres of the superior and inferior bases, and at a distance
from the inferior base, equal to one-third the height of the rectangle.
In fig. 146 the point C, in the line A B, distant from B one-third of
A B, is the centre of pressure.
147                     148
A                        A
146
C
D                                    3B  B
When the immersed surface is a triangle having one side horizontal,
and the apex in the surface of the fluid, the centre of pressure is in a.line joining the apex and the centre of the horizontal base at a distance
from  the centre of the base equal to one-fourth the bisecting line.
The centre of pressure in the triangle, fig. 147, is at c, distant from B
one-fourth of the line A B.
When the base of the triangle lies in the surface of the fluid, the




OF FLUIDS.                          150
centre of pressure is midway between the apex and the centre of the
base, as at c, fig. 148, which is equidistant between A and B.
198. Pressures vary as the specific gravities of liquids.-Two
liquids press on the same area and at the same depth, directly in the ratio
of their specific gravities. We have seen (191) that the pressure exerted
on the base of a vessel having vertical walls is equal to the weight of
the liquid the vessel contains. Plainly, therefore, the pressures exerted
on the base of two equal vessels filled with equal volumes of liquid of
unlike density will vary directly with their specific gravities; or representing the pressures in the two cases by P and P/, and the specific
gravities by (Sp. Gr.) and (Sp. Gr.)', we have
P: P" =  (Sp. Gr.): (Sp. Gr.)
III. EQUILIBRIUM OF LIQUIDS.
199. The conditions of equilibrium  in liquids.-The joint effect
of gravitation, and of the perfect mobility of the particles of a liquid, is:1. That the surface of a liquid at every point must be perpendicular to
the direction of gravity, i. e., it must be horizontal or level.
This principle, first distinctly enunciated by Archimedes, follows from
the nature of gravitation, which acting on a body free to move, causes
its centre of gravity to descend as low as possible. It is only when the
surface is horizontal that all the particles of the fluid mass are equally
solicited by the force of gravity.
The inequalities of the solid surface of the earth exist, because
cohesion is opposed to gravitation. Otherwise the mountains would
sink, and the valleys rise, until the whole mass had a uniform level.
By this principle a surface of water is perfectly horizontal only when
its area is so limited that the direction of the         149
forces of gravity can be regarded as parallel at          o      D
each point. If an observer is stationed at 0, fig.
149, and O A is one mile, the subtense of curva- 
ture (AB or IE) is eight inches. But O C and BC
are lines perpendicular to the points O and B, and        c
are therefore plumb lines (60), and hence the surface E O B is a spherical surface. In other words, we reach the more general principle:That the resultant of all the forces acting at any point on the surface
of a liquid mass, when in equilibrium, must be normal to the surface at
that point.
It follows from tis,, again:




160             THE THREE STATES OF MATTER.
2. That every liquid mass, when in equilibrium, can be considered-as
made up of an infinite number of very thin layers, sustaining at all
points the same pressure, and, at each point of surface, normal to all the
forces there acting.
200. Equilibrium of liquids when freed from the influence of
gravity. —It follows, as a consequence of the last principle, if a mass
of liquid is freed from the influence of gravity, and abandoned undisturbed to its own molecular attractions, that it will assume a spherical
figure; since then the sphere is the only form which can satisfy the
conditions of equilibrium. This theory is most beautifully demonstrated by a celebrated experiment calledThe experiment of Plateau, who conceived that the influence of
gravity might be avoided by suspending a mass of oil in alcohol,
diluted to exactly the density of the oil. This conception is perfectly
realized by experiment. By care and certain precautions to secure
clearness in the liquids, a considerable sphere of oil may be suspended
in any part of the alcoholic mixture, and by a wire arranged to rotate
as an axis, and about which the sphere of oil readily arranges itself,
the oblate figure of the earth, the appearance of satellites, or even the
rings of Saturn, may be imitated in a most instructive and striking
manner.
The spherical form of drops of rain or dew, and the globular drops
of mercury, are referable to the conditions of fluid equilibrium.
201. Equilibrium  of a liquid in communicating vessels.-If
two or more vessels communicate with each other, the liquids in both
or all the vessels stand at the same level. This law rests upon the fact,
that the pressure of liquids at equal depths,          150
is equal in all directions. If the fluid stands
at a higher level in one vessel than the other,
the particles of the former exert a greater   -L
lateral pressure on the channel of communi- 
cation than the other can; these particles are,
therefore, continually pushed upwards, until
they exert an equal and opposite pressure, 
which obtains when the columns are at an
equal height.  The effect is the same, whatever may be the size and number of the vessels. Fig. 150 represents a number of vessels           --  -
of different shapes and capacities, connected with a common reservoir;
if we pour water into one of them, it will rise to the same height in
the other vessels.




OF FLUIDS.                            161
202. Equilibrium  of liquids of different densities in communicating vessels.-When two liquids of different densities are placed
in communicating Vessels, their surfaces                151
will not rest at the same point or level; 
for in communicating vessels, the heiyhts
of the liquid columns are in the inverse
ratio of the specific gravities of the liquids.
If mercury is first poured into the lower
part of the apparatus, fig. 151, and the
tube AB  is then -filled with water, this
liquid will exert a pressure on the mercury,
causing it to be depressed in A B, and to rise
in the other tube.  Measuring the height
of the columns of mercury, C D, and water,
A B, which are in equilibrium, they will
be found to be as I to 13*59. These num- 
bers represent the densities of water and mercury.
Demonstration.-Let S represent the surface of the mercury at B, and H
be the height of the column of water, B A, and Sp. Gr. the specific gravity of
water; then, by ~ 198, the pressure on the surface is P = S H (Sp. Gr.) for the
column of water, and for the mercury, C D, it is P' - S' H' (Sp. Gr.)' But
by ~ 189 equilibrium can obtain only when the pressures exerted on B and C
are proportional to the area of those surfaces, or where P:P' -- S: S'. Substituting the value of P and-P', it follows that
H (Sp. Gr.) = H' (Sp. Gr.)'
H: H' =  ({Sp. Gr.)': (Sp. Gr.)
In other words, the columns are in equilibrium when their heights are
inversely as their specific gravities, which was to be proved.
203. The spirit level.-Since by ~ 199 the surface of a liquid at
rest is always horizontal, we have thereby a ready means for determining the horizontal line by use of the spirit level. This instrument is a
glass tube, A B, fig. 152, very slightly curved upwards, nearly filled
with alcohol, hermetically                     152
sealed and  sheathed  in
brass, C D.  The small    A _        _ -- 
bubble of air, M, always   
rises to occupy the high- _
est point of the apparatus. _
The base is carefully ad-    -      =
justed, so that only when
the instrument is placed horizontally, does the bubble remain in the
centre, at a fixed mark.




162              THE THREE STATES OF MATTER.
204. Artesian  wells.-All springs and fountains are examples
of the laws of equilibrium  of liquids in communicating  vessels.
Among similar phenomena, artesian wells are the most remarkable examples.  These are wells (named artesian from  the ancient
province of Artois in France, where they were early made, although
known long before in China), bored into the earth's crust, often to a
great depth. The crust of the earth consists often of various beds or
strata, some pervious to water like sandstones, and others, like clay,
impervious.
Fig. 153 presents an imaginary section of a portion of the earth's crust,
containing two impervious strata, A B, C D, and one pervious stratum,
KK. Let these strata reach the surface in elevated land, and we
153
have thus a basin into which the meteoric waters filter and from which
they cannot escape, being confined by the impervious strata already
named; now an artesian boring in the valley H, will reach the imprisoned water after passing A B, and the water will be thrown up in a
jet, the height of which will depend on the elevation of the edges of
the basin, which may come to the surface in lofty hills hundreds of
miles away from the well.
A well of this kind was sunk at Louisville, Ky., in 1857-8, to the great depth
-of 2086 feet (Dupont's well), which delivers, through a bore of 13 inches, over
three hundred thousand gallons of suiphuretted mineral water in 24 hours, at
170 feet above the surface, with a constant temperature of 76i~ F. (821~ at the
bottom). (Am. Journ. Sci. [2] xxvii. 174.) Belcher's well in St. Louis is 2199
feet deep, and yields also sulphuretted water; while the famous Grenelle well
in Paris is 1806 feet deep, and yields daily 600,000 gallons of soft water, warm
enough to answer the purposes of the great slaughter-houses surrounding it.
Artesian wells have lately been successfully bored in the African desert on the
great caravan route.
IV. BUOYANCY OF LIQUIDS.
205. Theorem  of Archimedes.-Solids immersed in liquids are
buoyed up by aforce equal to the weight of the liquid displaced.




OF FLUIDS.                         163
This very important principle was discovered by Archimedes, about
230 years B/c., and is called after him, the Principle of Archimedes.
Its correctness is proved by means of the hydrostatic balance, from
one of the arms of which (fig. 154) is hung a hollow cylinder, or
bucket, A, having a cylindrical mass of copper, B, exactly fitting into
it, and suspended from it by means of a hook. Having exactly counterpoised the beam by weights on the other arm of the balance, fill up
the glass vessel with water, until the cylinder B is wholly immersed.
The cylinder will then appear to have lost weight, the other arm going
down. If the bucket, A, is now exactly filled with water, the equilibrium will be restored; proving that the weight lost by the immersed
body is equal to its own bulk of water.
The same is true of any liquid whatever. It is also true, however,
that the weight lost in this case by the cylinder must, as a necessary
result of the law of action and reaction, be gained by the water in
the vase.
This fact is illustrated by arranging the apparatus as seen in fig. 155.
After first balancing the vase of water, the cylinder B is suspended in
154        it from a separate support C. The vase then
appears to have gained in weight, and it will
be found requisite in order to restore the equilibrium  to remove therefrom  enough water
exactly to fill the cup A.
155
The theorem of Archimedes is a necessary consequence of the me.




164             THE THREE STATES OF MATZEU.
chanical condition and laws of equilibrium  of liquids, and of the
impenetrability of matter. The whole immersed body is buoyed up
by a force equal to the resultant of all the forces normal to each point
of its surface, that is by a force equal to the weight of the liquid which
it displaces.
206. Another demonstration of Archimedes' principle.-Conceive a cube AB, fig. 156, of water for example, say one cubic inch or
a cubic centimetre in bulk, isolated and           156
sustained in its position by the pressure of
the surrounding particles-such being the
condition of equilibrium  existing among
the particles of liquids at rest (199).
Hence it is evident that the weight of the  
ideal cube A B is sustained in its position 
of equilibrium by a buoyant force exactly
equal to its own weight. If AB is now 
solidified by any cause which does not
change its volume, it is evident that the
conditions of its equilibrium  also remain                   _
unchanged. We may therefore replace it
by any other substance of whatever weight,
having the same dimensions, and the new solid-will still be buoyed up
by a force equal to the weight of the ideal cube of water, or of any
other liquid in which it is immersed.
The form of the body is evidently immaterial, and therefore it follows, as before, that a body plunged in a liquid is sustained by a power
equal to the weight of the liquid displaced.
Floating bodies.-Accepting the Theorem of Archimedes, it follows,
that if the immersed solid be of the same weight as the displaced fluid.
the former will remain at rest in the fluid, in any position in which
it may be placed, the upward pressure exerted upon the solid being
equal to its own weight.
Since the specific gravities of any two substances are to each other
as the weights of equal volumes of these substances (99), it follows that
any homogeneous solid will float when its specific gravity is less than that
of the liquid, and that it will sink when these conditions are reversed.
Hence, iron sinks in water, but floats on mercury; some woods
which float on water will sink in oil or alcohol; while oak, which floats
on salt water, will sink in fresh water. But if the iron is fashioned
into a thin-walled vessel, and the dense woods into hollow boxes,
they will then float on the same liquids in which they before sank,
because their volumes have been increased, respectively, without in



OF FLUIDS.                             166
creasing their weight, and they float because each displaces a volume
of water greater in weight than the weight of the floating body.
Examples illustrating this principle are of familiar occurrence. Iron shipse. g., the Great Eastern-float as buoyantly as ships of wood, and have besides a
vast capacity for floating their heavy machinery, coal, and cargo. The problem
of weighing a ship and cargo resolves itself into a question of mensuration of
the volume of water displaced by her.
Caimels are tanks of iron or wood, which are first filled with water, and after
being secured to the sides of loaded vessels the water is pumped out, when their
buoyancy aids the vessel in floating over a bar, or in shallow water.
Floating docks, so much in use in the seaports of the United States, are similar
zontrivaflces by aid of which the heaviest an I largest ships are safely raised entirely out of water for repairs. The elevating force is solely the buoyancy of large
sectional tanks previously sunk beneath the vessel, and then pumped out by
steam-engines.
Cartesian devil.-This hydrostatic toy, known also as the ludeon, exhibits the
principle just stated. It consists of a small glass or        157
enamel figure, fig. 157, at whose head is fixed a bulb of  
glass having a small opening, 0, beneath. It is filled
with water to such an extent, that when placed in the
cylinder of water as represented, it just floats. Over the
mouth of the vessel is tightly fixed a piece of caoutchouc.
Pressure exerted by the thumb on the caoutchouc will be 
conveyed through the water to the air contained in the
bulb O. Sufficient water will thus enter 0 to render the
specific gravity of the apparatus heavier than that ef
water, when it sinks. On removing the pressure, expansion of the air in 0 expels the water which was previously forced into it, and the apparatus rises. By a
contrivance similar to this, the beautiful nautilus shell
rises, to float upon the surface of the sea, or sinks again
at pleasure, by a voluntary contraction or expansion of
an internal cavity.
Fishes are bodies floating in a state of equilibrium, when immersed in their
own element. But in order to preserve this state at different depths, they have
an air bladder, by contracting or expanding which, their bodies acquire the
mean density of the water in which they are.
207. Equilibrium  of floating bodies.-In order that a floating
body may be in equilibrium it is necessary: First, That the weight of
the fluid displaced should be equal to the weight of the floating body:
Second, That the resultant of all the upward pressures of the liquid
should act in the vertical line, passing through the centre of gravity of
the body.
AX the weight of a body may be considered as acting at a single
point called the centre of gravity, so the upward pressure of a liquid,
acting upon a body immersed in it, may be considered as acting in a
single point which will be the centre of gravity of the fluid displaced.
This point is evidently different from the centre of gravity of the body,
17




166             THE THREE STATES OF MATTER.
and may therefore appropriately be called the centre of buoyancy. In
a homogeneous solid this point is always below the centre of gravity
when the body floats, and coincides with it when the body sinks. Let
a b cd, fig. 158, be a homogeneous solid,          158
G will represent the centre of gravity  
of the body, and P the centre of buoyancy, or upward pressure, situated at                        b i
the centre of gravity of the liquid dis-   e       1        f
placed.' 
When the floating body is not homogeneous the centre of gravity may be
below the centre of buoyancy, as in the  - _, —
case of a ship having ballast or heavy        _ —
cargo stowed in the hold.                   -
Let the floating body take the position shown in fig. 159, the force
of gravity will act at G in the direc-           15
tion G r, but the upward pressure will
act from a new centre of buoyancy,         a,
P/, at the centre of gravity of the
displaced fluid, and in the direction 
P q. This force being equal to the   ci     l  l --    _      ^
force of gravity and parallel to it, but 
acting in an opposite direction, the
two forces form a couple (48), and
tend to rotate the body till the two   -
forces again act in the same vertical        lii —-:
line. 
When the centre of gravity and centre of buoyancy are in the same
vertical line, thefloating body will be in equilibrium.
This equilibrium may be neutral, or the same in any position of the
floating body; unstable when by any movement of the body the centre
of gravity descends:-or stable equilibrium when movement of the body
in any direction causes the centre of gravity to ascend.
Neutral equilibrium.-A sphere of uniform density floating in a
liquid is an example of neutral equilibrium, because, whatever position
it may assume, the part immersed is a segment of a sphere of the same
magnitude and form, and no alteration can be effected in the relative
positions of the centre of gravity and the centre of buoyancy.
Unstable equilibrium.-Let a b c d, fig. 160, represent a rectangular
prism of uniform density, floating on one end, the centre of gravity
being at G, and the centre of buoyancy or upward pressure being at P.
Although G and P are in the same vertical line, it is evident that the




OF FLUIDS.                          167
equilibrium will be unstable, because when the body moves to any new
position, as at fig. 161, the centre of gravity descends.
160                                 161
=              _~                       Ot      =,.
Stable Equilibrium.-The centre of buoyancy, or centre of upward
pressure, may be considered as the centre of support of a floating body.
When this centre is above the centre of gravity, the body will evidently
be in a position of stable equilibrium. It will also be in a position of
stable equilibrium when the centre of gravity occupies a lower position
than it would acquire in any other position of the floating body. But
in such cases the stability of the equilibrium of the floating body is more
readily understood by reference to another point called the metacentre.
208. The metacentre of a floating body is the point where the
vertical passing through the centre of buoyancy, in the position of
equilibrium, meets the vertical drawn through the new centre of buoyancy,
when the body has been slightly displaced from. this position.
By reference to figs. 158 and 159 it will be seen that G r' or G q is the
vertical which passes through the centre of buoyancy in the position of
stable equilibrium, and P' q the vertical passing through the centre of
buoyancy when the body is moved a little from the position of equilibrium; hence, q is the metacentre related to the position of stable equilibrium, and in this case it is above the centre of gravity.
Referring to figs. 160 and 161, we see that the metacentre is at q', fig.
161, or at a point below the centre of gravity.
The metacentre may also be found by taking the point of intersection of verticals passing through the centres of buoyancy in any two positions near each
other.
A floating body will be in stable equilibrium whenever the metacentre is above the centre of gravity, and the degree of stability will
be in proportion to the distance of the metacentre above the centre of
gravity. This depends on the form of the floating body.
When the centre of gravity is below the centre of buoyancy, the metacentre




168              THE THREE STATES OF MATTER.
must evidently always be above the centre of gravity, and this condition is
always stable. It is also evident that the stability of a floating body increases
with the breadth of the part submerged. These principles are of great importance in the construction and loading of ships. The metacentre may be regarded
as a sort of fulcrum above which is the pressure of the sails, and below the
weight of the ship.
Vessels designed for transporting passengers and light cargo require heavy
ballast of iron or stone placed near the keel, to preserve the equilibrium. On
the other hand, vessels loaded with iron have the centre of gravity so low as to
cause injurious strain upon the ship, unless the cargo is elevated by cross piling
or other supports to raise the centre of gravity so as to allow the ship to roll
easily in a heavy sea. The equilibrium of small boats is from the same cause
often disturbed by the unguarded movements of the passengers. The rolling
of a vessel in a storm may so shift the position of the cargo, and thus remove
the centre of gravity, that the vessel may be thrown upon her beam-ends, and
be lost.
V. DETERMINATION OF SPECIFIC GRAVITY.
209. The problem  stated.-Methods.-We have already considered the relations of density and specific weight to mass and weight
(96-99). Most of the methods in use to determine specific gravity
depend on the principles of hydrostatics just considered, and serve as
illustrations of them.  The problem is:To compare the weight of any body whose specific gravity is sought
with the weight of an equal volume of wifter taken          162
as unity.  The specific gravity is found by dividing
the first weight by the second.
Methods.-This operation is performed first,
by the hydrostatic balance; second, by the specific
gravity bottle; third, by various floating instruments called hydrometers or areometers. 
All these methods resolve themselves into special
cases of the Theorem of Archimedes, { 205.
210. Specific  gravity by the hydrostatic
balance.-The solid (heavier than water) is suspended beneath the pan of a balance by means             \
of a fine filament of raw silk, and then weighed, 
hanging in air.  It is then immersed in water as 
in fig. 162, and the weight it loses determined.
This loss is equal (according to the principle of
Archimedes) to the weight of a volume of water
of the same bulk as the immersed body.  Subtracting the weight of the substance in water
from its weight in air, and dividing the latter
by the difference, the product will be the specific gravity required.




OF FLUIDS.                            169
Example.-A piece of iron weighed in air 460 grains, in water 401-16 grs.
Then 460-401-16 = 58-84 grs., which equals the weight of a volume of water
equal to the iron, and 460 -- 58-84 = 7-8 = specific gravity of the iron.
To make the case general, let Wbe the weight of the body, and WI
the loss of weight in water, then by the definition
(Sp. Gr.)= W.
The result thus obtained is always to be reduced to a standard temperature.
For solids lighter than water.-If the body whose specific gravity
is to be determined is lighter than water, it must be attached to some
solid (whose weight in air and in water is known) sufficiently dense to
sink it in water. The compound mass is weighed first in air, and then
in water, and the loss determined, the weight lost by weighing the
heavy body alone in water being known, the weight of the light body
in air, divided by the difference between these losses, gives the specific
gravity.
Example;-A  substance weighed in air 200 grains, attached to a piece of
copper it weighed in air 2247 grs., in water 1620 grs., suffering a loss of 627 grs.
The copper itself loses, when weighed in water, 230 grs., 627 - 230 = 397, ther
W                                              163
Sp. Gr. =-       =  200 - 397 =-  504.
For liquids.-The  hydrostatic  balance  also  applies  to
liquids as well as to solids-whether the liquids are denser
or lighter than water.
For this purpose a small glass tube is prepared, including
enough mercury to sink it in any liquid not heavier than 
mercury. It is hermetically sealed, the end bent into a hook,  I 
and the whole suspended by a very thin platinum wire from          I
the pan of a balance.  Fig. 163 shows this apparatus of full
size.
The weight of the volume of water which this system displaces at 60~ F. (or at 4~ C.) is first determined by the mode
described for solids.  This is a constant quantity, and may
be called C.  If the tube is now immersed in another liquid,
as in alcohol for example, it will require a certain weight to 
restore the equilibrium (the weight of the tube and mercury
is supposed to be counterpoised in each case by a constant
weight prepared for the purpose).  The amount of this
weight, W (required to restore the equilibrium), is the weight of a
volume of the liquid displaced by the tube. But the weight of the
17*




170             THE THREE STATES OF MATTER.
same volume of water is known (C.) Hence the specific gravity of the
liquid is C.
E xample.-A glass tube, like fig. 163, lost in water 2-9910 grains = C, in
W
alcohol it lost 2-4081 = W.  -      -80511 = Sp. Gr. of the alcohol.
211. Specific gravity bottle.-For liquids.-When it is required
to determine the specific gravity of a liquid, the specific gravity bottle
offers the easiest and most simple method. Such         164
a bottle is shown in fig. 164. It is closed by a
ground glass stopper, and the neck is drawn out
to a fine tube (the upper portion of which serves
for a funnel in filling the bottle), upon which, at
A, is traced a fine line to which the bottle is to be
filled at each experiment.  The tare of the bottle
is accurately determined and noted once for all.
It is then filled to A with pure water and weighed
again. This weight less the tare gives its capacity
of water at a fixed temperature.  To determine
the specific gravity of any other liquid, the bottle
is filled with it and weighed as before. Deducting
the tare of the bottle, we now know the weight of
a volume of the liquid equal to the same volume
of water. Representing these two weights by W' 
and W, we have (Sp. Gr.) -- Wl.  In all cases, 
the result must be reduced to a standard tempera- _   G
ture as described in the Chapter on Heat.
For solids, when broken in small fragments,
we may also use the specific gravity bottle. In this case the weight
of the bottle when empty, and also when filled with pure water, being
known, a known weight of the solid in fragments is    165
introduced, as in fig. 165. Calling the weight of the
bottle and water =  Wa, and the weight of the solid added
W, and the weight of the bottle solid and water Wb, it is
plain that the weight of water displaced by the solid is
W" =-  Wa -+  W -  Wb, and that the specific gravity of
the solid is
(Sp. Gr.)=  Wa-  W    Wb
Wa- Wa  W- Wb'
This value must be corrected for temperature as before.
For solids soluble in water we must employ some liquid




OF FLUIDS.                         171
in wLich the substance is insoluble, as alcohol, oil of turpentine, &c.
The specific gravity thus determined is reduced to the standard of water
by multiplying it by the known density of the liquid employed; thus, for
Example.-A substance soluble in water was weighed in oil, and its specific
gravity, compared with the oil, was 2-6, the specific gravity of the oil was'87;
then 2-6 X'87 = 2-262 the specific gravity of the substance.
212 Specific gravities by hydrometers or areometers.-In
this mode the balance is replaced by floating bodies called hydrometers
or areometers. There are two classes of these instruments, namely,
first, hydrometers with a constant volume; and, second, hydrometers with
a constant weight.
1. Nicholson's hydrometer or areometer is an instrument of the
first class, used for determining the specific gravity of solids. It consists
of a hollow cylinder of metal or glass, B, fig. 166, having attached at
its lower end a cone, C, loaded with lead, which causes the apparatus
to assume an upright position when placed in water.      166
The upper part of the cylinder is terminated by a    A
slender rod, on the end of which is a small pan, A,
for holding weights. The whole apparatus must            i
have a less specific gravity than water, so that a
certain weight, represented by C, must be put in the
pan to sink the areometer to the water mark, 0. If
we wish to determine the specific gravity of a soJid
(whose weight must be less than C), we place it in
the pan A, and add weights until O is brought to 
the level of the water. The weight C, minus the
weights last added, will be the weight of the body
in air. It is now taken from A, and placed in C; the
additional weight now required to sink the cylinder
to the index, 0, will be the weight lost in water.
We have now the data for determining the specific gravity of the solid.
For example, if the counterpoise weighed 250 grs., and a mass of
lead whose specific gravity we wish to ascertain, requires, when placed
in A, 50 grs. to be added in order to bring the hydrometer to the point
0, then (250-50) 200 is the weight of the lead in air; placing now
the lead on C, we find that it requires the addition of 17'47 grs. on A,
in order to counterbalance the instrument; consequently the specific
gravity of the lead is 11'45. T -c- = 11'45. If the substance is lighter
than water, it is confined under a perforated cover or wire cage placed
on C, which prevents its rising.




172              THE THREE STATES OF MATTER.
If we represent these successive weights by C, W  and WW, then in
any case
(Sp. Gr.)      w a
a. Fahrenheit'. hydrometer is the same instrument (omitting the lower pan)
constructed of glass and designed to measure the specific gravity of liquids.
Knowing (by the balance) the constant weight (C) of the instrument, and also
the weight (c) required to sink it to a fixed point on the stem-the sum of which
weights (by 210) is equal to the weight of the water displaced. We have only
to float it in any liquid whose specific gravity we would ascertain, and note the
weight, TV, required to sink it to the fixed point on the stem. The weight of
the liquid displaced is then C +  W, and since C + c and C -  W are the
weights of equal volumes of water and of the liquid, the specific gravity of the
liquid is found by dividing the latter by the former, or (Sp. Gr.) = (C +  W) -
(C+ c.)
b. Rousseau's hydrometer is a form of this instrument adapted to determining
the specific gravities of liquids of which we possess too small a portion to float a
common hydrometer. For this end, a cup of glass replaces the pan A, which holds
say one cubic centimetre. Thus loaded, the instrument sinks to a point marked
200 near the middle of the stem. The stem is divided between this point and
zero into twenty equal parts, each of which consequently measures one-twentieth
of a gramme or 0-05 gramme. The specific gravity of a liquid is then found by
this instrument by multiplying 0-05 by the number of the division to which it
sinks when loaded with one cubic centimetre of the liquid used.
2. Gay Lussac's and  Beaume's hydrometers are instruments
having a constant weight, and by which we determine the specific
gravity of a liquid by measuring the volume of fluid displaced by the
floating instrument-which weight, as we have seen, is the same as the
weight of the instrument itself.  But we have shown (99), that for
equal absolute weights the specific weight is inversely as the volume or
(Sp. Gr.) =  V  V, where PV  equals the volume of water displaced by
the instrument, and Vthe volume of any other liquid displaced by it,
In other words, we can find the specific gravity of any liquid by dividing the volume of a given weight of water by the volume of the same
weight of the liquid whose specific gravity is required.
Instruments of this class are very common and in constant use for
determining the specific gravity of alcohol, acids, alkaline solutions,
urine, milk, and many other liquids. Figs. 167 and 168 show the form
of Gay Lussac's densimeter, as it is often called. It is a glass tube containing enough mercury in the lower end to cause the tube to float in
pure water at the hundreth division of a scale of equal parts traced or
paper and sealed up inside the tube. If it displaces 100 measures of
water, floated in sulphuric acid it displaces only 54 measures, and
therefore the specific gravity of sulphuric acid is 100 — 54 =  185.




OF FLUIDS.                         173
For fluids lighter than water, the graduation is carried up say to 166
(as we know of no liquid of a less specific gravity than 0-60). Then
placed in pure alcohol it rises say to 125 degrees, or   167  168
the specific gravity of alcohol is 100 - 125 = 0-80.
By giving the instrument the form  shown in                  1o
fig. 168, much needless length is saved on the 
stem, since the ball is so placed as to be always 
immersed, and its buoyancy is equal to that of a
much greater length of tube. The scales are also  8 
usually divided among the instruments-one for
liquids lighter than water, one for specific gravities 
from 1' to 1-33 (corresponding to 100 to 75), and
another reading from 75 (corresponding to 1'33) at
the top down to 50 (corresponding to 2-06) near its  6  o
middle. These instruments are not of scientific accuracy, but are ready modes of determining off-hand  40
the approximate specific gravity of a given liquid. 
The scales of Beaum6 (that most in use), as well
as those of Cartier and Beck, are purely arbitrary.  2 
Table V. at the end this volume shows the correspondence of their degrees to real specific gravities.   1
Table VI. gives the specific gravity of some of the
more frequently occurring liquids and solids. 
~ 2. Hydraulics.
I. MOTION OF LIQUIDS.
213. Definition.-Hydratlics (from the Greek Ortwp, water, and
auvAo, a pipe), is that part of hydro-dynamics which treats of the flow
and elevation of liquids, especially water, and the construction of all
kinds of instruments and machines for moving them, or to be moved by
them. Hero of Alexandria (about 130 B. c.) appears to have been
the earliest author on this subject.
214. Pressure of liquids upon the containing vessel.-A vessel
filled with water, or any other liquid, and closed, is subject to two pressures acting in opposite directions: namely, 1. The atmospheric pressure, acting from without inwards; and 2. The pressure of the column
of contained liquid acting against the walls. If a vessel so situated is
pierced, and the pressure from within outwards is stronger than the
external pressure, the liquid will flow out; but if the external prwesurs
is the stronger, the liquid will not escape.




17 4             THE THREE STATES OF MATTER.
This statement may be illustrated by filling a glass vessel, as a wine-glass,
with water, placing a piece of paper over its top, and supporting the paper with
the hand, at the same time inverting the glass; then removing the hand from
the paper and holding the glass inverted, the fluid will not escape, the external
(atmospheric) pressure against the paper being greater than the weight of the
column of water pressing downwards.
The mass of liquid escaping fiom an orifice in a vessel, is called a
vein.
215. Appearance of the surface during a dis-              169
charge.-The surface of a liquid, discharging itself
from an orifice in a containing vessel, does not usually
remain horizontal.
When the vein issues from an opening in the bottom
of the vessel, and the level of the liquid is near the orifice, a funnel-shaped depression is found in the liquid,
fig. 169. If the liquid has a rotatory movement, the 
funnel is formed sooner than if it is at rest. If the
orifice is at the side of the vessel, there is a depression  170
of the surface upon that side, above the orifice, fig.
173.  These movements depend upon the form of the
vessel, the height of the liquid in it, and the dimensions
and form of the orifice.
216. Theoretical and actual flow.-The actual 
flow from  an orifice, is the volume of liquid which
escapes from  it in a given time.  The theoretical flow is a volume
equal to that of a cylinder which has for its base the orifice, and for its
height the velocity, furnished by the theorem of Torricelli. That is,
the theoretical flow is the product of the area of the orifice multiplied
by the theoretical velocity.
It is, however, observed that the vein escaping from an orifice, contracts quite rapidly, so that its diameter is soon only about two-thirds
of the diameter of the orifice. If there was no contraction of the vein
after leaving the orifice, and its velocity was the theoretical velocity,
the actual flow would be the same as that indicated by theory. But the
section of the vein is soon much less than at the orifice, and its velocity
is not so great as the theoretical velocity, so that the actual is much
less than the theoretical flow; and, in order to reduce this to the first,
it is necessary to multiply it by a fraction which is named "the co-efficient of contraction."
From Comparative experiments, made by a great number of observers,
the actual flow has been determined to be only about two-thirds of the
theoretical flow.




OF FLUIDS.                             175
Practically, the flow, F, in a unit of time, is calculated by the formula F 
m v s, where m is a constant, representing the ratio between the actual and theoretical velocity or flow; in other words, between the area of the orifice and the
area of the section of greatest contraction in the vein. This coefficient of contraction, in = 0'62; and thus the above formula becomes
F = 062. R8/2gH = 2-75f8v/H.
- the sectional area of the orifice.
The contraction of the vein is most noticeable in downward flowing
jets.  If the jet is thrown upwards, at an angle               171
of 25~ to 45~, the vein preserves its own diameter;  _
but if it surpasses 45~, its section increases.
By suspending solid particles in the water, the cur-;:
rents that are formed by an escaping vein are made 
visible. The solid particles direct themselves, in curved    _-.._ _ __
lines, towards and into the orifice, as a centre of attraction, fig. 171. The particles in immediate contact with -___~~
the orifice, owing to friction, not moving so easily as
those near the axis, contraction must result; we can see
also, that gravity, by accelerating the velocity, must cause continual decrease
in the section of the jet.
217. Reaction of the escaping vein.-Barker's mill.-When a
jet of liquid escapes from an orifice in a containing vessel, the pressure
of the liquid upon the walls at the point of                172
escape finding no counteracting force, the 
horizontal component of the column is not destroyed as when the opening is closed; and this
force reacts to thrust the vessel in a direction     -
opposite to that of the escaping vein. 
This reaction is made sensible by suspend-  
ing the containing vessel on a free vertical                           A
axis, as in the apparatus known as Barker's
Mill, fig. 172. The orifices of escape for the vein 
are here in the ends of a horizontal pipe bent
at right angles, and in opposite directions,
formed as seen  at AB, where  the arrow
shows the point of reaction of the escaping
vein upon the end-wall of the tube.
It might be supposed, as was assumed by Newton, that the moving
force in this case was only the horizontal component of a force equal
to a column of liquid whose base was equal to the area of the orifice,
and whose height was the distance of its centre of gravity from the




176             THE THREE STATES OF MATTER.
level. But the effects from pressure are not the same for a liquid in
motion as when in equilibrium; and D. Bernoulli has demonstratedThat it is, in this case, requisite to estimate the force of reaction as
double the height of the liquid above the centre of gravity of the orifice.
This principle is applied in the construction of reaction waterwheels.
218. Flow.-The volume of liquid escaping in a given time from an
orifice is called itsflow. This depends on the size of the opening and
the velocity of the jet.  Assuming the motion of the jet to be uniform
for a given time, say one second, the distance passed over by an escaping molecule in this time is called its velocity. The velocity depends
chiefly on the height of the liquid above the centre of gravity of the
orifice; this height is called the head or column.
The velocity of flow is modified among other causes also by the friction of the
liquid, both at the opening and against the walls. When the aperture is made
in a very thin wall of a large vessel, so as to reduce as much as possible the
causes tending to modify the motion of the oscaping fluid, the laws of the escape
are comprised in the following theorem, announced by Torricelli, in 1643, as a
consequence of the law of falling bodies discovered by Galileo.
219. Theorem  of Torricelli.-Liquid molecules, flowing from an
orifice, have the same velocity as if they fell freely in vacuo,from a height
equal to the vertical distance from the surface of the liquid to the centre
of gravity of the orifice.
If Hrepresents the height of the head above the centre of gravity
of the orifice, then the velocity is expressed by the formula
v= 1/2v.
Deductions from  the Torricellian Theorem. —1. The velocity
depends on the depth of the orifice from the surface, and is independent
of the density of the liquid.
Water and mercury in vacuo would fall from the same height in the
same time; and so escaping from an orifice at the same depth, below
the surface, would pass out with equal velocity; but mercury being 13*5
times as heavy as water, the pressure exerted at the aperture of a vessel
filled with mercury, will be 13'5 times as great as the pressure exerted
at the aperture of a vessel filled with water.
2. The velocity offlow of liquids from an orifice is as the square roots
of the head.
Thus, stating the velocity of a liquid escaping from an orifice one foot
below the surface, to be one; from a similar orifice, four feet below the
surface, it will be two; and at nine feet, three; at sixteen feet,four; and
so on.




OF FLUIDS.                             177
Let H represent the height of the liquid above the orifice, g the accelerating
force of gravityLnd v the velocity of discharge; we shall have v = 1/2gH.
220. Demonstration of the theorem of Torricelli.-The theorem
of Torricelli may be demonstrated by means of the apparatus shown
at fig. 173.
A cylindrical vase, a c, enlarged into a reservoir at the top, is filled with water.
In the side of the vase are orifices, k, I, n, n, o, so situated that m is at the
centre of a c, and k and o are equidistant             173
from m, as are also I and n. Let x represent the horizontal range of a spouting I        c.!!!
jet, and y the height of the orifice above           -
the horizontal line a b, let H  be the
height of the water above the orifice,       II
and a the angle of elevation of the direc-;
tion of the jet as it issues from the orifice:  l
then by the laws of falling bodies (71),
combined with the laws of projectiles         n  
(103) we shall have                          Bll
x - vt cos. a, and y -- gt2_vt sin. a.
Eliminating t from  these equations, we           l 
obtain                                       m3l 
(1.)   y =  2v2 co.2 a-x tang. a.
2v2 cos.2 a
When the water issues horizontally from
the orifice, a becomes zero andy -=        x 2  Z- v            and
(2.)        v=x  l_
\ 2y
The values of x and y being determined by observation in any case, the value
of v, or the velocity with which the jet issues from the orifice, is readily calculated by formula (2). This velocity is found to accord very nearly with the
velocity which a body would acquire in falling freely from a height equal to the
head of the fluid above the orifice.
Bossuet found by using mercury that the variation from this value of v was
less than one hundredth part of the velocity.
There is a remarkable consequence of this law which may easily be
verified by experiment. In the formula for the value of x replacing v
by its value  /2gH   we have x2 = 4Hy.
(a). The value of x is the greatest possible when H= y = Jac, as is
shown in the figure, where the jet issuing from the centre of the cylinder
has a greater range than any jet either above or below the centre.
(b). Since y = ac - H, the values of y and H may be interchanged
without altering the value of x; that is, twojets issuing from orifices at
equal distances above and below m meet the horizontal line ab at the
18




178             THE THREE STATES OF MATTER.
same point as is shown in the figure where the jets issuing from k and
o have the same range, and also the jets I and n.
The value of x and y being determined by observation, the value of v, or the
velocity of the jet, becomes known by the formula (2).
221. The inch of water named by hydraulic engineers as the unit
of measurement in the scale of water, is the volume of water which
escapes in a given time, say one minute, through an orifice of one inch
diameter whose centre is one and one-twelfth inches below a constant
surface.
PRONY has harmonized this unit with the French metrical system by employing a pipe of two centimetres internal diameter and 17 millimetres long, under a
head of two centimetres. He preserves the term inch of water, restricting it to
the quantity of water escaping in one minute from such an opening, equal to
13-333 litres, or 11 766 quarts. In 24 hours this orifice will furnish 20 cubic
metres, equal to 4,402 gallons English measure.
222. Constitution of liquid veins.-The form  and constitution
of liquid veins have been studied by a great number of experimenters.
The results of F. Savart, and more lately of G. Magnus (Poggendorff
Annalen, cvi., p. 1), are those here given.
It is determined, 1. That if a liquid vein issues quite calmly and
vertically downwards, from a circular orifice in a plane and thin horizontal wall, no movement of rotation existing in the mass of the liquid,
such a stream forms a continuous perfectly smooth cylindrical mass,
the diameter of which diminishes with the distance from the orifice to
the point where disintegration commences. From this point the vein
assumes a turbid appearance, enlarges in diameter, and commences to
spirt off small drops laterally.
2. If the mass of liquid is in rotation in the vase, or any cause of
vibration exists, as from the sounding of a musical note, then the vein
is separated into two distinct parts, fig. 174. The portion nearest the
orifice is calm and transparent, like a rod of glass, gradually decreasing
in diameter. The second, on the contrary, is constantly agitated, and
takes an irregular form, in which are distributed, at regular distances,
elongated  swellings, called "ventral segments," whose maximum
diameter is greater than that of the orifice: while the position of the
first swelling is always much nearer the orifice than the point where
the jet without swellings commences to become turbid.
Magnus found that the best means to produce these "ventral segments" were
a large tuning fork sounding C below the line-and the monotonous hum of the
magnetic hammer or break-piece used in electro-magnetic apparatus.
3. The swellings consist of separate isolated masses of water, as
shown in fig. 175. However regular their external form may be, they
are still formed of separate masses, as may be readily distinguished by




OF FLUIDS.                         179
holding a piece of wire in the hand so that one of its ends penetrates
a little way into the jet. A uniform pressure is felt when the wire
is struck by the smooth part of the stream, but       174       175
when struck by a swelling a strong vibratory and
intermitting motion is felt. The separate masses
of water forming the swelling, clearly communicate this motion to the air, and thus disturb the
flame of a gas jet brought near them, which the
smooth part of the stream does not do.
Savart found that the swellings are formed of
disseminated globules, elongated in the transverse
direction of the vein, and that the contractions or
knots are formed of globules, elongated in the
longitudinal way, fig. 175: also that the limpid
part of the vein is formed of annular swellings
which originate very near the orifice, propagating
themselves at unequal intervals to the troubled
part, where they separate, of the same form at the
instant of their separation, but changing periodically.
4. The "ventral segments" are produced by
the vibration of the orifice through which the
water flows, and they change with the strength
of the note producing the vibration, as well as
with the diameter of the orifice.
The vein itself occasions a tone, partly because its single separate masses of water set the
adjacent air in motion, but especially by the
impact of these masses upon some sonorous or elastic substance. Where
the orifice is made of caoutchouc, and this is carefully insulated by woolen
pads from the bottom of the vase, not even the loud tone of a heavy
tuning fork on a sounding box (377) sufficed in Magnus's experiments to
cause the production of ventral segments. Without such precautions
they are often, set up spontaneously by vibrations communicated from
the falling stream through the solid parts of the apparatus.
To observe the constitution of the swellings, Magnus used a revolving card
perforated by a narrow radial slit, like the toy known as the anorthoscope,
illuminating the stream by a lamp, but the details of his results exceed our space.
5. If the vein flows from a very small orifice (less than a millimetre),
the small drops into.which the stream breaks up move quite irregularly.
But on sounding a note the drops arrange themselves in groups with
great regularity-a certain number always follow each other imme



180              THE THREE STATES OF MATTER.
diately-a somewhat greater interval succeeds, and then the former
grouping of drops occurs again.
So in a stronger stream, under the power of a harmonious note, the swellings
and knots assume more regularity, and usurp the transparent part, which almost
entirely disappears-the flow of the liquid from the orifice remaining the same
as at first.
6. The constitution of veins thrown out in any direction is essentially
the same; but the number of pulsations is diminished in proportion as
the-vein is projected more vertically upwards.
223. Escape of liquids through short tubes.-Short tubes (called
adjutages) are often placed in an orifice to increase the flow. They are
either cylindrical or conical. If the vein pass through the tube without
adhering to it, the flow is not modified; if the vein adhere (the liquid
wetting the interior walls), the contracted part is dilated, and the flow
increased. In the last case, and with a cylindrical adjutage, its length
not being more than four times its diameter, the flow is augmented
about one-third.
Conical adjutages converging towards the exterior of the reservoir,
increase the flow still more than the preceding, the flow and velocity of
the vein varying with the angle of convergence. Conical adjutages
diverging towards the exterior, give the greatest flow. They may give
a flow 2-4 times as great as that which an orifice of the same diameter
in a thin wall furnishes, and 1'46 times greater than the theoretical
flow.
Practically, the flow during a second from cylindrical adjutages of a length
three and a quarter times the diameter, is found by the formula,
F = 0-82 s/2gH = 3-62 sl/H; s being the area of the tube and H the head.
224. Escape of liquids through long tubes.-When a liquid
passes through a long straight tube, the velocity of the flow soon diminishes greatly owing to the friction between the liquid particles and
the walls. Bends or curves in the tube increase the loss in velocity, for
the same reason. The discharge thus becomes very much less than it
would be fiom an orifice in a thin wall, and to obviate this evil the tube
is generally inclined; the liquid then passes down an inclined plane, or
it is forced through by pressure, applied at the opposite end.
Formula.-The discharge, D, per second through straight tubes of uniform
diameter entirely open at the end may be determined by the formula,
D    20-8/ Hd!5
I +  54d
in which H is the height of the water above the orifice of discharge, d the




FLUIDS.                             181
diameter, and I the length, of the tube. All these quantities are to be taken in
metres. The formula gives the value of D in cubic metres, which may be reduced
to " inches of water" (221) by multiplying the result by 75. This formula was
deduced from the experiments of Eytelwein. When the tube is very long, we
may neglect 54d as very small in comparison with 1, and the formula to determine the diameter required to discharge a given volume of liquid is,
d = 0'298 _
H
The velocity of the discharge is given by the formula,
4D
v  -- 2264 4
n(            I -+- 54d
For long tubes the term 54d may be neglected, and modifying the coefficient
to correspond with the results obtained by Prony with tubes 2280 metres long.
v = 26-79    d.
225. Jets of water.-As the velocity of a liquid escaping from an
orifice is the same as that which a body acquires falling from a height
equal to the distance from the surface of the liquid to the orifice, a jet
of water spouting upwards, should rise to                176
the level of the liquid in the reservoir. But   _.~ 
this never quite takes place, fig. 176, be- 
cause of-1st, the friction in the conducting  
tubes destroying the velocity-2d, the resistance of the air-3d, the returning water
falling upon that which is rising.  The
height of the jet is increased by having the
orifices very small, in comparison with the
conducting tube; piercing them  in a very
thin wall, and inclining the jet a little, thus
avoiding the effect of the returning water.
It has been determined that the differences between the height of vertical jets
and that of the reservoirs are approximately as the squares of the height of the
jets. Experiment has assigned the number 0-01 as the coefficient, and the formula which gives the height, h, of a jet under a head represented by H, is
H -   -= O —Olh1:-the unit of measure being the French metre.
If air is mingled in the water, the mixture being lighter than water, the jet
can be made to rise higher than its source.
226. Pressure exerted by liquids in motion.-When a liquid is
in motion, either in a conduit tube or an adjutage, the pressure it exerts
18*




182             THE THREE STATES OF MATTER.
on the walls is not the same as it is in equilibrium, and generally it is
less, as the velocity of flow is greater.
If the effective velocity is                177
equal to theory, the interior
pressure upon the walls of
the adjutage will be equal to                  l  
the statical pressure in  a
state of equilibrium. As the
effective velocity  increases,                                 a \
the interior pressure upon                    w r aM'n i t\
the walls of the  adjutage                         c ia  t
becomes less than the pressure in a state of equilibrium, and it may even become less than the
external atmospheric pressure, but it can never become null.
This principle may be demonstrated by the apparatus shown in fig.
177, where a bent tube, m n, is inserted into a cylindrical adjutage, and
when the lower end is placed in a vessel of water, as shown in the
figure, the fluid will mount up in the tube to a certain point n.
If the tube m n is not too long, the water will mount up and enter
the adjutage, and flow out with the jet. But the fact that the water
will not mount over in the tube m n, unless it is very short, proves that
the external atmospheric pressure is always opposed by a certain
amount of internal pressure. It may also be shown that the interior
pressure never becomes null, but that there is merely a diminution of
pressure, by placing the apparatus in a vacuum, when the water will
flow out in the direction mn n.
227. Velocity of rivers and streams.-The velocity of streams
varies very much. The slower class of rivers have a velocity of less
than three feet per second, and the more rapid as much as six feet per
second, whicl gives respectively about two and four miles per hour.
The velocities vary in different parts          178
of the same transverse section of a
stream, for the air upon the surface of                        a
the water, as well also as the solid bottom
of the stream, has a certain effect in retarding the current. The velocity is
found to be greatest in the middle, where the water.is deepest, fig. 178, somewhere in m, below the surface; then it dpcreases with the depth, towards the
sides, being least at a and b.
Stream measurers.-To measure the velocity of streams, various
means are employed. The most simple is a glass bottle filled with
water, sunk just below the level of the current, and provided at the
cork with a small flag, that stands above the surface.




OF FLUIDS.                            183
A wheel may also be used, furnished with float-boards, placed in the stream
and immersed, so that the whole surface of the boards is covered with water.
The friction in this case is very small, so that the wheel revolves with very
nearly the velocity of the stream. By observing the number of revolutions of
the wheel in a given time, the rapidity of the current is measured.
To ascertain the velocity at different depths, the simplest instrument is Pictot's
tube. It consists of a tube bent nearly at right angles, terminated by a funnelshaped mouth: the upper part of the tube, above water, is of glass. To observe
with this instrument, it is sunk with its funnel up stream at the depth where its
velocity is required. If the water was still, the height of the column within and
without the tube would be equal; but as it is in motion, the water will rise in the
tube to counterbalance the force with which the water is impelled (the impulse
of the stream), the column of water in the tube rising higher as the velocity of
the stream is greater.
II. WATER-POWER AND WATER-WHEELS.
228. Water-wheels.-The motive power of water is of extensive
practical importance, from  the number of machines driven by waterwheels.
229. The overshot wheel.-Fig. 179 is used when the supply of
water is moderate and variable. The water is delivered at the top of
the wheel, which may move with  the                     179
hands of a watch, as in the figure, or the
reverse.  It is furnished with buckets of
such a shape as to retain as much of the
water as possible, until they reach the 
lowest practicable point on the wheel, and
none after that point. In this wheel the
effect is produced both by impact, and by
the weight of the water.  The water is
received as near the summit as possible, and the buckets are so shaped
as to retain the water to the lowest practicable point in its descent,
corresponding to about five on the                   180
face of the watch.
230. The undershot wheel.Fig. 180 receives its impulse at the
bottom; it is furnished with floatboards instead of buckets.  If they 
are placed at right angles to the rim^ -
of the wheel, they may turn either 
way. When the wheel is required
to turn only in one direction, the
float-boards are placed as in the  -
figure, so as to represent an acute angle towards the current: the water
acts then partly by its weight.




184             THE THREE STATES OF MATTER.
The breast-wheel.-Fig. 181 is moved both by the weight and
momentum  of the water.  It is furnished with buckets, formed to
retain the water as long as possible. The breast-wheel is the form
most generally adopted, as it allows of a larger diameter for a given
fall than the overshot-wheel, with more economy of power than the
undershot-wheel.
A more distinct idea of these different           181
water-wheels may, perhaps, be gained
by illustration from the face of a watch. 
In the breast-wheel, the water may be           k    // 
received (according to the desired mo- -~ -- //-~- -
tion of the wheel) between eight and                         _I
eleven o'clock, or between one and four
o'clock. According as the water is received above half-past nine or below
half-past three on the watch, the wheel
is called a high or low breast-wheel.
231. Boyden's American Turbine.-The turbine is a horizontal
water-wheel, revolving entirely submerged, and is, of all forms of
water-wheel, the most energetic and economical of power.  This
machine was first constructed in an efficient form by M. Fourneyron in
1827 as the result of experiments commenced in 1823; but the honor
of perfecting the turbine and establishing the mathematical principles
by which it may be adapted to every variety of water-power, whether
with high or low fall of water, in both small and large streams, is due
to U. A. Boyden, Esq., of Massachusetts, under whose direction turbines have been extensively introduced in the cotton manufactories of
Lowell and elsewhere.  Two of the turbines constructed under the
superintendence of Mr. Boyden have been found to give a useful effect
to eighty-eight per cent. of the power of the water employed.
The water enters the centre of the wheel, descending in its vertical
axis, and is delivered through a great number of curved guides so
arranged that the water enters the buckets in directions nearly tangent
to the circumference of the wheel. The water is received by the curved
buckets in the direction of greatest efficiency, and having expended its
force, it escapes from the wheel in a direction corresponding very nearly
with the radii.
The upper part of fig. 182 shows a horizontal section of the turbine, and a
perpendicular section is shown in the lower part of the same figure. Fig. 183
shows a section of the turbine with the iron sluice and other attachments as
they stand in the wheql-pit. The letters refer to the same parts in both figures.
K K is a stationary disc of cast iron supported by the disc tube M M made fast
to the upper curb at P. The curved guides, gggg, made of plate iron, are




OF FLUIDS.                              185
secured to the disc K, and to the rim L L above, in such a manner as to give
the least possible obstruction to the water as it flows through the guides into
the revolving wheel. The arrrows show the course of the water through the
iron sluice E, and on the disc through the guides into the wheel. The wheel
itself consists of a central plate of cast iron, and of two crowns cc cc, of the
same material, between which are the curved buckets b b b b. The lower crown
is firmly secured to the central plate. The buckets are let into curved grooves
in the crowns, and have tenons, passing through mortices in the crowns, riveted
above and below.
182
The vertical shaft, dd, is made of cast iron, and is accurately turned in every
part. The entire weight of the wheel is supported by a series of collars attached
to the shaft and moving in the suspension box e. The box e is hung upon gimbals at h (like a mariner's compass), supported by framework resting in the
masonry of the wheel-pit. The lower end of the shaft is steadied by a pin passing into the step i, which is adjusted by a screw. RR is a cylindrical gate which
drops down between the guides and the movable part of the wheel, to regulate
the flow of water according to the amount of power required. Attached to the
gate are the brackets SS, connected with the rackwork and endless screw shown
at W, by which the gate is raised or lowered. A self-regulating adjustment of
the gate is secured by a governor not shown in the figure. Ordinary gearing,




186               THE THREE STATES OF MATTER.
183... ~..IIII5
m_!__      _1__1 --                       aH~~~~~~~e
M ~~~~~: —i —-.`And ——:
r~~~~~~~~~~MK____________                ~~~~~___
ffi    _                                 I~~~~~~~~______________  __________  Isi D__ =____
K....   _ _    _ _   _   _   __             _   _     _.;                                                   ~~~~~~~~~.




OF FLUIDS.                          187
attached to the upper part of the shaft, communicates the power of the wheel to
the machinery to be driven. The curved iron sluice E rests upon beams V',
secured in the masonry of the wheel-pit and by stancheons NV.
Turbines may be divided into high and low pressure machines. High
pressure turbines are adapted to hilly countries and deep mines where
high falls of water may be commanded; in these cases the height of
the column of water will compensate for the smallness of its volume,
reservoirs being provided to keep up a constant supply.
The low pressure turbines produce great effect with a head of water
of only nine inches, and are suitable for situations in which a large
volume of water flows with a small fall.
The results of an investigation by Arago, Prony, and others, who were
appointed by the French Academy of Sciences to report upon turbines,
are as follows:
(1). That these wheels are applicable equally to great and small falls
of water.
(2). That they transmit a useful effect equal to from 70 to 78 per
cent. of the total moving force of the water employed (88 per cent. has
been secured by Boyden's wheel).
(3). That they will work at very different velocities above or below
that corresponding to the maximum  effect, without the useful effect
varying materially from that maximum.
(4). That they will work from one to two yards deep under water,
without the proportion which the useful effect bears to the total force
being sensibly diminished.
(5). In consequence of the last-mentioned property, they utilize at all
times the greatest possible proportion of power, as they may be placed
below the lowest levels to which the water surface sinks.
The mathematical formulae for adapting turbines to every variety of water.
power, and much other valuable information, will be found in a treatise on the
Hydraulic Experiments at Lowell, by Mr. J. B. Francis, from whose work the
above condensed description has been principally obtained.
*MOLECULAR FORCES ACTING BETWEEN PARTICLES OF UNLIKE
KINDS.
I. CAPILLARITY.
232. Observation.-Definition.-The complete discussion of the
action of Molecular Forces between particles of unlike kinds belongs
appropriately to Chemical Physics. We have already noticed some of
the phenomena of adhesion properly referable to this section (147
and following). It now remains to consider briefly those special cases
of this general subject which affect the laws of fluid equilibrium. We
refer especially to the Phenomena of Capillarity and Endosmose.




188             THE THREE STATES OF MATTER.
The laws of fluid equilibrium  which we have already considered
apply only to vessels of considerable diameter, in which the effects of
adhesion between liquids and solids (148) may be safely neglected.
In very narrow vessels, and particularly in tubes of small bore, the
effects of this kind of molecular attraction become very sensible. Such
tubes are called capillary tubes, from capillus a hair, in allusion to the
hair-like fineness of their bore. The effects of such tubes on liquids
are distinguished by the general term capillarity.
233. General facts in capillarity.-If tubes of small bore, open
at both ends, are placed vertically in water, the liquid is seen to mount
both in the tubes and on the outside, fig. 184, rising higher within as
the tubes are smaller. If the bore is over half an inch in diameter,
this effect is not very sensible.  The experiment becomes more satisfactory if made in communicating vessels (202), of which one branch
is much narrower than the other, as in fig. 185. Two slips of glass
plunged in water, and brought near each other, also exhibit the effect
of capillarity. In narrow communicating vessels, then, the laws of
equality of level do not hold good.
If the experiment is tried with mercury (which does not wet the
glass) there is a depression of the surface of the liquid both within
and without the tube, fig. 186, and this becomes greater as the tubes
are smaller, as seen in the two branches of the communicating vessels,
fig. 187. In a greased tube water is similarly depressed.
185               184              186             187
These phenomena are independent of atmospheric pressure-taking
place equally in a vacuum  or in compressed air.  They are also independent of the thickness of the walls of the tube (148), but they vary
with the material of the tube, and with the nature of the liquid.
Thus, in tubes of the same internal diameter, placed in liquids
capable of wetting the surface of the glass, the elevation is different for
each liquid. In tubes of 0-0472 inch diameter of bore, water rises 0'905




OF FLUIDS                              189
inches (or about 4 inches in tubes of T- inch bore), essence of turpentine 0'385, pure alcohol 0'278, whale oil about the same, while ether
rises still less. In some liquids the elevation is scarcely sensible, while,
as we have seen in mercury and other liquids not wetting the surface
of the tube, there is a depression.
Form  of the surface.-These changes of level are accompanied by
a change of form  in the surface of the liquid in the capillary column.
It is concave if there is elevation-plane if there is no change of level,
and convex if there is depression. The first case is called the concave
meniscus, and the last the convex  meniscus.
The cause of these phenomena is to be sought in the mutual action
of molecular forces (146) and of gravity.
A needle covered with grease, gently placed upon the water, floats, because,
not being moistened by the liquid, there is produced a depression in which it is
supported. Thus, many insects walk and skim on the surface of water without
plunging in. Oil and other burning-fluids in lamps, and the melted tallow and
wax of candles, are supplied to their flames by means of the capillarity of their
wicks; so there is an absorption of liquids in wood, in sponge, in cloth, and in
all bodies that possess sensible pores.
234. Cause of the curve of liquid surfaces by the contact
of solids.-The form  of the surface of a liquid in contact with a
solid, depends upon the relation which exists between the attraction of
the solid for the liquid, and the liquid particles for each other.
Let A B, fig. 188, represent a fluid surface, and D E the surface of a solid
immersed vertically in the fluid. Any liquid particle, as A, is submitted to the
action of three forces, viz.: 1st. Gravity, which, as it      188
acts equally upon all the particles of the fluid, may be
omitted from the present discussion. 2d. The cohesive         m
attraction of the fluid acting through the quadrant
B A E, and having its resultant in A P. 3d. The adhe-            
A         C
sive attraction of the solid for the particle A. This         / 
latter force may be considered as divided into two
parts; the attraction of that part of the solid above          o
the surface of the fluid, whose resultant will be A Q;
and the attraction of that part of the solid below the /
surface of the fluid, which will have a resultant in A Q'. Let B P E be drawn at
the limit of sensible cohesive attraction of the fluid for the particle A, and let
A P, or P, represent the intensity of the resultant of all the cohesive attraction
of the liquid for the particle A; also let  1 n o have the same relation to the
adhesive attraction of the solid, and Q and Q' will represent the intensity of this
force above and below the surface of the liquid.
Completing the parallelogram A Q C Q', A C =  2 Q cos. 45~ will represent the
resultant of all the attraction of the solid for the particle A. On A C and A P,
construct the parallelogram  A P R C, and A R will be the resultant of A P
and AC.
19




190               PHYSICS OF SOLIDS AND  FLUIDS.
The direction of the resultant A R will be determined by the value of
2 Q cos. 450 - P cos. 45~, or 2 Q - P. There will evidently be three cases:
2Q-P > 0, 2Q-P-  0, and 2Q-P < 0.
In the first case the resultant will lie in the angle C A E, and the fluid will
wet the solid. In the second case the resultant will lie in A E, in the plane
wl.ich separates the solid and the fluid. In the third case the resultant will lie
in the angle B A E, and the fluid will not wet the solid. In this case there is
no necessity to suppose any repulsion between the solid and the fluid, but only
that the cohesive attraction of the fluid is more than twice as great as the attraction of the solid for the fluid.
As the surface of a liquid is always perpendicular to the direction of the forces
which solicit its molecules (199) in the first case, the surface of the fluid at A
will be tangent to the plane M N, fig. 189, which is perpendicular to the general
resultant A R. At A', where the attraction is more feeble, the resultant A' R'
will be more nearly perpendicular, and at a point A", where the sensible attraction is zero, the resultant A" R" will be vertical, and the curve A A' A" will
become tangent to a horizontal plane.
1S9                                 190
B  ~              i,f
11~~ Ac
In the case of a small tube, T, the concave surface of the fluid will be sensibly spherical. When 2 Q - P    0, the resultant A R lies in the line A E, and
the surface of the liquid in contact with the solid is horizontal, because the
attractive force of the solid and fluid combined is the same as if the surface of
the fluid was indefinitely extended.
When 2 Q - P is less than zero, or negative, the resultant A R will be found
in the angle B A E, and the surface will be tangent to the plane M N at the
point A; it will therefore be convex, as shown at A A", fig. 190. In a capillary
tube, U, the surface will be convex and sensibly spherical.
235. Experimental illustrations.-Capillary phenomena are easily
explained, when we know that under the double influence of the attraction of a solid and a liquid, the surface of the liquid may be either
concave, plane, or convex, as the relative intensities of these forces
vary; we can also see that the ascent or depression of the liquid in
capillary tubes is a direct consequence of the terminal form  of the
liquid. This explanation is easily verified by experiment.
a. Take a bent tube, similar to fig. 185, but let the capillary branch be
shorter than the other, and pour water, drop by drop, into the larger brancl,
the liquid, as it rises to the top of the tube, in the short capillary branch will




OF FLUIDS.                             191
present successively a concave, then a plane, and at last a convex surface. As
the water stands in a convex form above the end of the tube, the concave surface in the larger branch will rise above it, showing that the rise of the liquid
above the level due to hydrostatic pressure depends upon the form of the surface.
b. Let a capillary tube, with a small sphere blown in it, as shown in fig. 191,
be soldered into the bottom of a small glass vessel or tube, into which mercury
is slowly dropped. As the mercury rises into the sphere,      191
it will take, at A, the form of a very convex button. As
it rises to B B and C C, the convexity of the surface will
gradually diminish, although it will make a constant
angle (about 45~) with the walls of the glass sphere, as
shown by the dotted lines. When it arrives at D D,  Dn 
where the surface of the sphere is inclined 45~, the
surface of the mercury will be horizontal, and still 
higher it will be concave. These successive stages of C
curvature are seen in filling a mercurial thermometer.
This experiment, depending upon the constant angle      -
made by the surface of the mercury with the walls of the
tube, enables us to show that the level of the mercury in
the capillary tube is higher or lower than in the vessel
with which it communicates, according as the surface is
concave or convex.
The level at which a liquid may be maintailed in a capillary tube
depends on the diameter of the canal at the upper level of the liquid.
c. An impressive verification of this fact is obtained by soldering a capillary
tube to the top of a glass vase or low air-bell, like a cupping-glass or beaker.
If the diameter of the capillary tube is not more than the one-hundredth of an
inch, a column of water of the diameter of the vase will be sustained by the
capillary force at the height of nearly four inches-the height of the column
requisite to restore equilibrium being independent of the diameter of the vase.
The same apparatus being reversed and plunged in a bath of mercury will
evince a corresponding depression of the level of the mercury in the capillary
tube, the vase remaining void of mercury.
It is evident from  these experiments that capillarity  is a very
energetic force, and when we remember that the capillary cana'3 in
vegetables are usually smaller than the one-hundredth of an inch, and
those in the animal body are very much smaller, it is easy to understand the ascensional force of sap in plants, and the functions of the
capillaries in animals.
d. By this power it is that the soil in dry seasons receives moisture from below
to supply the waste of evaporation,-and conversely that the benefits of rain
descend to the lower strata. Hence in dry climates the surface soil is covered
with saline effloresenccs left by the evaporation of water holding salts in solution.
e. Rocks are split by the swelling of wooden plugs driven forcibly in the
dry state into holes drilled for the purpose, and afterwards wet with water.
236. Influence of the curve on capillary phenomena.-The
ascent or depression of liquids in capillary spaces, is owing to the




192             THE THREE STATES OF MATTER.
form  of the surfaces.  Let a b c d, fig. 192, represent a concave
meniscus, the particles of which are sustained in equilibrium by tho
forces before mentioned; these particles do not exercise any pressure
on those below them, and therefore at cb there is a line above which
the particles of fluid are sustained by upward attraction, and below
which it is sustained by equal external pressure of the column op.
192                          193
The s —-— en - --   o                 u                  
The sensible attraction of the walls of the tube does not extend so
far as the perpendicular height, d c, of the curve. It is only a small
portion of the wall of the tube just above the extremity, d, of the curve
that supports the fluid. The action of every part below d, while it
tends to elevate the fluid below, also tends to depress the portion of
fluid above it, and these two influences neutralize each other. The
particles of fluid about d, and within the limit of sensible attraction,
are drawn upward by the attraction of the tube, and these particles,
by their cohesive attraction, support those below, until the weight of
the capillary column becomes equal to the adhesive attraction of the
solid for the particles within the limit of attraction about the point d.
In determining the height of liquids in capillary tubes, the height of
the column supported by capillary attraction must be added to the
elevation produced by external pressure.
When, as in fig. 193, the meniscus is convex, the equilibrium  still
exists, for the liquid molecules being attracted obliquely inwards and
downwards, the downward pressure is greater than on the exterior of
the tube, and therefore the surface of the liquid within the tube
descends until the pressure on the base, m n, is the same as on any
exterior point, g, of the same layer.
237. Law of the elevation and depression of liquids in capil.
lary tubes.-It has been demonstrated by Laplace, that the attraction
of the meniscus is equal to a constant coefficient, depending on the
nature of the liquid and that of the tube. In a cylindrical tube with
a circular base, experience has demonstrated, that the concave surface
is sensibly a hemisphere, with a radius equal to half the diameter of
the tube. The attraction of the meniscus is, therefore, in inverse ratio




OF FLUIDS.                             193
with the radius, or the diameter of the tube, and in consequence, the
liquid column will be raised by this force to a height which varies
according to its intensity. The length of the liquid column contained
in the tube is a little less than calculation would indicate, according
to the above rule, because of the weight of the meniscus, but this error
is very small, less as the capillarity of the tube is less, the influence
of the weight of the meniscus decreasing rapidly as the diameter of the
bore diminishes. The height of the liquid in the tube is, therefore,
never absolutely in inverse ratio to the diameter, but the law is nearly
exact when we add to the height one-sixth of the diameter of the tube,
which is the correction required for the weight of the meniscus.
Corrections for this error being thus made, the law would be correct,
had the meniscus an accurately spherical surface, but this obtains
only when  the diameter is very small (2 or 3 m. m.,'07874, or
*11811 inches) the surface in general ceases to be truly spherical, and
the ascent or depression depends on the curve of the surface, which
varies much more rapidly than the diameter of the tube.
238. Depression of mercury in capillary tubes.-The rapidity
with which capillarity diminishes, in tubes of great diameter, is seen in
the following table:TABLE OF DEPRESSIONS OF MERCURY IN CAPILLARY TUBES.
Depressions in               
Diameter of   m. m. according   According to    According to   According to
tube.       to Laplace.     Young.         Jacoby.     Cavendish.
20- m. m.       0038           0'031          0-031
15-  "          0-137    j    0-111           0-118    1   0-131
10   "          0-445          0402           0-406         0 406
8-  "          0'712    i    0669           0-673         0820
6-  "          1-171     1    1-139         1-134         1-377
5'  "          1-534          1-510          1-513        1-735 
4.  "          2-068          2-063         2-066         2-187
3.  "          2-918          2-986         2-988         3-054
2-5  "         3-566
2-  "          4-454          4-887         4-888         4-472
The numbers contained in the first column have been calculated by
M. Bouvard, according to the formula of Laplace; those of the last
two columns have been obtained directly by experiment.
239. Ascent of liquids in capillary tubes.-For all liquids, the
ascent or depression in capillary tubes, decreases according to analogous laws. If the tubes are very small, the heights augmented with
one-sixth of their diameter, are inversely as the diameters. If the
tubes are very large, we may ascertain very accurately the heights to
19*




194             THE THREE STATES OF MATTER.
which liquids would rise by very complicated calculations, or we may
obtain, approximately, their capillary effects, in supposing them proportional to the depression mercury undergoes in tubes of the same
diameter. For the same tube, and for the same liquid, the capillarity
depends much on the temperature, decreasing more rapidly than the
density.
According to Gay Lussac, the elevation of water in a capillary
tube of I m. m., ('03937 in.) is 30 m. m., (-11811 in.) and different
liquids elevate themselves, in the same tubes, to heights, which are in
the following relation:Water,....100'
Saturated solution of chloride of ammonium,.102'7
t"      "       sulphate of potash,..  95.7
(' 9    "          "        copper,..  84'
Nitric acid,....  75'
Hydrochloric acid,......  70-1
Alcohol,.......                     40-8
Oil of lavender,....  37*5
240. Laws of the equilibrium of liquids between parallel or
inclined lamine. —Phenomena analogous to those presented in capillary tubes, may be observed when two laminse, plunged in a liquid,
are brought near to each other. If the laminae are made wet, the
liquid elevated between them, is terminated by a cylindrical surface;
if not moistened, the liquid is depressed, and is terminated by a convex
surface; and it is observed that:1st. A liquid is regularly elevated or depressed between two lacmince,
inversely as the interval which separates them.
2d. That the height of the                  194
ascension or depression for a
given interval, is half that
which would take place in a
tube having a diameter equal 
to that of the interval.
When we plunge two inclined  laminae (with their
line of contact in a verticall
position) in a liquid which_,. =MIt
wets them, a concave surface
may be observed between them, fig. 194, the liquid rising toward the
upper point of their line of contact. The surface of the liquid takes
the form of the curve known in geometry, under the name of the
equilateral hyperbola; this curve is produced by capillarity.




OF FLUIDS.                            195
241. Movement of drops of liquid in conical tubes or between
lamins. —When a drop of liquid is contained in a conical tube, or
between two laminae having their lines of contact horizontal, the liquid,
if it wets the tube or laminae, is terminated by           195
two concave surfaces, and the liquid is drawn
towards the smaller end of the tube, or towards m                     m
the angle of the laminae, i. e. in the direction
from m to m', fig. 195, because the liquid being
terminated by concave surfaces, the pressure from without inwards
decreases as the radius of the concave surface diminishes, so that the
resultant pressure is directed from m towards              196
n'. If the liquid is mercury, or any fluid that
does not wet the surrounding body, the two a                          M n
surfaces will be convex, and the pressure from
without inwards will be greater in proportion as
the radius of curvature becomes less, hence the resultant pressure will
be from mv towards m', fig. 196, and the drop will be driven towards the
larger end of the tube, or towards the more open parts of the laminae.
242. Attraction and repulsion of light floating bodies.-The
attraction and repulsion which we observe between light bodies floating
on the surface of liquids, is due to capillarity. Two floating bodies are
drawn near to each other either when both are, or both are not moistened,
and repelled if the liquid wets only one of them.
Let a and b, fig. 197, be two floating bodies         197
whose surfaces are wet by the liquid. Between  )
the bodies a small mass of fluid is elevated by 
capillary attraction, of which the point m is 
higher than the level of a b, the highest points 
of the exterior curves.
The weight of the column nm tends to draw
the two bodies together, acting like a loaded
cord suspended between the two bodies. The
mutual cohesion of the molecules of the liquid
surface, m, causes it to serve as a cord, and   -  _._       _
the adhesion of the liquid to the floating bodies
at the highest points, serves as the attachments 
of the extremities. When the two bodies are 
not wet by the liquid, the liquid is depressed
between the bodies, and the external pressure.      -
upon the two bodies drives them together, as
shown in the middle section of the figure.
When one body is wet by the liquid, and the other is not, the result of capillary attraction is to cause the two bodies mutually to repel each other.
If the body which is wet is removed beyond the influence of the other body,
the concave meniscus will rise on both sides of the body to the dotted line o, in
the lower part of the figure. In the same manner, if the body not wet were
alone, the meniscus of depression would extend on both sides to the dotted line, r.




196              THE THREE STATES OF MATTER.
If now wo suppose the two bodies brought.so near each other that the concave
meniscus of fluid attached to one body will come in contact with the convex
depression of the other, the surface of the liquid will take a form, n k, intermediate between the two curves which would have been formed when the bodies
were entirely separated; that is, the more elevated point n will be below o, and
the point of greatest depression at k will be above the point r. The body wet
will therefore be drawn outward by the weight of that part of the external
meniscus which is more elevated than the internal, as represented by the distance
o n; and the body not wet will be driven away from the first by the excess of
hydrostatic presssure due to the difference of level, k r, on the two sides of the
second body.
Escape of Liquids from  Capillary Tubes.
243. Flow  of liquids from  capillary  tubes.-Fluids escaping
from capillary tubes are subject to the following laws:1. For the same tube the flow is proportioned to the pressure.
2. With tubes having an equal pressure and length, the flow is pro.
portional to the 4th power of their diameters.
3. For the same pressure and the same diameter, the flow is in inverse
ratio to their length.
4. The flow increases with the temperature.
The inequalities in the flow of different liquids under the same circumstances does not seem to depend on their viscosity or their density;
for alcohol flows slower, and oil of turpentine, or sugar solution, faster
than water. So also nitrate of potash solution flows faster, and serum
flows less swiftly, than pure water; alcohol added to serum retards its
movement, while if nitrate of potash solution be added to the mixture,
the serum recovers its usual velocity.
These experiments made with glass tubes, were repeated on the bodies of animals recently killed, by injecting the various fluids into the principal arteries.
The results were found to accord, tending to prove that the circulation of blood
and other fluids in the arteries and veins of living bodies, is subject to the same
laws as the flow of liquids in capillary tubes of glass.
II. OSMOSE OR OSMOTIC FORCE.
244. Osmose, Exosmose, Endosmose.-Osmose is the transmission of liquids into each other through the pores of an interposed
medium which ordinarily offers more resistance to the passage of one
of the liquids than of the other.
When a membranous sac, or a vessel filled with a fluid, and closed
by a membrane, is plunged into another liquid capable of mixing with
the first, two currents are established through the membranous partition.
The current from within outwards is called exosmose (from Rew outwards, and S(,rp.oq impulsion), and the current from without inwards is
called endosmose (from &'vSov inwards, and cbi~uos).




OF FLUIDS.                             197
The more general term osmose has been sul)stituted by Graham  for
the two correlative terms just defined, as being a better expression of
all the phenomena concerned.
The phenomena of osmose are closely allied to those of capillarity. They
have been very accurately studied, particularly by Dutrochet, who brought
forward his researches in 1827, and more recently by Prof. Graham.
245. Endosmometer.-The existence and rapidity of these currents
is ascertained by the endosmnometer, an instrument which may be thus
constructed. To a membranous pouch or bladder is fitted, hermetically,
a glass tube as in fig. 198.
The jar or bladder, and part of the tube, is filled with a dense liquid,
as a strong solution of gum or sugar, and                 198
placed in a tall cylindrical jar, which is
then filled with distilled water, until it
stands exactly at the level of the fluid in
the tube.  For very exact experiments,
this level is constantly maintained by the
addition to, or the removal of the water 
in the outer jar.  After a time, gum will
be found in the outer vessel, a current
from without, inwards, also taking place.
If we wish to determine more accurately the
actual as well as the comparative flow of different liquids, we may use an apparatus constructed as follows:-Over the open mouth of
a bell jar, of a few ounces capacity, is placed 
a plate of perforated zinc, to support firmly a
piece of fresh ox-bladder, which is securely
tied over it. To the upper aperture is attached
a graduated tube, open at both ends, the capacity of whose interior bears a certain definite
relation, as Ti6th, to that of the lower opening of the bell jar; so that a rise or fall in the
tube as of 100 m. m. (3'937 in.) indicates the en- 
trance or removal of a stratum of liquid, 1 m. m.
(0-03937 in.) thickness over the whole surface. 
246. Necessary conditions.-According to M. Dutrochet, in order
successfully to produce the phenomena of endosmose, it is necessary:1st. That the liquids be susceptible of mixing.
2d. That they are of different densities.
3d. That the membrane or wall (septum) which separates them is permeable to one or both liquids.
Materials for septum.-All thin animal and vegetable membranes,
thin plates of burnt clay, slate, marble, pipe-clay, &c., produce endos



198             THE THREE STATES OF MATTER.
motic effects in a more or less notable degree. Of inorganic maLterials,
those which contain most silicic acid are less permeable. A chemical
action on the materials of the septum, invariably takes place (excepting with alcohol and cane-sugar solutions), whether it is formed of
bladder or of earthenware. Where the partition is not susceptible of
being acted upon, the endosmotic action is very slight.
247. Direction of the current.-The endosmotic current is in
general directed towards the more dense liquid, but alcohol and ether
are exceptions; they acting as denser liquids, although lighter than
water; so also as acids are more or less diluted, there is endosmose
towards the acid or towards the water. The excess in the quantity of
the liquid which passes into the endosmometer, is proportional to the surface of the membrane, and to the different heights to which the liquids
mount in capillary spaces, the elevation taking place from that side of
the liquid which has least capillary action.
248. Organic solutions.-Neutral organic substances, such  as
gum-arabic, urea, and gelatine, produce but little endosmotic action.
Of all vegetable substances, sugar solution; and albumen among
animal bodies; are those which, with equal density, possess the
greatest power of endosmose. The figures attached to the following
substances, indicate the proportional height to which the liquids rose
when the endosmometer, being filled successively with solutions of
them, of the same density, was placed in pure water: gelatine 3, gum
5, sugar 11, albumen 12.
249. Inorganic solutions.-Neutral salts do not possess any peculiar power of endosmose, but diffuse themselves with nearly the same
rapidity as if no porous partition was used. Alkaline solutions greatly
accelerate endosmose. This may be observed, even in solutions which
contain but I part of the alkaline salt in 1000 of water. In moderately dilute solutions (containing not more than 2 per cent. of the salt)
the action is most rapid.
The soluble salts in the soil are taken up by the rootlets of plants by
the combined action of capillarity and endosmose; the salts entering
the plant more rapidly than the water which holds them in solution.
250. Endosmose of gases.-There is endosmose between gases, as
between liquids; if we connect two vessels containing different gases,
having a dry membrane between them, the gases will gradually mix,
equal currents being established in both; but if the membrane is moist,
unequal currents (that is, endosmose) are formed. Thus, a soap bubble
placed in a jar of carbonic acid, will, in a little time, burst, owing to
the increase of volume caused by endosmose.
251. Theories of endosmose.-Many theories have been proposed to




OF FLUIDS.                               199
account for these phenomena: such as that endosmose was due to an unequal
viscosity of the two liquids; to currents of electricity passing in the direction
of the endosmose; to the unequal permeability of the membrane for the two
liquids, or, that the phenomenon was due to capillary action, joined to the affinity of the two liquids. Very probably endosmose depends on the same forces
that produce capillarity, but obviously they are not the only forces which exert
influence, for we find that heat, which always diminishes capillarity, augments
the strength of the endosmose.
Problems on Hydrodynamics.
Elasticity of Liquids.
93. A cubic foot of water at the freezing point is submitted to a pressure of 20
atmospheres. How great is the condensation? and what is the specific gravity
of the condensed liquid?
94. What is the specific gravity of sea water at the depth of three miles,
reckoning the specific gravity at the surface 1-026, and the compressibility
0-0000436, and allowing a column of fresh water 33 feet high to equal the
pressure of one atmosphere?
95. How much would the volume of a cubic foot of alcohol, at 45~ Fahrenheit,
be diminished by a pressure of four atmospheres?
Hydrostatic Pressure.
96. In the hydrostatic press, given the diameters of the two cylinders A and
B, and the force applied to the pump P: determine the pressure produced.
97. In the hydrostatic press, suppose the diameter of the smaller cylinder to
be 1 inch, and the diameter of the larger cylinder to be 15 inches, the length of
the pump-handle to be 3 feet from the fulcrum, and the distance of the piston 2
inches from the fulcrum, the lever being one of the second order: what is the
relation of the pressure exerted to the power employed?
98. A cubical vessel is filled with fluid: compare the pressures upon the sides
and bottom.
99. A slender rod is immersed vertically in a fluid: divide it into three portions which shall be equally pressed.
100. Compare the pressures on two equal isosceles triangles just immersed in
the same fluid, one with its base upwards, the other with the base downwards.
101. A cylindrical vessel is filled with a heavy fluid: what proportion does
the pressure on the cylindrical surface bear to the entire weight of the fluid?
102. If the tube, T, of the water-bellows, fig. 144, is 10 feet high, and the
surface of the bellows, B C, is 18 inches in diameter, what weight will be sustained when the tube is filled with water? and what when the tube is filled with
mercury?
103. The sides of a hollow pyramid are isosceles triangles, the base is- a
rectangle having sides a and b, and the height of the pyramid is.. If the
pyramid be placed with its base on a horizontal plane, and filled with water,
how does the whole amount of pressure on the four sides compare with the
pressure upon the bottom?
104. A hemispherical vessel, 6 inches in diameter, without a bottom, stands
on a horizontal plane. When just filled with water, the liquid begins to run out
at the bottom. Determine the weight of the vessel.




200                THE THREE  STATES OF MATTER.
105. What height must a column of mercury have to balance a column of
water 25 feet high in a communicating vessel?
106. If a vessel of water communicates with a vessel of ether, standing at a
height of 20 inches, at what elevation will the water stand?
Buoyancy of Liquids.
107. A man exerting all his force can raise a weight of 300 lbs.: what would
be the weight of a stone (Sp. Gr. =  2-5) which he could just raise under water?
108. If a given piece of silver be balanced by its weight of iron in air, what
addition must be made to the iron so that the iron and silver may be in equilibrium when immersed in water?
109. How much will 12 ounces of gold weigh when immersed in alcohol (ASp.
GI-. = 0-798)?
110. If an alloy of gold and silver, weighing 22 ounces in air, loses 1~ ounces
when weighed in water, how much of the alloy is gold, and how much silver?
111. To avoid imposition in the purchase of lead (due to the fraudulent introduction of pigs of iron encased in lead), the Russian government are in the
habit of weighing the lead offered for sale with weights of lead, on a balance so
arranged that both pans can be immersed in water after they are brought to
equilibrium. If the equilibrium remains undisturbed, the lead is pure. Otherwise its degree of adulteration can be calculated. Suppose, by the above test,
that 1500 lbs. of commercial lead is found to be adulterated to such a degree as
to require the addition of 10 lbs. of lead weights under water to produce equilibrium, what is the amount of iron encased in the commercial lead (Sp. Gr. of
lead =  11-45; of cast iron =  7-64)?
Floating Bodies.
112. Supposing the specific gravity of a man, of water, and of cork, to be
1'12, 1, and 0-24 respectively, what quantity of cork must be attached to a man
weighing 150 lbs., that he may just float in water?
113. A cylinder, whose length is greater than its diameter, having a specific
gravity of 0'63, floats in water, what portion of the diameter of the cylinder is
immersed?
114. What is the bulk of a hollow vessel of copper, weighing 5 lbs., which
just floats in water?
115. How much bulk must a hollow vessel of iron occupy, weighing one ton,
that it may float with only one-half its bulk immersed in water?
116. A ship entering a river from the ocean sinks 2 inches, and after discharging 12,000 lbs. of cargo rises one inch; what is the weight of the ship and
cargo, reckoning the specific gravity of sea water 1-026?
117. A life-boat contains 100 cubic yards of wood (Sp. Gr. =  0'8), and 50
cubic yards of air (Sp. Cr. =  0-0012).  When filled with fresh water, what
weight of iron ballast (Sp. Gr. = 7'645) must be thrown into it before it will
sink?
118. A parallelopiped of ice whose dimensions are 15-75 yards, 20-45 yards,
and 10'5 yards, is floating in sea water on its broadest face; the specific gravity
of sea water is 1'026, and that of ice 0-93. Required the height of the ice above
the surface of the water.
119. When two persons, A and B, descend together to the bottom of a lake iTn
a cylindrical diving-bell, it is observed that the water stands 1 inch lower within
the bell than when A descends alone; the pressure of the atmosphere is equal
to a column 9f water 33 feet high, the diameter of the bell is 4 feet, and the sur



OF FLUIDS.                              201
face of the water within it, at the bottom of the lake, is 20 feet below the surface
of the lake; find the volume of B.
120. A piece of flint glass weighs in air 4320 grains, and in water it weighs
3195 grains: what is its specific gravity?
121. Determine the specific gravity of granulated tin from the following data:
Weight of bottle filled with water at 60~ F.,. 44-378 grammes.
"    " tin,....  9431    "
"    " bottle tin and water,.                 52-515    "
122. The same specific gravity bottle used in the last example is supplied with
7-432 grammes of powdered glass.  The weight of bottle water and powdered
glass is 49'859 grammes, what is the specific gravity of the powdered glass?
123. A body weighs 14 lbs. in air, and 9 lbs. in water; another body weighs
81 lbs. in air, and 7 lbs. in water: what are their respective specific gravities,
and how do they compare with each other?
124. The counterpoise of a Nicholson's hydrometer requisite to sink it to
zero weighs 25 grammes; with a piece of brass on the upper pan it requires
8'171 grammes to sink it to zero, and 10-241 grammes when the same piece of
brass is on the lower pan: what is the specific gravity of the brass?
125. A Fahrenheit's hydrometer weighs 700 grains-to sink it in water 300
grains are requisite (volume of water  = to volume of hydrometer =  1000
grains), placed in alcohol 132 grains are required to bring it to zero (832 grains
=volume of alcohol =  volume of hydrometer).  What is the specific gravity
of the alcohol?
Motion of Liquids.
126. What volume of water will flow from an orifice 2~ inches in diameter, in
7 seconds, if the centre of the orifice is 10 feet below the surface of the fluid?
127. A vessel 20 feet deep is raised 5 feet above a plane: how far will a jet
reach issuing 5 feet from the bottom?
128. A jet of water issuing from a vessel, 3 feet below the surface, and an
equal distance above the horizontal plane on which it falls, is seen to have a
horizontal range of 2-3 feet; how does the velocity of discharge compare with
the theoretical velocity?
129. A jet of water issues from  a cylindrical adjutage 2 inches in diameter,
6_ inches long, with a head of 10 feet. What amount of water is discharged
per hour?
130. What quantity of water will be discharged per day through a tube one
inch in diameter and 19 feet long, under the pressure of 21 feet head?
131. If a fire-engine discharges 16-8 cubic feet of water through a I inch
pipe in one minute, how high will the water be projected, the pipe being directed
vertically?
Capillarity.
132. What will be the difference of level in a glass tube ^  inch diameter,
bent in the form of the letter U, when one branch is filled with mercury and the
other branch with alcohol?
133. A block of marble 10 feet long and 2 feet thick (the tenacity of marble
being 9000 lbs. to the square inch), is burst asunder by the capillary attraction
of a series of wooden plugs. The series of plugs being 8 inches apart, 1 inch
in diameter, and 5 inches long, the plugs are driven dry, and afterwards
allowed to absorb water by capillarity. What height would be required for a
series of columns of water, acting upon the orifices where the plugs are inserted,
to produce a similar rupture of the marble?
20




202              THE THREE STATES OF MATTER.
CHAPTER IV.
OF ELASTIC FLUIDS, OR GASES.
Pneumatics.
I. DISTINGUISHING PROPERTIES OF GASES.
252. Definitions.-Pneumatics -  Gases, vapors,-tension.Pneumatics (from flyseia, a spirit or breath,) is a subdivision of the
general subject of Hydrodynamics (186), and is devoted to the consideration of the properties of elasticfluids.
Gases are elastic fluids, aeriform, transparent, and usually colorless
and invisible.  The blue color of the air is due to watery* vapor in the
atmosphere. In gases, the molecular force of repulsion (146) prevails
over the force of attraction-and in the permanent gases this force has
never been overcome.
Vapors differ from gases chiefly in that they are produced by the
action of heat upon liquids-as steam is produced from water; and by
their returning again to the liquid state at ordinary temperatures by
the loss of heat.
Tension is an expression for the tendency of a gas to expand; the
degree of expansive force in each gas being specific and varied by temperature, and mechanical means.
Gases, simple or conmpound.-Of the thirty-four gaseous bodies known in
chemistry, four only are simple or elementary, viz.: oxygen, nitrogen, hydrogen,
and chlorine. The three first named of these gases, together with the compound
gases, oxyd of carbon (C 0 ) and the binoxyd of nitrogen (N 02), are the only
aeriform bodies which have thus far resisted the united effects of cold and pressure, and permanently retained their gaseous state.  Hence they are called
permanent or incoercible gases.
All other gases, whether simple or compound, have, by the means named,
been coerced into the liquid or solid state, and are hence called non-permanent
or coercible gases.
253. Expansion of gases.-Expansion is the most characteristic
property of gases. This molecular force, for all that appears, would
separate the particles of a gas indefinitely through all space, were there
no counteracting causes.
Under normal conditions, the atmosphere is in a state of equilibrium
between the earth's attraction and its own expansive force.  If we




OF GASES.                           203
disturb this condition of equilibrium, we see evidence of the exercise
of the power of expansion.  In fig.                 199
199, a moist bladder, partly filled with
air, is subjected to a partial vacuum
under the air-bell. As the pressure  
in the bell is diminished by working
the air-pump, the portion of confined
air expands, and distends the flaccid
bladder until it fills the jar. As soon 
as the equilibrium  of pressure is restored by opening a communication
with the external air, it contracts
again to its original dimensions.
It appears, therefore, that gases, like
liquids, are in a state of equilibrium,   11
the only difference in the conditions
of equilibrium  being that, in liquids,
this state results from the opposite
effects of the two molecular forces; while in gases, the repulsive force
is held in control by gravity, or some extraneous force.
254. Mechanical condition of gases.-Perfect freedom of motion
among their particles, as a consequence of equilibrium, brings gases
under the general definition of fluids. Being also elastic, ponderable,
and impenetrable (14), it follows that all the characteristic properties
of liquids already discussed, apply also to gases. Atmospheric air is
the type of permanent gases. For its chemical constitution, reference
is made to chemistry.
II. PROPERTIES COMMON TO BOTH LIQUIDS AND GASES.
255. Gases transmit pressure equally in all directions.-The
theorem of Pascal, already demonstrated with respect to liquids (189),
is also true of gases.
Suppose the vessel, fig. 200, to be filled with       200
air in the usual state of tension. By its elasticity it exerts an equal pressure in all directions; and by the reasoning in ~ 189, the
pressure it exerts on the pistons a, b, c, d, is
in proportion to their areas.  The same is
true of any part of the inner surface of the
vessel, or of any section of its interior.
If the air within and without the vessel has the same tension, then
the pistons have no tendency to move, the inner and outer pressures




204              THE THREE STATES OF MATTER.
exactly balancing each other.  Any pressure applied upon either of
the pistons develops an increase of elastic force in the gaseous contents
of the vessel, proportioned to the amount of compression. This pressure reacts on every portion of the inner surface of the vessel, and moves
each of the other pistons outwards with a force proportioned to its area.
The chief difference between the transmission of pressure in gases and liquids
is, that in gases, owing to their elasticity, the effects of pressure are not felt at
long distances, so instantaneously as in liquids.
The distribution of illuminating gas in cities through many miles of pipes,
illustrates both the law and the exception.
The reaction due to elasticity prevents, as is well known, the driving of a
blast of air in an effective manner through small and tortuous passages.
The laws and illustrations regarding the pressure and equilibrium of liquids,
contained in ~ 191, 192, 193, and 199, are also true of gases; and it is therefore needless to repeat them in this connection.
256. The atmosphere.-Its general phenomena.-A  vast aerial
ocean rests upon the surface of the earth, penetrates even its solid
crust, and is dissolved, to a certain extent, in its waters. It is composed
of the two incoercible gases, nitrogen and oxygen, in the proportion of
nearly four parts of the first, to one part of the second, by measure.
It is held in its place by the force of gravitation, which, counteracting
the molecular force of repulsion, brings it to equilibrium at about fortyfive miles above the earth. This height of the atmosphere has been
determined chiefly from the phenomena of refraction, as observed in
its effect on the rising and setting of the heavenly bodies.
It is the opinion of Bunsen and others that the atmosphere extends to a distance of about 200 miles, although its density, above 45 miles, is too small to
refract light to such a degree as to enable us to observe it. Many pneumatic
experiments are thought also to indicate an altitude of the atmosphere exceeding
45 miles.
The atmosphere partakes of the motion of the earth, but its state of
rest, with respect to bodies on the earth's surface, is disturbed by winds
and currents, caused by agencies to be considered hereafter.
Like the ocean, the upper surface of the atmosphere must, theoretically,
have a definite surface, since each particle is influenced by gravity in
a similar manner, and the resultant direction of these actions at any
point must be a radius of the earth (199).
It follows from ~ 191, that each molecule of air exerts, at a given
level, the pressure due to the weight of a continuous line of molecules,
extending vertically from  the point chosen to the outer limit! of the
atmosphere. Therefore its upward pressure (192), its pressure on the
sides of any vessel (193), and its buoyancy (205), are the same, and
governed by the same laws as those already enunciated for liquids;




OF GASES.                            205
provided always that there is a communication, however small, between
the outer air and the interior of any given vessel.
257.  Atmospheric pressure.-The great weight, and consequent
pressure of the atmosphere upon bodies near the surface of the earth,
was unsuspected by mankind in general, until Torricelli, in 1643, first
announced it.
As it is exerted, in obedience to the laws of fluid equilibrium (199),
alike above, below, and on the sides of all bodies, a man of usual size
moves about unconscious that he sustains a constant load of over 30,000
pounds, or more than fifteen tons. If this pressure is partially removed from one surface of a body, its existence then becomes very
manifest.
201                                   202
fllllllli                ftfBilll&
In fig. 201, the upper end of an air-jar is hermetically sealed by a bladder
skin tied on when wet and dried. Its lower edge rests upon the well-ground
plate of an air-pump. As the air in the jar is gradually exhausted by working
the pump, the surface of the bladder becomes more and more depressed, until,
finally, the membrane bursts, with a sharp report, owing to the pressure of the
atmosphere resting upon it.
This experiment demonstrates the downward pressure of the atmosphere only.
Its upward pressure is illustrated by the apparatus seen in fig. 202.
A glass jar having an open bottom, and sustained on a tripod, is covered by
an impervious caoutchouc bag. When a partial vacuum is produced in the jar
through the upper opening, the yielding bag rises and carries with it the
weight which is hung below. This heavy mass is sustained in mid air as on an
elastic spring by the upward pressure.
The upward pressure of the air may also be illustrated by a familiar experiment with a tumbler. Fill a tumbler with water, and lay over it a piece of
paper,-hold the paper in its place by laying upon it a board or the palm of the
hand,-turn the tumbler bottom upwards, and remove the hand or board, the
20*




206              THE THREE STATES OF MATTER.
upward pressure of the atmosphere will then retain the paper in its place, closing
the tumbler, and preventing the discharge of the water.
The pressure of the air from all sides is shown by the well-known
Magdeburg hemispheres.                                    203
This apparatus is composed of two hollow hemispheres of brass, fig. 203, whose accurately fitting
edges are well greased. One of the hemispheres is
furnished with a stop-cock, by which connection
is made with an air-pump. Placing this apparatus
upon the air-pump, and exhausting the air, it will
be found that the hemispheres can no longer be
separated, no matter in what position they may be
held; proving that the atmospheric pressure which
alone keeps the hemispheres together, is exerted in
all directions. Rings adapted to each hemisphere,
enable two persons to test their strength against    _ 
the atmospheric pressure. Otto V. Guerick, who
invented them, employed a pair which held all the.
power of a strong team of horses.
These illustrations, easily multiplied by the ingenuity of the teacher, give evidence of the fact of atmospheric pressure in all directions, but do not indicate its
amount.
258. Buoyancy of air.-Bodies weighed                   204
in air are sustained or buoyed up by aforce
equal to the weight of the volume of air dis- 
placed, in accordance with the Archimedean 
principle (205).
This law is well illustrated by the appa- 
ratus seen in fig. 204.  A  hollow  globe of
brass is counterpoised on one arm of a balance
by a brass weight at the other end.  Placed
on the plate of an air-pump, and covered by
a bell-glass, the air may be removed from
contact with  the two masses previously in
equilibrium; and, in proportion as the vacuum                -
is produced, the globe begins to preponderate by a force as much
greater than the action of gravity upon the counterpoise as the weight
of its own volume of air is greater than that of the counterpoise.
The brass and platinum weights used in delicate determinations of
weight are standards only when in vacuum. Let us then represent the
various values as follows:W' -  weight of the body in air as estimated by standard weights, and also
the weight of the standard weights themselves in a vacuum.
7= -   volume of the standard weights in cubic inches.
V = volume of the body in cubic inches.
ob = weight of one cubic inch of air at the time of the weighing.
W = weight of the body in a vacuum-which we wish to find.




OF GASES.                           207
We can now easily deduce the following values:VP0 = buoyancy of air on the weights.
Vw = buoyancy of air on the body.
W'- V'w == actual weight of standard weights in air.
W — Vwo = actual weight of body in air.
Since these weights just balance each other, we have,
W-Vt ec= W' — Vw, or W=  W' + w ( V- V).
The correction wo (V- V'), which must be made to the weight determined by
the balance in air in order to obtain the weight in a vacuum, is evidently additive when the volume of the body is greater than the weights, and subtractive
when these conditions are reversed. When the volumes are equal, the correction
becomes zero, and the balance yields the same results in air as in a vacuum.*
If a vessel, whose capacity is 100 cubic inches, is exhausted of air
and weighed, fig. 205, and after filling it with dry air at the ordinary
temperature and pressure, it is weighed again, it will       205
be found that its weight is 31-074 grains more than at
first; that is, 100 cubic inches of air weigh 31'074
grains.  Air is the standard of comparison in density
for all gases and vapors.
259. Impenetrability of air.-Air is impenetrable.
This may be shown by inverting a hollow vessel, as a
tumbler, upon the surface of water; when pressed
downward the water will not rise and fill the tumbler,
because of the impenetrability of the air.  The diving-       
bell depends on this quality of air: it consists of a large
bell-shaped vessel, sunk by means of weights into the       --
sea, with its mouth downwards.  Notwithstanding the open mouth,
and enormous pressure of the sea, the water is excluded from the bell,
because of the air contained within.
260. Inertia of air.-Wind is only air in motion. If the air had
no inertia, it would require no force to impart motion to it, nor could
it acquire momentum. We know that the force encountered by a body
moving through the air (that is, displacing the air), is in proportion to
the surface exposed, and the velocity with which it is moving (143).
The sailing of ships, the direction of balloons, the wind-mill, and the
frightful ravages of the tornado, are all familiar examples of the power
of moving air, and consequently proofs of its inertia.
III. BAROMETERS AND BALLOONS.
261. Torricellian vacuum.-Measure  of atmospheric  pressure.-The amount of pressure exerted by the atmosphere was first
determined by Torricelli, a disciple of Galileo, in 1643.
* Cooke's Chem. Physics, p. 269.




208              THE THREE STATES OF MATTER.
If a glass tube, a B, fig. 206, about 32 inches in length, is filled with
mercury, and then inverted in a vessel of the same fluid, the liquid
column will fall some distance, and after several oscillations will come
to rest at n, a height at the level of the sea, of about thirty inches
above the level, a c, of the mercury in the vessel.         206
The space n B, above the mercury, is the most
complete vacuum attainable by mechanical means,              a 
and is called the Torricellian vacuum.  If, after
having closed the mouth of the tube, we lift it out
of the dish, we shall find that the weight of the 
column of mercury pressing against the finger is
very considerable. When we place the tube in the
vessel of mercury, we have this same force exerted,
the column of mercury tending to flow out of the
tube, and another force, the weight and pressure
of the atmosphere, tending to push the mercury up
in the tube.  The length of the mercurial column,
it is evident, is in proportion to the atmospheric
pressure, which under ordinary circumstances, is
equivalent to a column of mercury thirty inches in
height.
We may now easily estimate the pressure on any given
surface, as, for example, a square inch. If we should
take a tube whose base is a square inch, and repeat the
above experiment, the column a n would, as before, be
sustained at a height of thirty inches; but the weight
of a column of mercury thirty inches in height and one
inch square, is very nearly fifteen lbs.; therefore the
atmospheric pressure on a square inch is fifteen lbs.   It
(accurately 14-7225 lbs).
If the tube were filled with a liquid lighter than mercury, a proportionally
longer column would be sustained by the pressure of the atmosphere: the length
of the column being inversely as the densities of the two fluids. If water, which
is about 13-5 times lighter than mercury, was used, the column of water sustained
would be 13-5 times as long as the mercurial column, or about thirty-four feet.
262. Pascal's experiments.-The experiment of Torricelli excited
the greatest sensation throughout the scientific world, and the explanation he gave of it was generally rejected.
Pascal, who flourished at that time, perceived its truth, and proposed to subject the experiment to a test which must put an end to all further dispute. " If,"
said Pascal, "it be really the weight of the atmosphere under which we live,
that supports the column of mercury in Torricelli's tube, we shall find by transporting this tube to a loftier point in the atmosphere, that in proportion as we
leave below more and more of the air, there will be a less column of mercury
sustained in the tube." Pascal therefore carried a Torricellian tube to the top of
a lofty mountain, called the Puy-de-Dome, in Auvergne (central France). It




OF GASES.                              209
was found that the column gradually diminished in height as the elevation to
which the instrument was carried increased. lIe repeated this experiment at
ltouen (France), in 1646, with a tube of water, and found that the column wassustained at a height of about thirty-four feet, or 13-59 times greater than the
height of the column of mercury.
263. Construction of barometers.-Barometer is the name given
to Torricelli's tube. This instrument has different forms, according to
the use for which ki is designed. There are, however, certain conditions to
be fulfilled in the construction of barometers, whatever may be their form.
1st. It is necessary that the mercury be perfectly pure and free from
oxyd, otherwise it adheres to the glass; again, by impurities, its
density is changed, and the height of the column in the barometer is
greater or less than it should be.
2d. It is necessary that there be a perfect vacuum above the surface
of the mercury in the tube; for if there be a little air, or vapor, as of
water, the elasticity of these will continually depress the mercurial
column, preventing its rising to the true height.
To obtain a perfect vacuum, a small portion of pure mercury is boiled in the
barometer tube, and when cooled, another portion            207
of mercury is added, and again boiled, and so on,
until the tube is full; by this means the air and 
moisture which adhered to the walls of the tube are
driven out completely. The boiling must not be too
long continued, otherwise a portion of oxyd will
be formed, which will dissolve in the mercury and          l
alter its density. The tube being filled, we invert   i 
it in a vessel of pure mercury. In order to determine
whether there is not some air or moisture in the
tube, we incline the tube quickly; if the mercury
gives a dry metallic sound when striking the summit of the tube, it is a proof of their absence, while,
if they be present, the sound is deadened.
264. Apparatus illustrating the principle of the barometer. —By means of the air-  
pump, and the apparatus fig. 207, the principle of the barometer is beautifully shown.
The apparatus consists of a large bell-glass, R,
with two syphon barometer tubes attached. One of
them, B, has its cistern within the bell. The other    R
barometer, whose cistern is without the bell, com- g llli -    li
municates with its interior by the curved tube  t'. 
When this apparatus is placed on the air-pump, and
exhausted of air, the mercury in B falls in proportion to the vacuum produced,
and rises in the tube C 1, in the same proportion. In B we see the effect of diminished pressure, as on a mountain or in a balloon; in C the pressure of the external
air causes the mercury in it to rise, forming a gauge of the exhaustion. When
the air is allowed to enter,thc mercury in the tubes resumes its former position.




210               THE THREE STATES OF MATTER.
265. Height of the barometric column at different elevations.
— The following table gives a comparative view of the height of mercury in the barometer at different elevations above the sea.
At the level of the sea, the mercury stands at    30         inches.
5,000 feet above  "        "                 "       24-773   "
10,000  "  [height of Mt. Etna,]              "        20-459   "
15,000  "  [height of Mt. Blanc,]             "        16-896   "
3 miles                                          16-361   "
6  "  [above the top of the loftiest mountain,] 8-923   "
9  "                                              4-866   "
15  "                                              1448   "
266. Cistern barometer.-The cistern barometer is               208
the most simple form of this useful instrument.  It consists of a Torricelli's tube of glass, filled with mercury   ii.iSi
and plunged into a vessel containing the same metal;
this vessel or cistern is of various forms.
That it may be transported easily, the cistern is divided into
two compartments, mt, i2, fig. 208; the upper division is cemented
to the tube, communicating with the atmosphere by the small
hole a. The two compartments are united by the narrow neck
into which the lower part of the barometer tube enters, fitting
closely, although not touching the walls; leaving only so small
a space, that capillarity will not allow the mercury to escape
from the lower compartment when we incline the barometer. So
that in whatever position we place it, no air can enter the lower
end of the tube.
This barometer is always fixed on a wooden support, at the
upper part of which is a graduated scale, whose zero is the level
of the mercury in the cistern. The sliding scale i indicates the
level of the mercury in the tube. There is attached  209
to barometers also a slider, moving by the hand
upon which is a vernier, by means of which we     El
can distinguish very small variations. But the
level of the mercury in the cistern varies as the
column of mercury in the tube ascends or descends, for then a certain quantity of mercury
passes from the cistern into the tube, or the reverse, so that the zero (the level) changing the
graduation on the scale, does not indicate the
true height of the barometer.
Fortin's barometer.-This  error  is
avoided in the barometer of Fortin, fig. 
211, by means of a cistern of peculiar con-  i
struction, shown in fig. 209.
The lower part is of deer-skin, and is elevated or depressed by means of the




OF GASES.                              211
screw, C, pressing the plate D B. At the upper wall of the cistern is fixed a
small ivory needle, A, whose point corresponds exactly to the zero of the scale,
graduated on the case. At each observation with this instrument, care is taken
to make the level of the mercury in the cistern, correspond with  212
this point, which is accomplished by turning the screw up or
dowvn.
Vernier.-To secure great accuracy in measuring    211
the height of the mercurial column, the barometer is  C
furnished with a vernier, B C, fig. 210. Ten divisions
on the vernier correspond with nine divisions of the
graduated scale. The vernier is        210
moved by a rack and pinion until its
lower extremity corresponds very I        ll           A
accurately with the surface of the
mercury in the barometer tube. In
the figure the mercurial column is
seen to stand a little above the division marked 760. Counting upward
we see that the seventh division of 
the vernier is exactly opposite one 
of the divisions on the graduated
scale. This gives the small portion
of the column above 760 equal to
seven-tenths of a division of the
scale, and the height of the column
is read 760-7.
This form of barometer has been
adopted by the Smithsonian Institution, and is made by Mr. Green, 
of N. Y.
267. The  syphon   baro
meter, invented by Gay Lussac, consists of two tubes, fig.
212, of the same internal dimensions, united  by a very capillary neck, both closed at their
upper extremities, the air entering the cistern through a small
hole at C. The large tubes being
of the same interior diameter,
the capillary action is mutually destroyed. The capillary tube is made
small, so that when we turn  the instrument over, it remains full,
because of its capillarity.  For measuring the height of the mercury,
there are two scales, E and D, graduated in different directions, having
their common zero at 0, on a line inteurlediate between the two mercurial surfaces; so that by adding the indications of these two scales,
we have the difference in the level of the mercury in the two tubes.




212              THE THREE STATES OF M&AIR.
But a quick movement, transportation in a carriage er on horseback, may
divide the mercurial column in the capillary tube, and thus ailow the air to pass
into the long arm, whereby the accuracy of the instrument would be destroyed.
In order to obviate this inconvenience, M. Bunten      215
has modified the instrument as represented in fig. 213.
The long arm A drawn out to a point, enters into and
is soldered to a larger tube, K, which is attached to
the capillary tube. With this arrangement, should
bubbles of air even pass through the capillary tube,
they cannot enter the long arm, but are   214
retained in the top of K. These bubbles
of air have no influence on the observations, and may be driven out by simply
heating the tube.
268. Wheel  barometer. —The
wheel barometer is an instrument
of no scientific value, but has a certain popular interest as it purports
to declare the state of the weather.
The apparatus consists, figs. 214 and
215, of a dial plate attached    213
to a syphon barometer having a small cylindrical cis-  
tern, upon whose surface  A
rests a float; this is attached  to a  silk  string, 
which winds around a pul-                       ll ll
ley, 0, and is terminated
by the counterpoise P; the K 
axis of the pulley carries
a needle, which rests upon
the face of the dial plate.
When the pressure of the atmosphere changes, the column rises or falls
in the tube accordingly, and carries along with it the float. The pulley
turns and moves the needle to the words rain-fair-changeable, &c.,
which are designed to correspond to certain heights of the mercurial
column.
269. Causes of error.-In order to obtain the true height of the
mercury in a barometer, we must, after making the observation, determine by calculation the error caused by capillarity, and by the variations
of density, caused by changes of temperature.
Correction for capillarity.-When the barometer tube is of capillary diameter, the surface of the mercury in it becomes convex (233)
and the depression is greater by as much as the tube is more capillary.




OF GASES.                            213
For correcting this error, it is necessary to know the diameter of the
tube. and then by means of the table (238), ascertain the depression,
whic.: must always be added to the observed height.
Correction for temperature.-In  all mercurial barometers, we
must have regard to the temperature, for as heat expands mercury, it
diminishes its density, and in consequence, under the same atmospheric
pressure the mercury would rise as much higher as the temperature was
more elevated.  Consequently barometric observations cannot be compared, unless they were taken at the same temperature, or are brought
by calculation to the same standard.
As it is entirely arbitrary what temperature shall be chosen; that of melting
ice has generally been taken. A table showing the expansion and contraction
of mercury at different temperatures may be found in the chapter upon heat.
The metallic and aneroid barometers have already been described (163, 164).
270. Variations of the barometric height.-When we observe a
barometer during many days, we notice that not only does its height
vary from day to day, but also in the same day. The amount of these
variations increases from the equator towards the poles. The greatest
variations (excepting extraordinary cases) are 6 m. m. ('2362 in.) at
the equator; 30 m. m. (1'181 in.) at the tropic of cancer; 40 m. m.
(1'5748 in.) in France, and 60 m. m. (2-3622 in.) 25~ from the poles.
The greatest variations take place in winter.
Thie mean diurnal height is the average of twenty-four successive observations
taken from hour to hour. M. Ramond has found the height of the barometer at
noon to be the mean of the day.  The                  216
mean monthly height is the average of the   l       
thirty mean daily heights of a month.         ~ - I    I
The mean annual height is the average of                       \
the three hundred and sixty-five mean                SJ 
daily heights of a year.                   \                        Y 
At the equator the mean annual height           _I'
is 758 m. m. (29-842 in.) It increases,  ~-    l        ~ I I [_   I
passing from the equator, and attains its 
maximum of 763 m. m. (30-04 in.) between            ET\ 
the latitudes of 30~ and 40~; it decreases
in more elevated latitudes. The mean
monthly height is greater in winter than in
summer, because of the cooling, and consequent increased density of the atmosphere. 
The scale, fig. 216, shows the barometric          C
variations of the different months. Equal     
distances, taken on the lower horizontal  j.. m. a. m.j. j. a. s. o. n. d.
line, j-d, represent the duration of the different months, and the curved lines at
the commencement of each interval, the mean barometric heights corresponding
to the successive months. We have then curves, whose inflexions make known
the variations of the mean from one month to another. The four curves repre21




'214            TIE THREE STATES OF MATTER.
sent the monthly means as observed at Calcutta, C, at IHavana, H; Paris, P,
and at St. Petersburg, S. P. The differences of the curves represent, with
great distinctness, the differences of the mean barometric heights. Calcutta
and Havana, on the same latitude, have, it will be seen, very different monthly
means.
Variations observed in Barometers are of two kinds.
lst. Accidental variations, which do not offer any regularity in their.movements, and which depend on seasons, the direction of the wind,
and geographical position.
2d. Diurnal variations.-It was about the year 1722, that the hourly
variations of the barometer were proved to take place in a regular
manner.  From that time, many observers have labored to determine
the extent and the periods for the different parts of the earth. Alex.
Von IIumboldt, with others, has demonstrated by a long series of very
accurate observations at the equator, that the maximum of height corresponds to 9 o'clock in the morning; the barometer then falls to its
minimum at four, or halfpast four o'clock in the afternoon; it then
rises, attaining a second maximum  about ten o'clock at night. These
movements are so regular, they almost serve to mark the hours like a
clock, but they are very small.  M. HIumboldt found that the distance
between the highest point in the morning, and the lowest point in the
afternoon, was but two m. m. In the temperate zones, these diurnal
variations also take place, but are very difficult to ascertain, because
of the accidental variations, so that it requires extended and very accurate observations in order to determine them. The hours of the maximum and minimum of the diurnal variations, appear to be nearly the
same in all climates, varying a little with the season.  Thus, in winter
(in France), the maximum is at nine o'clock in the morning, the minimum at three o'clock in the afternoon, and the second maximum at
nine o'clock in the evening. In summer, the maximum  takes place
before eight o'clock in the morning, the minimum at four o'clock in
the afternoon, and the second maximum at eight o'clock at night. In
spring and in autumn, the critical hours are intermediate.
271. Relation between barometric changes and the weather.
-Those variations of the barometer which are not periodic, are generally supposed to be indications of changes in the weather. For it has
been noticed that those days in which the column of mercury was
29-72 inches in height, there was very changeable weather; that in a
majority of those days when the mercury rose above this point, there
was fine weather; when it fell below this point, stormy weather, snow,
or rain, prevailed.  It is from  these coincidences between the height
of the barometer and the state of the weather, that there is marlked on




OF GASES.                          215
the scale or dial plate of barometers, at certain heights, the words
stormy, rain or snow, variable, fine weather, &c., and it is supposed
that when the mercury stands at the height indicated respectively by
these words, we should have corresponding weather. Now, although
this may be true to a certain extent, yet a little reflection will show the
fallacy of such indications. The height of the mercurial column varies
with the position of the barometer, and consequently two barometers,
in different places, not upon the same level, would indicate different
coming changes. The changes of weather are indicated in the barometer, not by the actual height of the mercurial column, but by its
changes of height.
Rules by which coming changes are indicated.-The following rules may, to some extent, be relied upon, but, for reasons already
stated, must be taken with a considerable degree of allowance.
1. The sudden fall of the mercury is usually followed by high winds
and storms.
2. The rising of the mercury indicates generally the approach of
fair weather; the falling of it shows the approach of foul weather.
3. In sultry weather, the falling of the mercury indicates coming
thunder. In winter, the rise of the mercury indicates frost. In frosty
weather, its fall indicates thaw, and its rise indicates snow.
4. Whatever change of weather follows a sudden change in the
barometer, may be expected to last but a short time.
5. When the barometer alters slowly, a long continuation of foul
weather will succeed if the column falls, or of fair weather if the
column rises.
6. A fluctuating and unsettled state in the mercurial column, indicates changeable weather.
272. Measure of heights by the barometer.-Since the level of
the mercury in the barometer falls, as we ascend above the earth, we
see that it is possible to determine by barometric observations, the elevation of a mountain, or of any other place above or below the level
of the sea. If the atmosphere had a uniform density, we could ascertain, by a very simple calculation, the height to which the barometer
was raised, from the amount of the fall of the mercurial column; for,
mercury being 10,466 times heavier than air, a fall of one m. m.
('03937 in.) of the barometric column, would indicate that the column
of air had diminished 10,466 m. m. (412'054 in.), and therefore the
height measured would be 10,466 m. m. But as the atmospheric
pressure diminishes very rapidly as we ascend, such calculations are
of no value except for small elevations, and it is necessary to deter



216               THE THREE STATES OF MATTER.
mine the rate of diminution in density of the air, in proportion as it is
further removed from the earth.  Tables have also been constructed by
which we can easily calculate the level between any two places, when
we know  the height of the barometer, and the temperature of the
atmosphere.*
The altitude of any place above the level of the sea may also be calculated by the following formula, given by Prof. Guyot, in the tables
referred to below:If we call
h  the observed height of the barometer,
T   the temperature of the barometer,. at the lower station.
t    the temperature of the air, 
h'   the observed height of the barometer, 
T' =  the temperature of the barometer,  at the upper station.
t'  the temperature of the air,
If we make, further,
Z = the difference of level between the two barometers;
L =  the mean latitude between the two stations;
H = the height of the barometer at the upper station reduced to the temperature of the barometer at the lower station; or,
H =  h' l I + 0-00008967 (T-  T') I;
The expansion of the mercurial column, measured by a brass scale, for 1~
Fahrenheit =  0-00008967;
The increase of gravity from the equator to the poles = 0-00520048, or
0-00260 to the 45th degree of latitude;
The earth's mean radius - 20-886,860 English feet;
Then Laplace's formula, reduced to English measures, reads as follows:t + t' -  64
+      900
Z -  log.   X  60158-6 Eng. feet,      + 0.00260 cos. 2 L.).
/     g + 52252         h   \
20886860  10443430 
z, in this formula, is the approximate value of Z, as given by that part of the
formula preceding the parenthesis in which z is introduced.
Heights may be calculated by the above formula, but the calculation is much
facilitated by the use of the Smithsonian Tables.
273. Balloons.-Bodies in air (like solids plunged in liquids) lose
a part of their weight, equal to the weight of the air displaced. From
this it follows, that if a body weighs less than an equal volume of air
it will rise in the atmosphere until it meets with air of its own density:
hence, heated air, smoke, &c., rise, because they are less dense than
cold air.
Dr. Black, of Edinburgh, announced in 1767, that a light vessel filled with
* Guyot's Meteorological and Physical Tables, Smithsonian Collections.




OF GASES.                               217
hydrogen gas, would rise in the air; and Cavallo, in 1782, communicated to the
Royal Society in London the fact, that soap-bubbles, filled with hydrogen, would
ascend in the atmosphere.  The brothers Montgolfier, in 1782, first constructed
balloons. These consisted of globes of cloth, lined with paper. The one that
they first exhibited publicly, was a globe about thirty feet in diameter, open at
the lower part, below which was placed a fire. This, expanding the air within
the globe, diminished its density, and the balloon rose to a height of nearly a
mile. Hot-air balloons are, therefore (in allusion to their inventors), usually
called Montgolfiers. Balloons filled with hydrogen were first introduced by Mr.
Charles, professor of physics in Paris, in 1782; and in November of the same
year, Pilatre de Rosier made the first aerial voyage, in a balloon filled with hot
air. The ascension took place from Boulogne. Soon after, Messrs. Charles and
Robert, in the garden of the Tuilleries, repeated the same experiment in a balloon filled with hydrogen gas. At this epoch, airial voyages multiplied.  In
January, 1784, seven persons rose from Lyons, three from Milan, &c.; and soon,
so familiarized were the public with this method of navigating, that it was not
uncommon for people to ascend in a balloon which was restrained from going
too far by means of a cord; when the adventurers had attained a certain height,
the balloon was drawn down by means of the cord, and other voyagers took
their place.
Gay Lussac, September 16, 1804, made an ascent remarkable for the facts
with which it enriched science, and for the height which was attained, namely
7016 metres, or about 23,019 feet. In those elevated regions, Gay Lussac found
respiration and the circulation of the blood much accelerated, because of the
rarefaction of the atmosphere; his heart making 120 pulsations in a minute,
while 66 was its normal rate. He also collected there specimens of air for
chemical analysis, and determined the cold of space.
Construction  and  fill-                           217
ing of balloons.-Generally
the  balloon  is pear-shaped.
It is made of a material impervious to hydrogen gas, often
of strips of taffeta sewed together, and  covered with a
varnish, composed of linseed
oil and caoutchouc, dissolved
in essence of turpentine, or                 t
of a tissue formed of a layer
of caoutchouc interposed be-              -
tween two layers of taffeta,
and called mackintosh.
To fill the balloon, A, fig. 217,
an aperture at its lower end is placed in communication, by means of a tube,
T, with vessels, t t, generating hydrogen (from  the action of dilute sulphuric
acid on iron). When the balloon is sufficiently filled, the aperture is closed.
Suspended by means of a net-work of ropes covering the whole apparatus, is a
boat formed of wicker-work, for the reception of the aeronauts, fig. 218. At the
upper part of the balloon is a valve, which the manager may open or shut at
21 *




218             THE THREE STATES OF MATTER.
pleasure by means of a cord. As illuminating gas can usually be procured more
easily than hydrogen, it is frequently used by aeronauts; but being at least seven
times more dense than pure hydrogen, the balloon requires to be of a correspondingly larger size, in order to obtain the same ascensional force.
218                                219
_:-en~ —e
The balloon must not be completely filled, for the atmospheric pres.
sure diminishing upwards, the gas in the interior will expand in a like
ratio, and tend to burst the balloon. A number of fatal accidents have
taken place from this cause.
When the aeronaut wishes to descend, he pulls the cord which opens
the valve in the upper part of the balloon, and thus the hydrogen
escapes, and the balloon comes down. If he wishes to ascend, he
throws out bags of sand which he has taken up with him, and the balloon, becoming thus lighter, rises to a correspondingly greater height.
Parachute.-Aeronauts often abandon their balloons, and descend
in a parachute.  This apparatus is composed of strong cloth, and when
extended, has the appearance of an umbrella, fig. 219, with this difference, that the whale-bones are replaced by cords, sustaining a small
boat, in which the aeronaut places himself. There is a small chimney,
or hole, in the top of the parachute, in order to allow the air, which
would accumulate, to escape regularly, otherwise it would escape fitfully
by the sides, throwing the apparatus violently around, to the imminent
peril of its occupants.
IV. COMPRESSIBILITY OF GASES.
274. Mariotte's law.-Boyle and Mariotte discovered the law of
the compression of gases, which is as follows:



OF GASES.                         219
At the same temperature, the volume occupied by the same bulk of air,
ts in inverse ratio to the pressure which it supports. From which it
follows, that the density and tension of a gas are proportional to the
pressure.
Let V and V' represent the volume of a gas at different pressures
P and P', and D and D' the different densities. Then
P              V
V: V =       P: P, whence V =-  V P  and P'  P.
D: D  = P: P', whence D' = D P- and P  - PD.
Experimental verification of Mariotte's Law.
In order to verify this law, the apparatus called Mariotte's tube is
employed. To an upright support of wood is attached a bent tube, fig.
220, whose two vertical branches are unequal in         220
length. The longer limb is open at the top, and furnished with a scale which indi-        219
cates heights; the shorter is closed                 J 
at the top, and is divided into
parts of equal capacity. Mercury 
is poured into the tube so that the 
level of the liquid in the two
branches is found on the same
horizontal line, la. The air in
the shorter limb then occupies a
definite volume, indicated by the       3                h/
graduation. If more mercury is 
added, until the measured volume
of air is reduced one-half, as from 
ten to five, occupying only the
space above 1, and we now measure the difference of level between
the two surfaces of mercury, viz.:
a/ h, we shall find that it is the
same as the height of the barometric column. That is, the pressure of the column of mercury in
the Mariotte's tube is equivalent
to one atmosphere; adding this:             __
pressure to that which the atmosphere exerts on the mercury, we
have the air subjected to double of its usual pressure, and it is, conse



220               TILE TIREE  STATES OF MATTER.
quently, reduced in volume one-half. If we subject it to a pressure ot
three atmospheres it will be reduced to one-third; of four atmospheres,
to one-fourth of its original bulk, &c. By this law, at a pressure of 814
atmospheres air would become as dense as water.
The law of Mariotte may also be verified for pressures less than one atmosphere, by using a barometer tube, about two-thirds filled with mercury, and
inverted in the deep cistern, fig. 221, filled with mercury. Sinking the tube to
such a depth that the level of the mercury within and without is the same; the
contained air is under the pressure of one atmosphere, and occupies a known
volume. If the tube is now raised until by a diminution of pressure the given
volume of air is doubled, it will be found that the length of the mercurial column
in the tube is half that in the barometer: that is, the air under a pressure of onehalf an atmosphere has doubled its volume. The volume here, as in the other
case, is in inverse ratio to the pressure.
275. Experiments of Despretz.-Mariotte's law  was generally
received as correct, until Despretz, not doubting its correctness, so fr
as air was concerned, undertook to test this law in its application to
other gases.  For this purpose he filled several tubes of the   222
same height with different gases, and inverted them in a vessel
of mercury, placing behind them  a graduated scale, as shown
in fig. 222.  This apparatus was then introduced into a glass
cylinder filled with water, and subjected to pressure by means 
of a forcing-pump.
As the pressure increased, the height of the mercury in the
different tubes varied, as shown in the figure, and this variation
increased with the pressure.  Carbonic acid, sulphuretted hydrogen, ammonia, and cyanogen were compressed more, and 
hydrogen less, than common air.  These experiments, in which
the probability of error is extremely small, show that each gas
has a special law of compressibility, differing more or less from the law
announced by Mariotte.
A series of very accurate experiments, subsequently conducted by Pouillet,
by a different method, confirmed the results of Despretz, who had announced
the unequal compressibility of different gases.
076. Experiments of Regnault.*-Mariotte's law has been subjected
to the test of very careful and repeated experiments by Dulong, Arago, and
others. But the most complete and reliable experiments are those conducted by
Regnault.
Regnault kept the column of gas upon which he was experimenting at a uniform temperature by a stream of cold water flowing through a cylinder which surrounded the tube of condensed air or other gas. The utmost precaution was taken
to remove every trace of moisture from the gases employed. The temperature
and atmospheric pressure were carefully noted at every experiment, and due
* Memoires de l'Academie des Sciences, Tom. XXI., p. 329.




OF GASES.                               221
allowauce made for their changes.  The temperatuie of the column of mercury
employed to measure the pressure was noted, and the height of the column corrected accordingly. Finally the condensation of the mercurial column due to
its own weight was also considered, and every possible precaution was observed
to secure the utmost accuracy in the experiments.
Results obtained by Regnault.
The following table gives some of the principal results obtained by Regnault.
Let P represent the pressure, when any gas occupies a volume V, and P' the
pressure when the volume of the same gas is V'. If Mariotte's law were strictly
PV
correct, we should have P V equal to P' V', or  -- ought to be equal to unity.
Air.            Nitrogen.         Carbonic Acid.       Hydrogen.
p  I pPI          t p  P    I p X             PV    P  ~ p
PV                 PV                 P'V                 PV. m.               m. m.              m. m.              m. m.
73872  1-001414   753-46 1-0000881 764-03 1-007597         " 
4209-48 1-002765  4953-92 1-002952  3186-13 1-028698  2211-18 0-998584
817748'1-003253  8628.54 1-0047681 9351-72 1-045625  284518 0-996121
933641 1006366 10981-42 1-0064561 9619-97 1155865  917650 0992933
PV
We here see that in the four gases examined, the ratio --    was found very
nearly equal to unity, showing that though Mariotte's law is not absolutely true,
it is sufficiently accurate for most purposes.
In the case of air, nitrogen, and carbonic acid, the compressibility augments
more rapidly than the increase of pressure, while in the case of hydrogen the
compressibility diminishes. It has also been ascertained that the rate of compressibility for any gas varies with the temperature. For example, carbonic
acid at 2120 F. agrees almost exactly with Mariotte's law.
277. General conclusions on the compressibility of gases.From a careful consideration of all the experiments upon the condensation of gases, it seems reasonable to conclude that:1st. There is some temperature, differing for different gases, at which
the compressibility of gases corresponds with Mariotte's law. That at
higher temperatures the compressibility diminishes, and at lower temperatures the compressibility increases.
2d. Almost all gases, by a certain amount of pressure, are liquefied,
and it is found that their compressibility increases very rapidly near the
point of liquefaction.
Although these conclusions are based upon the analogies of science,
and apparently indicated by experiments, yet further observations are
required for their confirmation.




222               TIE THREE  STATES OF MATTER.
V. INSTRUMENTS DEPENDING ON TI1E PROPERTIES OF GASES.
278. Manometers.-Manometers are instruments designed to measure the tension of gases or vapors above the atmospheric           223
pressure.  The unit of measurement which has been chosen u
for these instruments is the pressure of the atmosphere, 
which, at the level of the sea, is (261) equal to about 15 lbs. 
to the square inch, and therefore a pressure of two or of three 
atmospheres signifies a pressure of 30 lbs. or of 45 lbs. a 
Manometers are of very various construction,.two of which
will be mentioned, namely:- 
279. 1st. Manometer with free air.-This consists of
a glass tube, B D, fig. 223, open at both ends, placed in a
cistern of mercury, to which it is cemented.  The cistern is 
connected with an iron tube AC. By this tube the pressure
of the fluid is transmitted to the mercury. The gases whose
tension we wish to find, being often of a temperature sufficiently high to melt the cement attached to the apparatus, 
the tube A C is filled with water, which receives the pres- l
sure, direct, and transmits it to the mercury.                       -^
In order to graduate this instrument, A being      224
open to the atmosphere, that point where the
mercury rests in the tube is marked 1 (one atmosphere). At distances of thirty inches, the numbers 2, 3, &c., are marked, which indicate the   io
number of atmospheres, for it will be remembered, 
that a column of mercury thirty inches in height 
represents the atmospheric pressure. The appa- 
ratus being placed in connection with a steam- 
boiler, we ascertain the pressure to which it is
subjected by the height to which the mercury
rises in B D; if to 2-5, the pressure is 2-5 atmospheres, or 37I lbs. to the square inch.         2
280.  2d. Manometer   with   compressed air.-This form of the instrument 
consists of a glass tube filled with dry air, 
placed in a cistern of mercury, to which it    l
is cemented. This by a lateral tube, A, fig.
224, communicates with the vessel contain-                 A
ing the elastic fluid to be gauged.                              c
In order to graduate the manometer, such a 0o       0 
quantity of air is placed in the tube, that when A 
communicates with the atmosphere, the level of the mercury is the same in the
tube as in the cistern. At this point, therefore, 1 is marked upon the scale.
Following Mariotte's law, it might be supposed that we should mark for two




OF GASES.                                223
atmospheres, at a point in the middle of the tube, but when the column of air is
reduced half, the tension of two atmospheres is increased by the weight of the
column of mercury raised in the tube, and therefore the middle point of the tube
would represent a pressure greater than two atmospheres. The true position for
the second mark is at a point a little below the middle of the tube, where the
clastic force of the compressed air, added to the weight of the column of mercury, is equal to two atmospheres.
The true position of the points, indicating 3, 4, &c., atmospheres, is determined
on the scale of the manometer by calculation. This is not a very desirable form
of manometer, because the volume of air growing smaller, the divisions must
continually diminish in size, and therefore, even considerable variations of pressure are not easily observed in the upper portion.
Bourdou's metallic barometer, described in  1 163, is much used as a
manometer or gauge for steam-boilers.  It is sometimes called Ashcroft's gauge, and is the best instrument in use for the purpose.
[For the diffusion, effusion, and transmission of gases, the mixture
of gases and liquids, and the absorption of gases, see the Author's
" Chemistry."]
281. Bellows.-The most common instrument for producing a current of air is the ordinary bel-                       225
lows, fig. 225, consisting of two
leaves of wood united by leatler,
and terminating in a metallic
tube t.   A valve s is placed in
the  lower  leaf, opening  up-                 S
wards.                                           s
When the leaves are pressed jogctler, the valve s closes, and tie (mctailed
air escapes through t. But when the                      226
leaves are separated, air rushes in
through the valve and also through
the tube, through which last it is again
ejected upon pressing the leaves to-               p
gether.
Bellows with a continuous
blast.-In the ordinary bellows, 
the blast of air is intermittent.
Where a continuous jet is wanted,
as at a smith's forge, a double
blast bellows is used, fig. 226. 
This consists of three pieces of wood,
of which one, D, is immovable, the
others are connected with  this byP                            J 
means of leather. The apparatus is
divided into two compartments, U V. The blast-pipe communicates with tho one
above; in the lower one, air is introduced through the lowur valve, S.  When




224               THE TIIREE STATES OF MATTER.
the lever is drawn down, as shown by the arrow, the valve S closes, and the
air being compressed, passes into U through the valves r r, raising C B, and partially escaping through the tube. With the reverse motion (accelerated by the
weight P), the valves r r close, and the exterior air enters V by the valve S.
During this time, the upper weight, P', causes C B to descend, and thus there is
continually an escape of air by the blast-pipe. The weight may be replaced by
a spring.
282. Furnace blowers.-In blast, or high furnaces, blowing machines are employed, by means of which a large volume of air is forced
into the fire; these machines are of very various construction.
Fig. 227 represents one of them; it consists of a cast iron cylinder, containing
a piston, p, of which the rod, t, passes, air tight, through a packing-box, d;
there are four valves, two of which                 227
a a' opening inwards, draw in air;
the air passes out through the
valves b b' which open outwards.
The piston is set in motion by
a steam-engine or water-wheel;
during its descent the valves a and 
b' only are opened; through the
first, air is drawn in, through the
second, it is expelled; during the
ascent of the piston, the other
valves a' and b, act in the same
manner. The expired and com- 
pressed air is received into the 
tube g h, through which it is conveyed to the furnace. In the great 
blowing machines at Scranton, Pa. 
the blast is used under a pressure                            aof five pounds to the square inch,1
driven by two engines of 1200          ~  
horse power each. 
283. Escape  of compressed  gases.-When  a compressed  gas
escapes from  an opening in a thin wall, the velocity of its escape
depends on the difference of the interior and exterior pressures, and
on the density of the gas passing out. It has been proved,
1. That with the same gas at the same temperature, the velocity of flow
into a vacuum is the same at any pressure.
That is, if we had a vessel filled with air, compressed at 1, 2, 3, or 1000 atmospheres, and allowed it to escape by a small orifice, the velocity of its flow would
be the same during the whole time of its discharge. But the quantity of the
gas that could escape in the same time would vary, being evidently proportional
to the density of the gas, that is, to the pressure. If the escape took place in a
gas, as air, instead of in a vacuum, the velocity is then proportional to the difference between the elastic force of the interior and exterior air.
2. The velocity of the escape of gases into a vacuum is in inverse ratio
to the square root of their densities.




OF GASES.                            225
Where the gas escapes through long tubes instead of through orifices in
a thin wall, the velocity is very much diminished, because of the friction,
and is less in proportion as the tube is longer and its diameter smaller.
284. Pneumatic  ink-bottle.-In the pneumatic ink-bottle, fig.
228, the ink in the tube c is kept constantly at nearly the same level.
By inclining the bottle it may be filled as               228
seen in A.  The ink in A tends to force itself   A
in the tube C, but is opposed by the atmo-                        c
spheric pressure, which is much greater than
the pressure of the column of ink in A.  As
the ink in C is consumed, its surface, falling,
will allow a small bubble of air to enter A,
where it will exert an elastic pressure, and cause the ink in C to rise a
little higher. This effect will be continually repeated until the bottle
is emptied of ink. Bird-cage fountains are constructed on a similar
principle.
285. The syphon.-The syphon used for decanting liquids, depends
for its operation on the principle of atmospheric pressure.  It consists
of a bent tube, b bV, fig. 229, having one of its arms longer than the other.
It may be filled by turning it over, and pour-    229           230
ing the liquid in, or by immersing the shorter
arm  in a vesssel of water, and applying the            l            (?
mouth at b/; upon exhausting the air, the
water will be forced up by atmospheric pressure, to supply the place of the air withdrawni,                    ^
and there will then be a continual discharge
until the vessel is emptied.                   b
The two branches being filled with liquid, the
pressures exerted at the points b and n will be
equal, for they are on the same level; but the pressure exerted at b' will be greater, because of the
column n b', and the liquid will escape from this    b
long branch because of this excess of pressure, and will draw after it the liquid
in the shorter branch; if the end of this be immersed, there will be a continual
discharge as long as b is below the surface of the liquid, for the atmospheric
pressure will cause the liquid to ascend, to supply the place of that which is
passing out; otherwise there would be a vacuum produced.
It is evident that water could not be raised by means of a syphon
more than thirty-four feet: for a column of water of that height is in
equilibrium with the pressure of the atmosphere (261). The velocity
of the flow from a syphon will be the same as if the liquid fell freely
from a height equal to the distance between the level of the liquid in
the vessel and the end of the long arm. To avoid the necessity of filling
22




226               TIIE THREE STATES OF MATTER.
a syphon by pouring, the form represented in fig. 230 is employed. To
use this instrument, the open end, b/, of the longer limb is closed by the
finger, while a partial vacuum, created by sucking at the small ascending
tube, t a, occasions the liquid to pass over as in the ordinary syphon.
Intermittent syphon.  Tantalus' vase.-Fig. 231 consists of a
vessel, A, containing a syphon, of which one of the branches opens below the
bottom of the vessel; the other is curved. When water is poured into the vessel
A, it will rise to the same height in the interior  2:1          232
of the tube as it attains outside. The tube will
not act as a syphon until the vessel is filled to                  ~
the height 1, but when it reaches that point,      a''
the water will flow through a into the lon
branch, filling it completely, and the syphun
being now supplied, will discharge water until
the vessel is emptied.  The syphon may be 
concealed in a little image, fig. 232, B, repr  e- i
senting Tantalus, so that just before the water 
touches his lips the syphon is filled, and the
vessel is emptied.
286. Intermittent springs.-There exist in nature intermittent
springs, the water flowing regularly for a time, and then suddenly
ceasing.  Ill these springs the opening,                 234
as at a, fig. 233, communicates with a
subterranean  cavity, C, by means of a
channel, a n b, which has the form of a
syphon.  This cavity is gradually filled,               -
until at last the water attains the level
n n, when  the  syphon  is filled, and 
the water escapes.  If the syphon dis233  
s                        ~~~~ —-I                S~ A
charges the water faster than it flows into C, after a time its level would




OF GASES.                              227
be lowered to b; air would then rush in by the syphon, the flow of water
would cease, and would not recommence until it had again attained the
level n n.
Intermittent fountain.-The intermittent fountain consists of a
vessel of glass, C, fig. 234, whose aperture for the admission of water
is hermetically sealed by an accurately-ground stopper.
A glass tube A, passes through the vessel C, its upper end terminating above
the surface of the liquid; its lower end rests in a copper cistern, B, which has a
small aperture for the escape of water.  The globe being partially filled, the
water escapes through the capillary orifices of the tube at D, in consequence of
the atmospheric pressure transmitted through the lower end of the tube A.
When the end of this tube becomes covered with water, which after a time happens (because the orifice in the cistern B does not allow so great a flow of water
as can escape from the tubes at D), the exterior air cannot enter the globe, and
in consequence the flow ceases. The water continuing to escape from D, in a
little time the surface is so much lowered, that the end of the tube, A, is out of
water; the air then entering the globe, the escape recommences, and so continues
at intervals until C is emptied of water.
287. Air-pump.-The air-pump, designed to produce a vacuum  in
235
any confined space, was invented by Otto v. Guericke, burgomaster of
Magdeburg, in 1650.  Fig. 235 exhibits a very excellent form of the




228              THE THREE STATES OF MATTER.
air-pump, manufactured by Ritchie of Boston, usually called the Leslie
form of air-pump. The essential part of the air-pump is the cylinder
shown in section in fig. 236. This cylinder communicates with the bell
glass, by means of a tube, shown in fig. 235, and with the external air by
means of the tube g h (fig. 236). There are three         236
valves, a, b, and c, all opening upward.  The
piston-rod passes through a packing-box, d, in
which it moves air-tight, and the power is applied by means of a lever, as shown in fig. 235.
Suppose the piston to be standing at the bottom of the cylinder, when we depress the lever,
the air from  the  receiver expands, rushing
through the valve, a, into the empty space
formed in the bottom of the cylinder, while the
air above the piston is forced out through the
valve c and the tube g h. With the reverse
motion the valves a and c close, excluding the
external air from the cylinder, and preventing                    
the return of air from the cylinder to the receiver.
At the same time the piston-valve, b, opens and  
allows the air below the piston to pass through into the upper part of
the cylinder.  When the piston rises again, this new volume of air
which has passed above the piston is forced out through the valve c, into
the external atmosphere, while another portion of rarefied air from the
receiver expands into the cylinder below the piston, to pass upward and
be forced out through the valve c at the next stroke of the piston; and
so on continuously, as long as the rarefied air in the receiver and cylinder
has sufficient tension to open the valves. At each stroke of the piston
the air undergoes renewed rarefaction until the amount remaining in a
good instrument is about one-thousandth of the original quantity, and
the space within the receiver may be regarded as a vacuum.  The
pump here figured is furnished with a barometric manometer, seen in
the left of fig. 235, by which the degree of exhaustion is directly indicated. The efficiency of the air-pump depends in a great measure upon
the valves, which are best made of oiled silk.
The construction of the upper valve, c, as made by Ritchie, is shown in fig.
237. The disk of oiled sigk, i, is kept in place by the pin  237
e, and the whole is protected by the dome-shaped covering
c. The tube g h (fig. 236) discharges the air, and the oil
which escapes with it is collected in a reservoir placed
below the pump.
An air-pump with two cylinders is commonly used in France, the




OF GASES.                              29
pistons of which are alternately raised and depressed by a rack kand
pinion motion.
Degree of Exhaustion.-It is plain, on a moment's reflection, that by
mechanical means alone, it is impossible to produce a perfect vacuum. There
must always remain a certain volume of air, inferior in tension to the gravity
and friction of the pump valves. By employing an atmosphere of dry hydrogen
to rinse out the residue of common air from an exhausted receiver, an approach
to a perfect vacuum is made, inversely as the density of the two gases. Also
by using carbonic acid for the same end, and absorbing the residue of this gas
by dry quick-lime previously placed on the pump plate, a perfect vacuum may
be produced; but by chemical and not by mechanical means.
288. Compressing machine. —This machine is used to compress
the air or any other gas; it                       238
is constructed like the airpump, the  only  difference
being that its valves open in
a  contrary  direction, viz.:
downwards.
Fig. 238 shows a very neat
form of the condensing pump
as constructed by Ritchie, to
illustrate the Mariottian law
(275) and to liquefy gases.
289.   Water- pumps.- -li
Pumps  are  machines  designed to elevate liquids above their former level.  They are of two
classes: 1st, those acting by atmospheric pressure; 2d, those which
act independent of such pressure.  They are commonly called either
suction, or forcing pumps, or both united.
290. Suction-pumps.-The suction-pump, fig. 239, is composed of
a tube, A, whose lower end is immersed in the water to be elevated.
This is attached to the body of the pump, C, which contains a piston
furnished with a valve, r, opening upward.  The upper extremity of
the tube A, also contains a valve, o, opening in the same direction.
When the piston is elevated from the lower part of the pump by working the
handle, L, the valve r closes, and a partial vacuum is produced, but the elastic
force of the air in A causes the valve o to open, and part of the air thus
passes into C. The air in the tube is thus rarefied, and the water rushes up
to such a height, that the weight of the column of water raised, added to the
elasticity of the interior air, keep it in equilibrium with the atmospheric pressure. When the piston descends, the valve o closes by its weight, and prevents the return cf the air from the body of the pump, C, into the tube A.
The compressed air opens the valve r, and thus escapes into the atmosphere
through B. After a number of strokes of the piston, fewer as the capacity of
the tube a is less, the water will be elevated above the lower valve; now when
22*




230              THE THREE STATES OF MATTER.
the piston is lowered, the valve r will open and the water pass above it. Upon
elevating the piston, r closes, and the water is    239
raised in B, and escapes through the spout S.
As in this and the following pump, l
the water is elevated to the top of the  f
tube by means of atmospheric pressure,     B        r
it is evident, that even in the most per-  
fectly constructed pumps, the distance  
from the level of the water to the top           L                 B
of the pump must not exceed thirty-  al
four feet (261), but those of ordinary 
construction  contain defects, so that
generally we do not gain a greater 
height than twenty-six or twenty-eight                     I
feet. But after the water has passed  l,
above the piston, the height to which we 
may elevate it, is limited only by the 
power applied at the piston; for it is
the ascensional force of this which ele-   -_
vates the water.
291. Suction and lifting pump.- 
Sometimes the water raised above the 
piston, instead of passing upwards in                      -
the tube in which the piston works, rises by a lateral ascensional
tube, S, furnished with a valve which prevents            241
the return of the water, as is shown in a, r, S,
fig. 239.
That the rising of the water      240
in the tube is due to the atmospheric pressure, may be
demonstrated by the apparatus, fig. 240.' After forming
a vacuum  in the  reservoir           eP            [        7in
which contains the vessel of
water, the liquid will not rise
in the tube when the piston
in the pump, P, is raised, but
upon admitting the air it is
ilpidly elevated, as usual.
292. Forcing-pump. —In
the forcing-pump, the piston
has no valve. The lower part of the cylinder in which it works is




OF GASES.                            231
placed in the water to be elevated, so that the valve r, fig. 241, which
opens upward, is always immersed.  The ascending tube a b contains
a valve, S, also opening upwards, and an air chamber, mn n.
When the piston is raised, S is closed, and water is introduced by the open
valve r; upon the descent of the piston, r closes, and the water is forced into
the ascending tube, a b. The reservoir, m n, filled with air, is designed to render the jet of water continuous. When the water is forced by the piston into
the tube, the air is compressed in mo n; reacting afterwards by its elasticity, it
continues to drive the water into the upper part of the tube, after S is closed,
and while the piston Is rising.
It is found necessary to have the air-chamber twenty-three times the
capacity of the body of the pump, in order to render the jet continuous.
293. Rotary pump.-The rotary pump is a mechanical contrivance
for raising water by a continuous rotary movement. Fig. 242 represents one of the most successful of these pumps (Cary's). Within a fixed
cylinder is included a mova-                     242
ble drum, B, attached to the
axis, A, and moving with it.
The heart-shaped cam  surrounding A, is immovable. 
The revolution of B causes
the plates or pistons CG C to
move in and out, in obedi- 
ence to the form of the cam.
The water enters and is re-,1
moved  from  the  chamber
through the ports or valves,
L and M; the directions are
indicated by the arrows.
The cam is so placed that each valve is in succession forced back into its
seat when opposite E, while at the same time the other valve is driven fully
into the cavity of the chamber; thus forcing before it the water already there,
into the exit pipe H, and drawing after it, through the suction pipe F, the
stream of supply. When the pump is set in action, the suction-pipe is gradually
exhausted of air, in which, consequently, the water ascends, and being thrown
into the cylinder, it is there carried around by the plates C C, in the manner just
described.
This is a form of pump often employed in the steam fire-engines now
coming into general use.
294. Fire-engine.-In order to obtain a continuous and powerful
jet of water from fire-engines, they are usually constructed with two
forcing-pumps, which are alternately discharging water into a common
air-chamber.  The pistons are moved by brakes, having an oscillating
motion.  The water from  both pumps, forced into the air-chamber,




232              THE THREE STATES OF MATTER.
escapes through a long leathern hose, terminated by' a metal tube,
which serves to direct the jet.
295. Hiero's fountain.-In this apparatus we also obtain a jet of
water by means of air, compressed in this case by a column of water.
A common form of this apparatus is repre-               243
sented by fig. 243. 
It consists of a metallic cistern and two globes       i
of glass. The cistern, D, communicates with the
lower part of the globe N, by the tube B; a second       il
tube, A, joins the globes, ending in the upper part
of both; M  is partially filled with water; and
lastly, a third tube passes through the cistern, and
terminates at the bottom of M. The upper extremity      -
of this tube has a small orifice, from which the jet
of water issues.            
Upon pouring water into the cistern D, the          ~aM
liquid descends to N, by the tube B, consequently the water in the lower globe, N, supports, besides the atmospheric pressure, the
pressure of the column of water in the tube.           A    B
This pressure is transmitted to the air in the
globe, M, which, reacting on the water, forces
it out through the jet, as seen in the figure.
If there was no friction, and no resistance
from  the air, the water would spout to a
height equal to the difference in level of the
water in the two globes.  
296. Hydraulic ram.-In the hydraulic 
ram, the momentum  of a part of the fluid in
motion, is effective in raising another portion.
A simple form  of this apparatus is seen in
fig. 244. The water descends from the spring    -
or brook, A, through the pipe B, near the end of which is an air-chamber, D, and rising main,                       244
F.  The orifice at the ex-     F
treme end of B, is opened
and closed by a valve, E,  I 
opening downwards.
When the valve E is open,
the water flows through B, E                      R 
until the current becomes
sufficiently rapid to raise the
valve E, and thus to close
the orifice. The water in B having its motion thus suddenly checked, exerts a




OF GASES.                            233
great pressure, and having raised the valve C, will rush into the air-vessel D,
where it compresses the air. The compressed air in D, because of its elasticity,
causes the water to rise in the pipe F, until the water in A B is brought to rest.
When this takes place, the pressure is again insufficient to sustain the weight
of the valve E, which opens (descends), the            245
water in B is again put in motion, and the
same series of effects ensue as have already been
described.
The hydraulic ram, when well constructed, is capable of utilizing about 60;
per cent. of the moving power. 
297. Chain-pump.-The chain-pump 
acts independent of atmospheric pressure.                         l
It consists of a.ylinder, fig. 245, whose
lower end is immersed in the water of the       A               I
reservoir B, and whose upper part enters 
into the bottom of a cistern, C, into which
the water is to be raised. An endless
chain is carried around the wheels above
and below, and is furnished, at equal distances, with  circular plates, which fit                      ~
closely into the cylinder.  As the wheel                
is revolved by means of power applied 
usually by a winch, the circular plates i
successively enter the cylinder and carry
the water up before them into the cistern, 
from which it passes out by a spout. 
298. Archimedes' screw.-This machine is said to have been invented by Archimades in Egypt, to                   246
aid the inhabitants in clearing the 
land from the periodical overflowings'j   /  I
of the Nile.  The instrument varies 
in its form, according to the manner          1
and purposes of its application.  To
render the principle upon which it',           
works intelligible, let us suppose a 
tube bent in the form  of a cork-                              c
s3rew, and inclined in the manner
shown in fig. 246.  If a ball be                          \
placed in A, it will fall to B, and
there remain at rest; if the screw 
be now turned so that the mouth A is placed in its lowest position,
the point B, during such a motion, will ascend, and will assume the




234              TIIE THREE STATES OF MATTER.
highest position it can have. The ball will then fall to C; by continuing the revolution of the screw, the ball will ascend in the tube, and
finally will be discharged from  the upper mouth.  The same would
happen with a portion of liquid. If the lower extremity of the screw
was immersed in a reservoir of liquid, it would gradually be carried
247
along the spiral as the screw was turned, to any height to which the
screw might extend. In practice, the screw is more commonly formed
of a cylinder, to the walls of which is attached a spiral thread, as
shown in fig. 247. Besides liquids, these machines are used for elevating ores in mines, or grain in breweries, &c. They are commonly
used at an inclination of about 45~, but may be used at 60~; revolving
100 to 200 times a minute.
Problems on Pneumatics.
Atmospheric Pressure.
134. What weight could be lifted by the apparatus shown in fig. 202, if the
mouth of the jar is 5 inches in diameter, and the air within the jar is exhausted,
so as to leave it but one hundredth part its normal density?
135. What force would be required to separate two Magdeburg hemispheres,
having an internal diameter of ten inches, if a perfect vacuum were formed
within?
136. A mass of metal, whose specific gravity is 11-35, weighs in a vacuum
735 grains; how much will its weight be diminished if weighed in the open air?'*' In these problems the barometer is supposed to stand at 30 inches, and the
thermometer at the freezing point.




OF GASES.                                235
137. A mass of iron (Sp. Gr. 78S) weighed in air with brass weights (Sp. Gr.
8.3) 460 grains, what would it weigh in a vacuum?
138. A glass globe, from which the air has been exhausted, weighs 254-735
grammes; when full of air, it weighs 5422-737 grammes; when full of another
gas, 651-175 grammes; what is the capacity of the globe, and what is the specific
gravity of the gas?
Barometer and Balloons.
139. To what height will sea water (Sp. Gr. =  1-026) rise in a Torricellian
tube, when the barometer stands at 28'75 inches?
140. When the mercury barometer stands at 30 inches, what must be the
length of a water barometer inclined to the horizon at an angle of 30~?
141. What would be the height of a sulphuric acid barometer (Sp. Gr. sulphuric acid, 1-85) when the mercurial barometer stands 29-35 inches?
142. Measurement of the height of the highest peak of the Smoky Mountain,
(Lat. 36~ N.) in North Carolina, September 8, 1859, by Prof. A. Guyot. By
observation at 8 A. M.
Barometer. Temperature Temperature
Eng.. inches. of Barometer.   of air.
Lower station, R. Collins' house, 4 ft. above
ground,........ h   27-862, T =  660~4, t =  65~'1.
Upper Station, Smoky Dome, 4 feet below
summit,........... A'.                   - 23-963, T' =  510~, t =  510~4.
Mr. Collins' house being 2500-2 feet above the ocean.
Calculate from these data the height of Smoky Dome above the ocean.
Altitude calculated by Prof. Guyot, 6655-85 feet.
143. What is the ascensional force of a spherical balloon, 30 feet in diameter,
filled with common illuminating gas (Sp. Gr. -485), the weight of the balloon and
ear attached being 200 lbs.?  What if it were two-thirds filled with hydrogen
(Sp. Gr. of hydrogen, 0-069)?
144. A balloon entirely filled with illuminating gas (Sp. Gr. -500), is so ballasted that it rises to an elevation where the mercury stands at 15 inches. Suppose
one-half the gas is now liberated, will the balloon rise or fall? and what amount
of ballast should be put in, or thrown out, to cause the balloon to remain stationary, at the same elevation as before any gas was liberated?
Mariotte's Law.  (Regarded as ilnvariable.)
145. What proportion of a tube, 34 feet high, can be filled with water, the
contained air being assumed to be compressed at the bottom of the tube?
146. A faulty barometer (containing air) indicated 29-2 and 30 inches, when
the indications of a correct instrument were 29-4 and 30-3 inches respectively;
find the length of tube which the air in the column would fill under the pressure
of 30 inches?
147. A glass globe, 10 c. m. in diameter, hermetically sealed, weighs 45-120
gram. when the barometer stands at 74-5 c. m. What would it weigh if the
barometer stood at 76 c. m.?
148. A glass globe hermetically sealed, 30 c. m. in diameter, suspended to one
arm of the balance, is poised by 320-422 gram. in brass weights, when the barometer stands at 76-21 c. m. After a time, it is found to have lost in weight
0-022 gram. What is now the height of the barometer, supposing the temperature not to have changed?




236              THE THRE]E  STATES OF MATTIM.
CHAPTER V.
OF UNDULATIONS.
1. Theory of Undulations.
299. Origin of undulations.-By the operation of certain forces,
the different parts of all bodies are, ordinarily, held in a state of equi
librium  or rest.  If the molecules of a body are disturbed by any
extraneous force, they will, after a certain interval, return to the state
of repose. This return is effected by the particles approaching the
position of equilibrium, and receding from it, alternately, until at
length the body, by the resistance of the medium in which it is placed,
and by other causes, is gradually brought to rest.  The alternate
movements thus produced, are variously expressed by the terms vibrations, oscillations, waves, or undulations, according to the state or form
of the body in which such movements occur, and the character of the
motions which are produced.
300. Progressive  undulations.-Undulatory movements are of
two kinds, progressive and stationary. In progressive undulations, the
particles which have been immediately excited by the disturbing cause,
communicate their motion to the particles next them, and as this movement of the particles is successive, the position they assume at any
particular moment during their motion, appears to advance from one
place to another.
This kind of undulation is observed in a cord made fast at one end, while
the other is smartly shaken up and      d         248
down; the portion of the cord nearest               o
the hand will assume the position in                                 e
fig. 248, I, mn d E O. Such a wave
does not continue stationary; the II m
moment it is formed, it advances
toward the other extremity of the                                   e
cord, II, on reaching which, III, II'"- -"
an inverted curve is produced, IV,
and the wave returns, V, to the I               m                   e
position from which it started, the
relative position of the elevation         -
and depression being reversed. This V m --. ---             e
alternate movement may be repeated a number of times before the cord comes
to rest. These are sometimes called waves of translation.




OF UNDULATIONS.                           237
301. Mechanical illustration  of undulations.-In fig. 249 is
shown Powell's apparatus for illustrating progressive undulations.  A
series of balls are so mounted                     249
upon  metallic rods that they
have freedom of motion only in
a vertical direction. On a shaft
turned by a crank, shown in the
lower part of the figure, are
placed  a  series  of  eccentric 
wheels (one under each rod) so
arranged as to raise the rods one
after the other.  When one rod
is rising another is falling, and 
the wave appears to travel from 
one end of the series to the other.
As soon as one wave disappears
another is formed, and  these
waves succeed each other like
the undulations of a cord.
302. Stationary undulations.-Undulations are termed stationary
when all parts of the body assume and complete their motion at the
same time.
Thus, when a cord stretched between A B, fig. 250, is drawn at the middle
from its rectilinear position, it ultimately recovers its original position, after
performing a series of vibrations, in which all parts of the cord participate.
303. Isochronous vibrations.-Those vibrations that perform their
journey on either side of their normal position in equal times, are
terrmed isochronous (from etoq, equal, and Zpopoq, time).
The movements of a pendulum furnish a perfect illustration of such vibrations (78).
304. Phases of undulations.-In  every complete oscillation, or
perfect wave, the following parts may be recognised.  The curve
250                                   251
e
___ - _ - = _ = - - _ = _ = _ _   a   I    \b?    c
a ----. 2, is c d a w      T             b   
a e b d c, fig. 251, is called a wave. The part a e b, which rises above
the position of equilibrium, is called the phase of elevation of the wave,
e being the point of greatest elevation; the curve b d c is called the
phase of depression of the wave, the point d being that of greatest
23




238             THE THRBE STATES OF MATTER.
depression.  The distance ef, of the highest point above the position
of equilibrium, is called the height of the wave, and in like manner the
distance g d, of the lowest point below the position of equilibrium, is
called the depth of the wave. The distance a c, between the beginning
of the elevation and end of the depression, is called the length of thz
wave, the distance a b the length of the elevation, and b c that of
depression.
305. Nodal points.-When a body, as a string, is made to assume
a series of stationary vibrations, the points where the phases of elevation and depression intersect, are always at rest.
Let the cord stretched between A B, fig. 252, be temporarily fixed at the points
C and D, and the three parts be drawn at the same moment equally in contrary
directions, so that the cord will               252
assume the undulating form repre-                      D
sented in the figure; if now the   A      /'         _    _B
fixed points at C and D be removed,                      -..-~
no change will take place in the
vibratory motion of the cord; but as it continues to vibrate, the points C and
D, although free, will be in a state of rest.
Pieces of paper resting upon these points will be undisturbed, while,
if placed on the intermediate positions, they would be thrown off immediately. These are called nodal points (Latin, nodus, a knot).
Q 2. Undulations of Solids.
306. Solid bodies.-All solid bodies exhibit the phenomena of
vibration in various forms and degrees, varying in an infinite variety
of ways, according to the form of the body, and the manner   253
in which the force producing the vibration is applied.
307. Forms of vibration.-Bodies of a linear form,
as tense strings, fine wire, &c., are susceptible of three 
kinds of vibration, which are called (1st) the transverse,
(2d) the longitudinal, and (3d) the torsional vibrations.
A simple apparatus to exhibit these effects experimentally,  
contrived by Prof. August, is represented in fig. 253. It
consists of a spirally twisted wire, stretched from a frame 1f    A
by a weight. If the weight be raised to A, and then let
fall, it will advance and recede from  its normal position,
the wire performing a series of longitudinal vibrations.
Transverse vibrations are produced by confining the lower end of the
wire by a clamp.  The wire is then drawn from its position of equilibrium and suddenly let go. The vibrations which it then makes, shown
by the dotted lines, are transverse to the axis of the wire.  Torsional
vibrations are produced by turning the weight around its vertical axis;




OF UNDULATIONS.                            239
upon letting it go, the torsion, or twist of the wire, causes it to turn back,
its inertia carrying it beyond its position of equilibrium, until arrested
by the resistance of the wire, and these alternate twistings will continue
with a constantly decreasing energy, until gravity, and the molecular
forces of the solid, restore the equilibrium.
308. Vibration of cords.-Cords and wires, as is familiarly seen
in stringed instruments, have their elasticity developed by tension.
The transverse vibrations of a body are well illustrated by the simple
apparatus annexed.
Thus if the cord af, fig. 254, be drawn out in the middle to a c b, upon being
let go, its elasticity causes it to return             254
to its former position. This movement                   <
is effected with an accelerated velocity, ZI                _- ZI,I"b 
and is at its maximum when the cord has
reached the line of equilibrium a/b, con-              d
sequently it passes with a constantly decreasing velocity to a d b, where its
motion is nothing; it then returns to afb, and so continues.
One complete movement, (as from a c b to a d b,) is termed an oscillation or vibration, and the time occupied in performing it is called the
time of oscillation. The vibrations of tense strings are isochronous.
309. Laws of the vibration of cords.-Calculation and experiment have demonstrated, that the vibration of cords is in accordance
with the four following laws.
1. The tension being the same, the number of vibrations of a cord is in
inverse ratio to its length.
That is, if an extended cord, as of a violin, makes in a certain time a number
of vibrations, represented by 1, then, in order to make a number of vibrations,
represented respectively by 2, 3, 4, the cord must be i, i, I as long.
2. The tension being the same, the number of vibrations in cords of
the same material, is in the inverse ratio of their thickness or diameter.
That is, if we take two cords or wires of the same length, of copper or steel,
as those of a piano, one of which is twice the diameter of the other, and which
vibrate equal lengths, the small one will make, in the same time, twice as many
vibrations as the larger.
3. The number of vibrations of a cord is proportional to the square
root of the stretching weight.
That is, if we represent by I the number of vibrations made by a cord,
extended by a weight of 1, then the number of vibrations made by a similar cord
of the same length, in the same time, becomes respectively 2, 3, 4, &c., when the
weight is increased to 4, 9, 16, &c. Thus, if we would cause a given cord, as
of a violin, to vibrate with a four-fold velocity, it is necessary to strain it to
sixteen-fold the original tension.
4. All other things being equal, the number of vibrations of a cord is
inversely proportional to the square root of its density.




240              TIlE THREE STATES OF MATTER.
Thus, if we take a cord of copper which has a density of 9, and one of catgut, whose density is about 1, the number of vibrations of the last in the same
time will be three times that of the former.
It is evident that these laws apply only to homogeneous cords, anI
not to those cords which are covered with another material, as a hary
string of cat-gut, covered with metallic wire.
310. Vibrations of rods.-Rods, like cords, vibrate both in longi
tudinal and transverse directions. If they are fixed firmly by one of
their extremities, as in a vice, they will give, when set in motion, a
series of isochronous vibrations.
Elastic rods may, like strings, be divided by stationary undulations
into several vibrating parts. The nodal points may be ascertained by
placing upon the rods light rings of paper; these will be thrown off as
long as they rest upon any point except a node, but when they reach a
node, they will remain there unmoved.
The space between the free extremity and the first nodal point is equal to
half the length contained between two nodal points, but it vibrates with the
same velocity. Thus a, fig. 255, being the fixed,        255
and b the free end, the part between b and c is 
half the distance c c'. The nodal points may be           _b
rendered sensible by sand strewn upon the horizontal surface of the vibrating rod; the sand is seen to move to certain points,
where it remains stationary; these are the nodes.
Rods may also, like cords, vibrate longitudinally, and the nodal
points are formed in the same manner. It has been observed in elastic
rods of the same nature, that the number of longitudinal vibrations is
in the inverse ratio of their length, whatever may be their diameter
and the form of their transverse section.
A prismatic bar, vibrating longitudinally, undergoes a very considerable increase of length, which, in the state of repose, could not be
produced except by a very strong tension, while the vibratory movement
s obtained by a very feeble force.
The number of vibrations by torsion in rods, is in the inverse ratio
ef  their length, and is proportional to their thickness, the substance in,ll cases remaining the same.
311. Paths of vibration.-The  motion performed by vibrating
rods is often very complex.  This may be beautifully seen by the contrivance of Prof. Wheatstone, consisting of a polished bead fastened on
the extremity of an elastic rod, as of a knitting-needle, firmly fixed in
a board or vice.
Upon making the rod vibrate, the bead, by reflection, will produce a continuous line of light. It will be seen that the arc described is not circular, but the
rod appears to be impressed at the same time with two vibratory movements, at




OF UNDULATIONS.                           241
right angles to each other, and moves in a curve produced by the composition of
these forces.
312. Vibration of elastic plates.-Vibrations are readily excited
in elastic plates by the friction of a violin-bow or by blows. The plate
may be confined either at its centre                  256
or from one corner, in the vice, fig.
256, resting upon a cone of cork, c,
and pressed by the screw a, tipped
with cork.
In the vibration of plates, nodal   _lines will be formed, which do not 
participate in the movements of the
plane, but remain in a state of rest.                              \
313. Nodal lines.-These nodal
lines answer to the nodal points in
linear vibrations, and if we suppose
the plane to be made up of a series
of rods, these lines will answer to their nodal points. They run in
various directions across the vibrating surface, the contiguous ones
moving in contrary directions, dividing the planes into numerous por
tions in opposite phases of vibration.
This is shown in fig. 257, by the signs + and -, A B being the vibrating
plane. The dimensions of these internodes (vibrating portions), are regulated
in the same manner as those of vibrating rods.           257
The outside ones, a b, a b, are always half the                b 
size of those in the interior. The nodal lines  
vary in their number and position, according to    aI 
the form of the plates, their elasticity, the number of vibrations, the mode of vibrating, &c.   A
314. Determination of the position  "                              a
of the nodal lines.-The position of the         T                +
nodal lines may be determined by scatter-         b I          lb
ing sand or other fine material over the A  -.......
plate, and vibrating, as by  means of a 
violin-bow  drawn across the edge of the
plate; the grains of sand will remain upon the points which are at
rest, and which are therefore nodal points. Those which are upon
vibrating portions, will be thrown aside until, after a time, they will
settle quietly down upon the nodal lines.
It is observed that if lycopodium, or some other very light powder, is placed
upon the plates, it will accumulate on those parts which are in greatest vi;ration. Mr. Faraday proved that this phenomenon was due to small currents of
air produced during the vibration of the plate, and which drew the powder with
them; for in a vacuum, the powder of lycopodium is disposed, like sand, upon
28*




242               THIE THREE STATES OF MATTER.
the nodal lines, and for the same reason; if the plate covered with sand is
vibrated under water, the sand collects upon the most agitated portions of the
plate, because of the similar currents excited in the water by the vibrations.
315. Laws of the vibration of plates.-Observation has determined that the vibration of plates of the same substance, and having
the same degree of rigidity, are subject to the following laws:1. That the number of the vibrations is independent of the breadth of
the lamince.
2. It is proportional to their thickness.
3. The thickness being the same, it is in inverse ratio of the square of
their lengtlh.
316. Method of delineating nodal lines.-As these nodal lines
assume various a;nd complicated figures, difficult to delineate with
accuracy by common drawing, Savart replaced the sand by powdered
litmus, previously mixed with gum water, dried and pulverized to a
uniform size. Tie acoustic figures being produced with this powder, a
paper moistened with gum water was then gently pressed upon them,
thus giving an exact transfer.
This method gave great facilities for the comparison and study of these fugitive figures, so difficult to produce with perfect identity, and enabled the inventor
to determine the exact limits of the nodal lines and areas of unequal vibration.
258
a        b        c         d         e        f
317. Nodal figures.-Nodal (or acoustic) figures have always a great
symmetry of form, and                          259
their lines are generally 
as much more numerous                             -.
as the number of vibra —                  j,_.-                J, —tions is  greater.   The.,  ~'
same plate may furnish
an infinite variety of fig- I-J'i...
ures, which pass from one)  
to another in a continu- -\ \C
ous manner, and not by
sudden changes. Thus the'                        i       "'J.
figures a bc d ef, fig. 258,   (f'd.i^ 
pass into  one  another' -           L0S            O 
without intermission. 
Many hundred forms of nodal figures have been figured. Fig. 259 represents
a few of those obtained on square plates. Triangular and polygonal plates all




OF UNDULATIONS.                          243
give symmetrical figures, analogous to those obtained with square plates, as is
seen in fig. 260. With circular plates it is observed that the nodal lines distri260
A                 A
bute themselves in the direction of the diameter, dividing the circle into an
equal number of parts, or into more or less regular circular forms, having the
centre of the plate as their common centre, or in both of these forms combined.
Fig. 261 represents these different varieties of form.
261
_                 ///\  /\
318. Vibration of membranes.-The flexibility of membranes
does not permit us to vibrate them  unless they are stretched as in a
drum. They present modes of                       262
vibration which have much ana-  _
logy to those of solid plates,                 -- 
vibrating either by concussion,. \  
as in the drum, or by the influ- 
ence of vibrations in the air.  0,         0       0    -,
If we stretch over the top of a 
funnel a piece of moistened               
bladder, and when it is dry,  7   
suspend  the apparatus by a 
knotted  hair, passed through                  ))   CD
the centre of the membrane, we                     N   Tm 
can produce symmetrical nodal
lines upon its surface, stre*ed
with sand, by passing the fin-                                I 
gers, covered with resin, over the hair. The same phenomenon may be




244              THE THREE STATES OF MATTER.
observed, if we bring the membrane near a bell while it is vibrating.
The acoustic figures obtained by the vibration of membranes are extremely varied.  Savart has observed that square membranes are
divided by their nodal lines into the same forms as square plates under
the same circumstances, with this difference, that the vibrating parts
in the vicinity of the edges are smaller for the last, while they are
equal to the others in membranes. Fig. 262 represents a few of the
forms produced in the vibration of membranes.  It has been found
that wood and metals, in very thin laminae, vibrate like membranes.
Q 3. Undulations of Liquids.
319. Production of waves.-Liquids are capable of assuming
undulatory movements, similar to the vibrations of solids, differing
from them, however, in some respects, in consequence of the different
physical arrangement of their atoms. If a depression be made at any
point in the surface of a fluid in a state of rest, by the dropping
in of a solid, as of a pebble into water or by immersing and then
withdrawing the solid, a circular undulation will be produced. Around
the point of depression there first rises a circular elevation above the
level of the liquid when in equilibrium, and immediately beyond this
is a circular depression, and so, alternately, successive elevations and
depressions.  Thus the initial motion will be gradually propagated in
a series of progressively widening circles; wave follows wave, until
opposing causes allow the equilibrium to be regained. Thus, in fig.
263, the light circles D and F represent the elevations, and the shaded
ones, C, E, G, the depressions of these             263
circular waves.
As in the case of the vibrations of
solids, an entire undulation consists of a
phase of depression, and another of elevation. This may be rendered more intelligible by conceiving a vertical plane,
A B, to pass through the point C, whence                              B
the waves originate. It is plain that a
progressive lineal undulation will arise
on it, resembling that of the cord, fig.
248.  This section is seen in fig. 264,
A' C' B', and the nomenclature used for
the cord applies to it, with this difference
only, that by the breadth of the wave is meant the periphery of its circle, and by
its length, the length of both the elevated           264
and depressed portions. (Peschell.) 
320. Progressive undulations in    ----- 
liquids.-In a movement of the kind
just indicated, the fluid appears as if its entire mass advanced p)io




OF UNDULATIONS.                           245
gressively from the point of excitation; but this is a delusion. Floating bodies, as pieces of wood, are not hurried forward on the surface of the water, but merely rise and fall, alternately, as the waves
pass. The true nature of the motion is such, that each particle of the
fluid describes a vertical circle about the spot where it may happen to
be, revolving in the direction in which the wave is advancing. The
particle thus returns to its former position in the same plane, one-half
being above, and the other half below the level of the fluid. Each
particle of fluid thus set in motion, imparts a similar movement to its
contiguous particle, this again to the next, and so on. But as a certain
time must elapse for this transmission of motion, the different particles
will be describing different portions of their circular movement at the
same moment. Some will be at the highest point of their vertical circle,
while others are in an intermediate position, and others at the lowest,
giving rise to a wave which advances a distance equal to its whole
length, while each particle performs one entire revolution.
For the sake of simplicity, we will consider only eight of the many particles
which we may conceive as occupying the horizontal surface between a and nm,
fig. 265. Imagine the particle a to be at rest, when a descending wave strikes
it. It will be depressed, and will begin to revolve in a vertical circle in the
direction of the arrow. If we consider eight such particles to be situated on the
265
3    2_   1
line a n, and that each particle begins its motion J of a revolution later than its
neighbor next on the left hand; then at the instant when a has completed one
entire revolution, the second will be one-eighth behind it, viz.: at 7; the 3d,
two-eighths behind it, viz.: at 6; and the fourth, fifth, sixth, seventh, and eighth,
at the points 5, 4, 3, 2, and I respectively, whilst the 9th particle is but just
beginning to move. Connect the points a, 7, 6, 5, 4, 3, 2, 1, m, and the line will
represent the form of the fluid surface at that precise moment of the undulation.
The diameter of the circle which each particle describes, is the amplitude or intensity of the wave, c6 its depth, and g2 its height, each of
which is equal to the radius of a circle which any particle describes
during one oscillation. This radius is longer or shorter according to
the amplitude of the wave. It is sometimes twenty feet, which makes
a very high wave, probably the largest which ever occurs on the ocean
in a violent storm, unless it be those waves which have been increased
by the accumulation of wave upon wave.
321. Stationary waves.-Stationary undulations may be produced
by exciting waves in a circular vessel, from its central point. The
waves being reflected from the circular wall, will produce another series,




246              THE THREE STATES OF MATTIER.
which, combined with the first, will produce the effect of a stationary
undulation.  So also they may be produced on a surface of a liquid
confined in a straight channel by exciting a succession of waves, separated by equal intervals, moving against the side or end of the channel,
and reflected from it.
322. Depth to which waves extend.-Waves, or undulations,
are not only propagated laterally, but also in all other directions. It
has been ascertained (by the Messrs. Webber) that the equilibrium of
the liquid is not disturbed to a greater depth than about three hundred
and fifty times the altitude of the wave.
323. Reflection of waves.-If a series of progressive waves are
arrested by impinging against any solid surface, they will be reflected
again from that surface under the same angle at which they struck it.
This reflection of waves is occasioned by elasticity, and obeys, precisely,
the laws which regulate the impact of elastic bodies.
Since this law applies to all the rays which constitute the breadth of
a wave, the path of a reflected wave may readily be determined by a
knowledge of the surface and the angle of incidence.  If the wave is
linear, (that is, if the line resting upon the highest point of the elevation
at right angles to the direction in which it is moving, is a straight line),
and it meets a plane surface, it will be reflected, and return in the same
path. If it meet the surface at an angle of 20~ or 30~, it will be reflected
at the same angle, on the other side of the perpendicular to the reflecting surface.
324. Waves propagated from  the foci of an ellipse.-If the
vessel is in the form of an ellipse, and a wave originate at one of the
foci, all the rays will converge so as to fall          266
simultaneously, after reflection, on the other
focus.
Fig. 266 represents an ellipse, of which F and
F' are the foci, which have the following property.
If lines be drawn from the foci to any points, 
P, P, P, in the ellipse, these lines will form equal
angles with the ellipse at P, and their lengths
taken together, will be equal to the major axis
A B. If we suppose a series of circular progressive waves propagated from the focus F, their rays      I
will strike successively and at equal angles upon the elliptical surface, as at the
points P P P; they will be reflected in the direction P F', towards the other focus.
But as all the points of the same wave move with the same velocity, they will
all reach the focus F at the same time, for the distances they pass over are equal.
Hence it follows, that each circular wave that expands around F, will, after it
has been reflected from the surface of the ellipse, form another circular wave
around F' as a centre.
325. Waves propagated from the focus of a parabola.-If the




OF UNDULATIONS.                           247
surface be a parabola, and a wave originate at its focus, all the rays
will, after reflection, pass in parallel lines. Or, if the rays impinge in
parallel lines, they will, after reflection, converge to the focus.
Fig. 267 represents the parabolic curve. The point V is its vertex, the line
V M its axis. The point F, upon the axis, is the focus, and has the following
property. If lines be drawn from the focus to any points,     267
P, in the curve, and other lines be drawn from the points, P,   w 
severally parallel to the axis V M, meeting lines W W, drawn
perpendicular to the axis, the lines F P and P p will be in-         _
dined at equal angles to the curve at the point P, and the   -
sum of their lengths will be everywhere the same. Hence e.          ~
it may be demonstrated, as in the case of the ellipse, that if v  7' P M
a series of progressive waves be propagated from the focus
F, these waves, after striking the curve, will be reflected, so \ 
as to form a series of parallel straight waves.                     7
Moreover, it is evident that if two parabolas face        P"
each other, so as to have their axes coincident, a sys-         W  W
tem of progressive circular waves, issuing from one focus, will be followed by a corresponding system, having for its centre the other focus.
For if a series of parallel straight waves strike a parabolic surface,
their reflection would form a series of circular waves, of which the
centre would be the focus.
Rays reflected from spherical surfaces, whose extent is small compared with their diameter, will, in their direction, approximate closely
to those reflected from a parabolic boundary.
326. Circular waves reflected from  a plane.-If the diverging
rays of a circular wave fall upon a plane surface at right angles to it,
their path, after reflection, is the same as it would have been had they
originated from a point on the opposite side of            268
the plane, and as far back as the point of origin 
itself; that is, the form  of the reflected wave  \
will be the reverse of the incident wave, for the 
rays which first strike the surface will be re- c/           a   a  
fleeted first, and will have returned to the same   
distance from the surface at the time when the       \
last rays meet it, that these last rays were at the
moment when the first were reflected. 
Thus, suppose the wave g a d, proceeding from the centre c, fig. 268, impinges
on the plane surface, ef. The form of the wave, after reflection, will be the
same that it would have been had it proceeded from c', on the other side of ef,
(at the same distance). It is evident that with a circular wave, all its points
cannot impinge at the same time on a plane, therefore, the portions in advance will
impinge first, and will first be reflected; and when a impinges, the rays at d and
g have still to go through the distances d e and gf, before they can be reflected;
but in the space of time required for this, the ray at a will have returned to the




248             THE THREE STATES OF MATTER.
point k. In the same way it may be shown that the intermediate rays will
return to intermediate positions, and be found in the line e ]of, symmetrically
situated to the line e nf, in which they would have been had they not been
reflected from the plane. And it further follows, that the centre, c', of the
reflected wave d k g, is as far from ef, as is the centre, c, of the incident wave,
e nf, but on the opposite side of the median plane, e af.
327. Combination of waves.-Where two systems of waves,
coming from different centres, meet each other, several effects may follow, according to the mode of meeting, which curiously illustrate the
principles of undulation in all departments of physics. 1st. If the
elevations of the two waves coincide, and, consequently, their depressions
also, then a new wave will be formed, whose elevations and depressions
will be the sum of those of the two originals. 2d. If the two waves
of equal amplitude are so superimposed that the reverse of the last case
is true, i. e., that the elevation of one fits the depression of the other,
then both waves disappear, and the surface remains horizontal. Or,
3d, if one wave has greater amplitude than the other, and the two
waves meet in the same phase, then the resulting wave will have a
height equal to the difference between the greater and the ress.
Combinations, and interference of waves, are of universal occurrence
in all media, in which force of any kind is propagated by undulations.
328. Interference in an ellipse.-The two systems of waves formed
by an elliptical surface, and propagated, one directly around one of the
foci, and the second formed by reflec-            269
tion around the other, exhibit not
only the phenomena of reflection,
but also of interference.  These
phenomena are represented in fig.
269, where a and b are the two foci.
The strongly marked lines are the
elevations, the more lightly traced 
lines are the depressions, the points
where the more strongly marked  
circles intersect the more faintly
marked circles, are points where
an elevation coincides with a depression, and are therefore points
of interference.  The series of these points form lines of interference
which are indicated in the diagram by dotted lines, which, as will be
seen, arrange themselves regularly in the form of hyperbola and ellipses
about these foci.
329. Undulations of the waters of the globe.-The undulations
produced in the oceans, lakes, rivers, and other large collections of




OF UNDULATIONS.                         249
water upon the surface of the globe, are of extreme importance in the
economy of nature.  Did not water possess, as a consequence of the
mobility of its particles among each other, the property of being thus
set in motion, the ocean would soon be rendered putrid by the decomposition of the mass of organized matter it contains. The principal
physical cause which produces these undulations on a moderate scale,
is the motion of the atmosphere. On a large scale they are produced
by the combined effects of the attraction of the sun and moon upon
the surface of the ocean, which causes the ebb and flow of tides.
Differences in temperature and density of the waters of different parts
of the ocean, cause currents, by the efforts of these waters to assume a
state of equilibrium; and lastly, the rotation of the earth upon its axis,
originating the constant easterly current. A full discussion of these
interesting questions belongs to Physical Geography.
Q 4. Undulations of Elastic Fluids.
330. Waves of condensation and rarefaction.-The undulations
of liquids already described (319) are surface waves. Undulations of
the same kind may also be produced in elastic fluids.  Elastic fluids
are also subject to undulations of a totally different kind called waves
of condensation and waves of rarefaction. Such undulations are due
to elasticity, and are produced in air and gases by any disturbance of
density.  If any elastic fluid be compressed, and again suddenly
relieved from compression, it will expand, and in its expansion exceed
its former volume to a certain extent; after which it will again contract, and thus oscillate alternately on either side of the position of
repose. It is obvious that we must regard these undulations, or pulses
of air, as extending equally in all directions in the free air, and limited
only by the walls of the containing vessel or apartment when the air is
confined. Therefore, the effects of the united oscillations extend equally
in the course of radii, from the centre to every point of the surface of
a sphere.
331. Undulations of a sphere of air.-The oscillations of air will
not be confined to the sphere in which they commence.  When air
is first contracted, an aerial shell, bounding the sphere of contraction,
expands, and becomes thereby less dense than when in equilibrium.
Again, upon the expansion of the original sphere, the bounding shell
contracts, and becomes more dense, in virtue of its inertia and elasticity.
This exterior shell of air thus acts upon another, external to it; this in
its turn on another, and so on, and thus the initial force is propagated
upon successive concentric portions of air; its effects becoming less
marked with each enlargement, until, like the ripple of a wave of
water, it becomes too evanescent to be appreciated. Compare   653.
24




250               TIIE THREE  STATES OF MATTER.
This alternate condensation and expansion of an elastic fluid, extending spherically around the original centre of disturbance, is perfectly analogous to a series
of circular waves formed around a point on the surface of a liquid. The condensation of the elastic fluid being analogous to the elevation of a surface wave, and
the phase of rarefaction being analogous to the phase of depression.
The radius of the hollow sphere, or the distance the undulation had traversed
when the first particles resumed a position of rest, is called the length of a wave;
the entire sphere comprised within these limits constitutes a wave, and the time
of vibration is equal to the time in which motion is propagated through the entire
length of a wave. If the cause which excited the undulation continues to operate,
the first wave will expand, and there will arise a second and third wave, &c.,
within the first, and concentric with it.
This radial propagation of undulations in air can take place with equal velocity in all directions, only when the                  270
atmosphere is of uniform density, so                     1
far as the vibrations extend.  If this
is not the case, such a wave cannot
have a spherical form. 
Let fig. 270 represent a section of a    //
sphere of air, or other elastic fluid, in    
which waves of condensation and rarefaction have extended outwards from
the centre C; then the heavy lines, dZ' a  
a efg, b hi k, and d Ip q, will represent
the phases of greatest condensation, the
finer intermediate lines will represent  \ \
the spaces of greatest rarefaction, and
the distances an n, and n o, between cir- 
cles of greatest condensation, will be
the length of the waves.
Mechanical illustration.-Professor Snell has contrived the apparatus, represented in fig. 271, to illustrate these
undulations. It consists of a shaft turned by the crank seen at the left, on
which are elliptical grooves, inclined to               271
the axis, in which the rods carrying the
white balls are made to vibrate from
right to left and back again.  These
grooves are so arranged that each successive ball moves to the left later than
the preceding. Thus the balls are seen
crowded together at certain parts of the
series; and,-as the crank is turned, the
phases of greatest condensation travel across the field from left to right, while
other similar waves are formed and continually succeed them.
332. Velocity and intensity of aerial waves.-The velocity with
which such undulations are propagated through the atmosphere, depends
on, and varies with, the elasticity of the fluid. Waves, both large and
small, are transmitted with an equal velocity, so long as the elasticity
remains the same. The intensity of vibration, i. e., the dimensions of
the spaces which the individual particles traverse while in this state oi




OF UNDULATIONS.                            251
movement, depends on the energy of the disturbing force, which, it is
also evident, is a measure of the degree of compression of the wave.
333. Interference of waves of air.-If two series of aerial waves
coincide as to their points of greatest and least condensation, a new
series of waves will be formed, whose greatest condensation and rarefaction is determined by the sum of these points, as prevailing in the
separate undulations.  But where the series are so arranged that the
point of greatest condensation of one coincides with the point of
greatest rarefaction in the other, the resulting series will have condensations and rarefactions equal to the difference between the waves which
meet. If they are equal, total interference takes place, as in the case
of non-elastic fluids, and silence results, if the waves are those of sound.
Indeed all the effects described in the case of waves formed upon the
surface of a liquid are reproduced under analogous conditions in the
case of undulations of aeriform bodies. It must, however, be borne in
mind, that these aerial waves have always a spherical form.
334. Intensity of waves of air expanding freely.-The undulations produced in air form progressively increasing spheres (330),
the magnitude of whose surfaces are to each other as the square of their
radii, or as the square of tleir distance from their respective points of
impulse.  As the intensity of the wave is diminished in proportion to
the space over which it is diffused, it follows, that the effect or energy
of these waves diminishes as the square of the distances from the centre
of propagation increases. So soon, however, as the radial extension
of the wave meets with any resistance which reflects the rays in a
parallel or concentric direction, this rule ceases to be applicable.
Problems.
On the Laws of Vibrations.
149. If a cord of a given length makes 48 vibrations per second, what must
be the respective lengths of similar cords to make 63, 64, 72, 81, and 90 vibrations per second?
150. If a cord, 3 feet long, extended by a weight of 10 lbs., makes 96 vibrations per second, with what force must a similar cord, 2 feet long, be extended
that it may make 108 vibrations per second?
151. If an iron wire, one-tenth of an inch in diameter (Sp. Gr. 7'8), makes
72 vibrations per second, what must be the diameter of a platinum wire of the
same length (Sp. Gr. 21-23) which will make 45 vibrations per second?
152. An iron rod, vibrating by torsion, makes 30 oscillations per second; how
much longer must a rod, having twice the diameter, be to vibrate (with the
same force) 15 times per second?




252             THE THREE STATES OF MATTER.
CHAPTER VI.
ACOUSTICS.
I. Production and Propagation of Sound.
335. Acoustics.-Sound.-Acoustics (derived from  the Greek
verb, axobiw, to hear), teaches the science of sounds, their cause, nature,
and phenomena.  Sound is the impression produced on the sense of
hearing by the vibrations of sonorous bodies.  These vibrations are
transmitted to the ear by the surrounding medium, which is ordinarily
the atmospheric air.
Sound a sensation.-It will be understood, therefore, that all
sound, whether unmusical, like mere noise, or musical, like what is
technically called a tone (a sound of definite and appreciable pitch),
is a sensation; and the causes which produce this sensation may exist
without the sensation itself-that is, without sound. The cause of
sound being atmospheric vibration, if there be no delicately constructed
organ, like the ear, to receive the impression of this vibration, there is
no sound.  It would follow, that even at the Falls of Niagara, if there
were no ear present to receive the impression, those gigantic vibrations would exist only as such-without sound.
Key-note of nature.-The aggregate sound of nature, as heard in
the roar of a distant city, or the waving foliage of a large forest, is said
to be a single definite tone, of appreciable pitch.  This tone is held to
be middle F of the pianoforte-which may therefore be considered the
key-note of nature.
Noise.-The distinctive character of mere noise is determined by
the nature and duration of the irregular vibrations causing it. If these
vibrations are short and single, the effect is that of a crack, or an abrupt
explosion, as in the snapping of a whip, or the explosion of cannon.
If they are continuous and prolonged, the effect is that of a rattle, or
rumble, like the rolling of thunder, or the noise of carriages over a
stony road.
Musical sounds.-Sound, in a musical sense, or tone, is the sensation produced by a series of equal atmospheric vibrations. Noise is
the sensation produced by unequal vibrations. If we throw a single
stone into the centre of a placid lake, a single wave circles off to




ACOUSTICS.                              253
the shore: such is the effect upon the air when a tone is produced.
If a handful of pebbles is thrown into the lake, each separate pebble
produces its own circle, these circles intersect each other and become
confused to the eye: such is the effect upon the air when a noise is
produced. Pulling the string of a harp would correspond to the single
stone thrown into the lake: striking a table or chair, where the separate fibres of the wood vibrate unequally, would correspond to the
handful of pebbles.
A church-bell, to a cultivated ear, is noisy, or musical, according as the tones
in the vibrating metal (for every bell produces more than one distinguishable
tone) chance to be at musical or unmusical intervals. If the intervals are (musically considered) dissonances, the bell will be discordant; if they are concords, the bell will be harmonious. Again, if in these concordant tones the
intervals be "major," the bell will be cheerful; if they be "minor," the bell
will be sad.
336. All bodies producing  sound  are  in vibration.-If the
sonorous body is solid, and presents a large surface, as a bell-jar, the
vibrations may be shown by suspending a small ivory             273
ball, i, by a thread in the interior of the jar A B, inclined in the position seen in fig. 272.  When the jar
resounds with a blow, the ball is thrown from the sides,
as shown by the dotted line, and returning, is again    i    \
thrown off, and so continues bounding, in consequence
of the vibrations.  A touch from the hand arrests the
vibratory movement in the glass: the sound ceases,   I
and the ivory ball remains quiet.           2
If the sonorous body is a plane  
surface, its vibrations may be shown       A 
by the formation of nodal lines with  
grains of sand scattered upon it.
When the sound is produced by a 
stretched cord, the vibrations may
be felt by touching the cord lightly
with the hand, or may be seen by
placing bands or rings of paper           B      /
upon the vibrating cord. In wind
instruments, it is the air which they contain, whose vibrations produce the
musical sounds.
This may be proved by an organ-pipe, or by a glass tube, fig. 273, when a
current of air is passed into it through the foot, 0. A small membrane of goldbeater's skin, extended on a circle of pasteboard, B, is placed within the tube,
and sustained in a horizontal position by means of a thread. Grains of sand
strewed upon the membrane, will be arranged in nodal figures, proving that the
membrane obeys the vibratory movement of the air which surrounds it. That
the vibrations are not due to an ascending current of air, is-proved by the fact,
that the membrane does not vibrate when it is placed midway of the length of
24*




254               THE THREE STATES OF MATTER.
the tube [a nodal point], but above or below this point it vibrates, and more
strongly as it is further removed from the centre.
337. Sound  propagated  by waves. —Sound  is propagated  by
waves of condensation and rarefaction (330), as shown in fig. 274. The
274
vibrations of the sounding bell are communicated to the surrounding
medium, and by vibrations alternately forwards and backwards.  Motion is communicated to an ever increasing spherical portion of the
medium until it reaches the ear, by which the sensation of sound is
perceived.
338. Co-existence of sound-waves.-Many sounds may be transmitted simultaneously in different directions by the same medium without destroying each other, all the sounds penetrating and crossing in
space without modification. In complicated symphonies, a practiced
ear readily distinguishes the sound of each instrument. A very intense
sound may overpower a feeble sound, as a loud noise renders the human
voice inaudible.
339. Sound is not propagated in a vacuum.-The vibrations of
elastic bodies do not produce an impression on the ear, unless there
exists between this organ and the sonorous body an uninterrupted elastic medium, vibrating with it. This medium is ordinarily the atmospheric air, but other gases, vapors, liquids, and solids, transmit sound,
and generally with a facility varying with their density.
To prove that sound is not propagated in a vacuum, place under the receiver
of an air-pump, a bell, kept in constant vibration by a clock-work movement,
fig. 275. The bell apparatus should be placed upon wadding, otherwise the
vibrations would be communicated to the plate of the air-pump, and thus to the
air. While the receiver is filled with air at the ordinary pressure, the sound
is distinct; as the air is gradually exhausted, the sound grows more and
more feeble, until finally, when a vacuum is obtained, it ceases to be heard,
but is immediately revived by admitting air again.
y                    0::: C:::~:~::;:,~~




ACOUSTICS.                            255
340. Sound  is propagated in  all elastic bodies.-If, in the
experiment just described, the vacuum is supplied with hydrogen gas
(density 0.0692), or any gas of less density              275
than atmospheric air, a sound will be transmitted from  the bell, very feeble for the hydrogen, and increasing as the gas is more
dense. In like manner, a person whose lungs    / 
have been filled with hydrogen gas, utters'
only a shrill piping sound. 
Vapors, water and  other liquids, transmit'
sounds like gases, but with much more energy.               i
When two bodies are struck under water, the
sound is distinct to a person having his ear
under water, or communicating with the water
by means of some solid substance. The conductibility of sound is so great in solids, that if we apply
the ear to one end of a beam of wood, the slightest
shock, as the scratch of a pin at the other extremity, may be heard distinctly.
The noise of cannon has been heard a distance of more than two hundred and
fifty miles, by applying the ear to the solid earth. In several mines in Cornwall, England, there are galleries which extend under the sea, where the sound
of the waves is clearly heard when the sea is agitated, rolling the pebbles and
boulders over the rocky bottom of the ocean.
The music from a company of musicians, playing in orchestra upon numerous
instruments, has been transferred to an apartment in another house, by a cord
stretched across the intervening street, connecting at one end with a soundingboard, and at the other extremity with a wooden box. On placing the ear at an
opening in the box, the whole musical movement was heard, reproduced in
miniature, being transmitted by the vibrations through the cord. A bystander
in the same apartment was unconscious of there being any performance.
341. Hearing is a sense depending upon the ear, a beautifully constructed instrument, designed to gather in the vibrations of the surrounding air. This vibratory movement is communicated to the acoustic
nerve by the aid of organs which will be described in detail at the close
of this chapter.
342. Time is required for the transmission of sound. —Experience testifies to the truth of this statement.  We hear the blows of a
hammer at a distance a very sensible interval of time after we see them
struck. An appreciable time elapses after we see the flash of a cannon,
at a little distance from us, before we hear the explosion.  The report
of the meteor of 1783 was heard at Windsor Castle ten minutes after
its disappearance.
343. The velocity of all sounds is the same.* —The velocity of
sound is the space that it traverses in a second.  Theory demonstrates
that the velocity of the vibrations of sonorous bodies in the same meSee note ir, Appendix, p. 66S.




256               THE THREE STATES OF MATTER.
dium, is the same for all sounds, grave or sharp, strong or feeble, and
Whatever may be their pitch. Observation confirms this result, at least
for those distances at which experiments have been made. There is no
confusion in the effects of music, at whatever distance it may be heard.
If the different notes simultaneously produced by the various instruments of
an orchestra, moved with different velocities, they would be heard by a distant
auditor at different moments, so that a musical performance, except to those in
its immediate vicinity, would produce only discords. M. Biot, in playing an
air upon a flute at the extremity of a pipe of the aqueduct of Paris, found that
the sounds came to the other end, having exactly the same interval, demonstrating that the different sounds travelled with the same velocity.
344. Velocity of sound in air.-Numerous experiments have been
made for estimating the velocity of sound; that is, the space that it
travels over in a second.  The most extensive and accurate system of
experiments were those made in 1822, by the Board of Longitude of
France, conducted by Messrs. Prony, Arago, Humboldt, Gay Lussac,
and others.
Two pieces of cannon were used, one placed at Montlhdry, the other at Montmbartre, between which the distance is 18,612 m. (== 61,063-8 feet), or more than
ten miles. The discharges were reciprocal, so as to avoid the influence of the
wind. At each station were numerous observers, furnished with chronometers,
who noticed the time between th3 appearance of the light, and the arrival of the
sound. This time may be called that which the sound requires to pass from one
station to another, for the time occupied by the passage of the light between
the two points is wholly inappreciable. The mean time required to transmit the
sound was 54'6 seconds. By dividing the distance between the two stations by
this number, the velocity, per second, is obtained. The velocity of sound at
610 F. (160 C.), that being the temperature of the atmosphere during the experiment, is 1118-3 feet (340-88 m.), (for 61,0638 — 54-6 = 1118-3 +); or at
the temperature of 320 F. it would be about 1086-1 feet.
Messrs. Bravais and Martin, in 1844, have determined that the velocity of sound between the summit and base of the Faulhorn (a lofty
mountain in the Swiss Alps) is the same, whether ascending or descending, and that it is 1090'47 feet per second at 320 F.
It has been determined, 1. That the velocity of sound decreases with
the temperature; at 500 F. (10~ C.), it is 1106-091 feet (337 m.) So
that as the temperature is lowered, sound diminishes in velocity about
one foot and a tenth for every degree.  2. That at the same temperature the velocity of sound is not materially affected, whether the sky is
bright or cloudy, the air clear or foggy, the barometric pressure great
or small, provided the air is tranquil.  All of these circumstances,
however, exert a great influence on the intensity of the sound as it
reaches the ear from a given distance.  Fogs, snow, &c., prevent the
free propagation of sound, but do not materially affect its velocity. 3.
That its velocity varies with the velocity and direction of the wind.




ACOUSTICS.                            257
345. Velocity of sound in different gases and vapors.-The
velocity of sound in the different gases, is in the inverse ratio of the
square root of their densities.
Dulong has determined by calculation the velocity of sound in the following
gases, at the temperature of 32~ F. Carbonic acid 860 feet (262 m.), oxygen
1040 feet (317 m.), olefiant gas, 1030-2 feet (314 m.), air, 1092-54 feet (333 m.),
carbonic oxyd, 1105-6 feet (337 m.), and hydrogen, 4163 feet (1269 m.), each
in a second. The theoretical velocity of sound in vapor of alcohol at 140~ is
862 feet, in vapor of water at 154~ is 1347 feet. The observed velocities are
generally not very far from those given by calculation.
346. Calculation of distances by sound.-The known velocity
of sound per second (1118 feet), enables us to obtain a close approximation of the distance of the sonorous body. This follows as a consequence of the very experiments (344) by which the velocity of sound
was determined. From the known laws of falling bodies (71), we may
also, with the aid of the known velocity of sound, obtain an approximate estimate of the height of a precipice, or the depth of an abyss,
from the time occupied by the sound of any projectile, let fall from the
hand, in reaching the ear.
347. Velocity of sounds in liquids.-Sound is conveyed through
liquids as well as through gases. The velocity of sounds in liquids
is much greater than in air.  In 1827, Messrs. Colladon and Sturm,
experimenting upon the velocity of sound in the Lake of Geneva, found
it to be 4708 feet (1435 m.) per second, or about four and a half times
greater than in air, at the temperature of 46'6~ F.
Agitation of the water, liquids, &c., did not affect either the rapidity or
intensity of the sound. But the interposition of solid bodies, such as walls, or
buildings, between the sounding body and the observer, almost destroyed the
transmission of sound in water; an effect which does not take place nearly to
the same degree in air (350).
348. Velocity of sounds in  solids.-Sound is transmitted  by
solid bodies with much greater rapidity than by air, but by no means
with equal velocity, varying much with the elasticity and density of the
different solids, as well as their homogeneity and uniformity of structure.
Want of homogeneity in any medium interferes with the propagation of sonorous vibrations. Let a tall glass be half filled with champagne wine: as long
as there is effervescence, and the wine contains air bubbles, a stroke on the glass
gives only a dead disagreeable sound; as the effervescence subsides the tone
becomes clearer, and when the liquid is tranquil the glass rings as usual. The
dullness of sound alluded to is owing to the fact that the wine which forms part
of the vibrating system lacks homogeneity, and therefore is incapable of regular
vibration.
The most exact experiments have been made by M. Biot, with a series of waterpipes in Paris, which had a length of 3120 feet (951 m.). A bell was hung at
the centre of a r;ng of iron, fastened to the mouth of the tube, so that the




258               THE THREE STATES OF MATTER.
vibrations of the ring would affect only the metal of the tube, and the vibrations
of the bell only the included air. When the ring and bell were struck simultaneously, an observer, placed at the other end, heard two sounds; the first
transmitted by the metal, the second by the air. By noticing the interval of
time between the arrival of the two sounds, it was ascertained that the velocity
of propagation of sound in cast iron is about 10'4 times that observed in air;
that is, 11,609 feet (3538-5 m.). Similar experiments were made by Hassenfratz
on the velocity of sound in stone, on the walls of the galleries of the catacombs
which underlie Paris, by observing the interval of time between the arrival Jf a
sound transmitted by the stones and of that transmitted by the air of the gallery.
Were the earth and sun connected by an iron bar, nearly three years would
elapse before the sound of a blow applied at the sun could reach the earth.
The velocity of the propagation of sound has been determined theoretically
by Savart, Chladni, Masson, and Wertheim, from  the number of longitudinal and transverse vibrations of the bodies, or their coefficient of elasticity.
Chladni found, by the aid of longitudinal vibrations, that in wood, the velocity
of sound is from ten to sixteen times greater than in air. In metals, the velocity is more variable, being from four to sixteen times as great as in air.
349. Interference of sound.-When two series of sonorous undulations encounter each  other in opposite phases of vibration, the
phenomena of interference are produced. The undulations will become
mutually checked, and if the two sounds are of equal intensity, instead
of producing a louder sound, as might be expected, they will altogether
destroy each other and produce silence. If, however, one of the sounds
ceases, the other is heard immediately.
If two sounding bodies were placed in the foci of an ellipse, fig. 269, no sound
would be heard, if an ear was placed on any of the lines of interference indisated by the dotted lines, but if one sound was stilled, the other would be heard,
or if the ear was placed between the lines of interference, then both sounds
would be heard simultaneously, and would be louder than either alone.
The interference of sounds may be shown by means of a common
tuning-fork.                                                     276
When in vibration, its branches recede from, and approach each other, as shown by the dotted lines in fig.
276. If the instrument, when vibrating, is placed about
a foot from  the ear, with the branches equidistant, both
sounds will be heard; for the waves of sound combine
their effects; but as it is slowly turned around, the sound
will grow more and more feeble, until at length a position will be found in which it will be inaudible. For, as
the tuning-fork is turned, the waves of sound interfere, and
produce partial or total silence. This may also be illustrated
by attaching a tuning-fork, lengthwise, to any rotating support. When the fork is vibrating, no sound will be heard so
long as it continues to rotate.
350. Acoustic shadow.-Persons cut off from observation by a wall, or other obstacle, still hear sounds
distinctly, although with a diminished volume. Thus a band of music




ACOUSTICS.                            259
in an adjacent house, or neighboring street, is readily followed in the
softest melody.  Intervening obstacles, therefore, however opaque to
light, do not cast perfect shadows to sound. The sound is not entirely
cut off, because the obstacle is elastic, and propagates the vibrations it
receives in a manner analogous to light passing through a translucent
medium.
To a distant observer, the roar of a railway train is instantly hushed on
entering a tunnel, and as suddenly renewed on its emergence.
Acoustic shadows are much more distinctly recognised when large
masses, as edifices or rocks, intervene; so large as not to enter into
vibration.
Although there is not complete silence in the acoustic shadow, still it
is analogous to the shadow of light, for there is never complete obscurity
in the latter case, even when we take the utmost precaution, for the
light spreads behind the obstacles which arrest it.
351. Distance to which sound may be propagated.-The distance at which sounds are audible does not admit of precise measurement. In general, it may be stated, that a sound will be heard further,
the greater its original intensity, and the denser the medium in which
it is propagated. It also depends, greatly, on the delicacy of hearing
of different individuals. The intensity of sound, like that of all forces
acting in lines, diminishes in the inverse ratio of the squares of the
distance of the sounding body. Thus, if the linear dimensions of a
theatre be doubled, the volume of the performers' voices at any part of
the circumference will be diminished in a fourfold proportion.
That this difference of the agitating impression is the true cause, is shown by
confining the air on all sides in a tube. Biot experimented with 2860 feet of the
water-pipes of Paris. At this distance the lowest whisper made at one end was
accurately heard at the other extremity of the tube.
A powerful human voice in the open air, at the ordinary temperature, is
audible at the distance of seven hundred feet. In a frosty air, undisturbed by
winds or current, sound is heard at a much greater distance with surprising
distinctness. Lieut. Forster, in the third polar expedition of Capt. Parry, held
a conversation with a man across the harbor of Port Bowen, a distance of one
and a quarter miles. Dr. Young states, on the authority of Derham, that the
watchword " all's well" has been distinctly heard from Old to New Gibraltar, a
distance of ten miles. The marching of a company of soldiers may be heard,
on a still night, at from five hundred and eighty to eight hundred and thirty
paces; a squadron of cavalry at foot pace, at seven hundred and fifty paces;
trotting, or galloping, one thousand and eighty paces distant. When the air is
calm and dry, the report of a musket is audible at eight thousand paces. The
sound of the cannonading at Waterloo was heard at Dover.
Sounds travel further on the earth's surface than through the atmosphere. Thus
it. is said, that at the siege of Antwerp in 1832, the cannonading was heard in the
mines of Saxony, which are about three hundred and seventy miles distant. The




260               THE THREE  STATES OF MATTER
cannonading at the battle of Jena was heard feebly in the open fields near Dres.
den, 92 miles distant, but in the casemates of the fortifications it was heard with
great distinctness. The noise of a sea fight between the English and the Dutch
in 1672, was heard at Shrewsbury, a distance of two hundred miles. Sound
has been carried by the atmosphere to the distance of three hundred and fortyfive miles, as it is asserted, that the very violent explosions of the volcano at
St. Vincent's have been heard at Demarara.
Sir Stamford Raffles records however a similar, though much more extraord.nary, fact. The eruption in Tombers, in Sumbawa, was perhaps the most
violent volcanic action recorded; occasional paroxysms were heard, he says,
more than nine hundred miles distant.
352. Reflection of sound.-When the waves of air on which sound
is being borne impinge, in the course of their expansion, on a solid
surface, they will be reflected from it, agreeably to the laws regulating
the impact of solid bodies (112). Their return is made with equal velocity, and under an equal but opposite angle to that under which they
advanced.
Let a spherical wave whose centre is at S, fig. 277, encounter obliquely a
plane surface, a 0, separating two media of different density, a portion of the
sound will be reflected as though it emanated from           277
the point S', as far behind O as S is in front of it, 
and while a n would have been the surface of the 
wave if the reflecting medium had not intervened,
a s' will be the wave surface of the reflected sound.
Take any portion of the incident wave, as b s, let 
bp - m a, when the surface of the incident wave             \
reaches a, a wave starting from a new centre of vibration, b, will have extended to the circumference 
described upon b p; similarly a new vibration start- 
ing from c, will describe the circle of which c q is \
the radius. In the same manner, vibrations start-                  
ing from every point of the line a O, will make up.a.  
the compound wave surface a n', whose centre is at               e       N
S', and which is tangent to all the wave surfaces,         \      -....... —.   n
whose radii are c q, bp, &c. 
353. Echo.-An echo is the repetition of a..  
sound reflected by a sufficiently distant object, 
so that the reflected is not confounded with 
the direct sound.
The ear cannot distinguish one sound from ano-             R.
ther, unless there is an interval of one-ninth of a 
second between the arrival of the two sounds. Sounds must, therefore, succeed
each other at an interval of one-ninth of a second, in order to be heard distinctly. Now the velocity of sound being eleven hundred and eighteen feet a
second, in one-ninth of a second the sound would travel one hundred and twentyfour feet.
To have a perfect echo, therefore, the reflecting surface must be at
least sixty-two feet from  the sounding body.  (62 X 2   124.)  If we




ACOUSTICS.                            26T
speak a sentence at the distance of sixty-two feet from  the reflecting
surface, we shall hear the echo of the last syllable only.  If twice,
thrice, or four times the distance, two, three, or four of the syllables
will be echoed, the direct sounds and reflected sound of the other syllables of the sentence, being confounded with each other. If the reflecting surface is at a less distance from the sounding body than sixtytwo feet, the direct sound and the reflected sound become confused, so
that words and tones cannot be heard distinctly.  The original sound
will then be prolonged and strengthened; an effect which we express
by saying there is resonance. If the distance is comparatively small,
as in a common-sized room, the sounds reflected from  the walls, the
ceiling and the floor, reach the ear at almost exactly the same time as
the direct sound, and the apparent power of the voice is strengthened,
besides preserving its delicacy.  Where, however, the apartment is
larger, the direct sound only partially coincides with the reflected
sound, and more or less confusion arises.  Voices are heard in a remarkably sonorous manner, in large apartments with hard walls, while
draperies, hangings, carpets, &c., about a room, smother the sound,
because these are bad reflectors.  A crowded audience has a similar
effect, and increases the difficulty of speaking, by presenting surfaces
unfavorable' to reflection.
354. Repeated echoes.-Repeated or multiplied echoes, are those
which repeat the same sound many times.  This happens when two
obstacles are placed opposite to one another, as parallel walls, for
example, which reflect the sound successively.
A striking and beautiful effect of echo is produced, in certain localities, by the Swiss mountaineers, who contrive to sing their Ranz des
Vachles in such time, that the reflected notes form an agreeable accompaniment to the air itself.
There is a surprising echo between two barns at Belvidere, Allegheny county,
N. Y. It repeats eleven times, a word of either one, two, or three syllables;
and has been heard to repeat it thirteen times. By placing oneself in the centre,
between the two barns, a double echo is heard, one in the direction of each barn,
and a monosyllable is thus repeated twenty-two times.
At Adenach, in Bohemia, there is an echo which repeats seven syllables
three times; at Woodstock, in England, there is one which repeats a sound
seventeen times during the day, and twenty times during the night. An echo in
the Villa Smionetta, near Milan, is said to repeat a sharp sound thirty times
audibly.
The most celebrated echo among the ancients, was that of the Metelli at Rome,
which, according to tradition, was capable of repeating the first line of the
zEneid, containing fifteen syllables, eight times distinctly.
355. Change of tone by echo.-Dr. Chas. G. Page describes an echo in
Fairfax county, Virginia, which gives three distinct reflections, the second echo
much the most distinct. Twenty notes played upon a flute, are returned with
perfect clearness. But the most singular property of this echo is, that seme
2.5




262               TIIE THREE  STATES OF MATTER.
notes in the scale are not returned in their places, but are supplied with other
notes, which are either thirds, fifths, or octaves.
356. Whispering  galleries.-Whispering galleries are so called,
because a low whisper, uttered at one point in them, may be heard
distinctly at another and distant point, while it is inaudible in other
positions.
Such galleries are always domed, or of ellipsoidal shape; the best form is
that of the ellipsoid of revolution. In such a chamber, whispering in one focus,
is very audible to a person at the other focus, because the undulations striking
upon the walls, are reflected to the point where the hearer is placed, while in
any other position, a feeble sound, or none at all, will be heard, because only a
part of the reflected sound will reach the ear at one time. (See fig. 266.)
One of the halls of the museum of antiquities, of the Louvre, at Paris, furnishes an example of such an apartment. In the dome of the Rotunda of the
Capitol at Washington, is a fine whispering gallery. The principal room of the
Merchants' Exchange, in New York, is of a similar character, and at the same
time affords a painful example of confused echoes.
The new Halls of Congress, at Washington, and the Lecture room at the
Smithsonian Institution, have been designed with special reference to the best
form for public speaking, and to this end an elaborate series of experiments and
observations, upon the best proportions and forms of public halls, have been
undertaken by Profs. Henry and Bache, by order of the government, the results
of which are recorded by the former, in the Proceedings of the American Association for 1856, p. 119, and Smithsonian Report for 1856, p. 221.
357. Refraction of sound.-Although  sound is reflected by any
surface of different density from that in which             278
it originates, the sound also enters the second                          s
medium  by means of new vibrations originating at the interposed surface.
We have seen (345, 347) that the velocity of
sound is not the same in different media. Let a            \
sound-wave originating at S, fig. 278, meet with
another medium in which sound moves slower than 
in the first, and let a 0 be the surface of the second
medium. Let the difference of velocity be such
that while the new vibration, originating at b, \\ 
would advance to p', if the medium were like the  ~              _ 
first, it can move only to e in the new medium:                          N
it is evident that if an  be the wave surface with'....... 
the velocity unchanged, a N will be the wave sur- 
face with the retarded velocity, and the ray S b
will enter the second medium in the direction b R,
more nearly perpendicular to the surface a 0, than
its direction in the first medium.
For a fuller discussion of the laws of refraction, see the chapter on Optics.
The phenomena of refraction of sound are in,
accordance with theory.  The researches of Pois-                        "
son and Green have placed this beyond doubt. Sondhauss has demonstratel




ACOUSTICS.                            263
the same thing by the following experiment:-A cell, a in n, fig. 279, was formed
of two films of collodion, united at the edges by a rim of iron. The two films,
mn and n, were made spherically convex, and when inflated, the instrument took
the form of a lens, like                      279
those employed in optical experiments.  This                        a
apparatus was filled with
carbonic acid gas, by
means of an opening at.n                                         r
a. He placed a watch at   S
S, in the axis of the lens
that is in the line S r
which  passes through
the centres of the two
surfaces m and n. When
an observer placed his          l=-                _
ear on the opposite side in the axis of the lens, the ticking of the watch was
distinctly heard, if at a proper distance from the lens: this distance was
less in proportion as the watch was farther removed. If the lens was raised
up, the sound ceased to be heard; and the result was the same if the ear
was removed from the axis S r. Having replaced the watch by an organ-pipe,
having an opening like a flute, instead of the ear he employed the bent tube
fc, having gold-beater's skin extended over the opening c, and fine sand placed
upon it. When this apparatus occupied the positions in which the ear heard
the sound of the watch, the sand was agitated; but on removing the lens the
sand remained at rest.
To comprehend how these experiments demonstrate the refraction of sound,
we must refer to the principles of optics, in which multiplied experiments have
rendered the explanation very complete, and easy to be understood.
358. The speaking-trumpet is an instrument employed to convey
the voice to a great distance. This instrument consists of a conical
tube O P, fig. 280, terminated by a bell-shaped extremity, P. At O
is a mouth-piece which surrounds the lips without interfering with
-their movements.  The trumpet, it is said by history, was used by
280
Alexander the Great for commanding his army.  At the present day
it is employed at sea to cause the voice of the commander to be heard
above the roar of the winds and waves. On land it is used by firemen.
To explain the augmentation of sound by the trumpet, it was formerly supposed that the sound was reflected by the sides of the trumpet, so that the vibrations issued in the direction of the axis of the instrument, and that this effect




264              THE THREE STATES OF MATTER.
was also aided by the vibration of the walls of the instrument itself. It was
shown by Lambert in 1763 that the vibration of the instrument tended to render
articulate sounds confused.
The explanation by reflection of the rays of sound is inadmissible. In reality
the form of the extremity has considerable influence, but on the theory of reflection it should be without effect. On the contrary, the conical form should be all
important, but Hassenfratz has shown that a cylindrical tube, with a bell-shaped
extremity, strengthens the sound as much as a conical tube. In fact, when the
interior of the trumpet is lined with cloth, so that the reflection must be very
feeble or almost null, the intensity of the sound transmitted remains unchanged.
We may add that the sound transmitted through a speaking-trumpet is increased,
not merely in the direction to which it is pointed, but in every direction, whether
the extremity is bell-shaped or otherwise. The efficacy of the trumpet is, therefore, not due to the reflection of sound from its walls, but simply, as stated by
Hassenfratz, to the greater intensity of the pulsations produced in the column
of confined air which vibrates in unison with the voice at the mouth-piece. A
considerable effect is produced by the bell-shaped extremity of the trumpet, but
the nature of this influence has not been satisfactorily explained.
359. Ear-trumpet.-The hearing-trumpet, fig. 281, intended  to
assist persons hard of hearing, is in form  and application the reverse
of the speaking-trumpet, although in principle the same. It consists
of a conical tube, turned in any                   281
convenient direction, so that the
opening, o, may enter the ear.
The strengthening of the sound S 
by this instrument was formerly
attributed to reflection of sonorous waves caused to converge to the
ear, and it was sought to obtain the form most favorable to fulfill this
condition; thus the cone was replaced by a paraboloid, having its
focus at the point o. But these different forms have no effect upon the
result.  Moreover, the nature of the. walls, and the condition of the
interior surface, whether rough or polished, or lined with cloth, has no
effect upon the intensity of the sound. The only essential condition is
that the exterior opening should be greater than that which enters the
ear.  The effect of the ear-trumpet is explained as follows:-The portions of compressed or dilated air, which arrive at the exterior opening,
transmit their compression or dilatation to portions of air smaller and
smaller, and consequently transmit it with increasing intensity. In
this manner the portion of air at o receives and transmits to the membrane of the tympanum a compression or dilatation of much greater
intensity than in the absence of the instrument. Holding the hand
concave behind the ear, as deaf persons are seen to do, concentrates
sound in the manner of an ear-trumpet. The form of the external ear
in animals favors the collection of sound.
360. The siren.-This ingenious instrument was invented by M.




ACOUSTICS.                               265
Cagniard de Latour, for the purpose of ascertaining the number of
vibrations of a sonorous body, corresponding to any proposed musical
sound.
Fig. 282 shows the siren mounted on a wind chest, E, designed to supply a
current of air. Figs. 283, 284, show the interior details of the apparatus. Tho
282                         283                     284
it    A
0
siren is constructed entirely of brass. It consists of a tube, 0, about four inches
in diameter, terminating in a smooth circular plate, B, fig. 284, which contains,
at regular intervals near its circumference, small holes, which are pierced through
the plate in an oblique direction. Another plate, A, turning very easily upon
its axis, is placed as near as possible to B, without being in contact with it. This
plate is pierced with the same number of oblique orifices as those in the plate,
B, but inclined in an opposite direction, as shown in fig. 283, n, A; mr, B.
When a current of air arrives from the bellows, it passes through the holes
of the first plate, and imparts a rotary movement to the second plate, in the
direction in, A, fig. 283. As the upper plate revolves, the current of air is alternately cut off, and renewed rapidly by the constantly changing position of the
holes. In consequence of this interruption, when the plate A moves with a
uniform velocity, a series of puffs of wind will escape at equal intervals of time.
These puffs will produce undulations in the air surrounding the instrument, and
when the wheel revolves with sufficient rapidity, a musical sound is produced,
which increases in acuteness as the velocity of the wheel becomes greater.
A counter (like that on a gas meter) is connected with the upper plate, by
which the number of revolutions is indicated. Pressure upon the buttons, C D,
fig. 284, causes the toothed wheels to be set in communication with the endless
screw upon the spindle, T. The revolution of these wheels is recorded by the
motion of the hands upon the dials in fig. 282. To determine the number of
vibrations corresponding to a given sound, a blast of wind is forced from the
bellows into the siren, until it gives a corresponding note. The hands on the
dials being brought to their respective zeros at the commencement of the
experiment, their position, at the end of any known interval, will indicate the
25'




266               TIIE TIREE STATES OF MATTER.
number of puffs of air which have escaped from the revolving plate, and will,
consequently, determine the number of undulations of the air which correspond
to the sound produced.
The siren, with equal velocity, gives the same sound, excepting the timbre, in
the different gases, and in water, as it does in air, which proves, that the height
of any sound depends on the number of vibrations, and not on the nature of
the sonorous body.
361. Savart's toothed  wheel.-Savart has  employed  another
apparatus to count the number of vibrations corresponding to any
proposed pitch.
It consists, fig. 285, of a toothed wheel, D, to be revolved as regularly as possible, by means of the wheel R, and endless band r. The toothed wheel, D,
285
revolving rapidly, imakes the tongue, C, vibrate, producing in the air corresponding undulations, the effect of which is a musical sound. As the tongue is
struck on the passage of each tooth, the number of vibrations in a second will
correspond with the number of teeth which have struck the tongue in the same
time. This is learned from the dial plate, 0, which indicates the number of
revolutions of the axis, and multiplying this by the number of teeth, we have
the whole number of vibrations in a given time. Upon revolving the wheel
slowly, we may hear the successive shocks of the teeth against the tongue, and
as we increase the velocity, we obtain a more and more elevated sound.
362. Music halls.-Music halls, theatres, &c., should be so constructed as to convey the sounds that are uttered, throughout the space
occupied by the audience, unimpaired by any echo or conflicting sound.
On theoretical grounds, the best form for the walls would be that of a
parabola.  Ornaments, pillars, alcoves, vaulted ceilings, all needless
hollow and projecting spaces, break up and destroy the echoes, and
resonances.  The height of a room for public speaking should be not
more than from thirty to thirty-five feet; for at this point, called the
limit of perceptibility, the reflection and the voice will blend together
well, and thus strengthen the voice of the speaker; if it is higher than




ACOUSTICS.                          267
this, the direct sound and the echo will begin to be heard separately,
and produce indistinctness.
~ 2. Physical Theory of Music.
363. Qualities of musical sounds.-Musical sound is the result
of equal atmospheric vibrations, conveying to the ear tones of definite
and appreciable pitch. The ear distinguishes three particular qualities
in sound. 1. The tone or pitch, in virtue of which sounds are high or
low. 2. The intensity, in virtue of which they are loud or soft; and
3d, quality or timbre, in virtue of which sounds of the same intensity
and pitch are relatively distinguishable.
1. Tone or pitch.-The tone or pitch of a musical sound is high or
low. It depends on the rapidity of the vibratory movement. The more
rapid the vibrations are, the more acute will be the sound.
2. Intensity or loudness.-The intensity, or force of sound, depends on the amplitude of the oscillations; that is, upon the degree of
condensation produced at the middle of the sonorous wave.
A sound may maintain the same pitch, and yet possess greater or
less intensity, according as the amplitude of the oscillations varies.
Thus, if we vibrate a tense cord, the intensity or loudness of the tone will
vary, as the distance which the vibrating parts pass on each side of the line of
rest.
3. Quality.-Quality is that peculiarity in sound which allows us to
distinguish, perfectly, between sounds of the same pitch, and the same
intensity.
Thus, the sounds produced by the flute and clarionet are at once distinguishable. The quality of the sound of instruments appears to depend not only
on the nature of the sonorous body, and the surrounding bodies set in vibration
by it, but also on the form and material of the instrument; and probably, also,
on the form of the curve of vibration.
364. Unison.-Sounds produced by the same number of vibrations
per second, are said to be in unison.
Thus, the siren (360) and Savart's wheel (361) are in unison when we cause
them to make the same number of vibrations in the same time.
365. Melody.-Harmony.-When the vibrations of a progressive
series of single musical sounds bear to each other such simple relations
as are readily perceived by the ear, an agreeable impression is produced, called melody. When two or more sounds, having to each other
such simple relations, are produced simultaneously, it is called a chord,
and a succession of chords, succeeding each other in melodious order,
constitutes harmony.
If we take a series of sounds, the ratios of whose vibrations are as




268              THE THREE STATES OF MATTER.
the following numbers-1: 2: 3: 4: 5: 6: 7: 8: 9: 10-we have the
notes which will produce a series of chords, which, commencing with
the most simple, will gradually become more and more complicated,
until the ear can no longer perceive their relations; when this point is
reached, they will cease to produce chords and harmony.
In sounds whose vibrations bear to each other the relations of
1: 2: 4: 8: 16, every vibration expressed by the lower numbers corresponds with similar vibrations in the higher series. The interval
between such sounds is very great, and is called an octave, because
other sounds having simple relations may be so placed between 1 and 2,
or 4 and 8, as to form with the two extremes a series of eight sounds
having agreeable relations to each other.
Fig. 286 represents the relations                    286
of such tones as produce the most
pleasing effects when sounded together. The dots represent vibra- Octave   4    4               4       
tions; and those which occur simul-  2: 1                        4 
taneously, and therefore increase
each others' powers, are connected 
by vertical lines. On the left of the Fifth    <      ~   ~       o~
figure are the names applied to these  3:2               4       4 ~  
intervals, as explained in section
371.
Fourth     ~ ~ 
366. Musical scale.  Ga-  4.                
mut.-The tones forming a melodious series between any two
adjacent sounds which  are as Major            *                    ~:   **
one to two, are called the musical  5.       Thd          
scale or gamut.
It is generally supposed that the
musical scale was invented by Guido 
of Arezzio, or according to others Minor   
that it was an improvement upon  Third J,      
the Grecian scale, and called the  6: 
gamut from the Greek letter gamnla,
as an acknowledgment of the assistance he derived from that nation.
The sounds which compose the musical scale or gamut, are the
alphabet of music. They are designated, in English, by the letters C,
D, E, F, G, A, B. In French and Italian, by the words ut, or do, re,
mi, fa, sol, la, si.
We may also represent the notes of the gamut in numbers.  In order
to find the relation which exists between the fundamental note, C, or
do, and the other notes, the sonometer, or monochord, fig. 287, is employed




ACOUSTICS.                            269
367. The sonometer or monochord.-This instrument is used to
study the transverse vibrations of cords; and by it we ascertain the
relation between the different notes of the musical scale, and, with the
aid of the siren (360), the number of vibrations by which they are
respectively produced.
Above a case of thin wood, a cord, or metallic wire, A D, is stretched over the
pulley n, by the weights P, on the pan mn, fig. 287. The movable bridge, B, can
287.9 7 ~    B                -lA
be placed at any desired point; and for convenience of adjustment, the scale is
marked off beneath the wire, commencing with C. The string, A D, when
vibrating its whole length, produces the note C; in order to produce the note D,
the movable bridge, B, must be advanced toward the fixed bridge D, until the
length of the cord is but eight-ninths of that which produces the note C. Proceeding in the same manner for the other notes, it will be found, that the length
of the cord corresponding to each note is represented by the following fractions:
Notes,.                         D    E   F   G  A   B  C/
Relative length of cord,..1  ~   t            I  i I. 
Continuing to move the bridge on the sonometer, it will be found, that the
eighth sound, the octave, is produced by a length of cord half that of the fundamental sound. Upon this note, an octave higher than the fundamental note, we
may construct a scale, each note of which is produced by the vibration of a cord
half as long as the same note in the preceding gamut. In the same manner we
may have also a third and a fourth scale.
368. Relative number of vibrations corresponding to each
note.-In order to ascertain the relative number of vibrations corresponding to each note in the same time, it is sufficient to invert the
fractions of the preceding table.  For by the principles already established (309), the number of vibrations is in inverse ratio of the length
of the string. Representing, therefore, the number of vibrations corresponding to the fundamental note C, by 1, proceeding as above, we
form the following table:
Notes,.....        D   E    F    G    A   B    C
Relative number of vibrations,   1         i -     I -      V   a2




270              THE THREE STATES OF MATTER.
Which indicates, that in producing the note D, nine vibrations are made
in the same time that eight are made by the fundamental note C. So,
when the note E is sounded, five vibrations are made for four of C; for
B, fifteen to eight of C, &c.
369. Absolute number of vibrations corresponding to each
note.-By setting the siren, or Savart's wheel, in unison with a given
sound, we obtain the absolute number of vibrations corresponding to
it. If we set the siren in unison with the fundamental C, in order to
obtain the number of vibrations corresponding to the other notes, as D,
we have but to multiply it by the fraction 9, &c. But the fundamental
C varies with the nature, length, and tension of the cord of the sonometer, and therefore the number of vibrations may be represented by
an infinite variety of numbers, corresponding to the different scales.
The notes of the scale whose gamut corresponds to the gravest sound of
the bass, are indicated by 1. To notes of gamuts more elevated, are affixed
the indices 2, 3, &c.; to graver notes are affixed the indices - 1, - 2,
&c.  The number of simple vibrations corresponding to the note C, is
128, and in order to obtain the number of vibrations corresponding to
the other notes, we have but to multiply this number by the fractions
indicated in (368), which gives the following table:
Notes,...        C    D    E    F    G    A        B
Absolute number of simple
vibrations,... 128  144 160  1702 192 2131  240
The absolute number of vibrations for the superior gamut, is obtained
by multiplying the numbers in the table successively, by 2, by 3, by 4,
&c.; for the lower gamut, we divide the same numbers by 2, by 4, &c.
Thus, the number of vibrations of A3 is 214 X 4 = 856 simple vibrations, or 428 complete vibrations.'It must, however, be stated, that there is a slight difference in the actual
number of vibrations producing a particular note as performed in different cities.
Thus, A3 of the pitch adopted at different orchestras, which by the above table
should be produced by 4262- vibrations, varies as follows:
Orchestra of Berlin Opera,.. 437'32
Opera Comique, Paris,... 427'61
Academie de la Musique, Paris,...431-34
Italian Opera, in 1855,....... 449
Inpiano-fortes, which, for private purposes, are generally tuned below concert
pitch, A3 is produced by about 420 vibrations in a second.
There has been a curious progressive elevation of the diapason (pitch) of
orchestras, since the time of Louis XIV., when the la in the orchestra was
(according to Sauveur) 810 simple vibrations (= 405 complete vibrations) per
second; the number at the grand opera is now 898, or nearly a tone higher.
This rise has taken place mainly in the present century-being a semitone since
1823. The causes of this change (which is still in progress) are doubtless owing
* See Appendix, p. 668.




ACOUSTICS.                               271
to the process adopted for preserving and transmitting the true pitch of the
fundamental note.  The final tuning of the diapason is done by the file, and
filing a diapason heats it; at the moment it is in tune with the standard it is
thus heated, and when it afterwards cools the tone rises. When this second
diapason is used for tuning, there is another similar rise, and so it continues.
This gradual elevation of pitch becomes quite sensible after the lapse of one or
two generations. (Am. Jour. Sci. [2] xx. 262.)
370. Length of sonorous waves.-It is easy to ascertain the length
of a sonorous vibration, if we know the number of vibrations made in a
second. For, as sound travels at the rate of 1118 feet per second, if
but one vibration is made in that tinle, the length of the wave must be
1118 feet; if two vibrations, the length of each must be half of 1118,
559 feet, &c.
C corresponds, as we have seen, to 128 vibrations per second; the length of
its waves is, therefore, (1118 -- 128) = 8-73 feet.
The following table indicates the length of the waves corresponding to the
C of successive scales:
Length of waves in feet.  Number of vibrations in a second.
C_3.......   70'.......    16
C-2....              35'.......  32
C_0......   17-5.......        64
C1......      873.......   128
C2......  4-375....... 256
C3......  2-187.......512
C4......      1-093....... 1024
371. Interval.-Interval is the numerical relation existing between
the number of vibrations made in the same time by two sounds, or it is
that which indicates how much one sound is higher than another.
Musical intervals are named from  the position of the higher note
counting upwards from the lower.
C, D, E, F, G,  A,  B, C', D',  E',  F',  G',  A',  B',  C".
1, 9,  A,.A   1    ~   V, 2,  j8 4o,,       I.',   A ),   4.
1st, 2d, 3d, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th, 12th, 13th, 14th, 15th.,1,,, o,.,   1     -, 8,   3o, i     J,   V,   5o   J, 6
In the above table are given, 1st, the letters by which successive notes are
designated; 2d, the relative numbers of their vibrations as compared with the
lowest note; 3d, the names of the notes as compared with the first; and lastly,
the intervals obtained by dividing each note by that which immediately precedes
it. It will be seen that there are but three different intervals between successive notes of the scale; viz. 9, which (being the largest interval found in the
scale) is called a mlajor tone, go called a minror tone, and  t which is called a
semitone, though it is greater than one-half of the interval of either of-the other
tones.  This last is also called a diatonic semitone, to distinguish it from other
divisions made for particular purposes. The difference between a major tone
and a minor tone is $y of a major tone, and is called a comma.




272              THE THREE STATES OF MATTER.
Comparing the notes of the natural scale two and two, we obtain a variety
intervals named as in the following:TABLE OF MUSICAL INTERVALS.
D — FG =AB=                         1; major tone.
) E = G      A            -=         J         _  o of ~; minor tone.
E F = B C -                             = 14 of S- of a; diatonic semitone.
CE -FA =GB=                          5; major third.
E G   AC' —BD' —                     I=  2 of 5; minor third.
DF=                                  - of  =o 8_s  of 21 of; 1 of a
8     8-If 1          O ~T 
minor third.
CF =DG = EA =  GC'=             -; fourth.
AD'=-                                4 =     of 4; sharp fourth.
FB =.                    -=   f of 8 of t;  3 g of perfect
fourth.
CG = EB = FC' = G D'    AE' = I; fifth.
DA =                                 4i  ==  Sf  of; 1     1of a perfect fifth.
B F't=                               6; an inharmonious interval.
CA  = DB  - FD'  GE'-                ~; sixth.
AF' = B      G' =         =   -4 of ~; minor sixth.
F D' I=; an inharmonious interval.
C B = F E' 3'$; seventh, an inharmonious interval.
D C' =-' =G  B A'- =6; flattened seventh, 1-  of 4; decidedly more harmonious than the
seventh.*!
ED' =-  AG' =                          - -  2j of J; minor seventh.
CC'                                  i; octave.
372. Compound chords.-Perfect concord.-It is evidently easy
to take three or four notes whose vibrations have simple relations to
each other, and which taken two and two produce a sensation of harmony.  Such combinations are called compound chords.
If we take the three notes C, E, G, whose vibrations are to each
other as the numbers 4, 5, 6, compared two and two they give the
relations,, -, which constitute by their union three harmonious
intervals called the perfect major accord.  If we take the three notes
E, G, B, which compared two and two give the relations I, 4, -, we find
it differs from  the preceding only in the order of the intervals.  This
series is called the perfect minor accord.
373. A new  musical scale.-By examining the preceding pages it
will be seen that the relative number of vibrations, and the intervals
between different notes in the common musical scale, are made up
entirely of combinations formed from the three prime numbers 2, 3, 5.
and it has been generally stated that relations founded upon the prime
* The ratio 7 is claimed to belong to natural music; see section (373).
4




ACOUSTICS.                              273
7 were too complicated to be appreciated by the ear, or to be executed
either by the voice or by instruments. But the use of the prime seventh
in music has been recently pointed out by H. W. Poole, Esq., of Wor
cester, Mass.*
Multiplying the ratios of the ordinary scale by 48, we have the:TRIPLE DIATONIC SCALE.
(With Common Chord on C, G, and F.)
C,   D,    E,    F,    G,    A,    B,    C'.
48,   54,   60,   64,   72,   80,   90,    96.
I,, M6     9,.
11   _9 )  T-S,           8     1
By introducing the prime 7, Mr. Poole obtains a series which he calls the:DOUBLE DIATONIC SCALE.
(With Common Chord on C, and Chord of 7 and 9 on G.)
C,   D,    E,    (F),    G,    (A),,    C'.
48,   54,   60,    63,    72,    81,   90,   96..X.     )    i,,,,,,       o,   {.
In defence of this introduction of the prime 7 in musical composition, it is
claimed that it is required to fill up the series 1 to 10 (365), as all the other
numbers up to ten are universally admitted. It is further claimed that it is of
frequent use by such masters as Haydn, in the "Dead March of Saul," Mozart,
in the "0 dolce Concento," and that it also occurs in the compositions of
Rossini.
It may also be mentioned that the Chinese, in their musical scale, employ the
flat sevenths instead of the notes in use with us, which gives G to B as 72 to 84
or 6 to 7, and B to C' as 84 to 96 or 7 to 8, the very harmony contended for.
The following example of harmonies, rising through the entire series from
I to 10, is taken from the essay of Mr. Poole.
~- _- -~   - 1~ - -'e                 9 -t~- A- Iip
_    Resolution
Here we have a series of harmonies beginning with the common chord C, E,
(t, 4, 5, 6, and rising in the last example to the full chord of the 10th, all of
which can be appreciated, and are capable of giving a pleasing effect on an
instrument of perfect intonation. The full chord of the 10th contains the following series of vibrations and intervals:* Am. Jour. Sci. [2], IX., p. 68; also Math. Monthly, II., p. 16.
26




274             THE TIREE STATES OF MATTER.
E. 10.....10
M MINOR TONE.
D.   9..........   9
j MAJOR TONE.
C- 8                                              8.....  1..  ) EXTENDED. 7                                               7  SECOND (?)
} IDIMIINISHED
G.  6..                                  6 *6  THIRD (?)
} MINOR THIRID.
E.5.........5
J MAJOR THIRD.
G.  3.........
FIFTH.
C.    2..........   2
OCTA VE.
C.  I..........   1
374. Transposition.-Any tone of the common scale, or any pitch
whatever, may be taken as the basis of another similar scale, provided
the same relative intervals are preserved between the successive notes.
Such change is called transposition of tile scale. If such a change of
pitch is made on an instrument tuned to play the natural scale, additional notes must be provided in one or more of the intervals already
described.  Such additional notes are called sharps (4) orflats (b),
according as the tone corresponding to any given note is raised or
lowered. When new notes are interpolated in every major and minor
tone of the natural scale, there are obtained twelve intervals in the
octave, and the series thus formed is called the chromatic scale.
When the diatonic semitone, AJ, is taken from the major tone, j, the
remaining interval is called a chromatic semitone. When the diatonic
semitone is taken from the minor tone, o, the interval which remains
is called the grave chromatic semitone.
375. Temperament.-In transposing the scale, so as to commence
on any note of the natural gamut, it is supposed, in theory, that every
note may be raised or lowered through an interval of a diatonic semitone, 1.  This would involve the addition of an inconvenient number
of new notes; therefore, in the construction of musical instruments, it
is assumed that such notes as C~ and Db are identical, though they
are not strictly the same, and are not played alike on a violin or harp,
in the hands of a skillful performer.
Temperament is a device by which the multiplication of notes beyond
convenient limits is avoided. For practical purposes, organs, pianofortes, and other instruments, are so tuned as to divide the octave into
12 equal intervals, called chromatic semitones, of equal temperament.




ACOUSTICS.                            275
In this system, all the musical intervals employed, except the octaves,
differ more or less from their true value, as given by theory, and as
demanded by the cultivated ear.
True value. Value in equal temperament.
Minor semitone, 1 = 1042, )              1_
Major semitone, I = 1'067,          = 1.0
Minor third,    6- = 1-200,   /23 = 1-189.
Major third,        =  1-250,   1/2 = 1-260.
12 7
Fifth,            i = 1-500,     27 = 1498.
It is here seen that the minor semitones and major thirds are all too
sharp, while the major semitone, minor third, and the fifths are all too
flat.
Messrs. H. W. Poole and J. Alley have invented an organ, on which
every musical interval can be correctly given without tempering; and
the perfect musical scale can be performed in as many different keys as
may be desired. (Am. Jour. Sci. [2], Vol. IX., p. 68.)
The subject of temperament in all its relations is too extensive to be
treated in this work, and we must refer the reader to musical treatises
for further information.
376. Beating.-When two sounds are produced at the same time,
which are not in unison, alternations of strength and feebleness are
heard, which succeed each other at regular intervals.
This phenomenon, called beating, discovered by Savart, is easily explained.
Supposing that the number of vibrations of               288
the two sounds was 30 and 31; after 30 vibrations of the first, and 31 of the second, there
would be coincidence, and in consequence, beating, while at any other moment, the sonorous 
waves not being superimposed, the effect would be
less. If the beatings are near to each other, there
is produced a continuous sound, which is graver
than the two sounds which compose it, since it
comes from a single vibration, while the other
sounds are made of 30 and 31 vibrations.
The nearer the vibrations approach to exact
unison, the longer is the interval between the
beats. When the unison is complete, then no beats
are heard; when it is very defective, they produce
the effect of an unpleasant rattle.
377. Diapason, tuning-fork.-The diapason is a familiar instrument, -with which
we may produce, at will, an invariable note;
its use regulates the tone of musical instruments.  It is formed from  a bar of steel,
curved, as seen in fig. 288.  It is often sounded by drawing through it




276               THE THREE STATES OF MATTER.
a smooth rod of steel large enough to spring open the limbs, and its
vibrations are greatly strengthened to the ear by mounting it, as in the
figure, upon a box of thin wood, open at one end.  A diapason, giving
C 3, or 256 vibrations in a second, produces a sound comparable with
that from an organ tube.
The diapason is ordinarily formed to produce A3, corresponding to 428 vibra-.
tions in a second.
The whole diatonic scale is thus conveniently constructed, by a series of diapasons, arranged as in fig. 289, upon a sounding-box, A A.
378. Sensibility of the ear.-According to Savart, the most grave
note the ear is capable of appreciating, is produced by from seven to
eight complete vibrations per second.  When a less number is made,
the vibrations are heard as distinct and successive sounds.
The most acute musical sound recognised, was produced by 24,000 complete
vibrations per second. Savart maintains, however, that this is not the extreme
limit of the sensibility of the ear,                289
which is capable  of wonderful
also demonstrated, that two complete vibrations are sufficient to
enable the ear to determine the rapidity of these vibrations; that is,   L l      J  A I  ~
the height of the sound produced. Al           I''U    7  2'        
If his wheel made 24,000 vibra- _  f l                                 l
tions in a second, the two require but Ti66th of a second. The ear may,
therefore, compare sounds which act only during this wonderfully brief interval.
The limit of perceptible sound depends on the amplitude of the vibrations. By
enlarging the dimensions of Savart's toothed wheel, and increasing the distances
between the teeth, more rapid vibrations can be heard. Despretz was enabled
to recognise sounds made by 36,500 complete vibrations per second.
Many insects produce sounds so acute as to baffle the human ear to distinguish
them; and naturalists assert, that there are many sounds in nature too acute for
human ears, which are yet perfectly appreciated by the animals to which they
are notes of warning, or calls of attraction.
The natural la is said to be heard by rapidly moving the head; owing to the
motion of the small bones of the ear. See ~ 393.
Q 3. Vibration of Air contained in Tubes.
379. Sonorous tubes.-Mode  of vibrating.-In  wind instruments, withl walls of suitable thickness, the column of air contained in
the tubes alone, enters into vibration.
The material of the tube has no influence upon the pitch, but affects the
quality (363) in a striking and important manner. The pitch of the sound
produced, depends partly on the size and situation of the embouchure; still more
on the manner of imparting the first movement to the air, and partly also on
varying the length of the tube containing the column of air. The difference in
the quality of the tones produced by pipes of different materials is most probably
owing to a very feeble vibration of the materials themselves.




ACOUSTICS.                             277
Sonorous vibrations are produced in tubes in a number of ways.
1. By blowing obliquely into the open end of a tube, as in the Pandean pipe.  2. By directing a current of air  290                291
into an embouchure, or near the closed end of
the tube. These tubes are called mouth-pipes.                     V
3. By thin vibrating laminae of metal, or of
wood, called reeds, or by the vibration of the
lips, acting as reeds.  4. By a small flame of
hydrogen gas.
380. Mouth-pipes.-Fig. 290  represents
the embouchure of an organ tube, fig. 291,
that of a whistle or flageolet.  In these two   l              Io
figures the air is introduced by the opening, i                \
(called the lunmire); b o is the mouth, of which     \0 
the upper lip is beveled. The foot, P, fig. 291,       I
connects the pipe with a wind-chest.  When a
rapid current of air passes through the inlet,                  p
it encounters the edge of the upper lip, which
partially obstructs it, causing a shock, so that the air passes through
b o in an intermittent manner. These pulsations are transmitted to
the air in the tube, making it vibrate, and producing a sound.
In order to have a pure sound, there must exist a certain relation between the
dimensions of the lips, the opening of the mouth, and the size of the lumiire.
Again, the length of the tube must bear a certain ratio to its diameter. In those
wind instruments, like the flute, flageolet, &c., in which various notes are produced by the opening and closing of holes in their sides by means of fingers or
keys, there is a virtual variation in the length of the tube, which determines the
pitch of the various notes produced. The number of vibrations depends upon
the dimensions of the tube and the velocity of the current of air.
381. Reed-pipes.-A reed is an elastic plate of metal, or of wood,
attached to an opening in such a manner, that a current of air, passing
into the opening, causes the plate to vibrate. This vibration is propagated to the surrounding air. Reeds are found in hautboys,. bassoons,
clarionets, trumpets, and in the Jews-harp, which is the most simple
instrument of this species.
Fig. 292 represents a reed pipe, mounted on the box of a bellows, Q. A glass,
E, in one of the walls of the tube, allows the vibrations of the reed to be seen
The case, H, serves to strengthen the sound. Fig. 293 represents the reed separated from the tube. It is composed of a rectangular case of wood, closed at its
lower end, and open at the top, at a point o. A plate of copper, c c, contains a
longitudinal opening, designed to allow the passage of the air from the tube, M N,
through the orifice o. An elastic plate, i, almost closing the aperture, is confined
at its upper end. The sliding rod, r, curved at its lower end, permits the regulation of the pitch, by alterations in the length of the vibrating part of the plate.
When a current of air passes in through the foot, P, the reed vibrates, altor26*




278               THE THREE STATES OF MATTER.
nately opening and closing the aperature. The vibrations being very rapid, the
sound produced varies in pitch with the velocity of the current. This sound is
transmitted to the exterior air through         292             293
the opening o.                                                   7*
In this kind of reed, the vibrating 
plate passes through the aperture, with-         1li1il81      ilI
out its walls, and the tone is remarkably    H /l11.
pure and free from any harshness. The
quality of the tone of a reed-pipe depends
much on its figure, also upon the construction of the reed, and the material
of which it is composed.    294 
In the French horn,                           29 l  
the trumpet, and other
similarinstruments, the
sound is produced by
the vibration of the lips                                         be
of the performer, acting                                             o
like reeds.: 
382. Gas  jet. —                                               i
A  jet of hydrogen,
burned within a tall
tube  of  glass,  or
other material, occasions, if accurately                    iji' iAl,                  P
adjusted, a musical'note
note.                                   _
A simple form of this arrangement is seen in fig. 294, where hydrogen, generated by the action of dilute sulphuric acid on zinc in the bottle, is burned from
the narrow glass tube, within one of larger dimensions. It is better to take the
gas from a reservoir, or gas jet, with a key interposed, to regulate the volume
of the flame. The cause of the vibrations and sound in this case is to be found
in the successive explosions of small portions of free gas, mingled with common
air. The heat occasions a powerful ascending current of air, momentarily
extinguishing the flame, and at the same instant permitting the mixture of the
atmospheric oxygen with a portion of inflammable gas. The expiring flame
kindles this explosive mixture, and relights the jet. As these successive phenomena occur with great rapidity, and at regular intervals, the necessary consequence is a musical note.
For a full discussion of the phenomena of singing flames, see a memoir by
Prof. W. B. Rogers, Am. Jour. Sci. [2] xxvi. 1.
383. Musical instruments. —The principles already explained in
this chapter, will illustrate the peculiar power of the several sorts of
musical instruments in common use. It is inconsistent with our limited
space to describe, in detail, these several instruments. Such details
belong to a special treatise on music. Musical instruments are grouped
chiefly, under the heads of wind, and stringed instruments, and those
like the drum, in which a membrane is the source of vibration.




ACOUSTICS.                            279
Wind instruments are sounded, either with an embouchure, like a flute, or with
reeds. The first division includes the flute, pipe, flageolet, &c., and in the second
are found the clarionet, bassoon, horns, trombones, &c. The organ also is a
wind instrument, and is, incomparably, the grandest of all musical instruments,
as its power and majesty is without parallel in instrumental combinations.
Striged instrulnents are all compound instruments. The sounds produced by
the vibration of the cords are strengthened by elastic plates of wood, and
enclosed portions of air, to which the cords communicate their own vibrations.
They are vibrated either by a bow, as in the violin, by twanging, as in the harp,
or by percussion, as in the piano.
Druems are of three sorts; the common regimental or snare drum, which is a
cylinder of brass, covered with membrane, and beaten on one end only; the
bass, or double drum, of much larger dimensions, and beaten on both heads;
and thirdly, the kettle drum, a hemispherical vessel of copper, covered with
vellum, and supported on a tripod. This drum has an opening in the metallic
case, to equalize the vibrations. They all depend, of course, upon the vibration
of tense membranes (318).
384. Vibration  of air in  tubes.-Laws of Bernoulli.-The
following laws of the vibration of air contained in tubes, were discovered by Daniel Bernoulli, a celebrated geometrician who died in 1782.
We may divide tubes into two classes.
a. Tubes of which the extremity opposite the mouth is closed.
b. Tubes open at both extremities.
a. Tubes of which the extremity opposite the mouth is closed.
1st. The same tube may produce different sounds, the number of
vibrations in which will be to each other as the odd numbers, 1, 3, 5,
7, &c.
2d. In tubes of unequal length, sounds of the same order correspond
to the number of vibrations, which are in inverse ratio of the length
of the tubes.
3d. The column of air, vibrating in a tube, is divided into equal
parts, which vibrate separately and in unison. The open orifice being
always in the middle of a vibrating part, the length of a vibrating part
is equal to the length of a wave corresponding to the sound produced.
b. Tubes open at both extremities.
The laws for tubes open at both extremities, are the same as the preceding, excepting that the sounds produced are represented by the series
of natural numbers, 1, 2, 3, 4, &c.; and that the extremities of the
tubes are in the middle of a vibrating part.  Again, the fundamental
sound of a tube open at both extremities, is always the acute octave of
the same sound in a tube closed at one extremity.
Demonstration.-If the column of air contained in a tube vibrates as a
single wave, the number of vibrations will evidently be equal to the velocity
of sound, represented by V, divided by the length of the tube, L, or by the
V
quotient -. If the column of air is divided into a number of gegment6, eubh
Li




280               TIIE THREE STATES OF MATTER.
vibrating separately, let I represent the length of one of these segments, and
V
the number of vibrations per second will evidently be   -.
(a) If the pipe containing the column of air is stopped at both ends. there will
be a node at each end. Let n represent the number of nodes including the two
ends; the number of vibrating segments will be n - I, the length of each vibraL
ting segment will be I=, and the number of vibrations per second will be
n~1
V            V
=(i - 1).-, in which we may substitute for is any number greater than
L
V VV
unity, giving the series of possible vibrations 1.-, 2-, 3-, &c.
L   L. L
(b) If the tube is closed at one end, that end must be regarded as a node, and
the open end of the tube as the middle of a vibrating segment.. Therefore,
2, - 1
2(1 - 1) + 1 = 21I -1 will be the number of half segments, and    ~  will be
2
the entire number of vibrating segments contained in the length, L, and the
2n1-1 V
number of vibrations per second will become        - 
2   L
Substituting for is the integers 1, 2, 3, &c., we obtain the following series of
vibrations for the different tones of the pipe:V  V  V
i-L; -.; i. &-.
If the pipe is open at both ends, as before let n be the number of nodes. The
number of complete ventral segments will be n- 1, and there will be a half
segment at each end, making it segments in the length L. The length of a comL
plcte segment will therefore be -, and the number of vibrations per second is
V
~i —, making   = — 1, 2, 3, &c. We obtain the following series of vibrations corL
responding to different tones of the pipe:V  V  V
1.- 2-; 3.-, &c.
L    L'   L
The series of vibrations for the tones produced by a pipe will be as follows:In a pipe open at both ends, or closed at both ends,.    1, 2, 3, 4, 5, &c.
In a pipe open at only one end.,...,, I,,1. 
In the latter case the fundamental note is an octave lower than when both
ends of the tube are open, or when both ends are closed. The particular tone
that a pipe will produce in either of these series depends on the strength of the
blast.
385. Construction of musical instruments.-Practically, the end
of the tube where sound is formed is never entirely closed, and usually
the embouchure is on one side of the tube.  The laws of Bernoulli
adapted to these conditions give for the construction of musical instruments the following practical rules:1. The length of the tube is equal to the quotient of the velocity of




ACOUSTICS.                            281
sound divided by the number of vibrations and diminished by twice
the breadth of the tube.
2. The number of vibrations is equal to the quotient of the velocity of
sound, divided by the length of the tube, increased by twice its breadth.
3. The length of a cylindrical organ tube, flattened at the embochure,
is equal to the quotient of the velocity of sound divided by the number
of vibrations, and diminished by five-thirds the diameter of the tube.
(Comptes Rendus, T. L. 1860, p. 176.)
386. Vibrating dams.-Illustrations of the vibration of air in tubes're often found at waterfalls.  The horizontal column of air enclosed
behind the descending sheet of water is rarefied by friction of the water
which carries away a portion of the air, and the external air rushing
in at the sides is thrown into vibrations, which are often so perceptible
as to endanger the safety of persons approaching too near the cataract.
At the falls of IIolyoke, Mass., the descending sheet of water has a breadth
of 1008 feet, with a fall of 30 feet, and varying from 5 feet to 3 inches thick.
The pulsations of the air rushing in behind the waterfall vary from 82 to 258
per minute.
Says Professor Snell, who has described these phenomena at length,* "At
ore time, when I witnessed the comparatively slow oscillations of 82 per minute,
I was surprised by the great strength of the current of air, as it rushed into the
opening at the end of the dam.  I could not venture within the passage through
the pier, lest I should be swept in behind the sheet; nor could I stand at the
entrance of the arch without bracing myself, by placing both hands on the
corners." These vibrations are shown by Professor Snell to follow the laws of
Bernoulli for the vibration of air in tubes., 4. Vocal and Auditory Apparatus.
I. OF VOICE AND SPEECH.
387. Voice and speech.-In nearly all the air-breathing vertebrate
animals, there are nrrangements for the production of sound, or roice,
in some part of the respiratory apparatus. In many animals the sound
admits of being variously modified and altered during and after its production; and in man one of the results of such modification is speech.
388. The vocal apparatus of man  consists of tie thorax, the
trachea, the larynx, the pharynx, the mouth, and the nose, with their
appendages.
The thorax, by the aid of the diaphragm and the intercostal muscles acting
c, the lungs within, alternately compressing and dilating them, performs the
part of the bellows producing a current of air for the production of sound. The
trachea, or the widlpipe, extending from the larynx to the lungs, acts as a tube
to convey the air from the lungs to the organs more immediately corcerned in
the production of voice and speech. The larIcty, which may be considered as
the musical organ of the voice, corresponds to the mouth-piece or that part of
the organ tube which gives the peculiar character to the sound. The phar#a.x
* Am. Jour. Sci. [2] Vol. XXVIII. p. 228.




282               THE THIREE STATES OF MATTER.
is a large cavity above the larynx, which, by the varying form and tension of
its walls. modifies the tones of the voice. The mouth and nasal passages correspond to the upper part of an organ tube from  which the vibrations of the
column of air are thrown into the atmosphere.
The larynx.-This organ is composed essentially of four cartilages,
called respectively the thyroid, cricoid, and the two arytenoid cartilages.  The cavity of the larynx is nearly closed by two pairs of membranes, called the vocal cords, the opening between which is called
the glottis.                                                095
In fig. 295, showing avertical section through
the larynx and glottis, the position of the thy- 
roid and cricoid cartilages is seen in b b, a a.
The thyroid cartilage consists of two flat plates
whose upper edges are curved somewhat like
the letter S, and forms a prominent projection
on the throat of man, visible exteriorly, and
vulgarly called Adam's Apple.  The cricoid
cartilage, a, lies below the thyroid.cartilage,
and is in fact only an enlargement of one of
the cartilaginous rings forming the wind-pipe.
The position of the arytenoid cartilages is over
the cricoid cartilages. These several cartilages,
with the hyoid bone, serve as points of attachment for the muscles forming the proper vocal
apparatus. The two chief tongues oC the glottis,
or proper vocal cords, cc, extend from  the
thyroid cartilage to the arytenoid cartilages,
and leave between them  a fissure, the rima
vocalis, or glottis, shown better in fig. 297. This fissure leads on one side into
the trachea, which lies below the larynx, and on the other into the cavity of the
larynx itself, which communicates with the cavities of the mouth and nose.
Besides the proper vocal cords, there are the ventricular cords, d d, situated
a small distance above them in the epiglottis; they are less developed than the
first.  The ventricllar cords have no part in the production of vocal sounds,
which, however, they doubtless serve to modify and strengthen in the same way
as the conical case surmounting an organ tube.
Between these two sets of cords are seen the deep depressions, called the
ventricles of the glottis.                                            296
The voice is produced in the larynx; for if an opening is pierced
into the trachea, below the larynx, the air escapes by this opening,
and it is not possible to produce any vocal sound. If an opening
is made above the larynx, it does not prevent the formation of
sound. Magendie mentions the case of a man who had a fistulous
opening in his trachea, and who  could not speak unless he
closed it, or wore a tight cravat.  
The glottis.  A clear idea may be obtained of the form
and action of the glottis, by supposing two pieces of India
rubber stretched over the orifice of a tube, so that a small fissure is left
between them, fig. 296.




ACOUSTICS.                            283
By forcing air through such a tube, sounds will be produced, varying with
the tension of the membranes and the dimensions of the aperture. The glottis
is a fissure-like opening, bounded by similar membranes. By means of a series
of small muscles, the vocal cords may be extended or relaxed at pleasure, while
other muscles afford the power of altering the width of the vocal fissure.
The vocal ligaments being thicker at their free edges than elsewhere, they
vibrate like cords, but as they also extend like plates to the sides of the larynx,
their vibrations are very nearly allied to the vibration of reeds. There has been
much controversy as to whether the larynx and glottis are to be considered as
a reed, or as a stringed instrument. It is probably more correct to say that it
acts upon the principles of both combined.
389. Mechanism  of the voice. —The formation of sound in the
larynx, as has been already suggested, is produced by the vibration of
the vocal cords, acting as a species of membranous reed, under the
influence of air from the lungs. The sound being produced as in ordinary reeds (381) by the intermittent current              297
of air.
The glottis is the original seat of the sound,
and, although other parts of the respiratory
apparatus have a certain influence in modifying
the tone, they have no share whatever in the
production of the sounds, or in determining
their pitch.
When at rest, the lips of the glottis are  ly
wrinkled and plicated, so that the air in respiration passing through the fissure fails to put
the membranes in vibration. But as the musician tunes his instrument by increasing or diminishing the tension of its vibrating strings, so something like this
occurs with the human larynx.  The two conditions of the glottis are
beautifully shown by the two parts of fig. 297, from  Muller.  The
upper shows the organ at rest, the vocal cords, c c, being relaxed, while
in the lower, these cords are shown as in the act of vibrating; the small
air passage. o, opening into the trachea, is never closed. When sounds
are to be produced, the fissure is contracted and the membranes receive
the degree of tension necessary for vibration. The sound varies according to the tension of the membranes, the magnitude of the fissure, and
the form and magnitude of the passages through which the air thus put
into vibration, passes before it issues into the atmosphere.
390. Range of the human voice.-In speaking, the range of the
human voice is subject to but very little variation, being generally
limited to half an octave. The entire range of voice in an individual is
rarely three octaves, but the male and female voice taken together may
be considered as reaching to four.




284               THE THREE STATES OF MATTER.
There are two kinds of male voices, called bass and tenor, and two
kinds of female voices, called contralto and soprano, all differing from
each other in tone. The strength of the bass voice is in general greater
on the low tones than the tenor. The contralto is also stronger on the
low tones than the soprano.  But bass singers can sometimes go very
high, and the contralto frequently sings the high notes like soprano.
The essential difference between the bass and tenor voices, and
between the contralto and soprano, consists in the tone or "timbre"
which distinguishes them even when they are singing the same note.
The barytone is intermediate between bass and tenor, and the mezzosoprano is, in like manner, found between the contralto and soprano.
These two qualities of voice have a middle position as to pitch in the
scale of male and female voices.
The different qualities of tenor and bass, and of alto and soprano voices,
probably depend on some peculiarities of the ligaments, and the membranous
and cartilaginous parietes of the laryngeal cavity which are not at present
understood. We may form some idea of these peculiarities, by recollecting that
musical instruments made of different materials, e. g., metallic wires and gutstrings, may be tuned to the same note, but that each will have a peculiar quality
or " timbre."
The following are the limits of the different classes of voice, as determined by
Cagniard de Latour, Savart, and others, the numbers annexed being the number of double vibrations of the glottis produced in a second of time.
(1056,                    (930,                 0
So                 Mezzo-soprano, Me soprao,   20.    Contralto,  176.
264.                                         176.
Tenor,                                              Barytone,  { 110.   82'5.
391. Ventriloquism, stuttering, &c.- Ventriloquism is supposed by
many investigators to consist chiefly in the use of inspiratory sounds; this is
true only to a certain extent. The art of the ventriloquist depends greatly on
the correctness of ear and flexibility of organ, through which common tones
are modulated to the position and character in which the imaginary person is
supposed to speak; other means often being used to heighten the deception, as
concealing the face that the play of organs may not be observed; often in
speaking with expiratory notes, the air expelled by one expiration is distributed
over a large space of time, and a considerable number of notes.
In stuttering, the several organs of speech do not play in their normal succession, and thus are continually interfered with in convulsive impulses and inefficient adjustments. The cause of this result lies almost wholly in the nervous
apparatus which rules over the organs of speech. Important remedial means
are, to study carefully the articulation of the difficult letters, to practice their
pronunciation repeatedly and slowly, and to speak only when the chest is well
filled with air.
In deaf and dumb persons the organs of speech have originally no essential
defects. The true cause of their dumbness lies in their inability to perceive
sound. The impossibility of appreciating the several sounds, and thus gradually acquiring the power of properly adjusting the organs of speech, is the
chief reason why the second infirmity is associated with the first.




ACOUSTICS.                           285
392. Production  of sounds by inferior animals. —The sounds
which the different animals produce are peculiar to the class to which
they belong; thus the horse neighs, the dog barks, the cat mews, &c.
These various modifications depend on the peculiar structure of the
larynx, but more upon the form and dimensions of the nasal and other
cavities, through which the vibrating air passes.
The cat is distinguished from other maLmmifers by the almost equal development of the inferior and superior vocal cords. Many of its notes are almost
human. The horse and ass are supplied with only two vocal cords. Animals
which howl, and are heard at great distances, have generally large laryngeal
ventricles.
Birds are furnished with two larynx, a superior and inferior, which
serve at the same time for the entrance and exit of air, and for the
purposes of vocalization.  The upper larynx, which corresponds to the
larynx in mamrinifers, can only be regarded as an accessory of the
voice.  The lower larynx is the true larynx; it is placed at the lower
part of the trachea, where it branches. Those birds in which it is
absent are voiceless. The voice of birds is produced, like that of mammifers, by the vibration of the cords of the glottis.
Insects, in general, produce sounds remarkable for their acuteness.
Their sounds are produced in a great number of ways, some effecting
it by percussion, and some by the friction of exterior horny organs
upon each other, as, for example, in the grasshopper. In others, the
swiftly recurring beatings of the wings produce sounds, as with the
musquito.  Many insects produce sound by the action of some of their
organs on the bodies around them, as, for example, the various insects
which gnaw wood.*
II. THE EAR.-HEARING.
393. Auditory apparatus of man.-In the ear, impressions are not
at once made upon the sensory nerve, by the body which originates the
sensation, but they are propagated to it through the medium of the
atmospheric air.
The organ of hearing in man is composed of three parts: the external ear, the middle ear, or tympanum, and the internal ear, or labyrinth.
The external ear consists of (1) the pinna, or pavilion, a, fig. 298,
which collects the soniferous rays, and directs them into (2) the auditory canal, or meatus auditorius, b.
The peculiar form of the pinna, with its numerous elevations and depressions,
has not as yet been satisfactorily shown to be related to the principles of
acoustics.
The auditory canal proceeds inwards from the pinna, to the tympanum, c;
* See Appendix, p. 668.
27




28s;             THIE TIIREE STATES OF MATTER.
it is an elliptical tube, about an inch long. Its interior is protected by haira,
and by a waxy secretion.
The middle ear, tympanum, or tympanic cavity.-The middle
ear is a cavity in the temporal bone filled with air, and somewhat hemi298
spherical in form; it measures about half an inch in every direction.
It extends from the tympanum, c, fig. 298, to o andfJ and encloses the
chain of bones, c d ef, called the ossicles, or little bones, of the ear.
The middle ear is separated from the auditory canal by a thin oval
membrane, the menzbrana tympani, which is placed obliquely across the
end of the canal, at an angle of about 45~, its outward plane looking
downwards and forwards.
The Eustachian tube is a membranous canal leading from the anterior
portion of the middle ear downwards and forwards to the pharynx, with
which it communicates by a valvular opening that is generally closed.
The Eustachian tube gives exit to the mucus which forms in the middle ear,
and also permits the entrance of air to preserve equality of pressure on the
external and internal surfaces of the membrana tympani.
The discomfort produced by unequal pressure on the two surfaces of the
membrana tympani may easily be understood by closing the nose and pertorming the act of swallowing, when the air will be partially exhausted from the
middle ear. The external pressure on the membrana tympani then becomes
greater than the internal, an unpleasant sensation is produced, and the sense
of hearing is obscured. Forcible distension of the pharynx in blowing a horn
or trumpet often produces a disagreeable fullness in the ears, by forcing air




ACOUSTICS.                               287
through the Eustachian tube into the middle ear. A cold often impairs the
sense of hearing by obstructing the Eustachian tube.
A chain of three small bones, the ossicles of the tympanum, passes
through the middle ear from the membrana tympani to the entrance
of the internal ear. These bones are shown separated from each other
in fig. 299.
The malleus, or hammer-bone, m, the incus, or anvil, o, and the stapes, or
stirrup, t. They are connected with each other in such a manner      299
as to allow of slight movements. This chain of bones is attached
at one end, as is shown in fig. 298, by the handle of the malleus,        o
to the tympanic membrane, and at the other by the foot of the M2
stirrup, to the membrane of the fenestra ovalis.                      
The muscles which act upon these small bones are supposed to
have the power of giving more or less tension to the membranes
which they connect, and thus rendering them more or less sensi- 
tive to sonorous undulations.
The internal ear, called, from  its complicated structure, the labyrinth, has its channels curved and excavated in the petrous bone, the
hardest of any in the body. The labyrinth consists of three parts; the
vestibule, the semicircular canals, and the cochlea.
The vestibule, g, fig. 298, is a central chamber, formed in the petrous bone;
in it are a number of openings, for branches of the auditory nerve, small
arteries, &c. In its external wall, the fenestra ovalis is found.
The semicircular canals are three in number, opening into the vestibule at its
posterior and upper part, and placed in planes at right angles to each other.
Within these canals are placed flexible tubes, of the same form, called membranous canals, filled with fluid.
The cochlea, i, is a conical tube, wound spirally, making two and a half turns.
It resembles a snail's shell in appearance; whence its name. Its interior is
divided by a spiral lamina, called the lamina spiralis, into two passages which
communicate by a little hole in the upper part of the            300
helix. Between the membranous and the bony labyrinths,
a peculiar liquid (the perilymph) intervenes, which also
fills the cavities and cochlea; the membranous labyrinth.
is distended by another liquid (the endolymph). Within          /^
the labyrinth thus filled with liquid, the terminal filaments  //
of the auditory nerve are placed.
They are expanded in the vestibule, spread out upon  the
lamina spiralis, and also in: 
certain  enlargements, called  l                  8 
ampullie, at the entrance of -ii
the semicircular canals; but
they do not traverse the semi- 
circular canals.
Fig. 300 is a magnified view of the labyrinth, showing the form and relation
of the vestibule, semicircular canals and cochlea, partly laid open, so as to display their interior construction.




288               THE THREE STATES OF MATTER.
394. Functions of the different parts of the ear. —l. The waves
of sound passing into the external ear, are collected and directed into
the auditory canal, and strike upon the tympanic membrane, which is
thus thrown into vibration.
2. The chain of bones connecting the membrana tympani with the
fenestra ovalis, receives the vibrations and transmits them to the vestibule through the membrane which covers the fenestra ovalis.
3. Vibrations thus excited in the fluid which fills the labyrinth, are
received by the expanded filaments of the auditory nerve, and the
sensation of sound is thus transmitted to the brain.
In considering the uses of the different parts of the middle and internal ear,
it is necessary to refer to the following principles, which have been fully
demonstrated by experiment.
1. Atmospheric vibrations lose much of their intensity when transmitted
directly to either solids or liquids.
2. The intervention of a membrane greatly facilitates the transmission of
vibrations from air to liquids.
3. Vibrations are readily transmitted from air to a solid body, if the latter is
attached to a vibrating membrane, so placed that the vibrations of the air act
upon it.
4. Sonorous vibrations are communicated from air to water without any perceptible loss of intensity, when to the membrane forming the medium of communication there is attached a short solid body, which occupies the greater part
of its surface, and is alone in contact with the water.
5. A solid body fixed in an opening by means of a border membrane, so as to
be movable, communicates sonorous vibrations, from air on one side to water
or the fluid on the other side, much better than solid media not so constructed.
But the propagation of sound to the fluid is rendered much more perfect if the
solid conductor thus occupying the opening is by its other end fixed to the
middle of a tense membrane which has atmospheric air on both sides.
These principles enable us to understand that vibrations are communicated to
the internal ear with greater intensity, by means of the membrana tympani and
the chain of tympanic ossicles, than if these organs did not intervene between
the atmospheric air and the internal ear. We find that in the lower orders of
animals, where hearing is less acute than in man, the middle ear and tympanic
ossicles are wanting. The air in the cavity of the tympanum serves also to
insulate the chain of small bones, and preserve the purity and intensity of the
vibrations which are transmitted. The communication between the middle ear
and the external air, by means of the Eustachian tube, is thought to prevent
reverberation and echoes in that cavity.
The sound of a tuning-fork, or other sonorous solid body, applied to the teeth,
or any bone of the head, is heard more distinctly than when the sound is transmitted to the ear by means of the air; it has therefore been concluded that the
cochlea, and especially the lamina spiralis, facilitates the appreciation of such
sounds. In regard to the use of the semicircular canals, the opinions of physiologists are as yet divided.
For full discussions of the functions of different parts of the ear, the student
is referred to Carpenter's Physiology and to Todd & Bowman's Physiology.
395. Natural diapason.-Cagniard  de Latour, one of the best




ACOUSTICS.                            289
modern authorities in acoustics, satisfied himself that he heard the
sound la (A of the musical scale) sounding within his head when he
agitated it from side to side. Mr. Jobard suggests that this natural la
is caused by the contact of the malleus against the incus in the ear, a
contact easily made by a rapid movement of the head, the neck being
disembarrassed of clothing.  (Am. Jour. Sci. [2] XXVI. 97.)
396. Organs of hearing in the lower animals.-The zoophytes
appear to be wanting in the sense of hearing, and no special auditory
apparatus has been discovered in insects, although they do not appear
to be altogether insensible to sound.  In the mollusca, the organ is a
sac, filled with liquid, in which the last fibrils of the acoustic nerve are
diffused, or a nerve fibril, in connection with a little stony body (an
otolith), included in a sac of water. These animals can only distinguish
one noise from another, or their quality, and that imperfectly, and have
no perception of musical notes. This organ, corresponding, as is assumed, to the semicircular canals, increases in complexity as we rise in
the scale of being. In lizards and scaly serpents, the ear commences
with the tympanic membrane; and there is added a conical cochlea.
As we pass through them, the plan is further developed; the tympanic
cavity, Eustachian tube, the chain of bones, &c., appear. In birds
there is a continued improvement, and all the aerial tribes of mammals
have external ears, while a full development of all the auditory parts is
reached only in man.
Problems in Acoustics.
Velocity of Sound.
153. The rumbling of thunder was heard 71 seconds after the corresponding
flash of lightning was seen; what was the distance of the discharge?
154. Calculate the velocity of sound in air at a temperature of 90~; also at
40~ below zero of Fahrenheit's scale.
155. What time would be required to transmit sound ten miles in the waters
of a quiet lake?
156. In what time would sound travel a distance of 31 miles in each of the
following substances: iron, wood, carbonic acid, hydrogen gas, vapor of alcohol
at 1400, vapor of water at 154~?
157. What time was required to transmit the sound of the explosion of the
volcano at St. Vincent's to Demerara (see page 260), supposing the sound to
have travelled in the air alone?
158. At what distance from the source of sound must a reflecting surface be
placed that an echo may be heard three seconds after the original sound?
159. From the top of a precipice a stone was let fall, and after 51- seconds it
was heard to strike the bottom. What was the height of the precipice?
27*




290                TIIE  THREE STATES OF MATTER.
160. What was the distance of the meteor which was heard at Windsor Castle,
in 1783, ten minutes after it disappeared, assuming the air at 50~ F.?
161. An observer supposes himself in the range of a distant cannon, the report
of which he hears 19 seconds after seeing the flash; how soon may he apprehend danger from the ball, supposing it to fly at the rate of a mile in eight
seconds?
162. The flash of a gun throwing shells was seen due east from the observer;
after three seconds the report was heard; after another interval of three seconds
the shell was seen to explode 40~ south of east, and the explosion of the shell
was heard three seconds later; to what distance was the shell thrown? and what
was its velocity of flight?
Physical Theory of Music.
163. A metallic wire, placed upon the sonometer, vibrates 300 times in a
second; by how much must its length be diminished that it may make 370
vibrations per second?
164. What number of vibrations per second are required to give the note G 1
of the Italian opera?
165. What is the length of a wave in air when an instrument sounds E 3 of
the Berlin opera?
166. What are the relative numbers of vibrations required to form the notes
E and D sharp?
167. What is the interval between C sharp and D flat when both notes aro
correctly sounded?
168. How does the interval of four perfect fifths differ from a major third in
the scale two octaves above the key note?
169. What is the fractional expression for the chromatic semitone? What for
the grave chromatic semitone?
170. What is the number of beats in a minute formed by two tones whose
vibrations are as 24 to 25, when the higher note makes 750 vibrations per second?
171. Calculate the number of vibrations per minute at the Holyoke Falls, for
1, 2, and 4 nodes respectively, the breadth of the dam 1008 feet, the enclosed
column of air being entirely open at both ends.
172. Estimating the velocity of sound at 340 metres per second, what number
of vibrations per second will be produced in a square organ tube whose length
is 1-13 metres and its breadth 0-08 metres?
173. The organ of the church of Saint Denis, in Paris, is tuned to the normal
la (A 3) of 880 simple vibrations per second, and a square tube 9-566 metres
long and 0-48 metres broad, was constructed to play do_2 (C_2), but on trial it
was found too flat. What alteration of its length would correct its tone?
174. Calculate the respective lengths of a series of square organ tubes to play
the scale commencing with C 1, the longer tube having a breadth of 4 inches,
and each tube in the ascending scale having a breadth I of an inch less than
the preceding; the normal la being reckoned at 856 simple vibrations.
175. Calculate the dimensions of a series of cylindrical organ tubes for the
scale commencing with C 4, the longer tube having a diameter of 1 inch, and
the others in the series diminishing regularly in diameter by 26 of an inch; the
organ to be tuned as in the last example.
176. What are the names of the next three higher notes in the scale which
the tube playing G 4 in the last example would give by sufficiently increasing
the strength of the blast?




PART THIRD.
PHYSICS OF IMPONDERABLE AGENTS.
LIGHT, HEAT, AND ELECTRICITY.
CHAPTER I.
LIGHT, OR OPTICS., 1. General Properties of Light.
397. Optics.-Light.-Optics (from the Greek verb onroial, t(
is that branch of physical science which treats of the nature and properties of light.
Light is a mysterious agent, acting upon the organs of vision, and
imparting to us a knowledge of external things. It brings us into
relation with surrounding objects, enlarging the sphere of our habitation, in a measure annihilating distance, unfolding to us the beauties
of nature, and acting as a perpetual source of enjoyment.
398. Nature of light.-Theories.-In regard to the nature of
light, a great diversity of opinion has prevailed among philosophers.
(a) Corpuscular theory.-Sir Isaac Newton maintained that the
phenomena of light are produced by luminous corpuscles thrown off
from burning bodies, each particle producing, in its flight, vibrations
in the surrounding ether similar to the waves produced by a stone
falling into the water.
(b) Undulatory theory. —luyghens maintained, in opposition to
Newton, that light consisted solely of vibrations in an ethereal medium,
without the onward progress of any substance whatever. This theory
(291)




292          PHYSICS OF IMPONDERABLE AGENTS.
has been investigated and defended by many of the ablest philosophers:
by Young, Malus, Fresnel, Brewster and others, and is now generally
received.
The undulations producing the phenomena of sound take place in
the same direction that the sound itself moves; but the vibrations of
light are supposed to move at right angles to the direction in which
light is propagated. It is difficult to explain all the phenomena of light
even on this theory.
(c) An oscillatory theory of light has been proposed by Mr. Rankine,
of Glasgow.*  In this theory, the particles of luminiferous ether are
supposed to rotate on their axes, by the influence of a species of magnetic force, which is wholly destitute of effect in producing resistance
to compression, so that it is no longer necessary, as in the undulatory
theory, so suppose the luminiferous medium to have the properties of
an elastic body. The same mathematical formulae are employed, with
this hypothesis, as for the undulatory theory. Whether this theory can
be applied to explain all the phenomena of physical optics, remains to
be proved.
399. Sources of light.-Phosphorescence.-The sources of light
are the sun and stars, heat, chemical combinations, phosphorescence,
and electricity.
We know not the real cause of the light emitted by the sun and
stars, but we know that bodies become luminous at a high temperature,
and shine more vividly in proportion to the intensity of the heat, from
which we are accustomed to suppose that heat and light are only modifications of one and the same cause. Artificial lights depend, in general,
upon combustion, or the union of the oxygen of the air with burning
bodies. This chemical action is attended with the disengageinent of
considerable heat as the burning body becomes luminous. Other chemical combinations are attended with light, and it is doubtful whether any
bodies become luminous without chemical action of some kind.
The term phosphorescence is given to a pale light emitted in the dark
by certain substances which do not appear to emit any sensible heat.
Phosphorescence has been observed in animals, vegetables, and even in
minerals. During the heat of summer the glow-worm and fire-fly emit
a brilliant light.
In tropical regions phosphorescent insects are very numerous. The
waters of the ocean, especially in warm latitudes, are often covered
with little animalcules which become luminous at night when the water
is agitated, shining in the wake of a vessel like a track of living fire.
- See transactions of the British Association for 1853, p. 9.




OPTICS.                             293
In certain circumstances also rotten wood and decaying flesh become
phosphorescent.  By friction, or by long exposure to the rays of the
sun, certain minerals, as the diamond, white marble, and fluor spar,
acquire the property, it is said, of shining, for a brief period, in the
dark. The cause of phosphorescence is not known, but in some cases
it appears to depend upon electricity.
Electricity is a source of light so intense that its brightness is equal,
in some cases, to one-fifth, or even one-fourth that of the sun.
400. Relation of different bodies to light.-All bodies are either
luminous, transparent, translucent, or opaque.
(a) Luminous bodies are those in which light originates, as the sun,
and burning bodies.
(b) Transparent bodies allow light to pass freely through them, thus
permitting the form  of other bodies to be distinctly seen through
them.  Such are water, air, and polished glass.  Such substances are
also said to be diaphanous (from  ica, through, and   ai&vw, to shine).
(c) Translucent bodies permit only a portion of light to pass, and in
so irregular or imperfect a manner, that the outline of other bodies
cannot be clearly seen, as rough glass and oiled paper.
(d) Opaque bodies are those which do not ordinarily allow any light
to pass through them, as wood and the metals. But all bodies, even
the metals, may be made so very thin as to become partially transparent
or translucent.  Opacity is not absolute in metals, as is proved in the
case of gold-leaf on glass, through which a beautiful violet-green light
is seen. This light is found by optical experiments to be truly transmitted light, and not a color caused by the minute fissures of the goldleaf.  It is worthy of remark, that this greenish color is complementary
to the red, which is the color of gold when seen by successive reflections.
401. Rays, pencils, and beams of light.-A single line of light
is called a ray. A pencil of light is a collection of rays diverging from
a common source, or converging to a point.  A  beam  of light is a
collection of parallel rays. Diverging rays are those which gradually
separate from  each other. Converging rays are those which tend to
meet in a common point; hence we have the terms              301
diverging pencils, and converging pencils of light.
402. Visible bodies emit light from  every
point and in every direction, the rays diverging
from each point in right lines.
Let A B C, fig. 301, be three points in any visible object; 
from each of these points, light is emitted in diverging
pencils, as partially represented in the figure.
In this figure certain points arc seen, where rays from A B C cross each other,




29-            PHYSICS OF IMPONDERABLE AGENTS.
and between them are vacant spaces. No such vacant spaces exist, but the
rays from all points in the object are crossing each other at every point in the
space where the object is visible.
403. Propagation of light in a homogeneous medium.-A medium is something existing in space, capable of producing phenomena.
A  medium  is called luminiferous, which is capable of transmitting
light; and it is said to be homogeneous when the composition and density
of all its parts are the same. All space is supposed to be pervaded by
a luminiferous medium, called luminiferous ether, and yet the particles
of this ether may act upon each other at great distances.  In a homogeneous medium, light always moves in straight lines. If any opaque
body is placed in a direct line between the eye and a luminous body,
the light is intercepted.
When light enters a dark chamber by a very small opening, the
course of the light becomes visible by illuminating the fine particles of
dust always floating in the air. Rays of sun-light are thus easily
demonstrated to move in straight lines.
404. Velocity of light.-Light travels with such amazing velocity,
that, for any distances on the surface of the earth, the time occupied in
its passage from  one point to another is totally inappreciable by
our unaided senses.
In 1676, Roemer, a Danish astronomer, observed that the eclipses of the first
satellite of Jupiter, which occur at uniform intervals of time when the earth is
moving in that part of her orbit nearest to, or most remote from Jupiter, are
constantly retarded when the earth is moving from that planet, and as regularly
accelerated when the distance between the earth and Jupiter is diminishing.
He found that when the earth was in that part of her orbit most distant from
Jupiter, the eclipses of the first satellite take place 16m. 36s. later than when
in the opposite part of her orbit.
By this means the velocity of light was ascertained to be about 192,000 miles
in a second.                                     302
Foucault's  apparatus  -...
for measuring the velocity  of light.-Notwithstanding   the   prodigious  
velocity of light, M. Fou-  ------ --
cault  has  succeeded  in 
measuring it, by employing   i  
a revolving mirror, accord-       \
ing to the method devised by      M 
Wheatstone for measuring                                        303
the velocity of electricity.  In describing this apparatus, we shall suppose the properties of mirrors and lenses to be already understood.
The apparatus of M. Foucault is represented in fig. 302. The shutter of a




OPTICS.                                295
dark chamber is pierced with a square opening, K, behind which a fine platinum
wire, o, is stretched vertically. By means of a mirror, a beam of solar light is
made to enter the chamber, and being divided by the platinum wire, it falls upon
an achromatic lens, L, of long focus, placed at a distance from the platinum wire
less than double the distance of its principal focus. The image of the platinum
wire would be formed in the axis of the lens, somewhat enlarged.  But the
beam  of light, after passing the lens, falls upon the plane mirror, m, which
revolves with great velocity, and being reflected by it, an image of the platinum
wire is formed in space, which image is displaced with an angular velocity,
double the velocity of the mirror.-  This image is received by a concave mirror,
M, so fixed that its centre of curvature coincides with the axis of rotation of
the revolving mirror, i. The pencil reflected by the mirror, M, returns backward and is again reflected by the mirror, m,, and passes back through the lens,
L, and forms an image of the platinum wire, coinciding with the wire itself, if
the mirror, m, revolves slowly. In order to view this image without obscuring
the pencil of light which enters the chamber by the opening K, a piece of plate
glass, V, with parallel faces, is placed between the lens and the platinum wire,
inclined in such a manner that the rays reflected fall upon a powerful eye-glass,
P. If the mirror, mn, remains stationary, or if it revolves slowly, the returning
ray, M Ii, falls upon the mirror, mi, in the same position it occupied at the first
reflection, and returning in the direction it came, it meets at a the plate glass,
V, and is partially reflected, and forms in d, at a distance a d, equal to a o, an
image which is seen by the eye by means of the eye-piece, P.
The revolving mirror, m, causes this image to be repeated at each revolution,
and if the velocity of rotation is uniform, the image does not change its position.
When the velocity does not exceed thirty revolutions per second, the successive
appearances of the image are distinct, but when the velocity is greater, the
impressions upon the eye are continuous, and the image appears constant.
When the mirror, r, revolves with great rapidity, its position is sensibly
changed during the interval occupied by the light in passing from mt to M, and
back again from M to m, and the returning ray, after reflection by the mirror, m,
takes the direction m b, and forms an image in i; thus the image has deviated
from d to i. Strictly speaking, there is some deviation even when the mirror
turns slowly, but it is appreciable only when it has acquired a certain magnitude,
by making the rotation of the mirror sufficiently rapid, or by taking the distance,
M m, sufficiently great. By means of the deviation in the position of the image
and the velocity of rotation, the time required for the light to pass from mn to M,
and back again, becomes known, m'aking I   M m, 1' =  L im, r -  0 L, n =  the
number of revolutions per second, D  the absolute deviation d i, and V
the velocity of light per second. M. Foucault obtained the following formula
for the velocity of light,
8 tl21,r
D ( +  1'). To demonstrate this, let mn n, fig. 303, be the revolving mirror, 0, an object
placed before it, and forming its image at 0'; when the mirror arrives at the
position ni' n', the image will be formed at 0".  But the angles, 0' 0 0', and
m c m' are equal, because their sides are perpendicular to each other. But the
inscribed angle 0' 0 O" is measured by half the arc 0' 0", and the angle nim  m',
is measured by the entire arc m7 nm'; hence the are 0' 0", is double nii m7', which
thus demonstrates that the angular velocity of the image is double the angular
velocity of the mirror.




296            PHYSICS OF IMPONDERABLE  AGENTS.
In the experiments of M. Foucault, n7 M, was only about four yards, but by
giving the mirror, m, a velocity of 600 or 800 revolutions per second he obtained
a deviation of from eight one-hundredths to twelve one-hundredths of an inch.
Owing to the vibration of the apparatus revolving with such great rapidity, the
results yet obtained by this method for the absolute velocity of light are not
considered as entirely correct, although of the highest interest.
Experiments have been made with the same apparatus to determine the velocity of light in liquids as compared with the velocity in air. For this purpose
a tube, A B, three yards long, is filled with distilled water, or any other liquid,
and placed between the revolving mirror, rm, and the concave mirror, M', similar
to M. The rays of light reflected by the revolving mirror in the direction
m1 M', pass twice through the column of fluid in the tube, A B, before returning
to the mirror, V. The returning ray is reflected at c, and forms an image at h.
The deviations of the rays which traverse the liquid are greater than the deviation of the rays which are propagated in air alone, which shows that the velocity of light in fluids is less than in air.
Pizeau's method.-Another method of direct determination of the velocity of light has been devised by M. Fizeau, of Paris, in 1849. An exposition
of this method, by Prof. A. Caswell, will be found in the Smithsonian Report
for 1858, p. 130.
Results.-From  these and other methods the velocity of light has
been determined to be in air 192,000 miles per second; in water
144,000 miles; in glass 128,000 miles; and in diamond 77,000 miles.
405. No theory of light is entirely satisfactory.-In the corpuscular theory of light, advocated by Newton, it was supposed that
fluids and solids attracted the light, and refraction was explained by
supposing that light moves faster in dense bodies than in air, as is
known to be the case in regard to sound. According to the undulatory
theory, it is known that transverse waves or undulations must move
slower in dense bodies than in rarer media.
The discovery of Foucault, as just explained, that light actually
moves slower in denser media, tends to confirm the undulatory theory.
The immense power of resisting compression which a medium ought
to possess, in order to transmit transverse vibrations with a velocity so
much greater than the motions of the swiftest planets or comets, is an
objection against the undulatory theory that has not yet been satisfactorily answered.
The discussion of the theories of light belongs to the higher departments of
mathematics.
406. Properties of light.-(a) Absorption.-Light falling upon any
substance is either absorbed, dispersed, reflected, or refracted. A part
of the light disappears and is said to be absorbed; as when light falls upon
black substances. No substances absorb all the light, for the fact that
the blackest substance is still visible, shows that its different parts emit
some of the light which they receive.




OPTICS.                                297
(b) Dispersion.-Light falling upon opaque bodies, causes them  to
bucome luminous, or to emit light in all directions, and thus become
visible. Such bodies are said to disperse light, because they scatter the
light in all directions from which they are visible.
Bodies owe the property of dispersing light to the innumerable little
facets of the particles composing their rough surfaces. Only part of
the light is thus irregularly reflected or dispersed, while much of it is
probably absorbed or destroyed.
(c) Reflection.-When light falls upon polished surfaces, or on bodies
having naturally smooth and uniform  surfaces, it is thrown off in a
regular manner, as a ball rebounds from a hard floor.
If a ray of light, S A, fig. 304, falls upon a polished surface, B C, it will be
reflected in the direction A R. If N A is drawn perpendicular to B C, S A N
will be the angle of incidence, and N A R will be              304
the angle of reflection, and the two angles will be 
equal. The lines S A, N A, and A R, will lie in
the same plane; we have therefore the following
rules:-                                               B
1st. The incident ray, the perpendicular at the              A
point of incidence, and the reflected ray, are all sittated in the same plane.
2d. The angle of incidence and the angle of reflection are equal.
(d) Refraction.-If a straight rod is placed  obliquely, partly irrmersed in water, it appears broken or bent just where it enters the
water.  If a coin, a, fig. 305, is placed in a                 305
cup, in such a position that it is just hidden
from  view, and water is then gently poured
into the cup, the coin will appear to be lifted
up and will become visible.                       c    -
Let c d be the surface of the water, the ray, a b, \ 
is so bent or refracted, at the surface of the water, 
that the coin appears as if placed at a'.
This bending of the rays at the surface of any transparent medium  is called
refraction.                                                     306
Let C B, fig. 306, be the surface of water in a vessel,
S A a ray of light incident at A, and N A N' the per-            X
pendicular, A R the reflected ray, and A T the direc-    R
tion of the ray which enters the water and is refracted; then:The angle S A N is called the angle of incidence of   c\~.-           /
the ray S A. The angle N A R is called the angle of    \s''
-reflection, which is in all cases equal to the angle of
incidence.  The line N A N', is called the normal.
The angle T A N' is called the angle of refraction.         / 
If we take A a, fig. 307, equal to A b, and draw
mn and b n, each perpendicular to N A N', then a m is the sine of the angle of
incidence, and b n is the sine of the angle of refraction, and a m divided by b n
28




298             PHYSICS OF IMPONDERABLE  AGENTS.
is invariably the same for any given medium, whether the angle of incidence is
increased or diminished.  The quotient obtained by               307
dividing a m by b n, is called the index of refraction,
and it is represented by n. The index of refraction 
varies for different media; thus for light passing from    ^  
air into water, it is about I, for light passing from air
into glass, about -, and about A when light passes from  / A
air into diamond.  These fractions inverted give the  
index of refraction for light passing out of water, glass, 
and diamond, into air. 
When  light passes from  a rare to a denser 
medium, it is refracted towards the perpendicular
or normal, and when it passes from a dense to a rarer medium, it is
refracted from the perpendicular or normal.
The general law of the refraction of light is thus stated.  The incident ray, the refracted ray, and the perpendicular to the refracting surface
at the point of incidence, lie in the same plane; and the sine of the angle
of incidence bears a constant ratio, in the same medium, to the sine of the
angle of refraction;
am
or, -  = n.
bn
When a ray of ordinary daylight or sunlight is refracted by a dense transparent medium, the refracted light is not confined to a single line, but it is
spread out into a fan-like form, as shown in fig. 308,          308
between A r and A v, and the different parts of the
refracted  pencil show  different colors, the  most                       s
strongly refracted part being violet, and the least
refracted part being red. The index of refraction, for          A
a single color, is uniform for any given medium; but
the index of refraction in the same medium varies for   
differently colored light.
407. Amount of light reflected at differ-   //'    )
ent angles of incidence.-When light falls 
upon a transparent medium perpendicular to its surface, nearly all the
light enters the medium, and only a small portion is reflected. As the
light falls more and more obliquely upon the medium, the amount of
light refracted diminishes, and the amount reflected increases.
If we look at the image of the sun in water at midday, and again near sunset,
we shall see a remarkable difference. Near sunset the image is so brilliant, the
eyes can scarcely bear to look at it, while at midday we observe it without difficulty. The image of objects at a little distance are seen in water more distinctly
than the images of near objects, because the light from distant objects falls more
obliquely upon the water and a greater amount is reflected.
If we look very obliquely at a sheet of white paper, placed before a candle, an
image of the flame may be seen reflected from the surface of the paper, but the
image disappears when the rays fall upon the paper nearer to the perpendicular.




OPTICS.                                     299
When  light falls upon  any  polished  metallic surface, the greatest
amount of reflection  takes place when  the incident rays are perpendicular to the surface, and the amount of light reflected diminishes as
the angle of incidence increases.
Different substances, polished with equal care, differ in their power of reflect
ing light. The amount of light reflected depends also upon the nature of the
medium  in which the reflecting body is placed.  Bodies immersed in water
reflect less light than in air.
Table showing the number of rays of light reflected out of 100 rays incident, by
different kinds of glass and metals used for optical purposes.'
Crown glass,  Plate glass,   Flint glass,             Speculum
Sp. gravity,  Sp. gravity,   Sp. gravity,              metal,   Polished steel,
Angle of    2-541.       2-511.       3-225.       Glass of    Sp. gravity,   Sp. gravity,
incidence.  n = 1-524.    n = 1-517.    n = 1570.    Antimoy.      89.          7-8.
Specific heat,  Specificheat,  pe heat,             Specific heat, Specific heat,
0-38..       039.          43.'          0-4.          0688.
00       3-452        3-380         3-615        8-20        72-30
100        3-608        3-546        3-819         8-36        70-85        60-52
20~        3-837        3-790        4-117         8-60        69-43
30~       4189          4-164        4-574         8-98        68-11        58-69
40         4-767        4-778        5-320         9-59        66-91
50~       5-810         5-882        6-656       1.068         65-87        54-96
60~       7-964         8.155        9-369       12-93         65-03
70~      13-448       13-891        16-015       18-52         64-41
80~      32-396       33-155        36-422       36-65         64-04
85~      56-202       56-204        57-559       57-07
90~      75 776       74-261        72-074       72-20         63'91        53-60
408. Internal reflection.-When light passes through a transparent
medium, a portion of the light is reflected at each surface.
In fig. 309, S A is a ray of light incident upon the first surface of a transparent medium.  A portion is reflected in A R.  A T is the refracted ray, and
T V the emergent ray, but a portion of the light is re-                   309
flected at the second surface in the direction T A', of 
which a part emerges in  the  direction A' R', a part'I-'
suffers a second reflection downward from  A', a part
emerges from  the second surface, and another portion  \
suffers successive internal reflections before it is either
lost by absorption or finally emerges on one or the other
side of the medium.  In  general only the rays A R, 
T V, and A' R', have sufficient intensity to be visible to the naked eye.
409. Total reflection.-When  light passes from  a dense to a rarer
medium, the angle of refraction is greater than the angle of incidence,
and when the angle of refraction is 90~, the angle of incidence is much
less. For water it is 48~ 35', for ordinary glass it is 41~ 49', consei- From Potter's Physical Optics.




300            PHYSICS OF IMPONDERABLE AGENTS.
quently a ray of light traversing water or glass at greater angles cannot
escape into the air, but is totally reflected, obeying the ordinary law of
reflection.  The proportion of light suffering internal reflection from a
surface of glass or water, constantly increases from the perpendicular
to the point where total reflection takes place.
Since the angle of incidence for a dense medium is always greater than the
angle of refraction, when the angle of incidence is 90~ the angle of refraction
must be considerably less than 90~. If the angle of incidence is 90~, its sine
will be unity. The sine of the angle of refraction will be unity divided by the
1
index of refraction, = -, hence the angle of total internal reflection for any
1                         310
medium is the angle whose sine =-.
Fig. 310 shows light radiating from a point below            /
the surface of water and escaping into the air, the
angle of emergence increasing much faster than the
angle of incidence, until the light emerges parallel to
the surface of the water, after which total reflection
takes place.
To an eye placed below the surface of the water, all
objects above the horizon would be seen within an angle of 97~ 10', or double
the angle of total reflection for water.
410. Irregular reflection.-Diffused light.-The reflection from
polished surfaces, which follows the two laws already  announced,
is called regular reflection; but only a part of the light is reflected
regularly from any surface, when the reflecting body is more dense
than the surrounding medium.  A  part of the light is scattered in
all directions, and is said to be irregularly reflected or diffused.  This
is the portion of light which renders objects visible. Light regularly reflected gives an image of the object which emits the light,
while light irregularly reflected gives only an image of the body
which reflects it. When a mirror becomes dim by the accumulation of
light dust, or anything which tarnishes its surface, the amount of
regular reflection diminishes, and the irregular reflection increasing,
all parts of the mirror become distinctly visible.
411. Umbra and penumbra.-When an opaque object is held in a
pencil of light proceeding from a luminous               311
point, as s, fig. 311, a dark and well-defined
shadow is produced, which increases in size s
as it becomes more  distant.  The dark
shadow is called an umbra.  If the light proceeds from  a luminous
body having a sensible magnitude, as A, fig. 312, besides the dark
shadow, or trumbra, where no part of the luminous body is visible,
there will be a much broader partial shadow, called the penloCu




OPTICS.                            301
bra, where a part only of the luminous body is visible. The breadth
of the penumbra increases with the diameter of the light, and with the
312                                   313
distance which the shadow  extends behind the opaque object.  The
darkness of the penumbra gradually increases from the extreme border,
which is too faint to be easily seen, to the umbra or full shadow, as is
shown in a section of the shadow, at fig. 313.
412. Images produced  by light transmitted  through small
apertures.-If a white screen is placed near a small opening in a dark
chamber, the rays of light which pass                  314
through the opening will form on the screen  I   Bl
inverted images of external objects.
It will be seen in fig. 314, that the rays 1
of light from the top and the bottom of the
object cross each other in the small opening, and thus invert the image.
If the aperture is small, the image will be formed in the same manner,
whatever be the form of the aperture. But if the opening is large, the
image is indistinct, or entirely disappears.
413. Intensity of light at different distances.-The intensity
of light at any distance from a luminous body, is in        315
an inverse proportion to the square of the distance.        0
Let 0, fig. 315, be a luminous point; at 1 1, place a 
board one foot square; it will cast a shadow that will cover  1    \
a space two feet square at double the distance, three feet
square at three times the distance, and four feet square at    2
four times the distance. The areas will therefore be, 1, 4,    / 
9, 16, and the intensity of the light at the distances 1, 2,
3, 4, will therefore be in the proportions of 1, ~,, T-i  3 
If I and I represent the intensity of a light at the
distances D and D', we shall have
I   I    I    D'2
1: I' = — D: D2, or   = 7-2
D2  D'2   It   D2
Hence the intensity of a light at different distances will be inversely as the
squares of those distances.
414. Photometers are instruments employed to measure the comparative intensity of different lights.  The principle on which they are
constructed is, to so place the lights that they will illuminate a single
Surface, or two adjacent surfaces, with equal intensity.  The relative
~2n




302            PHYSICS OF IMPONDERABLE AGENTS.
intensities of the two lights are then as the square of their distances
from the illuminated surfaces.
Bunsen's Photometer is the simplest and most convenient photometer
yet invented. A disk of paper four or five inches in diameter, is rendered translucent by washing it with paraffine or stearine, dissolved in oil of turpentine or
naphtha, except a spot about an inch in diameter at the centre. When this disk
is held between two lights, at a point where their intensity is unequal, the translucent part of the paper is easily distinguished from the central part, but when
moved to a point where the two lights have equal intensity, all parts of the
paper have a uniform appearance.  No light appears to shine through, because
the illumination is e(ua.l on both sides. By means of a graduated bar, on which
the lights and disk are mounted, the distance of each light from the paper is
determined, and their respective intensities are calculated on the principles
above mentioned
This principle may be applied in many ways to determine the intensities of
lights; as, for instance, the portion which is transmitted or reflected from different substances.
Rumford's Photometer.-Rumford's photometer is composed of
two plates of ground glass, before which are fixed two opaque rods, A
-and B, separated by a screen, fig. 316.  The lights to be compared, as
a lamp and a candle, m n, are so placed opposite the rods that each
316
plate is illuminated by only one of the lights, and a shadow of the corresponding rod falls upon each plate, as shown in the figure. If the
two shadows, a and b, are of unequal intensity, by moving one of the
lights backward or forward a position is obtained where the shadows
appear equally dark, and the glass plates are thus known to be equally
illuminated. The relative intensities of the lights are determined as in
the preceding case.
Silliman's Photometer.-Silliman's photometer is the reverse of
Rumford's, comparing two discs of light thrown up by two equal triangular glass prisms, upon a disc of roughened glass in the body of a dark
rn.tlmber moving on a graduated bar. (Am. Jour. Sci. [2] XXII. 315.)




OPTICS.                              303
Q 2. Catoptrics, or Reflection by Regular Surfaces.
I. MIRRORS AND SPECULA.
415. Mirrors are solid bodies bounded by regular surfaces, highly
polished, and capable of reflecting a considerable portion of the light
which falls upon them.
The term mirror is generally applied to reflectors made of glass and
coated with an amalgam of tin and quicksilver.
416. Specula are metallic reflectors, having a highly polished
surface. The best speculum metal consists of 32 parts of copper, and 15
parts of the purest tin. Specula are also made both of silver and of steel.
In the use of glass mirrors, a portion of light reflected from the first surface,
interferes with the perfection of the imagre; hence, where the most perfect instruments are required, metallic reflectors are employed. In treating of reflectors,
we shall notice only the action of the principal reflecting surface, and use the
term mirror to comprehend all regular reflectors.
417. Forms of mirrors.-Mirrors are either plane or curved. Curved
mirrors may be spherical, elliptical, or paraboloid.  The properties of
elliptical and paraboloid reflectors have been mentioned in sections 324
and 325.  A concave spherical mirror is a portion of the surface of a
sphere, reflecting from the internal side.  A convex spherical mirror is
a portion of the surface of a sphere, reflecting from the outside. Curved
mirrors, whether concave or convex, may be regarded as made up of an
infinite number of plane mirrors, each per-                 317
pendicular to a radius drawn through it from                /I
the centre of the mirror.  /T
Fig. 317 shows a plane mirror, M A N, a concave  Y  
mirror, m A n, and a convex mirror, m' A n', having  t
a common point, A, and the line, P A C, perpen- N
dicular to each at the point A. If a ray of light,    /             -'
I A, is incident upon either mirror at the point A, 
the reflected ray, A R, will make the same angle 
with the perpendicular as is made by the incident
ray. At any other points, as t or t', the curved mirrors will act like little plane
mirrors, perpendicular to the radii P t and Ct'.
II. REFLECTION AT PLANE SURFACES.
418. Reflection by plane mirrors.-Parallel rays of light, fialling
upon a plane mirror, will be parallel after reflection.
If parallel rays of light, A D, A' D', fig. 318, fall upon the plane mirror, M N,
they will each make equal angles with the perpendicu-        318
lars, E D, E' D', and as the angles of incidence and  -\'              - A 
reflection will be equal, the reflected rays, D B, D' B',
will make equal angles with the perpendiculars, and
will consequently be parallel after reflection..If A D represent the upper side of the beam of light before reflection, it will




304            PHYSICS OF IMPONDERABLE AGENTS.
become, after reflection in D B, the lower side of the beam. Hence a beam of
parallel light.is inverted in one direction by reflection from a plane mirror.
Diverging rays of light, falling upon a plane mirror, will continue to
diverge after reflection, and will appear to emanate from a point as
much behind the mirror as the luminous point is            319
before it.                                                        ^
Let A be a radiant point in front of the plane mirror  \ 
M N, fig. 319. If the perpendiculars, E D, E' D', E" D", 
be drawn, the reflected rays will make the same angles.,.
with the perpendiculars as the incident rays, and hence.:
the reflected rays will make the same angles with each
other as they did before reflection, but they will appear to diverge from the
point A', behind the mirror.
Converging rays continue to converge after reflection from  a plane
mirror. After reflection they will converge towards a point as much in
front of the mirror as the distance of the point behind the mirror,
towards which they converged before reflection.
This is easily seen by tracing the rays of light backward in the preceding
figure.
Reflection from a plane mirror changes the direction of the rays of
light, and removes the point of apparent convergence or divergence to
the opposite side of the mirror.
419. Images formed by plane mirrors.-Let M N be an object
placed in front of the plane mirror, A B, fig. 320, and E the place of
the eye.  From the great number of rays emitted in          320
every direction from  M N, and reflected from the               N 
mirror, a few only can enter the eye at E.  These 
will be reflected from  those portions, D F, G H, of
the mirror, so situated with respect to the eye and A          /I   B
the points, M N, that the angles of incidence and
reflection will be equal.  If the rays, D E, F E, are    
continued backward, they will meet at m, and they 
will appear to the eye to radiate from that point. In'-:,
the same manner the rays G E, H E, will appear to radiate from n; a
virtual image of the object will therefore be formed between m and n.
This is called a virtual image, because it is not formed of rays of light
actually coming from the position of the image, but by rays so changed
in their direction, that they appear to the eye as though originating
from an object situated at m n, behind the mirror.
If the eye is moved about, the image remains stationary, hence it is
seen by means of rays reflected from other parts of the mirror. Two
or more persons may see the image at the same time and in the same
position, but by different rays of light.




OPTICS.                             305
The position of the image behind the mirror may be found by drawing lines from prominent points in the object, perpendicular to the
mirror, extending them as far behind the mirror as the points from
which they are drawn are situated before it, then uniting the extremities of the lines, the outlines of the image will be delineated. The
images of all objects seen in a plane mirror have the same form and
distance from the mirror as the objects themselves.
420. Images multiplied by two surfaces of a glass mirror.Glass mirrors produce several images.  This may be readily demonstrated by looking very obliquely at the image of a candle in a glass
mirror. The first image, caused by partial reflection from the first surface of the glass, is comparatively faint. The second         321
image is formed by reflection from  the quicksilver, R\X\            Awhich covers the second surface, and is very clear and    \ \   /
distinct.
When rays of light from any object fall upon the first      ^\.
surface of a plate of glass, M N, fig. 321, a portion of the..
light being reflected, forms the first image, a. The principal 
part of the light penetrates the glass, and is reflected at c, by 
the silvering which covers the back of the mirror, and coming to the eye in the
direction d I, produces the image, a', at a distance from the first image equal
to about once and a third the thickness of the glass. This image is much
brighter than the first, because the metallic coating of the mirror reflects a
greater amount of light than the first surface of the glass.
Other images, more and more obscure, are formed by rays which
emerge from the glass after successive interior reflections from the two
surfaces of the glass.  As this multiplicity of images diminishes the
distinctness of vision, metallic reflectors are often employed in optical
instruments.                                            322
421. Images formed by light reflected
by two plane mirrors.-Let AB, fig. 322, 
be an object, and C D, E F, two plane mir- 
rors, making an angle with each other less         \\ 
than -180~.  The light falling upon the                       /
mirror C D will form  an image at a b, the                B "
position of which may be determined by..... 
the method explained at section 419.  A                      \
portion of this light, after reflection, will            \
fall upon the mirror E F, and be reflected              i~' >a
as if coming from an image a/ b/, which will be seen by the eye at e.
To trace the course of the rays which enter the eye fromn any point, Q, in the
object A B; let q be the corresponding point in a b, and q' a similar point in
a' b'; the light will enter the eye as if it came from q', therefore draw the lines




306            PHYSICS OF IMPONDERABLE  AGENTS.
q' e, and they will show the final course of the pencil by which the point Q is
seen. From the points where these lines meet the mirror, E F, draw lines to q,
and they will represent the course after reflection by C D; from the points where
these lines meet the mirror C D, draw lines to the point Q, and they will show
the course of the rays which, after reflection by each of the mirrors C D, E F,
form the pencil by which the eye at e sees the point q' in the secondary image
a' b'.
The inversion of parts by the two mirrors are now seen to correct each other,
and all the parts of the image, a' b', have the same relation to each other as in
the object A B. The peculiar excellence of Wollaston's Camera lucida (518)
depends upon the fact that by means of two reflections all parts of the image
preserve their natural relations.
422. Multiplicity of images seen by means of inclined mirrors.-When an object is placed between two mirrors, which make
with each other an angle of 90~ or less, several              323
images are produced, varying in numbers according to the inclination of the mirrors.  If they are         c
placed perpendicular to each other, three images              / 
will be seen, situated as in fig. 323.                I
The rays 0 C and 0 D, from the point 0, form, after a 
single reflection, one the image 0', the other, the image  
0"; and the ray 0 A, which undergoes two reflections at    /
A and B, gives a third image, 0"'. When the inclination  /
of the mirrors is 60~, five images are formed; and when
they are placed at an angle of 45~, seven images are produced. The number
of images continues to increase as the inclination of the mirrors diminishes, and
when the mirrors become parallel, the number of images is theoretically infinite,
but as some of the light is lost at every reflection, and the successive images
appear more and more distant, only a moderate number of images are visible.
423. Deviation of light reflected by two mirrors.-When a ray
of light reflected by a mirror is again reflected by a second mirror, in
a plane perpendicular to the intersection of the two          324
mirrors, the deviation of the ray from  its original 
direction is equal to twice the angle formed by          s
the two mirrors.  
Let two mirrors, A  and B, fig. 324, be inclined to..      A
each other, so that their directions shall meet at some   B A  —...::\. -', -  n
point, C, forming an angle A C B =  a. Let the ray
of light, S A, be reflected by the first mirror in the 
line A B, and falling upon the second mirror be again   
reflected in the direction B D, meeting the original direc-.ion S A D in D. Let the angle of deviation A D B =  d. 
Draw N A n perpendicular to the mirror A, and B a perpendicular to the mirror B. The angle between these'
perpendiculars will be equal to the angle formed by the inclinations of the
mirrors, or A is B - A C B = a.




OPTICS.                              307
Let S A N = N  A B = i, and AB   = i'; then since N A B =  A B n -- A n B,
we have:ii'i-a.'. a=-i-i';
also  BAD+ABD+ADB=   180~,
or 2(90~-i) + 2i' + d=  180~.-. d =2(i-i') =  2a;
Or the deviation of any ray after two reflections is equal to twice the angle between the mirrors.
424. Kaleidoscope.-This beautiful toy depends upon the multiplication of images by inclined mirrors. Two mirrors, inclined at
angles of 30~, 45~, or 60~, are placed in a paper tube, one end of which
is closed by plain and the other by ground glass. Various objects, as
fragments of colored glass, tinsel, twisted glass, &c., are placed in a
narrow cell, at the end of the tube, closed with ground glass, just room
enough being left to allow the objects to tumble around as the tube is
moved.  On looking through this instrument towards the light, multiplied images of every object are seen, beyond all description splendid
and beautiful; an endless variety of symmetrical combinations appearing to the view as the instrument is moved, but never recurring with
the same form and color.
Let A C and B C, fig. 325, be the two mirrors of the kaleidoscope, and, let the
dotted circle, described about C as a centre, represent the tube in which they
are placed; let Q be the position of an object             325
within the angle formed by the mirrors. If Q is
in the circumference of the circle described about     A. —-~ —--.-...
C, the two series of images of Q will be formed in   q.  \..
the circumference of the same circle, q1  q q4 q be-  \
ing formed by the mirror A C, and q' q" q"' q"" 
being formed by the mirror B C. Since q, is in a 
line perpendicular to A C, and at the same distance from A C behind it as Q is before it, that  /  
perpendicular is the chord of the arc Q q,, and q q2     /, 
is in the circumference of the circle drawn about  
C as a centre. For the same reason q' is also in    q3.         >
the same circumference; so also q" being the image         T...."
of q(, is as far behind B C as q1 is before it, and as the line joining ql and q" is
perpendicular to B C, it must be the chord of the circle, and hence q" is in the
circumference. In the same manner it may be shown that every image, formed
by repeated reflections from A B and B C, is also in the circumference of the
circle described about C. When we arrive at any image, q4 or q"", falling, as
in the figure, between the directions of the mirrors produced, such an image
being- situated at the back of both  the mirrors must be the last of its series, as
no light from such an image can fall upon either mirror.
According to ~ 423, the distance between any two images, formed by
an even number of reflections, will be equal to twice the angle between
the mirrors. It is evident that images formed by an odd number of
reflections will be situated between each two of the former series;




308            PHYSICS OF IMPONDERABLE AGENTS.
hence the entire number of images seen in the kaleidoscope, including
the object itself, will be equal to 300~ divided by the angle contained
between the mirrors.  If the inclination of the mirrors is 60~, the number of images, including the object, will be six; if the inclination is 45~,
the number will be eight; and for 30~ every object will appear as
twelve. If the inclination of the mirrors is small, the images formed
by many successive reflections become too faint to be distinctly seen.
425. Hadley's sextant is an instrument depending on reflection
from  two mirrors, and used chiefly by seamen for measuring the altitudes and angular distances of the heavenly bodies.
Two mirrors, a and b, fig. 326, are so mounted that the angle of inclination
can be varied at pleasure. The mirror a is attached to a movable arm, a C,
yhich turns about the centre of the graduated           326
arc A B. This arm carries at C a vernier by
which minute divisions of the graduated arc 
are easily distinguished. The mirror b is
firmly attached to the frame of the instrument, and the outer portion has the silvering
removed, so that an eye placed at e sees the
distant horizon, or any other object to which
it is directed, in its true position.  The
mirror-a is turned with the index arm a C, 
until any other object, as the sun, moon, or a
star, whose light is twice reflected in the
directions S a b e, appears to coincide in
direction with the horizon or other object, H,
seen by direct light, from which its angular                   \.3b
distance is to be measured. The telescope at
e is used to facilitate accurate observation.
The divisions of the graduated arc and vernier are also read by the aid of a
magnifying lens, not shown in the figure. The deviation of the ray S a, after
being twice reflected, is, by ~ 423, twice the angle contained between the
mirrors, or twice the degrees contained between A C; half degrees on the
scale are therefore marked as whole degrees. The reading by the vernier gives
the altitude or angular distance of the observed object.
III. REFLECTION AT CURVED SURFACES.
426. Concave and convex spherical mirrors.-If an arc of a
circle, M N, fig. 327, is made to revolve around a line, A C L, drawn
through its centre of figure A, and                   327
its centre of curvature C, it will.M
generate a curved surface, which                                  -._
will be a segment of the surface of               -
a sphere. Internally, such a polished 
surface is called a concave mirror,
and externally a convex mirror. The line, A C, is called the principal
axis of the mirror, and any other line drawn through the centre of




OPTICS.                              809
curvature, C, is called a secondary axis.  The angle M C N  is called
the angular aperture of the mirror.  A section made by a plane passing through the principal axis, A C, is called the principal section, or
a meridional section.
The theory of reflection from curved mirrors is easily deduced from the laws
of reflectign by plane mirrors.  Every point in the curved mirror may be
regarded as a point in a plane mirror so situated that its perpendicular, where
the ray of light falls upon it, coincides with the radius of the curved mirror at
that point.
A line drawn from any point in a spherical mirror to the centre of
curvature, will be perpendicular to the mirror at that point, and also
perpendicular to any plane mirror touching the curved mirror at that
point.
427. Foci of concave mirrors for parallel rays.-The focus of
a concave mirror is the point towards which the reflected rays converge.
(a) Parallel rays falling near the axis of a concave mirror, fig. 327,
converge, after reflection, to a point equidistant between the mirror
and the centre of the sphere, of which the mirror forms a part. This
point is called the principalfocus.
Rays of light emanating from the principal focus of a concave mirror,
will be reflected parallel to each other.
Demonstration.-The lines C M, C B, C D, fig. 327, drawn from the centre of
curvature of the mirror, M N, are perpendicular to the mirror at those points.
The parallel rays, H B, G D, will converge, after reflection, to the point F. It
is evident that the angle of reflection, C D F, for any ray, will be equal to the
angle of incidence, G D C; but G D C is equal to D C F, which is the alternate
angle formed by a line D C, meeting two parallel lines, G D, L A; hence in the
triangle, C F D, the angles, F C D and F D C, are equal, and therefore the sides,
C F and F D, are equal.  If the point, D, gradually approaches the point, A,
C F -+ F D will differ less and less from C A, until their sum will be sensibly equal
to C A, and F A will be sensibly equal to one-half of C A; or the focus of parallel
rays, after reflection from a concave mirror, will be equal to one-half the radius
of curvature. If the point of incidence, D, recedes from A towards M, or N, the
point, F, will gradually approach A, or the focal distance will diminish. A
concave spherical mirror will therefore reflect parallel rays to a single focal
point only when the diameter of the mirror is small. Practically it is found that
the diameter of the mirror, or the angular aperture, M C N, should not exceed 8
or 10 degrees.
428. Foci of diverging rays. —If rays of light falling upon a concave mirror diverge from a point beyond the centre of curvature, they
will converge, after reflection, to a point between the principal focus
and the centre of curvature. This point of convergence is called the
conjugate focus, because the distance of the radiant point and the focus
29




810            PHYSICS OF IMPONDERABLE  AGENTS.
to which the rays converge, after reflection, have a mutual relation to
each other.                                            328
Let rays diverging from  a point, L,..-.....................................
fig. 328, fall upon a concave mirror, the
angle of incidence, L K C, will be smaller j                       -' 
than S K C, which is the angle of incidence 
for parallel rays falling upon the mirror at............................................
the same point. The angle of reflection,
C K 1, will also be smaller than C K F; hence the ray, L K, will be so reflected
as to cross the principal axis at a point, I, between F, the principal focus, and
C, the centre of curvature of the mirror.
The relation between the radiant point and point of convergence is easily
determined. In the triangle L K I the radius K C bisects the angle L K I, hence
by a well known principle of geometry:CL    IC
CL:C= -L K: K..            --
LK IK
When the incident pencil is very small, L K =  L A, and 1 K =  I A, very
nearly, hence we have,
CL   IC
-LA =-  nearly.
Let LA =  st,  A =  v, C A =- radius of the mirror =  r, and A F -= the
principal focal length = f. Then f   -, and by substituting these values, the
above equation becomes
t- r,' —v                          1   1    1    1
-  =        -~-.Dividing by r we have  - -    -    --;
u       v'   U    v    r
1   2    1    1    1
Or, -        _    - ---
v        -  2u-r
u-f   2u-r
From this formula we may deduce the value of v, or the focus of reflected
rays, whatever may be the point of divergence of the incident rays.
If the luminous point is removed to 1, the reflected rays will meet at
L. If the luminous point is placed at the centre of curvature, C, all
the rays will fall perpendicularly upon the mirror, and be reflected back
to the point C, from whence they came.
If the luminous point is situated between the centre of curvature and
the principal focus, the conjugate focus will be removed beyond the
centre of curvature, and become more and more distant as the luminous




OPTICS.                           311
point approaches the principal focus. When the luminous point arrives
at the principal focus, the conjugate focus will be removed to an infinite
distance, or, in other words, the reflected rays will become parallel.
While the radiant point has removed from C to F, the conjugate focus
has removed from C, to an infinite distance.
429. Converging  rays.-Virtual focus.-If the radiant point
passes from the principal focus, F, towards the mirror, as in fig. 329,
it is evident that the reflected rays will diverge, as     329
though emanating from a point 1, behind the mirror,              m
called the virtual bfcus.                             HL 
When the radiant point is near the principal "::1.      ~    ~ -
focus, between it and the mirror, the virtual focus 
of the divergent reflected rays will be at a very'
great distance. As the radiant point continues to approach the mirror,
the virtual focus also approaches it. While the radiant point passes
from the principal focus to the mirror, the conjugate virtual focus, or
point fiom which the reflected rays appear to diverge, passes from an
infinite distance behind the mirror, to the surface of the mirror, or to
the radiant point itself.
These propositions may be easily proved by giving to u appropriate
values in the formula.
430. Secondary axes.-Oblique pencils.-If the luminous point,
L, fig. 330, is not situated in the principal axis of the mirror,, a line
drawn from the radiant point through the centre          330
of curvature, as L C B, will constitute a secondary axis, and the focus of the oblique pencil of   - ~.
rays diverging from  L, will be found in this
secondary axis.  In the same manner we may 
draw secondary axes, and determine the foci,
whether real or virtual, for any number of points in a luminous object.
431. Rule for conjugate foci of concave mirrors. —Multiply the
distance of the radiant point from the mirror, by the radius of curvature,
and divide this product by twice the distance of the radiant point, minus
the radius of curvature of the mirror, and the quotient will be the distance
of the conjugate focus firom the mirror.
If the quotient given by this rule is negative, or if twice the distance of the
radiant point is less than the radius of curvature, the conjugate focus will be a
virtual focus behind the mirror, and the reflected rays will diverge.
432. Convex spherical mirrors.-The effects attending the reflection of diverging, converging, or parallel rays of light by convex
reflectors, are, in general, the opposite of the effects produced by concave reflectors.  The foci of parallel and diverging rays of light,




312            PHYSICS OF IMPONDERABLE AGENTS.
reflected by a convex reflector, are at the same distance as for concave
miirrors, but they are situated behind the reflector, and are, hence, only
virtual foci.  Light converging towards any point behind a convex
mirror, more distant than the centre of curvature, will diverge, after
reflection, from a virtual focus between the centre of curvature and the
principal focus. Rays converging toward the principal, virtual focus,
will be reflected parallel; but rays converging towards a point nearer
to the mirror than the principal focus, will be reflected to a real focus
in front of the convex reflector.                   331
These phenomena will be readi-  
ly understood by an examina-s                              "tion of fig. 33-1.  The ray S I is  _ 
reflected in the direction F I M;,
LE  is reflected in the direc- S 
tion I E G, and  reciprocally, 
G E is reflected in the direction E L, and M I in the direction I S.
The formula for the convex mirror may be determined in the same manner as
for the concave mirror, or we may deduce it at once from the formula for the
concave mirror. Since the focus of parallel rays is behind the convex mirror,
if we call the value of f for the concave mirror positive, it must be negative for
the convex mirror. If therefore we insert -f instead of f in the formula for
the concave mirror, it will become for the convex mirror: —
1      I   1
v      f    u
from which it appears that the value of v must also be negative when u is posi:
five, that is, u and v are on opposite sides of the mirror. Now by putting -v
instead of v in the above formula, it will represent the absolute value of the
focus of reflected rays reckoned on the back side of the convex mirror, and we
1        I1           fut
-have for the convex mirror,   - = - -.'. v —'  /J    U          f+u
433. Images formed by concave mirrors.-The principles already
explained enable us to understand the formation of images by concave
mirrors. Let A B, fig. 332, represent an object placed before a concave
mirror, beyond its centre of                       332
curvature.  The lines, A C
and B C, drawn through the  i
centre of curvature from the        -~
extremities of the object, are'_                   _     _ ~           x
the secondary axes in which
the extremities of the image, a b, will be formed, at a distance from the
mirror equal to the conjugate foci for the extreme points of the object.




OPTICS.                           313
This image is real, inverted, smaller than the object, and placed between
the centre of curvature and the principal focus.
If a b is regarded as the object, placed between the centre of curvature and the principal focus, an enlarged image will be formed at A B.
If the object is placed at the principal focus, no image will be formed,
because the rays from each point of the object will be reflected parallel
to an axis drawn through the centre of                333
curvature from  the points where they B           __      _
originate.
If the object, A B, is placed entirely on
one side of the principal axis, as in fig.
333, it is evident that its image, a b, will be formed on the opposite side
of the principal axis.
434. Virtual images. -If the object, A B, fig. 334, is placed between
the mirror and the principal focus, the incident rays, A D, A K, take,
after reflection, the directions, D I, K H, and        334
their prolongations backward, form  at a, a
virtual image of the point A.  In the same a...:::.::.-~-~ _:t
manner the image of B is formed at b, so'                      ~ 
that the image of A B is seen at a b. The
image, in this case, is a virtual image, erect, b —:-'-'-:.
and larger than the object.
From the preceding illustrations, it is evident, that, when an object
is placed before a concave mirror, more distant than the centre of
curvature, the image is real, but inverted, and smaller than the object;
as the object approaches the centre of curvature, the image enlarges
and becomes equal to the object and coincides with it; when the object
approaches nearer to the mirror than the centre of curvature, the image
becomes larger than the object, and more distant from the mirror.
When the object arrives at the principal focus, the image becomes
infinitely distant, and disappears entirely: when the object approaches
nearer to the mirror than the principal focus, an erect virtual image,
larger than the object, appears behind the mirror.
435. Formation of images by convex mirrors.-Let A B, fig.
335, be an object placed before a convex               335
mirror, at any distance whatever.  If weA  -_.
draw the secondary axes, A C, B C, it fol-... =
lows, from what has been said (433) concern- 1         -...
ing the construction of foci of convex mirrors, B   ~
that all the rays emitted from the point A, diverge after reflection, and
that their prolongations backward converge to.a point, a, which is a
29*




314           PHYSICS OF IMPONDERABLE AGENTS.
virtual image of the point A. In the same manner, rays emitted from
the point B, form a virtual image of that point in b.
Whatever may be the position of an object before a convex mirror,
the image is always formed behind the mirror, erect and smaller than
the object.
436. General rule for constructing images formed by mirrors.
-To construct the image of a point; 1. Draw a secondary axis from
that point; 2. Take from the given point any incident ray whatever;
join the point of incidence and the centre of curvature of the mirror by a
right line; this will be the perpendicular at that point, and will show the
angle of incidence; 3. Draw from the point of incidence, on the other
side of the perpendicular, a right line, which shall make with it an angle
equal to the angle of incidence. This last line represents the reflected ray,
which, being prolonged until it crosses the secondary axis, determines the
place where the image of the given point is formed.  4. Determine the
position of any other point in the object in the same manner.
437. Spherical aberration  of mirrors.-Caustics.-The rays
from any point of an object, placed before a spherical mirror, concave
or convex, do not converge sensibly to a single point, unless the aperture
of the mirror is limited to 8~ or 10~. If the aperture of the mirror is
larger than this, the rays reflected from the borders of the mirror meet
the axis nearer to the mirror than those which are reflected from
portions of the mirror very near to the centre.           336
There results, therefore, a want of clearness or distinctness in the image, which is designated spherical
aberration by reflection.
The reflected rays cross each other successively,
two and two, and their points of intersection form in
space a brilliant surface, called a caustic by reflection, curving towards the axis, as shown in fig. 336,
where C is the centre of curvature, F the principal focus, and d the
centre of figure.
{ 3. Dioptrics, or Refraction at Regular Surfaces.
I. DEFINITIONS.
438. Prisms and lenses, are bodies having certain regular forms,
sections of which are shown in fig.               337
337.                                 A      c   n:      I. 
A prism is a solid having three            _ 
or more plane faces, variously in- 
clined to each other, as shown at A, fig. 337. The angle formed by




OPTICS.                            315
the faces, A R, A S, is the refracting angle of the prism. For some
purposes prisms are used having more than three plane faces.
A lens is a portion of some transparent substance, as glass or crystal,
of which the surfaces are generally either both spherical, or one plane
and the other spherical. The axis of a lens is the line joining the
centres of the spherical surfaces when both are curved, and the line
perpendicular to the plane surface which passes through the centre of
the other surface when one side is plane. When the surfaces of lenses
are of different kinds, they are named in reference to the side on which
the light first falls.
If the figures C, D, E, F, G, tI, I, were revolved around the axis,
M N, they would severally describe the solid lenses they are intended
to represent.
In explaining the properties of lenses, and showing the progress of
light through them, we make use of such sections as are shown in the
figure, for every plane passing through the axis has the same form, and
what is true of one section is true of all.
A plane glass, B, is a plate of glass having two plane surfaces, a b,
c d, parallel to each other.
A sphere, shown in section at C, has all parts of its surface equally
distant from a certain point within, called the centre.
A double convex lens, D, is a solid bounded by two convex surfaces,
which are generally spherical.
A plano-convex lens, E, has its first surface plane, and the other
convex.
A double concave lens, F, has two concave surfaces opposite to each
other.
A plano-concave lens, G, has its first surface plane, and the other
concave.
A meniscus, shown at H, has one surface convex, and the other concave, their curvatures being such that the two surfaces meet, if continued.  As this lens is thicker in the centre than at its edges, it may
be regarded as a convex lens.
A concavo-convex lens, shown at I, has its first surface concave, and
the other convex, but the curvatures are such that the surfaces, if continued, would never meet.  As therefore the concavity exceeds the
convexity, it may be regarded as a concave lens.
II. REFRACTION AT PLANE SURFACES.
439. Refraction by prisms.-If a ray of light, In, fig. 338, falls
obliquely upon a transparent medium, whose opposite plane faces are
not parallel, the ray will be refracted at the first surface, and take




316            PHYSICS OF IMPONDERABLE AGENTS.
a direction nearer to the perpendicular. Now if the position of the
incident ray, and the inclination of the faces of the medium, are as
shown in the figure, it is obvious that the emergent            338
ray, n' 1', will be turned still further from its original  /
direction. It is evident that any other position of the 
second refracting surface would cause a corresponding alteration in the direction of the emergent ray.
Let a b c, fig. 339, be a section of a triangular prism, 1 n a
ray of light incident at n, 0 n 8 the perpendicular at that
point, n n' will be the course of the ray of light through the
prism, and nt' 1' the emergent ray. 
If the prism is more dense than the surrounding medium, the light will enter
the prism, whatever may be the angle of incidence, but if the angle of incidence,
I n 0, diminishes, then the ray, n a', will fall more obliquely upon the second surface of the prism, until it may arrive   339                   340
at an inclination where it will suf-                           b
fer total internal reflection. 
If the incident ray, I n, fig. 340,.......             o.
falls upon the prism  at such an                i,
angle, that, after refraction, it takes
the direction, n n', parallel to a c,                 i'....
the base of the prism, the angles at which it enters and leaves the prism will be
equal, and the deviation of the emergent ray from the course of the incident
ray, will be the least possible. The ray, 1' i, will emerge in the direction mi p',
and 1" ni will emerge in the direction op", each deviating more from the direction of the incident ray than nz'p deviates.
If a candle is viewed through a triangular prism, on slowly turning
the prism about its axis, a certain position will be found where the
apparent position of the candle differs least from its real position. In
whichever direction the prism is now turned, the difference between the
real and apparent position of the candle increases.
440. Method  of determining  the  index  of refraction.-Let
In an' p, fig. 341, be the direction of the ray of light when the deviation caused
by the prism is a minimum. Draw h b parallel to the           341
incident ray, 1 n, and r b o parallel to the emergent ray,
n' p. Let D -- h b r, the entire deviation caused by the    9.
prism; d =  h b i, the complement of the angle of inci- 
dence; g =   abc, the refracting angle of the prism;,  
q -= 1' b o = c t' p, the complement of the angle of emergence. In this case the angles of incidence and emergence are equal, hence d =  q =  900 - i, i being the
angle of incidence, D =  180~ - d —g - q; substituting in this equation the
values of d and q, we have D = 2 i   g, and i = -   (D - g). Let.xand y, as
in fig. 339, represent the angles formed with the perpendiculars by the ray
traversing the prism, x + y = g, and when the angles of incidence and emergence are equal, x = y. If n equals the index of refraction, we shall have:sin. i           sin. i (D + g)
n-. -,  or, nsin. xa              sin. ~ g




OPTICS.                              017
Now when the angle of minimum deviation and the refracting angle of the
prism are measured, this formula enables us at once to determine the index of
refraction. In this manner the index of refraction of any substance is easily
determined.
441. Plane glass.-A ray of light passing through a plane glass, or
any other medium of uniform density bounded by parallel faces, will
have the emergent ray parallel to the incident ray.  Parallel rays of
light passing through plane glass are parallel after emergence, and the
emergent rays are parallel to the incident rays.
If the two surfaces of the transparent medium are parallel, it is evident that
the ray of light traversing the medium will make equal angles with the perpendicular at both surfaces. Let I be the angle of incidence, R the angle of refraction at the first surface, and also the internal angle of incidence on the second
surface, and E the angle of emergence. Then, if n represents the index of
refraction, we shall have:Sin. I=  n sin. Rt = sin. E.. I=  E:
Or the angles of incidence and emergence are equal, and the incident ray is
parallel to the emergent ray. The same is true for any number of rays; hence
also parallel incident rays will, after passing through the glass, emerge parallel.
Let M N, fig. 342, be a plane glass, or any medium            342
bounded by parallel surfaces, the rays A B, A' B', will be
refracted towards the perpendicular, on entering the medium,          a /A,
and emerging at C, C, they will be refracted from the per- 
pendicular, and take the directions, C D, C' D', parallel to
each other, and parallel to their directions before entering   X 
the medium. The displacement, A a, A' a', is the lateral
aberration produced by transmission through a homogeneous medium bounded
by parallel surfaces. The amount of lateral aberration increases with the thickness of the medium, and it also increases with the obliquity of the incident rays.
442. Light passing through parallel strata of different media.
-It is found by experiment that if a ray of light passes through a
series of plates of dense media, all the refracting surfaces being parallel
planes, that the emergent ray is parallel to                343
the incident ray.  It therefore follows, that,  m
the direction of the ray in passing through
any one of the plates is parallel to the course 
it would have taken if it had entered the                ^ 
plate directly, or if that plate had been the            /       j
first in the series.. c n 
Let P A B C Q, fig. 343, be the course of a ray    /
of light passing through two parallel strata of A
dense media, the second medium being more dense
than the first, and P' D E Q' the course of a ray passing through the second
medium without entering the first; if P A is parallel to P' D, C Q will be parallel
to E Q', and also B C will be parallel to D E. We may consider the ray of




318            PHYSICS OF IMPONDERABLE AGENTS.
light as passing in the opposite direction, and make n" the index of refraction
for the medium traversed by the ray C B, then sin. Q C p' - n" sin. B C p,
hence the angle B C p depends only on the direction of the emergent ray C Q,
parallel to the incident ray P A, and upon the index of refraction, i", of the
lower medium. Let nm A m', a B n', p C p', be perpendicular to the refracting
surfaces at A, B, and C, and let n be the absolute index of refraction for the
first medium, n" that of the second medium, and n' the index of refraction for
light passing from the first medium to the second:
sin. PA1,        sin. QCp'
Then,              n =  -:  =
sin. BArn"       sin. BC'
sin. ABt    sin. BAr'   sin. BArn'   sin. QCp' 1"
I- _           -  =              -    x
sin. CBn'    sin. BCp     sin. PAm     sin. BCp     n
Hence: The index of refraction for light passing from one medium to
another, is equal to the index of refraction of the second medium divided
by the index of refraction of thefirst medium.
443. Pencils of light refracted  at plane  surfaces.-When a
pencil of light falls upon a plane surface of any dense medium, it is so
changed by refraction that a diverging pencil is made to diverge from
a focus without the medium more distant from the dense medium  than
before it entered it; and a converging pencil is made to converge to a
focus within the dense medium more distant from its surface than before.
Let Q, fig. 344, be the focus of incident              344
rays, and Q A B the ray which enters the
medium perpendicularly to its surface, suffer-  
ing no deviation. Let Q P be any oblique    N'.
ray meeting the surface at P; let N P N' be                               ": 
drawn perpendicular to the refracting surface )A. 
at P, it will also be parallel to Q A B; let
P R be the refracted ray which being extended
backward meets the line A Q at q'. The angle of incidence QPN = PQA, and
the angle of refraction RPN' = Pq'A.
sin. QPN     sin. PQA
Also the index of refraction, n ==        =
sin. RPN'   sin. Pq'A
PA               PA            Pq'
Sin. PQA   -- -   sin. Pq'A =  -.-. A     - 
PQ'              Pq'           PQ
If the pencil is very small, PQ == AQ, and Pq' =  Aq' nearly, hence
Aq' =  a.AQ. If we let AQ =  t, and Aq' - u', then u'- = n, which determines
the point q', from which the pencil diverges after refraction.
When the'pencil is large, and P is so far from A that we cannot consider
QP =  QA, let i =  the angle of incidence, i' -  angle of refraction:We have QP =; q'P=.
cos. i       cos. i'
cos. i'
And since q'P = n.QP.'. u' =a n.     u.
Cos. i




OPTICS.                            319
Since the cosine of i' is greater than cosine of i, this last value of u' is greater
than nu, the first value; this shows that a pencil of light suffers aberration
when refracted at a plane surface. The formula also shows that u' is greater
than iu, or that the focus of the pencil after refraction is more distant than the
focus of the incident rays. If the pencil of           345
incident rays converges to a point, Q, within
the dense medium, as in fig. 345, the pencil of   =                 N
the refracted rays will converge to point q'. 
Solving the triangle Q P q', we should find the
same result as before; or Aq' = n.AQ.
Therefore: When a pencil of light is
refracted at a plane surface, the focus of
the refracted rays is on the same side of the refracting surface as the
focus of incident rays, and at a distance equal to the distance of the
focus of incident rays multiplied by the index of refraction.
If the rays had been proceeding from  the dense medium to a rarer
medium, as from q', fig. 345, or towards q', fig. 344, then the focus of
refracted rays would be at Q, or nearer to the refracting surface than
the focus of incident rays.
If the rays proceed from a dense to a rarer medium, and if n still
represent the index of refraction for light entering the dense medium,
the index of refraction for light passing from the dense to the rare
1
medium will be n -  -.
The index of refraction for light passing from air into water is t = =,
1
and hence n/ =- -= a, for light passing from water into air.
If therefore u represents the actual distance of an object below the
surface of water, and u' its apparent distance, u-' = n'.u = u u, that is,
the apparent distance below the surface of the water is only three-fourths
of the real distance; or water is a third deeper than it appears to be.
As every point in an object appears elevated one-fourth as much as its
distance below the surface of the water, a pole or cane thrust obliquely
into the water appears bent, or broken (406), just at the surface of the
water.
It follows also, from the preceding considerations, that an object immersed in water, or any other transparent dense fluid, appears larger
than when seen in the air.
As the atmosphere diminishes in density very rapidly above the
earth's surface, a man upon the top of a steeple or tower looks much
smaller than when seen at an equal distance on level ground; and an
object at the foot of the tower, will, for the same reason, appear larger
when viewed from  the top than if placed at the top of the tower and
viewed from below.




320            PHYSICS OF IMPONDERABLE AGENTS.
444. Pencils of light transmitted through plane glass.-When
a pencil of light is transmitted through a plane glass, the focus of the
emergent rays is removed from the focus of the incident rays, in the
direction that the light is moving, a distance equal to the quotient
arising from dividing the thickness of the glass by the index of refraction, and multiplying tht quotient by the                346
index of refraction diminished by unity. 
Let a pencil of light fall upon a plane 
glass, fig. 346, so that QA shall be perpendicular to the surface of the glass, and QP._____
an oblique ray, Q A will be transmitted in the   -^              ~ y     7
line Q A B without deviation, and Q P will
be refracted in the direction q' P R, and
emerge in the direction q R, q being the focus
of the emergent rays. Let Q A = ut, q' A  = u' B q =  v, and AB   t.
By the formula already demonstrated (443), if the pencil is small u' -= nu;
and if the pencil had entered the other side of the plate, converging to q, we should
have,
Bq' ==.Bq; or, t +-u' === nv =  t + nil,
t
Hence v = is + -, by which the position of q is determined. The displacement
\      \     nn
ofthefocus Qq=-BQ - Bq==u +  t-v== t 1 —    }= - 
Or the rays diverge, after emerging from the glass, from a point nearer to the
glass than the focus of the incident rays.
If we suppose the rays to proceed in the opposite direction, we shall have the
case of a converging pencil, and the focus of the rays after emergence will be
more distant from the first surface of the glass than before. In both cases the
focus of the ra    rays is removed in       a  n the s ame direction     that the light is proceeding.
If we take the case of plate glass, for which n -, the distance to which the
focus is removed is equal to i the thickness of the glass.
III. REFRACTION AT CURVED SURFACES.
445. Principles  determining  the  foci of lenses.-A  double
convex lens may be regarded as composed of a number of segments of
prisms, the faces of each                        347
prism  more inclined  as 
we  proceed  from   the
centre to the borders of  so                        bA
the lens, as shown in fig.
347.  The  central portion, abed, may be regarded as a plane glass, having its faces, a c, b d, parallel, a gfb has
its face, a g, inclined towards fb, and the triangular prism, g hf, has




OPTICS.                              321
its sides still more inclined. Now since the deviation of any ray passing through a prism increases as the inclination of the two faces of the
prism increases, s I will deviate more than s i, and if the form of each
prism is properly adjusted to its distance from the axis, M N, the rays,
st and s i, or any number of rays, may be made to meet at a common
point, R, in the axis M N.
If the segments of prisms, of which we suppose such a lens to be
composed, are made sufficiently small, so that each face shall receive
but a single ray of light, the sides of the successive prisms will form a
regular curve, which, if the lens be of small diameter, will correspond
almost exactly with a segment of a sphere.
On account of the great difficulty of grinding lenses with any other
than spherical or plane surfaces, other forms are seldom employed, and
require no discussion in an elementary work.
446. Small pencils of light refracted  at a spherical surface
have the position of their                        348
foci changed.                                                  N
Let P A P', fig. 348, be a ~
convex spherical surface of a                             0
dense medium, O being the \                           0     A           Q
centre of curvature of the
dense medium, Q the focus of
the incident rays, and q' the focus of the refracted rays. Let Q A q' be the ray
which enters the medium perpendicular to its surface, and Q P another ray which
is refracted in P q', so as to meet Q A continued in q'. Draw 0 P N perpendicular
to the curved surface through the centre of curvature and point of incidence.
We shall then have the angle of incidence i == Q P N, the angle of refraction
i = q' P O. Let P 0 A =  o, then from the triangle, Q O P, we have:Sin. i: sin. o =  Q 0: Q P,
and from the triangle, q' 0 P, we have:Sin. o: sin. i' =  q' P: q' 0.
By compounding these proportions we have:sin. i        QO   q P         Q 0     q O
= a  - X -; or, -                -—.sin. i'       Q P   q O'        P' P
Since the pencil of rays is very small, we may consider Q P =  Q A, and
q' P =  q' A nearly. Let Q A == u, q' A  = u', A 0 =,; then the last formula
tu  - r' - r                             n n-       1
becomes   ~= n.,   which may be reduced to    = 
U         U'                            U'      r     ut
If we suppose Q to be situated at an infinite distance from A, the incident
rays will be parallel, and we shall have u = infinity, and:n    n -1 )1I
_;.-. u'           -   -- =.
u'      r  — I,1   ti    1
Making this value of u' = f', the general formula will be -=  - -.
30




322            PHYSICS OF IMPONDIERABLE AGENTS.
Refraction at a concave surface.-If the surface of the dense medium
is concave, as shown in fig. 349, let Q, as           349
before, be the focus of the incident rays, q'  r
the virtual focus of the refracted rays, and 0. 
the centre of curvature. Then the angle of 
incidence i =  Q P 0; the angle of refraction       " 
i    R PN    9' PO; let the angle P 0 A = o.
In the triangle Q P 0 we have:Sin. i: sin. o = Q 0: Q P,
and from the triangle q' P 0 we have:Sin. o: sin. i' = q' P: q' O.
Combining these proportions we have:sin.         Q O   q'P       QO       q'O
sin. -n  -   -   or, - =.si.'        QP'QP  O'0     QP     q' P
The pencil being small, we may put Q A = Q P, and q' A = q' P nearly, and
putting Q A = ut, q' A = i', and 0 A - r, we have:
QO      q'O      u   r-   u' -r..   or, -    n.Q A     q' A'      u         t'
It   n   1   1   n    1
From  this we obtain -=          -      -; in which f represents the
u'    r      u   f    U
value u' when u - infinity, or the incident rays are parallel.
We may take the general formula for refraction at a convex surface
of a dense medium, and, by applying proper values to the letters, deduce
formulae for all other cases, whether the medium be dense or rare, and
the refracting surface convex or concave.
n    n-1   I
In the formula,_ =  -- 
twe     r      u
we have supposed the value of u measured from  the convex surface of
the dense medium, in the direction A Q in the rarer medium. Callin'g
this direction positive, if the focus of incident rays were taken in the
dense medium u should be considered negative; u' has been reckoned
positive when measured in the dense medium, therefore if it is measured
in the rare medium, as in the example of the concave dense surface, it
should be reckoned negative; we also reckon r positive when it lies in
the dense medium, and negative when it lies in the rare medium.
Therefore, to apply the general formula for a convex surface of a dense medium
to the case where the incident rays converge to a focus in the dense medium,
s2 n-1    1
we make u negative, and the formula becomes    =   - + -.
To adapt the formula to the case of diverging rays refracted at the conca
To adapt the formula to the case of diverging rays refracted at the concave




OPTICS.                               323
spherical surface of a dense medium, we make r negative, and the formula becomes
n        t-i   1
- =  -  -        - -, which shows that u' is essentially negative, or that it lies
u'        r      u
Dn the same side of the refracting surface as the centre of curvature.
1n  n2 -       1
If then we change the sign of u' in the formula, it becomes  -         -,
u2r    r      u
in which u' represents the distance of the focus of refracted rays measured in the
direction of the rarer medium. This formula is the same as was deduced from
fig. 349, where the same conditions were applied to the analysis of the diagram.
To apply the formula to the case of rays of light proceeding from a dense to
a rarer medium, we have but to let u and u' change places in the formula, and
change the sign of r. Making these changes in the general formula for a convex
surface of a dense medium, the formula for diverging rays refracted at a convex
surface of a rare medium will become:n       n- i    1       1      n    n - 1, or —       -- -
U'      it 1 t    t   U 
The formula for diverging rays, refracted at a concave surface of a rare
1    n   n - I
medium (by similar changes), will become    =
Urt   u     r
The formula for converging rays issuing from a convex surface of a dense
medium, or, which is the same thing, entering a concave surface of a rare medium,
n    n -       1
will become-   = ~; u' being the focus of rays traversing the dense
ur'     r                CDu
medium, and v the focus of rays issuing from a dense medium or entering a rare
medium.
447. Action of a double convex lens upon small pencils of
light.-Let P A P' B, fig. 350, be a double convex lens, of which r is the radius
of the first surface, and 8 the                    350
radius of the second surface.
Let Q be the focus of the inci- 
dent rays, q' the focus of the
rays after refraction at the''....:    ~ <     ~    ~....
first surface of the lens, and  q...          /.
q the focus of the rays as they                          pf
emerge from the second surface of the lens. Also, let Q A =  i, A q' = u', B q  - r, and the thickness of
the lens A B - t.
1n    n-l 1 
After refraction at the first surface, we shall have (446)    =      -.
It'    r      u
n     n-1      1
By refraction at the second surface, we have (446)           =  --    -.
B q('     s     v
If the thickness of the lens is so small that when compared with B q' it may be
neglected, we make B q' - A q' = u' nearly; adding the two preceding equations;
n- I1 n-          I    1        1  1\ 1
0.   -—..- ~...  Or - -- (-1)  - +-   —.
r        s8          v        V              r    8 




324            PHYSICS OF IMPONDERABLE AGENTS.
1          1             1    1
For parallel rays, u = infinity, - =  0, and - =  (n -1)  - +u          v             r    8
Let f== this value of v when the incident rays are parallel, and the general
1    1    1
formula for a double convex lens becomes -=      -.
v   f    u
If t is small, but not small enough to be neglected, we shall have:n          n         n    nt        ntt2 
B'        ut'-t       u''uf2.'     (u   -     ));
but as t2 must be very small compared with't2 the quantity contained in the
brackets may be neglected; hence,
it   nt   n-1           1   n  1 -1   1
U'  Ut2      8      V   U'      r     u
1            /1    1      1     int
Adding and transposing, -= (n- 1)   - - - -         - +-;
v            \r   a8       U    U'
1n    n-      1      nt    t       n-1    \2
U      =              12   1  r          u 
1    1   1    t   t -1        \2
And -=- — +- -                   -.
v    j   u    ni \r   u
Conclusions deduced.-Analysis. —1. Parallel rays of light falling upon a convex lens, A B, fig. 351, will be refracted to some point,
as F, on the other side of                         351
the lens.  The distance of
the focus, F, from  the lens,.........
will depend upon the amount  
of curvature, and also upon 
the refractive power of the substance, of which the lens is composed.
If the two surfaces of the lens have the same curvature, and the index
of refraction, as for ordinary glass, is one and a half, the focus of'
parallel rays, called the principal focus, will be at a distance from the
lens equal to the radius of curvature of either surface of the lens.
11    1                   1          3
In the formula - =- (n -1)  +- --   -    let i=  -, the index of refracr             r    8      U          2
tion for ordinary glass, then since the incident rays are supposed to be parallel,
1
u =-  o, and - = 0, and if the two surfaces of the lens have the same curvature,, a   t  f                               
r -= 8, and the formula becomes — = - -+   -..-. v = r, or F the
v    2  r    r.'
focus of parallel rays is at a distance from the lens equal to the radius of
curvature.




OPTICS.                           325
2. Diverging rays.-If the rays falling upon the lens come from a
point, R, at a distance from the lens equal to twice the principal focus,
they will converge to a point, S, at an equal distance on the other side
of the lens.
It will be easily seen from fig. 351, that the angles, X and Z, are equal to
each other (being the alternate angles formed by the straight line, R A, meeting
two parallel lines), and also that the angles, X and 0, are equal. In the
triangle, A S F, the sides, F A and F S, are equal, hence the angles, 0 and Y,
are equal, and Y equals Z, therefore if the incident ray is bent inward to a distance represented by the angle, Z, the refracted ray must be bent outward by an
equal angle, Y, by which means the radiant point is removed from F, the principal focus of parallel rays, to S, which is at double the distance of F.
The formula shows the same thing. Making u = 2r, we find v = 2r.
If the radiant point is taken more distant than R, as at V, fig. 352, the
352
A
ah.                        R
R
conjugate focus will be removed from S, to some point, T, between S
and the principal focus.
1 1 1
The formula will then give   =  -  _;  >       or      2r.
v    r    u > 2r' v   2r o
3. Converging rays.-If rays of light falling upon the lens, A B, fig.
353, converge towards a point, V, be-              353
fore refraction, they will converge,
after refraction, towards a point, T, 
between the principal focus, F, and the -       ii
lens.  Conversely, if rays of light               ~
diverge from a point, T, between the
lens and its principal focus, they will diverge after passing through
the lens, from a virtual focus, V, more distant than the principal focus.
In the first case u becomes essentially negative, and with the same
11I 1              1
values of n, r, and s the formula becomes -   -   -+; and as - is
v   r   u          v
greater than, v must be less than f, hence T lies between the principal focus and the lens.
4. Plano-convex lenses.-The action of a plaho-convex lens is in
general the same as that of the double convex lens, but its foci are at
double the distance, the principal focus being at a distance equal to
twice the radius of the curved surface.
30*




326              PHYSICS OF IMPONDERABLE AGENTS.
To adopt the formula to this case, we make n =, and r=  o, hence
1     1    1                              1
- =.  If the rays are parallel, -     0, and v, orf=  2s.
v    2s    u                              u
448. Action of a double concave lens upon small pencils of
light.-Let P A P' p' B p, fig.                     354
354, be a double concave lens
of a dense medium, r being the R
radius of the first surface and 8     w
the radius of the second surface.  
Let Q be' the focus of the inci-     B
dent rays, q' the focus of the   -
rays after refraction at the first
surface, and q the focus of the
emergent rays p R, p' R. Let Q A    u, A q' =', B q   v, and A B = t.
According to the formula for refraction at a concave dense surface (446):n    n —      1
-        -=  -.
u'  r         is 2
and by the formula for rays emerging from a concave dense surface,
n        n-1   1
_ - - + V
Bq'         8      v
If the thickness of the lens is so small that when compared with B 9' it may
be neglected, and that we may consider B q' =  A q' =   u', combining these two
I              1    I1    1        1   1    1
equations we have -   (  - 1)  - + -            +-    Or, -=    + -.
v             r    8      iu      1'  f    u
If the thickness of the lens is too great to be neglected, we find by the same
I   1   1    t    n \2
method as for a convex lens -   - ~ -       -
v       /     n  n u  / 
This formula for the double concave lens may be deduced directly from the
formula for the double convex lens, by substituting in that formula for r and
s,- r and - s, and as the value of v would then be negative, changing that
sign also when its positive value is reckoned on the same side as u.
Conclusions deduced from analysis.-A concave lens produces,
upon rays of light transmitted through it, an              355
effect the opposite of that produced by a con- 
vex lens.
1. Parallel raysof light, transmitted through  
a double concave lens, diverge from a virtual 
focus in front of the lens, as shown in fig.
355; the virtual focus being at the centre of the sphere of which the
first surface forms a part. This is its principal focus.
2. Diverging rays.-If the radiant point is more distant than the principal focus, as at B, fig. 356, the virtual              356
conjugate focus, A, will be between the
principal focus, F, and the surface of the
lens, and the rays will diverge after refraction.
3. Converging rays, transmitted through a concave lens, will be ren



OPTICS.                             327
dered less convergent, parallel, or divergent, depending upon the
distance of the point towards which they converge before entering
the lens.
The above propositions are easily proved by reference to the formula for a
double concave lens, -=  (a-1) (-   -   --
v             r    8      U
449. Rules for determining the foci of lenses.-When lenses
are made of glass whose refractive index is one and a half, their foci
may be determined by the following rules:Rule for the Principal Focus.
Divide twice the product of the radii by their difference, for the
meniscus and concavo-convex lenses, and by their sum, for the double
convex and double concave lenses. The quotient will give the focus for
parallel rays. The focus of parallel rays, or principal focus, of the
plano-convex or plano-concave lens, is double the radius of curvature.
Rule for the Conjugate Focus, when the Focus of the Incident Rays is
given.
Multiply the length of the principal focus, with its proper sign, by
the focus of the incident rays, and divide the product by the difference
between the principal focus and the focus of incident rays, and the
quotient will be equal to the conjugate focus.
If the distance of the focus of incident rays is less than the principal focus,
the value of the conjugate focus will be positive, and it will lie on the same side
of the lens as the focus of incident rays; but if the value of the focus of incident rays is greater than the principal focus, the value of the conjugate focus
will be negative, and the focus of refracted rays will lie on the other side of the
lens.
450. Combined lenses.-If two convex lenses, A A, B B, are placed
near together, as in fig. 357, their com-             357
bined focus will be shorter than that —        -..
of either lens used alone.                                -- -
Let parallel rays be refracted by the first
lens, A A, to a focus at N; represent the distance of this point from the first lens
byf', and let the distance between the lenses be represented by a, letf" represent the corresponding focal length of the second lens for parallel rays, and
f the distance of the focus L from the second lens. In the general formula
I   1   1
-- = —, considered with reference to the second lens, u = - (/' - a), and;   f    It
f becomes f", v - f, and we have:1    1       1               ",  X (f' - a)
/.f               /" f"    ('' —+




328            PHYSICS OF IMPONDERABLE AGENTS.
If the distance between the lenses is nothing, then for the focus of parallel
f" X/'
rays, f -  -it —--     For rays not parallel, the formula will be:-,f" -+ 
1    1       1       1         uI —f
v    f,    +  vI a   f,, + f'u-a (u-f')
1    1    1    1
When the lenses are in contact,      -  +  --      For any number of lenses
V   f        f"   u
in contact,  +1      -  +     --  i+  &c., -  -   _
O      p  f    f'ed tu                     h ee 
451. Oblique pencils, when transmitted through lenses, have their
foci in secondary axes, and their foci are determined by the same rules
as the foci of direct pencils in the principal axis.
It has been shown, in ~ 439, that a ray of light transmitted through a
prism in a direction parallel to its base, suffers the least deviation possible;
hence in every other position the deviation is increased. From this principle it
follows that the foci of oblique pencils transmitted through lenses will be somewhat shorter than the foci of direct pencils. This fact requires consideration in
the formation of the images of large objects. (See ~ 455.)
452. The optical centre of a lens is a point so situated that every
ray of light passing through it will                  358
undergo equal and opposite refraction on entering and leaving the
lens.  It will, therefore, be found
where a line joining the extremi- o~ —                            - 40
ties of two parallel radii of the 
opposite surfaces cuts the axis of
the lens.
Let S P R Q, fig. 358, be a ray of light passing through a double convex lens
so that the radii O' P, 0 R, drawn from the points of incidence and emergence
are parallel. Let C be the point where this ray intersects the axis of the lens.
The triangles 0' C P, O C R, are similar, hence:0'P: O'C - OR:OC;
O'P - O'C: OR -OC=  O'P: OR;
AC: BC.-_ O'P: OR;
AC  - BC: O'P +  OR - AC: O'P.
Putting O' P - r, O R, and AB =  t.
tr            ts
AC:t=r:r-+s.-. AC=, B C=         - 
r + 8e         - -+ 8
If the lens were double concave, r and 8 both become negative, but the values
of A C and B C remain unchanged. Since these values are both positive and
constant, whatever may be the positions of the points P and R, the optical
centre of a double convex or double concave lens will be a fixed point in the
lens. For a plano-convex or plano-concave lens, r -=  o, A C =  t, B C - 0.




OPTICS.                                329
The optical centre will be at the intersection of the axis with the curved surface.
For a meniscus, either r or s will be negative, and the formulae show that in
that case the optical centre will be situated without the lens at a point depending upon the relative values of the two radii.
All rays of light passing through the optical centre emerge from the
lens parallel to the incident rays. The position, form, and foci of all
pencils of light passing through a lens are determined by their relation
to some line, or secondary axis, passing through the optical centre of
the lens, whether any ray of light from the radiant point actually
passes through that centre or not.
453. Images formed by lenses.-If an object is placed before a
convex lens at a greater distance than the principal focus, an image of
the object will be formed on the other side of the lens.
If from the extremities of the object A B, fig. 359, the secondary axes, A a,
B b, are drawn through the optical centre of the             359
lens, the image will be formed between these
axes prolonged, at a distance equal to the con- 
jugate focus of the lens, estimated separately for
every point of the object. If the object is placed
beyond the principal focus, and at less than  
twice this distance, the image will be more distant and larger than the object.
If the object recedes from  the lens, the image will approach it. When the
object is removed from the lens, more than twice the principal focus, the image
will be smaller than the object, and it will gradually approach the lens, and
diminish in size as the object recedes.  The image can never approach nearer to
the lens than the principal focus.  The linear magnitude of the image as compared with the object will be proportional to their respective distances from the
lens.                                                         360
If the object is placed nearer to the lens than the
principal focus, as A B, fig. 360, the rays will 
diverge after passing the lens, and a virtual image,
a b, will be formed on the same side of the lens as  
the object. The virtual image formed by a convex
lens is always larger than the object.
If an object, A B, fig. 361, is placed before a concave lens, the rays from
every point of the object will diverge after refraction more than they did
before entering the lens; consequently a virtual              361
image, smaller than the object, will be formed on 
the same side of the lens. The size of the virtual
image will be in proportion to its distance from 
the lens.
454. Spherical aberration of lenses.-It has been assumed that
spherical lenses bring rays of light issuing from a point to a sensible
focus. For many purposes, however, greater accuracy is required,
and it becomes necessary to consider the imperfections of spherical
lenses.




330             PHYSICS OF IMPONDERABLE  AGENTS.
If the diameter of the lens V W, fig. 362, is large in proportion to its
radius of curvature, rays of parallel light                  362
will not be brought to an accurate focus,  
but while the central rays cross the axis at
F, the extreme rays will intersect the axis 
at G, and intermediate rays will intersect  =                      IA
the axis at every possible point between           -w
F and G. The distance, F G, is called the longitudinal spherical aberration of the lens.
For lenses of small aperture, the aberration is nearly in proportion to the square
of the angular aperture of the lens; but for lenses of larger aperture, the aberration increases more rapidly than would be required by this proportion. If the
length of the principal focus be taken as unity, the longitudinal aberration for
lenses of different angular apertures will be as follows:For 15~ the aberration will be 0-025,
" 220  (       "   " "       0.062,
"  30~ "      "        "  " 0-150,
~' 450         "   " "  " 0.375.
This effect of spherical lenses causes images to be formed at every point
between F and G, the rays going from each image, more or less interfering with
the distinctness of all the others.
The amount of spherical aberration depends also on the form and position of
lenses. If n = index of refraction, r =  the radius of the anterior surface, and
R =  the radius of the posterior surface, then for parallel rays, the form of least
aberration will be expressed by the following equation:r    4 +    - 2n2
R      2n + an
If n =  1, the form of least aberration will be a lens whose surfaces have
their radii in the proportion of 1 to 6, the side of deeper curvature being towards
parallel rays. If the spherical aberration of such a lens, in its best position, is
taken as unity, the aberration of other lenses will be as follows:Plano-convex with plane surface towards distant objects, 4-2.
Plano-convex with convex surface towards distant objects, 1-081.
Plano-concave the same as plano-convex.
Double convex or double concave with both faces of the same curvature, the
aberration will be 1-567.
The spherical aberration of a convex lens is called positive, and the
aberration of a concave lens is called negative because it is in an
opposite direction from that produced by a convex lens.
Accurate estimate of spherical aberration. —To estimate with
accuracy the amount of spherical aberration in any given case, it is
necessary to calculate the exact course of a ray which falls upon the
border of the lens.
* Microscopical Journal, Vol. VIII. p. 21.




OPTICS.                            331
Let A C, fig. 363, be a section of a curved refracting surface in the plane of
refraction, Q C q being its axis. The refractive index =-. Here the distance
363
A
Q              CD                                      f
Q C of the radiant point from the refracting surface is given. Also C D and
D A co-ordinates of the point A. Hence, also the normal A E and sub-normal
D E may be found. Let A q be the refracted ray required, cutting Q C q in a.
Now sin. incidence is to sin. A E C -  Q E: Q A.
Sin. E is to sin. refraction =q A: q E.
qA  QA.'. Sin. incidence: sin. refraction — m: 1: 
qE   EB
q A   m.QA
~'~    = E   =. -c, (a known quantity).
q E    Q E.q. q A2 =  c2.q E2.
i.e.,   q E2  - E A2 - 2 qE.E D     c2q E2... (C2 - 1) q2  2 E D.q E     E A2
2ED          E A. 2.E —   qE c21
q    E    D  ) 2    E D         (ca2 1) EA2
E - -   1 
c2-1)      (c — 1)      (c —1)2.. qE = c           — 1   E D  l/E D 2 + (2 -  1) E A.
From this formula the accurate value of q E for any surface may be calculated.
455. Aberration of sphericity; distortion of images. —When a
straight object is placed before a lens, the extremities of the object not
being in the principal axis, if the images of the extreme points are
formed in the secondary axes at the same distance from the optical
centre of the lens, as the central portions of the image, the image will
not be straight, but formed on a curve, the centre of which is at the
optical centre of the lens, as at b, fig. 364. But as an object recedes
from  the lens, the image will                   364
approach it, therefore as A and
B are more distant from  the
lens than the centre of the
object, the extremities of the
image must be nearer than the 
centre, and instead of a' C b, we 
shall have the image a" C b /
described around a centre, somewhere between the lens and the centre




332           PHYSICS OF IMPONDERABLE AGENTS.
of the image. Oblique pencils are also more strongly refracted than
pencils which belong to the principal axis; hence this cause must tend
to curve the image still more. This curvature, or distortion of images,
is called aberration of sphericity. For ordinary purposes this imperfection of lenses may be disregarded. The practical method of overcoming
these difficulties will be best explained in connection with the description of achromatic lenses.
Q 4. Chromatics.
456. Analysis of light.-Spectrum.-Primary colors.-A beam
of sunlight, S H, fig. 365, admitted into a dark chamber, through a
small opening in the shutter, E, forms               365
a round white spot, P, upon a screen or   M
any other object upon which it falls. M li                    1    S
If a triangular prism, B A C, is interposed in its path, as shown in the figure,.. 
the light will be refracted both on enter-.    a
ing and leaving the prism, but instead.::
of forming only a circular white spot on
the screen, M N, it will be spread over'
a considerable space from  S to K, called the solar spectrum, in which
will be seen all the colors of the rainbow. Beginning with the color
most refracted, they are violet, indigo, blue, green, yellow, orange, and
red.
If an opening is made in the screen so as to permit only the rays of
a single color to pass, and we attempt to analyze this color by passing
it through a second prism, we find it cannot be further decomposed by
refraction; hence the colors of the solar spectrum produced by the
refraction of a triangular prism are generally called primary colors.
457. Recomposition of white light.-If a second prism, A B a,
exactly similar to B A C, is placed behind the first, but in a reversed
position, as shown in the figure, the differently colored rays will be reunited and form white light at P, as though no prism had been used.
Moreover, if, instead of the second prism, a double convex lens is so
placed as to receive the colored rays and converge them to a focus, a
round spot of white light will be again formed in the focus of the lens.
If colored powders are mixed in the proportions that the several colors occupy
in the solar spectrum, the color of the compound will be a grayish white. That
the resulting color is not pure white is probably owing to the fact that we cannot
procure artificial colors that will accurately represent the colors of the solar
spectrum.
458. Analysis of colors by absorption.-Although the colors of
the prismatic spectrum cannot be further divided by refraction, Brewster




OPTICS.                             33
has shown, that any of the colors may be still further decomposed by
transmission through variously colored glass. He thus ascertained that
red, yellow, and blue light are found in various proportions in all parts
of the spectrum, and that any other color whatever may be formed )by
suitable combinations of these three. Brewster and other eminent
philosophers have hence inferred that there are really only three primary colors, red, yellow, and blue.
Dr. Young considered red, green, and violet, primary colors. According to
Herschel, any three colors of the spectrum may be taken as primary, and all
other colors may be compounded from them, with the addition of a certain
amount of white. The distinction of colors into primary and secondary, should
therefore be considered to a certain extent as arbitrary, and as adopted principally for convenience of illustration.
459. Complementary colors.-Any  two colors which by their
union would produce white light, are said to be complementary to eaczother. If we take away from the solar spectrum any color whatever,
we may reunite all the remaining colors, by means of a double convey
lens, or by a second prism, and the resulting color will obviously be
complementary to the first, because it is just what the first wants to
make white light. In this manner it is found that,
Red is complementary to..... Green.
Violet red     "       ".....              Yellowish green.
Violet         "       "...... Yellow.
Violet blue    "       ".....   Orange yellow.
Blue           "       "......    Orange.
Greenish blue "        "...... Reddish orange.
Black. "......   W. hite.
The subject of harmony and contrast of colors, will be treated in connection
with the phenomena of vision.
460. Properties of the solar spectrum.-In the solar spectrum
there are found three distinct properties which exist in various degrees
of intensity in the differently colored rays. See fig. 368.
(a) Luminous rays.-According to Ierschel, Fraunhofer, and others,
it is found that the maximum illuminating power resides in the yellow
rays, and the minimum in the violet.
(b) Calorific, or heating rays.-The position of greatest intensity for
the calorific rays varies with the nature of the material of the prism
with which the spectrum  has been produced.  In the spectrum  produced by a prism of crown glass, the greatest heating power is found
in the pale red. If a prism filled with water is used, the greatest
heating power is found connected with the yellow rays. If the prism
is filled with alcohol, the greatest heat is connected with the orange
31




334           PHYSICS OF IMPONDERABLE AGENTS.
yellow. With prisms, formed of highly refracting gems, the maximum
heating power is found beyond the red ray. Flint glass resembles the
gems in this respect.
(c) Chemical rays.-In a great variety of phenomena, solar light acts
as a chemical agent. Under the influence of solar light, plants decompose carbonic acid, evolving pure oxygen, and most vegetable colors are
destroyed; phosphorus is changed to its red or amorphous state, and
loses its power of emitting light; chlorine and hydrogen may be safely
mixed in the dark, but combine with an explosion when exposed to
the sun's light; the green color of plants disappears in the dark, and
the nature of the vegetable juices is changed when withdrawn from
the chemical action of light; and the wonderful phenomena of photography depend upon the action of light upon sensitive chemical
substances.
The maximum chemical effect, produced by solar light, appears to
be connected with the violet rays, or with rays between the violet and
the blue.  Some chemical effect is produced by rays refracted entirely
beyond the extreme border of the visible violet rays. The lavender
light of Herschel results from the concentration of the so-called invisible rays, beyond the border of the violet.  A large convex lens gathers
these otherwise invisible rays into a faint beam of lavender colored
light.
461. Fraunhofer's dark lines in the solar spectrum.-In 1802,
Dr. Wollaston first discovered the existence of dark lines in the solar
spectrum, but the discovery excited no special attention, and was
applied to no practical purpose.
Unacquainted with Wollaston's observations, the late celebrated
Fraunhofer, of Munich, rediscovered the dark lines of the spectrum,
now distinguished as Fraunhofer's dark lines.  Viewing through a
telescope the spectrum formed from a narrow line of solar light, by
the finest prisms of flint glass, he noticed that its surface was crossed
by dark lines of various breadths.  None of these lines coincide with
the boundaries of the colored spaces.
From the distinctness and ease with which they may be found and
identified, seven of these lines have been distinguished by Fraunhofer
by the letters B, C, D, E, F, G, H.  Numerous other lines-varying
from  600 to 2000 in number, according to the power of the telescope
with which they are viewed-have since been counted in the solar
spectrum..To view these lines with the naked eye, a ray of sunlight is admitted into a
dark chamber through narrow openings in two screens, one placed behind the
other, as shown in fig. 366, and is then refracted by a prism of the purest flint




OPTICs.                               335
glass. The lines, or some of them, will then be seen on the screen. The positions
of these lines in the colored spaces of the spectrum is perfectly definite, but their
366                                  367
I)    BC   D       M    P 
bpw~~~ /"~~ ^FLINTGLASS
It'   IYB                            I            I  CBSCROG LASS
-BC D ]     G   H
III I    I ER
distances from each other vary with the substance of which the prism is formed.
Prof. O. N. Rood states (Am. Jour. Sci. [2] XVII. 429), that fine flint glass
prisms are by no means indispensable for viewing the fixed lines, as he found no
prism among twelve in a candelabrum which did not show several of them.
Fig. 367 shows the arrangement of the dark lines in the spectrum, formed by
prisms of flint and crown glass, and also by a prism filled with water. These
dark lines answer the important purpose of landmarks for determining the
indices of refraction for various substances. The exact limits of the several
colors in the spectrum are not well defined, but the dark lines establish definite
points from which the practical optician estimates the refractive power of any
medium, and also the comparative refrangibility of the differently colored rays
in which the dark lines occupy fixed positions.
Lines in light from  different sources.-In the spectrum produced
by the light of the sun, whether reflected by the moon or planets, or from the
clouds or any terrestrial object, the position of the dark lines is invariable. But
the light of the stars differs from that of the sun, and the light of one star differs from other stars in regard to the number and position of the dark lines in
the spectrum. Electrical light, and the light of flames produced by any burning body whatever, give bright lines instead of the dark lines in the spectrum
formed by solar or stellar light.
The relation of the dark lines to the colors of the spectrum is shown
in fig. 368.  B  lies in  the red portion near the end; C is farther
advanced in the red; D in the orange is a strong double line easily
368!1iIti   I        I
Red. Orange. Yellow. Green. Blue.  Indigo.  Violet.
recognised; E in the green; F in the blue; G in the indigo; and I in
the violet.  Besides these, there are also others very remarkable; thus
b is a triple line in the green, between E and F, consisting of three
strong lines, of which two are nearer each other than the third; A is
in the extreme border of the red, and a is a band of delicate lines
between A and B.




336           PHYSICS OF IMPONDERABLE AGENTS.
462. Fixed lines in the spectra from various colored flames.
-It is well known to chemists that characteristic colors are imparted
to the flame of alcohol by the salts of various metals. It has been
lately observed that the spectra from flames thus colored possess
characteristic fixed lines. Thus the spectrum of a soda flame is characterized by two bright lines in the position of the two dark lines at D in
the solar spectrum. Lithium gives a brilliant red line between B and
C, and potash salts give bright lines corresponding to the dark
lines A a B  shown in fig. 368. The spectrum  from  lime (in the
Drummond light) gives at first two bright lines like salts of sodium,
which however soon disappear as the heat is continued; but if an
alcohol-sodium  flame is held in the path of the rays, two dark lines
assume the place of the original bright lines in this spectrum, corresponding exactly in position to the two dark lines D of the solar spectrum.
These variously-colored flames held in the path of the rays producing
the solar spectrum render the dark lines more distinct although these
flames alone would produce bright lines.
From similar observations Kirchoff deduces the inference that the
sun's atmosphere contains compounds of sodium and potassium but no
lithium.*
463. Intensity of luminous, calorific, and chemical rays.Fig. 368 also shows how the intensity of the luminous, calorific, and
chemical rays, varies in different parts of the spectrum. The greatest
illuminating power resides in the yellow part of the spectrum. The
heating power is almost entirely absent in the violet and the blue, where
the chemical agency is at its maximum, and it is greatest beyond the red,
and extends a considerable distance, where no ill:i..tiatiii    chemical
power is ordinarily manifest. The relative positions of the maximum
illuminating, chemical, and heating powers of the solar spectrum, vary
somewhat with the nature of the substance composing the prism with
which the spectrum has been produced.
464. Refraction and dispersion of the solar spectrum.-Kalychromatics.-If a glass tube, retort neck, drinking glass, or any
similar instrument of glass, be held in the path of the colored rays
from  a triangular prism  in a dark chamber, a beautiful system  of
colored rings will be formed, varying their form, position, and color,
with every change in the position or form of the glass interposed.
This experiment exhibits, in a surprising and agreeable manner,
the wonderful resources of color contained in the solar beam. Language fails to express the exquisite and wonderful beauty of this
simple experiment, involving only the refraction and dispersion of the
* Monthly notices of the Berlin Academy, 1859, p. 662.




OPTICS.                            337
solar spectrum.  Kalyccromatics (from  the Greek for beautiful colors)
has been suggested as a word to distinguish these phenomena.
465. Chromatic aberration.-When rays of ordinary white light
are refracted by a lens of any form, consisting of a single transparent
substance like glass, or a transparent gem, the rays are each acted upon
as by a prism, and dispersed into all the colors of the solar spectrum.
This effect is shown by fig. 369, where V is the focus of the violet rays which
are most refracted, and R is the focus of red          369
rays which are least refracted. A violet image  a         r       r
is formed at V, and a red image at R, and as 
the other colors are situated between the violet
and the red, all the space between V and R is
occupied by images of intermediate colors.  
If an image of a point or line is formed at V,
its color will be violet, but it will be surrounded by fringes composed of all the
colors of the spectrum, the outer border of the fringe being red. This defect of
all single lenses, formed of whatever substance, is called chromatic aberration.
466. Achromatism.-We have seen, ~ 461, fig. 367, that the spectrum formed by flint glass is nearly twice as long as that    370
formed by crown glass.  If therefore we take a prism of
crown glass, A, fig. 370, and another prism of flint glass, 
B, having a refractive angle so much smaller than the   _
refractive angle of A, that the solar spectrum formed by
it will exactly equal in extent the spectrum  formed by
the first prism, we may place the two prisms in opposition,
as shown in the figure, and the colored rays separated by transmission through one prism, will be exactly reunited by the other. The
light transmitted through the two prisms, thus placed, will therefore
be of the same color as before transmission. But while the color of the
transmitted light is unaltered, its direction will be changed by about
one-half the refractive power of the prism A; for while the prism, B,
has neutralized all the dispersion of color produced by A, it has neutralized only about half of its refractive power.
Applying these principles to lenses, a double convex lens of crown
glass, A A, fig. 371, may be united with a plano-concave lens of flint
glass, B B, having a focus about double the focus of the convex   371
lens. These two lenses will act like the prisms in the preceding  A 
figure.  The concave lens of flint glass will correct the chromatic aberration of the double convex lens of crown glass, and
leave about one-half of the refractive power of the convex lens
as the effective refracting power of the compound lens.
An achromatic lens, formed of a double convex lens of crown 
glass, equally convex on both sides, joined with a plano-concave lens
31*




338            PHYSICS OF IMPONDERABLE AGENTS.
of flint glass, having its concave side ground to fit one side of the double
convex lens, will have the focus of a simple plano-convex lens, with its
convexity equal to one side of the double convex lens.
467. Formula for achromatism.-Let it be required to determine
the forms of two thin lenses composed of different media, which will
together form  a compound lens free from  chromatic aberration.  In
this problem we will consider only two colors of the spectrum, as red
and violet.
Let nm andl n be the indices of refraction for the mean ray in the two media;
m' and a' the indices for one of the colored rays, and ts" and n" the refractive
indices for the other ray.
Let f and f be the mean focal lengths of the two lenses, of which r and 8 and
r' and 8' are the radii of the surfaces. By the principles already established we
shall have:- _ (.,- 1) ( - +  )+ (, — 1) {            /)   ~
-l  1) 1
- =         ("  — 1)     + (n      ) (       )    U
Subtracting the first equation from the second,
0 =  (m" - m')  - -+      } + (n" - n') {',-   -
This equation may be put under the form,
m"   m' 1   n" - a' 1
0 =   r. - +.-.,
m.-      1 +. —1 /'
l" - fl' n " - n'
The coefficients       and, are called the dispersive powers of the
- 1        n   i
P   Pa'
two media, and may be represented by p and p', hence 0 = —-  -, and as p
and p' are either both positive or both negative, under any supposition this equation can only be satisfi, d by making either f or f' negative, that is, one of the
~    P
lenses must be concave. We shall then have;  f,,  Orf:f' = p: p'.
We therefore obtain the following conclusions:1st. An achromatic combination must be composed of two or more
lenses formed of media having different dispersive powers.
2d. One of the lenses must be concave and the other convex.
3d. The two lenses forming an achromatic combination must have
fvcal lengths directly proportional to the dispersive powers of the media
of which they are respectively composed.
As it was stated in   454 that the spherical aberration of a concave
lens is the opposite of the aberration of a convex lens, it is easy to see
that the combination of such lenses as are required to produce achromatismn will also wholly, or in part, correct the spherical aberration.




OPTICS.                              839
~ 5. Vision.
468. Structure of the human eye.-The human eye is the most
perfect of all optical instruments.  By means of this organ, stimulated
by the light reflected or refracted from external objects, we recognise
their presence, nearness, color, and form.  Some knowledge of the
structure and action of the eye is essential to a proper understanding
of the uses of other optical instruments.
The eye, situated in its bony cavity called the orbit, is maintained in
its position by the optic nerve and its sheath, by muscles which serve
to move it or hold it steady in any required position, and by the delicate
membrane called the conjunctiva, which covers its anterior surface and
lines the eyelids. The eyelids serve to protect the organ from external
injuries, and also to shut out light which might otherwise be troublesome or injurious by its excess, or too long-continued action.
Fig. 372 shows a horizontal section of the eye, the lower part of the
figure representing the side of the eye towards the nose.  The globe, or
ball of the eye, is nearly spherical,                  372
though the anterior portion is more
convex than the other portions, as
shown in the figure.
The principal portions of the eye
which require consideration, are the  i-...
sclerotic coat, the cornea, the choroid;,coat, the retina and optic nerve, the 
iris, the pupil, the crystalline lens,..."
the  aqueous humor, the vitreous          -."
humor, and the hyaloid membrane.                     A' "n
The sclerotic coat, i, is a strong opaque structure, composed of bundles of
strong white fibres, interlacing each other in all directions. This membrane
covers about four-fifths of the eyeball, and more than any other structure, serves
to preserve the globular form of the eye. It has a posterior sieve-like opening, for
the transmission of the fibres of the optic nerve, n; anteriorly, a transparent
membrane called the cornea, a, is see into a groove in the sclerotic coat, as a
watch crystal is set in the case, but these two membranes are so firmly united
that they are separated only with considerable difficulty. The cornea is more
convex than the sclerotic coat. 
The choroid coat, k1, is a strong vascular membrane, lining the sclerotic coat,
and covered internally by a dark pigment, the pigmentuttlm  igrurm, which prevents any reflection of light from the internal parts of the eye.
The third, or inner membrane of the eye, is the retina, m, which is merely an
expansion of the optic nerve, s, uniting it to the brain. It is on this delicate
lining membrane (the retina) that the images of external objects are formed.
The ii8s, d, which forms the colored part of the eye, is a dark annular curtain
or diaphragm, adherent at its outer margin, with a central opening which, in




340             PHYSICS OF IMPONDERABLE  AGENTS.
man, is circular; in cats and the feline tribe generally it is elongated vertically;
in the ox and other ruminating animals, in a horizontal direction. The central
opening of the iris, e, which allows light to penetrate the eye, is called the pupil.
It varies from one-eighth to one-quarter of an inch in diameter. In a strong
light the pupil contracts, but where the light is diminished it expands.
Every one knows the sensation produced by entering a house after spending
hours in the open air exposed to the light of the sun reflected from snow. In
this case the pupil becomes so contracted, and the eye so accustomed to a strong
light, that objects within doors are almost invisible until the pupil expands and
the eye recovers its sensitiveness in ordinary light. The movements of the iris
are involuntary.
The pupil of the owl is so very large that it sees distinctly at night, while in
the day-time the pupil cannot contract enough to protect the eye from the bliliding effect of the solar rays, and hence the owl is nearly blind by day.
The crystalline lens,f, is a transparent body, placed behind the iris and very
near to it; it is enveloped in a transparent membrane or capsule, which adheres
by its borders to the ciliary process, g. The posterior surface of the crystalline
lens, is more convex than the anterior. The crystalline lens is made up of
serrated fibres, arranged in layers which increase in density from the circumference to the centre of the lens.
Aqueous humor.-The space between the cornea and the crystalline lens is
filled with a transparent liquid called the aqueous humor. The iris divides this
space into two chambers, the anterior chamber, b, between the cornea and the iris,
and the posterior chamber, c, between the iris and the crystalline lens. These
two chambers communicate freely with each other through the pupil, e. The
free edge of the iris floats in the aqueous humor.
Vitreous humor.-The posterior compartment of the eye, h, behind the crystalline lens, constitutes by far the larger part of the internal cavity of this organ,
and is filled with a transparent gelatinous fluid, enclosed in exceedingly delicate
cellular tissue, which is condensed externally, and forms a delicate hyaloid
membrane, everywhere covering the retina and the posterior surface of the
crystalline lens. The vitreous humor, enclosed in its cellular tissue, and
enveloped by the hyaloid membrane, is called the vitreous body.
469. Action of the eye upon light.-The eye may be compared
to a dark chamber, the pupil being the opening to admit the light, the
crystalline lens being a converging lens to collect the light, and the
retina a screen upon which is spread out the image of external objects.
The effect is the same as when a double convex lens forms, at its conjugate focus, an image of any object placed in the other focus.
Let A B, fig. 373, be an object placed before the eye, and consider that rays
are emitted from any point, as                      373
A, in all directions; only those
rays which are directed towards
the pupil can penetrate the eye,
or contribute to the phenomena
of vision. The rays, on entering  the  aqueous humor, are
refracted towards the axis, 0 o, drawn through the optical centre of the crystalline lens; but on entering the lens, which is more dense than the aqueous
humor, they are still further refracted, and undergoing yet another refraction
on leaving the crystalline lens, they converge towards a pcint,, where they




OPTICS.                               341
form an image of the point A. The rays of light emitted from B form  its
image in the point b, and in the same manner every part of the object, A B, is
delineated in the very small image a b, which is a real image, inverted, and
formed exactly upon the retina.
470. Inversion of the image formed in the eye.-To prove that
the image formed in the eye is really inverted, take the eye of an ox,
cut away the posterior part of the sclerotic and choroid coats; fix the
eye thus prepared in an opening in the shutter of a dark chamber, and
look at it with the aid of a magnifying glass, when external objects
will be seen beautifully delineated in an*inverted position, on the retina
at the posterior part of the eye.
Philosophers and physiologists have proposed various theories to explain how
we come to perceive objects erect, when their images in the eye are actually
inverted. The most rational of these theories are the two following: 1st. That
we judge of the relative position of objects, or of different parts of the same
object, by the direction in which the rays come to the eye, the mind tracing
them back from the eye towards the object. 2d. That the image formed on the
retina, gives correct ideas of the relation of external objects to each other; up
and down being, in reference to impressions on the retina or brain, merely the
relative directions of the sky and earth; and we see all bodies, including our
own persons, occupying the same relations to these fixed directions as our other
senses demonstrate that they really occupy.
471. Optic axis.-Optic angle.-The principal axis of the eye,
called the optic axis, is its axis of figure, or the right line passing
through the eye in such a position that the eye is symmetrical on all
sides of it.  In a well formed eye this is a right line, passing through
the centre of the cornea, the centre of the pupil, and the centre of the
crystalline lens, as 0 o, fig. 373.  The lines A a, B b, which are sensibly right lines, are secondary axes.  Objects are seen most distinctly
in the principal optic axis.
When both eyes are directed towards the same ob.ject, the angle
formed by lines drawn from  the two eyes to the object, is called the
optic angle, or the binocular parallax.
To appreciate this difference of direction, look at two objects that are situated
in a line with one eye, the other being closed; then, without moving the head,
look at the same objects with the other eye, and the objects will not both appear
in the same line, but will seem suddenly to change their positions. By such
experiments it will readily be found that some persons see principally with the
right, and others chiefly with the left eye, when both eyes are open. Others
will find that a part of the time the direction of objects is determined by one
eye, and part of the time by the other.                  374
472. Visual  angle.-The  angle                          A
formed between two lines drawn from 
the eye to the two extremities of an                                      3
object, is called the visual angle, as A O B, fig. 374.  If the object is




342            PHYSICS OF IMPONDERABLE AGENTS.
removed to twice the distance, the visual angle A' 0 B' will be only
one-half as great as A 0 B, and the breadth of the image formed on
the retina will be proportionally decreased.
The apparent linear magnitude of an object is in inverse proportion to its
distance from the eye, or in direct proportion to the visual angle. The apparent
superficial magnitude is always the square of the apparent linear magnitude, and
is in inverse proportion to the square of the distance.
473. The brightness of the ocular image of any object will be
in direct proportion to the intensity of the light emanating from each
point in the object.
The amount of light received by the eye from any point in the object,
or from the entire object, will be inversely as the square of the distance,
and directly as the intensity of the light from each point (413). But
the superficial magnitude of the image will diminish as the square of
the distance increases: Hence, the apparent brightness of the image will
remain constant, whatever may be the distance of the object.
As the object recedes from the eye, the size of the image formed on the retina
diminishes, the details of the various parts become crowded together, and only
the bolder outlines occupy sufficient space to make a sensible impression, or to
be clearly discerned.
475. Conditions of distinct vision.-It may be stated in general,
that two conditions are essential to distinct vision. 1st. That an object
should be situated at such a distance as to form on the retina an image
of some appreciable magnitude.  2d. That the object shall be sufficiently illuminated to produce a distinct impression upon the retina.
The distance at which lan object can be seen varies with the color of the object,
and the amount of illumination. A white object illuminated by the light of the
sun can be seen at a distance of 17,250 times its own diameter. A red object
illuminated by the direct light of the sun can be seen only about half as far as
though it were white, and blue at a distance somewhat less. Objects illuminated
by ordinary day-light can be seen only about half as great a distance as when
illuminated by the direct rays of the sun. The smallest visual angle under
which an object can be seen with the naked eye, is estimated at twelve seconds.
All these calculations will vary for different eyes.
Persons having dark-colred eyes can generally see much farther than those
who have light-colored eyes. Those whose eyes are trained to view distant
objects, as sailors and surveyors, will see objects that are far too distant to be
seen by the eyes of inexperienced persons.
476. Background.-The distance at which the outline of any object
can be distinguished, depends very much upon the color of adjacent
objects, or of the background on which the object appears projected.
Objects are most distinctly seen when the color of adjacent objects, or
the background, presents a strong contrast to the colors of the object
we wish to see.




OPTICS.                             343
Colored signals.-For signal flags used at sea, the colors red, yellow, blue, and
white are employed, because they are readily distinguished, and are easily seen,
with the water or the sky for a background. For railroad signals, the colors
red, white, and black are mostly used.
477. Sufficiency of illumination.-It is not enough for distinct
vision, that a well-defined image of the object shall be formed on the
retina. This image must be sufficiently illuminated to affect the senses,
and at the same time not so intensely illuminated as to overpower the
organ. An image may be so faint as to produce no sensation, or it may
be so intensely brilliant as to dazzle the eye, destroy the distinctness
of vision, and produce absolute pain.
When we look at the meridian sun, its light is so brilliant as to overpower
the eye and render it impossible even to see distinctly the solar disc, but if a
sufficient stratum of vapor or a colored or smoked glass is interposed, we see a
well-defined image of the sun.
Many stars are so distant that the rays which enter the pupil, when converged
to a point on the retina, produce no appreciable sensation, but when the amount
of light from the same stars falling upon a large lens is concentrated upon the
retina, it produces sensation, and the stars become visible.
On passing from  a dark room to one brilliantly illuminated, or on going
out into the open air at night from a well-illuminated room, the sensations
experienced are owing partly to the contraction and expansion of the iris, as
explained in. 468, and also to the fact that the sensibility of the retina is
diminished by long exposure to intense light, and increased by remaining a long
time in feeble light.
478. Distance of distinct vision.-Although the human eye is
capable of seeing objects at both great and small distances, most persons, when they wish to see the minute structure of an object clearly,
instinctively place it at a distance of from six to ten inches from the
eye. This point, called the limit of distinct vision, sometimes varies for
the two eyes of the same person.  Persons who see objects at very
short distances are called near-sighted, while those who see objects distinctly only at greater distances, are said to be long-sighted.
479. Visual rays nearly parallel.-When we consider that the
diameter of the pupil, when the eye is adjusted for viewing near objects,
is only about one-tenth of an inch, if we take the limit of distinct vision
at six inches, it will be found that the cone of rays entering the eye,
from any single point, is included within an angle of one degree. If
we take the limit of distinct vision at ten inches, the angular divergence
of the cone of rays entering the eye from a single point will be little
more than half a degree.  In either case, therefore, the rays differ but
slightly from parallel rays. For all objects more remote, the rays may
properly be considered as parallel. Distinct vision is therefore obtained
only by rays that are sensibly parallel or very slightly divergent.




344             PIYSICS OF IMPONDERABLE  AGENTS
480. Adaptation of the eye to different distances.-Although
there is a definite distance at which minute objects are most distinctly
seen, the eye has a wonderful facility of adapting itself to viewing
objects at different distances.
Let two similar objects be placed, one three feet from the eye and the other at
a distance of six feet: If the eye is fixed steadily upon the nearer object for a
few moments, it will be distinctly seen, while the more remote object will appear
indistinct, but if the eye is steadily fixed upon the remote object, that object
will soon be clearly seen, and the nearer object will appear indistinct.  We thus
see that either the converging power of the eye is subject to rapid variation, or
that the distance of the crystalline lens from  the retina is changeable.  The
means by which the eye thus rapidly adapts itself to viewing objects at different
distances, have not been satisfactorily determined.
481. Appreciation of distance and magnitude:Aerial perspective. —The appreciation of the distance and magnitude of objects
is entirely a matter of unconscious training, or education, and depends
upon a variety of circumstanlces, as the visual angle, optic angle, comparison with familiar objects, distinctness, or dimness of the image
caused by intervening air or vapor.
When the magnitude of an object is known, as the height of a man, a house,
or a tree, the visual angle under which it is seen enables us to appreciate its distance. If its magnitude is unknown, we judge of its size by comparing it with
other familiar objects situated at the same distance.
In viewing a range of buildings, or a row of trees, the visual angle decreases
as the distance increases, and the objects decrease in apparent size in the same
proportion, but the habit of viewing the houses or trees, and their known altitude,
causes us to correct the impression produced by the visual angle, so that they do
not appear to decrease in size as fast as their distance increases.
Thus, whien distant mountains are seen under a very small visual angle,
occupying but a small space in the field of view, being accustomed to aerial perspective, we unconsciously restore to some extent their real magnitude.
The optic angle, or binocular parallax, is an essential element in appreciating
distances. This angle increases or diminishes inversely as the distance; the
movement of the eyes required, to cause the optic axes of the two eyes to converge upon any object which we are viewing, gives us an idea of its distance.
It is only by habit that we appreciate the relation between the distance of an
object and the corresponding movement, required to direct both eyes upon it.
Perfect vision cannot then be obtained without two eyes, as it is by the combined effect of the images produced on the retinae of both eyes, and the different
angles under which objects are observed, that a judgment is formed respecting
their solidity and distances.
A man restored to sight by couching cannot tell the form of a body without
touching it, until his judgment has been matured by experience, although a perfect image may be formed on the retina of each eye. A man with only one eye
cannot readily distinguish the form of a body which he had never previously
seen, but quickly and unwittingly moves his head from side to side, so that his
one eye may alternately occupy the different positions of a right and a left eye;
and, if we approach a candle with one eye shut, and then attempt to snuff it, we




OPTICS.                             345
shall experience more difficulty than we might have expected, because the usual
mode of determining the correct distance is wanting.
Infants plainly have no notions of distances and magnitudes till taught ny
experience and comparison of optical appearances with the sense of touch.
482. Single vision with two eyes.-When both eyes are directed
to the same object, images are produced in both eyes, and the inquiry
is most natural why all objects thus seen do not appear double? Passing by much learning bestowed on this subject, the simplest and most
satisfactory explanation of the phenomenon is deduced from the anatomical structure of the optic nerves, and their relations to each other,
and to the brain.
The eyes may be compared to two branches issuing from  a single
root, of which every minute portion bifurcates, so as to send a twig to
each eye. (Miller.) The optic nerve from the right lobe of the brain
sends a portion of its fibres to each eye, and also sends some branches
across and backward to the left lobe of the brain. A portion of the
optic nerve from the right eye, instead of proceeding to the brain, curves
around and enters the optic nerve and the retina of the left eye. In
the same manner the optic nerve arising from the left lobe of the brain
is connected with the right eye, and sends branches also to the left eye.
Branches of the same nerve fibres which go to the external side of
the retina of one eye, go to the internal side of the other eye.
It is thus that a perfect sympathy and correspondence is established between
similar parts of both eyes. Hence whatever object is observed, if the optic axes
of both eyes are directed towards it, the image is formed on corresponding portions of the retina in both eyes, and the mind receives the impression of a single
object; but the impression is more vivid than if the same object were seen with
only one eye. So perfect is this sympathy between the two eyes, that if one eye
only is exposed to a strong light the pupils of both eyes contract. If one eye is
diseased and protected from the light, it suffers pain from light entering only
the sound eye.
483. Double vision.-If both eyes are fixed steadily upon one
object, any other object seen at the same time will appear double.
Fix both eyes steadily upon the flame of a lamp or candle, and a finger held
between the eyes and the light will appear double.
Drunken persons, or persons about falling asleep, often see objects double,
owing to the inability to direct both eyes steadily upon the same object. The
same phenomena may occur when, from any cause, the nerves which control the
eye become diseased.
484. Binocular vision.-A picture of an object is formed on the
retina of each eye; but although there may be but one object presented
to the two eyes, the picture formed on the two retinae are not precisely
alike, because the object is not observed from the same point of view.
If the right hand be held at right angles to, and at a few inches from the face
32




346            PHYSICS OF IMPONDERABLE AGENTS.
the back of the hand will be seen when viewed by the right eye only, and the
palm of the hand when viewed by the left eye only; hence the images formed
on the retinae of the two eyes must differ, the one including more of the right
side, and the other more of the left side of the same solid or projecting object.
Again; if we bend a card so as to represent a triangular roof, place it on the
table with the gable end towards the eyes, and look a:t it, first with one eye then
with the other, quickly and alternately opening and closing one of the eyes, the
card will appear to move from side to side, because it is seen by each eye under
a different angle of vision. If we look at the card with the left eye only, the
whole of the left side of the card will be plainly seen, while the right side will
be thrown into shadow. If we next look at the same card with the right eye
only, the whole of the right side of the card will be distinctly visible, while the
left side will be thrown into shadow; and thus two images of the same object,
with differences of outline, light and shade, will be formed, the one on the retina
of the right eye and the other on the retina of the left. These images falling on
corresponding parts of the retinae convey to the mind the impression of a single
object, while experience having taught us, however unconscious the mind may
be of the existence of two different images, that the effect observed is always
produced by a body which really stands out or projects, the judgment naturally
determines the object to be a projecting body.A:
485. Near-sightedness.-Many persons are unable to see minute
objects distinctly unless they are placed within three or four inches of
the eye.  Such persons are often unable to see ordinary objects dis.
tinctly in a large room  or across the street; they are therefore said to
be near-sighted (478). This defect is owing to a too great convergent
power, the eye bringing parallel or slightly divergent rays to a focus
before they reach the retina.
To secure distinct vision in such cases, it is necessary to bring the object so
near the eye as to render the rays entering the eye considerably divergent, when
the image will be formed on the retina. The same object may be accomplished
by placing a concave lens before the eye, when the rays from distant objects will
be rendered divergent, and the strong convergent power of the eye will form the
image on the retina. Concave lenses for near-sighted persons should be such
as have a focus a little longer than the distance at which they see objects most
distinctly.
486. Long-sightedness commonly occurs in old people, when the
eye becomes flattened by diminution of its fluids, or some structural
change in the crystalline lens occurs, by which its convergent power is
diminished. In such cases the rays of light tend to form an image
behind the retina, and vision is most distinct when the object, as a
book when reading, is held at a considerable distance from the eyes, so
as to allow the image to be formed on the retina.
Thia defect of the eyes, when not accompanied by disease, may be entirely
* For a discussion of this subject, see Prof. W. B. Rogers on Binocular vision,
Am. Jour. Sci. [2] vol. XX.




OPTICS.                              347
remedied by using convex glasses, which make up for the diminished converging power of the eyes, and bring the rays to such a condition that the eye is
enabled to bring the light from near objects to a distinct focus upon the retina.
In such cases, however, the power of accommodating the eye to different distances is often not as great as in younger persons; hence many people in
advanced life find it necessary to use one set of glasses for near, and another for
distant objects.
487. Duration of the impression upon the retina.-Every one
knows that a lighted stick whirled rapidly around a circle appears like
a ring of fire. The rapidity of revolution required to produce this
impression is one-third of a second in a dark room, and one-sixth of a
second by daylight.
When a meteor darts across the heavens, it appears to leave a luminous track
behind it, because the impression produced upon the retina remains after the
meteor has passed a considerable distance on its way. The zigzag course of the
lightning appears, for the same reason, as a continuous track.
Winking does not interfere with distinct vision, because the continuance of the impression of external objects on the retina preserves the
sense of continuous vision.
488. Optical toys.-Thaumatrope.-A  great number of optical
toys and pyrotechnic exhibitions owe their effect to the continuance of
the impression upon the retina, when the object has changed its place.
If a horse is painted on one side of a card and a rider on the other side, the
rapid revolution of the card causes the rider to appear seated on the horse. In
the same manner, if any object which takes a variety of positions in moving is
painted in successive positions, at equal distances on a revolving wheel, so
arranged that one only of the figures shall be seen at a time, the object is seen
performing all the motions of real life. In this manner a horse may be made to
appear leaping a gate, or boys playing at leap-frog. These toys are called
thaumatropes and anorthoscopes. Other toys, called phenakistoscopes and phantascopes, are variations of the same thing, combined with mirrors and other ingenious
arrangements on the same principle.
489. Time required to produce visual impressions.-If an object
moves with sufficient velocity, it is entirely invisible, its image upon the
retina not remaining long enough to produce any impression.  This is
the case with a cannon-ball or rifle-ball, viewed at right angles to the
direction of its flight. But if the projectile is going from us, or coming
towards us, it preserves the same direction long enough to produce an
impression. Motions describing less than one minute of arc in a second
of time are not appreciable to us.  Hence we do not see the movements
of the hour hand of a clock, or of the heavenly bodies.
490. Appreciation of colors.-Color blindness.-The power of
the eye to distinguish colors, varies greatly in different persons. Some
eyes fail entirely in this particular, while in every other respect they




348            PHYSICS OF IMPONDERABLE AGENTS.
are perfect.  Such eyes are said to be color-blind.  Some confound
certain colors, -as red and green, while they distinguish others, or while
they recognise all the colors of the spectrum, they cannot appreciate
delicate shades of the same color.
Colors are greatly modified by proper contrast with other colors.
Thus the complementary colors mutually enhance, while those not complementary diminish each other's beauty when contrasted. The sensibility of the eye is much diminished by long inspection of any color,
and its power of perceiving the complementary color is proportionally
increased. This principle is the key to harmony of colors in nature
and art, and serves to explain the modification of color by contrast, and
proximity of two or more colors.
491. Chevreul's classification of colors, and chromatic diagram.-The chromatic diagram of Chevreul, fig. 375, greatly facilitates
375
YELLOWISH GR.:\ \                    GEENISH BLUE
GREE
ORANGE                                            10LET
the study of complementary colors, and the modifications produced by
their mutual proximity.
Three radii of a circle represent Brewster's three cardinal colors, red, yellow,
and blue; between these are placed orange, green, and violet. Between these
six colors are placed reddish orange, orange yellow, yellowish green, greenish blue,
violet blue, and violet red. We thus obtain twelve principal colors, each of
which may be again divided into five scales or hues, which gradually approach
the succeeding color.
We thus have the circumference of the circle, which represents the prismatic




OPTICS.                               349
spectrum, divided into sixty scales of pure colors. Each radius representing a
scale of colors is divided into twenty tones, to represent the intensity of each
color in its own scale. The tone of any color may be lowered by the addition
of white, when it will remain in the same radius or scale, but take a position at
a lower tone, or nearer the centre of the circle. A color modified by black, is
called a broken color, but as the color is deeper, the tone is carried towards the
circumference of the circle. To represent the modifications produced by black,
Chevreul employs a movable quadrant, not easily introduced in our illustration.
When two complementary colors are mixed, their combination produces white,
if the colors are pure. The combination of two colors not complementary produces a certain quantity of white, but principally a color which will be found
in the diagram intermediate between the two colors, if they are of the same
tone, or nearer to the color of deeper tone, when their tones or intensities are
different. The complementary color in the diagram is found at the opposite
extremity of the diameter of the circle.
This diagram thus explains the effect which two colors produce upon each
other by their mutual proximity.
When two colors are placed near each other, each color appears modified as
though mixed with a small portion of the complement to the color which is near it.
Examples. —(a) Suppose blue and yellow to be placed side by side; at one
extremity of a diameter we read yellow, and at the opposite violet, hence the
proximity of yellow gives to the blue a shade of violet, or makes it approach
violet blue. In the same manner we find orange complementary to blue; hence
the blue gives a shade of orange to the yellow, or makes it approach orange
yellow.
(b) Let green and yellow be contiguous, the yellow will receive red, the complement of green, and will become orange yellow, while the green will receive
from the yellow its complementary violet. A part of the yellow in the green
will thus be neutralized, and the green will appear bluer or less yellow, in fact,
greenish blue.
492. The study of colors upon the principles here laid down is
of great importance to the artist and manufacturer, whether in reproducing the beauties of nature, or in architectural decoration; also in
weaving, embroidery, and costume.
The skillful salesman knows how to enhance the brilliancy or beauty of his
goods by artfully contrasting the pieces which he hopes to sell by others having
complementary colors. Good taste in dress never violates these principles,
regarding with care the complexion of the wearer in contrast to the colors
selected. Florid skins can bear dark hues in dress, while delicate complexions
are made pallid by heavy colors. A green dress or wreath increases the freshness
of a rosy complexion. A crimson dress and scarlet shawl worn together appear
mutually dull and heavy, while either, with the contrast of an appropriate shade
of green, would be attractive and tasteful. These topics will be found fully considered in " Chevreul on Colors."
Q 6. Optical Instruments.
493. Magnifying  glasses.-Single lenses, used  for magnifying
small objects, occupy an important place in the arts. They are used
by watch-makers, jewelers, engravers, and other artisans, whose labors
32*




350            PIYSICS OF IMPONDERABLE AGENTS.
are performed upon minute structures. These instruments occupy a
middle place between spectacles and the regular microscope composed
of a variety of parts.
A thorough knowledge of the uses and powers of simple lenses forms the basis
of all calculations of the powers and uses of more complex instruments, like
the compound microscope and the telescope.
The eye takes no cognisance of real magnitude, which it can only estimate by
inference, but notices directly apparent magnitude, which is determined in all
cases by the visual angle under which objects are seen (472).
We have seen (479) that it is essential to distinct vision that the rays entering
the pupil from any one point of an object should be parallel, or slightly divergent, the distance of most distinct vision being generally from five to ten inches.
For near-sighted persons, this distance is as small, sometimes, as two or three
inches, and for eyes enfeebled by age, it extends from fifteen even to thirty
inches.
494. The magnifying power of a lens is found with sufficient
accuracy for ordinary purposes by dividing the limit of distinct vision
(ten inches) by the distance of the principal               376
focus of the lens.
Let A B, fig. 376, be an  object placed
before a convex lens, so much nearer to the
lens than the focus, F, that the rays, after
refraction by the lens, shall be in that state
of slight divergence best adapted to produce distinct vision, that is,
diverging as though  emanating from  a point at a distance of ten
inches or the limit of distinct vision. Let a b represent the virtual
image, formed where the refracted rays would meet if extended backward, then a b will be as much greater than A B, as its distance from
the lens is greater than the distance of the object, A B, from the lens.
The divergence of rays of light entering the small opening of the
pupil, from a point ten inches distant, is so small that we may consider
them parallel, and then the object, A B, will be nearly at F, the principal focus of the lens.
To estimate the magnifying power of a lens more accurately; let the distance
of most distinct vision be represented by e; with a lens interposed, the eye
sees a virtual image of the object, therefore, in the formula for a convex lens, let
1   1    1            ef
v  — e, and then   -          -.'. u   --, which is the distance of the
e   f    u          ~ +.f
object from the lens. If the eye is placed close to the lens, the magnifying
e e -f f            e
power represented by JI will be, M=  -=    -     = -1 +  -.
u   *f              f
If the eye is placed at a distance from the lens represented by d, we shall have
the distance of the virtual image a b from the lens represented by e' =  e -d,
e- d
and the magnifying power will become,   =  I --.
I




OPTICS.                               351
If the eye is placed at a distance from the lens equal to its principal focus,
e
or, d =  f, then M 1=  -, and in that case the magnifying power for different
eyes varies as the limit of most distinct vision.
If the eye is placed at a distance from the lens equal to the distance at which
e-d
it sees objects most distinctly, then   ~  = 0, and Mr=  1, or the object is not
f
magnified by the action of the lens.
The superficial magnifying power is equal to the square of the linear
magnifying power given by the rule stated above; but the linear magnifying power is alone commonly used in scientific treatises.
495. The simple microscope  acts in the same manner as the
single lens or magnifying glass. Instead of a single lens,. a doublet or
triplet, acting as a single lens, is often used.              377
Raspail's dissecting microscope, shown in 
fig. 377, is the most complete simple microscope. The  
magnifying lens, o, mounted in a dark cup, A, to   ni
protect the eye from extraneous light, is fixed in the
end of a movable arm which can be rotated on its                 M
support, elevated and depressed by the milled head
E, or lengthened by turning the milled head C.
Below the lens is the stage B, which supports the
object to be examined. The concave mirror, M, can
be so adjusted as to illuminate the object by a concentrated pencil of transmitted light.
In using this microscope, the eye is placed over 
the lens o, which may be elevated or depressed till
the focus is adjusted to give the most distinct view of the object on the stage.
Opaque objects are illuminated by a bull's eye lens.
By using lenses of different foci, magnifying powers may be obtained with this
instrument, varying from two to one hundred and twenty diameters.
496. The  compound  microscope  consists, essentially, of two
lenses, so arranged that when an object is placed             37S
a little beyond the principal focus of the first  
lens, its image may be formed in the principal             /
focus of the second lens, by which it is viewed          d
as an object is viewed by a common magnifier. 
The arrangement of the lenses in the compound  
microscope is shown in fig. 378, and also the position            /
of the object, and the images both real and virtual.
The object,, r, being placed near the first lens, a b, ~         ~
called the object-glass, an image, inverted and much
enlarged, is formed at R S, in the focus of the second
lens, de, called the eye-glass. By this lens, the rays            b
are transmitted slightly divergent, and in the exact
condition to produce distinct vision when viewed by           s
the eye. The rays transmitted through the eye-glass, if traced backward to the




352            PHYSICS OF IMPONDERABLE AGENTS.
distance of distinct vision, form a virtual image at R' S', much larger than the
real image R S, formed by the action of the first lens.
Such a compound microscope as the one shown in this figure, is subject to
chromatic and spherical aberration, and the image viewed by the eye is not
straight as shown in the figure, but curved so as to appear convex towards the
eye. These imperfections are almost entirely corrected in the achromatic compound microscope described in ~ 511.
497. The telescope is an instrument constructed for viewing distant objects.
Telescopes are of two kinds. Refracting telescopes are constructed
of lenses. Reflecting telescopes contain one or more metallic reflectors.
498. The telescope used by Galileo in 1609, is the oldest form
of which we have any definite description.  The Galilean telescope
consists of a convex lens, of long focus, and a concave lens of short
focus placed at a distance apart, equal to the difference of their principal foci. The light from distant objects collected by the large surface
of the convex field-lens, is brought to such a state of divergence by the
concave eye-lens as to produce distinct vision in the eye.
The magnifying power of the Galilean telescope is found by dividing
the principal focus of the convex lens by the principal focus of the concave lens.
The convex lens, M N, fig. 379, tends to form an image of a distant object,
AB, very near its principal focus, as at a b. The concave lens, E F, being
379
placed between the convex lens and the image, a b, renders the rays which were
converging to a, slightly divergent, as though emanating from a point, a', at
the distance of distinct vision, about ten inches. The same effect is produced
on the rays converging to b. The direction of the obliqne pencils is changed,
and the extremities of the image appear in the secondary axis a 0' a', and b 0' b',
drawn from a and b through 0', the optical centre of the lens E F. It is especially to be noticed, that while the rays from any one point in the object are
rendered parallel, or slightly divergent, by the concave lens, the pencils from the
extreme points converge at 0' much more than at 0, making the visual angle
a' 0' b', under which the object is seen by the telescope, much greater than the
visual angle a 0 b, under which the object would appear without the telescope.
Since the angle A 0 B is equal to a 0 b, and a' 0' b' is equal to a 0' b, the
visual angle a' 0' b' is to the angle A 0 B as 0 F is to 0' F, and the image a' b'
appears as much greater than the object as the focal length 0 F of the convex
lens xrexeds the focal length 0" F, of the concave lens.




OPTICS.                             353
The opera-glass consists generally of two Galilean telescopes, placed
near together, to allow of distinct vision by both eyes.
Night-glasses, used by seamen, are constructed like large operaglasses. They serve to concentrate a large amount of light in such a
condition as to allow of distinct vision, and thus enable the eye to see
objects distinctly in the night. They have a low magnifying power.
With the Galilean telescope in all its forms the object appears erect.
499. The astronomical telescope  may be constructed with a
convex lens placed beyond the image formed by the field-lens. The
second lens then magnifies the image formed by the first lens. The
object appears inverted, but this occasions very little inconvenience in
astronomical observations.
500. Eye-pieces are certain combinations of lenses used in both
telescopes and microscopes to magnify the image formed by the lens
nearest to the object. They have less spherical and chromatic aberration
than a single lens, and also enable the eye to take in a larger extent
of the object to be examined than could otherwise be seen.
The positive eye-piece, invented by Ramsden, consists of two
plano-convex lenses, with their convex surfaces turned towards each
other, and placed at such a distance that the object or image to. be
viewed by it is seen distinctly when brought very nearly in contact
with the first lens. To secure this result, the distance between the
lenses must be a very little less than one-half the sum of their focal
lengths for parallel rays.  The spherical aberration produced by this
eye-piece is only about one-fourth as much as if a single lens were used.
The chromatic aberration also is less than with a single lens.
Let F F, fig. 380, be the field-lens, and E E the eye-lens of the positive eyepiece. Let m n be an image formed by the              380
object-glass either of a telescope or a micro-    n c
scope, then each ray from  the image on      1~ 
passing the lens F F becomes colored, c r, b v,
representing the violet rays, and c r, b r,  
representing the red rays. The red rays, 
which are least refracted by the first lens, 
fall near the borders of the second lens, where the refractive power is greater
than where the more refrangible violet rays fall; hence the second lens tends to
correct the chromatic dispersion of the first, and the violet and red rays enter
the eye very nearly as though emanating from a common point. This is an
important excellence of the positive eye-piece; but a yet more important advantage of this eye-piece is, that the image is less distorted than when only a single
lens is used.
The negative eye-piece, which was invented by Huyghens, consists generally of two plano-convex lenses, having the convex surfaces




354            PHYSICS OF IMPONDERABLE AGENTS.
of both turned towards the object-glass.  The two lenses are placed at
a distance from each other equal to one-half the sum of their focal
lengths.  The image is formed between the lenses.  This arrangement
considerably enlarges the field of view, and diminishes the spherical
aberration; the chromatic aberration is also less, and it is more
equalized in all parts of the field than in other eye-pieces.
In the most perfect form of the negative eye-piece, according to Prof. Airy,
the first, or field lens, is a meniscus whose radii are as four to eleven, with the
convex side toward the object, and an eye-lens having the form of least spherical
aberration (454), with the more convex side towards the object.
The focal lengths of the field and eye lenses should be to each other as 3 to 1,
and their distance apart equal to one-half the sum of their focal lengths.
In eye-pieces designed for the microscope, instead of estimating the principal
focal length of the field-lens, we must take its conjugate focus when the object
is placed in the position of the object-glass of the microscope.
The action of the negative eye-piece will be more fully explained in connection
with the compound achromatic microscope (511).
The terrestrial eye-piece consists of four lenses, two of them being
added solely to produce an erect image.
Fig. 381 shows a section of the common spy-glass or terrestrial telescope, with
381
the erecting eye-piece. The several tubes which shut one within another, allow
the instrument to be reduced to a convenient length when not in use.
501. Reflecting telescopes are extensively used for astronomical
observations.  A  variety of forms have been  invented  by different
observers, but in all a metallic speculum is employed to form an. image
of distant objects, and an eye-piece is used to magnify the image.
502. Sir William  Herschel's telescope, shown in fig. 382, con382
sists of a speculum, S S, set in a tube somewhat larger than the diameter
of the speculum, and an eye-piece, ef, placed at one side of the open




OPTICS.                              355
end of the tube. The axis of the speculum, represented by the dotted
line a N, is so inclined that parallel rays, falling on every part of the
speculum, will be reflected, converging to the side of the tube where
the eye-piece is placed to receive them. The size of the tube, and the
inclination of the axis of the speculum, is so adjusted that the eye of
the observer may be placed at E without intercepting any part of the
light which can fall upon the speculum  in such a direction as to be
reflected to the eye-piece.
Sir William Herschel's great telescope had a speculum four feet in diameter,
three and a half inches thick, weighing two thousand one hundred and eighteen
pounds. Its focal length was forty feet, and it was set in a sheet-iron tube
thirty-nine and a half feet long, and four feet ten inches in diameter. When
directed to the fixed stars it would bear a magnifying power of six thousand
four hundred and fifty diameters.
This is called the front view telescope, because the observer sits with his back
to the object and looks into the front end of the telescope.
503. Lord Rosse's telescope.-By far the largest reflecting telescope ever constructed was made by the Earl of Rosse.  It was commenced in 1842, and was so far completed as to be used for the first
time in February, 1845.
The great speculum is six feet in diameter, has a focal length of
fifty-four feet, and weighs four tons. An additional speculum to be
used in the same instrument weighs three and a half tons.  The tube
is of wood, hooped with iron, seven feet in diameter, and fifty-two feet
in length.
This telescope has fittings to mount the eye-pieces either for front view, as in
Herschel's telescope, or at the side, as in the Newtonian form: for this purpose a
small speculum is placed at an angle of 45~, reflecting the rays at a right angle
through an orifice in the side of the tube, where the eye-piece is placed.
The base of the instrument is supported upon a universal joint; and by chains
and windlasses this mammoth telescope is moved with ease, between two lofty
walls supporting movable galleries, which enable the observer to follow the
instrument in any required position.
The amount of light on any surface being as the square of the diameter, if we
reckon the pupil of the human eye at one-tenth of an inch in diameter, this
telescope will be seven hundred and twenty times as broad as the pupil, or have
an area five hundred and eighteen thousand and four hundred times as great as
the unaided eye. If one-half the light is lost by reflection from the mirror, we
shall still have two hundred and fifty thousand times as much light as commonly
enters the eye. We need not wonder therefore at the marvellous power with
which this instrument penetrates the remoter regions of celestial space.
504. Achromatic telescopes.-The principle of achromatism  has
been briefly explained in ~ 466, where it has been shown that a convex
lens of crown glass may be combined with a concave lens of longer
focus, made of flint glass, which has a higher refractive and disnersive




356            PHYSICS OF IMPONDERABLE AGENTS.
power, the combination producing refraction without dispersion, and
consequently forming an image free from the primary prismatic colors.
The common form of achromatic compound lens is a plano-concave lens of
flint glass, united with a double convex lens of crown glass. Such lenses are
found in opera-glasses and spy-glasses, called achromatic, used both on land and
at sea. This form of lens is also often employed in the smaller astronomical
telescopes. But in such glasses a certain amount of spherical aberration remains
uncorrected.
To secure perfect correction of spherical and chromatic aberration at the same
time, a double concave lens of flint glass has been placed between two double
convex lenses of crown glass, the curved surfaces of the several lenses being
carefully estimated in view of the refractive and dispersive powers of the two
kinds of glass employed.
The refractive and dispersive powers of glass are so variable, that the optician
is obliged to determine them anew for every new specimen of glass, and estimate
again, by the formulae already given, the proportional curvatures of the lenses
to be constructed from it.
Sir John Herschel found that an achromatic object-glass of the form
shown in fig. 383, will be nearly free from spherical aberration, if the
exterior surface of the crown lens is 6'72, and the exterior sur-  383
face of the flint lens 14'20, the focal length of the combination A   B
being 10'00; and the interior surfaces of the two lenses being
computed from these data to destroy the chromatic aberration
by making the focal lengths of the two glasses in the direct
ratio of their dispersive powers (467). The two interior surfaces
that come in contact may be cemented together if the lenses are
small.                                                             A B
Until quite recently, almost insuperable obstacles interfered with the manufacture of flint glass in large pieces of uniform density, free from veins and
imperfections.
In 1828, an achromatic lens fourteen inches in diameter was considered a true
marvel of optical art. The object-glass in the great achromatic refracting telescope at Cambridge, Mass. (one of the largest in use), is about sixteen inches in
diameter, with a clear aperture of fifteen inches, and it cost, unmounted, about
$15,000. Mr, Bontemps, a French artist, employed in the glass works of Messrs.
Chance, Brothers & Co., Birmingham, Eng., has succeeded in producing a disk
of flint glass twenty-nine inches in diameter, two and a half inches thick, weighing two hundred pounds, and pronounced by the most skillful opticians very
nearly faultless.
505. Equatorial mountings for telescopes.-With telescopes of
great power, the diurnal motion of the earth causes a celestial object to
pass out of the field of view too rapidly tq allow of satisfactory observation.  To obviate this difficulty, a system  of machinery called an
equatorial mounting, has been devised, to give to the telescope such a
uniform motion as to keep any celestial object constantly in the field
of viow.




OPTICS.                              357
An axis firmly supported is placed parallel to the axis of the earth, and is
caused to revolve by clock-work with a motion exactly equal to the sidereal
motion of the heavens. A second axis, acrosSwhich the telescope is mounted,
is fixed upon the first axis, and at right angles with it. The telescope can
be elevated or depressed in declination by motion of the second axis, and it can
be moved in right ascension by motion on the first axis. When the telescope
has been thus directed to any celestial object, it may be clamped on both axes,
and the movement of the clock-work will cause it to follow the motion of the
object in the heavens.
506. The Cambridge telescope with equatorial mountings is
shown ill fig. 384.
It stands on a granite pier surmounted by a single block of granite ten feet
in height, to which the metallic bed-plate of the telescope is secured by bolts
384
1i??21 iii! /
and screws. It is covered by a dome moving on a circular railway, which is
easily rotated so as to allow the great telescope, twenty-three feet in length, to
be directed to any part of the heavens. A narrow window, closed by shutters
33




358            PHYSICS OF IMPONDERABLE AGENTS.
moved by chains, is opened when the telescope is in use. The hour circle
attached to the equatorial axis is eighteen inches in diameter, divided on silver,
and reads by two verniers to cape second of time. The declination circle is
twenty-six inches in diameter, divided on silver, and reads by four verniers to
four seconds of arc.
The movable portion of the telescope and machinery is estimated to weigh
about three tons, but it is so perfectly counterpoised and adjusted that the
observer can direct the instrument to any part of the heavens by a very slight
pressure of the hand upon the balance rods. This great achromatic telescope
has eighteen different eye-pieces, giving to the instrument magnifying powers
varying from 103 to 2000 diameters.
507. The visual power of telescopes, or the aid which they afford
in viewing distant objects, depends upon the combined effects of
increased light and magnifying power.
Sir William Herschel relates that, on a certain occasion, when on
account of the darkness a distant steeple was invisible, a telescope
showed very distinctly the time by the clock on the tower. Here but
little magnifying power was required, and there was a deficiency of
illumination, yet the telescope supplied both.
To understand the principles upon which this power of telescopes
depends, it is necessary to attend to the following particulars:1. Magnifyingpower is measured by the enlargement of the image
seen in the telescope, as compared with the apparent dimensions of the
object as seen by the naked eye.
2. The illuminating power of the telescope is the amount of light
which it collects from any object, and transmits to the eye for the purposes of vision, as compared with the amount of light from  the same
object received by the unassisted eye.
The illuminating power of the telescope should be carefully distinguished from
illumination of the object.
3. Penetrating power is the ratio of the distances at which the eye and
telescope would collect, for the purposes of vision, an equal amount of
light.  Ience the penetrating power of a telescope is equal to the
square root of the illuminating power.
4. The visual power of a telescope is found by extracting the square
root of the product obtained by multiplying the penetrating power by
the magnifying power.
Putting P for the penetrating power of a refracting telescope, x for the proportion of light transmitted by a single lens, n for the number of lenses in the
instrument, A the available diameter of the field-lens, and a for the diameter of
A2"X
the pupil of the eye, we shall have the illuminating power =.
\A-     A,
The penetrating power,  P -=  =- ~-  / -     " 
V          aI




OPTICS.                             359
The value of x in this equation will vary with the thickness of the lenses, the
degree of polish, and the amount of curvature; but for ordinary purposes of
calculation we may consider its value as varying from -T8 to -96.
Let M represent the magnifying power and V the visual power of a telescope,
and we shall have generally,   V = i/MP  = { M.-.x  } -.
It will be evident that the best effect with the telescope will be obtained when
the penetrating and magnifying powers are nearly equal. If the magnifying
power is in excess, though the image may be enlarged, it will be too faint to
produce a clear impression. If the magnifying power is too small in proportion
to the penetrating power, the eyes will be dazzled by the excess of light, while
the several parts of the image will not be clearly separated upon the retina.
The magnifying power of the telescope is therefore varied by the use of different eye-pieces (506) to suit the state of the atmosphere and the degree of
illumination of the object viewed.
508. Achromatic object glasses for microscopes, if constructed
of the forms used in telescopes, are very unsatisfactory. In the first
place, it is found exceedingly difficult to construct such lenses sufficiently
small for the high magnifying powers required in the microscope.
Secondly, the largest achromatic lenses for telescopes have but a small
diameter in proportion to the length of their foci, and if lenses for the
microscope have a diameter equally small in proportion to their foci,
they admit too little light to be of much practical utility. But if their
diameter is increased, the light admitted through the borders of the
lenses produces fringes, with colors in the inverse order of the solar spectrum, showing that while the color is perfectly corrected in the centre,
the correction effected by the concave lens is too great at the margin.
509. Lister's aplanatic foci, and compound objectives.-The
discoveries of Joseph Jackson Lister, Esq., communicated to the Royal
Society in 1830, have proved of the utmost value in perfecting the compound achromatic microscope. His preliminary principles are, 1st, that
plano-convex achromatic lenses, shown in fig. 371, are most easily constructed. 2d, that if the convex and concave lenses have their inner
surfaces of the same curvature, and are cemented together, much less
light is lost by reflection than if the lenses are not cemented. Mr.
Lister discovered that every such plano-              385
convex achromatic combination as A A,. -.
fig. 385, has some point, as f, not far...............................
from  its principal focus,` from  which  " 
radiant light falling upon the lens will  i-...............::::::::. 
be transmitted free also from spherical                      
aberration.  This point is therefore called an aplanatic focus.  The
incident ray, fd, makes with the perpendicular, i d, an angle considerably less than the emergent ray, e g, makes with e h the perpendicular at the point of emergence. The angle of emergence is nearly




360            PHYSICS OF IMPONDERABLE AGENTS.
three times as great as the angle of incidence, and the rays emerge from
the lens nearly parallel, or converging towards a focus at a moderate
distance from the lens.
If the radiant point is now made to approach the lens, so that the ray fd e g
becomes more divergent from the axis, as the angles of incidence and emerence
become more nearly equal to each other, the spherical aberration becomes negative or over-corrected. But if the radiant point, f, continues to approach the
glass, the angle of incidence increases, and the angle of emergence diminishes
and becomes less than the angle of incidence, and the negative spherical aberration produced by the outer curves of the compound lens becomes again equal to
the opposing positive aberrations produced by the inner curves which are
cemented together. When the radiant has reached this point f' (at which the
angle of incidence does not exceed that of emergence so much as it had at first
come short of it), the rays again pass the glass, free from spherical aberration.
The pointf' is called the shorter aplanatic focus.
For all points between the two aplanatie foci f and f the spherical aberration
is over-corrected, or neg:ative; and for all radiant points more distant than the
longer aplanatic focusf, or less distant than the shorter aplanatic focus f', the
spherical aberration is under-corrected, or positive. These aplanatic foci have
another singular property. If a radiant point in an oblique or secondary axis
is situated at the distance of the longer aplanatic focus, the image situated in
the corresponding conjugate focus will not be sharply defined, but will have a
coma extending outwards, distorting the image. If the shorter aplanatic focus
is used, the image of a point in the secondary axis will have a coma extending
towards the centre of the field. T'hese peculiarities of the coma produced by
oblique pencils are found to be inseparable attendants on the two aplanatic foci.
These principles furnish the means of entirely correcting both chromatic and spherical aberration, and of destroying the coma of oblique
pencils, and also of transmitting a large angular pencil of light free
from every species of error.
Two plano-convex achromatic lenses, A M, fig. 386, are so arranged
that the light radiating  from                       386
the shorter aplanatic focus of.
the anterior combination is re-.........
ceived by the second lens in the'/ —-— "...
direction of f, its longer aplanatic focus.                                     -7
If the two compound lenses are fixed in this position, the radiant
point may be moved backwards or forwards within moderate limits, and
the opposite errors of the two compound lenses will ba-            387
lance each other.
Achromatic lenses of other forms have similar properties.  It is found in practice that larger pencils free
from errors can be transmitted by employing three compound  lenses, the middle and posterior combinations'
being so united as to act as a single lens, together balancing the aberrations of the more powerful anterior combinations.  Fig. 387 shuows




OPTICS.                              361
a common form of the triple aplanatic and achromatic objective, used
for the compound microscope.
510. Aberration of glass cover corrected.-If an object viewed
with an achromatic microscope, which has all its aberrations corrected
for an uncovered object, is covered with even a thin film of glass or
mica, spherical aberration is again produced, thus sensibly impairing
the distinctness of vision when a high power is used.
Let a b c d, fig. 388, be a film of glass or mica bounded by parallel surfaces.
If rays of light, diverging from 0, pass through this film, the ray 0 T' R' E'
will suffer greater displacement than the ray 0 T R E,        388
which makes a smaller angle with the perpendicular  P          E 
0 P. If R E and R' E' are extended backward, they
will cross the axis or perpendicular at the points X and.. 
Y. This separation of the points X and Y is exactly
similar to the spherical aberration of a concave lens, and  
is therefore called negative spherical aberration. Chro-  
matic aberration is also produced by the same means. 
The effect observed by the eye in such cases is, that lines are not so sharply
defined, and the outline of an object appears bordered with broader fringes, with
colors of the secondary spectrum upon the borders of the object. These errors
are easily corrected by diminishing the distance between the anterior and
posterior combinations of the compound objective, which is furnished with an
adjusting screw for this purpose.
511. The compound achromatic microscope is composed of the
389
rR V.......o::;:..  It,' V
triple achromatic objective, A M P, fig. 389, and the negative eye-piece,
formed of the field-lens F F, and the eye-lens E E.
The section drawn in the figure, shows how the light is acted upon in passing
through the different parts of the instrument. Pencils of rays from all parts of
the object, s t, pass through the compound objective A M P, and tend to form a
red image at R R, and a violet image at V V, the object-glass being slightly
over-corrected, so as to project the violet rays as far beyond the red as may be
necessary to make up for the want of absolute achromatism in the eye-piece.
The converging pencils S, C, T, being intercepted by the field-lens F, are foreshortened, and at the same time the lateral pencils are bent inward, so that the
images v v, r r, are smaller, nearer together than V V, R R, and curved in an
opposite direction. The reversion of the curvature of the images is produced by
the form of the field-lens, which meets the central pencil, C, much farther from
33*




362            PHYSICS OF IMPONDERABLE AGENTS.
the images V V, R R, than where it meets the lateral pencils S T; thus the focus
of the central pencil is more shortened than the others. The field-lens of the
negative eye-piece does not reverse the curvature in every variety of instrument,
but it always changes the form of the images so as to improve the definition.
The violet rays S 1n, T 1, fall upon the eye-lens nearer its axis, than the red rays
S m, T nm, which are less refrangible, and hence the eye-lens counteracts the
divergence of the colored rays which were separated by the field-lens, and causes
them to pass to the eye so nearly parallel that they appear to diverge from the
same point of the virtual image S T, formed at the distance of distinct vision.
The distance between the red and violet images r r, v v, is just equal to the difference between the red and violet foci of the lens, and these images being curved
just enough to bring every part into exact focus for the eye-lens, the eye sees
the image at S' T' spread out in its true form on a flat field.
By means of this beautiful system of compensations, for the various errors of
chromatic and spherical aberration and curvature of the image, which interfere
with the performance of a single lens, the compound achromatic microscope has
been brought to a degree of perfection unsurpassed by any instrument employed
in practical physics.
512. Solid  eye-piece.-A  negative eye-piece, constructed  of a
single piece of glass, has been patented by Mr. R. B. Tolles, of Canastota, N. Y.  In the solid eye-piece there is much less loss of light
by reflection, as there are only one-half as many refracting surfaces
as in the ordinary eye-piece. The image is of course formed in the
substance of the glass.  This eye-piece allows the use of a higher
magnifying power than the eye-piece formed of two lenses, and it is
thought also to give more perfect definition.
513. Visual power of the achromatic microscope.-The great
distinction between the telescope and the microscope consists in the
fact that while the former, practically speaking, is suited to receive
parallel rays from  a distant object, the latter has to deal with rays
which diverge from a closely approximate point. On this account the
formula for visual power will require some modification.
Angular aperture.-The angular breadth of the cone of light which
a microscope receives from an object, and transmits to the eye, is called
its angular aperture.
Illuminating power in the microscope depends upon the square of the
angular aperture, due allowance being made for the light lost in its
passage through the instrument.
When the formula for visual power is applied to the microscope, A must represent the angular aperture of the instrument measured in degrees; and a will
represent the angular breadth of a cone of light which can enter the pupil of
the eye from an object at the distance of distinct vision =  1~ very nearly. We
shall then have:
The penetrating power of the microscope, P =  A l/x"; or the penetrating
power varies directly as the angular aperture. This is not absolutely correct,
for the loss of light by reflection causes x to diminish as A increases.




OPTICS.                              363
Let C =  1/x", and we shall have:-The visual power of the microscope,
V= /MP = 1/AMAC-   /A X 1/,11'C:
Or (since the magnifying power, or the eye-piece, which may be employed,
varies with the angular aperture), generally:The visual power of the microscope is proportional to the square root of the
angular aperture of the object-glass.
Defninng power, or sharpness of minute details in an object seen by the microscope, requires perfect correction of chromatic and spherical aberration.
In fig. 390, A, B, C, D, show the successive appearances of a scale of JMorpho JMenelane, by regular enlargements of the angular aperture of the micro390
A              B             C            D
scope with which it was viewed. The available angular aperture of a single
lens seldom exceeds fifteen or twenty degrees. In the triple achromatic objective, the aperture for ordinary                    391
observations has been extended
to 1000. With the highest powers
used for viewing infusoria, both
English and American opticians
have advanced the angular aper- 
ture to 1500, and in some glasses 
to 1750~.
514. The mechanical arrangement of the  micro-  
scope  is well exhibited in
fig. 391, which has been en-                      ^
graved from a very excellent
instrument, manufactured by
J. & W. Grunow, New Haven,  
Conn.
The instrument is mounted on
trunnions, which allow it to be
inclined at any angle. The body
of the microscope is moved in a
grooved support, by a rack and
pinion motion for adjusting the
Focus. The stage has a fine, deli- 
cate movement, by a screw and  _..
milled head, acting upon a lever 
at the back of the instrument, by 
which movement the focus can be
adjusted with the utmost delicacy.                        — ~
The stage itself can be moved freely in any direction by a lever at the right,




364            PHYSICS OF IMPONDERABLE  AGENTS.
A mirror, con cave on one side, and plane on the other, is so mounted below the
stage as to illuminate the object with either parallel or converging rays.
Polarizing apparatus, and other accessories, are fitted to the stage, and to the
body of the microscope.
515. The magic lantern is an instrument for projecting upon a
screen, images of transparent pictures painted on glass.
A lamp is placed in a dark box, before a parabolic reflector, M N, fig. 392,
which throws the light upon a convex lens, A, by which it is strongly condensed
392
upon the object painted on the glass slide, inserted at C D. The magnifying
lens, B, forms an image of the illuminated picture upon a screen E F, placed at
its conjugate focus. The picture is placed in an inverted position, to produce
an erect image upon the screen.
A great variety of objects painted on glass can thus be exhibited either for
amusement or instruction. The magnifying power of the magic lantern is
equal to the distance of the screen from the lens, B, divided by the distance of
the lens from the object.
516. The solar microscope is a species of magic lantern illuminated by the sun. It is, however, much more perfect in its structure,
and it is commonly employed for viewing on a screen images of natural
objects, very highly magnified.
The structure and arrangement of the solar microscope are shown in fig. 393.
393
s
H X
in \           t            - ra
It is mounted over an opening in the shutter of a dark room, on the side towards
the sun. A plane mirror, M, is so arranged outside the shutter as to reflect the




OPTICS.                               365
rays of sunlight, S, through the condensing lens, A, into the microscope. By turning the screw, B, the mirror may be elevated or depressed, and by means of another
screw, T, it can be rotated on the axis of the microscope, so as to follow the motions
of the sun. A small lens, E, moved by the rack and pinion with the milled head
C, serves to condense the light upon the object slide, 0. The slide 0, which carries
the object, is secured between the brass plates K K, by the screws, Ii HI.
The object, strongly illuminated, is adjusted to the focus of the small lens, L
(which may be either a small globule of. glass, or a compound achromatic objective, of short focus), and an image, a b, greatly enlarged, formed in the conjugate
focus of the lens, is received upon a white screen placed in a convenient position.
By diminishing the distance between the object and the lens, L, the conjugate
focus will be more distant, the screen may be placed farther from the lens, and
the magnifying power will be proportionally enlarged.
Instead of employing the light of the sun, the solar microscope may be illuminated by the electric, or by the oxyhydrogen light.
517. The camera obscura consists of a dark chamber in which
images of external objects are formed by the aid of a mirror, and a
concave lens.  This instrument affords a con-                394
nient method of sketching natural scenery.
A plane mirror, m, fig. 394, placed at an angle of       "      m
45~ with the horizon, reflects the light downward,
through a converging lens, placed in the top of the.....
dark chamber. A sheet of paper placed on the table 
in the focus of the lens, receives the image of a land- 
scape or other object, which can be traced with a
pencil by the artist, sitting, as shown in the figure,
with his head and shoulders protected from extraneous light by a dark curtain.
The student can easily prepare an instrument of
this kind, by inserting a spectacle glass in an orifice in the top of a box about two feet high, and
placing a common mirror at the required angle
above it. The paper on the table can be placed on
a drawing-board, and fixed at such a distance from
the lens as gives the most distinct image. A cloak thrown over the side of the
box where the observer sits, will darken the chamber so as to permit sketches to
be made with great facility.                                        395
Instead of the mirror and lens shown in fig. 394, a rectangular prism is often used as a reflector, and if one side of the prism
is ground in the form of a lens, the two parts of the instrument
are combined in one.
518. Wollaston's camera lucida is another instru- 
ment used for sketching from  nature.  It consists of a
prism, abed, fig. 395, of which the angle, b, is a right
angle, the angle, d, is 135~, and the angles at a and c
are each 67~. 
It is mounted on a suitable stand, and the eye, P P', placed
as shown in the figure, sees the image of a distant object as though projected




366            PHYSICS OF IMPONDERABLE AGENTS.
upon the paper M N, where the outline may be traced by the pencil S, the eye
seeing the image and the pencil at the same time.' The light from a distant
object entering the prism nearly at right angles with the face, b c, twice suffers
total reflection, and emerges perpendicular to the face a b, when it enters the
eye, and appears as if coming from the paper, MN. The image projected upon
the paper is as much smaller than the object as its distance from the prism is
less than the distance of the object. The image can be made to assume any
required dimensions by varying the relative distances of the paper and the
object. This instrument is principally employed by artists for sketching landscapes.
A number of other forms of camera lucida are employed to suit different purposes, but in all of them, either the object, or the pencil and paper, are viewed
by reflected light, made to coincide in direction with the direct light.
519. Photography is the art of producing pictures by the chemical
action of light.  The daguerreotype, ambrotype, crystallotype, and
photo-lithograph, are all produced by modified applications of the
camera obscura.  Instead of the plain paper and pencil used by the
artist for sketching with the camera, a surface of silver or collodion,
made sensitive by iodine, bromine, or some other chemical preparation,
is placed in the camera and subjected to the action of the light of the
image projected there by the lens.                        396
A camera employed for photography in any
of its forms, requires to be achromatic, and
also that the chemical rays shall be brought to
a focus at the same point as the visual rays, or
at a well-defined distance from them. As objects
copied by photography are seldom flat, the objective of the camera requires to be so constructed
as not only to give perfect definition of all objects
situated in the focal plane, but also it should be adapted to give tolerably good
definition of parts of an object that are situated a little anterior or posterior to
the focal plane.
The usual form of the camera employed in photography, is shown in fig. 396.
The achromatic compound lens, A, is attached to the box, C, and can be moved
backwards or forwards by turning the milled head, D. The second box, B,
slides within the first. A plate of ground glass set in the frame, E, is inserted
in B, and when the focus is so adjusted as to give a perfect image on the ground
glass, this is removed, and the sensitive plate covered by a dark screen is inserted
in its place. The dark screen is then removed, and the light produces a chemical change where the image is projected. This image is then made permanent
by vapor of mercury or other chemical applications.
520. Railway  illumination.-For illuminating  railroads, it is
important to throw upon the track a powerful beam of light, consisting
of rays nearly parallel.  When the track is thus illuminated, objects
upon it are more readily distinguished by contrast with surrounding
darkness; it is therefore desirable to limit the light to the immediate
vicinity of the track.
The common method of effecting this object is to place an Argand lamp in




OPTICS.                               3 67
the focus of a large parabolic reflector (325),.situated in front of the locomotive.
The light is thus thrown forward in parallel lines, and the lateral illumination
produced by light radiated directly from the lamp is comparatively small.
521. The Fresnel lens, a section of which is shown at o Ag, fig.
397, is also employed for projecting a powerful beam of parallel light
upon objects to be illuminated at a dis-                    397
tance.  This form  of lens, invented and 
first applied  to  practical purposes by
Fresnel, consists of a central plano-convex
lens, surrounded  by  segmentary  rings,:..': 
with curvatures successively diminishing   b            i 
as much  as is necessary  to avoid  the
spherical aberration of a single lens, the
central lens, and all the angular segments having their curves so
adjusted as to have a common focus.
The segmentary rings are sometimes made entire, but generally, when the
size is considerable, each ring is composed of several parts. The central lens
and lateral segments are all cemented to a plate of glass, as shown in the figure.
For most purposes, where the Fresnel lens is employed, it is necessary to give
the illuminating beam of light a slight degree of divergence. It will be easily
seen from the figure, that if the centre of the lamp is placed at the principal
focus of the lens, F, the divergence of the beam, after passing the lens, will be
equal to the angle b A b, which the flame of the lamp subtends at the surface of
the lens. A concave mirror is also placed behind the lamp, to throw forward
the light in a condition to be refracted nearly parallel by the lens in front of the
lamp. A much more brilliant beam of light is obtained in this manner than by
the parabolic reflectors alone. This lens is also used in France for railway
illumination.
522. Sea-lights, designed as beacons to the mariner upon dangerous coasts, or for lighting harbors, are usually placed in towers, called
light-houses.  The great elevation of the light                 398
permits it to be seen far out at sea. It is evident _......
that all light thrown out above or below  the.......  
plane of the horizon, is of no avail to the.              -
mariner.:""::1          " -
By an ingenious application of the principres of the......._
Fresnel lens, a sheet of light is thrown out in every.....::..
direction in the plane of the horizon. If fig. 398 is. —. i'     ^..
revolved about the central perpendicular line, as an'.. -
axis, it will generate the apparatus known as the
Fresnelfixed light. The central zone will consist of a  -...
series of hoops whose perpendicular section is everywhere the same as a section
of the Fresnel lens. This zone will therefore so act upon the light of a lamp
placed at the centre, as to project a sheet of light in every direction in the plane
of the horizon. Above and below the central zone, are series of triangular




368             PHYSICS OF IMPONDERABLE AGENIS.
hoops.  A section of one of these hoops, and its action upon light radiating
from the central lamp, is shown in fig 399; A C and B C are plane faces, while
A B is a convex surface. Light from the focus, F,             399
Is refracted on entering the face B C, it underoes -'
total reflection at the surface A B, and a second
refraction at A C, from which it emerges in lines..
parallel to the horizon.                          -...    1
The focus of each prismatic hoop is carefully.,.
calculated for the place it is to occupy, so that
every part of the apparatus throws out the light.... 
that falls upon it in a horizontal direction..<\'
523. Revolving  lights.-To  distinguish'
one lighthouse on the coast from another, the 
Fresnel light is so modified  as to give a                                  F
steady light, and also revolving flashes of light of very great intensity.
In the revolving Fresnel light, the triangular             400
prismatic hoops above and below the central zone
are the same as for the fixed light, but the central
zone is made of eight Fresnel lenses, fig 400, set
as shown in the lower part of figure. The upper
part of the same figure shows a front view of the
central zone. While the entire apparatus revolves  
as shown by the direction of the arrows, each of.
the eight lenses gives a very intense light in.
certain directions, and between any two there is, /. 
no light from the central zone of lenses. The... -   i    ~.
light seen from any position appears gradually  - -.
to increase to very great brilliancy, and then to..':
fade away to much less than half its maximum
intensity, after which it atgain increases to its,f}^//' I "    2^J:?i
former brilliancy. These changes are repeated at
regular intervals.
Fig. 401 shows a plan of a revolving Fresnel light fixed in the tower of a
lighthouse. At A B are the parts shown in fig. 400 which produce the flashes
of light. The whole apparatus is made to revolve by means of the clock-work
shown at M, which is moved by the weight P.  The balcony surmounting the
tower is seen in the lower part of the figure, also the stairs leading to the light.
A dome, supported on iron frame-work, protects the illuminating apparatus.
The distance at which the light can be seen will depend upon the height of the
tower in which it is placed.
The lamp used for the Fresnel light is an Argand burner, with four
concentric wicks, -with currents of air passing up between them.
The wicks are defended from the excessive heat of their united flames by a
superabundant supply of oil, which is thrown up from below by a clock-work
movement, and constantly overflows the wicks. A very tall chimney is required
to supply a sufficiently strong current of air to support the combustion. The
dimensions of the Fresnel light, and the number of lenses and hoops of which
it consists, are varied to suit the purposes for which it is used; the light pro



OPTICS.                             369
duced varying in intensity from twenty-five to three thousand Argand lamps of
common size.
401
524. The telestereoscope.-The image upon the retina of every
human eye represents a perspective projection of the objects situated
in the field of view. As the positions from which these projections are
taken are somewhat different for the two eyes of the same individual,
the perspective images themselves are not identical, and we make use
of their difference to obtain an idea of the distances from the eye of the
different objects in the field of view.
The images of the same object on the two retinse are more different
from each other as the object is brought nearer to the eyes. In the
case of very distant objects, the difference between the pictures on the
34




370             PHYSICS OF IMPONDERABLE  AGENTS.
retinae of the two eyes becomes imperceptible, and we lose the aid just
spoken of in estimating their distance and bodily figure.
The telestereoscope is an instrument which causes distant objects to
appear in relief. It increases the binocular parallax of distant objects,
and by presenting to each eye such a view as would be obtained if the
distance between the two eyes were greatly increased, it gives the same
appearance of relief, as if the                       402
objects were brought near to 
the observer.
Let b and b', fig. 402, be two
plane mirrors placed at angles of- 
45~ with the line of vision; let                                     f'
c and c' be two smaller mirrors 
placed parallel to b and b', and,  n.t
let d and d' represent the position of the two eyes of the observer. It is evident
that the light from distant objects falling upon the mirrors in the direction a b
and a' b', will be reflected to the small mirrors c and c', where it will be again
reflected to the eyes at d and d'. The two views seen by the eyes will evidently
be the same as if the eyes were separated to the positions?n and Wn'. The relief
with which objects will be seen by this instrument, will obviously be increased
as much as the distance b b' exceeds the distance between the eyes d and d'.
But while this instrument increases the perspective difference of the images seen
by the two eyes, the visual angle under which each object is seen remains unchanged, and hence, as the apparent distance of the objects is diminished, their
dimensions appear diminished in the same proportion.  If the small mirrors are
made to rotate on perpendicular axes, while the large mirrors are fixed, the
distortion of figure may be easily corrected by turning the small mirrors until
objects appear in their true proportions.
If the lenses of an opera glass are inserted in the instrument, the convex fieldgl:ise3 being inserted atJ and f, between the large and small mirrors, and the
concave eye-glasses between the eyes and small mirrors, the effect will be to
increase the visual angle of every object in the field of view. If the glasses
magnify as many diameters as the distance between the large mirrors exceeds
the distance between the eyes, every object will appear in its due proportions, and the effect will be surprising.  The appearance will be as though
the observer had been actually transported to the immediate vicinity of the
objects themselves.  The distance between the large mirrors of the telestereoscope should not exceed the breadth of an ordinary window, unless it is to be
used in the open air, when it may be made of any dimensions that are desired,
and the effect produced will be in proportion to its magnitude.
525. The stereoscope (from  o'reperq, solid, and 6xo75)w, to see) is
an instrument so constructed that two flat pictures, taken under certain
conditions, shall appear to form a single solid or projecting body.
In order to produce this illusion, different images as observed by the
two eyes (484) must be depicted on the respective retinae, and yet
appear to have emanated from  one and the same object.  Two pictures
are therefore taken from the really projecting or solid body, the one as




OPTICS.                              371
observed by the right eye only, and the other as seen by the left.
These pictures are then placed in the box of the stereoscope, which is
furnished with two eye-pieces, containing lenses so constructed that the
rays proceeding from the respective pictures, to the corresponding eyepieces, shall be refracted or bent outward, at such an angle as each set
of rays would have formed had they proceeded from a single picture in
the centre of the box to the respective eyes without the intervention
of the lenses.
It is an axiom in optics that the mind always refers the situation of
an object to the direction from which the rays appear to proceed when
they enter the eyes; both  pictures will therefore appear to have
emanated from one central object.  As one picture represents the real
or projecting object as seen by the right eye, and the other as observed
by the left, though appearing by refraction to have both proceeded from
the same object, the sensation conveyed to the mind, and the judgment
formed thereon, will be precisely the same as if both images were
derived from one solid or projecting body, instead of from two pictures.
Consequently the two pictures will appear to be converted into one
solid body.                                           403
If two pictures of an octahedron, as A      /   \        7.i 
and B, fig. 403, such as would be formed
on;he retinae of two eyes, are placed in 
the stereoscope, fig. 404, they give to
the observer the idea of a real solid octahedron, instead of the ordinary picture, C. Photographs of natural scenery,
taken from two positions, when viewed in this instrument, appear in relief like
real objects.
The construction and action of the stereoscope will be readily understood by
reference to figs. 405 and 406.  From a double concave lens, A B A' D, two
eccentric lenses, represented by the smaller            406
circles, are formed. E A e, in the lower               40
part of the figure, represents a transverse             1:
section of one of these eccentric lenses, and
E A' e the other. Each lens is equivalent. 
to a triangular prism E A e, with a plano-            /i
404                 405                    /;..
eouvex- i                          E'i
sonvex lens cemented to each refracting face of the prism. Fig. 406 shows a




372              PHYSICS OF IMPONDERABLE  AGENTS.
section of the stereoscope, the eccentric eye-lenses A E, A' E', being placed at
the ordinary distance of the eyes, with their thin edges towards each other  Let
P and P' represent two corresponding points in the stereoscopic photographs
which are to be examined. The rays of light, diverging from the point P, falling upon the eye-lens, are refracted nearly parallel, and by the prismatic form
of the lens are deflected from their course, and emerge from the lens in the
same direction as if emanating from the point.0. In the same manner the rays
from the point P also appear to diverge from the point 0. The same is true of
all similar parts of the two pictures; thus the pictures appear superimposed
upon each other, and together produce the appearance of relief, for which the
stereoscope is so much admired.
The eccentric lenses of the stereoscope are sometimes fixed in position, but
they are often inserted in tubes, as in fig. 404, which can be extended to adapt
the focus to different eyes, or separated to a greater or less distance, to suit the
distance between the eyes of different persons.
If stereoscopic photographs are taken from positions too widely separated
from each other, objects stand out with a boldness of relief that is quite unnatural, and the objects appear like very reduced models. In taking stereoscopic
miniatures especially, great care is required to preserve, natural appearance.
In general, a difference of a few inches in the two positions of the cameras, gives
sufficient relief to the pictures when seen in the stereoscope.
For public buildings and landscapes, two cameras are usually employed,
placed on a stand three or four feet from each other. If it is desired to show a
great extent of a distant landscape, or to exhibit in miniature the grouping and
form of distant mountains, two stations should be selected that are widely separated; but in such cases, care should be taken that no near objects are admitted
into the picture.
526. The stereomonoscope (described by Mr. Claudet, of London)
is an instrument by which  a single  image is made to present the
appearance of relief commonly seen in the stereoscope, and by means
of which several individuals can  observe these effects at the same
time.
Let A, fig. 407, be an object placed before a large convex lens, L, an image
of the object will be formed at a, in the conjugate focus of the lens, and from
the image a the rays of                           407
light will diverge as from              L                S
a real object, which will
be seen by the eyes placed
at ee, e' e', or any other A_-_                  _.
position, in the cone of
rays b a c. Thus several
persons may at the same
time see the image sus-                                  S
pended in the-air. If a screen of ground glass is placed at S S, the image will
appear spread out upon the glass, but it will appear with all the perspective
relief of a real object. An image thus formed on ground glass can be seen only
in the direction of the incident rays.  This is not the case with an image formed
on paper, which radiates the light in all directions, and is hence incapable of
giving a stereoscopic effect in such circumstances.




OPTICS.                               373
The stereomonoscope consists of a screen of ground glass, S S, fig. 408, and
two convex lenses, A L, B L, so placed as to form images of two stereoscopic
pictures, M and N, at the                       408
point a on  the screen        ~t,                       S
S S.  Though  the two
pictures have theirimages
superimposed on the same 
part of the screen S S,
each picture can be seen
only by the rays proceeding from the photograph        ~     ~"                 S
by which it was formed. If the eyes are so placed that the right eye is in the
direction of the rays coming from one lens, and the left eye in the direction of
rays coming from the other lens, the object will appear in relief as in the stereoscope, and several persons can witness the effect at the same time.
~ 7. Physical Optics.
I. INTERFERENCE, DIFFRACTION, FLUORESCENCE, &C.
527. Interference of light.-The interference of vibrations and
waves, has been already alluded to in the theory of undulations (328,
333), but the phenomena of luminous interference require some further
special consideration.
Let A B, B C, fig. 409, be two plane mirrors, making with each other a very
obtuse angle (very near 180~); let a beam of sunlight, entering a dark room by
a small opening, be brought to a focus by a lens, L;        409
if this light, diverging from a focus, F, is allowed
to fall very obliquely upon the two mirrors, as.. \
shown in the figure, it will be reflected as if diverg-           /   
ing from two luminous points, M and N, and the..D? 
light thus reflected will be in a condition to inter-      A 
fere. Draw 0 P perpendicular to M N, from  a             /  ~'
point 0, midway between them. It is evident that 
every point in the line B P, will be equally distant.'
from the luminous points M and N; the waves of
light which cross each other in the line B P, will 
therefore be in the same phase of vibration, and
consequently produce a line of light of double
intensity. Let the smooth circular arcs represent. \,'::.
the phases of elevation, and the dotted arcs phases
of depression; then where, a dotted arc crosses a        "    7 
smooth arc, the two waves should counteract each other and produce darkness.
The open dots represent vibrations meeting in the same phase, and the black
dots represent vibrations meeting in opposite phases, which produce darkness.
The symmetrical curves formed by the intersection of light from the two points
M and N, on both sides of the central line, are of the form known in geometry
as hyperbolas.
The distance on each side of the line B P, where the luminous waves will be
again in a like state of accordance represented by the crossing of the smooth
arcs in the figure, will depend on the interval between them, which is different
for different colors; for red, it is half as much again as for violet light; hence
34*




874            PHYSICS OF IMPONDERABLE AGENTS.
the distance between the curves of double intensity will be least for violet light,
greatest for red, and intermediate for the other colors of the spectrum, so that
while all the colors are united in the central line B P, they will be separated in
the other bars, and form a seriesof colored fringes. In experiments, this serves
to distinguish the central bar, namely, that the other bars-are colored symmetrically on each side of it.
Half way between two places of complete accordance there must occur a
place of complete discordance, where the difference of distances from M and N
is I an interval, or 3, -, or a, &c.; and according to the undulatory theory,
there would be complete darkness. Between these and the places of complete
accordance, there would be intermediate stages of accordance and discordance;
hence there would be bright bars shading into dark ones, all more or less colored
except the central bars, where all the colors are in, a state of complete accordance.
By careful measurement of distances between the luminous and dark bars,
the lengths of luminous waves of different colors have been very accurately
ascertained.
528. Facts at variance with theory.-When the atmosphere is
free from clouds, and the sunlight is brightest, the central bar (which,
according to theory, should be bright) is found to be a black one, whatever be the material of which the mirrors are composed. But when
the sun is near setting, the central bar has been seen undoubtedly a
bright one.  It has also been seen as a bright bar when the luminous
point was formed at a hole in a thin plate of metal, and the light which
had grazed the edge of the hole was used.
The existence of a central black bar, in normal circumstances, where the
vibrations must meet in the same phase, is thought to be inconsistent with
the undulatory theory of light.
It appears that light is so modified in passing through haze, or at an opaque
edge of a small hole, as to acquire an anatropy or inversion of properties.*
529. Interference colors of thin plates are seen in thin films of
varnish, cracks in glass, films of mica, various crystals, and in other
transparent substances, as in soap bubbles.  The colors of such thin
fils are due to the interference of light twice reflected by the surfaces
of the film.
Two surfaces of glass, pressed together, furnish a thin plate of air between
two reflecting surfaces. Let C A D B, fig. 410, be          410
a transparent film, such as a thin blown bulb of S               *3
glass, or a soap bubble; let S A B T be the trans- 
mitted ray, S A R theray reflected at the first surface, S A B A' R' the portion reflected from  the  D ---
second surface, and emergent at the first surface,
S A B A' B' T' the portion emerging from the second 
surface, after the two internal reflections, then the
ray A' R' will be retarded behind the ray A R, by the interval n m, owing to the
* Potter's Physical Optics.




OPTICS.                               375
increased length of path it has to travel in twice traversing the film, and B' T'
will, in a similar manner, fall behind the ray B T, by the interval p q. If these
retardations equal the interval of an odd number of half vibrations, they will
interfere, as they originated from a common wave, in the ray S A. The reflected
rays do not differ greatly in intensity, which is for each about one-thirtieth that
of the incident light for glass, and therefore their interference produces blackness where they destroy each other. The transmitted light has the principal
beam of little less intensity than the incident beam, having lost only about onethirtieth part by reflection at each of the points A and B; but the intensity of
the twice reflected beam which interferes with it is about one-thirtieth of onethirtieth, or one nine-hundredth of that of the incident beam; hence the difference of the intensities of the bright and dark bands formed by transmitted light
is never as great as in the reflected beams. But the difference between the
bright and dark bands is different for different colors of the spectrum, being
least for violet light, and greatest for red. This fact is thought to be contrary
to what should have been expected, according to the undulatory theory.
530. Newton's rings.-If a plane plate of polished glass is pressed
against a plano-convex lens whose radius of curvature is known, the
interference bands become colored rings, and the exact thickness of the
film of air by which each color is produced is easily estimated.
The form of this apparatus is shown in fig. 411. The letters and explanation
of the figure are.similar to the preceding. When the two glasses are pressed
sufficiently near together, the centres appear black         411
by reflected light, and bright by transmitted light.
The thickness of the film of air where the first s  /I
color appears, is equal to one-half the retardation  9\  9
producing that color; hence the length of the wave,
or vibration, for any color, is estimated as equal i      
to twice the thickness of the film of air where the           ~"
color appears. The colors succeed each other in   R^'
the order of the length of the vibrations required
to produce them. A second, third, and fourth series of colored rings will be
found, where the thickness of the film is an exact multiple of the thickness
required to produce the first series of colors. The distance between the first and
second series depends on the rapidity with which the thickness of the film
increases. In the case of a lens pressed against a plate of glass, the distance
between the glasses, or the thickness of the film, increases as the square of the
distance from the centre. The diameters of the bright rings will therefore be as
the square roots of the numbers 1, 2, 3, &c., and the diameters of the dark rings
will be as the square roots of the numbers 1, 2~, 3~, &c. The distance between
successive rings of violet will be much less than the distance between successive
rings of red; one series of colors will therefore overlap some of the colors in
the succeeding series of colored images, and by their admixture produce colors,
the successive groups of which are designated as Newton's first, second, third,
&c., orders of colors.
531. Length of luminous waves or vibrations.-By such means
as we have described, the lengths of the vibrations required to produce
different colors have been estimated.




376             PHYSICS OF IMPONDERABLE AGENTS.
The following table exhibits the numerical results which have been deduced
for the length and velocity of luminous vibrations of different colors.
Length of undulations Number of undula- Number of undulations
Colors.     in parts of an inch.   tions in an inch.   per second.
Extreme red,.        00000266             37640         458,000000,000000
Red,....           0-0000256            39180         477,000000,000000
Orange,..         00000240             41610         506,000000,000000
Yellow,..         00000227             44000         535,000000,000000
Green,...          00000211             47460         577,000000,000000
Blue,...          00000196             51110         622,000000,000000
Indigo,...         00000185             54070         658,000000,000000
Violet,...         00000174             57490         699,000000,000000
Extreme violet,       0-0000167            59750         727,000000,000000
According to Eisenlohr (Am. Jour. Sci. [2] XXII.), the length of the vibrations in the extreme red ray is just double the length of the vibrations of the
invisible rays beyond the violet, which, by concentration, produce the lavender
light of Herschel. The entire range of visible rays differs in the length of
vibrations only by the amount of one octave in music.
When we consider the almost inconceivable velocity with which these wonderfully minute vibrations are propagated, it is evident that absolute demonstration
of the real nature of light must be among the profoundest researches of physical
science.
532. Diffraction.-If a razor is held with its flat surface towards
the rays of the sun, the rays that pass in close proximity, both to the
edge and to the back, will be deflected as shown in fig. 412. A portion
of the rays are deflected outwards, appearing to suffer reflection; the
back of the razor deflecting the rays outward, more than the sharp
edge; but the edge of the razor deflects                    412
more light into the place of the geometri- 
cal shadow, than is deflected inwards by  s
the back of the instrument. These differences  are  represented  by  the closeness                             A
of the lines drawn to represent the rays
where the greatest amount of light is de-                    /        l
fleeted. If the body interposed is narrow,  \
like a fine needle or a hair, the rays de-  
fleeted inwards cross each other, and pro-            / 
duce the phenomena of interference in
accordance with the undulatory theory. The rays deflected outward
produce interference with the rays not deflected, but bright lines appear
where the undulatory theory would give dark lines. All the bright
and dark lines are bordered with colored fringes, as in ordinary cases
of interference.  These phenomena are best seen in a dark room by




OPTICS.                              377
looking through an eye-lens at a hair or needle, at a considerable distance from a lamp, or by looking at a beam of sunlight admitted to a
dark room between two sharp parallel edges. The rays that have been
diffracted or bent into the geometrical shadow, are not as readily
deflected again in the same direction, but are more easily deflected in
the opposite direction than rays which have undergone no such previous change.
533. Fluorescence.-Epipolic  dispersion.-Certain  bodies, as
fluor-spar, glass colored yellow  by oxide of uranium, called canary
glass, solution of sulphate of quinine, infusion of the bark of the horsechestnut, and many other vegetable infusions, possess the remarkable
property of so dispersing some part of the light passing through them,
that the course of the luminous rays becomes visible.
These phenomena are best exhibited by bringing a pencil of light to a focus
in the interior of any of these substances, by means of a convex lens, when the
course of the rays will become visible, as though the portion through which the
light passed had become self-luminous. The rays of light of high refrangibility,
especially the violet and the invisible chemical rays, are subject to this kind of
dispersion, their refrangibility is at the same time changed, and probably the
length of their luminous waves is increased, so that rays previously invisible
may be seen by the eye. These phenomena have been called by various names,
as internal dispersion, epipolic dispersion, and fluorescence. The latter term,
derived from fluor-spar, and adopted by Mr. Stokes, is considered the-more
appropriate term, as it involves no theory.
This change of the refrangibility and length of luminous waves is analagous to the change of pitch in reflected sounds heard in certain remarkable
echoes (Q 355).
534. Phosphorescence.-Certain bodies after being exposed to the
action of light, acquire the property of shining in the dark (399). The
most remarkable phosphorescent bodies are the sulphurets of barium,
strontium  and calcium, some kinds of diamonds, most varieties of
fluoride of calcium, particularly the variety known as chlorophane,
compounds of lime, magnesia, soda and potash, salammoniac, succinic
and oxalic acids, borax, dried paper, silk, sugar, sugar of milk, teeth, &c.
The time during which these bodies emit light varies from a fraction
of a second to several hours, and the intensity of the emitted light
varies in a similar manner.
The study of these phenomena requires the use of delicate apparatus adapted
to the purpose.
1. The more refrangible rays of the spectrum in general act more powerfully
to produce phosphorescence in bodies exposed to their influence than the less
refrangible rays. In some cases the invisible rays of the spectrum, i. e., the
rays beyond the violet, produce a brilliant phosphorescence.
2. The least refrangible rays. as the red, not only generally produce no
phosphorescence, but even counteract the influence of the more refrangible rays
when mixed with them.




378            PHYSICS OF IMPONDERABLE AGENTS.
3. The wave lengths of light emitted in the dark by phosphorescent bodies
are in general greater than those of the exciting rays; i. e., the phosphorescent
light shows a color belonging to a part of the spectrum nearer to the red than
the light which produced it, though in a few cases the color is unaltered.
4. The refrangibility of the light emitted by phosphorescent bodies depends
upon their molecular condition, and not merely upon their chemical constitution.
Each phosphorescent body appears to be adapted to vibrate in harmony with the
wave lengths of some colors more readily than with others.
5. One and the same body may emit rays of very different colors, according to
the time which intervenes between the action of light and the moment of observatin. This last result shows that vibrations of different velocities are preserved
for unequal times in different bodies; sometimes it is the vibrations corresponding to the less refrangible rays which continue longest, as in bisulphate of
quinine, double cyanide of potassium and platinum, diamond, &c. Sometimes
the most refrangible rays are most durable, as in Iceland spar.
6. Many bodies, such as glasses and certain compounds of uranium; owe their
fluorescence entirely to the persistence of the luminous impressions for a very
short time, not exceeding a few hundredths of a second; the intensity of the
emitted light is then very brilliant.
It is probable that phosphorescence and fluorescence differ from one another
only in the time during which a luminous impression is preserved in bodies.
These conclusions, which support the theory of undulation as at present
admitted, prove that luminous vibrations, when transmitted to any body, or at
least to a great many bodies, compel its molecules to vibrate for a time, and
with an amplitude and wave length which depend not only on the chemical constitution of the body but also on its physical condition.*:
535. Colors of grooved plates.-Fine lines engraved upon polished
steel, and lines drawn upon glass with a diamond point, if sufficiently near
together, cause a beautiful iridescence by the interference of light reflected from such surfaces. The beautiful play of colors seen upon mother
of pearl is caused by the delicate veins with which the surface is covered.
II. OPTICAL PHENOMENA OF THE ATMOSPHERE.
536. The rainbow is one of the most wonderful and beautiful phenomena in nature.  In it reflec-                      413
tion, refraction, dispersion, and         s
interference of light, are all 
combined.  It is seen in that s
part of the heavens opposite to 
the sun, when the sun is less
than forty-two degrees above 
the horizon.  The shadow  of
the eye of the observer will
always point to the centre of 
the circle of which the rainbow
forms a part; hence, as the sun descends near the horizon, the rainbow
* Edmond Becquerel, Bibliotheque Universelle, vol. XVI. p. 21.




OPTICS.                               379
rises higher, and as the sun ascends the morning sky, the height of the
rainbow diminishes.
To understand the formation of the rainbow, we must first examine the action
of a single drop of water upon parallel rays of light. Let the circle, fig. 413,
represent a drop of water, and S A, S B, &c., parallel rays of light falling upon
it. The ray S A, which Talls perpendicularly upon the drop, will suffer no deviation in its direction, but will be partially reflected backward in the line of incidence, though it will principally pass through the drop. The ray S a, will be
refracted to b, where it will be reflected to c, and will emerge in the direction c d,
making a certain angle with the direction of the original ray S a. As the distance
of the incident ray from A increases, the emergent ray will make a greater angle
with the incident ray, till we arrive at B, where two successive rays will emerge
parallel, as shown by the heavy line, S By ep, which deviates more from the
direction A S, than any ray incident at a greater or less distance from A. As
we proceed from A, towards C, the deviation of the emergent ray will diminish,
and every ray between B and C will emerge parallel to some other ray, which
entered the drop between A and B; S y will emerge in e' n, parallel to e" n, which
entered the drop at the ray S x. The ray S C, which is tangent to the drop, will
be refracted to i, and emerge in the direction k o, making an angle of about
twenty-five degrees with e p, the line of greatest deviation.
The light which enters the drop in parallel rays will therefore emerge, spread
over the entire space between ep and c d; but having its greatest intensity near
the direction e p, and rapidly diminishing towards c d.
If A Y, fig. 414, represent the position of the line el) of fig. 413, the dotted
curve, by its height above A X, will show how rapidly the intensity of the
light fades away, as the distance from ep increases             414
toward c d, where the intensity is zero.                   y;!
Since we have at every angle between ep and c d, 
parallel rays which have traversed different paths
through the drop, we shall have all the phenomena of 
bright and dark bands, produced by interference..\       b
The intersection of the emergent rays will form a
caustic curve k q, tangent to the circle at k, and ap-       A -
proaching constantly to parallelism with the asymptote ep, which it will never
meet. If the emergent rays between c and e were extended backwards, they
would form another caustic h 1, having e p produced backward for its asymptote.
The caustic curve h 1, commences in a direction perpendicular to the surface of
the drop, and approaches the asymptote without ever touching it. The curves
q r, formed by unwrapping a thread from  the caustic k, q, and q r', formed by a
thread from the caustic I h, show, by their gradual separation, the amount of
retardation of the wave surface of the two sets of parallel rays which interfere
between e p and c d.
According to the undulatory theory, we shall have bright bands where the
rays have traversed equal distances, or distances differing by any number of
entire vibrations, and dark bands where the rays differ by an odd number of half
vibrations.
These bright and dark bands are readily seen, with proper precautions, with
light reflected from a drop of water suspended at the point of a fine glass tube.
When monochromatic light is used, thirty or forty of these bright and dark bands
may be counted.
The breadth of the bright and dark bands varies with the size of the drop




380            PIIYSICS OF IMPONDERABLE AGENTS.
from which the light is reflected. The interference bands vary also for the different colors, being nearly twice as broad for red as for violet light. When
white light is employed, the first red band only is pure, the other bands being
more or less confused by the unequal super-position of different colors.
If we consider only the first two bright bands of each color, we can
easily explain the common phenomena of the rainbow. A little within
the caustic curve, k q, fig. 413, on its convex side, we shall have a
bright light, represented in intensity by the curve a, fig. 414, and a
second band of the same color at b, of feebler intensity. As the refractive index for red rays is less than for the other colors, the red will
diverge more from the incident ray, after refraction, than the violet,
and other colors will appear intermediate.
Suppose now that in a shower of rain a ray of light from the sun
falls upon a drop of water at r, fig. 415, and is reflected from its posterior
surface, so as to give to the eye the                 415
red ray of maximum  intensity, r E, a
drop below it will give a violet ray of
maximum intensity, v E, and intermediate colors will be formed in the same
manner by intermediate drops. Let
the planes of incidence and reflection
revolve about a-line S E S, drawn from
the sun through the eye of the observer;  the  position  of  the  drop 
from  which light can reach the eye
will describe the arch of the rainbow.
The radius of the primary rainbow measured from  the extreme rea
was found, by Sir Isaac Newton, to be 42~ 4'.
The purity of the several colors in the rainbow is the result of interference, which produces dark bands for each particular color, giving a
clear space for the delineation of the other colors of the rainbow before the
first color is repeated. When the rain-drops differ greatly in size, as is
often the case, the different colors of the first and second interference
bands overlap and mingle together, and the bow is but imperfectly
developed.
A secondary rainbow, with violet above and red below, is formed by light
which has been twice reflected within the drops, as shown in fig. 415, the rays
entering the lower border of the drop, and emerging near the upper border. The
same principles of interference determine the purity of colors, and angle of
maximum intensity, as in the primary bow. The loss of light occasioned by
two reflections accounts for the feebler intensity of the secondary bow. In
the secondary bow, the order of colors is the reverse of the primary, violet
being outermost.




OPTICS.                              381
Newton found the distance between the primary and secondary rainbows to
be 8~ 30'.
A spurious rainbow  is often seen within the primary bow, as shown at
p q, fig. 415. This is formed by the second bright band of each color, the
position and intensity of which is represented at b, fig. 414. A third and fourth
bow is also sometimes seen, still interior to the second, but the colors of the
third and fourth orders are so much mingled that only two or three appear in any
bow interior to the first spurious bow.
537. Fog-bows.-Halos.-Coronas.-Parhelia.-Fog-bows, which
are sometimes seen, differ from the rainbow by the extreme minuteness
of the spherules of water from which the reflection takes place.
Halos are prismatic rings seen around the sun or moon, varying
from  20 to 46~ in diameter: these are explained by reflection from
minute crystals of ice floating in the atmosphere.
Coronas, encircling  the moon, are formed by reflection from  the
external surface of watery vapor, the light thus reflected interfering
with direct light front the same source. They generally indicate change
of weather.
Parhelia, and bands of light passing through the sun, are also attributed to reflection from prisms of ice.
Many of these phenomena require for their explanation a refinement of investigation not proper to be introduced in an elementary work.
538. Atmospheric  refraction  causes all bodies not directly in
the zenith to appear more elevated than they                  416
really are.
Let A B C D, fig. 416, represent the external surface....
of the atmosphere, and the inner circles strata of in- Oe  
creasing density around the earth, E. Light from any e    ~  
of the heavenly bodies situated at a or c will suffer a
refraction by every stratum of air more dense than the
preceding; and by a gradually increasing density, it
will be made to travel in curved lines, until entering the eye of the observer, the
bodies at a and c will appear situated at b and d.                417
539. Looming  is a term  applied to the elevation
of objects at sea which appear raised above their real 
position by atmospheric refraction.
Islands often appear thus raised above the water, and an
inverted image is seen below them. Distant vessels sometimes
appear above the horizon, when their distance is so great that
they would be far below the horizon if they were not elevated in 
appearance by extraordinary refraction.
In peculiar states of the atmosphere, ships have appeared
suspended in the clouds, and occasionally an inverted image
has appeared below, when the real ship was mostly below the
horizon, as shown in fig. 417.  ~
540. The  mirage, often  seen  in Egypt, and  sandy  deserts, is
85




382           PHYSICS OF IMPONDERABLE AGENTS.
caused by rays reflected from strata of air heated by the burning
sands.  Distant objects are seen reflected by the heated air as in
418
the waters of a beautiful lake, which disappears as the thirsty
traveler approaches.  The phenomena of the mirage are shown in
fig. 418.
III. POLARIZATION OF LIGHT.
541. Direction  of luminous vibrations. —The phenomena of
polarized light are justly regarded as the most wonderful in the whole
science of optics. These phenomena are most readily explained and
understood by reference to the undulatory theory. It has been stated
(398) that the vibrations of light move at right angles with the direction of the rays.
This species of vibration may be illustrated by those.of a cord, made fast at
one end, and moved rapidly upward and downward by the hand shaking the
other extremity, as shown in fig. 419. If            419
we suppose another cord vibrating from    B
right to left, and others in every inter-..c'.
mediate direction, we may form a tolerably.
clear idea of the vibrations of a collection            " 
of rays in a beam of ordinary light. A
single luminous atom may be supposed to originate vibrations moving in only
a single plane, but an infinite number of independent luminous atoms, constituting a luminous body, will produce vibrations moving in every possible plane.
which may be illustrated by revolving that plane around the line representing
the direction of a ray of common light.
542. Transmission of luminous vibrations. —Opaque substances
allow no luminous vibrations to pass through them.  Some bodies




OPTICS.                          383
transmit nearly all the luminous vibrations which fall upon them;
other bodies are capable of transmitting only those vibrations of light
contained in a single plane, or that portion of the vibrating force which
can be resolved into vibrations in that plane. Other bodies, capable
of vibrating in two directions, reduce all the vibrations which they
transmit to vibrations in the two planes in which these bodies themselves are capable of vibrating. Some bodies, by reason of the position
in which an incident beam of light falls upon them, alter the direction
of the vibrations which they transmit, and thus produce a beam of
light, whose vibrations are all limited to a single plane.
543. Change produced by polarization of light.-A beam of
light is said to be plane polarized when all its vibrations move in a single
plane, or in planes parallel to each other. This may be illustrated by
a bundle of stretched cords, all vibrating in one direction. If the cords
differ in size or tension, the lengths of their vibrations will differ. This
may illustrate the vibrations of different  420           421
colors, which vary in the lengths of their
vibrations (531). A round rod may be 
taken to represent a small beam of common light, and the radii shown in fig.
420 may represent the transverse vibra-   /\\ 
tions by which light is propagated in
ordinary media. Fig. 421 will then represent a transverse section of a
polarized beam, with vibrations in planes parallel to each other.
544. Resolution of vibrations.-The principle of resolution of
forces (50) will enable us to understand how vibrations, in an infinite
number of planes passing through the general direction of a beam of
light, may be resolved into vibrations in two planes, making with each
other any required angle. If 0 E, fig. 422, represents the direction and
intensity of a vibration, it will be equivalent      422
to O a and 0 c, in axes, at right angles to
each other. Vibrations represented by 0 F,    ^ 
O G, and 0 I, may, in the same manner, be
resolved into vibrations in the axes AB and
CD. Then Oa+Oa' +-Ob+Ob  will C   C 
repres#tithe intensity of the resulting vibrations in be axis A B, and O c + Oc Od  J               \ 
+ 0 d' will represent the intensity of the
resulting vibrations in the axis C D. If we
thus resolve vibrations in an infinite number 
of planes into vibrations in the axes AB and C D, the sum of the
resulting intensities in the axis A B will be exactly equal to the sum




384             PHYSICS OF IMPONDERABLE AGENTS.
of the intensities in the axis C D.  A ray of common light may therefore be considered as consisting of vibrations moving in two planes at
right angles to each other.  Any medium  that will, either by its position or internal constitution, separate light into two parts, vibrating in
planes at right angles to each other, will produce that change denominated polarization of light.
545. Light polarized by absorption.-Certain crystals have the
remarkable property of polarizing all the light which passes through
them in particular directions.  They appear to absorb part of the light,
and cause the remainder to vibrate in a single direction only.
If a transparent tourmaline is cut into plates one-thirtieth of an inch thick
and polished, the plane of section being parallel to the vertical axis of the
hexagonal prism in which this mineral crystallizes, the light transmitted through
such a plate will be polarized. If a second plate is placed parallel to the first,
as shown in fig. 423, the light transmitted    423               424
through the first plate will also be transmitted through the second plate; but the          i
light will be entirely obstructed if the axis
of the second plate is placed at right angles
with that of the first, as shown in fig. 424.
A plate of tourmaline becomes, therefore, a
convenient means of polarizing light, and 
also an instrument for determining whether
a ray of light has been polarized by other means. A tourmaline plate so used is
called an analyzer.  Crystalline plates of sulphate of iodo-quinine (called Herapathite, from the name of their discoverer, 3Mr. Herapath), act in all respects
like plates of tourmaline.
546. Polarization by reflection.-When light falls upon a trans-!arent medium, at any angle of incidence whatever, some portion of
trhe light is reflected.  When the incident light falls upon the medium
at a particular angle, which varies with the nature of the substance, all
the reflected light is polarized.
Let G, G, fig. 425, be a plate of glass or any other transparent medium, and
let a ray of light, a b, fall upon it at such an angle that the reflected ray, b c,
shall make an angle of 90~ with the refracted ray,            425
b d, then the reflected ray b c, which represents but         P 
a small portion of the incident light, will be polarized.
If the medium is bounded by parallel surfaces, the 
portion of the light reflected from the second surface
will also be polarized.
The angle of polarization by reflection may be de- 
termined by the following law.  The tangent of the
angle of incidence for which the reflected ray is polarized, is equal to the index
of refraction for the reflecting medium.  This law supposes the reflecting substance more dense than the surrounding medium. If the light is reflected from
the second surface, as whV  n passing from glass or water into air; the icndex of
refraction equals the cotangeat of the angle of polarization.  The polarizing
igle for reflection from glass, is 56~ 25', reckoned from the perpendicular.




OPTICS.                             385
The polarizing angle for water is 53~ 11'. As the index of refraction varies for
different colors, the polarizing angle varies in the same manner.
If a polarized ray falls upon a reflecting surface at the angle of polarization,
and the reflecting surface is rotated around the         426
polarized ray as an axis, when it is so placed that
the plane of incidence corresponds with the plane
in which the ray was polarized, the polarized light
will be reflected just as if it were not polarized;
but when the plane of incidence makas an angle 
of 90~ with the plane of polarization, the light is
entirely intercepted, as shown in fig. 426. In this
respect a reflecting surface, at the proper angle of
incidence, serves the purpose of an analyzer, just
like a plate of tourmaline.
Polarization by metallic reflection.-To obtain a beam of plane
polarized light by reflection from metallic plates, the light must be
reflected many times at the angle most favorable to polarization. A ray
of light once reflected from a metallic plate at the most favorable angle
appears to consist of light vibrating in two planes, in one of which the
phase of vibration is retarded from 0 to I of a vibration behind the light
vibrating in the other plane.  This is called elliptical polarization.
When the two planes of vibration are at right angles to each other,
and the phases of vibration differ lby i of a vibration, the light is said
to be circularly polarized.
The diamond, sulphur, and all bodies possessing an adamantine
lustre, produce elliptical polarization, and if employed as analyzing
reflectors, they change plane polarized to elliptically polarized light.
The investigation of these varieties of polarized light would exceed the
limits of an elementary work.
547. Polarization  by refraction.-When  light is polarized by
reflection from  either the first or the second surface of a transparent
medium, a portion of the transmitted light is polarized by refraction.
The amount of light polarized by refraction is just equal     427
to the amount polarized by reflection, but as the amount    R
of light transmitted  by transparent substances very
much exceeds the amount reflected from their surfaces,
only a small portion of the transmitted rays are polarized, or, more properly, the light transmitted through a
single plate is but partially polarized.
548. Polarization by successive refractions.If a ray of light, R IR, is transmitted obliquely through
a number of parallel transparent plates, as shown in fig.
427, a portion of the light is polarized at every refrac- 
tion, and after a sufficient number of refractions the whole of the transmitted light is polarized.
35*




386             PHYSICS OF IMPONDERABLE  AGENTS.
Light polarized by refraction, is polarized in a plano at right angles with the
plane of polarization by reflection. Light polarized by reflection vibrates at
right angles with  its plane of                       428
polarization, or its plane of reflection, as shown at B, fig. 428.              B
Light polarized by refraction, 
vibrates also at right angles with  A  
its plane of polarization, but parallel to its plane of refraction, as
shown at C, fig. 428. Light not i
polarized, though vibrating in an
infinite number of planes, is equivalent to a system of vibrations in
two planes at right angles to each,
as shown at A, fig. 428.
549. Partial polarization.-Light reflected  or refracted  at any
oblique angle is, in general, partially polarized, and by repeated reflections or refractions the degree of polarization is increased, until, after
a sufficient number of reflections or refractions, it is apparently completely polarized.
Let M N, fig. 429, represent the plane of refraction, and A B, C D, the axes of
vibration for common light, then by repeated re-             429
fractions these axes will be gradually made to   w                        e
approach each other, until they sensibly coincide,   c' c  7   /          1 
as shown in the figure, when the light is said to < 
be completely polarized.  The portion of light  k-                 B     n
reflected, undergoes a similar series of changes, until the axes of vibration
sensibly coincide, in a plane at right angles to their position in light polarized
by refraction.
550. Double refraction is a property in certain crystals that causes
the light passing through them in particular directions to be separated
into two portions, which pursue different paths, and which causes
objects seen through the crystals to appear double.
The most remarkable substance of this kind with which we are familiar, is
Iceland spar, or carbonate of lime, which crystallizes        431
in the rhombic system, as shown in fig. 430. The
line a b, about which all its faces are symmetrically
arranged, is called the major axis of the crystal, and  /.
the plane a c b d, passing through the axis, and
through the obtuse lateral edges, is called the plane
of principal section.                    430.       )/ —----- d 
If a crystal of Iceland spar, from                                    X
half an inch, upwards, in thickness, is  /
laid upon a sheet of paper, on which  \..\ A\are drawn various lines, they will         /. 
appear double, as shown in fig. 431.                           1
A B, C D, E F, G H, are the real lines, seen in their true positions. The dotted
lines show the position of the additional lines, caused by extraordinary refrac



OPTICS.                             387
tion. The line A B, in the plane of principal section, is not doubled. Any line
parallel to A B, will also appear single.
The index of refraction for the ordinary ray remains constant, in whatever
direction light passes through the crystal. The index of refraction for the
extraordinary ray, when parallel to the axis, is the same as that of the ordinary
ray, and differs most from the ordinary ray when it passes through the crystal
at right angles with the axis.
The index of refraction for the ordinary ray in Iceland spar is constantly 1.6543 = m. The index of refraction for the extraordinary ray,
when it makes an angle of 90~ with the major axis, is 1.4833 = n.  Let
x = the angle which the extraordinary ray makes with the major axis
in any other position, and let N=_ the corresponding index of refraction
for the extraordinary ray, its value may be determined by the following
formula:N = V/m2   (sJ2 _ m2) sin2x = -/2.7367 -  0.5365 sin2x.
551. Positive and negative crystals.-Positive crystals are those
in which the index of refraction for the extraordinary ray is greater
than for the ordinary ray, and the extraordinary ray is refracted nearer
to the axis than the ordinary ray. Quartz and ice are examples of this
class.
Negative crystals are such as have the index of refraction for the
extraordinary ray less than for the ordinary ray, the extraordinary ray
being refracted farther from  the axis than the ordinary ray.  Iceland
spar, tourmaline, corundum, sapphire, and mica, are examples of negative crystals.
Some crystals have two axes of double refraction, as nitrate of potash,
sulphate of barytes, and some varieties of mica.
552. Polarization by double refraction.-When the light transmitted through a doubly refracting substance is examined with an
analyzer, it is found that both the ordinary and extraordinary rays are
completely polarized, whatever be the color of the light employed. The
tourmaline plate, or other analyzer, will, in one position, transmit the
ordinary image and wholly intercept the other, but when         432
the tourmaline has been rotated 90~, the ordinary ray is
intercepted, and the extraordinary ray is transmitted.
553. Nicol's single image prism  is an instrument
formed of Iceland spar, by which the ordinary image, proluced by double refraction, is thrown out of the field, and  K
only a single image (the extraordinary) is transmitted.
An elongated prism of Iceland spar is cut through by a plane,  
E F, at right angles with the principal section, from the obtuse
solid angle E, fig. 432, making an angle of 22~ with the obtuse 
lateral edge K. The terminal face, P, is ground away, so as to make an angle




388            PHYSICS OF IMPONDERABLE AGENTS.
of 68~ with the obtuse lateral edge, K, and the opposite face, P', is ground in
the same manner. All the new faces are carefully polished, and the two parts
are cemented together again with Canada balsam, in the same position they
previously occupied. The lateral faces of this compound prism are all painted
black, leaving only the terminal faces for the transmission of    433
light. 
When a ray of light, a b, fig. 433, falls upon this prism, it is refracted into the ordinary ray b c, and the extraordinary ray b d. The
index of refraction of Iceland spar, for the ordinary ray, being 1.654, 
and that of balsam only 1.536, the ordinary ray cannot pass through
the balsam, unless the incident ray diverges widely from the axis
of the prism, but it suffers total reflection, and is absorbed by the
blackened side of the prism. The extraordinary ray has a refrac- 
tive index in the Iceland spar generally less than in the balsam, 
varying, for Nicol's prism, between 1.5 and 1.56; therefore it passes
through the balsam into the lower part of the prism, and emerges
in the direction g h, parallel to the incident ray. 
These prisms are capable of transmitting a colorless pencil of
light, perfectly polarized, from 20~ to 27~ in breadth.
554. Polarizing instruments are made in a variety of forms, to
suit particular purposes. A simple instrument, and yet one of the
most convenient in use for exhibiting the phenomena of polarized light,
is shown in fig. 434.                                434
A mirror, M, made of plate glass,
covered with black varnish or cloth^ 
on the back, or, better, a bundle of
ten to twenty thin plates of polished                     A
glass, is mounted on a mahogany
support at the polarizing angle. A
Nicol's prism, or a tourmaline plate,
at E, serves as an analyzer.  The
objects to be examined are mounted in discs of wood or cork, and supported at
A or B, where they are most distinctly seen by the eye, looking through the
analyzer. The student who has not a tourmaline, or a Nicol's prism, can use
as an analyzer a small piece of plate glass, mounted so as to rotate on an axis
parallel to the base of the instrument.
Polarized light may be applied to the microscope, by mounting a
Nicol's prism beneath the stage as a polarizer, and another for an
analyzer, in the body of the microscope, above the object glass.
555. Colored polarization.-When a thin plate of selenite, mica,
or any other doubly refracting substance, is placed between the polarizer
and the analyzer in the polariscope, the light is separated into two
beams, which follow different paths, and as the vibrations of one ray
are more retarded than those of the other, when they are reunited
they interfere, and produce the most beautiful colors, varying with the
thickness of the plates, and the position of their axes with reference to
the axes of the polarizer and the analyzer.




OPTICS.                               389
If the film is rotated, while the polarizer and analyzer remain fixed, the color
will appear at every quadrant of revolution, and disappear in intermediate
positions. If the film and the polarizer remain fixed, and the analyzer is rotated,
the color will change to the complementary at every quadrant of revolution;
that is, the same color will be seen in positions of the analyzer differing 180~,
and the complementary color will be seen at 90~ and 270~, from the first position.
Films of selenite, varying between 0-00124 and 0'01818 of an inch in thickness,
will give all the colors between the white of Newton's first order, and white
resulting from the mixture of all the colors. If two films of selenite are placed
over each other, with their axes parallel, the color produced will be that which
belongs to the sum of their thicknesses. But when the two films are placed with
their axes at right angles, the resulting tint is that which belongs to the difference of their thicknesses.
556. Rotary  polarization  is a property which some substances
possess of changing the plane of vibration in a ray of polarizedl light,
even when it falls perpendicularly upon it.  The entire amount of
rotation  depends  upon  the  thickness of the medium.  Quartz, cut
transversely to its major axis, solution of sugar, camphor in the solid
state, and most of the essential oils, possess the power of rotating the
plane of polarization of a ray passing through them.
Different substances, and sometimes different specimens of the same substance,
rotate the plane of polarization in contrary directions. When the rotation takes
place in the direction of the motion of the hands of a watch, the medium is
said to have right-handed polarization. Thus we have right-handed quartz, and
left-handed q(;i.rtz.
In a beam of white liLght, the vibrations which produce red have their plane
of polarization rotated much more than the colors of greater refrangibility.
This property varies inversely as the squares of the lengths of the luminous
waves which produce the several colors.  The power of rotating the plane of
polarization becomes a valuable test for speedily determining the nature of
various chemical substances, or the strength of a solution of any substance
having this power. Soliel's saccharimeter, for measuring the relative amount
of cane and grape sugar in solutions or syrups, is constructed on this principle.
Such an instrument affords also a ready method of detecting the presence of
sugar in diabetic urine.
557. Arago's chromatic polariscope is a very simple instrument
for testing polarized light, and for determining its plane of polarization.
In one end of a brass tube is inserted a prism  of Iceland spar; in the
other end of the tube a circular opening is covered by two plates of
quartz cut parallel to the axis and united by their edges, one of these
plates having right-handed, and the other left-handed, rotary polarization.
When polarized light is viewed through this instrument (the Iceland
spar being turned towards the eye), the  circular opening appears
double, and in each image is seen the line dividiun  the two plates of
rotary quartz, with complementary colors on opposite sides of the line.




390            PHYSICS OF IMPONDERABLE AGENT8.
If the instrument is now rotated, two positions will be found at right
angles to each other where both parts of the opening in the same image
appear of a uniform  tint, though the two images still have complementary colors.
When both segments of the extraordinary image have a uniform  red
tint, the principal section of the prism is parallel to the plane in which
the light has been polarized, and when both segments of the extraordinary  image are uniformly  green, the plane of polarization is
perpendicular to the principal section of the prism.
A plate of selenite or mica, or a single plate of quartz, may be substituted for
the two segments of right and left-handed quartz, and two images with complementary colors will be seen as before. All the phenomena of atmospheric
polarization may be demonstrated with this form of the instrument, and the
plane of polarization may be determined, but with less accuracy than in the
first form of the instrument. As before, when the extraordinary image is red,
the plane of polarization is parallel to the principal section of the prism. When
the extraordinary image is green, the plane of polarization is perpendicular to
the principal section of the prism.
558. Colored rings in crystals.-Colored rings of great beauty,
with a black cross, are seen in thin plates of doubly refracting crystals,
when viewed in certain directions, with polarized light.
Figs. 435 and 436, show the appearance of the rings and cross in thick plates
of quartz, in positions at 90~ from each other. Other uniaxial crystals show a
similar system of rings beautifully colored. Figs. 437 and 438 show the form
435               436               437           438
of the colored rings in biaxial crystals; e. g. some micas. Every doubly
refracting crystal presents some peculiarity in the form and arrangement of the
colored rings seen in its thin sections. This subject is of great interest to the
mineralogist.
559. Polarization by heat, and by compression.-Glass irregularly heated, or heated and irregularly cooled, possesses the power of
double refraction, and when viewed by polarized light, it exhibits dark
crosses, bands, or rings, varying with the form of the glass, and difference of density in different parts. Similar phenomena may be produced
by compression, or by bending rods or plates of glass.




OPTICS.                              391
560. Magnetic rotary polarization. —If a thick plate of glass is
applied to the poles of a powerful electro-magnet, the glass is neither
attracted nor repelled; but if a ray of polarized light is transmitted
through the plate in a certain direction, the plane of polarization is
rotated as by a plate of quartz, or other rotary polarizer, showing
that light and magnetism have some intimate relation to each other.
This rotary effect may depend upon change in the tension of the molecules
of the glass by the magnetic force, and not upon any direct relation between
light and magnetism.
561. Atmospheric polarization of light.-The light of the sun
reflected by the atmosphere is more or less polarized, depending upon
the angular distance from the sun.
If the earth had no atmosphere, the sky would everywhere appear perfectly
black. The color of the sky is produced by light reflected by the atmosphere.
If we look at the sky through a Nicol's prism, we shall find, on rotating the
prism, that light from some parts of the sky is polarized to a very appreciable
extent. There are several points in the sky where no polarization is perceptible.
The point in the heavens directly opposite to the sun is called the anti-solar
point. At a distance above the anti-solar point, varying from 11~ to 18~, there
is a point of no polarization, and another neutral point at an equal distance below
the anti-solar point. Another neutral point, or point of no polarization, is
found from 12~ to 18~ above the sun, and a similar one below it; but the latter
is observed with great difficulty. When the sun is in the zenith, these two points
coincide in the sun. At all other points in the sky, the light is more or less
polarized, the degree of polarization amounting sometimes to more than onehalf as much as by reflection from glass at the angle of complete polarization.
562. The eye a polariscope.-The structure of the crystalline lens
is such, that the unaided eye is capable of analyzing a beam of light
polarized by reflection or by double refraction. A person accustomed
to use his eyes in viewing the phenomena of polarization, can thus
detect with ease facts of this nature, which are wholly inscrutable to
one not familiar with such observations; another of the numerous
proofs we have that the eye is capable of very exact training; but
nevertheless it is a proof also of an imperfection in the eye itself.
M. Haidinger has observed a remarkable phenomenon of polarized light, by
which it may be recognised by the naked eye, and its plane of polarization
ascertained. This phenomenon consists in the appearance of two brushes of a
very pale yellow color, the axis of which coincides always with the trace of
the plane of polarization; these are accompanied, on either side, by two patches
of light of a complementary or violet tint. In order to see them, the plane of
the polarization of the light must be turned quickly from one position to another;
this may be done by revolving before the eye a Nicol's prism directed towards
a white cloud.
The most probable explanation is that given by M. Jamin, in which the production of the phenomenon is ascribed to the refracting coats of the eye, they
being compared to a pile of parallel plates of glass.




392             PHYSICS OF IMPONDERABLE AGENTS.
563. The practical applications of polarized light are nume.
rous.  The water telescope consists of an ordinary marine telescope,
with a Nicol's prism inserted in the eye-piece.
The light reflected from the surface of the water is the principal obstruction
to viewing objects beneath its surface. Nicol's prism, in a certain position,
entirely cuts off the polarized portion of the reflected light, and allows objects
far below the surface to be seen in the telescope. A Nicol's prism, in the same
manner, will enable the fisherman to direct his spear with greater certainty.
Amateurs, in visiting  galleries of paintings, find Nicol's prisms
mounted as spectacles of great service.  Let the observer place hiimself in an oblique position, and look at an oil painting; when the sheen
of reflected light renders the objects in the painting invisible, he has
but to look through a Nicol's prism, set in a proper position, and the
entire details of the painting at once become visible in all their proper
colors.  An opera-glass, provided with Nicol's prisms, would be a
valuable instrument in examining a picture gallery.  Polarized light
is also of great value in microscopic investigations.
Fig. 439 shows the appearance of a grain     439              440
of starch, brilliantly illuminated on a dark 
ground, when seen in the microscope with 
polarized light. By rotating the analyzer,
the field becomes light, and the dark cross
changes its position, as shown in fig. 440.
The appearance of the starch distinguishes
it from  every other substance.  Different 
kinds of starch are also thus readily distinguished from each other. 
By means of polarized light, the chemist can detect one thirteenmillionth of a gramme of soda, and distinguish it from potassa or any
other alkali. In physiological chemistry, especially in the examination
of crystals found in various cavities and fluids of both animals and
plants, the use of polarized light is especially important.
Instead of a few isolated facts, of interest only to the curious inquirer,
the polarization of light presents itself as a great fact in nature, meeting us with wonderful revelations in almost every department of natural
science. By this marvelous property of light, the astronomer determines
that the planets shine by reflected light, and that the stars are selfluminous bodies.
Problems in Optics.
Velocity and Intensity of Light,
177. What time is required for light to come to the earth from the sun, the
distance being 95,000,000 miles?




OPTICS.                                  393
178. How long does it take the light of the north star to reach the earth, the
distance being estimated 2,961,000 times greater than the distance of the earth
from the sun?
179. Two lights give equal illumination upon Bunsen's photometer, when it
As placed between them at a distance of 3 feet from one light, and 4 feet 7
inches from the other; what is their relative illuminating power?
180. A screen is equally illuminated by two flames, when one of them is 40 inches
from it, but when a plate of glass is interposed, the same light is required to be
brought to a distance of 38 inches that the illumination may be again equal;
what proportion of the light is transmitted by the glass?
181. At one extremity of a bar, 100 inches long, is placed a standard candle
murning 120 grains per hour (the usual standard in photometric measurements
of gas), at the other end is a gas burner consuming 5 cubic feet per hour. A
Bunsen's screen, moving on this bar, is distant 17-36 inches from  the candle,
when both sides are equally illuminated; what is the illuminating power of the
gas in terms of the candle as a unit?
182. By a similar trial, the photometer is 1916 inches distant from  the
standard candle when the disc is equally illuminated, but it is found that the
candle is burning 129 grains per hour, while the gas burner consumes only 41
cubic feet of gas per hour; what is the illuminating power of 5 cubic feet of
this sample of gas in terms of the standard candle at 120 grains as a unit?
Reflection of Light.
183. At what angle must two mirrors be inclined, so that a ray of light incident parallel to one mirror may, after reflection at each mirror, be parallel to
the other?
184. How many images will be seen in a kaleidoscope when the two mirrors
of which it is composed are placed at an angle of 20?
185. A concave mirror collects solar light to a focus 6 inches from its surface;
where will it form an image of an object placed 12 feet in front of it?
186. A luminous point is placed at a distance of 3 feet in front of a concave
mirror of 1 foot radius; find the distance of the focus of reflected rays.
187. What must be the position of a luminous point before a concave mirror,
that the distance between the foci of incident and reflected rays may be equal to
the radius of the mirror?
Refraction of Light.
188. Find the thickness of a plane glass mirror silvered at the back, so that
an object one foot in front of its first surface may have the image formed by
reflection at the second surface twice as distant from the object as if the reflection took place from the first surface; the index of refraction being n1 =  1.
189. A fish is seen in a position known to be 4 feet below the surface of the
water, and the direction in which it is seen makes an angle of 45~ with the
perpendicular; at what angle must a lance be thrown to strike the fish?
190. If a pool of water appears to be 5 feet deep, what should we consider its
real depth?
191. A small pencil of solar rays, incident upon the surface of a refracting
sphere, is brought to a focus upon the opposite surface; what is the refractive
index of the material of which the sphere is made?
192. A small pencil of light falls upon a concave spherical surface of glass
(n =-  i), the radius of which is 2 feet. Supposing the radiant point distant 3 feet
from the refracting surface, where will the focus of the refracted rays be found!
36




391-            PHYSICS OF IMPONDERABLE  AGENTS.
193. When divergent rays are incident from  a certain point upon a spherical
surface of glass, the refracted rays are found to converge to a focus at exactly
the same distance on the opposite side of the surface; is the surface convex or
concave? and if the position of the point of incidence be 3 feet from the refracting surface, and n =  1'5, what is the radius of the refracting surface?
194. A double convex lens of glass (it =  1-534), whose radii are respectively
2 inches and 4J inches, is placed 15 inches before a luminous point; what is the
position of the focus of refracted rays?
195. What is the form of a double convex lens, having the least spherical
aberration, when the glass of which it is made has an index of refraction
m =  1-635?
196. What is the distance of the principal focus from a lens of flint glass
(n =  1-635) whose radii are, r =  21, and s =- 5?
197. What single lens is equivalent to a combination of a double convex lens
of focal length 2 inches with a double concave lens of focal length 4 inches?
198. Determine the form of two lenses of flint and crown glass, that may be
cemented together so as to constitute a plano-convex achromatic combination
of 7 inches focal length, using flint-glass in which i =- 1'635, and the dispersive power p =  1000, and crown-glass in  - 1-534, and p' =  625.
199. Two convex lenses, whose focal lengths are 3f and f, are separated by an
interval of 2f; how must a pencil of rays be incident upon the first lens, so as
to emerge parallel after refraction through the second lens?
Optical Instruments.
200. Considering the distance of distinct vision 8 inches, what will be the
magnifying power of a lens whose solar focus is 3 inches, when it is placed at a
distance of 5 inches from the eye?
201. Calculate the radii of the two surfaces of a meniscus of crown-glass
(n s    1l5) to be used as the field-lens of Prof. Airy's eye-piece (500), when the
eye-lens has a solar focus of half an inch, and the field-lens is 2 feet from the
object-glass.
202. Calculate the illuminating power of Herschel's great telescope, allowing
~6 of the incident light to be reflected by the speculum.
203. On the same conditions calculate the illuminating and penetrating powers
of Lord Rosse's great telescope (503).
204. Estimate the illuminating and penetrating powers of the Cambridge
refracting telescope (506). A -  15 inches, a =  0-1 inch, x =  09, a =- 2.
205. Compare the illuminating and penetrating powers of two achromatic
objectives for the microscope, one of which has an angular aperture of 1000,
and the other 150~, calling n =- 6 in both cases, and x = 0-8.
Polarization of Light.
206. Calculate the angles of most perfect polarization by reflection from the
three kinds of glass whose index of refraction is given in ~ 407.
207. What proportion of the incident light is reflected in each of the cases
considered in the last problem, supposing the increase of reflection uniform
between any two angles whose amount of reflection is given in the table,
page 299?
208. What is the index of refraction for the extraordinary ray in Iceland
spai, when it makes an angle of 540 with the principal axis of the prism?




HEAT                               395
CHAPTER II.
HEAT.
1. Nature of Heat.
564. Heat.-Its  nature.-The  sensations, which  we call heat
or cold, are produced by an agent or cause whose real nature is
unknown.  Whatever this agent may be, it influences matter of all
kinds without changing  its nature.  Scientific opinion is divided,
chiefly, between two views of the nature of heat.  These are, the
corpuscular theory, or theory of emission, and the undulatory theory.
According to the corpuscular theory, heat is attributed to a peculiar imponderable fluid, existing in all bodies in combination with their atoms. The particles of this supposed fluid are self-repellent, and thus the atoms of bodies are
prevented from coming into absolute contact with each other. This fluid is thrown
off from all hot bodies with inconceivable velocity, and upon its absorption by
other bodies the effects of heat are manifested. Thus hot bodies lose what
colder bodies gain.
By the undulatory theory, heat is attributed to the vibratory movements of
the molecules of a hot body, communicated to those of other bodies, by means
of a highly elastic fluid called ether. This ether pervades all space, and in it
the undulations of heat are propagated with inconceivable rapidity, in a manner
analogous to the slower progress of sonorous waves in air, as already explained.
This same medium, by another kind of motion, is supposed to produce light
and electricity.
565. Temperature.-Heat and cold.-All bodies receive or part
with heat, as their conditions change from time to time; the relations
which they sustain to heat at a gicen moment are distinguished by the
word temperature, which term implies nothing as to the quantity of heat
present in a body, but only its relation at a specific time to an arbitrary
standard.
Heat and cold are relative terms; cold implying not a quality antagonistic to heat, but merely the absence of heat in a greater or less degree.
There are no bodies so cold that they will not be warm to bodies colder
than themselves.  Our sensations give us but little evidence respecting
actual changes of temperature.
If we place one hand in hot and the other in cold water, and then suddenly
transfer both to water having an intermediate temperature, our sensations are




396           PHYSICS OF IMPONDERABLE AGENTS.
at once reversed; one hand will feel cold, and the other warm, although both
are exposed to the same temperature.
566. Action of heat on matter.-Assuming that cohesion and
heat are counteracting forces, it follows that the three states of matter
are effects of the relative intensities of these two agencies; and heat
being a repellent force, its increase must be accompanied with an
enlargement of volume in either of the three states of matter, while a
loss of volume must accompany an increase of molecular force, or a
loss of heat.
Many familiar facts of daily experience confirm this statement. All
bodies (with few exceptions) expand with an increase, and contract
with a loss of heat.  The expansion may be measured by an increase
of length; in which case it is called linear expansion, or by an increase
of volume, and then it is called cubic expansion.  The first measure is
commonly used for solids, the second for liquids and gases, but the first
is easily converted into the second by cubing. Substances vary very
much in their degree of expansion for the same increase of temperature:
solids expand less than fluids, and liquids less than gases.
But the laws of expansion will be better studied after some anquaintance is obtained with the means of measuring differences of temperature.. 2. Measurement of Temperature.
I. THERMOMETERS.
567. Thermometers.-The measurement of temperature is accomplished by observing the amount of expansion or contraction in any
substance arbitrarily assumed as a standard for the purpose. Such an
instrument, whether the substance selected is a solid, a liquid, or a
gas, is called a thermometer, or measure of temperature.  For special
purposes, thermometers are constructed with either solids, liquids, or
gases. In much the greater number of cases, however, mercury is the
only substance employed, not only because of its great range of temperature between freezing and boiling, but also because its changes of
volume for equal changes of temperature are more nearly proportional
to the temperature than those of any other liquid.
568. Construction of mercurial thermometers.-Thermometer
tubes.-A capillary glass tube of which a thermometer is to be made,
should be one whose bore, throughout, is of the same calibre, so that
equal lengths within it will contain equal quantities of mercury.  The
equality of the bore is ascertained by causing a short cylinder of mercury (say one inch) to pass from end to end of the tube, and if it
measures an equal length throughout, then the calibre is equal; otherwise the tube is rejected. Only about one in six of thermometer tubes




HEAT.                           397
are found to possess a canal of equal bore. A proper tube having been
selected, a bulb (cylindrical or spherical) is blown upon it by means
of a gum elastic bag fitted to the open end. The breath would fill the
tube with moisture. The form of the bulb is conventional. A cylindrical bulb will be more readily affected by the temperature of the
surrounding medium than a spherical one, because it exposes a larger
surface.
Filling the tube with mercury is facilitated by tying a paper
funnel on the open end of the tube, or a glass reservoir, C, fig. 441,
is employed to hold a portion of pure mercury.       441
As so dense a fluid could not enter a capillary           C
opening, the air in the bulb, D, is expanded by
the flame of a spirit lamp, holding the tube 
as seen in the figure. As the air expands, a
portion of it escapes, passing the mercury in
C. Allowing the bulb D to cool, the pressure
of the air soon forces a portion of the mercury
from  C through the capillary tube into the
lower reservoir, exhibiting in its progress the
successive stages of the capillary surfaces
explained in ~ 235. The lamp is again ap- 
plied to boil the mercury in D, and after
several minutes, all the air and moisture
are expelled from  the tube by the mercurial
vapor. The bulb is then cautiously cooled
once more, when it will be found, as well as              D 
the stem, completely filled with mercury. The
extremity of the tube, C, is then drawn out to
a narrow neck, and broken off preparatory to
sealing. A  greater or less portion of the
mercury remaining in the stem, must now be
removed, according to the range designed to be indicated by the thermometer. This is accomplished by gently heating the bulb. When
about two-thirds of the mercury contained in the stem has been driven
out, and while the stem is yet full, the flame of a blow-pipe is directed
upon the end of the stem, the glass melts, and the tube becomes hermetically sealed.
569. Standard points in the thermometer.-Graduation.-As
variations in the height of the mercurial column in the thermometer
depend upon the changes of temperature to which it is subjected, it is
necessary to graduate the instrument, or construct a scale, whereby
these variations may be indicated, and the temperatures indicated by
36*




398            PHYSICS OF IMPONDERABLE AGENTS.
one thermometer compared with those shown by another.  If there
existed a natural zero, or absolute limit to temperature, the thermometric scale might be numbered upwards from  it.  But there is no
natural zero, and therefore the thermometric scale must be arbitrary,
although based upon certain well-determined physical phenomena.
Experiment has determined that the melting point of ice, and the boiling point of pure water, under certain given conditions, are always the
same, and these points (called, respectively, thefreezing and boiling
points) have been adopted in all countries as the two temperatures, with
reference to which thermometric scales are constructed.
Freezing point.-To fix the freezing point in a thermometer, a tin vessel,
like fig. 442, is filled with pounded ice or snow; a hole in the bottom of the
vessel allows the water from the melted ice to escape. Into this vessel the bulb
of the thermometer is thrust, with part of the stem.
When the mercurial column becomes stationary, that is, when the mercury
contained in the bulb has attained the temperature of the melting ice, its level
is marked with a diamond point, upon the glass, or with a pencil upon a paper
previously attached to the tube. This indicates the melting point of ice, and
consequently the freezing of water. This point may be indicated by the expression %,0 for the centigrade scale, or sn2 for the Fahrenheit scale.
Boiling point.-This point is accurately fixed by immersing the whole
thermometer in vapor of boiling water. For this purpose Regnault has contrived
the apparatus, a section of which is seen in fig. 443. The course of the steam
442                                443
rising through A, and descending in the outer vessel, is shown by the arrows,
and the drawing is so easily understood as to need no description. An equally
efficacious apparatus may be made by using a chemical flask, in the elongated




HEAT.                                399
neck of which the thermometer is suspended by a cork, through which a small
glass tube allows also the escape of the steam. The stem of the thermometer (t)
is adjusted so that the point a, to which the mercury rises when heated to the
temperature of boiling water, is just visible above the cork. This point is
definitely marked when the level of the mercury becomes stationary, thus indicating the boiling of water. Let this point be indicated by the expression nT,
which corresponds to the temperature 7, at which the observation was made.
This temperature T is equal to 100~ C. or 212~ F., when the barometric pressure is 30 inches (or 760 millimetres).  But as the temperature of ebullition
varies with the barometric pressure, it is plain that the value of Twill vary with
the height, H, of the barometer.  It is essential, therefore, to accuracy in
graduating the thermometer, that the boiling point should be fixed when the
barometer is at 30 inches.
After dividing the space between the freezing and boiling points into as many
equal parts as there are designed to be degrees in the scale, the divisions are
continued both above and below the fixed points. This mode of graduation
involves, however, serious errors, some notice of which is taken in ~ 576.
570. Different thermometric  scales.-Having fixed  these two
standard points in a thermometer, the space between them  is next to
be subdivided into a certain number of equal parts, called degrees.
Unfortunately, in different countries, this interval has been differently
subdivided.  In scientific researches, tJie Centigrade scale is almost
exclusively in use, while in common life, in the United States, England;
and Holland, Fahrenheit's scale alone is used.
Fahrenheit's scale.-In the Fahrenheit scale, the interval between
the boiling and freezing points is divided into 180 equal parts, which
are called degrees.  The zero, or 0~, of this scale, is 32 of these degrees
below the freezing point.
Fahrenheit adopted, as the zero of his thermometer, the temperature which
had been observed at Dantzic, Holland, in 1709, and which he found he could
always reproduce, by using a mixture of ice and salt. At that temperature
(which he believed to be an absolute zero of cold) he computed that his instrument contained 11,124 equal parts of mercury, which, when plunged into melting
snow, were increased to ] 1,156 parts.  Hence the space included between these
two points (viz., 11,156- 11,124 = 32) was divided into 32 equal parts, and
32~ indicates, therefore, the freezing point of water. When his thermometer
was plunged into boiling water, Fahrenheit estimated that the mercury was
expanded to 11,336 parts, or 212 parts above his zero, and therefore 2120
(11,336 - 11,124 =  212) was marked as the boiling point of that fluid. In
practice, Fahrenheit determined the boiling point of water, and the melting point
of ice, and then graduated the tube by equal divisions to his zero. To Fahrenheit belongs the merit of having introduced the use of mercury in thermometers,
which had previously been made only with alcohol, water, or air, and his
graduation of the thermometric scale, although unscientific, is not irrational as it
is often represented.
Centigrade scale.-In  the year 1742, the  Swedish philosopher
Celsius, professor at Upsal, introduced the Centigrade scale (from




400           PHYSICS OF IMPONDERABLE AGENTS,
centunt, one hundred, and gradus, degree).  It is adopted universally
in France, and in the north and middle of Europe.  The interval between the freezing and boiling points in this scale, is divided into 100
equal parts or degrees; the degrees being counted upwards and downwards, from the freezing point of water, which is zero.  The temperatures below zero in this, as in all thermometers, are indicated by the
negative algebraic sign -; those above, by the positive algebraic
sign +; thus - 20~ signifies 20 degrees below zero, but + 20~ signifies
20 degrees above zero.
Reaumur's scale.-Reaumur, a French philosopher, introduced his scale
in 1731. Ite proposed to use spirits of wine, of such a strength, that between
the two standard points, 1000 parts should become 1080. He divided the
interval between these points into 80 equal parts; the zero being placed at the
freezing point of water. Reaumur's thermometer was the only one used in
France before the Great Revolution (A. D. 1789); it is still best known in Spain,
and in some of the older European states.
All thermometric scales are purely arbitrary.  We know  only a
small part probably of the vast possible range of temperature, and we
select the two great natural phenomena adopted for the fixed points
of our scales because they can be readily verified, and because the
range between them  includes the temperatures which we have most
occasion to measure in the common experience of life.
571. Comparison and conversion of thermometric scales.The scale employed in a thermometer is indicated by the name, or by
one of the initial letters, F., C., R.  The degrees of one thermometric
scale are readily converted into those of another. Since 180~ F. = 100~
C. = 80~ R., therefore 1~ F. =    C. =-  ~ R.
As the value of a degree in Fahrenheit's thermometer is greater by 32 than
the number of divisions from the freezing point, 32 must always be subtracted
before the + degrees of Fahrenheit are converted into those of the other scales,
and added upon the conversion of other degrees into Fahrenheit.
Easy rules for mental calculation are:-lst, to convert Centigrade to
Fahrenheit degrees, double the number of Centigrade degrees, subtract onetenth, and add thirty-two; or, multiply the Centigrade degrees by 1 8 and
add 32~. And concisely, to reduce Fahrenheit degrees to Centigrade,
subtract 32~ fr'om the Fahrenheit degrees, and divide the remainder by 1-8.
572. House thermometers.-For common use, the thermometer is
mounted on a plate of brass, ivory, porcelain, or wood, on which the
degrees are marked, as in fig. 444.  The words summer heat, blood heat,
andfever heat, are often placed opposite the points 68~, 98~, 108~ F.
House thermometers are usually graduated by comparison with a standard,
and not by determining the two fixed points. For this purpose the standard
is immersed in a water bath with the tube to be graduated, and a number of




HEAT.                                 401
points are thus fixed, at different temperatures, as the bath slowly cools from boiling. The distances between the marked points are divided into equal parts.
This mode of graduation is capable of giving results accurate 
enough for common use, between boiling and freezing, say within a
degree on Fahrenheit's scale. But above and below these points            _s
little reliance can be placed on it, and at low and high temperatures
common thermometers will be observed to vary often several 
degrees, even when made by the best makers.
Some thermometers have their graduated wooden support divided
near the lower end into two parts, connected together by a hinge, 
so that the lower part may be turned back, and the bulb thrust
into any liquid whose temperature it is desired to ascertain.
Other thermometers have their stem very small, and completely
surrounded by a larger tube; the scale being marked upon a  7
porcelain strip, or a roll of paper, inserted  between  the two
tubes.
In very accurate thermometers, the degrees are marked on the
glass tube with fluohydric acid in a manner described in ~ 577.
Tests of a good thermometer. —In order to ascertain
whether a thermometer is correct or not, it is first plunged 
into melting ice, and then into boiling water; the level of
the mercury should indicate upon the scale exactly 32~, and 
212~ F.  When inverted, the mercury should fall with a    I
sudden click, and fill the tube, thus showing the perfect
exclusion of air.
To determine whether the value of the degrees is uniform, a
slight jerk is given to the thermometer, by which a little cylinder  c    l
of mercury is detached from  the column.  On moving the little
column through the tube, it should occupy equal spaces in all
parts, if the bore is perfectly accurate, and the scale is properly
graduated.
Sensibility  of thermometers. —The sensibility of a
thermnoneter is of two kinds; it may indicate very small
differcnces, or it may be very sensitive to sudden changes    1 
of temperature.
If the capacity of the reservoir is large, compared with the bore of the tube,
a slight change of temperature will affect, considerably, the height of the mercurial column. If the capacity of the reservoir is small, and the glass bulb
thin, the mercury contained in it will be more rapidly affected than if a larger
amount were to be acted upon. A cylindrical reservoir is, therefore, better than
a spherical one, because it exposes a larger surface.
The two kinds of sensibility indicated, are obtained in a thermometer which
has a small cylindrical reservoir and a very capillary tube.
573. Displacement of the zero point.-One source of error in the
mercurial thermometer is found in the displacement of the zero point
by changes subsequent to graduation.  If a thermometer which has




402            PHYSICS OF IMPONDERABLE AGENTS.
been made some time is thrust into melting ice, the column of mercury
will not sink to the original freezing point, but will remain at a distance
above it, sometimes as much as two or three degrees, and even more.
Mr. Legrand has found that the cause of this change is, that the capacity of
the reservoir is enlarged at a high temperature (as during the construction of
the thermometer), and that it does not return to its original dimensions until
after a long time, sometimes not until after two or three years.
The effect is also supposed to arise from the pressure of the atmosphere upon
the bulb, which, when not truly spherical, seems to yield slightly and in a gradual
manner.
This defect may be avoided by giving the bulb a certain thickness. Mr.
Crichton's thermometers, of which the freezing point has not altered in forty
years, were all made of unusually thick glass.
Before making important observations, therefore, thermometers should be
examined as to the position of their freezing point.
574. Limits of the mercurial thermometer.-Mercury is by far
the most available thermometric fluid. It may easily be obtained pure;
it does not adhere to the sides of the tube, and above all, it has a greater
range of temperature, between its freezing and boiling points, than any
other liquid; fieezing at -39~'2, and  boiling at 662~ F.  Between
these two points, its expansion for equal increments of heat is very
regular, excepting near its freezing point. Owing to this last irregularity, mercurial thermometers cannot be accurately used for temperatures lower than -31~, or-  35~ C.  Above the boiling point of
mercury, heat is measured by instruments called pyrometers. For very
low temperatures, spirit of wine thermometers are usually employed.
575. Spirit thermometers; other liquid thermometers.-Alcohol
has never been frozen, and is, therefore, generally employed for the
estimation of low temperatures.
Thermometer tubes are filled with alcohol (which is generally colored red)
by heating the bulb, with the open end of the tube thrust into alcohol, and completing the process in the manner already indicated (568). The tube is graduated
by comparison with an accurate mercurial thermometer, exposing both to the
same temperature, and marking, successively, upon the alcoholic thermometer,
the temperatures indicated by the mercurial thermometer as they are gradually
heated. The alcoholic thermometer should not be divided into equal parts
between the freezing point of water and its boiling point, because it expands
unequally for equal increments of heat. Alcoholic thermometers often differ
much from each other, because there is great difficulty in obtaining alcohol perfectly pure, or of exactly the same degree of concentration.
Capt. Parry, in his arctic voyages (whose experience was confirmed by )r.
Kane, Arct. Exp. II., 405), found a difference of 18~ F. between alcoholic
thermometers constructed by the most celebrated makers; and a difference of
14~ F. has been observed even at a temperature of only 15~ or 20~ F. In coniequence of this, other liquids have been proposed for thermometers, intended to
indicate low temperatures. From the experiments of M. Pierre, of all liquids,




HEAT.                             403
ordinary sulphuric ether, chlorid of ethyle, and bromid of methyle, were found to
be best adapted for such instruments.
It is plain from these statements that a more accurate mode of measuring lot
temperatures is one of the desiderata of science.
576. Defects inherent in  mercurial thermometers.-Besides
those sources of error in this instrument already noticed, there are
others inherent in the nature of the materials employed.
As glass and mercury expand unequally by heat, it is plain that we
read in the mercurial column not the absolute expansion of the
mercury, but the difference between its expansion and that of the glass.
If they expanded equally, no movement of the mercurial column would
be perceived, and if the glass expanded more than the mercury, the
latter would appear to fall when the temperature rose.  But as in fact
the mercury expands about seven times as much as glass, the apparent
expansion of the metal in glass is about one-seventh less than its
absolute expansion.
Again, it is proved that the expansion of mercury for equal increments of heat is not absolutely equal, but increases slightly with the
temperature.  At temperatures between freezing and boiling, this
increase is very slight, and may be disregarded, since the division of this
distance into parts of equal length gives the degrees a mean length,
slightly in excess for the degrees near freezing, and as much too short
for those near the boiling point, but exact for the intermediate degrees.
But above the boiling point the error is more serious, since while the
degrees have the same length, the space occupied by a unit of mercury is constantly increasing, consequently the degrees become too
short, and the thermometer reads too high a temperature.  For the
same reason, below the freezing point, the thermometer constantly
indicates a temperature higher than the true temperature.
The error here pointed out could be easily allowed for in the graduation; the coefficient of expansion of mercury for various temperatures
being known.  But this correction is rendered almost impossible, from
the fact that the rate of expansion of the glass is found not only to
increase about as rapidly as that of the mercury (and sometimes even
more so), but to render the case yet more difficult, it is found that glass of
different kinds varies in its rate of expansion, and the same glass under
different conditions may also vary.
Regnault, to whom we are indebted for these data, has illustrated
the facts by a series of observations, the results of which are shown
in the following table.
He has shown that the air thermometer may be relied on as
giving results almost invariable and exact.  His frnm of this instrument is described at length in his memoir before quoted (p. 220).




404              PHYSICS OF IMPONDERABLE AGENTS.
COMPARISON OF DIFFERENT THERMIOM1ETERS (CENTIGRADE DEGREES).
Air Thermometer.  Thermometer    Thermometer,   Thermometer,   Coefficient of Exo               o               o               o
TruelTempera-   without Glass.    Flint-glass.   Croun-glass. Dansio of Mercury
0               0               O               O        X   0
0               0               0                0           0'000 1790
50-00           49-65                            50-20  0000 1815
100-00          100-00          100-00           100-00        0000 1830
120-00          120-33          120-12          119-95         0'000 1850
140-00          140-78          140-29          139-85    1  0000 1860
160-00          161-33          160-52          159-74          0000 1870
180-00          182-00          180-80          179-63         0000 1880
200-00          202-78          201-25          199-70         0-000 1890
220-00          223-67          221-82          219-80         0-000 1901
240-00          244-67          242-55          239-90         0'000 1911
246-30                                          246-30
260-00          265-78          263-44          260-20         0-000 1921
280-00          287-00          284-48          280-52         0000 1931
300-00          308-34          305-72          301-08         0-000 1941
320-00          329-79          327-25          321-80         0000 1951
340-00          351-34          349-30          34300          0000 1962
The temperatures indicated by an  air thermometer, recorded in the first
column, were taken as a standard, and are very near the truth.  The second
column gives the temperatures which would be shown by a mercurial column
graduated in the ordinary way, assuming the glass to be without expansion,
thus showing the errors attributable only to the varying rate of expansion in that
metal. In the third and fourth columns are given the comparative temperatures shown by thermometers of flint and crown glass respectively, showing the
discrepancies due to differences of material. The rapidity with which the rate
of expansion in the mercury increases with the temperature is shown by column
fifth.
At and between the fixed points of 0~ and 1000 a perfect accord was observed,
the small differences there existing being distributed among all the degrees.
Above 100~, how\ever, it will be seen the differences between the true temperatures and the several thermometers are more and more sensible; and most
conspicuous in the thermometer without glass. The effect of the expansion of
the flint-glass is seen to be approximately to correct the expansion of the
mercury.  The crown-glass thermometer, owing to the peculiar rate of expansion in crown-glass, is seen to march very closely with the true temperature
up to 246~030, where the coincidence is perfect. Above that point the differences
increase, until at 340~, the error is three degrees. A thermometer of crown-glass
is plainly to be preferred for accuracy over one of flint-glass.
The facts embodied in this table are made conspicuous by a geometrical
construction,? fig. 445, in which the figures on the horizontal line (or axis of
ordinates) stand for the temperatures of an air thermometer assumed as invariable, and those on the vertical line (or axis of abscissas), for the differences found
between the air thermometer and various mercurial thermometers. The variation
of the theoretical thermometer, without glass, from the true temperature, is seen
* Cook's Chemical Physics.




TErAT.                              405
in the curve 0 n a m; while the curves 0 n a c, 0n a v, 0   a s, 0 n a o, show
respectively the variation of thermometers made with flint-glass, green glass,
445
Swedish glass, and "verre ordinaire" of Paris. The last curve (corresponding
to column fourth in the table) is a beautiful illustration of the anomalies indicated by observation.                                          i      446
577. Standard thermometer.-The unavoidable defects in
the mercurial thermometer, just pointed out, are in  common
instruments  greatly  exaggerated  by  errors  of construction.
Standard thermometers for scientific purposes are constructed
with a scale engraved in the glass, as in fig. 446.  The divisions
of this scale are marked by a dividing engine on the surface of
a covering of varnish, with which the tube is coated preparatory
to etching.  As no calibre is absolutely uniform  in any glass
tube for a considerable length, the value of the calibre for every
part of the tube is exactly measured by a cylinder of mercury
drawn in at one end of the open tube, and taken so short that
the error in the length chosen may be disregarded. This cylinder
of mercury is then gradually moved from end to end of the tube
by the force of air from  a gum  elastic bottle, dividing the tube
into  lengths equal to the successive lengths of the mercury
column.  The position of these successive points is marked, and
each of these divisions is then subdivided by the engine into an
equal number of degrees; varying in length, of course, in proportion to the lengths of the several cardinal divisions. These graduations are then etched into the glass by exposing it to the
vapor of fluohydric acid.  This graduated tube is then soldered
to a cylindrical reservoir prepared of a size proportioned to the
diameter of the tube, and the destined range of the thermometer.
The mode of determining the required size of this reservoir is as follows:We wish to know what size to give the reservoir for a given graduated tube
that 2N divisions of the thermometer may correspond to 100~ C. Weigh thi tube
37




406            PHYSICS OF IMPONDERABLE AGENTS.
empty, and also when containing a column of mercury of an observed length. We
thus learn the weight of mercury,., occupying n degrees of the tube. From this
w
we obtain N-, the weight of mercury which will fill N divisions of the tube,
and by (99),  e know the corresponding  olume               But this
and by (99), we know the corresponding volume =        (S N    ~.  But this,, (s. Gr.)
volume represents the expansion which the mercury in the reservoir of the proposed thermometer must undergo when heated from 0~ to 100~ C. Now the
apparent expansion of mercury under these conditions is known to be A  of its
volume at 0~. Representing, then, by V the unknown volume of the reservoir,
V          to                       tw
we shall have:   5 ==N       G    and V== 65 N    -~          If the reser65     n (Sp. G-.)               n (Sp. Gr.)
voir is spherical, V-=  JnD, from  which we can calculate the required
diameter. If it is cylindrical, V =  st D2h, from which the approximate length
of h is calculated when the diameter is given.
The thermometer thus graduated is filled, and the fixed points marked as already
described (568). Its scale, of course, is arbitrary, and may be reduced by calculation to the Centigrade or any other scale. Observation determines the number
of divisions between freezing and boiling, which we call N, and also the point on
the arbitrary scale, corresponding to the freezing point (0~ C). Call the number of
divisions below this point (1~, the degrees centigrade C~, and those of the arbitrary
100
scale A~. We then have, N= 100, and C = -  (A' - dO). Suppose there are
379 divisions on the arbitrary scale between the fixed points, and the freezing
point is the 147th division from the bottom, and it is required to know to what
temperature the 303d division corresponds in Centigrade degrees, we shall have
C =  Al  (303 - 147) =  41-16. Every such thermometer has, of course, its
own equation; a table is readily calculated for its convenient use.
Every good standard has both the boiling and freezing points included in its
range. The cavity a, fig. 446, is designed to allow for any sudden expansion
of the mercury above the limit of the scale, to avoid the fracture of the instrument. Similar expansions are often introduced at particular points on the stem,
to avoid undue length in the stern when a long range is required. The whole
scale in this case is distributed between several thermometers, and the swellings
so placed as to cover in each case the range of the preceding instrument. It is
thus possible to divide each Centigrade degree into twenty or more parts.
In accurate observation, the whole instrument should be immersed in the
medium whose temperature we seek, but when this is not possible, a correction
may be calculated by a formula which our space requires us to omit. (See
Cooke's Chemical Physics, p. 444.)
II. SELF-REGISTERING THERMOMETERS.
578. Maximum  and minimum  thermometers.-It is often desir
able to ascertain, in the absence of an observer, the highest and lowest
temperature of the night, or of any other interval of time. This may
be done by the employment of what are called maximum and minimum,
or self-registering thermometers. One of the most simple instruments
of this kind was invented by Rutherford, and is represented in fig.
447.




HEAT.                                407
(a.) Rutherford's maximum  and minimum  thermometer consists
of two thermometers attached to a plate of glass, or to wood; their tubes are
447
A
Di i
mercury; the minimum thermometer, B, contains alcohol.  In the tube of the
former is a small piece of steel (seen at A); when the mercury expands, it
pushes the steel before it, but when the fluid recedes toward the bulb, the wire
GJB   20    10      0     10    20    50    40    50i P
\    i B40    50   20       10     0     10    20    301
does not follow  it. The steel is thus left at the extreme point to which the
bent at right angles moved, and indicatesnear the bulbs. The maximum thermometer, A, contains
mercury; to which it has been exposed. The alcoholicnimum thermometer, B contains a smalln the tube of the
former is a small piece of steel (seen at B), sunk belowwhen the rface of the liquid. The positi
of the enamel is not affected by expansion, because the alcohol readily passes it;
but by contraction it is drawn back with the column of alcohol, by the cohesive
pushesattraction of the steel before it, but hen the luid recedes toward the column. Thus theire
does not follow it. The steel is thus left at the extreme point to which the olumn has retreated, and repreents, theruryefore, the movedit, and indicates the highest, or maximum temperature which has occurred.
b.) Nere, to which it has been exposed. The alcoholic thermometer contain smallght
piece of en given to Rutherford's maximum the rmometer will of   The position
of the enamel is not aectd by ex tpansion, become immersed in the alcohol readily passes it;
but by contraction it is drawn back with the column of alcohol, by the cohesive
attraction of thewill particles of liquid at the steel, and thus the instrument will faThus the
enamel is left at the lowest point to which the column has retreated, and represents, therefore, the minimum temperature which has occurred.
(b.) Negretti and Zambra's maximum  thermometer.~A slight
agitation given to Rutherford's maximum thermometer will often cause
the steel index to become immersed in the mercury, which, upon expansion, will pass by the steel, and thus the instrument will fail to
fulAll the purpose for which it was designed.  This source of error is
avoided in the use of Negretti and Zambra's instrument, fig. 448.
448
A small rod of glass, a b, is introduced into the thermometer tube, which is




408            PHYSICS OF IMPONDERABLE AGENTS.
then bent just above the point where the rod is placed; the rod nearly fills the
bore of the tube. When in use, the instrument is suspended horizontally. The
mercury, by expanding, will force its way past the obstruction, to the point c for
example; when the temperature falls, and the mercury contracts, the cohesion
of the particles of mercury to each other will prevent the column from passing
the rod. The extremity of the column, c, will therefore indicate the highest
temperature to which the instrument has been exposed. It has been observed
that in this form of instrument the mercury does not move steadily, but by jerks.
(c.) Walferdin's maximum  thermometer.-The upper part of
the tube of this instrument, fig. 449, terminating with a small 449
orifice, is surrounded  by a reservoir which contains mercury.
When the instrument is to be used, it is first heated, whereby the
mercury rises in the tube and flows over into the reservoir; 450
it is then inverted.  The elongated point of the tube thus
dips into the mercury of the reservoir.  It is now exposed, 
while inverted, to a lower temperature than the one to be
determined. During this cooling, the tube will remain full
because its point dips into the reservoir of mercury. The
instrument is now placed in its proper position, and it is
evident that as the temperature rises, a portion of mercury
will pass out of the full tube into the reservoir; and this
portion will be greater as the temperature is higher.
To determine afterwards the highest temperature to
which it has been exposed, it is compared with a standard thermometer. Both being placed in a water bath,
gradually heated, the temperature indicated by the standard
thermometer is observed when the mercurial column has
risen to the top of the tube of the maximum thermometer.
579. Metastatic thermometer.-Walferdin  has applied the same principle to the construction of a thermometer designed to indicate very small differences of
temperature. In this instrument, fig. 450, the reservoir,
and calibre of the tube are very small, so that the instrument is extremely sensitive to small changes of temperature.
The bulb, B, corresponds to the reservoir in fig. 449. Just
below this bulb, the capillary tube suddenly contracts at C.  The stem  is
graduated into parts of equal capacity, each of which represents a very small
fraction of a degree. In using this thermometer, it is first heated to a temperature somewhat higher than the one it is desired to estimate. The mercury
rises in the tube and partially fills the bulb. A slight jar given to the instrument while cooling, causes the mercurial column to break at the point of contraction, and while a portion of mercury remains in the bulb, the mercurial
column sinks down to a point somewhere above the reservoir. The thermometer




HEAT.                               409
must now be exposed to a known temperature, very near to that we wish to
estimate: the position of the level of the mercury in the tube is then noted. The
thermometer is next subjected to the medium, whose temperature is to be estimated. Suppose there is a difference in the level of the mercurial column in the
two cases, of 18 divisions of the arbitrary scale, and if 300 of these divisions are
equal to one degree, then the difference in temperature must be Ye8. of a degree.
Walferdin has employed thermometers of this kind which indicated one onehundredth (T-Oi) and even one one-thousandth (T-eO-) of a degree, Centigrade.
(ls and  -g of a degree F.). By causing more or less mercury to flow into the
upper bulb, differences in temperature may be estimated for different points on
the scale. A single thermometer of this description may take the place of a
series of thermometers with a fractional scale.
III. METALLIC THERMOMETERS AND PYROMETERS.
580. Breguet's metallic thermometer.-This instrument, remarkable for the extreme sensitiveness of its indications, depends upon the
unequal expansion of different metals; it is represented in fig. 451.
Strips of platinum, gold, and silver, after being soldered together throughout their whole length, are rolled into a thin ribbon,        451
which is then formed into a spiral, or a helix. The
upper extremity of this helix is fixed to a support, 
and to the lower end, at right angles to it, is attached
a needle, moving over a graduated circle, resembling 
the dial of a watch. The silver, which is the most ex- 
pansible of the three metals, forms the inner face of the
helix; the platinum, which is the least expansible,
forms the outer face, and the gold, which has an intermediate expansibility, is included between them, and moderates their effects.
When the temperature rises, the silver,
expanding more than the other metals,
unrolls the helix; the contrary effect
takes place when the temperature is 
lowered. This thermometer is graduated by comparison with a standard
mercurial thermometer. The instrument is particularly useful when very
rapid variationsof temperature are to be determined. Another form is sometimes given to it. The compound ribbon being bent into the form of a letter
U, one of the extremities is fixed, and the other is left free to move. By means
of a lever and toothed wheels, the movements which changes of temperature
cause in the free end are communicated to a pointer, moving over a dial.
581. Saxton's deep  sea metallic  thermometer.-Mr. Joseph
Saxton, of the United States Coast Survey, has adapted the principle
of Breguet's metallic thermometer, to the construction of an instrument
by which numerous very accurate observations have been made upon
the temperature of the sea in deep soundings. Silver and platinum
form the compound spiral, and its torsion is registered by an index,
moved by multiplying wheels, and carrying forward a tell-tale, or stopU7 *




410            PHYSICS OF IMPONDERABLE AGENTS.
hand, to the lowest temperature attained. This instrument has been
some years in use for deep sea soundings, with the best results. A
small correction in the readings is made (not exceeding one degree
for 600 fathoms) proportionate to the depth of the sounding.
The term pyrometer is sometimes applied to instruments intended to
measure changes of dimensions in bodies at low temperatures by the
expansion of solid rods; such is:582. Saxton's reflecting pyrometer.-In the measurement of the
base lines of the larger triangles, in the survey of the coast of the U. S.,
the greatest accuracy is required. These lines are sometimes forty or fifty
miles in length. An instrument constructed by Saxton, under the direction of Prof. Bache, accomplishes this object perfectly.
The measuring rods are compound bars of iron and brass, so proportioned in
their cross section as to equalize their differences of specific heat and conductibility, while their unequal expansions compensate for each other, and preserve
an invariable length. To verify these bars, the ends are brought into contact
with two blunt knife edges; one immovable, the other forming the shorter end
of a compound lever; having at the other end a rotating mirror. Any variation
of length in the bar, by changing the angular position of the mirror, gives evidence of the change to an observer, whose eye is placed at a telescope directed
towards the mirror, in which the one twenty-five thousandth of an inch on a
scale is magnified into a unit of graduation, about one-fourth of an inch long,
from which the one hundred-thousandth of an inch, or about one four-millionth
of a metre is easily read. If desirable, this degree of minuteness might be
greatly increased. This simple and beautiful contrivance has superseded all
methods previously known for verifying rods of any length. It is sensibly
affected in bars six metres long, by changes of temperature otherwise quite
inappreciable, and it then becomes the most sensitive of thermometers. This
method is good only for end measurement.
583. Wedgewood's pyrometer.-The range of the mercurial thermometer is limited by the boiling point of mercury; higher temperatures are measured by the effects of heat upon solids with instruments
called pyrometers.
The celebrated English potter, Wedgewood, invented the first pyrometer used,
founded upon the contraction which clay undergoes when exposed to high
temperatures. Ice assumed this contraction to be as much greater as the
temperature was higher. The results obtained with this instrument are, however, inaccurate, as it is now known that the contraction which clay undergoes
depends rather on the duration than on the intensity of the heat, and is much
modified by the particular sort of clay employed.
584. Daniell's pyrometer is an instrument capable of exact measurements of high temperatures by the expansion of a bar of platinum
encased in a sheath of black lead. The bar and its case are adjusted
both before and after the experiment to a measure which indicates on
a graduated arc the degree of expansion. The degrees of temperature
are then calculated from the known rate of expansion of platinum.




HEAT.                              411
585. Draper's pyrometer.-This instrument registers its results by
the expansion of a little strip of platinum, heated (in free air) by a
measured current of voltaic electricity.
The platinum strip is connected with the short end of a lever, whose longer
limb marks upon a graduated arc the degree of expansion. With this delicate
instrument, Prof. Draper conducted a series of experiments upon the temperatures at which bodies become visibly red, in the dark and in diffused light, the
temperatures being determined from the coefficient of expansion in the several
metals. (Am. Jour. Sci. [2] IV. 388.)
586. Estimation of very high temperatures.-According to Bunsen's calculations (Gasometry, p. 236-243), the temperature of a hydrogen
flame burning in free air is 3259~ C. (= 5898~ F.), and of olefiant gas
5413~ C. (= 9775~ F.).  Since it is probable that at high temperatures
the radiating power of a body for heat is proportional to its radiating
power for light, we are in possession of the means of comparing the
intensity of glow of a coil of platinum heated in a furnace, or in a
stream of lava, with the glow from  a like coil heated in a flame of
known temperature, and thus approximately of estimating the temperature of a furnace or of a volcano.
IV. THERMOSCOPES.
587. Thermoscopes.-This name (from  Oipp7r, temperature, and
axomrw, to see) is applied to a class of instruments designed to indicate
small differences of temperature, and not to measure them in degrees.
Air thermometers.-As air contracts and expands uniformly and
quickly, it is often used where slight and sudden       452        453
variations of temperature are to be observed.  The                ~
contractions and expansions which it undergoes, 
are rendered visible by the movements that it
causes in  liquids.  Such instruments are often
called air thermometers, but are not to be confounded with the form of air thermometer described A 
by Regnault, which is the most accurate measure
of temperature yet made known.  The results in
the first column  in  the table on p. 404 were
obtained by the air thermometer here alluded to,
some notice of which will be found in the section 
on expansion.                                         
The simplest air thermometer is that represented by' 
fig. 452, and is often called the thermometer of Sanctorius, an Italian philosopher of the 17th century. It is a bulbed tube, filled
with air, having for an index a drop of colored liquid in the stem at A. The
movements of the index show the variations of temperature. Another form of
the same instrument is represented by fig 453. The extremity of the tube rest.




412            PHYSICS OF IMPONDERABLE AGENTS.
in the colored liquid contained in the open vessel. If the bulb is heated, the
liquid falls in the tube, and rises if the bulb is cooled.
Amontons' thermometer, fig. 454, is essentially the same as the last; the
bulb, C, is partially filled with coloredJiquid. Expansion of the air contained
in the upper part of the bulb, C, causes the liquid to      45
rise in the tube A B.
These instruments are necessarily imperfect, owing to' 
the varying pressure of the atmosphere, and they serve
only as means for the illustration of principles in the
class-room.                               454
(a.) Leslie's differential thermometer.-This  instrument, fig. 455,
avoids the objection to the open air                In
thermometer.  It was used by Leslie
in  his experiments on radiant heat,
and consists of a two-bulbed tube filled
with air, bent twice at right angles. It 
contains a column of sulphuric acid in        C  
the stem, which stands at the same 
height, if both bulbs are equally heated, but if one is heated more than
the other, the difference is seen in the unequal height of the two columns
as shown in the figure.
(b.) Howard's differential thermometer, fig. 456, contains ether,
and the vapor of ether, in   456                   457
place of common  air.  It
is by far the most sensitive  
instrument of its class. It   
was invented by Professor
Howard, of Baltimore, in..
1819.
(c.) Rumford's thermo- 
scope, fig. 457, is an instru- 
ment resembling Leslie's,
and like-it, contains air.  The horizontal tube is longer, and the bulbs
larger, than in Leslie's, and a short column of sulphuric acid, n, separates the two masses of air, and by its motion over a scale of equal
parts, serves to indicate differences of temperature.
588. Thermo-multiplier.-By far the most delicate of all means of
measuring small variations in temperature, is the thermo-multiplier, or
thermo-electric pile of Nobili and Melloni.  Its indications depend on
the production of electric currents by small changes of temperature.
It was with this instrument that Melloni conducted the remarkable
series of researches on the transmission and radiation of heat which
are noticed in their appropriate place, farther on.




IEAT.                             413
Q 3. Expansion.
I. EXPANSION OF SOLIDS.
589. Linear expansion.-Pyrometers.-The general fact of the
expansion of bodies by heat, has already been stated in g 566. Linear
expansion, or expansion in a single direction, is illustrated by the
apparatus seen in fig. 458. A metallic rod, A, securely held by a screw
458
at the end, B, is heated by the flame of an alcohol lamp. The expansion is shown by the movement of the index, K, over the graduated
arc, occasioned by the pressure of the fore end of the rod against the
short end of the index.  At the beginning of the experiment, the rod
A is adjusted by the screw B, so that the index stands at zero; as the
rod cools the index returns. Rods of various metals and alloys may be
used for comparison. Such an instrument is called apyrometer; but
it has no scientific value, being replaced by instruments of far greater
delicacy.  Those named in ~ 582, 584, and 585 are examples of the
accurate application of linear expansion of solids for the exact admeasurement of changes of temperature.
590. Cubical expansion in solids may be shown by the apparatus,
fig. 459. The ring of metal, m, allows the            459
ball of copper, a, merely to pass through
it at the ordinary temperature.  If the
ball is heated, it expands in all directions, and  will then  no  longer pass
through the ring, but rests upon it, as is        I t
shown in the figure.  As the ball cools,
it gradually returns to its original dimensions, and again passes through the ring
as before.
Different solids expand unequally, but,
for the most part, uniformly, in all directions, and return to their original dimensions on cooling.




414            PHYSICS OF IMPONDERABLE AGENTS.
There are some exceptions to this general statement.  Wood expands and
contracts more in the breadth of its fibres than in their length; and, when it
is considerably heated, it contracts permanently. Clay also contracts permanently by heating, and becomes vitrified; new chemical compounds being
formed. The particles of lead slide over each other during expansion, and do
not return again on cooling to their original position. Lead pipes, which convey hot water or steam, become permanently elongated; and the leaden linings
of bath-tubs and cisterns, which receive hot water, become gathered into ridges
from this cause.
Relation between cubical and linear expansion.-The linear
and cubical expansion in any homogeneous solid, is so related, that,
by the same elevation of temperature, its length, breadth, and depth
will be increased in the same proportion.  Thus:If a solid, heated to a certain temperature, increases in length one one-thousandth of its original length, its surface increases two one-thousandths of its
original area, and its volume, three one-thousandths of its original bulk.
This theoretical view is found to be nearly, but not quite, true, in fact.
Expansion  of crystals.-Crystals of the  monometric  system
(154, a), like common salt, fluor spar, &c., expand equally in all directions.  In this system, all the crystallogenic axes are equal, and at
right angles to each other.  In crystals of all other systems, the
expansion is the same in only two directions (dimetric system, 154, b),
or it is different in all three, depending upon the position of the
crystallogenic axes to each other.  The amount of expansion in some
crystalline compound bodies, e. g., fluor spar, aragonite, sulphate of
barytes, quartz, &c., is found to be greater than in metals, contrary to
the generally-received opinion.
591. Coefficient of expansion.-The small gain in length in a rod
1 foot or I metre long, when heated from 32~ to 33~ F., or from 0~ to 1~
C., is called its coefficient of linear expansion.
1. Coefficient of linear expansion.  If the length of the bar is 1, at the
temperature of 32~, its length at 33~ is I +  1K, composed of its original
length, 1, and a small fraction, 1K, variable with the substance experimented on.
If the rod is carried successively through the scale of temperatures, it gains,
at each degree, a new elongation, which experiments show to be nearly constant,
and equal to 1K, so that if the rod is elevated from 32~ F., to t degrees above
32~ F., its total gain in length is expressed by IKt, and its new length, It, is
I+ 1Kt,  or,          It=  (l — Kt).
At any other temperature, t',-this expression becomes, t1' b == 1(1 + Kt'), and
if the value of It' (any temperature above 32~), is sought in terms of It, we write
approximately,          It' =  It [1 + K (t' -t)].
The coefficients of expansion for some of the most frequently occurring solids is given in Table III., in terms of the decimal system.
2. The coefficient of superficial expansion, is obtained from  the expres —
sions for linear expansion, by substituting S and St for I and It; thus:Si ==  S  (1  - 2Kt), where 2Kreplaces Kin the formula for linear expansion.




HEAT.                               415
3. The coefficient of cubic expansion, is the small fraction of its volume,
by which a solid, liquid, or gas is increased when heated from 32~ to 33~ F.
Assuming the expansion to be proportional to temperature, we must admit the
volume V at t degrees and at 32 degrees to be proportional to the cubes of their
homologous dimensions. By the same reasoning as before, we have, therefore,
the formula;  V =  V (1 +  3Kt), by which the increased volume ( V) of any
mass of matter may be calculated when the value of V, t, and K are known.
The coefficient of cubic expansion may also be determined accurately from
the specific gravity of the solid taken at different temperatures, thus:Let (Sp. Gr.) and (Sp. Gr.)' represent the specific gravities of any solid at the
two temperatures, t and t'; let W be the weight of the solid under trial, Vits
volume at 32~, and K the co-efficient to be found; then, since by the last
expression, we know the value of the solid at t~ and t'~, V (1 + 3Kt), and
W
V(1 - 3Kt',) we have from ~ 99          (Sp. Gr.)   V       (1    tand
V(L -[- 3Kt)
W
(Sp. Gr.') -=  V    - 3K      The value of the co-efficient of cubic expansion,
V (1 +\ MKI)
is obtained from the reduction and combination of these two equations
Thus:  K-=  (Sp. Gr.) - (Sp. Gr.)'
3(Sp. Gr.)'t -3(Sp. Gr.)t
This coefficient may also be obtained from the apparent expansion of mercury.
It is plain that all questions relating to the expansion of solids, may be solved
by these expressions, when the value of K is known; and that this quantity
must be the subject of exact experimental determination in each solid. Our
limits do not permit the description of the various means by which the linear
expansion of solids has been measured. In the researches of Lavoisier and
Laplace, a bar of the substance under examination was heated in a water-bath.
One end was fixed, the other free, and touched the end of a lever, acting by any
expansion of the bar, and causing a movement observed in a telescope attached
to the lever, as already described in ~ 582. The expansions, from 32~ to 212~,
were thus read off upon a scale placed at a proper distance.
The capacity of hollow  vessels is increased by the expansion of their walls, to the same amount which a solid mass of the
same material and volume would expand by a like change of temperature. Hence it is easy to calculate from the known co-efficient of glass,
or any other substance, the changes of capacity of hlollow vessels.
The amount of expansion in solids, between freezing and boiling,
is, after all, but a very small fraction, being, for zinc, which is the most
expansible of all metals, only one three-hundred and fortieth of its
length; while glass expands only about one-third of this quantity, for
a like change in temperature (1 in 1248). The order of the expansibility of metals and glass is as follows, commencing with the most and
ending with the least expansible:-zinc, lead, tin, silver, brass, gold,
copper, bismuth, iron, steel, antimony, platinum, glass.
*In all these formulae, t is taken to represent the number of decrees above
the freezing point.




41.6          PHYSICS OF IMPONDERABLE AGENTS.
This, it is worth while to remark, is also very nearly the order of
compressibility of the same substances.
Ice is more dilatable than zinc, in the ratio of -a' to -S. The contraction of ice by cold has been observed for 30~ or 40C below the
freezing point.
The most expansible solids are, in general, the most fusible,...,
ice, zinc, &c.; while the least expansible metal, platinum, is also the
least fusible; but in other cases this comparison fails.
The hardness, ductility, and other physical properties of the metals,
appear to sustain no relation to their expansibility.
592. The ratio of expansion increases with the temperature.Between 32~ and 212~ F., the increase in the coefficient of expansion
in solids, is hardly appreciable; but for high temperatures, the increase
becomes a considerable quantity.  Regnault has determined the mean
coefficients for glass, when blown in hollow vessels between zero C. and
the following temperatures-the coefficients being in each case ten-millionths of the whole:
Coefficients.  K. = 276   284   291   298   306   313
Temperatures, C.   100~  150~  200~  250~  300~  350~
This increase in the coefficients of expansion of bodies by rise in
temperature, is probably due to the distance between the particles aug.
menting with the heat. Their mutual cohesion is thus more readily
overcome.
In the case of glass, which has been more carefully studied than any other
solid, it appears from the results of Regnault, not only that glasses of different
composition differ in their coefficient of expansion, but the same glass, in solid
rods, expands more than in the form of tubes; and that great and sudden
changes of temperature, as in making a thermometer (573), may vary the coefficient of expansion, owing probably to slow molecular changes in the glass.
593. Amount of force exerted by expansion.-The enormous
force exerted by an expanding or contracting solid, may be conceived
by estimating (from the coefficient of elasticity, ~ 161) the power requisite to produce an equal change of length by compression or by traction.
Assuming, in round numbers, the coefficient of elasticity of iron at
212~ -  21,000 kilogrammes, a bar of iron, one metre long, expands
0-0012 m., if heated from 32~ to 212~ F. Therefore a bar of iron, one
square inch in section, raised from the temperature of freezing to
boiling water, expands with a force of 35,847 pounds; or it exerts a
force of 199'15 pounds for every degree Fahrenheit that its temperature is elevated.
When a bar of iron one inch square has its temperature changed
12~ F., its expansion or contraction exerts a strain equal to one ton




HEAT.                                417
weight; and if varied from  10~ to 90~, a common change from winter
to summer, it expands with a force of about seven tons.
The force of contraction in a cooling solid, is equal to the force of expansion
when it is heated. This force is constantly used in the arts.
The walls of an arched gallery in the Museum of Artg and Trades in Paris,
having bulged outwards by the weight of the arch,            460
Molard placed a series of iron bars, fig. 460, through
the wall, secured by nuts on the outside. The alternate bars were first heated( by charcoal furnaces,
and, when they were expanded, the nuts were
screwed firmly up to the walls. As the bars cooled, 
they drew up the walls to an extent equal to their
contraction. The other half of the bars were in 
like manner heated and cooled; and, by a series  
of such operations, the walls were gradually brought 
to an erect position. A similar proceeding was  
adopted in the Cathedral at Armagh, and in a store- 
house in Providence, R. I.
Wheelwrights and coopers make iron tires and hoops a little smaller than
the wheel or barrel for which they are designed; these are applied in a heated
state, and quenched; as they contract, they bind the parts firmly together. The
heavy wrought-iron rims of the driving-wheels of locomotive engines, are shrunk
on in the same way. Rail car wheels are often cast with split hubs, to allow
play for the unequal contraction of the heavy rims and lighter arms, or the latter
would be broken at the hub, or rim, on cooling. The same precaution is requisite in all castings where heavy and light parts are united. Boiler-plates are
riveted together with red hot rivets, which, on cooling, draw the plates together
more firmly than any other means could do. When the stopper of a bottle
sticks, it may usually be withdrawn by heating the neck of the bottle with a
spirit-lamp, or with a cloth dipped in warm water. The neck is thus expanded,
and the stopper is released.
594. Common  phenomena produced  by  the  expansion  of
solids.-In every-day life may be seen numerous phenomena, caused
by the expansion and contraction of substances by variations in temperature.
A stove snaps and crackles when the fire is lighted, and again when it is
extinguished, because of the unequal expansion and contraction of the different
parts. The pitch of a piano-forte, or harp, is lowered in a warm roodm, owing to
the expansion of the strings being greater than that of the wooden frame which
supports them; and for the reverse reason, the pitch is raised, if the room is
cooled.
Nails driven into wood often become loose; the expansion and contraction of
the nails, through variations of temperature, gradually enlarging the holes.
A gate in an iron railing may be easily shut, or opened, in a cold day, but only
with difficulty in a warm day, because the gate itself, and the surrounding railings, have become expanded by the heat.
Astronomical instruments, placed on elevated buildings, are sometimes sensibly
deranged by the expansion of the walls exposed to the sun. Iron and platinum
wires may be successfully soldered into glass, because their mutual expansibility
differs very little, while silver, gold, and copper, similarly treated, drack out as
38




418            PHYSICS OF IMPONDERABLE AGENTS.
the joint coils, because their expansibility is much greater than that of the
glass.
Glass and earthen vessels, with thick walls, are liable to break when h,t
liquids are suddenly poured into them. The surfaces in contact with the hot
liquid, expanding before the other parts are affected, have a tendency to warp,
or bend the sides unequally, and the brittle material breaks. We use this peculiarity of glass to convert broken vessels in the laboratory to useful purposes.
Since, by a red-hot iron, or the point of a burning coal, we can lead a crack in
any direction, and thus safely divide the thickest glass.
Bunker Hill Monument, an obelisk of granite, two hundred and twenty-one
feet high, moves (as observed by Horsford), at top, with the sun's rays, so as to
describe an irregular ellipse with the sun's motion. This movement commences
about 7 A. M., of a sunny day, and has its maximum in the afternoon. In a cloudy
day, no motion exists, and a shower restores the shaft to its position; showing
that the heat which produces the deflection penetrates but a short distance.
Railroad bars must be laid with open joints, or their expansion an4 contraction between the extremes of natural temperature would destroy the road.
Between 4~ F., and 100~ F., the expansion of one mile of rails (5280 feet) is 5
feet 7 inches.
The two tubes of the Britannia Bridge (172), are secured at the centre to the
main pier, called the Britannia Tower; but the other points of support rest on
friction rollers, admitting of free motion with changes of temperature. An
increase of 26~ F., from 32~ to 58~, gives a total increase of 3i inches in the
whole length of each tube, or one-half that amount at each end. The daily
change of dimensions varies from half an inch to three inches; the maximum
and minimum effects being about 3 P. M., and 3 A. M., respectively. The same
changes noticed by Horsford in Bunker Hill Monument, are produced in this
bridge by the sun's rays. The heated portions of the tube expand, warping the
free ends to the cooler side about two and a half inches, both vertically and
laterally.
The Victoria Bridge, at Montreal, shows the same phenomena, but not so remarkably, as the several tubes are much shorter (page 137).
Fire regulators.-The expansion of solid bodies is often used to
regulate the temperature of stoves.
A metallic bar, usually of copper, is placed within, or beside the stove or
furnace, and as it becomes heated it expands, and moving a lever, turns a
damper, or valve, thus regulating  or arresting the draught, with perfect
fidelity and accuracy.
595. Unequal  expansion  of solids.-Breguet's  thermometer,
already described (580), is a beautiful example of the application of
unequal expansion to measurement of temperatures.
If a compound bar of iron and copper, secured together by rivets,
fig. 461, is heated, the copper ex-                   461
panding more than the iron, the:          -- 
bar is thereby curved, as seen in                    461 b
fig. 461b, to accommodate the ir-                       -
regularity of length resulting. If 
this compound bar is cooled below the temperature at which the two
metals were united, it curves in the opposite direction.




HEAT.                              419
596. Compensating  pendulums.-The  length of a  pendulum
alone determines its times of oscillation (82). A difference of one
one-hundredth of an inch in a seconds pendulum would cause a clock
to vary eleven seconds in twenty-four hours, and a difference of 60~ F.
produces this effect.
In ordinary clocks, this defect in the length of the pendulum is
remedied, by raising or depressing the ball at the end of the rod by
means of a screw.  Pendulums in which this defect is remedied by a
self-adjusting arrangement, are called compensating pendulums.  The
compensation is effected by the unequal expansion either of mercury
and glass, or of different metals.
Harrison's gridiron compensating pendulum, fig. 462, is one
of those most commonly employed.  The large weight at the bottom
of this pendulum  is supported by a series of rods of          462
brass and steel arranged in alternate pairs. The middle
rod is of steel, and, like all the other steel rods, is shaded
in our figure.  The cross-pieces connect the two systems  
of rods, alternately at top and bottom, in such a way
that while the expansion of the steel rods lengthens the
pendulum  the expansion of the brass rods shortens it.
The length of the pendulum  is plainly the sum of the
length of the steel rods less the sum of the brass rods (the
supporting crotchet being added to the length of the
steel rods), each pair of rods being reckoned as only 
one rod.  In order that the length of the pendulum 
should remain invariable with changes of temperature,
it is obvious that the expansion of the two systems of, 
rods must exactly balance each other. 
To determine the length of rods required to effect this, let
L and I be the sum of the lengths of the steel and brass rods
respectively, and K and K' their respective coefficients of
expansion. Then, if the amount of expansion in both systems is equal, L K
will equal I K'. But since, at London, the length of the seconds, pendulum is
39-14056 inches (82), it follows that L -   -- 39-14056 inches.
If, therefore, we take from Table III., the values of K and K', and combine
these two equations, we shall find the respective lengths of L and 1.
K'                             K 
L == -~-   X 39-14056 inches, I -=          X 39-14056 inches.
K - A                          K' -K
But the position of the centre of oscillation, which determines the virtual
length of the pendulum (83), may vary, although the sensible length remains
unchanged.  Hence the necessity of adjusting the position and mass of the
suspended weight after the length of the rods is approximately accurate.
In Graham's compensating pendulum, fig. 463, the rod, a, 6, is of




420             PHYSICS OF IMPONDERABLE  AGENTS.
glass, and the ordinary weight is replaced by a glass vessel containing mercury
sustained in a metallic stirrup. When the temperature rises, the pendulum
lengthens, and the mercury also expanding, rises in the glass.
The compensation in this instrument is not quite perfect, since the position of
the centre of gravity (which remains unchanged by the construe-    46
tion) does not entirely coincide with the centre of oscillation, on
which the virtual length of the pendulum depends.                i
Mr. Henri Roberts' compensating  pendulum   is
remarkable for its extreme simplicity. The rod of the pendulum,
fig. 464, is of platinum, and supports at its lower end a disk of
zinc. The centre of gravity of this disk will        465
always be preserved at the same distance from
the point of suspension, if the expansion of the
platinum rod is equal to that     46 
of the zinc disk; this condition
is obtained when the radius of 
the disk is equal to one-third
of the length of the rod.
Martin's  compensating pendulum  is a corm-                      m 
pound bar of iron and copper  -.....:     b
soldered together throughout    
their length, and fixed trans-                 t'
versely upon the pendulum  
rod, fig. 465.  The copper,                                      C 
being the most expansible, is
placed below the iron. When the temperature rises, and the centre of oscilla.
tion is, by the expansion of the pendulum, removed to a greater distance from
the point of suspension, the copper, expanding more than the iron, bends the
rod into the curve, m f n, whereby the metallic balls, m m, at the extremities of
the rods, are raised, and being brought closer to the point of suspension, compensate for the increased distance of the weight of the pendulum from that point.
If the temperature is lowered, the rod bends into the curve, sm' c mn', and the
balls are lowered. These balls are of such a size, and placed at such a position
upon the compound bar, that the centre of oscillation is not displaced by variations in temperature, and thus perfect compensation is produced.
Compensating balance wheels of watches and chronometers
are constructed precisely on the plan of Martin's pendulum. The balance wheel
of a watch varies with changes of temperature,-the duration of an oscillation
depending on the radius of the wheel, the strength of           466
the spring, and the mass of its rim.  The expansion 
of the wheel, by enlarging the radius, retards the timepiece, and, conversely, cold accelerates it.  The three a
metallic arcs, aaa, fig. 466, are designed to counteract
and correct the effect of expansion on the wheel. Each
arc is composed of two strips of metal, the most expansible being placed outside. Heat, therefore, carries the 
masses, n n i, inward and nearer to the axle of the wheel,       ~      a
while cold throws them outward, thus preserving the virtual length of the radius under all changes of temperature. Any errors of compensation are adjusted by turning the masses, n n a, on the screws at the ends
of the arcs.




HEAT.                             421
II. EXPANSION OF LIQUIDS.
597. General statement.-All liquids expand by heat more than
solids; thus mercury, the least expansible of all liquids, expands more
than zinc, the most expansible of all solids.
The rate of expansion in liquids is not so uniform as it is in solids,
and especially near their points of solidification and vaporization they
are subject to great irregularities.
598. Apparent and absolute expansion.-We have already (576)
noticed the fact that it is only the apparent, and not the absolute, expansion of mercury which is read in the thermometer. It is plain that
in any.case the absolute expansion of a liquid must be the sum of its
apparent expansion, and of the increased capacity of the containing
vessel (591) at the given temperature.  Either two of these quantities
being known, the third can be calculated.
The absolute expansion of mercury, being one of the most important
constants in physics, and one on which many others depend, has been
determined with the greatest accuracy. This determination was originally made by Dulong and Petit, and has been confirmed and corrected
more recently by Regnault.
The method giving most exact results depends on the familiar
principle of hydrostatics (202), that the heights of liquid columns in
communicating vessels are in the inverse ratio of the specific gravities
of the liquids. What is here true of different liquids is of course true
of the same liquid at different temperatures. To determine this point
accurately, a glass tube, bent into a syphon, is filled with mercury, and
so arranged that, while the two legs are respectively exposed to the
required temperatures, the corresponding heights may be exactly measured by a cathetometer.  The coefficient of expansion for each tenperature may then be calculated from (591'3) by means of the specific
gravities thus determined.
Let C and C' represent the two columns; H and (Sp. Gr.) the height and
specific gravity of C at 320, and H' and (Sp. Gr.)' the height and specific
gravity of the column C' at t~. Then, by 202, H(Sp. Gr.) -  H' (Sp. Gr.)'. Let
K represent the coefficient of absolute expansion in mercury, and by 591 and
99, we have (Sp. Gr.) =  (Sp. Gr.)' (1 + Kt.) Hence the value of K, obtained
H' - H
by combining these equations, is,    K-'
The mean absolute expansion of mercusy was by this method found by Dulong
and Petit to be between 32~ and 212~ F. for 1~ F., K=   im =- 0.0001001.
This number has been corrected by the later researches of Regnault to
K=  0'00010085 for each degree of Fahrenheit's scale; or, K=  0-00018153 for
each degree Centigrade.
The increase of the coefficient of expansion for mercury, with increase of
temperature already alluded to (576), is shown in the following table copied
from Cook9d tbe'Ymfal PIfy'fcs, p. 510. The degrees are Centigrade.
38 *




422             PHYSICS OF IMPONDERABLE  AGENTS.
COEFFICIENT OF EXPANSION FOR MERCURY.
True Temperature   Mean Coeffcientof   Actu    icient of  VolumActual   icie  of Equal
by Air Thermo-   Expansion of Mercury  Expansion from 0 to   Weights.
meter.         from 00 to to.        (t + 1)o.
00          0                    00017905      1'0000000
30           0-00017976          0-00018051           1-0053928
50           0-00018027          000018152            1-0090135
70           0-00018078          0-00018253           1.0126546
100           0-00018153          0-00018305           1-0181530
150           0-00018279          0-00018657           1-0274185
200           0-00018405          0-00018909           1 0368100
250           0-00018531          0-00019161           1-0463275
300           0-00018658          0-00019413           1-0559740
350           0-00018784          0-00019666           1-0657440
The last column of this table shows the volume to which one cubic centimetre
of mercury will expand when heated to the temperatures given in the first
column. Whenever the mean coefficient between 0 aid tO (as given in the
second column) is known, the corresponding volume may be calculated by the
formula V' =  V(1 +  Kt); and, by interpolation, the volume can be calculated
for temperatures for which the coefficient has not been determined.
599. Correction of the observed height of the barometer for
temperature.-As the volume and density of mercury vary with the
temperature, the height of the mercurial column in a barometer varies
not only with changes of the atmospheric pressure, but also with changes
in temperature. Before comparing barometric observations, therefore,
made at different times, it is necessary to reduce the observed heights
of the mercurial column to the height they would have at some standard
-temperature.
The principles enunciated in the last section enable us to obtain the following value for the height of the barometer reduced to 32~ F.
t
H =  H'- H' 991-           t being the degrees Fahrenheit above freezing; or,
9916 -j- t
t
H =      0H' - H', when t is given in degrees of the Centigrade scale.
5508 ~- t
The true height of the barometer is therefore to be obtained by subtracting
the correction from the observed height when the temperature is above the
freezing point. There is also a small correction to be made for the expansion
of the scale, which for present purposes may be neglected.
600. Apparent expansion of mercury.-The apparent expansion
of mercury in glass is readily determined by means of the simple
apparatus, seen in fig. 467, consisting only of a glass tube, r, drawn
out into a narrow neck, which is recurved so as to dip conveniently into
the cup c. The weight of the empty tube is first taken, and it is then
filled with mercury in the manner described in ] 568; taking care to
expel, by continued boiling, the last traces of air and moisture. The
tube and its contents are then cooled to 32~ F. by immersion in melting




HEAT.                               423
ice, the point o being kept constantly beneath the mercury in c. It is
then weighed again, and thus by deducting the weight of the empty
tube we learn theweight ( W) of the mercury it contains           46;7
at 32~.  Lastly, it is exposed to a constant temperature, to
(say of 212~ F., see fig. 443), and the weight of the escaping         0
mercury (w) ascertained. The weight of the mercury which
fills the tube at t~ is therefore W-  w. From these data the         c
coefficient of apparent expansion is calculated.
7/
The volume, V, of a weight of mercury, represented by W- w
- to
at 32~, is V =      G)  Now this weight of mercury at to filled
the same' volume (i. e., the whole apparatus), not regarding the
expansion of the glass, which was filled by the weight, W, at 32~.
W
The volume of the weight WI- w at to is therefore V'.      r
(s8. Gr.)
Let the coefficient of apparent expansion be K, and then
V' =  V (1 +  Kt); then substituting the values of Vand V',
r g, w   for common French
and reducing, we have K = — = for common French'W- Iw)t
glass g-8-.
A similar mode of experiment gives of course the coefficient
of apparent expansion for all other liquids. It is also applicable for the determination of the coefficient of expansion of all solids not acted on by mercury,
since it is true that the coefficient of apparent expansion for mercury is equal
to the coefficient of absolute expansion less the coefficient of expansion of the
material for the containing vessel. As the coefficient of absolute expansion for
mercury is known with the greatest accuracy, it follows that, by an application
of the reasoning in this section, we have the means of determining the coefficient
of expansion in glass and other solids.
601. Amount of expansion  of liquids.-Liquids expand very
unequally for equal increments of heat; the law of their expansion
has not been fully determined. Generally the most expansible liquids
are those whose boiling points are the lowest.  Those whose boiling
points are high have usually a small but very regular expansibility,
especially at temperatures much below their boiling points.
The rate of expansion in all liquids increases with the temperature,
but it varies with each substance according to laws not well understood.
Between 32~ and 212~, mercury expands 1 in 55, water 1 in 21'3,
sulphuric acid 1 in 17, alcohol 1 in 9 -, &c.  See Table IV.
The statement, in the first edition of this work, that in many liquids of analogous chemical constitution, the rate of expansion is nearly uniform at equal
distances from their respective boiling points, appears, from the observations of
Pierre, not to be sustained.
The expansibility of liquids is not in proportion to their density, but
is more nearly the inverse of this than in any other known ratio.




424           PHYSICS OF IMPONDERABLE AGENTS.
602. Expansion of liquids above their boiling points.-The
late researches of C. Drion* show that the coefficient of expansion in
liquids, above their boiling points, increases at an accelerated ratio, and
even surpasses the coefficient of expansion in gases. As long since as
1835, Thilorier, in his memoir on liquid carbonic acid, states that this
liquid expands between 0~ and 30~ C. (32~ to 86~ F.), four times as much
as air expands for the same range of temperature, being as j-A. for the
liquid gas to  -  for air.  Twenty volumes of liquid carbonic acid.
between 32~ and 86~ F., become therefore twenty-nine volumes.
Liquid sulphurous acid, and cyarnogen present the same apparent
anomaly, as well as certain fluids found in the minute cavities of topaz
and quartz crystals.
The experiments of Drion were made on chlorid of ethyl, sulphurous acid, and hyponitric acid.
Curves of expansion of liquids.-The variation in the expansion
of liquids may be graphically represented as in fig. 468. The diagram
shows the lines representing the                  468
expansion of six liquids. In each  1000 980 960 Y40 920 000 880
case 1000 parts of liquid are taken  F-                            oC
at 212~ F. The horizontal lines 30s\                    -I         20
(reading from above downwards)  
show the bulk of the liquid at 72_\            X      G    -     J40
temperatures below the boiling 108\               ^                60
point. These temperatures are         \   g
represented in degrees of Falh- i44                          ~     so_  Y  80
renheit's scale on the left hand       A \                         loo
column, and in Centigrade degrees on the right hand.  The line A indicates the contraction of mercury; B, that of water; C, for alcohol; D, for wood spirits; E, for
formic ether; F, for terchlorid of silicon; G, for ordinary ether.
Thus at 108~ below the boiling point (at 104~ F.), 1000 parts water have
contracted into 966 parts; alcohol into 931 parts; and formic either into 918
parts.
603. The amount of force exerted in the expansion of liquids
is enormous; being equal to the mechanical force required to compress
the expanded liquid into its primitive volume.
Thus the expansion of mercury for 10~ F., is'0010085. Its compressibility
for a single atmosphere is'0000053. Therefore the amount of force required to
restore the mercury to its original bulk, after heating it 10~ F. is equal to 190
atmospheres (10085 -- 53 = 190), or 2850 pounds pressure to a square inch.
Owing to this enormous force exerted during expansion, closed vessels filled
with liquid, however strong they may be made, burst when heat is applied.
- Ann. de Ch. et de Phys. 1859.




HEAT.                               425
604. Expansion of water.-Water, which presents so many remarkable exceptions in its physical history, does so in no respect
more than in the singular irregularities observed in its expansion for
equal increments of temperature between 32~                  469
and 212~.  Its total expansion for this range is
by no means large, while its coefficient of expansion is found, by an examination of Table
IV., to be smaller than  that of any liquid
except that of mercury.  The expansion  of
water, which is irregular through the whole
range, from freezing to boiling, is especially so
between 32~ and 40%F. While all other liquids
are most dense at their freezing points, the
maximum density of water occurs some degrees
above that point (39~'2 F.), and above or below
this temperature it expands.
Maximum  density of water.-To illustrate,
by experiment, this signal exception in water to the
ordinary laws of expansion, a water thermometer, like
fig. 469, may be used. The flask, holding about a
quart, is filled with water, and the tube passing into
it is secured water-tight by a brass cap or well-fitting
cork, so that at ordinary temperatures the column 
of water stands at some convenient point on the
scale of equal parts. It is then set in a cold room
(below freezing), and the loss of temperature indicated by the fall of the column of water, is more
accurately noted by a mercurial thermometer seen in
the figure placed within the flask. When that tem-     i- 
perature reaches about 42~ F. (6~ C.) the fall of the                    6
water column ceases-it comes to rest for a short
time, and at 39~ or thereabouts (4~ C.), it is seen to
mount more and more rapidly as the temperature
falls, until it reaches 32~ (or even lower, if the apparatus is kept quite still).
If the apparatus is filled with water near the temperature of maximum density,
and placed in a warmer room, we have evidence of the converse, and not less remarkable fact, that expansion equally occurs, whether we heat or cool the water.
These results are somewhat obscured by the expansion of the glass; but for a
few degrees above and below 38~, the density of water is nearly uniform.
At the moment of freezing, water expands about ten per cent. of its volume,
and the fact is often evidenced in the apparatus here figured, by a jet d'eau from
the tube at the moment of freezing.
Owing to the difficulty of compensating the errors involved in the expansion
of the containing vessels, the point of maximum density cannot be settled with
absolute accuracy. Hassler assumed it at 39-83 F. in his determination of the
value of the United States standards of measure. Gineau determined the
French unit of weight at 40~ F. (4-5 C.), and Despretz, in 1839, fixed it at
39~'2 or 4~ C. The later researches of Plicker and Geissler reduced it to




426            PHYSICS OF IMPONDERABLE AGENTS.
38~'84; but it is agreed by physicists to assume 4~ C., or 39~'2 F., as representing the true point of maximum density for water.
The apparatus shown in fig. 470, serves well to illustrate the effect of this
law in the freezing of lakes and rivers. A glass jar, around     470
the central part of which is fitted a metallic vessel, c, is provided above and below with two delicate thermometers, t t',
entering the sides of the jar horizontally by openings drilled   1
for that purpose. After filling the jar with water, a freezing          t
mixture of ice and salt is placed in c, which rapidly cools the 
water. The two thermometers continue to indicate nearly the      i
same temperature until the water is cooled to 390~2 F., when it C11 1 
will be observed that the lower thermometer remains at that
point, while the upper one indicates a lower temperature, until
it finally reaches 32~ F., or even lower.                              t
The explanation of these phenomena is, that the rater,
cooled by the freezing mixture, becomes more dense and sinks,
while other and lighter portions rise, to be cooled and sink
in turn. Thus a system of currents is established, by which 
the whole of the water gradually reaches the temperature of 39~02. On cooling
below this point, the water expands, and, thus becoming lighter, the colder
portion remains at the surface, and is further cooled by the freezing mixture, while the water in the lower part of the vessel, not coming in contact
with the freezing mixture, and being no longer disturbed by currents, remains
at the temperature of 39~02.
Effects of the unequal expansion of water.-Under the influence of this law of unequal expansion in water, the cold of our most
severe winters produces only a comparatively thin covering of ice upon
the lakes and rivers.  Water freezes at 32~, but, before that temperature can be reached, expansion sets in at the surface, and the water,
although colder, is specifically lighter than the warmer water below,
and, consequently, floats buoyantly upon it. Ice is formed only on the
surface, but, being a very bad conductor, it cuts off the escape of heat
from the water below, and this renders the freezing process a very slow
one. In fact, a film of ice may be likened to a blanket, which, although
of itself cold, becomes a means of preserving heat by cutting off radiation.
Lake Superior has, uniformly, throughout the year, the temperature of about
40~, at a short distance below the surface; and the deep sea soundings show, that
the sea, at the bottom of the ocean, even under the Gulf Stream, is below the
temperature of maximum density, which, in saline solutions, is lower than in
pure water. The temperature of the deep Alpine lakes is 390~2 F., at all
easons of the year.
Maximum  density of different aqueous solutions.-The solution of various salts in water has the effect of lowering its point of
maximum density.  Thus, the point of maximum density of sea-water
is 25~.70.  The point of maximum  density of solutions falls more
rapidly than their point of congelation, and is proportional to the
quantity of salt dissolved.




HEAT.                             427
The volume of water, at different temperatures, has been determined by several experimenters, and the results, according to Kopp,
are given in Table XXIV., with the corresponding specific gravities,
both when taken at 32~, for the unit of volume and density, and also
at 4~ C. (390~2 F.).
III. EXPANSION OF GASES.
605. General statement.-Gases and vapors, being under the
influence of repulsion, and having little cohesion, expand, for equal
increments of heat, much more than either solids or ordinary liquids.
(Compare ~ 602.)
The expansion of air, and of all gases, may be shown by plunging the open
end of a bulbed tube into water; a slight elevation of temperature, even the
heat of the hand, will expand the air in the bulb, and cause a part of it to escape
in bubbles through the water. And when the source of heat is withdrawn, the
rise of the water in the tube indicates the amount of expansion (604).
606. Gay Lussac's laws for the expansion of gases by heat.Gay Lussac was the first to discover the general laws of the expansion
of gases by heat. The gases on which he experimented were not freed
from moisture; but the laws which he deduced are remarkable for their
great simplicity and general accuracy, considering the state of experimental science at that time (A. D. 1805). They are as follows:1st. All gases have the same coefficient of expansion as common air.
2d. The coefficient of expansion remains the same, whatever may be the
pressure to which the gas is subjected.
These laws, like the laws of Mariotte (274), though sufficiently accurate for
ordinary purposes, are found, by the more complete experiments of modern
science, to be not strictly correct.
607. Results of Regnault's experiments upon the expansion
of gases.-Very valuable experiments were made by Dulong and
Petit, but the most recent and complete investigation of the expansion
of gases by heat, was conducted by Regnault. In all his experiments,
the different gases experimented upon were completely deprived of
moisture, and the results of his experiments are contained in the following tables:EXPANSION OF GASES BETWEEN 32~ AND 212~ F. (JAMIN).
Gases.          Under Constant Volume.   Under Constant Pressure.
Air.......                    0-3665                  0-3670
Nitrogen......                03668                   0-3670
Hydrogen...                  0-3667                  0-3661
Oxyd of Carbon...          0-3667                  03669
Carbonic Acid..            0-3688                  0 3710
Protoxyd of Nitrogen           0-3676                  0-3719
Sulphurous Acid...           0-3845                 0-3903
Cyanogen.....              0-3829                  0-3877




428            PHYSICS OF IMPONDERABLE AGENTS.
From this table it appears that the coefficients of expansion of those
gases which have never been condensed to liquids, are very nearly the
same as air; while the coefficients of the condensible gases, carbonic
acid, sulphurous acid, and cyanogen, are considerably greater, and the
greater in proportion as they are more readily condensed into liquids.
Each gas has two coefficients of expansion,-the coefficient of expansion for a constant volume being less than for a constant pressure,*
except in the case of hydrogen, in which the reverse takes place. This
agrees in a remarkable manner with the fact (276) that hydrogen alone
is less compressible than the law of Mariotte would indicate.
It is further shown, by the experiments of Regnault, that:1st. The coefficients of expansion are very nearly, but not absolutely,
the samefor different gases.
2d. The coeffcients of expansion, for different gases, vary more fiom
each other in proportion as the pressure to which they are subjected is
increased.
3d. The coefficients of expansion for all gases, except hydrogen, increase
with the pressure to which they are suljected, and this increase is most
rapid in those gases which deviate most from.  ariiotte's law (276).
4th. For ordinary calculations, under the pressure of the atmosphere,
the coefficient of expansion for all gases may be considered as 0-3666
between the freezing and boiling points of water, or 4-T of the volume at
32~, for each degree of Fahrenheit's scale.
For accurate scientific purposes, the coefficient of expansion of every gas considered must be taken from the tables given for that purpose.
Table V., Appendix, gives the coefficients of expansion of common gases
under varying pressures.
608. Formula for computing changes of volume in gases.-In
physical researches it is often desirable to ascertain the increase or
decrease in volume which a given gas undergoes by measured differences in temperature. This is easily done by the following formulae: —
Let V represent the volume of the gas at 32~ F., V' its volume at the higher
temperature, and t the number of degrees between 32~ and the higher temperature. The increase in the volume will therefore be expressed by V' - V. And
V
since the increase in volume for 1~ F. is generally 4, the increase for the
V
higher temperature is -  X t.
491
Therefore, V' — V      ) X t and V49V  (- +  )'
If the gas is subjected to a lower temperature, it suffers a diminution in volume, expressed by V' - V, and if t expresses the number of degrees below 32"
* This may be due to the action of cohesion.




TEAT.                               429
V
to which it is reduced, and -  its diminution for 1~ F., then the diminution
491
V                     V
for the lower temperature will be -  X t, and V — V =  -  X t.
491                   491
Therefore, V' == V  1If the volume of a gas at 32~ F. is known, its volume at any other temperatuce above or below 32~ may be calculated by the following:RULE.
Multiply the difference between the number of degrees of temperature
and 32~, by the coefficient of expansion of the gas (for ordinary purposes
this coefficient equals I divided by 491).  Add the quotient to 1, if the
temperature be above 32~, and subtract it from  1, if it be below 32~.
Multiply the number thus found by the volume of the gas at 32~, and the
product will be the volume of the gas at the observed temperature.
609. Formulae expressing general relation between volume,
temperature, and pressure. —The volume which a gas occupies depends not only on the temperature, but also upon the pressure to which
it is subjected (274); the pressure of a gas being inversely as the
volume into which it is compressed.
As the volume of a gas at the same temperature is inversely as the pressure,
if V and V' be two volumes under the same temperature, and under the pressures P and P'; then,
P
V: V' =          P' P, and V' =  V X --
If t and t' express the number of degrees above or below 32~, at which
the temperature stands (-+ being used when above, and - when below), if a gas
be simultaneously subjected to changes of temperature and pressure, the relation between its volume, pressure, and temperature, will be expressed by the
general formula
V     I +  Kt    P'    491 + t   P'
V'    1 +-  Kt' X        491 -- t'  P
610. Relation between expansibility and compressibility.It has been found, generally, that the most expansible liquids are the
most compressible.
Solids expand less than liquids, and are likewise less compressible,
while liquids have a less expansibility and compressibility than gases.
Among solids, the most expansible are generally the most easily compressed.
The expansibility of a substance increases with the temperature, as
does also its compressibility.
611. Density of gases.-The density of gases and vapors is compared with atmospheric air as the standard, air being called 1, or 1000.
39




430            PHYSICS OF IMPONDERABLE AGENTS.
The method for the determination of the density of gases is, in principle, the same as for the density of liquids.  The determinations are
made in a glass globe, fig. 205 (& 258), to which an accurately fitted
stop-cock is attached.  The globe is first weighed, when filled with
dry and pure air, and again after being exhausted of air by means of
the air-pump; the difference in the two weights gives the weight of air
contained in the flask.  The globe is then filled with the perfectly dry
gas under examination, and again weighed; the weight found, less the
weight of the globe, gives the weight of the gas. The weight of the gas,
divided by the weight of the same bulk of air, gives the specific gravity,
or density of the gas, as compared with air.
Example: A glass globe held 28'73 grains of atmospheric air, and 43-93
grains of carbonic acid. The specific gravity of the latter is therefore 43-93 -
28-73 =  1-529, or, 2873: 43-93 =  1000: 1-529.
A number of corrections must be made, in order to obtain the true density
of the gas under examination. Thus, the barometric height, and the temperature of the air at the time of weighing, must be reduced to the standard barometric height, 30 inches, and the standard temperature, 62~ F. Corrections
must also be made for the film of hygroscopic moisture, always adhering to the
globe, and for the buoyancy of the globe in the air.
Regnault has reduced the number of corrections ordinarily necessary, by
counterpoising the globe in which the gas is weighed by a second globe of equal
size made of the same glass. Thus, the corrections for the film of hygroscopic
moisture, and the buoyancy of the globe in the air, may be dispensed with, as
they are equal in both cases.
The most important applications of a knowledge of the density of gases have
been made in chemistry. As in demonstrating and elucidating the discovery
of Gay Lussac, that the volume of a compound gas is either equal to, or bears
a very simple relation to the volumes of its constituent gases. Also, in calculating the atomic weight of numerous elementary substances.
Table XI. c., Appendix, gives the density of the most important gases, as
obtained by distinguished authorities.
2 4. Communication of Heat.
I. CONDUCTION.
612. Modes in which heat is communicated.-Heat is communicated in three ways: 1st. By conduction (chiefly in solids). 2d. By
convection, or circulation, in liquids or gases. 3d. By radiation.
613. Conduction of heat.-Heat travels in solids slowly, from
particle to particle. It implies contact with, or close approach to, a
hotter body.  The end of a bar of iron thrust into the fire, becomes
red-hot, while the other end can yet be handled.  Things vary very
much in their power to conduct heat, every substance having its own
rate of conductibility.
A metallic vessel, filled with hot water, is at once as hot as its contents, while
an earthen vessel becomes heated slowly. The metal is a good. and the earthenware is a bad, conductor. A pipe-stem, tr glass tube, held in a spirit lamp,




HEAT.                                 431
may he heated red-hot within a short distance of the fingers, where a wire of
silver or copper would become at once too hot to hold.
The progress of conducted heat in a solid is easily shown by a metallic rod,
to which are stuck by wax several marbles, at equal distances; one end is held
in a lamp, when the marbles drop off, one by one, as the heat melts the wax;
the one nearest the lamp falling first, and so on. If the rod is of copper, they
all fall off very soon; but if a rod of lead, or platinum, is used, the heat is conducted much more slowly.
Solids conduct heat better than liquids, and liquids better than gases, which
are the poorest conductors of all. The metals, as a class, are good conductors,
and their oxyds, as a class, are bad ones. The more matter, then, is present
in a given body (i. e. the higher its density), the greater, as a general rule, is
its conducting power, and vice versa.
614. Determination of the conductibility of solids.-The apparatus of Ingenhausz, fig. 471, may be employed to determine the unequal
conductibility of solids.
This is a small copper box, one side of which is pierced with holes, in which
are fitted, by means of corks, small cylinders of different substances, of the
same size, covered with wax. When the vessel is               471
filled with boiling water or hot sand, the wax will
be melted from the rods in the order of their con- 
ductibility, viz., copper, iron, lead, porcelain,
glass, wood. Or small bits of phosphorus may
be placed at equal distances upon the rods, and
these will be fired in corresponding succession.
To determine the relative conductibility of
solids, the apparatus of Despretz may be
employed, fig. 472.                                         -        _
It is a series of prismatic bars, a b, heated at one end, a, by an argand lamp.
Each bar has a series of small cavities, T, formed in it, at equal distances
(1 c. m. =  39 in.) throughout its length, and filled with mercury.  In each
472
of these cavities is placed a thermometer, which indicates the progressive propagation of the heat along the bar. Bars of various metals are used. By heating
these bars successively over a steady lamp flame, their relative conductibility
will be indicated by the times required for them each to attain the same temperature.




432             PHYSICS OF IMPONDERABLE AGENTS.
615. Conductibility of metals, &c.-Gold is a better conductor
of heat than any other metal, or other solid. Its conductibility is represented by 1000.  The order of the conductibility of other metals is
(according to Despretz) platinum, copper, silver, iron, zinc, tin, lead.
The conductibility of the last-named metal is only 179-6.
The precise rate of the conductibility of these metals, according to different authorities, may be seen in the Appendix, Table VII. A., and in Table VII. B, showing the conducting power of different materials used in the construction of houses,
as observed by Mr. Ilutchinson. The substances are arranged in the order in
which they most resist the passage of heat, those substances which are most
valuable in construction in this respect (viz., the warmest) being placed first.
The substances marked H. P. are the building-stones employed in the construction of the new houses of parliament.
616. Conductibility of crystals.-The conductibility of homogeneous solids, and of crystals belonging to the monometric system, is
the same in every direction. But in crystals of other systems, the
conductibility varies in different directions, according to the relation
of the direction to that of the optic axis of the crystal.
Senarmont, in his experiments, took thin plates of crystals, some cut parallel
to the optic axis, and others at right angles to it. In the centre of each plate a
small hole was drilled for the reception of a silver wire,      473
which was heated by a lamp; the surfaces of the crystals 
were covered by a thin coating of colored wax. The con-  /,, \
duction of the heat was observed by the melting of the wax, 
the melted portion assuming, with crystals of the monometric
system, the form of a circle, 1, fig. 473, and in the other
systems, ellipses of different forms, 2, fig. 473.
617. Conductibility of wood.-The dependence
of the conduction of heat upon molecular arrangement is shown as well in organic structures as in, ~
crystalline media. This subject was investigated most 
carefully by Dr. Tyndall, who examined the conducting power of various organic substances, especially 
wood.
He found that at all points not situated in the centre
of the tree, wood possesses three unequal axes of calorific
conduction. The first and principal axis, is parallel to the
fibres of the wood; the second, and intermediate axis, is
perpendicular to the fibres and to the ligneous layers, and
the third, and least axis, is perpendicular to the fibres, and
parallel to. the layers. It may be stated, as a general law, that, the axes of
calorific conduction in wood coincide with the axes of elasticity, cohesion, and
permeability to liquids, the greatest with the greatest, and the least with the least.
The heat-conducting power of wood bears no definite relation to its density.
American birch, one of the lightest of woods, conducts heat better than any
other. Oak wood, which is very dense, conducts nearly as well, but iron wood,




HEAT.                              433
which has the great density of 1'426, is very low in the scale of conduction.
Green woods conduct heat better than dry.
618. Vibrations produced by conduction of heat.-When a
hot bar of metal, having a narrow base, is supported on knife edges
of metal or crystal, or upon metallic points, a vibratory motion of the
bar is produced, and continued until the temperature of the bar and
the supporting body become nearly the same. This vibration produces
a musical tone varying with the nature of the metal and the form of
the bar.
It was formerly supposed that these vibrations indicated that heat was produced by molecular vibrations. But it has been shown by Tyndall (Phil. Trans.
1854) that these vibrations are caused by the want of synchronism in the sudden
expansion of the points of support, as heat is communicated from the metallic bar.
Dr. Page produced similar vibrations by employing a rocker having a cylindrical surface supported on two narrow bars, using voltaic electricity as a source
of heat. Anm. Jour. Sci. [2] XX., p. 165.
619. Conductibility of liquids.-Count Rumford concluded, from
his experiments, that liquids were absolutely non-conductors of heat,
but later experimenters have determined, that               474
liquids do conduct heat, but only  to a very...
limited degree. That the conductibility of liquids
for heat is very slight, is shown by Rumford's
apparatus, fig. 474.
The glass funnel is nearly filled with water. A thermometer tube, with large bulb, is so arranged, that the
bulb is just below the surface of the water. The stem
passes through a tight cork, and contains a few drops
of colored liquid at A, which will move with any 
change in bulk of the air contained in the bulb. A Little 
ether poured upon the surface of the water and ignited, 
does not cause any movement in the column of fluid (as    I   A
may be found by pasting a line of paper on the stem at
one of the drops of liquid), which would be the case if
any sensible warmth was communicated. The warmth
of a finger, touching the bulb, will at once cause the
fluid to move by expanding the air within. As the
walls of the glass vessel gradually become hot by conduction, the water will slowly rise in temperature. By 
heating a vessel on the top, therefore, we should never
succeed in creating anything more than a superficial elevation of temperature;
at a small depth the water would remain cold. The heating of liquids is effected
by means of currents, as will be presently explained (627).
620. Conductibility of gases.-Gases are more imperfect conductors of heat than liquids. It is difficult to make accurate experiments upon this subject, from the readiness with which currents are
formed, and which thus diffuse the heat, but we know that gases, when
39*




434            PHYSICS OF IMPONDERABLE AGENTS.
confined, are almost non-conductors of heat. Thus, substances which
imprison large volumes of air within.their pores, as down, wool,
feathers, &c., are very poor conductors of heat.
Air, loaded with moisture, is rendered thereby a much better conductor of heat than dry air, in the proportion of 230 to 80; hence,
damp air feels colder to the body than dry air of the same temperature,
because it conducts away the heat from the body more rapidly.
The sense of oppression experienced before a thunder storm is due to
the combined effect of the heat and moisture of the atmosphere.
621. Relative conductibility of solids, liquids, and gases.If we touch a rod of metal heated to 120~ F., we shall be burned;
water at 150~ will not scald, if the hand is kept still, and the heat is
gradually raised; while dry air at 300~ has been endured without injury.
The oven-girls of Germany, clad in garments of woolen and thick socks to
protect their feet, enter ovens without inconvenience, where all kinds of culinary operations are going on, at a temperature above 300~, although the touch
of any metallic article while there would severely burn them.
622. Examples and illustrations of the different conductibility of solids, are very evident to common observation.
The crust of the globe is composed of poor conducting materials, and notwithstanding the intensity of the central fires within, the amount of heat which
escapes is so inconsiderable, that it has now no sensible influence on the temperature of the surface. It has been calculated, that the quantity of central heat
which reaches the surface in a year would not suffice to melt an envelope of ice
surrounding the earth one-quarter of an inch in thickness.
Water-pipes laid at a distance of a few feet under ground, are not frozen
by the winter's cold, because the soil is a comparatively poor conductor.
Fire-proof safes are boxes of iron, constructed with double or treble walls,
the intervening spaces of which are filled with gypsum (plaster of paris), burnt
alum, or some other non-conducting material. These linings prevent the exterior
heat, in case of fire, from passing to the books and papers within. Furnaces are
lined with fire-bricks, because, being of poor conducting and infusible material,
they prevent the waste of heat. Ivory and wooden handles are attached to
cooking vessels, and to tea and coffee pots, because, being poor conductors, they
prevent the heat from passing to the hand so rapidly as to burn it. Hot dishes
are placed upon mats that the table may not be injured. Water is sooner heated
in a metallic vessel than in one of glass or porcelain, because the first conducts
the heat more rapidly from the fire than the others.
Buildings constructed of wood and brick are cooler in summer and warmer in
winter than those of iron, because they are poorer conductors of heat.
The hearth-stone feels colder than the wooden floor, and this than the carpet,
owing to the difference in their conducting powers, although all are at the same
temperature.
623. Examples drawn from  the animal and vegetable kingdoms.-The covering of animals not only varies with the climate
which the several species inhabit, but also with the season. This




HEAT.                                435
covering is not in itself a source of warmth, but prevents the escape
of the vital heat from within.
Animals in warm climates are generally naked, or are covered with coarse
and thin furs, which in cold countries are fine, close, and thick, and are almost
perfect non-conductors of heat.  The plumage of birds is likewise formed of
substances which are poor conductors of heat, containing also a large quantity
of air in their interstices. Besides this protection, the birds of cold regions are
provided with a more delicate structure beneath the feathers, called down, which
intercepts the heat still more perfectly. The fossil elephant of the White River,
in Siberia, was covered with three sorts of hair, of different lengths, the shortest
being a fine, close wool, next the body, a protection against the arctic cold. The
arctic navigator and the Esquimaux endure the cold of —40~, or -60~, F. with
the aid of fur bags and clothes. Animals with warm blood, which live in the
water, as the whale and seal, are surrounded with a thick covering of oil and
fat, which acts in a manner similar to the furs and feathers of land animals.
The bark of trees is much more porous than the wood, and, being arranged in
plates and fibres around the body of the tree, prevents such a loss of heat as
would be injurious to its life.
624. The conducting power of substances in a pulverized or
fibrous state, is less than that of the same thing in a compact mass,
partly because the continuity of the substances is diminished, and also
because of the air imprisoned among the particles.
Saw-dust in a loose state, is a very poor conductor of heat, much poorer
than the wood of which it was formed. Ice-houses are built with double walls,
between which dry straw, shavings, or saw-dust are placed, keeping the interior
cool by excluding the heat. Ice wrapped in flannel is preserved by excluding
the warm  air. Refrigerators are generally double-walled boxes, the space
between the walls being filled with powdered charcoal, or some other porous
non-conducting substance.  (See Ventilation.)  Similarly constructed vessels
form the ordinary water-coolers.
Snow is made up of crystalline particles, enclosing a large quantity of air
among their interstices, which, being a very good non-conductor, prevents the
escape of the heat from the earth and limits the penetration of frost, which
always reaches a much greater depth in winters without snow, than when snow
abounds. On the flanks of Mount.Etna, the winter snows often reach near to
the border of the fertile regions, and it is the practice of the mountaineers to
cover those parts of the snow which they wish to preserve for summer use, with
two or three feet thickness of volcanic sand and powdered pumice, everywhere
abounding. The snow, thus protected, remains all summer under an almost
tropical sun, and is distributed from these natural ice-houses over the whole
Island of Sicily. There exists even to this day a heavy bed of ice near the
summit of 2Etna, covered first by an eruption of ashes and sand several yards
thick, and subsequently by a flow of molten lava, many centuries since. This
store of ice has been opened and used when the supply below on the mountain
fell short. Straw-matting, and other fibrous materials, being poor conductors,
are used to envelop tender plants and trees to protect them from severe cold.
625. Clothing.-The object of clothing, in cold climates, like the
furs and feathers of animals, is to prevent the escape of heat from the




436            PHYSICS OF IMPONDERABLE AGENTS.
body. Fibrous materials, as wool and furs, are best adapted for clothing, because they are themselves very poor conductors of heat, and
likewise contain air in their interstices.
The order of the conductibility of the different substances used for clothing,
is as follows:-linen, cotton, silk, wool, furs. Hence a woolen garment is
warmer than one of cotton, or silk, or linen. The linen sheets of a bed feel colder
than the woolen blankets, because they are better conductors of heat. Fine cloths
are warmer than coarse ones, because they are poorer conductors of heat. In
summer, coarse linen goods are used, because they allow the escape of heat from
the body more readily than other materials, while a dress of fine, close woolen
goods, is a better protection from the cold of winter than anything else,
excepting furs. A thick dress of non-conducting material is sometimes used
to exclude heat, as when workmen enter a hot furnace in certain manufacturing
processes.
II. CONVECTION.
626. Convection.-Although liquids and gases are very poor conductors of heat, yet they admit of being rapidly heated by a process
of circulation called convection, and which depends upon the free
mobility of their particles. The particles of liquids and gases in
immediate contact with the source of heat, becoming warm, and also
specifically lighter, rise, and, moving away, make room for others; this
is continued until all the particles attain the same temperature. Currents are thus produced both in water and air.
627. Convection in liquids.-The circulation just mentioned may
be rendered visible by heating in a flask, water containing a little bran
475       or amber (or other substance of about the same density
as water), over a spirit lamp, as shown in fig. 475.
The particles of liquid at the bottom  of the vessel,
where the heat is applied, becoming heated, rise, and
other particles of colder liquid come in below, and
l::.H et  supply their place.  Thus two systems of currents are
formed. In the centre of the jar, currents of the hot
particles ascend, and descending currents of colder
particles, flow down the sides; this circulation continues until the whole mass has attained the same.. temperature.
Anything that checks this free circulation, and occasions viscidity, impedes
the heating of the liquid, and likewise prevents its rapid cooling.
Starch and gum, during boiling, require to be constantly stirred, for the purpose of presenting fresh surfaces to the action of the heat, and preventing portions from adhering to the hot bottom, and thus being charred.
628. Currents in the ocean.-In consequence of the unequal heat
to which the waters of the ocean in different parts are subjected, currents of great constancy and regularity are formed. Under the tropics,




HEAT.                              437
the waters become highly heated and flow off on either side towards the
poles, while other colder currents flow from the poles towards the equator. These currents are modified in their direction by the form and
distribution of land and water on the surface of the earth, and the
rotation of the earth upon its axis.
One of these currents (called for that reason the Gulf Stream) is directed
into the Gulf of Mexico, around the western end of Cuba, and sweeping through
it, passes by the narrow channel between Florida and the Bahama Islands. It
has a temperature 8~ or 10~ F. higher than that of the surrounding ocean.
This current Spasses northward, parallel to the coast of the United States,
gradually widening and becoming less marked, and finally is directed toward
the frozen ocean and British Islands. It carries away the excess of heat from
the Antilles, and warm regions near the equator, beyond the western Atlantic,
ameliorating the climate of the British Islands and all north-western Europe.
The researches of the U. S. Coast Survey have greatly extended our knowledge of this remarkable river of the ocean (or rather union of many rivers of
warm water), first brought to the notice of the scientific world by the illustrious
Franklin in 1770.
III. RADIATION.
629. Radiation of heat.-Hot bodies radiate heat equally in all
directions. Radiant heat proceeds in straight lines, diverging in every
direction from the points where it emanates. These diverging lines
are called thermal rays, or heat rays.  Heat rays continue to issue from
a hot body, through the whole process of its cooling, until it sinks to the
actual temperature of the air, or surrounding medium. It is generally
by radiation, that bodies become heated at a distance from the source
of heat.
Standing before a fire, or in the sun's light, we feel the genial influence of the heat radiated from  these sources.  A candle, or gas light,
gives off its heat as it does its light, in all directions. A thermometer,
placed at equal distances around the flame, indicates the same temperature.
630. Radiant heat is but partially absorbed by the media
through which it passes, and is not sensibly affected by any motion
of the media, as of winds in air.
The sun's rays lose about one-fourth (0'277) of their heat in passing
through the atmosphere, the remainder being absorbed or reflected at
the surface of the earth. The air receives, however, the greater part
of its warmth by reflection, conduction, and convection, from the surface of the earth thus heated by the sun.
We receive warmth from the fire upon our persons, although the air
remains cold, and may be continually renewed.
The conduction of heat is probably internal radiation from  particle to
particle; for the material atoms of which any substance consists, are not




438            PHYSICS OF IMPONDERABLE  AGENTS
supposed to be in absolute contact, although held near each other by a strong
attraction.
631  Intensity of radiant heat.-The intensity of radiant heat is
according to the following laws:1st. It is proportional to the temperature of the source.
2d. It is inversely as the square of the distance fron  the source.
3d. It is greater in proportion as the rays are emitted in a direction
more nearly perpendicular to the radiating surface.
1st. If a thermometer be exposed at the same distance from different sources
of heat, having, for example, the temperatures of 1000, 150~, and 2000, the
amount of radiant heat will be directly as these numbers.
2d. Thus, the heating effect of a body at a distance of two feet is only onefourth, at three feet, one-ninth, and at four feet, one-sixteenth of what it is at
one foot.
This law may be exemplified by supposing two globes, one of one foot diameter, the other of two feet diameter, having a body equally heated in both. The
larger globe exposes four times as much surface as the smaller one; consequently, each square inch of the larger one will receive only one-fourth as
much heat as each square inch of the smaller one, while the distance to this
surface is only twice as great.
3d. This law may be demonstrated by the apparatus, fig. 476. In the focus
of the mirror, a thermoscope, f, is placed. A A, B B, are screens, pierced with
476
equal openings. The vessel, a e, is filled with hot water. The position of the
index of the thermoscope will be the same, whether ac is perpendicular, or
more or less inclined. And, as in the latter case, there is a greater surface exposed, and consequently a greater number of heat-rays pass through the screen;
yet, as the same effect is produced, the oblique rays must be less intense than
the perpendicular rays, the intensity diminishing with their obliquity.
632. Law  of cooling by radiation.-Newton supposed that the
rapidity of cooling of a body was proportional to the difference between
its temperature and that of the surrounding medium. This law is correct only for those bodies differing in temperature not more than 15~ or
20~ C. (59~ to 68~ F.)
Dulong and Petit made elaborate investigations upon this subject,




HEAT.                              43J
and determined that where the heated body was placed in vacuo at
temperatures ascending according to the terms of an arithmetic progression, the rapidity of cooling increased according to the terms of a
geometric progression, diminished, however, by a constant quantity,
this constant being the heat radiated back upon the cooling body from
the walls of the confining vessel. If the temperature of the vessel,
and that of the heated body, were both raised according to the terms of
an arithmetic progression, so that the difference between the two was
always constant, the rate of cooling increased according to the terms
of a geometric progression.
Radiation is found to take place more freely in vacuo than in air.
633. Universal radiation of heat.-Heat is radiated from  all
bodies, at all times, whether their temperature be the same as, or
different from, that of surrounding bodies; for it is the tendency of
heat to place itself in equilibrium.
In an apartment where all the articles are of the same temperature, each receives as much heat as it radiates, and, consequently, their temperature remains
stationary. Where some bodies are warmer than others, the warmer radiate
more than they receive, until finally all attain the same temperature. Hence
all bodies, however cold, will warm bodies colder than themselves; thus, frozen
mercury, placed in a cavity of ice, will be melted by the heat received from
the ice.
634. Apparent radiation of cold takes place when two parabolic
mirrors are placed opposite to each other, having a delicate thermometer in the focus of one, and a mass of ice suspended in that of the
other. The temperature of the thermometer will be seen to fall, apparently by the radiation of cold from the ice. The true explanation is,
that the thermometer is warmer than the ice, and radiating more heat
than it receives, thus loses heat, and the temperature falls. If the thernometer had been at a lower temperature than the ice, the phenomenon
would have been reversed.
The following remarkable instance of the apparent focalization of cold, is
explained in a similar manner. The experiment is due to the Florentine
Academician Porta in the sixteenth century. If a parabolic mirror is placed
with its axis pointing towards the sun, the heat-rays will be reflected to the
focus of the mirror. But if the mirror be turned so as to face the clear blue
sky, its focus becomes a focus of cold, and a delicate thermometer placed at that
point will sink, in clear weather, a few degrees in the day time, and as much
as 17~ F. at night. This ihenomenon is thus accounted for:-the thermometer
is constantly radiating heat in all directions; the mirror, being a paraboloid,
reflects to its focus only those rays that come in a direction parallel to its axis.
In that direction no rays come, for there is no source to reflect them, consequently the temperature of the thermometer falls. If a cloud passes over the
axis of the mirror, the thermometer instantly rises to its usual height.




440             PHYSTCS OF IMPONDERABLE  AGENTS.
e 5. Action of different Bodies upon Heat.
I. SURFACE ACTION.
635. Reflection  of heat.-Conjugate  mirrors. —Radiant heat,
like light, is reflected at the same angle at which it falls upon any reflecting surface. This law in respect to light has been fully illustrated
in the chapter on that subject.
If a piece of bright tin-plate is held in such a position as to reflect the light
of a clear fire into the face, the sensation of heat will be felt the moment the
light is seen.
Colnjugate mirros. —The reflection of heat may be shown in a still more
striking manner by the apparatus called the conjugate mirrors, fig. 477, consisting of two similar parabolic mirrors,                 4
arranged exactly opposite to each other,
at a distance of ten or twelve feet. In
the focus of one mirror is placed a heated  
body, as a mass of red-hot iron, and in  B
the other a portion of an inflammable
substance, as gunpowder or phosphorus.
Certain of the heat-rays pass directly
from A to B; the greater part, however,
reach B, by being twice reflected. The
rays emitted from A are reflected by the
mirror, M, in a direction parallel to its
own axis; these rays are received by the
second mirror, M, and, by reflection, are  -
conveyed to the focus B, igniting the gunpowder or phosphorus placed at that
point.
The reflection of heat in vacuo, takes place according to the same
laws as in air.
636. Determination of reflective  power.  Different bodies possess very different powers of re-                       478
flection.  This is well illustrated
by the  apparatus, fig. 478, de-  
signed by Leslie.
The source of heat is a cubical
tin canister, M, filled with boiling
water. A plate, a, of the substance
whose reflective power is to be determined, is placed between the mirror and its focus. The rays of heat
emitted from M, which are directed
upon the mirror N, are reflected 
upon the plate a, and from  this, —..
upon the bulb of the thermoscope, placed at the point where the rays are
brought to a focus.  The temperature indicated by the thermoscope is found to
vary with the nature of the plates.
The causes which modify the reflective power of bodies will be given hereafter.




HEAT.                                 441
637. Absorptive  power.-Different bodies possess very different
powers of absorbing the heat thrown  upon  them.  The absorptive
power of a body is always in the inverse ratio of its reflective power;
that is, the best reflectors are the worst absorbents, and vice versa.
The absorptive power of bodies may be determined by a modification of the
apparatus, fig. 478. At the focus of the mirror, N, is placed the bulb of a thermoscope, which is successively covered with different substances, as with lampblack, Indian ink, gum lac, metallic leaf, &c. Leslie has been the principal
experimenter in this department of beat. A smoke-blackened surface, and a
surface covered with carbonate of lead, absorb nearly all the radiant heat thrown
upon them; glass, -i9O; polished cast iron, T 5; tin,'46; silver,. 3-. Table
no. VIII., Appendix, gives the results obtained by Messrs. de la Provostaye
and Desains.
All black and dull surfaces absorb heat very rapidly when exposed to its
action, and part with it again slowly by secondary radiation. The different
powers of absorption, possessed by the different colors, may be illustrated by
repeating Franklin's experiment.  Pieces of the same kind of cloth, of different
colors, were placed upon the snow; the black cloth absorbed the most heat, so
that after a time it sunk into the melted snow beneath it, while the white cloth
produced but little effect; the other colored cloths produced intermediate effects.
Ranged according to their absorbent powers, we have, 1. Black (warmest of
all); 2. Violet; 3. Indigo; 4. Blue; 5. Green; 6. Red; 7. Yellow; and 8. White
(coldest of all).
638. Emissive or radiating power.-The earliest, and some of the
most valuable, observations upon this subject, were published by Sir
John Leslie, in his Essay on IIeat, in 1804.  Leslie proved that the
rate of cooling of a hot body is more influenced by the state of its
surface, than the nature of its substance.  It also varies greatly with
different substances, as may be seen in the table below.
Leslie employed in his experiments the apparatus, fig. 478. A bulb of a
thermoscope was placed in the focus of the mirror, the other bulb being protected from the radiant heat by a screen. The cubical vessel containing boiling
water, has its lateral faces covered with different substances, which are successively turned toward the mirror.
The table below gives the results as obtained by Leslie. Lampblack, possessing the greatest emissive power, is called 100.
Lampblack... 100  Indian ink... 88  Polished lead... 19
Water (by calc'n).100  Ice...... 85  Mercury.... 20
Writing paper.. 98  Minium...80  Polished iron... 15
Sealing wax.. 95  Plumbago.... 75           "   silver, tin,
Crown glass... 90  Tarnished lead.. 45          "   copper, gold, 12
Messrs. De la Provostaye and Desains, and also Melloni, have obtained results
differing somewhat from those of Leslie. See Table VI., Appendix. Melloni
found that the radiant and absorbent powers of surfaces were not always proportional, as the following table shows: —
~I            LpbaLampblaok. Carbonate of Lead. China Ink. Isinglass. Lac. Metallic Surface.
Absorptive power. 100            53         96       52   52       14
Radiant power. 100            100         85      91   72        12
40




442              PHYSICS OF IMPONDERABLE AGENTS.
Melloni has also found that the absorbent power of surfaces varied considerably, according to the source of the radiation, and the temperature of the
radiant body. (See Table IX.)
From Melloni's experiments may be drawn the following conclusions:
1. That bodies agree very nearly, but not exactly, in their emitting and
absorbent powers.
2. That their absorbent power varies very remarkably with the origin and
intensity of the calorific rays.
3. That they approach each other more and more in their power of emitting
and absorbing rays of heat, when the temperature approaches that of boiling
water; and that, when at exactly that temperature, the emitting and absorbent
powers coincide.
639. Causes which  modify  the  emissive, absorbent,  and
reflective powers of bodies. —Not only do different bodies possess
the powers of reflection, absorption, and emission in different degrees,
but the physical condition of the material affects them  in an important
manner. So also the obliquity of the incident rays, the source of heat,
and the thickness of the superficial layer, exercise great influence.
The absorbent and emissive powers of metallic plates are diminished if they
are hammered or polished. The opposite effect is produced if the plates are
scratched or roughened. This is doubtless owing to the change in density which
the superficial layers of the plates undergo by these operations. For the same
reason, the reflective power of a substance is generally increased by polishing
or hammering, and diminished by roughening or scratching it; which latter
also causes a portion of the heat to be irregularly reflected. That this is the
true explanation is probable from the fact, that if such materials as ivory or
coal are taken, whose density will not be changed by roughening or polishing,
the reflective and absorbent powers remain the same.
The thickness of the superficial layer has an influence on the reflective power
of bodies. Leslie covered a mirror with successive coatings of varnish; the
reflection diminished as the number of layers increased, until their thickness
amounted to twenty-five thousandths of a millimetre, when it remained constant. While a vessel covered with layers of varnish or jelly had its emissive
power increased with the number of layers, until they reached sixteen (with a
thickness of 0O034 m. m.), when it remained constant, even upon the addition
of other layers. The absorbent power of substances varies with the nature
of the source of heat. Thus a substance covered with white lead, absorbs
nearly all the thermal rays from copper, heated to 212~ F.; 56 of those from
incandescent platinum; and 53 of those from an oil lamp. Lampblack is the
only substance which absorbs all the thermal rays, whatever be the source of
heat. This subject has been ably treated by Prof. A. D. Bache.?
The absorptive power varies with the inclination of the incident rays; the
smaller the angle of incidence the greater is the absorption. This is one of the
reasons why the sun heats the earth more in summer and less in winter.
The reflective power of glass increases with the angle of incidence, but with
metallic surfaces the proportion of heat reflected diminishes with the angle of
incidence, and is the same as the proportion of light reflected, ~ 407.
640. Applications of the  powers of reflection, absorption,
*Am. Jour. Sci. [1] XXX. 16, 1836.




HEAT.                              443
and radiation are often made in the economical use of heat.  We
shall refer only to the more familiar examples.
Meat-roasters and Dutch-ovens are constructed of bright tin, to direct the
heat from the fire upon the article cooking.
Hoar frost remains longer in the presence of the morning sun upon lightcolored objects than upon the dark soil, because the latter absorbs much of the
heat, while the former, reflecting it, remain too cold to thaw the frost. Water is
slowly heated in bright metallic vessels, as in a silver cup or a clean bright
kettle, because they are poor absorbents, but if the sides and bottom of the
vessels become covered with soot, the water is heated quickly.
To keep a liquid warm it should be contained in a vessel composed of a poor
radiating material. Hence if tea and coffee pots, &c., are made of polished
metal, they retain the heat much longer than those which have a dull surface or
are composed of earthenware.
Stoves of polished sheet-iron radiate less heat, but keep hot longer than those
made of cast-iron with a rough and dull surface.
Pipes conveying steam should be kept bright or thoroughly covered with felt
or cloth until they reach the apartments to be warmed, and there their surfaces
should be blackened in order to favor the process of radiation.
II. DIATHERMANCY.
641. Transmission of radiant heat.-Light passes through all
transparent bodies from whatever source it may come.  The rays of
heat from  the sun also, like the rays of light from the same luminary,
pass through transparent substances with little change or loss. Radiant
heat, however, from terrestrial sources, whether luminous or not, is in
a great measure arrested by many transparent substances as well as by
those which are opaque.
The glass of our windows remains cold, while the heat of the sun, passing
through it, warms the room. A plate of glass held before the fire stops a large
part of the heat, although the light is not sensibly diminished.
Melloni terms those bodies which transmit heat diathermanous, or
diathermic (from the Greek, 8ad, though, and OzplaCivw, to heat); those
bodies which do not allow this transmission of heat are termed alhermanous, or adiathermanic (from alpha, privative, and Ozp.pai(w).
It appears that many substances are eminently diathermanous, which
are almost opaque to light; smoky quartz for example.
Prevost of Geneva, and De la Roche, in France, in  1811 and
1812, discovered many of the phenomena of diathermanous bodies, but
it is from the beautiful researches of Melloni, in 1832-1848, that our
knowledge upon this subject has been chiefly derived. Melloni, called
by De la Rive " the Newton of heat," died of cholera at Naples, in
August, 1854.
642. Melloni's apparatus.-The apparatus used by Melloni in his
researches upon the transmission of heat, is represented in all its
essential details in fig. 479.




444            PHYSICS OF IMPONDERABLE AGENTS.
At one end of the graduated metallic bar, L L, is placed the thermo-multiplier,
m, and in connection with it, by fine wires, A B, the anastatic galvanometer,
j 905, D. Upon the stand, %, is placed the source of heat; in this case a Locatelli lamp: F is a double screen to prevent the radiation of the heat from the
479

source, and is lowered at the moment of observation: E is a perforated screen
which allows only a certain quantity of rays to pass through it and to fall upon
C, which represents the substance whose diathermancy is to be determined.
In experimenting, the source of heat is placed at such a distance, that when
F is removed, the heat directed upon nm, will cause the needle of the galvanometer to move through 30~. The screen, F, is then raised, and the plate, C, to
be experimented upon, is placed upon the stand. When the needle of the galvanometer, D, has returned to 0~ (its normal position), the screen, F, is removed.
The proportion of heat transmitted through the plate, C, is then indicated by
the arc of vibration of the needle, over the dial plate of D. The construction
of the galvanometer and thermo-multiplier is more particularly described in the
chapter on thermo-electricity.
643. Influence of the substance of screens.-In experimenting
with liquids, they were placed in glass cells. The stratum of liquid
was 9'21 m. m. ('362 in.) in thickness.  The source of heat used was
an argand oil lamp.
The independence of transparency and diatherniancy was clearly
shown  in  these researches, for it was found that the bisulphid of
carbon transmitted three times as many heat-rays as ether, four times
as many as alcohol, and more than five times as many as water,
although these liquids are equally transparent and colorless. Table X
gives the diathermancy of different liquids.
It is found that those solids which are transparent to light do not
necessarily allow the passage of heat, and vice versa. Thus sulphate
of copper transmits the blue rays of light, but entirely arrests the rays




HEAT.                              445
of heat. Again, black mica, smoked rock-salt, and opaque black glass,
transmit a considerable portion of the heat-rays, but prevent the
passage of light.
Rock-salt is the only substance that permits an equal amount of heat
from all sources to pass through it. Melloni experimented with plates
of this substance of a thickness varying from one-twelfth of an inch to
two or three inches, and in all cases 92'3 of 100 rays incident upon
them  were transmitted.  The loss of 7-7 per cent. being due to a
uniform quantity which is reflected at the two surfaces of the plate.
Rock salt is, therefore, to heat, what clear glass is to light, and well
deserves the name which Melloni gave it,'of the glass of heat.
The diathermanic power of different solids for different sources of heat
may be found in detail in Table XIII.
644. Influence of the material and nature of the source.-The
quantity of heat transmitted through different solids of the same thickness is very variable. The nature of the source of heat exercises a
great influence on the diathermanic power of bodies. Melloni, in his
experiments, used four sources of heat, viz.: 1. The naked flame of a
lamp; 2. Incandescent platinum; 3. Copper heated to 700~ F.; and,
4. Copper heated to 212~ F.
645. Other causes which modify the diathermanic power of
bodies are the degree of polish, the thickness and number of the
screens, and also the nature of the screens through which the heat has
been previously transmitted.
The quantity of heat which a diathermanic body transmits, increases with the
degree of polish of its surface. The diathermanic power of a body diminishes with
its thickness, although according to a less rapid rate. Thus with four plates whose
thickness was as the numbers 1, 2, 3, 4; of 1000 rays, the quantity absorbed by
each was, respectively, 619, 577, 558, 549: so that beyond a certain thickness
of the body, the quantity of heat it can transmit remains nearly constant. Rocksalt is the only exception to this law; it always allows the same quantity of heat
to pass through it, at least for thicknesses between 2 and 40 m. m. ('0787 and
1-575 in.)
The increase of the number of screens produces an effect similar to
an increase of thickness. If many plates of the same kind are placed
together, they absorb more heat than one plate having the combined
thickness of several, owing to the numerous surfaces.
wle thermal rays which have passed through one or more diathermanic bodies,
are so modified, that they pass with more facility through other diathermanic
bodies than direct rays do. Thus the heat from an argand lamp, where the
flame is surrounded with a glass chimney, differs much in its transmissibility
from the heat of a Locatelli lamp, where the flame is free and open. Thus in
making use of.n argand lamp surrounded with a glass chimney, and a Locatelli lamp which is not thus protected, Melloni obtained the following results.
40*




446            PHYSICS OF IMPONDERABLE AGENTS.
TABLE OF HEAT TRANSMITTED FROM DIFFERENT SOURCES.
Of 100 rays.                Argand lamp.    Locatelli lamp.
Rock-salt transmitted                         92              92
Iceland spar  "                               62              39
Quartz (limpid) blackened, transmitted        57              34
Sulphate of lime              "               20              19
Alum                          "               12                7
646. Thermochrosy, or heat-coloration (OZspjo~, heat, and XpwIa,
color).-As Newton has shown that a pencil of white light is composed
of different colored rays, which are unequally absorbed and transmitted
by different media, and which may be combined together or isolated,
so Melloni argues from  his results, that there are different species of
calorific rays emitted simultaneously in variable proportions by the
different sources of heat, and possessing the property of being transmitted more or less easily through screens of various substances.
If a pencil of solar light falls successively upon two plates of colored glass,
one red and the other bluish-green, it will be wholly absorbed, the second plate
absorbing all the rays transmitted by the first. This is precisely analogous to
what may happen with a thermal pencil, its entire absorption being caused by
passing it through two media successively, each of which absorbs the rays
transmitted by the other. Viewed in this manner, it may be said that rock-salt
is colorless as respects heat, while alum, ice, and sugar-candy, are almost black.
It is a fact of common observation, that snow melts more quickly under trees
and bushes than in those spots which receive the direct rays of the sun. This
is proved by Melloni to be owing to the. fact, that the rays emitted by the heated
branches are of a different nature from the direct rays of the sun, and more
easily absorbed by snow than the latter.
647. Applications of the diathermancy of bodies.-The air is
undoubtedly very diathermanic, or else the upper layers would be heated
by the solar rays passing through them, while we know that they are
only slightly heated by this means.
In certain processes of the arts, workmen protect their faces by a
glass mask, which allows the passage of the light but arrests the heat
In certain physical experiments, where heat is to be avoided, the
light is first passed through a solution or plate of alum, whereby the
heat is arrested. On the contrary, if the heat is directed upon rocksalt
covered with lampblack, the light is arrested but the heat passes through
but slightly diminished.
648. Refraction of heat.-Heat, like light, is refracted, or bent
out of its course, in passing obliquely through diathermanic bodies, as
is shown by the burning-glass. A double convex lens, fig. 480, con



HEAT.                              447
centrates the rays of heat from  the sun, or other heated body, in
the same manner as it concentrates the rays of light.  It is only
with a lens of rock-salt, that the rays                480
of all our sources of heat can be con.
densed, for a lens of glass concentrates 
only the solar rays, and becomes itself
heated by artificial heat.  _
A lens of ice was made in England in
1763, having a diameter of 3 metres (118-112
in.), at whose focus gunpowder, paper, and
other combustibles were inflamed. Burning-glasses have generally more power than mirrors of equal diameter. Both produce their more intense effects on high mountains after a fall of snow, for then
the air is free from moisture, and the solar rays lose less of their intensity in
passing through it.
649. Polarization of heat. —Heat is polarized in the same manner
as light. It undergoes double refraction by Iceland spar, and the two
beams are polarized in planes at right angles to each other. A pencil
of heat, polarized by a plate of tourmaline, or by a Nicol's prism, is
transmitted or intercepted by another tourmaline plate or Nicol's
prism, in the same circumstances that a pencil of polarized light
would be transmitted or intercepted.
Heat also suffers a rotation of its plane of polarization, by plates of right or
left-handed quartz, in the same direction, and to the same extent as light of the
same refrangibility. Polarization of heat is also effected by reflection from
plates of glass, or by repeated refraction, also by reflection from the atmosphere,
in which points of no polarization and of maximum polarization exist corresponding with similar points in regard to polarized light. The phenomena
of magnetic rotary polarization of heat have also been observed.
Prof. Forbes of Edinburgh first demonstrated the polarization of heat.
Knoblauch has obtained distinct evidence of the diffraction and interference of the rays of heat.
1 6. Calorimetry.
650. Calorimetry.-The amount of heat required to produce a given
temperature varies greatly for the different bodies to which it is applied.
Calorimetry (from  calor, heat, and j/izpov, measure) is the measurement of the quantity of heat which different bodies absorb or emit
during a known change of temperature, or when they change their
state. Water absorbs or emits a much greater quantity of heat during
a change of temperature than the same weight of any other substance.
It is therefore selected as the standard of comparison.
Unit of Heat.-The quantity of heat which is required to raise
a pound of pure water from 32~ to 33~ F., is reckoned as the unit of
heat, or thermal unit, both in this country and in England.




448            PHYSICS OF IMPONDERABLE AGENTS.
In France, and in Europe generally, the thermal unit is the quantity
of heat necessary to raise one kilogramme (2-20486 lbs.) of water from
0~ to 1~ C.
651. Specific heat.-If equal weights of water and mercury at the
same temperature be placed over the same source of heat, it will be
found, that the mercury becomes heated much more quickly than the
water.  That when the water is heated 10~ the mercury will have
become heated 330~; the capacity of water for heat is, therefore, 33
times as great as that of mercury. Each substance in this regard has
its own capacity for heat. This relation is called caloric capacity, or
more commonly, specific heat. Table XI. contains the specific heats of
certain solids and liquids as determined by Regnault.
Three methods have been devised for determining the specific heat
of bodies: these are, 1st, the method of mixture; 2d, by the melting of
ice; 3d, by cooling.
Method of Mixture. —This method is exceedingly simple in theory,
and, with suitable care, exact in its results.
In determining the specific heat of solids by this method, a weighed mass of
each substance is heated to the proper degree, and is then plunged into a measure of water of known temperature and weight. The elevation of temperature
produced in each case is carefully noted.
If a pint of water at 150~ be mixed quickly with a pint at 50~ F., the two
measures of water will have a temperature of 1000, or the arithmetical mean of
the two temperatures before mixture. If, however, a measure of mercury at 50~
be mingled with an equal measure of water at 150~, the temperature of the
mixture will be 118-. The mercury has gained 68~ while the water has lost
32~. Hence it is inferred, that the same quantity of heat will raise the temperature of mercury through twice as many degrees as that of an equal volume of
water, and that the specific heat of water is to that of mercury as 1: 0-47 when
compared by measure.
If, however, equal weights of these bodies be taken, the resulting temperature
is then still more in contrast. A pound of mercury at 40~, mixed with a pound
of water at 156~, produces a mixture whose temperature is 152~-8. The water
loses 3~'7, while the mercury gains 112~03, and therefore, taking the specific
heat of water as 1, that of the mercury will be 0'033, since,
1120~3: 30~7 =  1: x  = (0-033.)
Method by Fusion of Ice.-This method is founded on the quantity of ice melted by different bodies in cooling through the same number
of degrees.
Lavoisier and Laplace contrived the apparatus, fig. 481, used for this purpose,
and called a calorimeter. It consists of three vessels made of sheet tin or
copper. In the interior vessel, c, pierced with holes and closed by a double
cover, is placed the substance whose specific heat is to be determined. This is
entirely surrounded by ice contained in the second vessel, b, and also on the
cover. In order to cut off the heat of the surrounding air, the exterior vessel, (,
is also filled with ice. The water from the ice melted in this outer vessel, passes




HEAT.                               449
off by the stop-cock, r. The body in the interior vessel, cooling, melts the ice
surrounding it, and the water from it flows off through the stop-cock, 8, and is
weighed.                                                     481
The specific heat of different substances is determined
in this apparatus by the comparative weights of the
water produced during the experiments; in which a
certain weight of each body cools from  an agreed 
temperature, e. g. (212~ F.), to 32~, the constant tem-          
perature of the vessel C.
The specific heat of a liquid is determined by placing
it in a vessel, as of glass, whose specific heat is known. 
The amount of ice melted by the liquid, is the whole
quantity of water produced, minus that which would
be melted by the glass alone.
This method, though excellent in principle, is subject
to many inaccuracies, and is now seldom employed.            _
The method of cooling is founded on the different rates of cooling
of equal masses of different substances; those having the greatest specific
heat cooling most slowly.
The application of this method is also attended with so many sources
of error that it is seldom employed, and need not be described.
Specific heat affected by change of state.-A body in the liquid
state has a greater specific heat than when it is in the solid form, as might be
concluded from the fact that the addition of heat is necessary to convert the
solid into a liquid.
Thus ice has a specific heat of 0'505, water being 1-000; sulphur solid, 0-2026,
fluid, 0-2340; phosphorus, between 45~ and -6~, 0-1887, at 212~, 0-2045, &c.
The high specific heat of water moderates very greatly the rapidity
of natural transitions from heat to cold and from cold to heat, owing to
the large quantity of heat emitted or absorbed by the ocean, and other
bodies of water, in accommodating themselves to variations in external
temperature.
652. Specific heat of gases.-If a unit of weight of any gas,
allowed to expand freely without change of pressure, is heated from
the freezing point one degree, the amount of heat thus absorbed, measured in fractions of the unit, is called the specific heat under constant
pressure. If the same gas is heated one degree, when so confined that
its volume cannot be increased, the amount of heat required to produce
the change of temperature is called the specific heat under a constant
volume.
When the heat required to raise the temperature of equal volumes
of different gases one degree, is determined, the results obtained are
called specifc heat by volume.  In these determinations the unit of
volume is the volume of a unit of weight of air when the barometi 
pressure is 30 inches.




450            PHYSICS OF IMPONDERABLE AGENTS.
The determination of the specific heat of gases is a problem involved in
the greatest practical difficulties, and authorities vary somewhat in the results
obtained.
The most valuable researches in regard to the specific heat of gases
have been made by Regnault.  He has established the following very
important preliminary principles:First. The specific heat of gases is sensibly the same at all temperatures.
Second. The amount of heat required to raise the temperature of a
given weight of any gas one degree does not vary with the pressure to
which it is subjected, and hence the specifc heat of gases is the same for
all densities.
Regnault experimented on air and other gases under pressures varied from
one to ten atmospheres, and found no sensible difference in the quantity of heat
which the same weight of a gas lost under these different pressures in cooling
the same number of degrees. Nevertheless he thinks it possible that slight differences may exist.
Table XI. c. gives the specific heats of different gases and vapors as determined
by Regnault. The specific heat by weight being determined under a constant
pressure, the gas being allowed to expand freely.
The specific heats by volume given in the table were obtained by multiplying
the specific heat by weight, by the specific gravity of the several gases and
vapors, as compared with air taken as unity.
653. Specific heat of gases under a constant volume.-It is
well known that the temperature of a confined mass of air can be
raised sufficiently high to ignite tinder by mechanical condensation,
# 739, and it seems reasonable to suppose that the same amount of heat
is expended in producing an equal degree of expansion when a gas is
heated.
It has been stated (608) that gases expand   ]-T part of their volume for an
elevation of temperature of 1~ F. Let t represent the small increase of temperature which a mass of gas undergoes when compressed 4aT of its volume, and
if S represent the specific heat of the gas under a constant pressure, and S' the
specific heat under a constant volume, we shall have for the specific heat under
S
a constant volume:-              S' =
1 +t
It is obvious that if the value of t could be determined by condensing a gas,
and observing the increase of temperature the value of S', the specific heat
under a constant volume could be readily calculated. The unavoidable loss of
heat absorbed by the walls of the containing vessel, when a gas is compressed,
has rendered it hitherto impossible to obtain accurate values of t by this method,
and similar difficulties have attended the determination of the specific heat under
a constant volume by other direct methods.
The principles of acoustics have happily furnished an indirect method
of determining the specific heat of gases under a constant volume with
great accuracy.




HEAT.                              451
Specific heat determined by the laws of acoustics.-By con
sidering the conditions of an elastic fluid during the transmission of a
sonorous wave, Newton obtained the following formula for the velocity of sound in any gas:               V=   g. L., d
In this formula V is the velocity of sound, g the force of gravity, H
the height of the barometer, and d the density of the gas referred to
mercury as unity. This formula gives for the velocity of sound in dry
air at 32~ F., when the barometer stands at 30 inches, V-  883 feet,
which is less than the true velocity of sound (1086 feet, 1 344) by more
than one-sixth of the whole.
Laplace discovered that this error resulted from the effect of heat
developed and absorbed by alternate compression and rarefaction of
the air in the transmission of sonorous waves, and he showed that the
formula for the velocity of sound, taking into account this effect of heat,
should be,  V= -     g.. i ~, in which S represents the specific heat
\ d S/
of the gas under a constant pressure, and S' the specific heat under a
constant volume.
From this formula we obtain, by transposition, S' =-  Vd ~    from which
we readily obtain the value of the specific heat of a gas under a constant volume, when the velocity of sound in the medium, and the other
constant quantities, are known.
By this method Dulong has obtained for the specific heat of gases,
under a constant volume, the values given in the following table; but
the results obtained are regarded only as approximations:SPECIFIC HEAT OF EQUAL VOLUMES.*
N     of   lfUnder Constant Under Constant   Difference
me ofGas.    pressure.     volume.  S-                 1 + t.
Air.....           0-2377   1   0-1678t  0-0699t  1417t
Oxygen,...        0-2412   1 0-1705          00707         1-415
Hydrogen,..       02356   1   0-1675          0-0681       1-407
Oxyd of carbon,      0-2399        0 1681       0-0718        1-428
Carbonic acid,.     0-3308        02472        00836         1-338
Olefiant gas,..      03572       0-2880        0-0692        1-240
Comparing these results in the case of air, we see that when air is heated
in a situation where it is free to expand, only about 4 of the heat applied
is expended in producing elevation of temperature-as in heating. a
* Cooke's Chemical Physics.
t Corrected according to the most recent experiments.




452           PHYSICS OF IMPONDERABLE AGENTS
room-while about I of the heat is expended in producing expansion
of the air, to be given out again as the room cools.
Dulong has deduced from  his experiments the following conclusions:
1. Equal volumes of all gases, measured at the same temperature and
pressure, set free or absorb the same quantity of heat when they are compressed or expanded the same fractional part of their volume.
If all gases had the same specific heat, the same change of volume
would be attended by the same change of temperature.  But this is
the case only with oxygen, hydrogen, and nitrogen. The specific heats
of compound gases differ considerably from each other, and change of
volume causes less change of temperature in proportion as the specific
heat of the gas is greater.
2. The variations of temperature which result, are in the inverse ratio
of the specific heats under a constant volume.
Whether these laws are the exact expressions of the truth, or only
approximately correct, remains to be determined by further investigation.
654. Relation between the specific heat and atomic weight of
elements and compounds.-Dulong and Petit, from their researches
upon the elements, were led to conclude, that the ultimate atoms of all
elements possessed the same capacity for heat, and they accordingly
announced the law, that:The specific heat of elementary substances is in inverse ratio to their
atomic weights.
This law appears to be true for most of the elements, as will be seen by
examining Table XI. of Atomic Weights and Specific Heats. It will be noticed,,that the one increases in almost the exact proportion in which the other
diminishes, and that by multiplying them together, a very nearly constant product is obtained. Some elements, as those given in the lower part of the table,
give a product (C X p) double of the others. So that equivalent weights of
these would contain twice as much heat as equivalent weights of those first
given.
The relation between the specific heat and atomic weight of compounds is
expressed by Regnault in the following law:In all compound bodies containing the same number of atoms, and oJ
similar chemical constitution, the specific heats are' in inverse ratio to
their atomic weights.
~ 7. Liquefaction and Solidification.
655. Latent heat.-During the conversion of a solid into a liquid,
or of a liquid into a gas or vapor, a certain quantity of heat is absorbed
or disappears.  As the thermometer and the senses give no evidence
of the existence of this heat, it is called latent heat.
Let a pound of ice and a pound of water, each at the temperature of 32~, be




HEAT.                               453
exposed to the same source of heat in precisely similar vessels; it will be
found, at the moment when all the ice is melted, that the water into which it is
converted has still the temperature of 32~; while the temperature of the other
pound of water has risen from 32~ to 174~. As both have received the same
amount of heat, it follows, that the 142~ which have disappeared, have been used
in converting the ice into water, and have become latent or insensible.
If a pound of water at 212~ be mixed with a pound of powdered ice at 32~,
when the ice is melted the two pounds will have the temperature of only 52~;
the ice gains only 20~, while the water loses 160~. Here again 142~ have disappeared or have become latent.
656. Liquefaction and congelation are always gradual, owing
to the absorption or evolution of heat during these processes.
If this was not so, water at 32~ would immediately become ice, upon losing
the smallest additional portion of its heat, and on the other hand, ice would
suddenly pass from the solid to the liquid state by the smallest addition of heat.
This fact, coupled with the law of irregular expansion of water, will explain
why ice never acquires any very great thickness. The high specific heat of
water acts to moderate the natural changes of temperatures.
657. Freezing mixtures.-Solids cannot pass into the liquid state
without absorbing and rendering latent, a certain amount of heat.  If
the heat necessary for the liquefaction is not supplied from some external
source, the body liquefying will absorb its own sensible heat. A knowledge of this fact enables us at pleasure, in the hottest seasons and
climates, to produce extreme degrees of cold.
The so-calledfreezing mixtures are compounds of two or more substances, one of which is a solid.  These, when mixed together, enter
into combination and liquefy.  The operation should be so conducted,
that no heat can be absorbed from external sources, and hence, as the
substances liquefy, a depression of temperature results proportional to
the heat rendered latent.  (See TableXII.)
The most convenient freezing mixture is salt 1 part, and ice or snow 2 parts,
universally used in the freezing of ices and creams. With this freezing mixture,
a temperature of 4~ or 59 below zero can be maintained for many hours. A
solution of equal parts of nitre and sal-ammoniac will reduce the temperature
from 50~ to 10~ F. Very well constructed ice-cream freezers are now commonly
sold in the shops, in which an adroit use has been made of the laws of radiant
heat and conduction, to facilitate the rapidity of this operation.
Thilorier, with a mixture of solid carbori-. acid and sulphuric acid, or sulphuric
ether, obtained a temperature 120" below, zero. Mbre lately, Mitchell obtained by
the same means a temperature.of-130~ and — 146~ F. At the former temperature,
alcohol (Sp. Gr. 0'798) had the consistency of oil, and at the latter temperature
resembled melting wax.
In the liquefaction of metallic alloys, a similar depression is observed. When
an alloy composed of 207 parts lead, 118 tin and 284 bismuth, is dissolved in
1617 parts mercury, the temperature will sink from 63~ to 14~ F.
In producing extreme degrees of cold, the substance to be operated upon is
first cooled to a certain degree by a less powerful freezing mixture, before the
more energetic one is used; the full effect of the latter is thus obtained.
41




454            PHYSICS OF IMPONDERABLE AGENTS.
658. Laws of fusion and latent heat of fusion.-Expansion (the
first effect of heat) has a limit, at which solids become liquids.  The
powers of cohesion are then subordinate to those of repulsion, and
fusion results.
Fusion takes place in accordance with the following laws:1st. All solids enter into fusion at a certain temperature, invariable
for the same substance.
2d. Whatever may be the intensity of the source of heat when the
fusion commences, the temperature remains constant until the whole mass
is fused.
3d. The latent heat of fusion is obtained by multiplying the difference between the specific heat of the substance in its liquid and solidform,
by the quantity obtained by adding the number 256 (an experimental constant furnished by researches upon the latent heat of water) to the melting
point ofj the substance in question.
The fusion points and latent heat of fusion of a number of the more
important substances are given in Table XV. of the Appendix, drawn
from the labors of Regnault and others.
659. Peculiarities in the fusion of certain  solids.-Certain
solids soften before they become liquefied; such are tallow, wax, and
butter, while others never become entirely fluid. This is because the
former are composed of several substances, which melt at different temperatures. Metals, like iron and platinum, that are capable of welding,
soften before they fuse. Glass, and certain metals, never attain perfect
fluidity. The fusion of sulphur presents striking peculiarities. (See
Chemistry.)
660. Refractory bodies.-Substances difficult of fusion are called
refractory bodies.
Among the most refractory bodies are silica, the metallic oxyds, lime, baryta,
alumina, &c. Their fusion may be effected by the oxy-hydrogen blow-pipe, or
by the use of the voltaic battery. By these means, also, the fusion of platinum
is effected, which resists the heat of a powerful blast-furnace, although a thin
wire of this metal can be melted by the mouth blow-pipe.
Carbon is the most refractory of all bodies. Its fusion has not yet been per.
fectly effected; although, by means of the voltaic battery, Professor Silliman
obtained (in 1822) unequivocal evidences of the volatility and partial fusion of
this substance: and more lately these results have been verified by Despretz,
with a carbon battery of 600 cups; boron and silicon also yielding to the same
power.
661. Solution.-Saturation. —When a solid immersed in a liquid
gradually disappears, the process is termed solution. Thus, sugar and
salt dissolve in water, camphor in alcohol, &c. Solution is the result
of an attraction existing between the particles of a liquid and those oe




HEAT.                               455
a  olid. A liquid is said to be saturated when, at a given temperature,
it has dissolved as much as possible of a solid.
The causes which diminish cohesion among the particles of a solid, generally
facilitate solution.  Thus, a pulverized body dissolves quicker than the same
quantity in large masses. Heat also facilitates solution by diminishing the
cohesive force and producing currents. The solubility of some bodies is diminished by heat, and the precipitation of bodies from solution is sometimes
hastened by heat,-sulphate of soda and hydrate of lime are examples of the
former.
662. Laws of solidification.-The passage of a body from  the
liquid to the solid state, always occurs in accordance with the following
laws:1st. The solidification of a body takes place at a certain fixed temperature, which is also that of its fusion.
2d. The temperature of a body remains constant from  the commencement to the end of its solidification.
663. Elevation  of temperature  during  solidification.-When
liquids return to the solid state, the heat which has been absorbed
during their liquefaction, and rendered latent, is given out.
If the solidification takes place suddenly, the heat evolved is often very apparent. Thus water may be cooled to 22~ or 23~, and yet remain liquid, but if in
that state it is shaken, it becomes at once a confused mass of ice crystals, and
rises to 32~, the freezing of a part giving out heat enough to raise the temperature of the whole 8~ or 10~. Thus we arrive at the seeming paradox, that freezing
is a warming process; and, owing to the absorption of heat during liquefaction,
it is equally true, that melting is a cooling process. Hence, in part, the cooling
influence of an iceberg, or of a large body of snow on a distant mountain.
664. Change of volume during solidification, and its effects.Mercury, and most metals, contract while solidifying; hence, the freezing of a mercurial thermometer does not burst its reservoir. Water
expands during freezing to the amount of one-eleventh of its bulk;
hence, ice floats on the surface of water, and close vessels, even of iron,
are burst, if frozen when full of water.
This fact is familiar to housekeepers, who prevent the bursting of their watercasks during winter, by a stick of wood placed in the cask, about which the
bulge from expansion takes place. Aqueduct service-pipes are often saved from
the same accident in cold weather, by allowing the water to flow uninterruptedly,
thus preventing the formation of ice crystals, both by motion and the supply
of warmer water.
A brass globe filled with water burst at 32~, in the experiments of the Florentine Aeademicians, who estimated the force exerted as equal to 2S,000 pounds
on the square inch. A bomb-shell, filled with water, and tightly closed by an
iron plug, when exposed to severe cold in Montreal, discharged the plug to a
distance of 400 feet, and a cylinder of ice eight inches in length protruded from
the hole. All metals which, like water, assume the rhombohedral form  on
solidification, produce sharp casts. Such are cast-iron, antimony, tin, zinc, and
bismuth. All alloys capable of producing sharp casts, must contain such a




456            PHYSICS OF IMPONDERABLE AGENTS.
metal. Type-metal (3 lead and 1 antimony), brass (2 copper and 1 zinc), and
bell-metal (7 copper and 3 tin), are familiar examples. Copper, lead, gold,
silver, and indeed most metals, except those above enumerated, crystallize in
the monometric system, and occupy less space as solids than as fluids, producing
imperfect casts. Hence, coins are stamped, and gold, silver, and copper utensils,
and ornamental wares are wrought by the hammer, or stamped, to secure sharpness and beauty.
665. Freezing of water.-Water ordinarily freezes at 32~; but it
has already been stated (663) that, under certain circumstances, it
may be cooled near to 220, and remain liquid.  If, however, water is
turbid, or contains carbonic acid, it always freezes at 32~.
Certain experiments made in France indicate that the temperature to which
water may be exposed without freezing, falls in proportion as it is exposed in
tubes of smaller diameter. This remarkable circumstance seems to throve light
upon the fact, that plants, whose capillaries are full of juices, resist frost in a
manner so noticeable as many of them do. Nevertheless, in very severe weather,
the trunks of large trees are sometimes burst open by frost.
Water, containing salts in solution, freezes at a lower temperature than pure
water. Thus, sea water freezes at 27~. The ice formed from salt water, and
from impure or turbid water, is comparatively fresh and pure, since it is the
water which freezes, and not the foreign bodies it contains. Frozen ink, and
other colored fluids, precipitate the coloring matter, and are spoiled as colors,
until, by boiling, the precipitate is again diffused. Likewise, the watery portion
of cider, and other weak alcoholic liquors, exposed to moderate cold, congeals;
and the alcoholic part may thus be obtained in a more condensed state.
Some absorbent rocks are pulverized, and gradually covered by a thick bed
of soil, by the effects of freezing water in breaking down their solid mass. The
value of building-stones, in our climate, depends much upon the resistance they
offer to the action of frost. In hot climates the effect is not seen, and the crags
and summits of mountains are there generally more sharp. Experiments to
determine the resistance of rocks to frost, are made by saturating cubes of the
material with water, and repeatedly freezing them.  But the same result is more
conveniently obtained by using a solution of sulphate of soda. This salt, crystallizing on exposure to the air, effects the same results.
666. Absolute zero.-Since the permanent gases contract dT of
their volume at 32~, for each degree of Fahrenheit below that point (or
expand that quantity for each like increment of heat above 32~), it has
been inferred by Clement and D6sormes that, at the temperature of
-459~ F. they would cease to exist as gases, since the amount of contraction would then be equal to their initial volume. Likewise, since
the volume of a gas is doubled by heating from 32~ to 523~, they further
inferred that the quantity of heat added must be equal to that held by
the initial volume, and that at -459~ F. there must be an absolute zero.
~ 8. Vaporization and Condensation.
667. Vaporization.-Liquids become vapors upon receiving a certain quantity of heat. Thus, water at 212~ is rapidly converted into
steam, which, at or above that temperature, remains as an invisible




HEAT.                                457
vapor. This change of state presents some of the most interesting and
important phenomena of physics.
Evaporation occurs only at the surface of liquids, quietly, as in the insensible
changes of water to vapor in an open vessel. Boiliyg or ebullition,, is the rapid
formation of vapor throughout the whole mass of liquid, producing more or less
agitation.  Sublimation is the change of solids to vapors without the intermediate liquid condition. Arsenic, iodine, and camphor are examples of solids
which may be so changed.
The remarkable disappearance of nearly one thousand degrees of
heat when water is turned into steam (and correspondingly for other
liquids), will be considered under Latent Heat of Steam,   683.
668. Formation of vapors in a vacuum.-Evaporation takes place
slowly in the open air, owing chiefly to the atmospheric pressure.  In
a vacuum, however, it occurs instantaneously, because the vapor then
meets with no resistance.  This phenomenon occurs in obedience to
the following laws:1st. All volatile liquids, in a vacuum, volatilize instantly.
2d. At the same temperature the vapors of diflerent liquids possess
unequal elastic force.                                       482
These laws are illustrated in the apparatus, fig.      4       1? A 1 C-D 
482, where four barometer tubes, originally filled
with pure dry mercury, are supported by the stand
in a mercurial cistern, and will all indicate upon the
scale, C, the same height of column. A drop of ether 
passed up to E, instantly flashes into vapor, and de-  
presses the column perhaps half its height or more.
This illustrates the first law. A drop of bisulphid of
carbon introduced into D; of alcohol into B; and of
water into A, will also be respectively changed to
vapor, wholly, or in part, and will depress the mercury unequally, in the order of their volatility as
enumerated. This illustrates the second law. If all
the ether introduced into E has disappeared, then
successive small portions may be added, and with
each addition an increased depression of the mercury
will be observed, until, finally, a point is reached
where the ether remains liquid. This is the point
of saturation, or maxinmum tension of ether vapor for 
that temperature. A change of temperature will, of
course, vary these conditions.  If either of the tubes _           I
ia surrounded by one of larger diameter dipping
under the mercury, and so affording a cell into which 
hot water may be poured, the liquid ether in E, for
example, will be vaporized, still further depressing the mercury, according to
the temperature. If a freezing mixture were similarly used, the reverse would
be seen-a portion of vapor would be liquefied, and the mercury will rise in
proportion.
41*




458            PHYSICS OF IMPONDERABLE AGENTS.
669. Saturated space or maximum  tension of vapors.-The
meaning of these terms may be still further illustrated by the use of
the apparatus in fig. 483, which is provided with a          483
well, filled with mercury, and deep enough to allow
the tube to be depressed nearly its whole length.
Suppose the tube to have the condition of E in the last
paragraph; that is, the vapor of ether has nearly filled
the whole tube, and is at its point of saturation or maximum tension. If the tube is now depressed, the contained
vapor is subject to increased tension, in proportion to the
amount of depression; and the result is, that a portion
of it becomes liquid, and the mercury takes the place
of the vapor. If the tube is raised, then the pressure is
again diminished, and a fresh portion of ether is vaporized.
There is, therefore, a maximum tension or elasticity for the:
vapor of different liquids at every temperature; so that, in
a saturated space, at a given temperature, the maximum 
tension is the same, whatever may be the pressure to which
the vapor is subjected.
670. Dalton's law  of the tension of vapors is
as follows:
The tension or elasticity of different vapors is equal,
if compared at temperatures the same number of degrees above or below the boiling point of their respective
liquids.
This law does not perfectly accord with the results
of experiment, but it is nearly correct (except for
mercury), at short distances above and below the               -1
boiling point.  See Table XIV.
671. The tension of vapors in communicating vessels unequally heated is the same, and is equal to that of the lower temperature.
Thus, if a vessel containing water at 32~, communicates by a tube with a
vessel in which the water is boiling, the pressure in both of the vessels will be
the same, as may be ascertained by a manometer. This is explained by the
condensation which the vapor constantly suffers in the colder vessel. Application is made of this principle in the condenser of the steam.engine.
672. Temperature and limits of vaporization.-The evaporation
of liquids takes place at temperatures much below their boiling points,
as common experience testifies.  Even at the ordinary temperature of
the air, water, many liquids, and even some solids vaporize.
Even mercury, whose boiling point is 662~, evaporates at all temperatures
above 60~ F., as was proved by Faraday. He suspended from the cork of a flask
containing mercury, a slip of gold leaf. After six months, the gold leaf was
found to be whitened by the mercury which had risen in vapor. A dew of
metallic globules is sometimes seen in the Torricellian vacuum. Iodine, camphor, and other solids, rapidly evaporate at the ordinary temperature. Snow




HEAT.                              459
and ice disappear from the surface of the earth during cold weather when there
has been no thawing. Boyle found that two ounces of snow, in' a very cold
atmosphere, lost ten grains in six hours.
The experiments of Faraday, however, appear to show that vapori
zation does not occur at all temperatures.
Thus, mercury gives off no appreciable vapor below 60~. Sulphuric acid
undergoes no appreciable evaporation at ordinary temperatures.  Faraday
proved that several substances which are volatilized by heat at temperatures
between 300~ and 400~, did not suffer the slightest evaporation when kept in a
confined space at the ordinary temperatures during four years.
The limit of evaporation is reached when the Cohesive force of the particles
of the solid or liquid overcomes the feeble tendency to evaporation.
673. Circumstances influencing evaporation.-Evaporation, as
has been said, is the slow production of vapor from the surface of a
liquid. The elastic force of a vapor which saturates a space containing
a gas (like air) is the same as in a vacuum. The principal causes
which influence the amount and rapidity of evaporation, are as follows:
1st. Extent of sulrface. As the evaporation takes place from the surface, an
increase of surface evidently facilitates evaporation.
2d. Temperature, by increasing the elastic force of vapor, increases the rapidity
of evaporation; therefore, the temperature of ebullition marks the maximum
point of evaporation.
3d. The quantity of the same liquid already in the atmosphere, exercises an
important influence on evaporation. When the air is saturated, evaporation
ceases; it is, therefore, greatest when the air is free from vapor.
4th. Renewal of the air facilitates evaporation, since new portions of air,
capable of absorbing moisture, are presented to it; hence evaporation is more
rapid in a breeze than in still air.
5th. Pressure on the surface of the liquid influences evaporation, because of
the resistance thus offered to the escape of the vapor.
Prof Daniell, from a series of researches on the rate of evaporation, deduced
the following law, viz.:The rapidity of evaporation is inversely as the pressure upon the surface of the
evaporating liquid.
674. Dew-point.-If air saturated with moisture is cooled, a portion of the moisture will be precipitated as dew.  The temperature at
which this deposition of moisture commences, is called the dew-point.
The dew-point is nearer the temperature of the atmosphere, the more
fully the air is saturated with moisture. The methods of determining
the amount of moisture contained in the atmosphere, will be described
in the chapter on Meteorology.
675. Ebullition. —The elasticity of the vapor from a boiling liquid
is equal to the pressure of the superincumbent atmosphere.
When water is boiled in a glass vessel, the phenomena of ebullition may be




460            PHYSICS OF IMPONDERABLE AGENTS.
distinctly seen. On first heating a liquid, the dissolved air is expelled in
small bubbles. As the heat is continued, bubbles of transparent and invisible
steam are formed in the lower part of the vessel where the heat is applied.
These grow smaller and smaller as they rise, and finally condense in the colder
liquid with a series of little noises, producing what we call simmering. After a
time, when the mass of liquid attains a nearly uniform temperature, these bubbles increase in size as they rise to the surface, owing to the evaporation from
their interior surfaces, as well as from the less pressure to which they are there
subjected. As they reach the external air, at the surface of the liquid, they condense in a cloudy vapor, which is commonly called steam, but which, in reality,
is water in exceedingly minute globules, steam itself being invisible.
When a liquid has reached the boiling point, a comparatively small quantity
of heat maintains it at that temperature.  Water, or any other liquid, boiling
moderately, has the same temperature as when it is in violent ebullition; the
excess of heat only causing a more rapid evaporation of the water. The boiling
points of certain liquids are shown in Table XVII.
676. Circumstances influencing the boiling point. —The principal of these are: —
1. Adhesion. It is probably owing to the different degrees of adhesion between the liquid and the surfaces of the vessels, that the boiling
point of water varies in vessels of different materials.
2. Solids in solution in liquids raise their boiling points in proportion to the
quantity dissolved. Thus, a saturated solution of common salt boils at 227~ F.;
of nitre at 240~; of carbonate of potash at 275~; and of carbonate of soda at
2200. This is probably owing to the adhesion existing between solids and
liquids, which opposes itself to the repulsive force of heat. The vapor rising
from boiling solutions, Rudburg says, has only the temperature of steam from
pure water boiling in free air. According to Regnault, the temperature of the
vapor of a boiling saline solution, appears very nearly equal to that of the
liquid. It is extremely difficult to obtain accurate results, because the bulb of
the thermometer becomes covered with a film of condensed water.
3. Pressure.  As ebullition consists in the rapid formation of vapor
of the same elasticity as the superincumbent atmosphere, it is evident,
that if the pressure is diminished, the boiling                484
point will be lowered; and if it be increased, that
the boiling point will be raised. 
The influence of pressure on the temperature of ebul-   
lition, is strikingly shown by placing a vessel of water,
which has cooled considerably below the boiling point,       I 
beneath the receiver of an air-pump and exhausting the
air, fig. 484. As the air is removed, the water enters               l
into violent ebullition, even at a temperature of 125~.           I
Liquids generally boil in vacuo at a temperature of from
70~ to 140~ below their point of ebullition under the ordi-  -
nary atmospheric pressure; Black says 1400 forall liquids.
TableXVI., fromRegnault, shows the temperature at
which water boils under different pressures, represented by the corresponding
heights of the barometric column. These results have been confirmed by direct
observation.




HEAT.                               461
In Table XVIII. is given the boiling point of water at different places, with
their corresponding elevation above the level of the sea.
677. The culinary paradox is an excellent illustration of the phenomena of boiling under diminished pressures.                  485
A small quantity of water is boiled in a glass flask
until the steam  has driven out the air. When the,/
water is in active ebullition, a good cork is firmly    -. 
inserted in the mouth, and the heat is removed. The
flask is then supported in an inverted position, as 
is shown in fig. 485. The water still continues to 
boil more violently than when over the flame. If cold
water be poured upon the flask, the ebullition becomes
still more violent, but will be speedily arrested by the 
application of hot water.
The cause of this seeming paradox is plain. When
the flask was corked, there was only the vapor of          ll        1
water above the liquid, the air being driven out by         l   I
the previous boiling. By the application of cold'
water, a portion of this vapor becomes condensed,
and the water within being under diminished pressure, boils at a correspondingly low temperature.
But hot water thrown upon the flask increases the
elasticity of the vapor, and the water being thus
subjected to a greater pressure, ceases to boil.             - 
Franklin's pulse glass, a double bulbed glass, fig. 486, partly filled
with ether and closed while boiling; boils from the         4S6
heat of the hand, a sensible coolness being felt as
the last portions of fluid rush out of the empty:  
bulb, the hand furnishing the heat needed to vaporize the ether.
678. Useful applications in the arts are constantly made of the
facts just explained, to concentrate vegetable extracts, cane-juice, &c.,
under diminished pressure, and consequently at a temperature below
the point where there is any danger of injury from heat. Sugar is
usually concentrated thus in large close copper vessels, called vacuumpans, at a temperature of 150~ F., aided by a powerful air-pump and
condenser to remove the vapor rapidly. There is no economy of fuel
by boiling under diminished pressure, as will be understood from what
is said hereafter.
679. Measurement of heights by the boiling point.-Hypsometer.-On ascending mountains, the boiling point of liquids falls,
because the atmospheric pressure is less, and conversely in descending
into mines, it rises. Accurate observations show, that a difference of
about 543 feet in elevation produces a variation of 1~ F. in the boiling
point of water. The metastatic thermometer (579) is used in these
observations. Fahrenheit first proposed determining the heights of
mountains by the depressed temperature cf boiling water.




462            PHYSICS OF IMPONDERABLE AGENTS.
Regnault has designed an apparatus called a hypsometer, fig. 487, for
determining elevations by the boiling point of water. It consists of a copper
vessel, C, containing water. This is surmounted by a brass cylinder which
supports and encloses a thermometer. The upper part of this cylinder is formed
in pieces, t, which slide into each other like the tubes of a telescope, and serve
to confine the steam about the thermometer tube, as in fig. 443. Air is supplied
to the lamp, I, by the holes, o, o. The steam escapes by a lateral  487
orifice in the upper part of the instrument.       488 
680. High  pressure  steam.-The 
boiling point rises as the pressure increases.  This fact is  readily  demon- 
strated  in a general way by  Marcet's
apparatus, fig. 488. 
A spherical boiler is supported over a lamp      A
upon a tripod of brass.  A thermometer, t,
enters the upper hemisphere, and its bulb is                           t
exposed directly to the steam. A stop-cock
and safety valve, V, opens a communication
to the outer air. A manometer tube, A, with  l
confined air (280) descends into some mercury
placed in the boiler (whose lower hemisphere
is for that reason made of iron). The boiler
is filled with water to the equator.  When the   l
water boils and the air has been expelled, the
open stop-cock is closed and the steam commences to accumulate.  The thermometer,
which stood previously at 212~, begins to rise 
higher and higher as the column'of mercury
rises in the gauge. When the mercury has  _-   I_                     l
risen in the gauge a little less than half  _^I B
the height of the tube, the thermometer will..
indicate 2490~5 F., when two-thirds of the way 2730~3, and so on. Table XIX.
gives the boiling point of water at different atmospheric pressures as ascertained by Regnault.
Advantage is taken of the temperature of high steam in the arts to extract
gelatine from bones, and to perform other difficult solutions and distillations
which, at 2120, would be impossible. Papin, a French physicist, who died in
1710, first studied these effects of high steam with an apparatus known as
Papin's digester. It is only a boiler, of great strength, provided with a safety
valve (then first used).
681. Production of cold by evaporation.-A liquid grows sensibly colder, if while evaporating it does not receive as much heat as it
loses, and the more sensibly so, as the evaporation is more rapid.
Eau de cologne, bay-rum, or ether, evaporating from the surface of the skin,
produces very sensible coldness, due to the rapid absorption of the bodily heat
in the evaporation. Portions of body may be thus benumbed and rendered
insensible to pain during surgical operations.




HEAT.                                463
A summer shower cools the air by absorbing heat from the earth and the air
during evaporation. Curtains wet with water, called tatties, much used in India;
leafy branches of trees, mossy banks, and fountains draped by climbing plants,
are cool for the same reason. Fanning the surface produces coolness both from
conduction and evaporation. Wet clothes are pernicious, chiefly from the rapid
loss they cause of animal heat during evaporation, thus impeding the circulation. In hot climates, where ice is rare, water is cooled to an agreeable
temperature by the use of jars of porous earthenware placed in a draught of
air. The surface moisture is rapidly evaporated by the dry air, and the water
in the vessels falls 20 or 30 degrees below the exterior air, even at 80 or 90
degrees.  Water is readily frozen in a thin narrow test-tube by the constant
evaporation of ether from a muslin cover drawn over the outside of the tube.
In the East Indies, water is frozen by its own evaporation, aided by radiation,
in cool serene nights, when the external air is not below 40'. For this purpose
shallow earthen pans are used, placed in a slight pit or depression of the earth
upon straw to cut off terrestrial radiation.                 489
Water is endowed with a remarkable emissive
power, and will, as shown by Melloni, lose 7~ be-      --          -
low the atmosphere by simple radiation in serene
nights.  Compared to this remarkable Indian
result, Leslie's experiment of freezing water in
the vacuum of an air-pump (over sulphuric acid 
to absorb the vapor, fig. 489) seems simple; and easier still is the same effect
produced in the cryophorus (orfrost-bearer) of Dr. Wollaston, fig. 490, where a
portion of water in one                           490
bulb of a vacuous glass
tube is frozen by its own
rapid evaporation due to   I <'
cooling the empty bulb in
a freezing mixture.
Twining's ice machine.-An apparatus has been successfully contrived by Prof. Alex. Twining
for producing ice upon a commercial scale in those hot climates where it cannot
be carried from colder countries, by the rapid evaporation of a portion of ether
confined in metallic chambers contiguous to the water vessels-the process, by
aid of an air-pump and condenser, being continuous and without sensible loss
of ether. This plan is equally applicable to cooling the air of apartments, either
for the preservation of provisions or for the comfort of the occupants.
682. Latent heat of steam.-A  large amount of heat disappears
or is rendered latent during evaporation.  According to Regnault, the
latent heat of steam is 957~05.  Its determination is made in a number
of ways.
If a vessel containing water at the temperature of 32~ is placed over a steady
source of heat, it receives equal additions of heat in equal times. Let the time
be noted that is required to raise the temperature to 212~. If now the heat is
continued until all the water is converted into steam, it will be found that the
time occupied in the evaporation was 5~ times that required to heat the water
through the first 180~, i. e., from 32~ to 212~. Consequently 51 times as much
heat is absorbed during the evaporation of water as is required to bring it to
boiling point. The latent heat of steam is therefore about (1800 X  5X) 990~.




464            PHYSICS OF IMPONDERABLE AGENTS.
Again, the latent heat of steam is determined by distilling a certain amount
of water and condensing the steam in a large volume of the same liquid. If
the temperature be noted before and after the experiment, it will be found that
the heat from the steam formed from a pound of water, was sufficient to raise
the temperature of ten pounds of water 99~. The latent heat of steam is therefore again found to be (99~ X 10) 990~.
Experiments conducted in the simple manner just mentioned cannot be
entirely accurate, owing to a certain loss of heat by vaporization, conduction,
and radiation. Numerous precautions are therefore to be adopted to insure the
accuracy science demands in such an investigation, the details of which aro
inconsistent with our limited space.
The latent heat of steam obtained by different experimenters, varies
somewhat as follows: —Watt, 950~; Lavoisier, 1000~; Despretz, 9550-8;
Brix, 972~; Regnault, 967~'5; Fabre and Silberinann, 964~'8.
683. Latent and sensible heat of steam  at different temperatures.-The whole amount of heat in steam is the latent heat, plus the
sensible heat.  Thus the heat of steam at the temperature of ebullition
is 967~'5 + 212~ =  179~'5.  It has heretofore been generally stated,
that the heat absorbed in vaporization is less as the temperature of the
vaporizing liquids is higher. So that if the sensible heat of steam at
any temperature is subtracted from the constant 1179~'5, the remainder
is the latent heat of steam at that temperature. For example: the latent
heat of steam  at 279~05, is 900~, at 100~, 1079~'5, &c.  This statement
however is found to be somewhat inaccurate, although in practice it
may be assumed to be nearly correct.
From the experiments of Regnault, it appears that the sum of the
latent and sensible heat increases with the temperature by a constant
difference of 0~'305 for each degree F., as is shown in Table XXII.
684. Mechanical force developed during evaporation.-During
the conversion of a liquid into vapor, a certain mechanical force is exerted.
The amount of this force depends on the pressure of the vapor and the
increase in volume which the liquid undergoes.
Equal volumes of different liquids produce unequal amounts of vapor at their
respective boiling points.
1 cubic inch of water expands into 1696 cubic in. vapor at boiling point.
1  "    "    alcohol "    "   528  "   "   "            "     "
1  "    "    ether   "    "   298  "   "   "            "      "
1  "    "    turpentine     "   193  "   "   "          "     "
Now although the latent heat of equal weights of other vapors is less than
that of steam, yet no advantage would arise in generating vapor from them in
place of water in the steam-engine. For equal volumes of alcoholic and aqueous
vapor contain nearly the same amount of latent heat at their respective boiling
points, and such is the case to a great extent with other liquids. The cost of
the fuel in generating vapor would be in proportion to the amount of latent
seat in equal volumes of the vapor.




HEAT.                             465
685. Liquefaction of vapors, or the conversion of vapors into liquids,
is accomplished ill three ways. 1st, by cooling; 2d, by compression;
and 3d, by chemical affinity. Only the first two of these methods will
be spoken of. When vapors or gases are condensed into liquids, the
same amount of heat is given out as sensible heat which was absorbed
and rendered latent when they assumed the aeriform condition.
686. Distillation is the successive evaporation and condensation of
liquids. The process depends on the rapid formation of vapor during
ebullition, and the condensation of the vapor by cooling.
Distillation is used, first, for the separation of fluids from solids, as the distillation of ordinary water, to separate the impurities contained in it; 2d, for
the separation of liquids unequally volatile, as in the distillation of fermented
liquors, to separate the volatile spirits from the watery matter.
687. Distilling apparatus of various kinds is employed according
to the special purpose to which it is applied.  The most ancient is
the alembic; its invention is attributed to the Arabs. It consists of a
boiler of copper or iron, furnished with a dome-shaped head; to the
upper part of this is attached a metal tube which passes through a
vessel of cold water, whereby the vapor (as it passes over when heat
is applied to the boiler) is condensed, and flows into a proper receptacle.
Where small quantities                      491
of liquid are to be distilled,
glass retorts, fig. 491, or
flasks are used. These are
heated by alcohol lamps, or             1
by small charcoal furnaces.
The receiver may consist s'
of a small flask connected          i
with the neck of the retort,
as represented by S. By
means of water flowing                             __
continually on it from B, a         -_
proper cooling is effected.      -     ~- -
688. Physical identity of gases and vapors.-The difference
between gases and vapors is merely one of degree, and their identity
in many physical properties has already been shown.  Thus the ratio
of their expansion by heat is the same as that of the permanent gases.
A permanent gas may be considered as a super'-hleated vapor; the vapor
of a liquid which volatilizes at very low temperatures.
Theory of the liquefaction and solidification of gases.-By
the last section, if the excess,f heat is removed from a gas, it is in the
same condition as an ordinary vapor, containing only sufficient heat to
42




466            PHYSICS OF IMPONDERABLE  AGENTS.
maintain it in the aeriform condition. By the compression of a gas,
heat is evolved, by rendering sensible the heat before latent. If the
compressed gas is then surrounded by a freezing mixture, the further
abstraction of heat causes the condensation of a corresponding portion
of gas into a liquid. It is thus by condensing and cooling gases, that
their liquefaction and solidification have been effected.
689. Methods of reducing gases to liquids.-In 1823, Faraday
liquefied chlorine, cyanogen, ammonia, carbonic acid, and some other
gases, by the following simple means.
The materials from which the gas was to be evolved, provided they were solids,
were placed in a strong glass tube,                   492
bent at an obtuse angle near the
middle, fig. 492, and the open ends
hermetically sealed. Heat was then 
applied to  the end containing the
materials (e. g. cyanid of mercury),    
while the empty end was cooled in a
freezing mixture. The pressure of the gas evolved in so small a space, united
with the cold, liquefied a portion of it. Otherwise, if fluids were to be employed,
the tube had the shape seen in fig. 493. The fluids were introduced by the small
funnel o n, into the curves c and b, and the ends, a, d, were then sealed by the
blow-pipe. By a simple turn of the tube, all the fluid       493
contents are transferred to the end, a, fig. 494, and the
empty end, d, is placed in a freezing mixture where the   f G   cZ
liquid gas collects. Any fluid which distils over from 
a, collects in the bottom of the middle curve. A minute  f 
manometer was introduced by Faraday into these tubes,  
in order to determine the pressure at which liquefaction 
occurred. The manometer was a small glass tube sealed  
at one end, and holding a drop of mercury; the mode:          C      j
of reading the pressure has been before explained (280).
Later researches of Faraday.-In  1845,
Faraday published the results of his experiments          l         d
on the liquefaction of gases by means of solid  ll 
carbonic acid. A mixture of this solid with ether,       I  l
in the vacuum of an air-pump, gave him a tempe- I                l
rature as low as -166~ F.  
In such a bath, at the ordinary pressure of the
atmosphere, chlorine, oxyd of chlorine, cyanogen, am-        494
monia, sulphuretted hydrogen, arseniuretted hydrogen, hydriodic acid, hydrobromic acid and carbonic acid, were obtained in the liquid form under moderate
pressures. These liquids were colorless, with the exception of those from chlorine and oxyd of chlorine, which are colored gases in the ordinary state. A
number of the liquefied gases were solidified. The results obtained by Faraday
on the liquefaction and solidification of gases may be found in Table XX.
690. Thilorier's and Bianchi's apparatus for condensation of




HEAT.                               467
gases.-To avoid the danger of explosion in the use of glass tubes,
and at the same time to obtain large supplies of liquid gases in a
manageable form, a powerful apparatus of iron has been contrived by
Thilorier; and, more lately, another by Bianchi with mechanical compression, for a description of which reference may be had to the Author's
Chemistry.
691. Properties of liquid and solid gases.-Liquid carbonic acid
is colorless, like water, and has a density of 0'83. Its coefficient of
expansion is more than four times that of air. Twenty volumes of the
liquid at 32~, becoming 29 volumes at 86~.
The solidified acid obtained by the evaporation of a portion of the liquid,
appears in the form of snow; when congealed by intense cold alone, it is clear
and transparent like ice. It melts at a temperature of -70~ F., and is heavier
than the liquid bathing it. The solid acid may be preserved for many hours if
it be surrounded with cotton or some other poor conductor of heat. It gradually
vaporizes without assuming the liquid form. The temperature of this solid, as
determined by Faraday's experiments, is about 106~ below 0~ F. Although so
intensely cold, it may be handled with impunity, and when thrown into water,
the latter is not frozen. By moistening it with ether, to which it has a strong
adhesion, its low temperature is at once manifested. If mercury is placed in a
wooden basin and covered with ether, and then solid carbonic acid be added,
the mercury will soon be frozen. The temperature required to freeze the mercury is about -40~ F. This frozen mercury may be drawn into bars, or moulded
into bullets, or beaten into thin plates, if the operations be performed with wooden
instruments.
NATTERER, with a mixture of liquid protoxyd of nitrogen and bisulphid of carbon, records a temperature of -220~ F. Even at this low
temperature, liquid chlorine and bisulphid of carbon preserve their
fluidity.
In protoxyd of nitrogen gas, combustibles burn with nearly as great intensity
as in pure oxygen; combustion also takes place in liquid protoxyd of nitrogen,
notwithstanding the intense cold. A fragment of burning charcoal, thrown into
this liquid, burns with brilliant scintillations, and thus almost at the same point
there is a temperature of about 3600~ above and 180~ below Fahrenheit's zero.
692. Latour's law.-From  his experiments on the conversion of
liquids into vapors, Caignard de Latour announced the following law:There is for every vaporizable liquid a certain temperature and pressure at which it may be converted into the aeriform  state, in the same
space occupied by the liquid.
In these experiments, strong glass tubes, furnished with interior manometer
gauges, were partially filled with water, alcohol, ether, and other liquids, and
hermetically sealed. The temperature of the tubes was then gradually raised.
Ether becomes a vapor at 328~, in a space equal to double its original bulk,
exerting a pressure of 37'5 atmospheres; alcohol at a temperature of 404~05,
with a pressure of 119 atmospheres, and water disappeared in vapor, in a space




468           PHYSICS OF IMPONDERABLE AGENTS.
four times its own bulk, at the temperature of about 773~. If Mariotte's law
held good in these cases, the pressures exerted would have been very much
greater than were actually observed. Even before a liquid wholly disappears,
the elasticity of the vapor is found to increase in a proportion far greater than
is the case with air at equally elevated temperatures. It is not therefore surprising that mere pressure fails to liquefy many bodies which exist ordinarily
as gases. Compare the statements respecting Mariotte's law in  2 274-277.
693. Density of vapors.-The accurate determination of the density
of vapors, is of much importance in Chemical Physics.  It is accomplished by filling a globe, or other vessel of glass, with the vapor at a
given temperature, and weighing it; this weight, divided by the weight
of an equal volume of air, under the same circumstances of temperature and pressure, gives the density of the vapor.  The details of
the methods in use for this purpose, belong more appropriately to
chemistry.. 9. Spheroidal condition of Liquids.
694. Spheroidal state.-Drops of water scattered on a polished
surface of heated metal do not immediately disappear, but assume the
form of flattened spheres, rolling quietly about, until they gradually
evaporate.  If the metal has not a certain temperature, it is wetted by
the water with a hissing sound.  This observation was made in 1746,
and ten years after, Liedenfrost called particular attention to the phenomenon.  Dibereiner, Laurent and others, also experimented upon
this subject.  They found that saline solutions, as well as simple
liquids, would act in the same manner as water. It is, however, to
Boutigny that we are particularly indebted for the investigation of the
phenomena of the spheroidal state of liquids.
Illustration of the spheroidal state.-The above experiment may
be variously performed, according to the ingenuity of the experimenter.
A small smooth brass or iron capsule is heated over a lamp, fig. 495, and a few
drops of water allowed to fall upon it from a pipette; the
drops do not wet the metallic surface, but roll about in   495
spheroidal globules, uniting together after a time into a
single mass, which, it will be seen, has the form of an
oblate spheroid, and evaporates but slowly. This is the
condition distinguished by Boutigny as the spheroidal
state. If the metal is allowed to cool gradually, when
the temperature falls to a certain point, the liquid will
burst into violent ebullition and quickly evaporate. 
The spheroidal state may be produced in a vacuum as well as in the
air, upon the smooth surface of most solids, and also upon the surface
of liquids.
Noticeable phenomena connected with the spheroidal state.
-There are several important points to be noticed as regards this
curious subject. The chief of these are, that,



HEAT.                                469
1. The temperature of the plate must be greater than the boiling point of the
liquids, in order to produce the spheroidal state, and it varies with the boiling
point of the liquid employed.
Thus, with water, the spheroidal state is produced when the plate is at a temperature of 340~, and may attain it even at 288~; with alcohol     4
and ether, the plate must have at least the temperature of 273~
and 142~ respectively.
2. The temperature of the spheroids is always lower than the?
boiling points of the liquids. This was determined by Boutigny,
by immersing a delicate thermometer in the spheroid, as shown
in fig. 496.
Thus, 2050~7 is the temperature of the spheroid of water; 168~'5
that of alcohol; 93~.6 that of ether; 13~I1 that of sulphurous
acid.
The temperature of a spheroid is not quite as definite as the
temperature of ebullition of the liquid, but rises somewhat as the 
plate upon which it rests is more intensely heated.
3. The temnperature of the vaporfrom a spheroid is nearly the 
same as that of the plate upon which it rests, which proves that
the vapor is not disengaged from the mass of the liquid.
4. The rapidity of evaporation from a spheroid, increases with
the temperature of the plate aupon which it rests, as is proved by 
the following experiments of Boutigny. The same quantity of
water (0-10 gramme, or 1-534 grs.) was evaporated in each case.
With the plate at the temperature of 3920, the water evaporated in 207 seconds.
With the plate at the temperature of 752~, the water evaporated in 91 seconds.
With the plate at dull red heat, the water evaporated in 73 seconds. With the
plate at bright red heat, the water evaporated in 50 seconds.
Water, in the spheroidal state, evaporates much more slowly than at the temperature of ordinary ebullition. Thus, when the plate was at the temperature
of 212~, 0-10 grms. of water evaporated in 4 seconds; and when at the temperature of 392~, in 207 seconds, or about one-fiftieth part as rapidly.
695. Spheroidal state produced upon the surface of liquids.A highly heated liquid may cause the spheroidal state in another liquid of lower
boiling point than itself.
Thus, Pelouze found that water assumed the spheroidal state on very hot oil of
turpentine, although the water is the denser liquid. Boutigny has thus sustained
water, alcohol, and ether on sulphuric acid, nearly at its boiling point. With
sufficient precautions, a number of liquids may be thus piled one upon the other.
696. A liquid in a spheroidal state is not in contact with the
heated surface beneath.-This must appear, on reflection upon the
facts already stated, and may be demonstrated as follows:A horizontal silver plate is surmounted by a tube of the same metal, fig. 497,
whose lower edges have two longitudinal slits opposite to each other. The plate
is placed upon the eolipile (704) containing alcohol, which is nicely adjusted to
a perfect level by the screws in the triangular base. Silver is employed to avoid
the formation of scales of oxyd of copper, which would interfere with the observation by interposing themselves to the light.
When the plate heated over the lamp reaches the proper temperature, a portion of water is placed upon its centre, and immediately assumes the spheroidal
42 *




470            PHYSICS OF IMPONDERABLE AGENTS.
condition. Placing the eye on a level with the surface of the plate, and looking
through the apertures in the sides of the tube, the flame of a candle opposite
497......................            498
may be distinctly seen. This could not happen if the liquid was in contact
with the plate. If a thick and heavy silver capsule is heated to full whiteness
over the eolipile, it may, by an adroit movement, be filled entirely with water,
and set upon a stand, some seconds before the heat declines to the point when
contact can occur between the liquid and the metal. When this happens, the
water, before quiet, bursts into steam, with almost explosive violence, and is
projected in all directions, as shown in fig. 498.
697. A repulsive action is exerted between the spheroid and
the heated surface.-This proposition follows, indeed, as a consequence of the last. It has already been demonstrated, that a liquid does
not wet a surface, when the cohesion which exists between its particles is
double of their adhesion for the solid (234).  This adhesion is not only
diminished by heat, but a repulsive action is exerted between the hot
body and the liquid, which becomes more intense as the temperature
is higher. This repulsive action is strikingly demonstrated by the
following experiment of Boutigny:A few drops of water were let fall into a basket, formed of a net-work of
platinum wires, heated red-hot. The water did not pass through the meshes,
even when the basket was rapidly rotated. But when the metal was sufficiently
cooled, the water immediately ran through in a shower of small drops, or was
quickly dissipated in vapor. It would also seem, that vapors, like liquids, are
repelled from the heated surface, for Boutigny found that a hot silver dish was
not attacked by nitric acid, or one of copper by sulphuric acid or ammonia.
The latter substance had no action upon either iron or zinc at a high temperature. The suspension of chemical affinity under certain conditions of high
temperature, is a fact of great interest in the physics of the globe.
698. The causes which produce the spheroidal form in liquids
are at least four:1st. The repulsive force of heat exerted between the hot surface and
the liquid, and which is more intense as the temperature rises.
2d. The temperature of the plate is so high, that the water in momentary contact with it, is converted into vapor, upon which the spheroid rests as upon an elastic cushion.




HEAT.                             471
3d. The vapor is a poor conductor of heat, and thus prevents the conduction of heat from the metal to the globule. Another cause which
prevents the liquid from becoming highly heated is, that the rays of
heat from the metal are reflected from the surface of the liquid. This
is shown by the fact, that, if the water be colored by lampblack, heat
is absorbed, and the evaporation is much more rapid.
4th. Evaporation from the surface of the metal carries off the heat as
it is absorbed, and thus prevents the liquid from entering into ebullition. The form of the oblate spheroid, which the liquid assumes, is
the combined result of the cohesion of the particles to each other, and
the action of gravity upon the mass.
699. Freezing water and mercury in red-hot crucibles.-The
remarkable phenomena of freezing water, and even mercury in red-hot
crucibles, are striking examples of the production of the spheroidal
state of liquids.
Boutigny placed a portion of liquid sulphurous acid in a red-hot vessel. It
assumed the spheroidal state immediately, at a temperature below that of its
ebullition, that is, below 14~ F. A little water placed in the spheroid becomes,
therefore, cooled below 32~ F., its freezing point, and is converted into ice.
Faraday placed in a heated crucible a mixture of solid carbonic acid and
ether, which immediately assumed the spheroidal state. Into it was plunged a
metal spoon containing mercury; almost immediately the mercury was frozen
into a solid mass. The temperature in this case was probably as low at
-148~ F.
700. Remarkable phenomena connected with the spheroidal
state.-On the principle explained, the hand may be bathed in a vase
of molten iron, or passed through a stream of melted copper unharmed,
or one may stir fused glass under water without danger. In all similar
cases, if the temperature be sufficiently high, the moisture of the hand
assumes the spheroidal state, and does not allow of contact with the
heated mass. If, however, the hand is drawn rapidly through the
melted metal, contact is mechanically produced, and injury follows this
rashness. The finger, moistened with ether, may be, for the same
reason, plunged into boiling water without injury.
701. Explosions produced by the spheroidal state.-The experiment illustrated by fig. 499, may be modified to illustrate explosions, and some other interesting facts consequent on the spheroidal
state.
A copper bottle, fig. 499, is heated as hot as possible over a double current
lamp, and in this state a few grammes of pure water are introduced by a pipette.
The water at once assumes the spheroidal condition, and has a temperature (as
may be ascertained by a thermometer) below that of its ebullition. If the neck
of the bottle is now tightly closed by a good cork, the evaporation is so slight,
that the pressure of the vapor within is not immediately sufficient to drive out




472            PHYSICS OF IMPONDERABLE AGENTS.
the cork. If, however, the lamp is withdrawn, the metal will soon cool sufficiently to allow contact of the water with it. There will then be so sudden an
evolution of a large volume of vapor as to drive the cork   499
from the bottle with a loud explosion.
Steam  boiler explosions may sometimes be'\
explained by a knowledge of the principles here
elucidated.  Thus, whenever from  any cause a 
deficiency of water occurs in a boiler, as when the 
pumps fail of a supply, or when, by careening, a        ]part of the flues are laid bare while the fire is
undiminished, a portion of the boiler may become
heated even to redness.  Water coming in contact  
with such over-heated surfaces, would first assume  _
the spheroidal state, and, almost at the next 
instant, burst into a volume of vapor so suddenly
as to rend the boiler with frightful violence. Numerous accidents are
on record where the explosion has been so sudden as not to expel the
mercury from the open gauges. The fact that explosions on our American rivers have occurred most frequently just at or after starting from
a landing, is explicable on the view here presented; the vessel, while
landing and receiving freight, being careened, so as to render the exposure of some part of the flues possible.
702. Familiar illustrations of the spheroidal state, and effects
of the spheroidal state of liquids, are not unfrequent in common life
and in manufactures.
The most common example of the spheroidal state, is that of a drop of water
on a heated stove, which moves around in a spheroidal mass, slowly evaporating.
The laundress determines whether her flat-irons are heated sufficiently for her
purpose by touching the surface with a drop of saliva on the finger. If it
bounds off, the iron is judged to be heated to a proper temperature. In the
manufacture of window-glass, constant application is made of the principles
here explained. The masses of glass are first formed into a rude hollow cylinder by blowing them in wooden moulds. In order to prevent the charring of
the mould, its interior is moistened with water, which, assuming the spheroidal
state, protects the wood, while it does not injuriously cool the glass.
Saline solutions are more efficacious for tempering steel than pure
water.  Now, as the point of ebullition of saline solutions is higher
than that of pure water, contact between the liquid and the metal is
produced sooner, and thus the steel is cooled more quickly, and the
temper is better.
Melted metals, like iron or copper, allowed to fall into water, do not throw the
water into violent ebullition, as might be supposed, but pass in a brilliant stream
to the bottom of the vessel, the water in contact with the metal assuming the
spheroidal state.




HEAT.                               473
{ 10. The Steam-Engine.
703. Historical.-The principles involved in.he construction and
theory of the steam-engine, have already been sufficiently discussed.
A few words must suffice respecting their practical applications in the
discovery and perfecting of this remarkable machine.
For the first rudiments of our knowledge of steam as a motor, we
must go back, as upon many other so-called modern inventions, to
Egypt, where, 130 years B. c., Hero, or IHeiro, describes in his " Spiritalia sen Pneumatica," among many other curious contrivances, what
he calls the eolipile.
704. The eolipile is a metallic vessel, globular, or boiler-shaped,
containing water, and provided at top with two horizontal jet pipes,
bent into the form of an S.
This apparatus, fig. 500, is suspended over a flame, and being free to move,
when the water boils, the steam rushing out, strikes against the atmosphere,
and the recoil drives the apparatus around with great           500
rapidity. This is in fact a direct-action rotary steam
engine, and undoubtedly the earliest mechanical result
achieved by steam power. It has often been re-invented,
in numberless forms, in modern times. In another form
the eolopile is made to blow by its jet the flame of a lamp, 
and in this case the boiler is fixed and filled with alcohol in
place of water, the jet descending through the flame of the
lamp as in the apparatus seen in fig. 497. Hero describes
also other devices where steam was the moving power.
705. First steamboat.-Blasco de Garay, a seacaptain of Barcelona, in Spain, in 1543, moved a
vessel of 200 tons burthen three miles an hour by
paddles propelled probably by steam, as the moving
force came, it was said, from  a boiler containing
water, and liable to burst.
This experiment was made on the 17th day of June, 1543, in presence of
Commissioners appointed by the king, Charles V., whose report secured the favor
of the crown to the projector. But what is unaccountable, nothing more ever
came from this singular success. De Garay probably employed Hero's eolipile
on a large scale, as Hero's work above named was about that time translated
into several languages and generally diffused. Passing the early efforts of Baptista Porta and De Caus (A.D. 1615), of Brancha (in 1629), Otto V. Guerick
(1650), and the Marquis of Worcester (1663), we come to the first efficient steam
apparatus (that of Savary).
706. Savary's engine.-In  1698, Capt. Thos. Savary obtained a
patent " for raising water and occasioning motions to all kinds of mill
work by the impellent force of fire."  His apparatus can hardly be
called an engine, or machine, since it has no moving parts.




474            PHYSICS OF IMPONDERABLE AGENTS.
Fig 501 is Savary's engine. Two boilers, L and D, are connected together
by the pipe, H. Two "condensers," P and P', are connected with the larger
boiier, L, by pipes entering at top of both, and capable of being alternately
shut off from the boiler by a valve, moved by              501
the lever Z. By two branch pipes beneath the       f ~
condensers, communication is established at plea-!i!    ->
sure, by the aid of the cocks 1, 2, 3, 4, alternately  
with the well by T, and the open air by the outlet
pipe S. The boiler, L, being in action, the condenser, P, for example, was filled with steam, the
cocks 1 and 3 being closed. By moving Z, the   
condenser, P', was next filled with steam also,
cocks 2 and 4 being closed, and at the same
instant cock 3 being opened, the water rushed up  
through T, to fill the vacuum occasioned by the
condensation of the steam in P. The lever, Z,        ^
was then moved to close P' and open P again to
the boiler. Cock 4 now admitted cold water to 
P', and cock 1 being opened, the direct pressure 
of the steam  from  the boiler forced the water Z  l
out of P, in a stream  through the discharge j.
pipe, S. The water in P' was also discharged
in the same manner, and so on, alternately, each
condenser was filled with cold water, and again 
discharged, maintaining a continuous stream of water from S. To supply the
waste of water in the boiler, L, the contents of the smaller boiler, D, were from
time to time forced by superior steam pressure into L, through the pipe 11
(provided with a valve for that purpose), reaching near the bottom of D, whose
capacity was such as to fill L to a suitable height.  The boiler, D, was then refilled through the pipe, E, from the supply box, X, attached to the discharge
pipe.
All the details of Savary's contrivance show  a nice adjustment of
means to the end to be accomplished.
707. Papin's  steam   cylinder, Newcomen's  engine.-Denys
Papin (Prof. of Mathematics at Marburg), whose name is connected
with the high-steam digester, suggested in 1690 the use of steam to
produce a vacuum in lieu of the air-pump before used.
For this purpose he constructed the cylinder of sheet iron, and built a fire
beneath its bottom, to boil a portion of water there placed. When the cylinder
was filled with steam, the piston, before held up by a latch, descended as the
steam was condensed. No practical result followed this clumsy contrivance, on
which Papin's countrymen rest his claims to be considered as the inventor of the
steam-engine.
THOs. NEWCOMEN, in 1710, first put in practice the use of a cylinder
and piston in the steam-engine, in which the steam  was alternately
admitted and again condensed by a stream of cold water. This engine
operated against the pressure of the atmosphere, and was effectual in
only one direction, i. e., it was a single acting engine.




HEAT.                              475
708. The atmospheric engine is well illustrated by the apparatus
shown in fig. 502, which was contrived by Dr. Wollaston, to show the
nature of Papin's cylinder.                                    502
A glass, or metallic tube, with a bulb to hold water, is fitted    a
with a piston. This piston-rod is hollow, and closed by a
screw at a. This screw is loosened to admit the escape of the
air, and the water is boiled over a lamp: as soon as the steam
issues freely from the open end of the rod, the screw is tightened, and the pressure of the steam then raises the piston to
the top of the tube, the experimenter withdraws it from the   T
lamp, the steam is condensed, and the air pressing on the top 
of the piston forces it down again; when the operation may be
repeated by again bringing it over the lamp.
In all the early steam-engines, the steam was condensed
within the cylinder, either by water applied externally, or by a
jet of water thrown directly into the cylinder. It is very obvious, that a great loss of fuel and time was thus involved in 
bringing the cylinder up again to 212~, before a second stroke
could be made. 
NEWCOMEN and S.MEATON constructed very large engines, however, on this
principle, and applied their power directly to the pumping of mines. Although
Smeaton introduced an improved kind of mechanical work and many improvements in minor details, and better boilers, he succeeded only in raising the
average duty of steam-engines from about five and a half millions of pounds,
raised one foot by a bushel of coal (80 lbs.) burned, to about nine and a half
millions, in his best engines. A good pumping engine now raises from ninety
to one hundred and thirty millions of pounds for every bushel of coal burned.
709. Watt's improvements in the steam-engine.-The steamengine as it was left by Sneaton was, as we have seen, only a steam
pump, confined to the single function of raising water, and incapable
of general use, as well from its imperfections as from the enormous
cost of fuel it required.-Watt, in 1763, was a maker of philosophical
instruments at Glasgow, and had occasion to repair a model of the
Newcomen engine.  The study of this machine and its defects, led
Watt to construct a new model, in which the steam was condensed in
a separate vessel, in connection with which he subsequently found it
advantageous to use an air-pump-to aid in keeping the vacuum  good,
as it was otherwise vitiated by atmospheric air leaking in, and coming
from the water of the boiler. These ideas were matured and realized
in 1765, and in 1769 he took out his patent, in which all the essential
features of our modern steam-engines are included. In connection first
with Mr. Roebuck, of Carron Iron Works, and subsequently with Mr.
Boulton, of Soho, he put his ideas in practice, and by reserving to the
patentees one-third part of the saving of fuel effected by his improvements, his genius was rewarded by the accumulation of a princely
fortune.




476            PHYSICS OF IMPONDERABLE AGENTS.
Watt's in -ntion of low pressure condensing engines stands without a parallel
in the history of science for the perfect realization of all the conditions of the
problems to be solved-the perfect mastery of the laws of nature-the use
of matter, by which they were accomplished, and the thorough exhaustion of
the subject even in its minutest details, so that to this day we have no improvements in this machine involving a single principle unknown to Watt. In the
beauty and perfection of mechanical work, in size of parts, and the strength
of boilers, we have machines greatly superior to any Watt ever saw, but it was
his genius that rendered those perfections possible, and supplied the very power
by which they have been worked out.
710. The low  pressure or condensing engine. —The low pressure engine is employed in all situations where economy of fuel and
the best mechanical effect from  it are the ruling considerations, and
where lightness and simplicity of construction is unimportant. This
machine now remains almost exactly as Watt left it.  Owing to the
nearly perfect vacuum obtained in it by the condenser and air-pump,
much less pressure of steam is required to produce a given mechanical
result; e. g., if the vacuum is equal to fourteen lbs. atmospheric pressure, then a steam pressure of six lbs. would give an efficient moving
force of twenty lbs. to the machine. Hence the propriety of the term' low pressure" engine; but in practice it is found advantageous to use
higher pressures in the condensing engines than Watt ever contemplated.
Fig. 503 is a section of the cylinder, A, condenser, e, air-pump, hot and cold
well, and a view of the most important attached parts of a modern condensing
engine. The cylinder, A, is seen receiving steam at top through the throttle503
_ _i
valve, a, driving down the piston, B, with its rod, C. A stream of cold water
injeeted into the condenser, e, has completely condensed all the residual steam




HEAT.                                477
of the former stroke which has found its way from A by the eduction pipe, d,
so that the piston, B, is descending into a nearly perfect vacuum (671). The
hot water of this condensation is constantly drawn off through the valve, k, by
the air-pump whose valves, i i, rise to allow its flow into the hot well, I, whence
it finds its way, solicited by the plunger pump, S, to the boilers by the pipe, P,
and its valves, o o. The cold water pump, q, supplies a steady stream of cold
water by the spout, r, to the cold well. By the time the piston, B, has reached
its lowest point of descent, the valve rod, V, and eccentric bar, S, have moved
so as to open the lower steam ports and reverse the direction of the piston.
when the steam above, B, is in its turn taken into the condenser, e, by the
appropriate channels, and removed as already explained for the downward
stroke. The piston rod, C, and valve and pump rods, are connected above
with the great working-beam, whose further extremity conveys the power ot
the engine by the pitman, G, through the crank pin, H, to the main shaft, K,
on which is the fly-wheel, L, to give steadiness of motion to the whole apparatus. The arrows show the motion of these parts as the piston descends
The governor, z, controls the throttle-valves a, by connections not shown in
this drawing.
711. The high  pressure  engine.-In this machine, the escape
steam  is driven out against the pressure of the atmosphere, and no
attempt is made to utilize its capacity to form a vacuum, consequently
this form of apparatus could be used as well with condensed air, or
any other elastic fluid, as with steam, if there was any other that could
compete in economy with it.  The lightness, simplicity, and low cost
of the high pressure engine, make it availa-                504
ble in spite of its uneconomical use of steam,
in many situations where a condensing engine would be unavailable.
The steam arrives by the pipe, Z, fig. 504, to 
the steam chest, R, and is admitted alternately 
by the ports e d, to the top and bottom of the
cylinder, A A, as the valve rod, S, actuated by
the eccentric, /, on the main shaft, opens and 
shuts the ports by the slide valve in K. The
escape steam  makes its exit through q to the 
atmosphere. The pitman, P, conveys the motion 
of the piston, C, to the crank, Q, and the main 
shaft, on which is the large fly-wheel, x, to
accumulate momentum. The flow of steam  is
regulated by the governor, V, whose balls fly
out with the centrifugal force of a more rapid
motion, and by the rod, h b, close more or less 
the throttle-valve, z, which regulates the supply
of steam; the pump, o o, supplies water to the
boiler, and is moved by the rod and eccentric, g,
on the main shaft.
712. The cut off. —The supply of steam  both to the high and low
Fressure engine is further regulated by a contrivance called the "cut
43




478            PHYSICS OF IMPONDERABLE AGENTS.
off," which may be set to cut off the flow of steam entirely, or at any
portion of the stroke, as one-half, or one-third. The expansion of the
steam  then completes the work, and great economy of fuel is found to
follow its use.
713. Steam  boilers.-The form of steam  boilers varies very much
with the purpose to which they are to be applied.  On land, large
boilers may be safely used, which would be wholly valueless at sea, or
oil a locomotive engine.
Plate-iron strongly riveted and braced, is the material combining the greatest
economy and strength. Copper can be used only when the fuel contains no sl:lphur, and is the best material to resist corrosive agents. Simple cylindrical
boilers, laid horizontally, with a fire-flue under the whole lower surface, are
commonly used for high pressures. When these are made large enough to
receive the furnaces within and distribute the heat in interior flues, they are
called Cornish boilers. When their,                 505
construction is still further modified, with reference to the greatest
possible increase of fire surface,
they are called locomotive boilers,
as in the annexed figure, 505;
which is the common locomotive 
boiler seen in section. D, is the                                       b
feed-door, for fuel to the furnace D 
or fire-box, A, which communi- I        --        _:,
cates by numerous small horizontal tubes, entirely surrounded 
by water, with the base of the
chimney, B, into which the blast of exhaust steam from the engine is driven at
K. E, is the steami chamober, where a trumpet tube in the dome conveys the
dry steam on its way to the cylinder through F. Steam boilers are supplied
with hot water by a force pump, aun gauge cocks indicate the water level.
714. Mechanical power of steam.-Horse-power.-As steamengines were originally employed to take the place of horses in raising
water, it was natural to estimate their power by the number of animals
they replaced.  The value of any force is correctly stated as the nuniber of pounds raised one foot high in a given time (foot-pounds).  As
the use of steam  became general, the term  horse-power was retained,
but its use was restricted by Watt to mean 33,000 lbs. raised one foot
per minute, or nearly 2,000,000 lbs. raised one foot per hour.
As one cubic foot of water converted into steam yields, in round numbers,
1700 cubic inches of vapor, its mechanical effect at atmospheric pressures, is
equivalent to raising 15 lbs. 1700 inches (or 142 feet) in a tube of one inch area.
But 15 lbs. raised 142 feet, is the same thing as 142 times 15 lbs. raised one foot,
or'130 lbs., or nearly a gross ton. The total mechanical force developed by
cl nging one cubic inch of water into 1700 cubic inches of steam is, therefore,
nearly one ton. Only 60 or 70 parts of this power are, however, reg-trded as
a rually available in use, deducting friction and loss from other caues.  TiLAre



HEAT.                               479
fore, the evaporation of a cubic foot of water in an hour, subject to this deduction,
will give the full force of about 1000 cubic inches of water converted into steam,
as the expression of one-horse power (viz., 33,000 lbs. X 60 =  1,980,000 lbs.),
or nearly 2,000,000 lbs. raised one foot. This is a somewhat rough approximation, but it gives constants easily remembered and sufficiently near the truth.
A boiler of one-hundred horse power means, then, a boiler capable of evaporating 100 cubic feet of water per hour.
In practice, it is common to allow, in large land engines, for every horse
power, one square foot of fire bars in the grate, three cubic feet of furnace
room, ten cubic feet of water ill the boiler, and ten cubic feet of steam chamber.
In locomotives and steamships, these proportions vary very much.
715. Evaporating power and value of fuel.-In England, engineers estimate ten pounds of bituminous coal for every cubic foot of
water (i. e. every horse power) to be evaporated.  In carefully constructed boilers, however, this effect is produced by seven or eight
pounds of coal.  In the Cornish boilers, where a very large evaporating
surface is allowed, five pounds of coal only, and sometimes less, are used
per horse power.  In the United States, anthracite coal averages ten
pounds of water evaporated, for every pound of coal burned.  This
would give 6(25 lbs. of anthracite for each cubic foot of water evaporated.  A well regulated current of vapor conducted over the flame of
bituminous coal by Dr. Fyfe, raised the evaporative effect produced 37
per cent. above what was obtained from  the unassisted coal.  This
increase is due to the decomposition of the steam  by the hot fuel, and
the consequent effect of the pure oxygen on the carbon. Well seasoned
wood (beech or oak), still containing about 20 per cent. of water, and
well dried peat, have about equal evaporating power, and are only
about two-fifths as effective as an equal weight of ordinary bituminous
coal.
Welter has observed that those quantities of a combustible body which require
an equal amount of oxygen for combustion, evolve also equal quantities of heat;
although later researches show this conclusion not to be strictly true, it is supported by many facts. In all cases of combustion, the action is reciprocal; the
oxygen is burned in the fuel as truly as the fuel by the oxygen, and, therefore,
the same amount of heat is generated by a given amount of oxygen, whether in
converting carbon into carbonic acid, or hydrogen into water. To burn one
part of carbon, requires 266 parts of oxygen (CO2 = 16 -- 6 = 266), and to
burn one part of hydrogen, requires 8 parts of oxygen. It has been proved
experimentally (by Rumford) that 78 parts of water are raised from 32~ to 212~
by burning one part of carbon, while one part of hydrogen so burned will raise
236'4 parts of water through the same degrees. It therefore follows, that one
part of oxygen, burning carbon, will heat 78 - 2-66 = 29-25 parts of water
from 32~ to 212~; and also that the same quantity of oxygen, in burning
hydrogen, will heat 2364  - 8 = 29-56 parts of water through the same degrees.
The heating effect of oxygen may, therefore, be assumed to be 30, or, in units
of heating power, 5400.
If the heating effect of pure carbon is taken at unity, the relative heating




480            PHYSICS OF IMPONDERABLE AGENTS.
effects of combustibles will range as follows for equal weights:-hydrogen, 3;
vegetable oil, 1-15-1-22; ether, 1-02; carbon, 1; wood charcoal, 0-96; alcohol,
0-86; good coal, 0-77; dry wood, 0-46; wood (with 20 per cent. water), 035;
peat, 0-33-0-38.-(Knapp.)  Compare   753.
The best expansive steam-engines, it is calculated, give back, in the
form of mechanical work, only about 18 per cent. of the heat generated
by the fuel burned in driving them.
Prof. W. R. Johnson ("experiments on coals") and others, argue,
as the result of experiment, that the total amount of carbon in a fuel,
is the measure of its practical evaporative power. His results very
nearly sustain this view. He found, also, that about 86 per cent. of
the total heating power were expended in evaporating water, and about
14 per cent. were lost in the products of combustion. Of the total
heating power, by calculation, about 26 per cent. were lost in practice,as deduced from the experimental effects stated in his tables.
11. Ventilation and Warming.
I. VENTILATION.
716. Currents in air and gases depend upon principles which
have already been fully explained,-but the subjects of ventilation and
artificial heating are of such great importance in daily life, that they
demand a brief and separate consideration.
Currents arise in air from differences of temperature and variations
of pressure. The perfect freedom of movement in air, renders its fluctuations from these causes incessant. If the air was visible, every
candle, gas-light, stove, furnace-flue, and human body, would be seen
to be the centre of an ascending                     506
column of heated air, whose place
was constantly supplied by other and               s  
colder particles.  
On the law of the equilibrium of fluids, the ascending currents must induce
others, descending and horizontal, and                           i
thus a circulatory motion is imparted,          
even by a single lighted candle, to the     a  _ 
whole gaseous contents of a quiet apart-            I 
muent. These currents are made visible
whenever the candle smokes.  If the
door of a heated apartment stands ajar,             1
and a candle is held near the top crack, c,
fig. 506, the warm air of the room is seen
to draw outwards, carrying the flame with 
it, and a corresponding cold current, a,
flows in at the bottom,-while a point, 
b, will be found, midway its height, where the candle flame is undisturbed. So




HEAT.                               481
a window, partly open, will occasion a draught of cool air, blowing in at the
bottom of the opening, and a compensating warm current will escape outwards,
above.
This constant interchange of motion in unequally heated masses of
air, while it soon poisons the confined atmosphere of a close apartment,
where many persons, with or without lights, are assembled, also supplies
the easy means of curing one of the greatest evils of civilized communities.
717. Draught in chimneys.-Chimneys draw because the products
)f combustion discharged into them, are specifically lighter than the
)uter air.  The column of heated air, C D, fig. 507, rises with a velocity
proportionate to the excess of weight in a column of the outer air, A B,
of the same area and height.  The laws of falling bodies (71) apply
to this case in every particular.
Suppose, for example, a chimney is 18 feet high, and the gases in it are
heated to 100~ F., the outer air being 70~. The contained column would, therefore (607), expand -g4-, or about -18th of its
original bulk at 70~. A column of 19 feet of 
such air would, therefore, be required to coun- 
terbalance one of 18 feet high in the exter-:'     H
nal air at 70, and of the same area. The.
heated air will, therefore, rise (for the same                       \\
reason that a balloon rises), with a velocity    i     I1''' l    \1
equal to that acquired by a body falling through                1. u 
one foot, i. e., a space equal to the difference in' X
height of the two columns-of equal weight.
The laws of gravity, therefore, supply the  B      X
means of calculating the theoretical velocity
of the ascending column, and of course that,
with the area of the cross section of the flue,       1 I \ ME\   M
will determine the quantity of air passing
through the chimney in a given time. But the
friction of the air against the sides of the flue, 
and the varying density of the products of
combustion compared with air, diminish the
theoretical velocity, and it is usual to allow a   /
deduction of one-fourth for these causes. The following rule will be found to
give a sufficiently exact practical expression of the velocity of air in chimneys
and ventilating flues.
MIultiply the square root of the difference in height of the two columns
of air (deduced as above) expressed in feet and decimals of a foot, by
eight; deduct one-fourth, and the product of the remainder, multiplied
by sixty, will give the velocity of efflux per minute; and the area of the
flue in feet, or decimals of a boot, multiplied by the velocity, will give the
number of cubic feet discharged per ninute.-(Hood.)
This rule, in the case supposed, would be a (81/1) X 60 - 360 cubic
43*




482            PHYSICS OF IMPONDERABLE AGENTS.
feet of gases discharged per minute, by a flue 18 feet high and one foot
area, whose temperature is 30~ above the outer air.
Chimneys, in the sense we mean, were not known to the ancients. Holes in
the roof, and windows allowed the escape of smoke from the kitchens of the
luxurious Romans. But the mild climate of the Mediterranean shores did not
require much attention to means of artificial warmth. In the houses of ancient
lierculaneum and Pompeii, exposed in modern times, there are no chimneys.
But even in England and France, where fires in winter are necessary, chimneys
were first introduced only in the middle of the 14th century. The Curfew Bell
(eoutve-feu, fire cover) was needed as a precaution against the danger of fires,
without chimneys.
Reversed draughts and smoky chimneys occur, 1st, when the
flue or fire-place is badly constructed; 2d, when two flues open into
one apartment, or two connecting apartments, and there is a fire in
only one flue; 3d, when a powerful fire exists in one part of the house,
as the kitchen, for instance, without an adequate supply of air from
without, it will draw the needed supply through the smaller flues in all
parts of the house, reversing the draught in them; 4th, when (as in
many old houses) the flue is so large that cold currents may descend in
the angles, while a heated one ascends the axis; 5th, when a neighboring higher house or eminence directs, in certain states of the wind, a
cold current down the flue.
The remedy for reversed draughts is best found in one commanding
central stack, into which all the minor flues discharge, while exhausting cowls, like fig. 511, are the best cure of smoky chimneys.
718. Products of respiration and combustion, and necessity
for ventilation.-By contact with the lungs, and with burning fuel,
the air is contaminated, chiefly with carbonic acid, water, effete nitrogen, oxyd of carbon, and animal odors.  Every full grown individual
consumes, in every minute of quiet respiration, about 500 cubic inches
of air. About 14 ounces of carbon are burned by the air out of the
body of a man in twenty-four hours, and all this is returned in the
form of carbonic acid to the air.
Such air cannot be breathed again without danger. Mixed with the suirounding air, it contaminates that also. Headache, languor, uneasy respiration,
nausea, faintness, and syncope are results which always follow from breathing
air contaminated with these poisonous exhalations, even in very moderate
quantity. Even two per cent. of carbonic acid, derived from respiration or
combustion, may produce all the symptoms above named. The full chemical
and physiological evidence upon this important subject cannot be here given,
but the evils arising from the slow and insidious effects of the poison of bad
ventilation, can hardly be over estimated. In ordinary combustion, especially
with slow fires and an imperfect supply of air, carbonic oxyd is also produced,
and this is one of the gases most likely to leak from hot-air furnaces when the
joints are not tight. It is much more destructive of life than carbonic acid, or
those gases of sulphur, whose presence is at once declared by their odor.




HEAT.                              483
719. The quantity of vapor given off by the body, in sensible
and insensible perspiration, and by the lungs, is very considerable,
being not less than ten or twelve grains each minute, or about three
pounds per day, which, with the quantity of carbonic acid expired,
makes about three and a third pounds, besides other excrementitious
matter, given off in twenty-four hours.
If the air of a crowded apartment is conducted through water, so much animal matter is collected in the water as to occasion a speedy putrefactive fermentation, with a disgusting odor. The blast of air escaping at the upper ventilator
of a crowded assembly room, is so oppressive as to produce immediately the
most distressing symptoms. While we instinctively shun all contact with
unclean persons, and what we call dirt, even refusing a cup that has pressed
the lips of another, and esteem all water not transparent as foul, it is marvellous
with what thoughtlessness we resort to crowded and ill-ventilated public places,
and drink in the subtle poison exhaled from the lungs, skin, and clothing of
every individual in the assembly. Especially when we remember that while
the digestive apparatus can select and assimilate nutriment from food of questionable quality, the lungs have no such power of selection, and can discharge
their duty to the blood only by a full supply of pure air. If the transparency
of air was troubled by the exhalations of the lungs as water is by the washings
of the body, no argument would be needed to secure attention to the importance
of ventilation; and yet it is quite true that the bodily health suffers more from
inhaling effete air, than it could from drinking the wash alluded to.
720. The quantity of air required for good ventilation, is very
variously stated by different authorities. Enough fresh air must bo
supplied, obviously, to replace all that is contaminated by the lungs,
the body, and sources of illumination. But to determine exactly how
much these several sources of deterioration demand, is not so easy.
The amount of air needed to remove the products of respiration, is
very much less than is required to absorb the vapor of water given off
from the lungs and the skin.  The quantity of vapor the air can take
up, will depend on its dew-point and temperature.  Hood estimates
three and one-quarter cubic feet of air per minute, for each individual,
in winter, with an external temperature of 20~ or 25~, and a quarter
of a cubic foot per minute to supply the waste from the lungs, making
three and a half cubic feet per minute, or two hundred and ten cubic
feet per hour in winter, and five hundred in summer. Peclet estimates
it at two hundred and twelve cubic feet per hour. Dr. Reid estimates
the quantity, as high even as thirty cubic feet per minute per individual.
Brenan puts it at 10-25 cubic feet.
721. Products of gas illumination.-Every cubic foot of gas, of
average quality, requires the oxygen of about twenty cubic feet of air
(viz. 4'25 cubic feet oxygen) to burn it, and produces rather over a
cubic foot of carbonic acid, still more water, and, if the gas is impure,
sulphurous acid and compounds of ammonia will be added, which.




484             PHYSICS OF IMPONDERABLE AGENTS.
dissolving in the watery vapor, condense upon and corrode furniture,
books, metallic articles, &c. Every pound of coal gas burned produces
2-7 Ibs. of water, and 2'56 Ibs. of carbonic acid; and, as a cubic foot
of coal gas weighs about 290 grains, twenty cubic feet will weigh a
pound, a quantity which four common fish-tail burners consume in an
hour. The capacity of air for moisture at 68~, is 7-31 grs. per cubic foot.
[t would, therefore, require 2373 cubic feet of air at 68~ to retain the
water from twenty feet of gas, and nearly five times as much at 20~ F.,
not to name the amount required to dilute the carbonic acid and free
nitrogen produced.
It is needless to add, that the ventilation of gas burners is an important
matter. Fortunately, a gas chandelier affords one of the best means of producing an upward current in an assembly room. Candles and oil consume more
air, and, of course, produce more effete products for an equal amount of light
than gas.
722. The actual ventilation of buildings is a practical problem, to be wrought out in each case, with careful regard to the principles and facts just stated. The supply of air required may be obtained
in two ways: —1st, by the ascending column of heated air in a shaft,
drawing after it the effete air to be removed, and supplying its place
by fresh air, warmed in its progress to the apartments.  This is called
thermal ventilation; or, 2d, mechanical force may be           508
employed, by means of revolving fan-wheels driven by
a steam-engine, or otherwise, forcing the air through
the apartments to be warmed and ventilated.  This is
called mechanical ventilation.
By the first method, Dr. Reid ventilated the House of Commons in England. By the second, Mr. Rice ventilated the
House of Lords with a fan-wheel, over thirty feet in diameter.
723. Stone's ventilating shaft.-An excellent combination of the thermal ventilation, with the plan of 
hot-air furnaces, so generally used in the United States,
has been devised by S. M. Stone, Architect, which has
been found efficient in the New Haven City Prison, the
State  Reform  School, and  other similar buildings.
Fig. 508 shows a plan and section of this system.
A ventilating shaft of brick, C, rises in the centre of the  I
house, through the axis of which passes a cast-iron smoke
flue, A, carrying off the waste products of the furnace. The
radiant heat of this iron flue heats the air in the shaft B.
Openings, D and D, are pierced from the various apartments
into this shaft, and allow the air of the rooms free opportunity
of escape, solicited by the powerful ascending draught of the vertical shaft.
Distant apartments are connected with the shaft by horizontal pipes of wood or




HEAT.                                485
tin. The openings, D, should be covered with wire gauze, and fitted with Dr.
Arnott's self-acting noiseless valve, which allows the passage of an upward current only. The apartments are supposed to receive their supply of fresh and
warm air through hot air flues, ascending in the walls. In summer it would be
found needful to establish a current in the shaft by an occasional fire in the
furnace, or by a special furnace for that purpose in the top of the house. In
cities, the air taken into buildings may be strained through fine wire gauze and
spray of water, as was accomplished by Dr. Reid in the House of Commons.
By the rule (717), the power of such a shaft to discharge air can be calculated.
724. Cold currents produced by ice.-Refrigerators.-Air, in
contact with ice, acquires, of course, a low temperature, and parts with
a large part of its moisture. Thus, snow-clad mountains and glaciers
naturally send down to the valleys below a current of cold air, flowing
like water over the surface, especially at night, when the absence of
the sun prevents the accumulation of heat on the earth's surface.
Adroit use has been made of this cold dry current, in the construction of refrigerators for preserving food in warm weather; and the same principle has
been applied, on a large scale, to the cooling of large apartments. Figs. 509
and 510 show a section and elevation of Winship's Refrigerator. The ice, A,
509
510
fig. 510, is sustained upon a shelf in the upper part of the box, surrounded with
double charcoal linings. The air enters by the register openings, C, and coming
in contact with the ice, is cooled, and falls to the bottom, as indicated by the
arrows, where it finds its egress at E, between hollow walls, and finally escapes
at F, as in an inverted syphon. In this way a gentle current of about 45~ F.
is steadily maintained as long as the ice lasts, and, being dry, articles of food
are preserved sweet and free from mould for a long time. A similar device has
been used for large apartments.
725. Cowls.-Emerson's ventilators.  Advantage is taken of the
currents in the external air, to aid in establishing ventilation in houses,
and draught in chimneys, by the use of ventilating cowls.
These contrivances are often conical, and hung with a vane, to turn against
the wind. One of the most generally approved, however, in common use, appears




486            PHYSICS OF IMPONDERABLE AGENTS.
to be the ventilator of Emerson, fig. 511, which is simply a cone of metal, surrounding the flue, over whose vent, and a short distance       511
above it, is sustained a disc of metal. If the wind blows
from any point, its effect, on striking this conical surface, is 
to pass upwards and across the open flue, with an increased
velocity. The result is to solicit an upward current in the
shaft, as shown by the arrow, in the figure.
If it is desired to direct a current of fresh air into the
shaft, an injecting ventilator is used, which is simply the
above cone inverted, or two or three such placed one over the
other. These are found very efficient in projecting fresh air
into the cabins of ships, and other similar situations.
726. The supply of fresh air in dwellings is derived, in the winter, almost exclusively from the cracks
and joints of doors, windows, and other openings.  In
all good systems of general warming, this supply is
derived from the open air, or a free basement, and is
warmed in its progress through the heating apparatus. 
When it is requisite to introduce cold air into a house,
it is important to do so in such a manner as to avoid
local and sharp currents; for this purpose, perforated
cornices, or openings covered by wire gauze, are provided. A too rapid
current is both inconvenient and costly, from the needless waste of fuel.
In public buildings, the supply is best obtained through a trench, or horizontal tube, opening into a clean area, and protected against powerful winds. The
injecting cowl may be advantageously used to cover the opening of such a supply. The distribution of the ascending warm current is best made through a
hollow or double floor, perforated with numerous openings, while the spent air
is taken off above, as already described.
II. WARMING.
727. The artificial temperatures demanded in cold climates
are produced, 1st, either by radiant heat solely, as in the common
open fire-place, 2d, by convection only, as in hot-air furnaces of every
description, in which the air is warmed by its passage through a heating chamber, and then introduced into the apartments to be warmed,or 3d, by radiant heat and convection united, as in stoves, and steam
or hot water pipes.
728. The open fire contained in a simple brick fire-place, fig. 507,
whether coal or wood is burned, warms the air of the room  solely by
radiant heat. The burning fuel solicits the air of the apartment to be
warmed towards the chimney, where, coming in contact with the fire, it
parts with a portion of its oxygen to sustain combustion, is intensely
heated, and rising, escapes at the flue, with the heated products of combustion. Hence only the heat radiated from the burning fuel and hotwalls,
is effectual in warming the apartment, while much the largest part of the
heat (three-fourths to four fifths of the whole) escapes up the chimney.




HEAT.                                487
The genial effect and cheerful aspect of an open fire, combined with the eficient means of ventilation it affords, render this old system very popular, when
combined with some competent general plan of warming the whole house.
Dr. Franklin improved the common fire-place by introducing iron stoves, of
the same general form, and connecting them with the chimney by a circuitous
pipe, by which means a much better economical effect was attained. Rumford
improved the form of the fire-place very much, and especially with reference to the
throat of the chimney and angle of the jambs. He also combined it with a circulation of hot air behind and at the sides of the fire, so as to obtain the effect of a stove.
Stoves of iron, standing in the apartment to be warmed, offer, perhaps, the
most economical mode for burning fuel-but when, as is too often the case, they
are closed tight, except a very small opening for draft, they are among the vilest
contrivances in use for the ruin of the public health. The atmosphere of the
room unavoidably becomes over-heated and corrupted by the products of respiration, in the almost universal absence of any mode of ventilation.
729. Hot air furnaces.-Large buildings and dwelling-houses are
frequently warmed by air heated in its passage through a structure in
the lower part of the house.  One of                     512
the simplest forms of apparatus for
this purpose is seen in fig. 512, being  
a sectional view of a hot air furnace,        IB   =l
in which the cold air entering at A,                              ll1
passes, as indicated  by the arrows,
through an extended system of iron
passages set in brick work and heated                _         g
by the products of combustion, and 
the direct action of the fire, F.  The  X 
heated air gains the apartment, nm,
by openings, B, in the floor or sides
of the wall, while the gases of corm-     2YG/'
bustion escape by the flue, 0.  Such  an  apparatus serves only to
illustrate the general principle, and would prove valueless in practice.
Very numerous forms of hot-air furnaces are in use in the United States, chiefly
for the combustion of anthracite coal. They are essentially alike in principle, I ut
very unlike in construction. All take cool air from with-       513
out, or from an airy basement, and after heating it in a 
brick chamber, by contact with surfaces of hot iron surrounding the fire, and conveying away the products of
combustign, distribute it by flues in the wall to the several
apartments. Fig. 513 presents a sectional view of one of 
the best hot-air furnaces at present in use (Chilson's).    l
The fire of anthracite is contained in a large shallow pot
of cast-iron, with soap-stone, or iron staves, and the heated
products of combustion are expanded in an extensive system of chambers of cast-iron, all communicating with an
annular cast-iron pipe, leading to the chimney. This
arrangement affords a very extendcel  radiating surface,
with few joiLts, to allow the escape of noxious gases into the surrounding hotair chamber.  The arrows indicate the direction of the current.




4388           PHYSICS OF IMPONDERABLE AGENTS.
In fig. 514 is seen the furnace, surrounded in the brick work, which is hollow.
The cold air enters at the bottom, and being gently heated by contact with the
hot-air surfaces within the chamber, as well as by the      514
radiant heat from  the same source, it escapes by the 
openings, o o, to the various apartments. The extended
iron surface in this apparatus prevents any part of the
furnace from becoming very hot, usually the chief causes
of complaint against this mode of heating. Air is mate- 
-ially injured for purposes of respiration by contact with  5I1;    l
over-heated surfaces, owing to the charring of the parti-  i
eles of dust and dirt always floating in it. The chief
objection resting against this and similar modes of heating is the entire absence of radiant heat in the apartmcnts,
whose occupants are, so to speak, immersed in a warm 
air bath, and require, consequently, several degrees more 
heat, by the thermometer, for comfort, than when radiant heat forms a part
of the means of an artificial temperature.
Hot-air furnaces are commended on account of their economy of
construction, and ease of management, and when combined with a
good system of ventilation, such as is secured by an open fire in one
or more apartments, the objections to them  are in  great measure
removed.
730. Heating  by hot water, distributed in pipes, offers many
advantages for the salutary and economical distribution of heat.  The
high specific heat of water (653), enables it to heat over three thousand
times its own bulk of air in cooling through a single degree of temperature.  That is, one cubic foot of water, by cooling one degree, will
raise the temperature of 3419 cubic feet of air a like amount; for
0'2379: 1 =  813-435: 3419.  In this proportion the specific heat of
air is the first term, and the third term is the bulk of air equal to a
unit weight of water.  As hot water is usually distributed in cast-iron
pipes, experiments have been made upon the rate of cooling of these
pipes, which show that one foot in length of pipe four inches in diameter,
will heat 222 cubic feet of air one degree per minute, when the difference between the temperature of the air and the pipe is 125~. The
advantage of hot water as a means of heating, depends much on its
high capacity for heat, and its slow rate of cooling, by which the temperature declines very slowly, after the fire is extinguished.
For horticultural and manufacturing structures, and other buildings where
large pipes are not an objection, it has prominent claims. In private houses,
where the hot water pipes occupy a chamber in the basement, and the air is
heated by passing among them, all advantage of the radiant heat is lost, and
the apparatus becomes comparatively inefficient, and very costly, if a sufficient
number of pipes are laid in to do the work.
731. Perkins' high pressure hot water apparatus.-The system
just named uses water at a very low pressure, nea-er over six lbs. to the




HEAT.                                489
square inch.  Mr. Perkins has, however, patented a system, in which
the hot water is distributed in very small iron pipes, under enormous
pressure.'
The plan of this system is seen in fig. 515. A coil of pipe, S (1 inch outside
and i inch inside), is heated by the fire,f. The rising       515
pipe, ttt, is carried to the top of the circulation,
and in each story or apartment, a coil, c' c', c c, distributes the heat, the water returning by the descend- cl  - i'
ing pipe, t' t' t', as indicated by the arrows.  At the
highest point of the circulation is placed a ten inch  
pipe, called the "expansion-pipe," fitted with a cock -,h,,
for the escape of air, and the admission of water. A
sufficient void is left to accommodate the expansion
of the water, which is about one-twelfth the whole
bulk. Thus arranged, the temperature of the pipes
can be raised to any required degree-and in practice it varies from 300~ to 5500-i. e., from about 75   " -        <
lbs. to about 675 lbs. to the square inch. No safety 
valve is used on this apparatus, and numerous ex-   c  Ic   f.
plosions of the fire coil have happened with its use.
The high temperature of the pipes endangers build- 
ings, and gives to the air heated by it the empyreu- 
matic, burnt odor, which is so objectionable from
cast-iron stoves. It is undoubtedly more efficient          tl
than the low pressure hot water system. The sys-                        N OE
tem of high pressure steam pipes is very similar to
this, and equally open to the objection of over-heat-            S _ ll
ing the air, and endangering buildings from fire..   X 1
732. Gold's steam  heaters.-The radiators.-In this system, the
heat is radiated from surfaces of japanned sheet-iron, fastened together
by rivets at the bottom of concave depressions in the outer sheet, as
seen in fig. 516.  This arrangement                       516
divides the whole steam  space  into
numerous communicating cells, as seen
in the cross section, D; the steam  arrives from  the boiler, fig. 517, under
very low pressure (one pound  to the
inch), by the inlet cock, A, and the air
escapes at an outlet cock in the opposite corner above.  The water of con- 1^                  D..
densation returns to the boiler by the same pipe that conveys the
steam, which is made sufficiently large for that purpose.
These radiators are placed in the apartments to be heated, either singly or in
groups of three or four, concealed under an ornamental screen and covered with
marble. The heat, in that case, is both radiant heat and heat of convection.
The radiators may also be confined in a space below the apartments, and the
air to be warmed passed through or among them, in which case only heat of
convection reaches the apartments, as in the common hot-air furnaces. This
44




430             PHYSICS OF IMPONDERABLE  AGENTS.
system is economical of fuel, efficient for the most severe weather, and when
combined with a proper system of ventilation, entirely unexceptionable. It bas
the great merit of securing exactly the desired degree of heat just where it is
wanted, however remote from  the boiler, and is, by means of the air-cock,
adjustable to any temperature.
733. The boiler of Gold's steam  heater is perfectly automatic,
and is a beautiful illustration of the ease with which so powerful an
agent as steam can be brought under entire self-control and rendered
quite free from all danger.
Fig. 517 is an elevation of this boiler, set for use in its masonry, A. The
water rises in the tube, J, which is open to the air, to counterpoise the pressure,
which is adjusted to one pound on the inch.  J                517
is therefore a hydrostatic balance. The lower
ash door, C, being closed, no air has access to
the fire except through the side vent, E. This 
closes by a conical cover at the end of a chain,  _                       F
as soon as the limit of pressure is reached, for
then the lever, F, rises, by reason of the water
pressing up the elastic cover of F.  A like ar-      j 
rangement, G, next opens the upper feed door,
C; if the fire is not sufficiently held in check by
F, C continues to open until sufficient cold air    1;    ll
enters the flues to reduce the steam  to its limit  1ii  ii
and hold it there. The safety valve, I, is like-                             i i
wise under the control of a similar arrangement. |11  i' l                 llih
IH, which comes into action after F and G, if              _l      l
needed. K, K, are the steam-pipes leading to           B         l
the radiators, and the smoke reaches the chimney    -
by the pipe, R.  Such nice adjustments secure great economy of fuel, as the
combustion cannot proceed faster than the demands of the radiators require., 12. Sources of Heat.
734. Sources of heat.-Four great sources of heat may be named:1. Mechanical sources.-The principal of these are friction, compression, and percussion.
2. Physical sources, of which the chief are solar radiation, stellar
radiation, terrestrial radiation, and atmospheric electricity.
3. Chemical sources, comprising chemical combinations, the chief of
these being combustion.
4. Physiological sources, comprising the production of heat in living
beings.  This, according to views now  generally received, is only an
extension of the third head.
I. MECHANICAL SOURCES OF HEAT.
735. Friction.-When  two  bodies are  rubbed  together, heat is
generated by the friction of their surfaces.  The supply of heat from
this source  is apparently  unlimited.  As the  generation of heat is




HEAT.                               491
unaccompanied by any change in the calorific capacity of the bodies,
and generally by no chemical action, it must be attributed to a moiecular movement of the bodies excited by friction.
736. Quantity of heat produced by friction.-The experiments
of Joule show that the amount of heat developed by friction depends
3nly on the amount of force exerted, and not upon the nature of the
substances rubbed together.
Count Rumford published in the Royal Philosophical Transactions, 1798, the
results of some of his experiments upon this subject. A brass cannon, weighing
113 lbs., was revolved horizontally, at the rate of 32 revolutions per minute, against
a blunt steel borer with a pressure of 10,000 lbs. In half an hour the temperature of the metal had risen from 60~ to 130~ F. This heat would have been
sufficient to raise the temperature of 5 lbs of water from 32~ to 212~. In another
experiment, the cannon was placed in a vessel of water, and friction applied as
before. In two hours and a half, 1S8 lbs. of water actually boiled. The heat
generated in this case was calculated by Rumford to be at least equal to that
given out, during the same time, by the burning of 9 wax candles, J inch in
diameter, and each 245 grains in weight. A remarkable instance of the excitation of heat by friction is afforded by an experiment of Sir Humphrey Davy, in
which two pieces of ice rubbed together in vacuo at a temperature below 32~
were melted by the heat developed at the surfaces of contact.
737. Circumstances which  vary  the  quantity  of heat developed by friction.-The quantity of heat developed by friction
depends, 1st, on the nature and state of the surfaces (138); 2d, on the
pressure; 3d, on the velocity.
738. Illustrations and application of the heat developed by
friction are of frequent occurrence in common life.
When a piece of steel is struck by a flint, particles of the metal are torn off,
and are so intensely heated as to ignite in the air. These heated particles falling upon tinder or gunpowder cause it to burn. Similar sparks often fly off
from the iron shoes of horses as they strike a stone. In grinding knives and
other instruments upon a dry grindstone, or upon an emery wheel, a brilliant
train of sparks is produced. Among uncivilized nations fire is frequently produced by the friction of pieces of wood against each other. Seneca relates the
same fact, and adds that it is necessary to employ particular species of wood; as,
laurel and ivy.
Sufficient heat is caused by rubbing a match on a rough surface to ignite the
phosphorus on its end. The axles of car wheels, and other parts of machinery,
when not well greased, are sometimes heated sufficiently hot to cause the ignition
of the surrounding woodwork. It is by friction that the brown rings sometimes
seen on wooden articles, turned in a lathe, are produced. A pointed piece of
wood is held against the rapidly revolving article, the heat generated by the
friction is sufficient to cause the wood to smoke and partially char it.
In a few instances in this country the fall of water has been used to produce
friction, and thus develop heat. In the state of Vermont, plates of iron were
rapidly revolved against each other, and, by the heat developed, the mill was
warmed. The thermogenic apparatus of Messrs. Beaumont and Mayer (Am.
Tour. Sci. [2] XX., 261) is a most successful contrivance for converting motion




492            PHYSICS OF IMPONDERABLE AGENTS.
into heat by means of friction, and where there is abundant and cheap water.
power, may be of economical importance as a source of heat.
739. Compression.-When any substance undergoes a diminution
in volume, there is generally a development of heat. The evolution
of heat by compression is most strikingly seen in gases which undergo
a great diminution in volume by pressure.                   518
The condensing syringe, fig. 518, is an admirable
instrument for showing the phenomenon referred to.
It consists of a metal or glass tube closed at one
extremity. Into the other extremity fits tightly a
piston which has a bit of tinder on its end. When
the piston is forcibly driven into the cylinder, the
compression of the air develops so much heat that 
the tinder becomes ignited.
Owing to the small compressibility of liquids,
and their great capacity for heat, it is not easy to
determine the heat developed in them by compression. Messrs. Colladon and Sturm have obtained,
with certain liquids, at a pressure of 30 atmospheres, 
an elevation of temperature of as much as from 7~
to 10~ F. The heat generated by the compression
of solids may better be considered as by percussion.
740. Percussion is a combination of friction and compression, and is an active mechanical source of heat. The amount of heat
developed by percussion seems to depend to a
great extent on the diminution in bulk which
the body struck undergoes.
This is strikingly shown by an experiment of
Berthollet, in which a piece of copper was sub-       ~         - ~_mitted to the action of a stamping-press. The greatest development of heat
occurred with the first blow, where the metal underwent the greatest diminution
in bulk, and diminished with the succeeding blows as did the amount of condensation. The quantities of heat evolved at the first three strokes were 17~ 3,
70 5, and 1~-9 F.
741. Capillarity.-Pouillet has shown that the simple act of moistening any dry substance is attended with a slight, yet constant, disengagement of heat.
Pouillet operated on the powdered metals, the insoluble oxyds, glass, brick,
clay, &c. The liquids used were water, alcohol, ether, acetic acid, turpentine, &c.
The rise in temperature was only from 5~ to 2~ F. It appears to be independent
of the nature of the body. Organic bodies of various kinds were operated upon;
as, flax, wool, silk, starch, wood, sponge, ivory, horn, &c.: with these there is a
rise in temperature of from 3~ to 18~ F.
These results cannot be attributed to chemical action, for the different liquids
produced the same heat when they were absorbed by the same porous body.
The development of heat in these cases is attributed to the condensa



HEAT.                              493
tion of the liquid on the surface of the solid which it moistens. It may
also be due in part to the effect of the friction of the liquid molecules
upon those of the solid, as they move into their position of equilibrium.
II. PHYSICAL SOURCES OF HEAT.
742. The sun is the most abundant source of heat to our globe. Its
distance from the earth is 95,000,000 of miles. The diameter of the
sun is about 888,000 miles, or about 111 times that of the earth, consequently its volume is 1,400,000 times the earth's volume.  The sun
turns on its axis once in about 25 days. Philosophers are divided as
to the cause of the immense amount of heat which escapes from this
body.
It is conjectured that there are three atmospheric strata about the sun. That
nearest his surface is called the cloudy stratum. It is incapable of reflecting
light, and is heavily loaded with vapors. The next in elevation is thought to
consist of an intensely luminous medium. To this is attributed the diffusion of
light and heat. Beyond this there probably exists a third envelope of a transparent gaseous nature.
Dark spots are often seen on the sun's surface (by the aid of a telescope).
These are of immense size, and often rapidly change their form. One noted by
Sir John Herschel contained an area of 400,000,000 square miles. These spots
are supposed to be formed by the opening and dispersion of the stratum of luminous clouds, revealing the dark mass within.
743. Quantity of heat emitted by the sun.-Pouillet, by means
of an instrument called a pyrheliometer, has made observations from
which he estimated that the amount of heat annually received by the
earth from the sun, would be sufficient to melt a crust of ice surrounding the earth 101 feet thick. The atmosphere absorbs nearly 40 per
cent. of the heat of the sun's rays.
From the size of the earth, and its distance from the sun, it has been determined that the entire amount of heat emitted by the sun, is 2,381,000,000 times
as great as the heat which it gives to the earth; and it is calculated that the
intensity of heat at the surface of the sun, is seven times as great as the heat
of an ordinary blast furnace.
The fixed stars, the suns of other systems, notwithstanding their great distance, exert a very important influence upon the temperature of the earth. It
has been estimated that they furnish to our earth four-fifths as much heat as
the sun; and that, without this addition to the sun's heat, neither animal nor
vegetable life could exist upon the earth.
744. Extremes of natural temperature.-Captain Parry, in 1819,
found at Melville Island, a tempefature of —.59~ F., and Captain Black,
at Fort Reliance, at 60~ 46' N. latitude, observed a temperature of
-70~ F. Dr. Azariah Smith records the extreme heat at Mosul, Western Asia, in 1844, as 114~ F. (Am. Jour. Sci. [2] ii., 75.) At Bngdad,
in 1819, the thermometer rose to 120~ F. in the shade. In the sun, at
44*




494            PHYSICS OF IMPONDERABLE AGENTS.
Mosul, near the site of the ancient Nineveh, Dr. Smith records the
summer temperature at 146~ F. This is probably the highest natural
temperature authentically recorded. Thus, the extreme range of natural
temperature observed is 206~'46 F.  In this latitude, between summer
and winter, there is often a difference of 110~ F., and in the shade,
comparing the temperature in the sun of summer, there would be an
increase of at least 30~.
745. Terrestrial radiation.-The heat which the earth receives
from the sun, does not penetrate more than from 50 to 100 feet. At
Paris, this stratum (called the first stratum of invariable temperature)
is found at a depth of 86 feet.  Descending into the earth, below the
point of constant temperature, there is a gradual and regular increase
of temperature.  The amount of this increase is about 1~'8 for every
hundred feet of descent.
Observations on this point have been extensively made in deep mines and
Artesian wells, and always with a nearly constant result. The variations undoubtedly arising from the nature of the soil, and its conductibility for heat.
Water from Artesian wells has always a higher temperature than surface water.
Thus, the water arising in the Grenelle Artesian Well near Paris, from a depth
of about 2100 feet, has a temperature of 86~ F. At Neusalzwerke, in Westphalia, is a well 2200 feet deep. The water rising from it has a temperature of
91~ F. Compare. 204.
Assuming the ratio given above for the increase in temperature as we descend
into the earth, at the depth of two miles water would boil; at about 23 miles,
or only TAU of the earth's radius, there would be a temperature of 2200~ F.
At this temperature cast-iron melts in the open air, and trap, basalt, obsidian,
and some other rocks, become perfectly fluid. But, as Pouillet observes, the
enormous compression produced by the weight of the upper strata resting upon
the lower portions of the earth's crust, raises the point of fusion, so that the
point of perfect or partial fluidity is carried far lower than a direct ratio would
give; but, with due allowance for the effect of pressure upon the temperature
of fusion, the thickness of the earth's crust cannot be supposed to exceed one
hundred miles.
746. Origin of terrestrial heat.-Numerous theories have been
advanced to account for terrestrial heat. Some attribute the heat to
local chemical action. Thus, Boyle explained it by the decomposition
of pyrites-a view no longer esteemed tenable. The belief in a central fire within the earth, now generally entertained, is found in the
mythology of many nations, originating, most likely, in observation
of volcanic fires. For evidence that the earth was once a fluid mass,
see H 91 and 102. This question is of the highest geological interest,
and its discussion must be referred to treatises on that science.
747. Atmospheric electricity.-Another source of heat is atmospheric electricity, the origin of which is, at present, shrouded in mystery. The more usual form in which its calorific powers are presented




HEAT.                             495
to us, is seen in the effects of a powerful flash of lightning, which not
unfrequently fuses metals and earthy matter with which it comes in
contact.
III. CHEMICAL SOURCES OF HEAT.
748. Chemical combination. —When two substances enter into
chemical combination, there is generally an elevation of temperature,
but sometimes also a depression.
Where there is a slow and gradual chemicar combination, the development of
heat cannot always be appreciated. The same amount of heat is developed as
if the combination took place quickly, but, being extended over a greater time,
it is inappreciable at any single moment, and cannot be accurately measured.
Chemical combination sometimes takes place at the ordinary temperature;
but it is often necessary to heat the bodies before they will unite. An example
of the first class, is the mixture of sulphuric acid with water, or the slaking of
burnt lime,-in both cases a large amount of heat is developed. As examples
of the second class, are wood, sulphur, and phosphorus, which do not inflame
at the ordinary temperature.
749. Combustion.-When the heat developed by the chemical combination of two bodies produces luminosity, the bodies are said to burn,
and the phenomenon is called combustion. If one of the bodies burning
is solid, it is called fire; if gaseous, flame. As bodies are usually
burned in the atmospheric air, the term combustion has come to be
restricted, in a popular sense, to the union of bodies with oxygen,
developing light and heat.
In a chemical sense, however, the term combustion has a wider range, and
refers, generally, to chemical union, even when the bodies combining together
do not evolve either light or sensible heat. Thus, iron slowly rusts or oxydizes
in the air, wood gradually decays; these, to the chemist, are as truly cases of
combustion, as those more rapid combinations with oxygen, which are accompanied by the splendid evolution of light and heat.
750. On the cause of the heat generated by combustion, there
is a great diversity of opinion. According to the dynamical theory of
heat, it is the vibratory motion of the constituent atoms of the bodies,
as they combine together, that produces the rise in temperature.
When the state of aggregation of one or both of the bodies combining
is changed, the heat which was latent becomes sensible; or if there is
a depression of temperature, as is sometimes the case, a portion of the
sensible heat becomes latent. When there is no change in the state
of aggregation of the bodies combining, it is explained by the specific
heat of the compound being less or greater, according as there is a
depression or elevation of temperature.
751. The amount of heat developed by chemical action, is of
great practical importance, and has, for a long time, engaged the attention of physicists. The first experiments upon this subject were made




496            PHYSICS OF IMPONDERABLE AGENTS.
in 1790, by Lavoisier and Laplace, by means of their ice calorimeter.
Count Rumford, in 1814, Welter, in 1822, and Despretz, in 1823, are
among those who have contributed valuable researches upon this subject.
Compare ~ 715.  The most elaborate series of experiments upon this
subject, was made by Favre and Silbermann, in 1844; a portion of
their results is found below.
The thermal unit is the heat necessary to raise a weight of water,
equal to that of the combustible, one degree of the scale of Fahrenheit's
thermometer.
HEAT DEVELOPED BY BURNING DIFFERENT SUBSTANCES WITH OXYGEN.
Names of substances.      Formulae.   Quantity of heat emitted
by one of the combustibles.
Hydrogen.....                          62031
Oxyd of carbon...   CO                 4325
Marsh gas......              C2H4               23513
Wood charcoal.                        14544
Natural graphite...                          14006
Diamond.....                        14184
Sulphur.....                         4032
Olefiant gas.....           C4114              21344
Good coal......                              10800
Sulphuric ether..50    i                       16248
Wood spirit.....           C211402             9552
Alcohol.......         CH602              12931
Stearic acid.....        C8H3804            17676
Acetic ether....       Cg8H04             11326
Beeswax.                        18892
Essence of turpentine..      C20oHI             19533
Dry wood......                                   6180
Peat........                                      4860
The quantity of heat disengaged during the combustion of an elementary
body, is the same, whether it attains at on once its maximum of oxydation, or at a
number of times.
Thus, carbon disengages a certain amount of heat during its conversion into
carbonic acid. The same amount of heat is evolved when it is first converted
into carbonic oxyd and afterwards burned to convert it into carbonic acid.
752. The pyrometrical heating effect of a substance, is the
intensity of the heat evolved during its combustion. This varies much
with different substances, and depends not only on their composition,
but also on their state of aggregation. The conclusions of an economic
character derived from this subject, are as follows:1st. The pyrometrical heating power of carbon is greater, and that of
hydrogen smaller, than those of any other combustible.
2d. The pyrometrical heating power of the ordinary fuels, composed




HEAT.                              497
of carbon and hydrogen, is greater in proportion to the amount of carbon
they contain.
3d.. The pyrometrical heating powers of different fuels are much greater
in oxygen than in air.  Thus, between carbon and hydrogen burned in
oxygen, there is a difference of 12,000~ F., in air only 1500~ F.
753. Relative value of fuel.-In the following table is given the
absolute, specific, and pyrometrical heating effects of different combustibles:
TABLE SHOWING THE HEATING EFFECTS OF DIFFERENT BODIES BURNED IN
AIR.
Ieating effect.
Absolute.       Specific.      Pyrometrical.
Hydrogen......  023                   0'0077             2900~
Gaseous combustibles..  0-80-0'25   0.00010 —000027    1850-1150~
Vegetable oils, &c.....15 —122   0-30
Sulphuric ether..     1-02         0'21
Wood....  0-36 —0-47   0-14-0-28         1575-1750~
Peat.....  0-37~0-65                      1575-2000~
Lignite.......  043-0-85                                 1800-2200~
Bituminous coal (5 p. c.
water, 5 p. c. ash.)..  0-79-0-96   1-06-1.44          2200-2350~
Peat charcoal....  0.33-0-85                        2050-2350~
Wood charcoal....  0-64-0-97   0-10-0-20               2100-2450~
Coke (not more than 5 p.
c. ash.)......  0-84-0-97   0-38-0-46                  2350-2450~
The lighter woods burn more quickly, with a greater flame, and more intense
heat than the more dense woods. The amount and intensity of the heat from
the different fuels depends, to a great extent, on their state of dryness.
754. Combinations in the humid way.-Messrs. Hess, Andrews,
and Graham have made important researches upon the heat evolved in
combinations in the humid way.  Their principal results may be
summed up as follows:1st. Equivalents of the different acids combining with the same base,
produce the same quantity of heat.
2d. Equivalents of the different bases combining with the same acid,
produce different quantities of heat: generally the more energetic bases
disengaging the most heat.
3d. When a neutral salt is converted into an acid salt, there is no disengagement of heat.
4th. When a neutral salt is converted into a basic salt, there is a disengagement of heat.
755. Animal heat; warm  and cold-blooded animals.-The temperature of organized beings is seldom that of the medium which sur



498            PHYSICS OF IMPONDERABLE AGENTS.
rounds them.  There is within the living body a series of chemical
actions taking place, and these are sources of heat.
In warm-blooded animals, as the mammifers and birds, the heat produced at
each instant compensates for that lost from the exterior, and thus the body is
kept at a uniform temperature. In cold-blooded animals, as reptiles, fishes, and
mol!isca, heat is also generated, but so slowly, that their temperature is but a
very few degrees above that of the surrounding medium, and often is only
equal to it.
756. The cause of animal heat, it has long been conjectured, was
the chemical action taking place within the body.
Crawford appears to have been the first to advance the doctrine that respiration was the cause of animal heat. Lavoisier supposed that the air underwent
in the lungs a real combustion; its oxygen combining with the carbon and
hydrogen of the blood, forming carbonic acid and the vapor of water. The
lungs, according to this view, were the furnaces, the arterial blood carrying
the heat developed by the combustion into all parts of the body. This view of
Lavoisier has been essentially modified. A new theory, founded upon the researches of Spallanzani and Magnus, is now generally received. They determined that the arterial blood contained a large quantity of oxygen, and the
venous blood a large quantity of carbonic acid. It has been concluded that the
venous blood reaches the lungs loaded with carbonic acid, which, by endosmose,
traverses the humid walls of the pulmonary cells, and passes into the air. Carbonic acid is thus exhaled, and oxygen is absorbed. Becoming then arterial
blood, the blood is forced through the arteries into the capillaries of the different organs, where a more or less considerable combustion of carbon takes place.
It has not asyJet been demonstrated, that the hydrogen of the blood combines
with the oxygen of the air. Indeed, most physiologists think that the vapor
of water exhaled in respiration, is simply an evaporation from the lungs.
757. Temperature of vegetables.-As the plant is the seat of
numerous chemical actions, so also it is a source of heat.  The temperature of plants is, in general, from 0~'9 to 1~'1 higher than that of
the surrounding air. In a few exceptional cases, it is much higher.
Thus, the Arum cardifolium of the Isle of France, at the time of blos.
soming, reaches a temperature of 120"'2 F., while that of the air is
about 670. Plants attain their highest and lowest temperatures some
hours later than the maxima and minima of daily temperature.
# 13. Correlation of Physical Forces.
I. MECHANICAL EQUIVALENT OF HEAT.
758. Relations of heat and force.-It is well known that there is
an intimate relation between heat and mechanical force, and that one
may be exchanged for the other.  A  given quantity of one may be
converted into a determinate quantity of the other, as is shown in the
case of the steam-engine, and in the production of heat by mechanical
means (~ 735-741).




HEAT.                             499
759. Unit of measurement, the foot-pound. —In the experiments
upon the mechanical equivalent of heat, the unit adopted in England
and in this country, is the foot-pound, or the mechanical force expended
in raising a pound weight, one foot high (714). In France and other
European countries, the unit adopted is the mechanical force expended
in raising one kilogramme (2'2046 lbs.) one metre (39'37 in.) high.
760. Determination of the mechanical equivalent of heat.According to the Dynamical Theory of Heat, the mechanical equivalent
of heat is independent of the nature of the body by whose agency the
transformation of mechanical force into heat is effected; hence the same
result should be arrived at, whatever course of experiment is adopted.
Mr. J. P. Joule, of Manchester, England, has made the most exact
determination of the mechanical equivalent of heat in a series of very
careful and elaborate experiments, conducted between the years 1840
and 1843.*  He determined the mechanical equivalent of heat in a
number of ways, reversing the question, and determining the amount
of heat produced by a certain expenditurG of mechanical force.
One method was by the compression of gases; compressing air with
a great force in a copper receiver; in one series of experiments filled
with air only, and in another with water.  The whole apparatus was
placed in the water of a calorimeter, whose temperature, before and
after the experiment, was carefully determined.
The heat developed by the friction of water and of oil, was determined in an
apparatus consisting of a brass paddle-wheel, fig. 519, having *volving arms,
b, g, working between stationary vanes, c,f. This wheel     519
was made to revolve by the descent of a known weight,
and thus the mechanical force exerted was determined. A
similar apparatus, of smaller size, and made of iron, was
used for experiments on mercury. In all cases, the apparatus was placed in a metallic vessel filled with the liquid,
and the temperature noted before and after the experiment.'    -
In his experiments on the friction of solids, Mr. Joule b
used an apparatus consisting of a vertical axis, which 
carried a beveled cast-iron wheel, against which a fixed             c
cast-iron wheel was pressed by a lever. The whole was g
plunged in an iron vessel filled with mercury, the axis  l
passing through a hole in the lid. In all of these experiments, the temperatures were noted by thermometers, which indicated a variation of temperature of the one two-hundredth of a degree F.
761. Results of Joule's experiments.-In the following table are
given the most important results obtained by Mr. Joule.  The second
column gives the results obtained in air, the third column, the same
results corrected for a vacuum.
* Phil. Trans. 1850, p. 61.




500            PHYSICS OF IMPONDERABLE AGENTS.
FORCE REQUIRED TO HEAT ONE POUND OF WATER 1~ F.
M   Equivalent (in foot-  Equivalent in 
Material employed.  Ipounds) in air.   vacuo.           Mean.
Water,...         773640           772692           772-692
~Mercury,..  776-303       775-352          774083
________ _    {776'997           776  045
Cast-iron,           774-880          773 930          774987
Conclusions deduced from Joule's experiments. —. The quantity of heat produced by the friction of bodies is always proportional to
the force employed.
2. The quantity of heat capable of increasing the temperature of one
pound of water (weighed in vacuo, and between 55~ and 60~) by 1~ F.,
requires, for its evolution, the expenditure of a mechanical force represented by the fall of 772 lbs. through the space of one foot.
Consequently a force of one horse power (714) would raise 427 lbs. of water
1~ F. each minute, and would bring it to boil from 60' in two and a half hours.
Prof. Thomson (Phil. Mag., Feb. 1854) says, it is mathematically demonstrated
from the dynamical theory of heat, that any substance may be heated 30' F.
above the atmospheric temperature, by means of a properly contrived machine
driven by an agent, spending not more than one thirty-fif   f the   rg of   the energy of the
heat communicated, and that a corresponding machine, or the same machine
worked backwards, may be employed to produce cooling effects.
When a bod. is heated by such means, 3  of the heat is drawn from
surrounding objects, and Y; is produced by the action of the agent.
II. DYNAMICAL THEORY OF HEAT.
762. The dynamical theory of heat, which rests upon the supposition that heat is motion, or the result of motion, is founded upon the
constant relation which exists between heat and mechanical force.
763. Motions of the molecules.-In this theory it is assumed
that the particles of all bodies are in constant motion, and it is this
motion which constitutes heat; the kind and quantity of the motion
varying with the solid, liquid, or gaseous state of the body.
Thus in solids, it may be assumed that the molecules are continually oscillating about their position of equilibrium. This motion may be vibration of the
constituent atoms of a molecule, or of the entire molecule, and may be rectilinear
or rotary.
In liquids, the molecules have no constant position of equilibrium, the repulsive and attractive forces being nearly equalized. The movements of the liquid
molecules may therefore be either vibratory, rotary, or progressive.
In gases, the repulsive force predominating, the molecules move onward in
straight lines.
764. Changes in  the state or volume of bodies.-This view




HEAT.                            50t
explains the production and consumption of heat, which accompany
changes of state or volume in bodies. The work performed is partly
internal and partly external.
Thus when a solid is melted, there is an internal work, employed in changing
the relative position of the molecules, and in consequence, an absorption of heat
proportional to the work accomplished. In evaporation there is an internal
work, employed in separating the molecules, and an external work in overcoming
the forces which oppose themselves to the expansion of the vapor.
When, on the contrary, a gas or vapor is liquefied by compression, the external
work is supplied, and the internal work due to the cohesive force which draws
the atmosphere together, is transformed into heat. Again, when a liquid solidifies, the internal work which unites the molecules is transformed into heat, and
appears as sensible heat.
It is evident that this theory would modify the ideas generally received of the
amount of heat in bodies. Thus the heat which is rendered latent, when a solid
is liquefied, cannot be regarded simply as being insensible; it must be considered as being converted into motion.
III. ANALOGY OF LIGHT AND HEAT.
765. Vibrations producing heat and light.-A careful consideration of the phenomena and laws of heat has led many able physicists
to conclude that heat is not, as was formerly supposed, a fine imponderable substance, but that, like light, it is a peculiar vibratory motion of
the ultimate particles of bodies. The exact nature of the vibratory
motion of atoms which constitutes heat is more difficult to determine.
The polarization of heat is best explained, like the polarization of
light, by the theory of transverse vibrations. On this theory:-Heat and
light are different effects produced by one and the same cause, and they
differ physically only in the rapidity and amplitude of their vibrations.
While the phenomena of light are due to vibrations whose utmost range
of velocity is comprehended within the limit of an octave in music
(531), vibrations of less rapidity and greater amplitude produce heat,
while the vibrations which produce light, also in their turn produce the
phenomena of heat.
766. Impressions of light and heat.-It is natural to admit that
the more rapid vibrations of ether are generally those which have the
least amplitude. In fact this result is deduced from an examination of
the spectrum, which presents a more feeble illumination in the blue and
violet. It is the same with sounds. The more acute sounds have generally the least intensity, whild the bass notes are more prolonged. As
grave sounds have little intensity, because their amplitude is great, so
with vibrations of the luminiferous ether, we observe that the extreme
red of the spectrum has but little brilliancy.
Vibrations impressed upon the air by sonorous bodies may produce upon us
two sorts of sensations; the one perceived by a special organ, the ear, when the
46




502             PHYSICS OF IMPONDERABLE  AGENTS.
vibrations are sufficiently rapid, the other affecting the entire surface of our
bodies, producing that general trembling which results from energetic vibrations, as in the case of thunder or the roar of cannon. Only grave sounds correspond to vibrations of sufficient amplitude to produce this general effect. On
the other hand, vibrations of too great rapidity, and consequently too little
amplitude, may fail to affect even the ear, as is the case with vibrations exceeding 36,500 per second, ~ 378. We may consider the same vibrations communicated
to the ether by the molecules of luminous bodies as giving rise to two sorts of
impressions; the one peculiar to the organ of vision, the other affecting the whole
surface of the body; the former constituting the impression of light, the other
giving the impression of heat when the amplitude of the vibrations is sufficiently
great.
But the colored rays which pertain to the extreme violet of the spectrum  are
produced by vibrations which are very rapid, and which consequently have very
little amplitude. Such vibrations are not suited to produce the general effect
which is denominated heat. But when the vibratory energy is feeble, as in the
spectrum obtained from the electric light, there are more evident signs of heat
in the violet portion of the spectrum. In general, the less rapid vibrations found
in the yellow, orange, and red, produce heat, and even beyond the extreme red,
where the vibrations are too slow to produce light, the greater amplitude of the
vibrations gives them great power to produce the phenomena of heat. Compare
% 463.
Aerial vibrations of great amplitude, and a moderate degree of rapidity, affect
the entire system (386), and when less than 32 per second, they seldom produce
the sensation of sound. So also if the vibrations exceed 36,500 per second, their
amplitude is so small that no audible sound is produced.
The gradual weakening of the violet tint of the spectrum, and the existence
of invisible rays beyond the extreme violet, as attested by chemical action and
fluorescence, ~ 463, 533, prove the same thing in regard to light.  Heat and
light may therefore be regarded as different effects of the same cause.
767. Bodies become  luminous by incandescence.-When a
body is heated, the source of heat first communicates vibrations to the
ether, and then to the molecules of the'body.  The vibrating molecules
in turn react upon the ether, and excite undulations of different lengths;
the longer vibrations corresponding to the calorific rays of least refrangibility, will have a greater amplitude, and will be the first to become
sensible as light.
Melloni discovered that the heat rays, emitted by bodies of low temperature,
are but little refracted by a prism of rock-salt, but as the heat of the body
becomes more intense, and the amplitude of all the vibrations may be considered greater, the rays of heat are more refracted, the more refrangible rays
appear as light, and the body becomes luminous. This result takes place at tho
temperature of about 947~ Fahrenheit, whatever be the nature of the luminous
substance. Draper formed a spectrum by mears of light from a narrow opening,
and examined with a lens and micrometer the positions of the dark lines of
Fraunhofer (461). He afterwards employed, instead of the narrow opening, a
platinum wire, the temperature of which he caused to vary by means of an electric
current, more or less intense, and he found that the red part of the spectrum
appeared first, and as the heat and brilliancy of the wire increased, the other
colors of the spectrum successively appeared up to the violet.  This result is in




HEAT.                              503
beautiful harmony with the theory stated above. Common observation also
shows that a heated body becomes first red, then yellow, purple, and at length
a full white heat. Compare ~ 178.
768. Heat and light produced by chemical and mechanical
action.-It is easy to understand that, in the molecular conflict which
constitutes chemical action, the ether around the molecules will be
violently agitated, and become the seat of undulations of different
rapidity. If the chemical action is weak, the vibrations will be slow,
and they will have only sufficient amplitude to be sensible, and it has
been observed that the heat thus produced furnishes rays more and
more refrangible as the chemical action becomes more active.  When
this action becomes sufficiently energetic to give to the more rapid
vibrations a sufficient amplitude, light accompanies the heat.
Experiments show that the color of the luminous rays depends upon the nature
of the substance from which they proceed, and it is also probable that the temperature at which light begins to appear, depends also on the nature of the
substance or the color which it gives forth. We can easily understand that the
nature of the molecules will affect the rapidity of the vibrations, and we may
presume that, if it were possible to augment gradually the energy of the chemical action, we should find the temperature at which light begins to appealt is
more elevated in proportion as the color of the light which the substance affords
approaches to white or violet. This conjecture is confirmed by the fact that the
incandescence due to chemical action, when it is feeble, gives forth red light.
In inechanical action, the vibrating molecules impress upon the ether vibrations of different rapidity, and when the action is sufficiently violent, as in the
shock of two flints, or in the sudden compression of a gas, light is emitted in
connection with the heat. Here, again, if we could graduate the intensity of the
action, we ought to obtain a color approaching more nearly to white as the mechanical action is more energetic.
We thus see how the effects which heat and light exercise upon bodies can be
explained by the theory of undulations.
The phenomena of heat in the interior of bodies are more difficult to comprehend, and it is impossible to explain them by the system of emission; but by
comparing them with other effects in elastic bodies, they are readily explained
by the theory of undulations.
769. Dilatation and change of state.-The heat received by a
body agitates the ether; this agitation is communicated to the molecules, and the volume of the body is increased in proportion as the
amplitude of the oscillation of the molecules becomes greater. It is
thus that bodies which vibrate longitudinally appear larger, and a
vibrating cord appears swollen. In the same manner, obstacles opposed
to vibrating parts become repelled, if they are so light as not to arrest
the vibrations.
This explanation leads us to a very simple and clear definition of
temperature:-Temperature consists in the vibratory state of the ether




504            PHYSICS OF IMPONDERABLE AGENTS.
within the body, and its intensity depends upon the amplitude of the
vibrations.
The theory of changes of temperature is naturally explained by the tendency
to establish an equilibrium between the amplitude @f the vibrations of bodies
near each other, through the medium of the ether which fills the space that
separates them. The molecules of bodies should, therefore, be considered as in
a perpetual state of agitation. There can, then, be no absolute zero only where
there is a state of perfect repose.
The only difficulty in admitting the existence of such a state, is the fact that
celestial space is certainly filled with agitation by the transmission, in every
possible direction, of the different radiations which emanate from the multitude
of stars which people space.
Change of state produced by heat.-If the motion of the molecules is sufficiently energetic, they leap out, as it were, from each other,
and become independent, as a glass rod vibrating rapidly in the direction of its length, is divided into many pieces.  We thus explain the
phenomena of fusion.
If we revert to the theory of the mechanical equivalent of heat, we can under.
stand how the conversion of heat into mechanical work, and vice versa, is a
direct consequence of the preceding; for, according to this theory, heat is a
species of motion, and the work which produces this motion of the ether, ought
to be changed into vibrations of this latter sort; that is, it should be transformed
into heat.
It is the same with the mechanical work developed by a vibrating body. The
work represented is that which has been expended in putting it into vibration.
The heat developed in moving bodies, by electro-dynamic induction, and the
work which it represents, are all related to the same theory.
770. Quality of heat changed by absorption and radiation.In all experiments upon radiant heat, it has been observed, that heat,
once absorbed, retains none of the peculiarities of the source from
which it was derived; but its refrangibility and other properties, when
again radiated, depend only on its temperature, and the nature of the
body fron which it is again emitted.
Heat, transmitted through diathermanous bodies, appears to be sifted, or to
leave behind some of those rays which are transmitted with difficulty through
that substance;that uane  that a larger percentage of the remaining heat will be transmitted through another similar screen.
Even rock-salt, generally considered colorless for heat (646), has been found,
by the later researches of Prof. Forbes, to transmit a somewhat greater proportion of heat of high temperature than of heat of low temperature.
It is well known that heat of great refrangibility, or small wave-length, passes
more readily through glass and mica than heat having the opposite qualities.
The difficulty with which heat radiated by rock-salt penetrates these substances,
as compared with ordinary heat, would lead us to infer that heat from rock-salt
has a greater wave-length than ordinary heat radiated from lampblack.*
* See an able article on radiant heat, by B. Stewart, Esq., in the Trans. of
Royal Soc. of Edinburgh, Vol. XXII., part I.




HEAT.                               505
771. Difference between quantity and intensity  of heat.Another curious fact connected with this subject is, that no amount of
heat of low temperature can be so applied to an object as to raise it to
a higher temperature than that of the source from which the heat emanated. Thus, the heat of the sun, when absorbed by a blackened wall,
and radiited, cannot be again raised to the intensity requisite to ignite
ordinary combustible substances, which are readily ignited by the direct
rays of the sun concentrated by a burning-glass.
The same degradation of heat, or loss of intensity, is observed in condensing
steam in distillation. The whole heat of the steam, both latent and sensible, is
transferred without loss to perhaps fifteen times as much condensing water; but
the intensity of the heat is reduced from 212~ to perhaps 100~ F. The heat is
not lost; for the fifteen parts of water at 100~ are capable of melting as much
ice as the original steam. But by no quantity of this heat at 100~ can temperature be raised above that degree; no means are known of giving it intensity.
If heat of low, is ever changed into heat of high intensity, it is by mechani..
cal means, as by the compression of gases or vapors to a smaller volume, when
the temperature is elevated; but this is rather the conversion of mechanical
force into heat, than the elevation of the intensity of heat previously existing
as such. Graham's Chemistry, Vol. I., p. 100.
It is stated that Dr. Wollaston received the beam of the full moon, concentrated by a powerful lens, in his eye, without feeling the least heat. Melloni
obtained only an extremely feeble indication of heat, by concentrating the rays
of the moon by a lens over three feet in diameter, and directing the brilliant
focus of light upon the face of a very sensitive thermo-multiplier. This may
merely show that the heat reflected or radiated by the moon, has become heat of
too low intensity to pass through a glass lens, or to warm bodies at the ordinary
terrestrial temperature.
All these phenomena are more readily explained on the undulatory theory,
than by the theory of emission.
772. Conclusion.-We conclude, from what has been stated, that
the theory of undulations, which so completely explains the phenomena
of heat and light, as well as the different sensations produced upon our
organs by the two sorts of radiations, may also enable us to compute,
with a little uncertainty in some cases, the different effects which heat
and light exercise upon bodies.  We see that heat and light are due to
the same cause, to ethereal vibrations; and that the same vibrations also
produce the two sorts of effects when their amplitude is sufficient, and
their rapidity comprised between certain limits.
It remains only to explain, by these movements of the ether, the numerous
and complex phenomena which are presented to us by electricity.
It is possible that these effects are produced by either longitudinal or rotary
vibrations, which accompany the- transverse vibrations corresponding to light
and heat.
But, while it is very easy to understand the facts relative to the propagation
of electricity, it is somewhat difficult to conceive how vibratory movements
45 *




506            PHYSICS OF IMPONDERABLE AGENTS.
produce attraction and repulsion. We ought not to regard this difficulty as
insurmountable, especially when we remember that polarization was, for a long
time, considered inconsistent with ethereal vibrations, until the idea of transverse vibrations dissipated the objection, and gave new clearness to the whole
series of phenomena.
If this difficulty were once conquered, there would appear a possibility of
uniting to the system of ethereal vibrations, the grand phenomena of universal
gravitation, which has been attempted hitherto without success.
But, when all the phenomena of nature, in their infinite variety, are reduced
to one and the same cause, wonderful simplicity will be joined to the idea which
we form of the power and majesty of the GREAT AUTHOR of all things.
To bring the detailed study and interpretation of facts to prove this grand
unity of cause, is the mission which science should propose to herself at the
present day.
This close correlation of physical forces, is in harmony with recent
philosophical views entertained by many of the first Physicists of our
time, but by no one more felicitously expounded than by Prof. Grove.*
A full and satisfactory discussion of this subject will be found in the
excellent Traite de Physique of Daguin (Vol. III., 1859), from which
the foregoing is condensed.
Problems on Heat.
Thermometers.
209. What number of Centigrade and Reaumur degrees correspond to the following temperatures in Fahrenheit's degrees?
Melting-point of mercury,......          40 F.
"    "      bromine,....              -  4
"    "      white wax,... +158
"    "      sodium,..  194
"    "      tin....                       442-4
"    "      antimony..771'8
Incipient red heat,.....  977
Clear cherry-red heat..... 1,832
Dazzling white heat,.......9,732
210. How many Fahrenheit and Reaumur degrees correspond to the following
temperatures in Centigrade degrees?
Temperature of maximum density of water,.       + -3~87 C.
Boiling-point of liquid ammonia,..           -40
i"    "     sulphurous acid,. -10
"     "      alcohol,...75
"     I     phosphorus,... 290
"     "      mercury,.... 360
211. How many times must the capacity of the bulb of a thermometer exceed
the capacity of the tube, in order that the thermometer may measure temperatures from 40~ below zero to 500~ F.?
* The Correlation of Physical Forces: pp. 229. London, 1855.




HEAT.                                507
Expansion.
212. If rods of the following substances, iron, brass, copper, glass, platinum,
silver, measure each 3 feet 2 inches in length at the temperature of 50~ F., what
will be their respective lengths at temperatures of 100, 250, 75~, and 100~ F.?
213. If a glass globe holds exactly one gallon at 60~ F., what will be its capacity if measured at the temperature of boiling water?
214. If a railroad is constructed in winter, when the average temperature is
25~ F., how far apart must the ends of the iron rails, 18 feet long, be laid to
allow sufficient room for expansion at the temperature of 120~ F.?
215. What change of temperature is required to produce an elongation of 3
inches in a portion of the Britannia tubular bridge (Q 172), 917 feet in length?
216. Gas-pipes, laid 3 feet below the surface of the earth, are exposed to a
change of temperature of 60~ F., from summer to winter; what is the extent to
which the joints (10 feet apart) will be opened in winter, if the strain is equally
divided among the several joints?
217. Calculate the lengths of the steel and brass rods required to adapt Harrison's gridiron pendulum to vibrate seconds at the following places: London,
Paris, New York, and St. Petersburgh.
218. Reduce the following heights of the barometer, observed at the annexed
temperatures, to the equivalent heights at the freezing-point:1.      30-1 in.       t   40~ F.      5.       23 2 in.       t=  50~ F.
2.      29 4   t= 250                   6.       24-7 "        t-80~
3.      279 "          t - 65~          7.       17-4  t  19~
4.      283 "          t=  75~          8.       158 "         t-10~
219. Reduce the following barometric observations made at 8~ C., to the temperatures indicated by the values of t, given below:1. 24  in. reduce to t   30~ C.         3. 28-5 in.  reduce to t    55 C.
2. 27-5 "       "          t —25~       4. 19-5 "       "   " t- 19~
220. A sphere of brass, 3 inches in diameter, immersed in water, is suspended
from the pan of a hydrostatic balance, and counterpoised at the temperature of
60~ F. What weight will be required to restore the equilibrium when the temperature of the water and globe is raised to 200~ F.?
221. To what temperatures must an open vessel be heated, the pressure remaining constant, that a, i, and I of the air it originally contained, may be
successively driven out of it?
222. A balloon containing 1000 cubic feet of gas at 80~ F., and 29 inches
barometric pressure, rises to a position where the thermometer stands at 40~,
and the barometer at 22 inches. Calculate the volume of the gas, supposing
the capacity of the balloon to allow it to expand freely.
Specific Heat.
223. How much heat is required to raise the temperature of
50 lbs. of water   from 40~ F. to 150~?
24 "  " sulphur,  "   63~   " 212~?
45 "  " charcoal, "   45~   " 930~?
25 "  " alcohol,   "   35~   "  65~?
11"  " ether,    "    5~' 132~?
224. The following quantities of water were mixed together,-2 lbs. of water
at 40~ F.; 5 lbs. at 65~; 7 lbs. at 70~; and 3 lbs. at 900. What was the temperature of the mixture?
225. How much water at 200~ F., and how much water at 50~, must be mixed
together, in order to obtain 20 lbs. of water at 85?




508             PHYSICS OF IMPONDERABLE AGENTS.
226. Equal volumes of mercury at 212~ F., and water at 32~, are mixed toge.
ther. What is the temperature of the mixture?
227. What temperature will be produced by mixing equal volumes of mercury
at 32~ F., and water at 212~?
228. Five pounds of ice at 32~, are mixed with 7 lbs. of water at 200~ F.
What will be the temperature of the mixture after the ice is melted?
229. How much ice at 32~, must be mixed with 100 lbs. of water at 50~ F., in
order to reduce the temperature of the mixture to 35~ F.?
230. How much ice at 32~, is required to cool 10 lbs. of mercury at 300', to
the freezing-point of water?
231. In order to determine the heat of fusion of lead, 200 ounces of melted
lead at the melting-point were poured into 1850 ounces of water at 50~ F. After
the lead had cooled, the water was found at 20~'76 Centigrade. Required the
heat of fusion of lead in degrees Fahrenheit.
232. How much heat is required to raise the temperature of a cubic foot each
of air, oxygen, carbonic acid, and hydrogen from 32~ F. to 75~, if the gas is
allowed to expand freely, and the barometer remains stationary at 30 inches?
233. In a room 20 by 30 feet, and 10 feet high, the barometer standing at 30
inches, how many units of heat are required to raise the temperature of the air
from 40~ F. to 75~?
234. In the last example, how many units of heat are expended in expanding
the air of the room?
Tension  of Vapors.
235. Before filling a barometer with mercury, a small quantity of water was
poured into the tube. How high will the mercury stand in the barometer when
the temperature is 75~ F., and the pressure of the air is 29 inches in an accurate barometer?
236. Solve the last problem, assuming, first, that alcohol, secondly, that sulphuric acid, and thirdly, that oil of turpentine were used instead of water.
237. Calculate the tension of the vapor of water at the following temperatures:
500, 750, 1100, 175~, 220~, 265~, and 300~ F.
238. Determine the boiling-point of water, ether, and alcohol at the following
pressures: 31 in., 29-75 in., 29-21 in., 28 in., 27-4 in., 23-7 in.
239. A cylinder is filled with steam at a temperature of 250~ F., and a pressure of two atmospheres. What will be the tension of the vapor if its volume
is diminished one-half by pushing down the piston? What will be the tension
of the vapor if it is allowed to expand to twice its former volume?
240. If a cubic inch of water is hermetically sealed in a bomb-shell, capable
of holding 200 cubic inches, and strong enough to sustain a pressure of 450 lbs.
to the square inch; what temperature is required to burst the bomb-shell?
Ventilation  and Warming.
241. How many flues, each six by twelve inches, and fifty feet high, are required to ventilate a lecture-room seating 1200 persons, when the temperature
of the room is 70~ F., and the external air at 30~, allowing each person three
and a half cubic feet of fresh air per minute?
242. Repeat the calculations of the last problem, on the supposition that 1500
persons are in the room, and make additional allowance for illumination by 50
gas burners, consuming each 3~ cubic feet of gas per hour, at an expenditure
of 20 feet of air for every cubic foot of gas consumed.




ELECTRICITY.                         509
CHAPTER III.
ELECTRICITY.
773. General statement.-Electricity is conveniently subdivided
into, 1. Magnetic electricity or magnetism; 2. Statical or frictional
electricity; and, 3. Dynamical or Voltaic electricity. We will consider
the subject in this order.
1. Magnetic Electricity.
I. PROPERTIES OF MAGNETS.
774. Lodestone-natural magnets.-There is found in nature an
ore of iron, called by mineralogists magnetite, or magnetic iron, some
specimens of which possess the power of attracting to themselves small
fragments of a like kind, or of metallic iron. This power has been
called magnetism, from  the name of the ancient city of Magnesia, in
Lydia (Asia Minor), near which the ore spoken of was first found. It
crystallizes in forms of the monometric system, often modified octohedra, like fig. 520, and is a compound of one equivalent    520
of peroxyd of iron with one of protoxyd.  (FeO +  Fe20       /\
-  FeO,.)  It is one of the best ores of this valuable /  
metal.
Formerly all magnets were lodestones, or natural magnets. A fragment of this ore rolled in iron filings or magnetic sand, becomes tufted, as in fig. 521, not alike in all parts, but
chiefly at the ends. Fig. 522 shows a similar mass mounted in a
frame, 1l, with poles, pp', of soft iron.      521            522
Thus mounted, the lodestone gains in
strength, by sustaining a weight from 
the hook below, on a soft iron cross-bar.
775. Artificial magnets are made
by touch or influence from a lodestone,       _              il
or from another magnet, or by an electrical current. Hardened steel is found to retain this influence permanently, while masses of soft iron become magnets only when in contact
with, or within a certain distance of a permanent magnet. Artificial
magnets are more powerful than the lodestone, and possess properties




510            PHYSICS OF IMPONDERABLE AGENTS.
entirely identical with it. Magnets attract at all distances, but their
power increases, like all forces acting from  a centre, inversely as the
square of the distance. Heat diminishes the power of magnets, but if
not heated beyond a certain degree (full redness), this power returns
on cooling, and is increased at lower temperatures.  Above that point,
the coercitive force is destroyed, and they lose all magnetic power.
Various forms are given to magnets. The bar nimag.et is a simple straight bar
of hardened steel. If curved so as to bring the ends near together, it is called
a horse shoe magnet, and if several bars, straight or curved, are bound together
into one, fig. 523, it is called a compound magnet, or magnetic battery. The
52-:
most powerful artificial liaclits canl sustain ouly about twenty-eight or thirty
times their own weight. Usually they sustain very much less than this.
Magnetic needles are light bars, fig. 524, suspended on a central point
so as to move in obedience to terrestrial or artificial at-   524
tractions. The mode of making magnets, and the circum-,.'
stances influencing their power, are noticed hereafter.
776. Distribution  of the  magnetic  forcepolarity.-The magnetic force is not equally distributed in all parts of a magnet, but is found concentrated chiefly about the ends, and diminisliing 
toward the centre, which is neutral. The points of greatest attraction
are called poles.  When a magnet is rolled in iron filings or magnetic
sand, the position of the poles is seen as in the bar magnet, fig. 525,
525
whose centre is found to be quite devoid of the attracted particles which
cluster about the ends. The point of no attraction is called the neutral
point-line of magnetic indifference, or equator of magnetism.  Every
magnet has at least two poles, and one neutral point.  The magnetic
poles are distinguished as N or S, Austral or Boreal (A and B), or by
the signs, plus (+) and minus (-), all these signs having reference to
the earth's attraction, and to the antagonism between the poles of unlike
name. The law regulating the distribution of magnetic force in a bar,




ELECTRICITY.                           511
was determined by Coulomb, by means of the torsion balance, ~ 820,
to be very nearly as the squares of the distance of any given point,
from the magnetic equator or neutral point.
777. Magnetic phantom —magnetic curves.-The distribution
of the magnetic force about the poles of a magnet is beautifully shown
by placing a sheet of stiff paper over the poles of a horse-shoe magnet,
and scattering fine iron filings or magnetic sand from a sieve or gauze
hag over the paper.  As they touch the surface of the paper, each
filing assumes a certain position, marking the exact place of the magnetic poles and of the neutral line, as seen in fig. 526.  The magnet
may be laid horizontally, or a series of magnetic bars may be placed
as in fig. 532, producing very pleasing and instructive results. Tapping
526
the edge of the paper gently with the nail, or a pen-stick, facilitates
the adjustment of the filings. The curves exhibited by the magnetic
phantom have been mathematically investigated by De lialdat, who for
that purpose transferred them to a glued paper.
To fix the curves, Nickles uses a waxed paper, and when the figures are produced, they may be fixed in position by holding a heated plate of iron near the
surface of the paper. As soon as the wax is fused, which is easily perceived by
its shining appearance, the source of heat is withdrawn, and as the wax cools
the filings become fixed in position and in full relief. (Am. Jour. Sci [2] XXX.
62.) The curves may then be more conveniently studied.
778. Magnetic figures mav be produced on the surface of a thin
steel plate, by marking on it with one pole of a bar magnet. Magnetism
is thus produced in the steel along the line of contact, which is afterwards made evident by magnetic sand, or iron filings sprinkled on the
plate.  These lines may be varied or multiplied at pleasure, with
pleasing effects; their polarity is always their polarity is always the reverse of that carried by
the bar. They may be nade even through parer or card-board, and
will remain for a long time.  Blows, or heat, will remove them. Hard
plate. Tiy
pleasing effects; their polarity is always the reverse of that carried by~i
th  br    Teymy  emae  vn   hruh  aerorcrdbor, n
will   remainfor a longtime. Blow, or heatwill    remov them. Har




512            PHYSICS OF IMPONDERABLE AGENTS.
plate steel is best for this purpose, about one-twentieth to one-eighth of
an inch thick, and six inches to twelve inches square.
779. Anomalous magnets are such as have more than two poles.
Thus the bar seen in fig. 527 has a pair of similar poles (-), at the
centre, and its ends are con-                     527
sequently similar (+), while it   \i
has two neutral points at a and        
c. Fig. 528 shows a bar with __                                     +
three sets of poles, arranged                     528
alternately -  and +, with three neutral points at m, o, and n. Broken
at these neutral points, every magnet becomes two or more separate
magnets, with corresponding polarity.
780. Attraction and repulsion.-The law of magnetic attraction
and repulsion is, that like poles repel, and unlike poles attract each other.
If a piece of soft iron is presented to either pole of a magnetic needle, fig.
524, there is attraction, which is reciprocal between the needle and the iron; for
if the iron is suspended, and the needle approached to it, the iron is attracted
by either end of the needle. If, however, a magnet is approached to the needle,
-4- to -, there is attraction; if -to -or - to.+, there is repulsion.
If the unlike poles of two equal magnetic bars, tufted with iron filings, are
approached, the tufts join in a festoon; but if the poles are of the same name,
most of the filings fall. For the same reason, if a magnetic bar, B, fig. 529, is
529
~A.~~~: A
slid upon another bar, A, of equal power to B, as the two opposite ends approach
each other, the key, previously suspended, falls, because the two bars mutually
neutralize each other by the opposing action of the austral and boreal magnetism.
781. Magnetism  by contact.-When a mass of iron, or of any
magnetizable body, is placed in contact with a magnet, it receives magnetism throughout its mass, and of the same name as the pole with
which it is in contact.  Thus, in fig. 530, the soft iron key is sustained
by the north pole of a magnetic bar; a second key, a nail, a tack, and
some iron filings, are, in succession, also sustained by the magnetism
imparted by contact from the bar magnet through the soft iron. The
series of soft iron rings, in fig. 531, is sustained from  the bar magnet
under the same conditions of polarity. Tested by a delicate needle,




ELECTRICITY.                          513
every part of the sustained masses will manifest only north polarity, and
we may regard them as only prolongations of the original pole. This is
analogous to electrical conduction.                             530
Pure soft iron receives magnetism sooner and more power-! 
fully than steel or cast iron, and also parts with it sooner. 
Hardened steel and hard cast iron retain more or less of the 
magnetic force permanently.  No other metals beside iron, 
nickel, cobalt, and possibly manganese, can receive and retain
magnetism  by contact.                   531!
These  are, therefore,
called the magnetic_  
metals.
782. Magnetism in                                  "             l'
bodies not ferrugin-   
ous.-Beside the magnetic metals, so called, (                                      E
Cavallo has shown that 
the alloy, brass, becomes
magnetic (slightly) by 
hammering, but loses
that property again by heat.  Some minerals are magnetic, particularly when they have been heated.  The pure earths, and even silica,
are found to have the same property.  In the case of silica, and some
other minerals containing oxyd of iron in combination, this is not so
surprising. M. Biot determined in the case of two specimens of mica,
one from Siberia (muscovite), and the other from Zinnwald (lithia mica),
that their magnetic powers were (by the method of oscillations) as 6'8
to 20, and he remarked, if the oxyd of iron be the cause of their magnetic
virtue, it should exist in the minerals in the above proportion; and curiously enough, the result of Vauquelin's analyses (then unknown to M.
Biot) corresponded, almost exactly, to these numbers.
Some states of chemical combination, however, appear to destroy, or cloak,
the magnetic virtues of iron; e. g. an alloy of iron, one part, with antimony
four parts, was found by Seebeck to be utterly devoid of magnetic action; and the
magnetic power of nickel is entirely concealed in the alloy called German silver.
The researches of Faraday have shown matter of all kinds to be subject to a
certain modified degree of influence by magnetism (Q 799. Diamagnetism).
II. MAGNETIC INDUCTION OR INFLUENCE.
783. Induction.-Every magnet is surrounded by a sphere of magnetic influence, which has been called its magnetic atmosphere. Every
magnetizable substance within this influence becomes magnetic also
(without contact), the parts contiguous to the magnet pole, having an
46




514            PHYSICS OF IMPONDERABLE AGENTS.
opposite, and those remote from it, a similar name.  This influence is
called induction.
Thus, in fig. 532, the north end of a bar magnet induces south polarity in the
contiguous ends of the five bars surrounding it, and north polarity in their
remote ends. If these bars are of hardened steel, they      532
will retain a small portion of the magnetic force induced
from a powerful bar, but if they are of soft iron, they
will part with their magnetism as soon as the source     L 
of excitation is withdrawn. In this case, the magnetized
bars have a tendency to move up to the magnet, and are        IT.,
prevented from doing so only by friction and gravity.   l'
The attraction is reciprocal, and we hence infer that
there is induction in every case of magnetic attraction.
In the iron filings, arranged in magnetic curves, fig.
526, on a glass plate, or card-board, the same tendency 
is observed.
Small pieces of soft iron wire suspended from the ends of a thread near, and
parallel to each other, when approached by a bar magnet, receive induced magnetism, the farther ends diverging by mutual repulsion. Two sewing-needles
thus suspended and influenced, become permanent magnets.
The ingenuity of the teacher will furnish many pleasing and instructive illustrations of magnetic induction.
784. Theoretical consideratons.-The real nature of the magnetic
force is unknown to us; but the analogies offered by electro-mnagnetism1
and magneto-electricity, lead to the conviction that it is one mode
of electrical excitement. Unlike light, heat, and statical electricity,
magnetism affords no phenomena immediately addressed to the senses.
It is distinguished from  statical electricity chiefly by its permanent
character when once excited, and by the very limited number of substances capable of receiving and manifesting it.
785. Theory of two fluids.-It may be assumed that tliere are two
magnetic or electrical fluids (the Boreal or positive, and the Austral or
negative), which are in a state of equilibrium or combination in all
bodies; that in iron, nickel, &c., these two forces are capable of separation, by virtue of the inductive influence of the earth, or of another
magnet, while, in other bodies, this permanent separation cannot be
effected. The two magnetic forces are never seen isolated from each
other, but are always united in one bar.  Ience, we cannot have a
boreal magnet, or an austral magnet, as we may in statical electricity
produce, at pleasure, vitreous or resinous excitement over the whole
surface of a body.  Both poles must coexist in every magnet.  If we
break a magnetic bar at its neutral point, we have two magnets of
diminished force, but each half has its two poles like the original bar,
and its neutral point also.  The anomalous magnets, figs. 527, 528, will
render this statement intelligible.  Every magnet must, in this view,




ELECTRICITY.                           515
be regarded as an assemblage of numberless small magnets, every
molecule of steel having its own poles antagonistic to those of the next
contiguous particle.  This conception is rendered clearer to the senses
by fig. 533. IIere the N and S poles                  53
of the several particles are each re-    c=cL=_=              c=-IN       c z  m
presented as pointing one way re-               C 3 -        - Cm ~   — a
spectively, and towards the N and S   ns n5S n S ns ns ns ns ns
ends of the bar.  These opposing forces, therefore, constantly increase
from the centre or neutral point, where they are in equilibrium, to the
ends, where they find their maximum.  This arbitrary illustration
enables us to conceive how such a body may excite similar manifestations of power in another, without itself being weakened, and how
each part becomes a perfect magnet, if the bar is broken. The experiment shown in fig. 529, illustrates well the reunion of the two fluids,
to form the neutral state of the undecomposed influence.
De Haldat has shown that a brass tube, filled with iron filings, confined by
screwed caps of brass, can be magnetized by any of the modes used for bars,
and have its poles and neutral point like a bar magnet; but if, by concussion,
the particles of iron are disarranged, the magnetic force diminishes, and finally
disappears.
The magnetic pastes of Dr. Knight and of Ingenhausz, also illustrate the fact,
that little particles of magnetic iron, or of pulverized lodestone, may determine
the existence of the magnetic poles, and a neutral line, when they are compacted
into a mass, by drying oils, or by the use of some gummy substance.
Even so small a quantity as one-sixth of ferruginous particles, in five-sixths
of sand or earthy matter, can be magnetized as a bar, showing clearly the decomposition of the neutral fluid in each particle.
786. Coercitive force.-The resistance which most substances show
to the induction of magnetism, has been distinguished by the term coercitiveforce. In soft iron, this force may be regarded as at a minimum,
since this substance will receive magnetic influence even from being
placed in the line of magnetic dip, while in steel which has been hardened, a peculiar manipulation is required to induce any permanent
magnetism.  Soft iron parts with its induced magnetism as readily as
it receives it; but, if it is hardened by blows, or violent twisting, or by
small portions of phosphorus, arsenic, or carbon combined with it, a
portion of magnetism is permanently retained by it from induction.
As blows, by hardening, may induce permanent magnetism in soft iron, so, in
steel, the coercitive force may, by simple vibration, as by blows on a magnetic
bar, or by an accidental fall, destroy a large part of the force developed, by
giving opportunity to the coercitive force to resume its supremacy. In general,
whatever cause induces hardness, increases the coercitive force; and, conversely,
it is diminished by annealing, or any cause which results in softening the mass.
III. TERRESTRIAL MAGNETISM.
787. Magnetic needle.-Directive tendency.-A magnetic nee



516            PHYSICS OF IMPONDERABLE AGENTS.
die, suspended over the poles of a horse-shoe magnet, comes to rest in
the plane of the poles; and, in obedience to the fundamental law of
magnetic attractions, its A and B poles                534
will be opposite to the B and A poles
of the attracting  magnet.  The sus-                            A
pended needle, in fig. 534, assumes its
position by reason of the same law, and
comes to rest with its A pole toward the
N pole of the earth, and its B pole to- 
wards the south.  All bar magnets, ~ Shaving a free motion in a horizontal
plane, arrange themselves in this manner in every part of the earth.
This directive tendency of the magnet has    _
been known to European nations since the
twelfth century; but was known, it is said, to the Chinese, 2000 B. c. The
earliest mariner's compass, used by Syrian navigators in 1242, was a common
sewing-needle, rendered magnetic, thrust through a reed or cork, and allowed
to float on water. (Klaproth.)  This directive power renders the compass invaluable to the explorer of a pathless wilderness, to the surveyor and the miner;
the mineralogist and the physicist also find it indispensable in many researches.
The terms Austrll and Boreal have been applied to the polarity of the magnetic needle, in allusion to the free Austral and Boreal magnetism assumed to
exist respectively in the southern and northern regions of the earth. In accordance with magnetic law, the end of the needle pointing north is called Austral,
and that pointing south, Boreal. For greater simplicity, the mariner's compass
is marked N on that point which turns to the north, and conversely; but the
terms austral and boreal may be used interchangeably with positive and negative, or north and south polarity.
The mariner's compass is arranged in a box (K, fig. 535) called a
535                              536
binnacle, iliuminated at night through the glass, M. The magnetio




ELECTRICITY.                           517
needle, a b, fig. 536, delicately poised on a socket of agate, is attached
to the lower side of a card or plate of mica, t, on which is printed the
star of thirty-two points,-seven between each two of the cardinal
points, N., E., S., and W. The compass-box, oo, is hung on points
called gimbals, c d c z (pronounced ginmles), which allow it to remain
always horizontal, however the ship may roll. The transom or crosssights, A, may be placed at pleasure on the face, m, of the compass,
wheni the object is to measure points on the coast. Both parts of the
figure are similarly lettered.
The astatic needle is an instrument in which the directive tendency of
the earth's magnetism is neutralized, by placing two equal needles, a b, b' a',
fig. 537, parallel, one above the other, with their unlike poles  53
opposed to each other. This system is suspended by a fibre
of raw silky and is a most sensitive test for feeble magnetic
curreints. Such is the construction adopted in the galvaniscope, to be hereafter described. The two needles must be
of exactly equal force, or a b and a' b' will not neutralize
each other, and the system will have a directive tendency,
equal to any difference of force in the two needles.     a       I
The most simple astatic needle is made by touching a steel
sewing-needle, at its centre of weight, by the N. pole of a''
powerful magnet; the point touched develops two S. poles, 
ahd the two ends are N. Such a needle is very nearly astatic.
788. Magnetic meridian-declination or variation.-There are
but few places in the world where the magnetic needle points to the
true, or astronomical North; and in all other places, a plane passing
through the axis of the magnetic needle (the magnetic meridian), fails
to coincide with the geographical meridian.  Moreover, the magnetic
meridian in any given place is not constant, but changes slowly from
year to year (called secular variation), being now on the E., and again
on the W. side of the true North.  This is called the declination or
variation of the magnetic needle.  The declination is called Eastern,
or Western, according as it may be to the East or to tip West of the
astronomical meridian.  The angle formed by the meeting of the true
and the magnetic meridians is called the angle of declination.  Thus,
at Washington City,* the angle of declination in 1855-6, was 2~ 36' W.,
and at New Haven it was 6~ 37/'9 W., August 12, 1848.  Js. Ruth,
observer.
Columbus, in his first voyage to America, found the needle to have,'as he
sailed westwards, an increasing variation from the true North, a circumstance
not before observed, and which caused the greatest consternation in his superstitious crew, "who thought the laws of nature were changing, and that the
compass was about to lose its mysterious power." (Irving's Columbus.) Not* U. S. Coast Survey Report, 1858, 196. C. A. SCHOTT, Observer.
46*




518            PHYSICS OF IMPONDERABLE AGENTS.
withstanding these and other similar observations, it was not until the middle
of the seventeenth century, that the variation of the compass was an established
fact in magnetic science. The observations on the declination cf the compass
in England, date from 1580. The following table, from Harris, contains the
declination with the mean rate of motion, as referred to certain periods of observation in London, between 1580 and 1850, or about two hundred and seventy
years. Eastern declination being distinguished by the negative sign, and western by the positive sign.
Eastern Declination.   Zero.                Western Declination.
Years,         1580.  1622. 1660. 1692. 1730.   1765    1818    1850
Declination, -11~ 15' -6~   0    +60  +13~  +20~ +24~ 41' +22~ 30'
Rate per year,    7'      8' 10'    11'  11'5    9'         0'       5'
Thus, in a period of eighty years from the first observation, the needle gradually reached the true meridian, and then, for a period of one hundred and fiftyeight years, it moved Westward, reaching its maximum Westerly declination in
1818, and it is now again slowly moving Eastwards. The rate of this movement is not uniform, but is greater near the minimum, and least near the maximum, point of declination.
Observations since 1700 establish the same facts in the United States, at a
great number of places. Thus, at Burlington, Vt., in 1790, the declination was
+7~'8; in 1830, +8~'30; in 1840, +9~ 07; and, in 1860, +10~'30. In Cambridge, Mass., in 1700, it was +9~'9, and steadily diminished to 1790, when it
was — 6"'a and has since regularly increased to the present time, being, in
1855, +100~90. At Hatborough, Pa., in A. D. 1680, the declination was +8~'5;
in 1800 it had, by a regular rate, decreased to +1~'8, and, in 1860, was -5~032.
At Washington, D. C., it was +0'6 in A. D. 1800, and in 1860 had increased to
+2-~9.
South of Washington, the declination is uniformly Easterly, ranging, at
Charleston, S C., from -3~07 in A. D. 1770, to -1~-7 in 1860. On the Western
Coast of North America, it is also Easterly; being, for example, at San Francisco, in 1790, -13~'6, and in 1860, -15'~8. The annual change (increasing E.
declination) being, in 1840, — 1'6; in 1850, -1'2; and in 1860, -0'"8.
For a full discussion of Magnetic Declination in the United States, the student will refer to the Reports of the United States Coast Survey; and for an
able extract of all the results of secular change on the Atlantic, Gulf, and Pacific Coasts of the United States, refer to a "Report by Assistant Charles A.
Schott," in Am. Jour. Sci. [2] XXIX., p. 335.
The first attempt to systematize the variations of the magnetic needle,
and to connect by lines, called isogonic lines, all those places on the
earth where the declination was similar, was made by Halley, about
1700. He thus discovered two distinct lines of no inclination, called
agonic lines, one of which ran obliquely over North America and across
the Atlantic Ocean, and another descended through the middle of China
and across New Holland; and he inferred that these lines communicated near both poles of the earth.
789. Variation  chart.-Isogonal lines.-In fig. 538, is seen a
projection of the lines of equal and no declination, on a Mercator's
chart of the earth, embracing observations down to 1835. The Ameri



ELECTRICITY.                          519
can line of no variation, or agone, crosses the eastern point of South
America, in latitude 20~ S., skirts the Windward Antilles, enters North
538
140 120 100 80 60 40 20  0 20 4060 80100 120 140 160
40                                                            to
140 120100 80 60 40 20  0 20 40 60 80 100 120 140 160
Carolina near Cape Lookout, and passing through Staunton, in Virginia, crosses Lake Erie midway on its course to Hudson's Bay. The
chief Asiatic agone (for, in fact, there are two lines of no variation),
after traversing the Indian Ocean in a southerly direction, crosses the
western part of New Iolland near 120~ E. All the entire lines on this
chart indicate western declination, while the dotted lines mark eastern
declination. According to the theory of Gauss, the eminent Germali
astronomer, no lines of equal variation can form diverging branches, or
be tangents to each other; but when there is a space within which
the declination is less than outside any portion of its limiting line,
that line must form a loop, the two                  539
branches intersecting at right angles.           - lx
The observed line of 8~ 40' in the
Pacific, beautifully illustrates  and
confirms this theoretical position, as
shown on the chart, fig. 538. 
Figure 539 illustrates the circum- l
polar relations of the corresponding s
lines of equal variation in the north- 
ern hemisphere.  It will be seen
that much the larger number of the
isogonal lines, converge on the Mercator's projection at a point near
Baffin's Bay, in lat. 730~0 N., long. 70~-0 W., its opposite pole is to the
southward of New Holland.




520           PHYSICS OF IMPONDERABLE AGENTS.
Halley's original chart assumes the existence of two magnetic poles in each
hemisphere, one fixed, and the other revolving about it in a certain period.
Hansteen, in 1828, in his well-known chart, accepts the same view. By Gauss's
theory of terrestrial magnetism, only one magnetic pole in each hemisphere is
required, and thus far observation has shown a wonderful conformity between
the theory of Gauss and the facts.
790. Daily variations of the magnetic needle.-Besides the
great secular movements of the magnetic needle already noticed (788),
it is found to vary sensibly from day to day, and even with the different
periods of the same day.. The most refined means have been in our
time applied to the exact investigation of this phenomenon, first noticed
by Graham, a London optician, in 1722. It has been shown that the
north pole of the needle begins between seven and eight A. M. to move
westward, and this movement continues until one P. M., when it becomes
stationary. Soon after one o'clock it slowly returns eastward, and at
about ten P. M., the needle again becomes stationary at the point from
which it started. During the night, a small oscillation occurs, the north
pole moving west until three A. M., and returning again as before. The
mean daily change, as observed by Capt. Beaufoy, is not quite one
degree. This daily disturbance of the magnetic needle is undoubtedly
due to the action of the sun, and it will therefore vary in different latitudes. In the Southern hemisphere, the daily oscillations are of course
reversed in direction to those of the Northern hemisphere.
The, annual variation of the needle was discovered by Cassini, in 1786.
We have, therefore, 1st, the great secular variations, continued through long
periods of time; 2d, annual variations, conforming to the movement of the sun
in the solstices; 3d, daily variations, conforming nearly to the periods of maximum and minimum temperature in each day, and lastly, irregular variations,
connected with the aurora borealis, or other cosmical phenomena, which Ilumboldt has called magnetic storms.
791. Dip or inclination.-A needle, hung as in fig. 540, within a
stirrup upon the points a b, the whole system being suspended by a
thread, will, before magnetizing, if carefully adjusted, stand in any
position in which it may be placed. If now the needle be magnetized,
it forthwith assumes the position seen in the figure, its pole dipping
toward the North pole of the earth. In this latitude (41~ 18'), the dip
was, in 1848, 73~ 31-'9. Such a needle is called a dipping needle, and
if constructed as in the figure, it shows both the declination and dip, or
inclination, of terrestrial magnetism for any given locality. As the
whole system is free to move, it will obviously arrange itself in the
magnetic meridian, and its position of equilibrium will be the resultant
of the two forces of declination and dip. Approaching the equator,
the dipping needle becomes constantly less and less inclined, until at




ELECTIrCITY.                             521
last a point is found where it is quite horizontal, and this point will be
in the magnetic equator; an imaginary plane near, but not coincident
with, the equator of the earth.                              540
The discovery of the magnetic dip or inclination,
was made in 1576, by Robert Norman, a practical
optician of London, who constructed the first dipping
needle, by which he determined the dip at London at
that time to be nearly 72~. The magnetic dip, like
the declination, is subject to continual and progressive changes, both secular and periodical, and it is
at this moment rapidly decreasing. Thus at London
in 1576 it was 71~ 50', in 1676 it had become 73~ 30',
and in 1723 it was 74~ 42', having then reached its 
maximum. In 1790 it had decreased to 71~ 3', and 
in 1800 to 70~ 35'. Sabine, in 1821, fixed it at 70~ 3',
and Kater, in 1830, at 69~ 88'. It is now, in England, 
about 68~ 30', having decreased in 128 years.about
60 12', or at the rate of nearly 3' yearly, the mean
annual movement from 1830 to 1850 being at the
rate of more than 4' yearly, while between 1723 and
1790 it was about 2 5' yearly, showing an accelerated
and retarded movement in the secular changes of the
dipping needle, or magnetic inclination. 
792. The action of the earth's magnetIsm on the dipping needle is neatly illustrated 
by the simple arrangement seen in fig. 541, where the magnetic bar sn,
is placed horizontally on the diameter of a semicircle, representing an
arc of the meridian, on which a small dipping needle is made to
uccupy successively the position                     541
seen at a, a', a", a'.
At a', the needle is horizontal,. 
being at the magnetic equator, and                                 al
equally acted on by both poles. In
every other position, the influence 
of one pole must predominate, to a/..\ 
greater or less extent, over the other.  /                       A
Several sewing-needles, suspended.  lillllllllt  ~
over a magnetic bar at equal distances, one over each end, one over
the centre, and one intermediate, will
illustrate the same point satisfac- 
torily.
793. Dipping needle.-The dipping needle of Biot, shown in fig.
542, is wholly of brass, and embraces two graduated circles, m and M,
one horizontal and one vertical. The circle, M, with its supporting
frame, A, moves in azimuth over m, by which it is placed in the
magnetic meridian.  It is leveled by the level, n, adjusted by three




522           PHYSICS OF IMPONDERABLE AGENTS.
milled heads in the feet. The needle, a b, is suspended on the bars,
r.  To fix the magnetic meridian by this instrument, the circle, m, is
revolved until the needle,                   542
ab, stands vertical and
points to 900, it is then
in the magnetic equator,
a position of course exactly 90~ from  the mag-         ld 
netic meridian, which is                           i
then obtained by revolv-        e  
ing the frame, A, 900
backwards.  The angle,
acd, is the angle of inclination (or dip), and is  1
read on the arc M.                         _ 
Two small errors of observation exist in this instrument; 1st, from the fact
that the magnetic axis of                          _
the needle does not coincide
with the axis of its form,:      =-_
and 2d, from  the circu m-                                          -
stance that the centre of
gravity of the needle does
not lie in the points of sus-            i - o
pension, and that therefore the angle, dc a, is greater or less than the true
angle of inclination, by a very small quantity. The first is corrected by
reversing the plane of the instrument, by a revolution of 1800, and taking the
mean of the two readings; the second, by reversing the polarity of the needle
by touch on the opposite poles of two bar magnets, provided for the purpose.
By this means, the centre of gravity is brought, first above, and then below
the point of suspension, and the mean of the two readings is the true angle
sought.
794. Inclination map, or isoclinal lines.-In fig. 543, is presented a Mercator's projection of the line of no dip' or magnetic
equator, and the position of the isoclinal lines of 300, 500, 700, 800, and
850 north, and 30~, 500, and 700 south. It will be noticed that the
magnetic is below the terrestrial equator, in all the western hemisphere, and is above it in the eastern, crossing it near the island of St.
Thomas, in longitude 30 E., and again in the Pacific ocean. These
points of intersection of course vary with the progressive changes of
the magnetic dip. The greatest declination of the magnetic equator
from the equinoctial line, amounts to about 200 N., near 530 E. longitude, and its greatest southern declination is 13~, in about 40~ W.
longitude, near the bay of Bahia, on the East coast of South America.




ELECTRICITY.                          523
The inclination of the needle at any place is, approximately, twice
its magnetic latitude.  (Kraft.)
543
160 140 120 80 60 40  20 0  20 40 60 80 100 120 140 160
160i -14   80 -    40  200204600                      6
Figure 544 shows the relation of the isoclinal lines of 80~ and 85~ in
the northern hemisphere, to the lines of latitude, and to the N. magnetic
pole, near Baffin's Bay.  Sir James                 544
Ross, in 1832, found the needle to
dip near Prince Regent's Inlet, lat.
70~ N., longitude 96~ N., within one.. \
minute of 900.                                   
It is to be observed, that the lines   -
of equal magnetic inclination (isocli-                           \
nal lines), are' found to approach in''
position, with very considerable conformity, to the isothermal lines, or
lines of equal temperature, thus indi- 
cating a close relation between the
earth's magnetism  and the distribution of the terrestrial heat.
795. Magnetic intensity.-It is plain, from the phenomena of the
magnetic declination and dip already considered, that the distribution
of magnetic force over the earth is unequal, although in general it is
most active about the poles, and least so about the equator. The question arises, how may the magnetic intensity at any given point of the
earth be determined?  This question is answered by the use of the
needle of oscillation.  A large number of facts serve to show, that a
freely suspended needle in a state of oscillation, is influenced by the




524            PHYSICS OF IMPONDERABLE AGENTS.
magnetic force of the earth, in a way analogous to that of a common
pendulum, oscillating by the influence of gravity; and that hence by
means of such a needle, we may determine the ratio of the intensity
of terrestrial magnetic force throughout the whole extent of the earth's
surface.
This mode of determining the magnetic intensity in different regions of the
earth, was first suggested by Graham, in 1775, and was afterwards more fully
perfected and employed by Coulomb, Humboldt, Hansteen, and Gauss. Humboldt carefully determined the time of a given number of oscillations of a small
magnetic needle, first at Paris, and afterward in Peru. At Paris, the needle
made two hundred and forty-five oscillations in ten minutes: in Peru, it made
only two hundred and eleven in the same time. The relative intensities were
therefore as the square of these two numbers, or as 1: 1'3482, which, assuming
the point on the magnetic equator in Peru as unity, will give the magnetic
intensity at Paris as 1 3482. This kind of observation has since been extended
to nearly every known part of the globe, and full tables have been published,
giving the results. Thus the intensity at Rio de Janeiro is 0 887; Cape of Good
Hope, 0-945; Peru, 1; Naples, 1-274; Paris, 1-348; Berlin, 1-364; London,
1-369; St. Petersburg, 1-403; Baffin's Bay, 1-707.
The most complete statement of the results of American observations on the
magnetic elements has lately been published by Dr. A. D. Bache, in Am. Jour.
Sci. [2] XXIV., p. 1, where all the earlier observations are collated, with the
more extended results of the Coast Survey, with maps.
796. Isodynamic lines, or lines of equal power, are such as connect places in which observations show the magnetic intensity to be
equal.  These lines are not always parallel to the isoclinal lines,
although nearly so, and the points of greatest and least intensity are
not exactly identical with the points of greatest and least inclination.
Hence the intensity of the magnetic equator may not be everywhere the
same.  These lines are probably curves of double curvature returning
into themselves, implying the existence of two intensity poles, the
western, near Hudson's Bay, in lat. 500 N., ion. 90~ W; and the eastern
or Siberian pole, about 70~ N., and Ion. 120~ E.  The two southern
poles have been placed, one to the south of New IIolland, in lat. 60~
S., ion. 140~ E.; the other, in the South Pacific, also in lat. 60~ S., but
ion. 120~ W. These four poles are not therefore diametrically opposite
to each other.
The terrestrial magnetic force increases toward the south pole, nearly in the
ratio of 1: 3, and as both the maximum and minimum magnetic intensity on
the globe are found in the southern hemisphere, it would appear that the ratio
of I: 3 expresses very nearly the maximum and minimum magnetic force of the
whole earth. From the profound inquiries of Gauss, it appears that the absolute
terrestrial magnetic force, considering the earth as a magnet, is equal to six
magnetic steel bars of a pound weight each, magnetized to saturation, for every
cubic yard of surface. Compared with one such bar, the total magnetism of the
earth is as 8,864,000,000,000,000,000,000: 1, a most inconceivable proportion.
(Harris.)




ELECTRICITY.                             525
797. The inductive power of the earth's magnetism  is manifested by the polarity developed in any bar of soft iron, or of steel,
placed in an erect position, as in fig. 545, or better, in the angle of the
dip of the place.  The end of the bar toward the earth is always
Austral, Boreal magnetism existing at the upper end, B, and a neutral
point at the centre, M.  These facts are demonstrated by the action of
a small needle, held in the hand at the three                 545
positions, shown in the figure. If the experiment were made in the southern hemisphere,                b
the polarity would be reversed.
For this reason, all masses of iron standing in a
vertical position become magnetic. In soft iron this
magnetism is transient, but in steel tools, especially
such as are subject to vibration, as drills, the magnetism developed is permanent.
Barlow found that globes of iron, like bomb shells,
a foot or more in diameter, become miniature copies
of the earth by virtue of the inductive force exerted
upon them by the earth's magnetism; having a mag- 
netic axis in the line of dip at the place of experiment, 
and an equator at right angles to their axis. Delicate
needles, poised on the equatorial line of such globes,
suffered no disturbance, while in any other position 
on the sphere, both declination and dip were nlanifest.
Barlow  further discovered, that such a sphere
of iron, placed in a certain relation to a compass''illIliillit/lIllil il 1!,
needle on board a ship, united, and harmonized the local attractions of the
ship's iron, so as to free the compass from the effects of such disturbing causes.
798. System  of simultaneous  magnetic  observations.-The
distinguished Prussian philosopher, Alex. v. Iumboldt, in 1836, proposed to the scientific world to set on foot a series of connected and
simultaneous observations, to be made over as large a portion of the
earth's surface as possible, for the purpose of establishing the laws
relating to the magnetic forces.
In accordance with this suggestion, the leading governments of Europe
(France excepted), and many of the scientific societies both in the old and new
world, commenced such observations, with instruments specially contrived for
the purpose, and in buildings made without iron, both on and beneath the earth's
surface. Expeditions were sent to the Arctic and Antarctic circles, to Africa, to
South and North America, and to the Pacific Ocean, while at numerous stations
in India, Russia, Europe, and North and South America, hourly and simultaneous observations have been carried on for a long period, and in many places
are still continued. In this way a great mass of facts has been accumulated,
from a careful comparison of which the laws of terrestrial magnetism already
announced have been educed or confirmed.
Perhaps the most remarkable result of these observations is the fact, first
47




526             PHYSICS OF IMPONDERABLE AGENTS.
established by them, that not only the greater variations in the earth's magnet.
ism, but the most minute and irregular disturbances occur at the same instant
in places the most distant from each other, showing a wonderful connection and
coincidence in the causes of these phenomena throughout the world.
799. Lines of magnetic force.-The illustrious English philosopher, Faraday, has demonstrated that all matter is subject to magnetic
influence.
As the evidence on which this important induction rests is chiefly derived
from the use of electro-magnetism, its particular consideration is more conveniently referred to that subject. His general views, connected with terrestrial
magnetism, may be thus stated. All space both above and within the limits of
our atmosphere may be regarded as traversed by lines of force, among which
are the lines of magnetic force. The condition of the space surrounding a
magnet, or between its poles (777), may be taken as an illustration of this
assumption. It is not more difficult to conceive of force existing without
matter, than the converse, and it is certain that we know matter chiefly by the
effects it produces on certain forces in nature. The lines of magnetic force are
assumed to traverse void space without change, but when they come in contact
with matter of any kind, they are either concentrated upon it, or dispersed,
according to the nature of the matter. Thus we know that a suspended needle
is attracted axially by a magnet, while a bar of bismuth, and many other solid,
liquid, or gaseous bodies, similarly placed between the poles of a magnet, are
held in a place at right angles to the axis, or eqiatorially. Hence all substances
may be classified either as those which, like iron, point axially, and are called
PARAMAGNETIC substances, and those which point equatorially, and termed
DIAMAGNETIC. The force which urges bodies to the axial or equatorial lines is
not a central force, but a force differing in character in the axial or radial directions. If a liquid paramagnetic body were introduced into the field of force, it
would dilate axially, and form a prolate spheroid; while a liquid diamagnetic
body would dilate equatorially, and form an oblate           546
spheroid.
The diagram, fig. 546, will serve to render more  lili    l
clear the action of diamagnetic and paramagnetic
substances, upon the lines of magnetic force. Thus
a diamagnetic substance, D, expands the lines of
force, and causes them to open outwards, while a paramagnetic body, P, concentrates these lines upon itself. Bodies of the first class swing into the equator
of force, or lie at right angles to the lines of force, while tlyse of the paramagnetic class become axially arranged, parallel to the lines of force.
800. Atmospheric magnetism.-The discovery, by Faraday, of the
highly paramagnetic character of oxygen gas, and of the neutral character of nitrogen, the two chief constituents of the atmosphere, is
justly esteemed a fact of great importance in studying the phenomena
of terrestrial magnetism.  We thus see two-ninths of the atmosphere,
by weight, consisting of a substance of eminent magnetic capacity,
after the manner of iron, and liable to great physical changes of density, temperature, &c., and entirely independent of the solid earth.  In
this medium  hang suspended the tagnetic bars, which are used as




ELECTRICITY.                              527
tests, and this magnetic medium is daily heated and cooled by the sun's
rays, and its power of transmitting the lines of magnetic force is thus
affected, influencing, undoubtedly, those diurnal changes already considered.
801. Notions of the origin  of the earth's magnetism.-Two
hypotheses have hitherto divided the opinions of philosophers in explaining the phenomena of terrestrial magnetism.
The older of these views (Hansteen's) assumes the existence of an independent magnetism  in the earth, with its focus, or seat, near the earth's centre.
This internal power manifests itself chiefly at four points near the surface, two
of which, at the opposite ends of the supposed magnetic axis, are the most energetic, and are known as the magnetic poles. The minor poles have their own
independent axis, and move around the principal axis from west to east in the
western hemisphere, and the reverse in the southern, giving origin to the wellknown phenomena of the secular variation of the needle. However well this
hypothesis met the facts of terrestrial magnetism some years since, the rapid
progress of our knowledge'of magnetic. phenomena, both terrestrial and general,
within a short period, has materiail hanged scientific opinion. The diurnal
and irregular variations in the magnetic forces, cannot be explained upon Hansteen's hypothesis, and especially the simultaneous occurrence of these disturbances at different points of observation. Nearly all bodies are now known to be
susceptible to magnetic influence, while the maximum and minimum magnetic
intensity are found in those.regions of the globe where the minimum and maximum of superficial heat exist.
It is hence now argued, that the crust, or surface, and not the interior of the
earth, is the seat of the magnetic force. That this force is manifested with least
energy at the equator of magnetism, and with increasing power toward the
poles, where, as in an artificial magnet, it attains its maximum development,
because there we find the most perfect separation of the magnetic fluids: that
the coercitive force (786) of the materials of the earth's surface is resolved by
the solar heat, and that the depth to which this separation occurs is closely connected with the mean heat of the earth's crust, if not absolutely dependent upon
it. Axes and poles have, therefore, in view of this hypothesis, no existence in
fact, but are merely convenient mathematical terms for expressing our ideas of
magnetic phenomena more closely, just as in crystallography we employ the
same terms for the same reasons.
In conformity to this view, the manifestation of the magnetic forces will vary
with all the diurnal changes of temperature, giving the relation of cause and
effect between these changes, and the magnetic perturbations. The annual fluctuations in the mean temperature of the earth's surface will, therefore, be reproduced in corresponding movements in magnetic declination and dip. Hence,
the magnetic meridian, and the system of isoclinal and isogonic curves ought to
correspond closely, as they do with isothermal lines, and the peculiar distribution of temperature in both hemispheres. Indeed, we may assume, should this
hypothesis prevail, that the differences now noticed between the isothermes and
isogones (due, probably, to imperfect observations), will vanish under new and
more extended researches.
IV. PRODUCTION OF MAGNETS.
802. Artificial magnets are produced (1.) by touch, or friction from




5298             PIrrTSI       OF IMPONDERABLE AGENTS.
another magnet; (2.) by induction; (3.) by electrical currents; and
(4.) by the solar rays.
The method by touch is accomplished by very various modes of manipulation, of which we shall describe only one or two, referring the
reader to larger treatises on magnetism for fuller details. Since the
introduction of the method by electro-magnetism, the old methods of
producing magnets by touch are far less important than formerly.
The circumstances affecting the value of magnets, are chiefly
the nature and hardness of the steel, the form and proportion of its
parts, and the mode of keeping. The most uniform and fine-grained
cast-steel, wrought with as little dis-                547
turbance of its particles as possible,
forms the best magnets.
This is tempered as high as possible,
and the temper is then drawn by heat to
a violet straw color, at which hardness
it has been found to receive and retain
a maximum  of magnetism.  The proportions of a bar magnet should be, for
width, about one-twentieth the length;
and the thickness, one-third to one-fourth 
the width.  In a horse-shoe, the distance between the poles ought not to be
greater than the width of one of the
poles. The faces should be smooth and
level, and the whole surface be highly
polished. It is quite essential for preserving the power of a magnet, that its
poles should be joined by a keeper or
armature of soft iron, made to fit its  
level ends, and be suspended, as seen in
fig. 547. Thus armed, a magnet gains          ____
power; but if left unarmed, it suffers          --- 
material loss. Bar magnets are arranged as in fig. 548, either four magnets
with their opposite poles in contact, or two magnetic bars, side by side, with
two pieces of soft iron joining their opposite poles.
548
803. Magnets by touch.-Touch one pole of a powerful magnet
with one end of a sewing-needle, or the point of a pen-knife, and it
becomes instantly a magnet, attracting iron filings, and repelling or
attracting the magnetic needle. The coercitive force has, in this case,




ELECTRICITY.                             529
been decomposed by simple touch.  If the magnet is very powerful, a
near approach of the needle to it without contact will develop a feeble
magnetism by induction.
More powerful magnetism is, however, developed by drawing the bar to be
magnetized, from its centre to the end, several times over one pole of a magnet,
returning it each time through the air, and repeating the stroke in the same
direction. Then place the other pole in the middle of the bar, and stroke the
opposite end as before.
Two magnets may be placed together, with their dissimilar poles in the middle
of the bar, as in fig. 549, and then be moved in opposite directions, at a low
549
B  *-W  _  BA_
angle, to the extremities of the bar.  The impregnation of the bar will be
more powerful and speedy if it rests by its ends on the two opposite ends of two
other magnets, as practiced by Coulomb. By inspecting the letters in fig. 549,
this arrangement will be quite clear. Care is taken to prevent the ends of the
two inclined bars from touching, by placing a bit of dry wood between them.
This is called single touchh, and is to be explained in accordance with ~ 785.
To magnetize a bar by means of the double touch, two bars, or horse-shoe
magnets are fastened together, with a wedge of dry wood between them, so that
their dissimilar poles may be about a quarter of an inch asunder; or a horseshoe magnet may be used if its poles are quite near together. The magnet, in
this mode, is placed upright, on the middle of the bar, and is then rapidly drawn
towards its end, taking care that neither of its poles glides over the end of the
bar. The magnet is then passed over the opposite end           55
of the bar as before. The poles will be dissimilar to
those of the touching magnet.                         M
804. Horse-shoe  magnets are easily  magnetized by connecting the open ends by a soft iron
keeper, while another horse-shoe magnet of the
same size is passed from the poles to the bend, in
the direction of the arrow  in fig. 550; the poles K ll
being arranged as indicated by the figure.
The easiest mode of obtaining a maximum magnetic effect in a bar, by touch,
is that of Jacobi, viz.: to rest its ends             551
against the poles of another magnet,
and then to draw a piece of soft iron, 
called a feeder, from it several times         H                           
along the bar. This mode is applied to 
horse-shoe magnets, as seen in fig. 551.
The dissimilar poles are placed together, and the feeder is drawn over the
horse-shoe, in the direction of the arrow; when it reaches the curve, it is to be
47*




530            PHYSICS OF IMPONDERABLE AGENTS.
replaced, and the process repeated; turn the whole over without separating the
poles, and treat the other side in like manner.
A horse-shoe of one pound weight may be thus charged, so that it will sustain
26-5 pounds. By the best pnethod of touch before known, fig. 550, 21 Ibs. 9 oz.
was the highest attainable result. (Peschel.)
805. Magnets by electro-magnetism.-The mode of producing
electro-magnetic currents will be hereafter described. By their means,
powerful magnets of soft iron are easily produced, and, from these, by
the methods of touch just described, very powerful artificial magnets
may be made.
Logemann, of Ilaarlem, in Holland, has in this way produced the most powerful magnets ever made. One in possession of the author, sustained 28. lbs.;
its own weight being 1 lb. The mode of producing these powerful magnets
will be understood from fig. 552.
A spiral of insulated copper wire,
t, is wound on a paste-board tube,
A B, in the manner of the electro-                                    -
magnetic helix. The bar to be
magnetized is armed with two 
heavy cores, or cylinders of soft
iron, S N, just fitting the inside    -
of th'e spiral; when in its place,
the ends of the spiral, c z, are connected with a few cells of Grove's or Bunsen's
battery, and the powerful temporary magnetism induced in the masses of soft
iron, reacts, to induce an uncommonly strong permanent magnetism in the bar
of steel. A horse-shoe magnet is charged in a similar way, by encircling it
with a helix of proper form, with similar armatures of soft iron. The close
analogy of this mode to that of Jacobi, in the last section, will be noticed.
806. Compound magnets are made of several plates of steel, separately magnetized, as in fig. 523 and 549. As the coercitive power of steel
appears to be overcome, chiefly, on its surfaces,             553
there is an advantage in multiplying the number
of plates, but as each plate serves to neutralize a
portion of the polarity of its neighbor (similar 
poles, of necessity, being brought into contact),
there is soon found a limit beyond which there is
no advantage in extending these batteries.  _
Large magnets are not as powerful, in proportion to
their weight, as small ones. Sir Isaac Newton is said
to have worn in his finger-ring a magnet (lodestone)
weighing three grains, and capable of sustaining over
250 times its own weight (760 grains). A lodestone
of three or four pounds weight, mounted as in fig. 534,
can rarely sustain over two or three times its own
weight.
The most powerful artificial magnet on record, was
that made by Dr. G. Knight, of London, and now in
possession of the Royal Society. It consisted of two prismatic bundles, each




ELECTRICITY.                           531
of 240 powerful bar magnets five feet in length, mounted on wheels; between
the end plates of this combination, the poles of the most energetic single magnet
were reversed or powerfully reinforced.
807. Magnetism  of steel by the sun's rays.-Although the fact
is doubted by some experimenters, the weight of testimony appears to
support the conclusion, that the sun's violet rays possess the power of
inducing permanent magnetism, when concentrated by a lens, on steel
needles.
808. To deprive a magnet of its power, it is only necessary to
reverse the order adopted to impart magnetism to it, stroking it from
the ends to the centre with poles of the same name opposed. In this
way the magnetic virtue may be wholly or very nearly destroyed.
The approach of a feeble magnet to a strong one may reverse its polarity.
Leaving a magnet without its keeper greatly impairs its power. Suddenly jerking
it off the keeper, or striking it with a hammer, in a way to make it vibrate, does
the same. Heat accomplishes the total destruction of nfagnetism, and in short,
anything which weakens its coercitive power. Conversely, hanging an armed
magnet in the position it would assume if free to obey the solicitation of the
forces of terrestrial magnetism, is the best position to favor its greatest development. Every magnet which has been charged while its poles are connected by
a keeper, possesses more power before the keeper is removed than after. It is
indeed overcharged, and the excess may be likened to that residual force which
retains the keeper of an electro-magnet in its place after the circuit which excited
it is broken, or to the residual charge of a Leyden jar. Every time the keeper
of a magnet is moved suddenly, a loss of power is sustained, and hence the
keeper should be removed by sliding it gradually off endways, and only when
it is required for the performance of an experiment.
~ 2. Statical or Frictional Electricity.
I. ELECTRICAL PHENOMENA.
809. Definitions.-Electricity is the ethereal or imponderable power
which in one or another of its forms affects all our senses. In this
respect it is unlike all other ethereal influences. It appears, as far as
our knowledge goes, to extend throughout nature, and is probably connected inseparably with matter in every form. Bodies in their natural
state give no evidence of its presence, but by different means it may
be evoked from all.  Hence statical electricity implies that condition of
this subtle ether existing in all bodies in a state of electrical quiescence.
Statical electricity is the opposite of that state of excitement following
friction, chemical action, &c., which is called dynamic electricity, or
electricity in motion.
An arbitrary meaning has, however, attached itself to the terms
statical and dynamical electricity, materially different from  the exact
meaning of those terms as used in mechanics.  Statical or frictional
electricity means only that form of electrical excitement produced by




532            PHYSICS OF IMPONDERABLE AGENTS.
friction, while dynamical electricity is a term confined to the electrical
excitement produced by chemical action, or voltaic electricity. Strictly
speaking, all quiescent electricity is static, and all electricity in motion,
from whatever source, is dynamic. Such, however, is not the established
use of these terms.
Electricity is a term derived from the Greek word for amber ().CxTrpov).
The ancients knew this resin to be capable of what we now call electrical
excitement, when it was rubbed.
810. The  chief sources of electrical excitement are:-lst,
Friction of dry substances, as of glass, by cat's fur or silk, and of
sulphur or resin by flannel: this is ordinary or statical electricity; that
of the atmosphere and of common electrical machines; 2d, Chemical
action, or the contact of dissimilar substances, under circumstances
favorable to chemical change; 3d, Magnetism, producing magnetoelectricity; 4th, Heat, or thermo-electricity; 5th, Animal-electricity.
The electricity from all these several modes of excitement differs in degree
and intensity, according to its source, but not in kind, and each may, in turn,
be cause or effect. Each will be the subject of separate consideration.
811. Electrical effects.-A dry and warm  glass rod, rubbed with
a cat's fur or silk handkerchief, is excited in such a manner as to
attract to itself bits of paper, shreds of silk or cotton, metallic leaf,
pith, feathers, and a variety of light substances, holding them for an
instant, and then repelling them again, to the table or support, as in
fig. 554.                                                    554
In the dark, a feeble bluish light is seen in the path
of the rubber. If the excited glass is presented to the    _.
knuckle, or to a metallic body, a bright purple spark 
will dart off from the glass, with crackling sound, to
the object presented.  Brought near to the face, a creeping sensation
is felt, as if a delicate cobweb was in contact with the skin. These
effects are produced by the rubber, as well as by the body rubbed, and
may be evolved from a number of substances as well as from glass. A
peculiar odor always accompanies electrical excitement, thus completing
the list of the effects of this subtle agent on our senses, if we add the
taste from voltaic electricity.
Bodies thus excited are said to be electrified; a condition which is only
transient.
These very simple experiments, which can be repeated anywhere and with the
simplest means, contain the germ of electrical science.
812. Attraction and repulsion.-In the electrical pendulum, fg.
555, the pith-ball is first attracted to the excited glass or resin, and at
the next instant is repelled, until, by touching some body in connection




ELECTRICITY.                         538
with the earth, or in some other way, it has parted with its excitement.
The two balls in fig. 556, when thus               555
excited, mutually repel each other,
because they are similarly excited.
The light bodies in fig. 554, oscillate
between the table and the rod, first
by attraction, and then by repulsion; when, losing their excitement
by contact with the table, they are
again attracted, and so     556
on. So with the balls in
fig. 556. We recognise  
in these simple experi-     /
ments the similarity be-   /    \   
tween these actions and..- 
the  law  of magnetic
attractions and repulsions. Bodies similarly excited relel, and those which
are of unlike excitement attract each other.
The phenomena of attraction and repulsion are not however so simple as
might at first appear, since for their correct explanation a knowledge of the
phenomena of indZuction is required, and these remain to be explained further on.
813. Vitreous and resinous, or positive and negative electricities.-The species of electrical excitement depends upon the kind
of material which is subjected to friction. If the pith-balls, fig. 556,
are repelled by the excitement from glass rubbed by silk, they will be
attracted by a stick of wax, gum lac, or sulphur rubbed by flannel; or
vice versa.
This difference of action is due to an inherent difference in the two
substances, and the kind of electrical excitement which the two respectively produce, is entirely opposite and antagonistic each to the other.
The one is vitreous or positive, the other resinous or negative. This
fundamental distinction in the kind of excitement produced by friction
in various substances, was first recognised by the French philosopher,
Du Fay, in 1733, and was re-discovered by Franklin in 1747. Glass
and resin are but types of two large classes of substances, which possess more or less perfectly this characteristic difference in respect to the
sort of electricity which they are capable of developing.
Electroscopes serve to distinguish the two sorts of electrical excitement from  each other.  The pith-balls, fig. 556, form  a convenient
eleciroscope-two silk ribbons, or the electrical pendulum, fig. 555,
answer the same purpose. Much more delicate instruments of this
kind will be described shortly.




534           PHYSICS OF IMPONDERABLE AGENTS.
It is only requisite to excite the balls, fig. 556, with known vitreous or resinous
electricity, when the approach of any excited body whose electrical state is unknown, will, if of the same kind, cause a farther repulsion, and if of a different
sort, will occasion an attraction of the balls.
814. Conductors of electricity.-Bodies electrically excited part
with their excitement variously,-some instantly, others very slowly, —
depending both on the nature of the substance excited, and of those
with which it is brought in contact.  The pith-balls of the electroscope
lose their excitement very slowly, the electricity being removed only
by the surrounding air.  Touched by the finger, or a metallic body in
connection with the earth, they are instantly discharged, and return to
their natural unexcited condition. The electricity is removed by conduction over the touching body.  And as bodies vary very much in
their power to conduct electricity, they are called good and bad conductors, or conductors and non-conductors.
Good conductors propagate the excitement to all parts of their
surface, and when in connection with the earth, part with it as quickly
as they receive it.
The following are among the good conducting bodies, placed in the
order of their conducting power.  The metals, as a class (silver and
copper standing first, and lead and quicksilver last), well-burnt charcoal, plumbago, coke, hard anthracite, acids, saline solutions, numerous
fluids, metallic ores, sea, spring, and rain water, ice above 13~ F.,
snow, living things, flame, smoke, vacuum, vapor of alcohol and ether,
earths and moist rocks, powdered glass, and flowers of sulphur.
Bad conductors receive and part with electricity very slowly.  If
touched by an electrified body, they receive excitement only at the
point touched; or if, when excited over their whole surface, they are
touched by a good conductor, the excitement is removed only from the
part touched. They retain free electricity for a long time, and obstruct
its motion.
Insulation.-Good conductors are capable of manifesting electrical
excitement only when their communication with the earth is cut off by
some bad conductor. So situated, they are said to be insulated, and the
poor conductors used for this purpose (glass, resin, or dry wood), are
called insulators.  Fig. 557 shows              -=     -
a brass tube thus insulated by a
handle of glass. Among the chief insulating bodies are the following,
placed in the reverse order of their insulating power, viz.: dry metallic
oxyds, oils, ashes ice below 13~ F., many crystalline bodies, lime and
chalk, lycopodium, native caoutchouc, camphor, porcelain, dry vegetables, baked wood, dry air, and gases, steam above 212~, leather, parh



ELECTRICITY.,r535
ment, paper, hair, dyed silk, white silk, diamond and precious stones,
mica, glass, jet, wax, sulphur, the resins, amber, gum lac. Gutta percha, and whalebone rubber, are among the best insulators known;
probably better than gum lac.
Some bodies which, when solid, are non-conductors, become conductors when
liquefied by fusion, viz.: metallic chlorids, glass, wax, sulphur, resin, &c. Heat
diminishes the electric conducting power of metals. Length of conductor
retards electrical motion, while an increase in other dimensions favors the
rapid transmission of electricity. Every body has a certain electrical retarding
power (818), which is inverse to its conducting power. Tables of electrical
conducting powers will be found in larger works; but, in general, this power is
very nearly the same as any given body has for conducting heat.
815. The earth is the great common reservoir or receptacle into
which all electrical excitements are returned, and, regarded as a whole,
is a good conductor.  The air, even in its ordinary condition, is a very
poor conductor, and, in view of its immense extent, is by far the most
important of non-conductors.  It serves to insulate the earth in a nonconducting envelope, more or less perfect, in proportion to its density,
and the absence of aqueous vapor.  Except for this property of the air,
all electrical phenomena would have remained invisible and unknown
to us. The earth is always negatively excited.
In a vacuum, all electrified bodies speedily lose their excitement,
while in dry, dense air, they retain it longest.  Nevertheless, slight
electrical excitement can be produced in a vacuum 1,y fi iction.
816. Theories of electricity, or electrical hypotheses.-Philophers generally agree in attributing the phenomena of electricity to
the existence of an assumed electrical fluid.  This supposed fluid is so
subtle and ethereal as to escape detection by all the means used to recognise matter, being imponderable, and manifesting itself only by its
effects.  It is assumed to pervade all nature, and to exist in a state of
combination or electrical quiescence in all bodies in their natural state.
This quiescence is disturbed by friction, and various physical and
chemical causes. All electrical phenomena are supposed to be due to
the efforts of the electrical fluid to regain its previous condition of
static equilibrium. Two principal hypotheses have been devised to
explain the phenomena of electricity, namely: 1st, that of Franklin
and }Epinus; 2d, that of Symmner, sometimes attributed to Du Fay.
Franklin's single-fluid hypothesis is recommended by its sinplicity, and was, for a long time, the view generally adopted, both in
England and America. It assumes a single electrical fluid, whose particles are self-repellent, but attracted by matter of all kinds, combining
therewith, and when so combined, losing this self-repellent tendency.
This fluid is present in all bodies, but in varying proportion, each sub



530f 3         PHIYSICS OF IMPONDERABLE AGENTS.
stance possessing a certain capacity of saturation peculiar to itself.
In its natural state, every substance has exactly its own quantity of the
electric fluid, and is consequently in a state of electrical indifference.
If any cause of electrical excitement exists, this state of quiescence is
disturbed, and the body becomes negatively electrical, if its natural
charge is diminished, and positively, if it is in excess. By this hypothesis, bodies become electrical either by addition to, subtraction from,
or disturbance in the equal distribution of, the normal quantity of the
electric fluid proper to them. In those bodies which manifest positive
electricity, the equilibrium is restored by parting with the excess, and
in those whose excitement is negative, by receiving from  surrounding
bodies enough to satisfy their deficiency.
This hypothesis will be recognised as strikingly like that commonly received
in explanation of the' equilibrium of heat.
Epinus found, that, in order to account mathematically for the mutual repulsion of two negatively electrified bodies on the single-fluid hypothesis, it was
necessary to assume that the particles of matter were mutually repulsive instead
of attractive, according to the Newtonian law of universal attraction. This
reductio ad absurderm has led to the almost universal rejection of the Franklinian hypothesis.
The hypothesis of Symmer, or Du Fay, assumes the existence
of two fluids, extremely tenuous, imponderable, in the highest degree
expansive, mutually repellent (as a consequence of this expansive
nature), and yet possessing a strong mutual attraction when not opposed
by any obstacle. They therefore combine, when favorably situated so
to do; and when equally combined, their expansive and repellent forces
are neutralized, and electrical quiescence results. Each of these kinds
of electricity may exist separately; they are then in a state of antagonism, and exhibit polarity, and other electrical effects. Every substance becomes thus excited whenever any part of its natural electricity
is decomposed by friction or otherwise. If a plate, it may possess the
two electricities on its opposite sides, one being vitreous, and the other
resinous; if a rod, the decomposition of a part of its natural electricity
will make the rod vitreous at one end and resinous at the other. When
the cause of excitement ceases, the two fluids reunite, and quiescence is
restored. By this hypothesis, all electrical phenomena arise from the
tendency of the two fluids when separated to reunite and neutralize
each other.
Either of these two views is capable of explaining most electrical phenomena,
but the weight of scientific opinion is now in favor of the last. Neither view
can be actually true, since the term fluid is only a convenient expression for an
unknown cause, and there is no reason why we should assume the existence of
a separate fluid or ether, as a medium for light, heat, or magnetic electricity,
when it is more in accordance with a sound philosophy to assume that these




ELECTRICITY.                          537
separate manifestations are but functions of the ethereal medium which fills the
universe, and from whose correlations to the particles of matter, all physical
phenomena proceed. Compare ~ 765-772.
817. Electrical tension. —This term  is employed to express that
condition of bodies in which the electricity is free-a condition the
reverse of electrical quiescence. This condition is well illustrated in
the phenomena of the Leyden jar, ~ 847, where there is perfect equilibrium between the excitement of the outer and inner surfaces, due to
their antagonism. The energy with which the decomposed electricities
reunite, when communication is made between them, shows the state
of tension in which they existed.  This may be regarded as analogous
to the tension of a bent spring, in which equilibrium is regained by a
reaction equal to the compressing force. Electrical tension is a condition of constrained equilibrium, and when the free electricities to which
it is due, reunite, an electrical current is produced from the reaction of
the opposing fluids, analogous to mechanical motion from the recoil of
a spring.  From this state of electrical tension are derived the primary
effects of electricity, and from electrical currents arise its secondary
effects. All electrified bodies manifest electrical tension; they attract
other bodies, decomposing their natural electricity, deriving from them
a portion of the opposite fluid. If this is insufficient to satisfy the
antagonism of the excited electric, the attracted bodies are next repelled (812). Hence, two bodies equally excited, but of opposite names,
attract each other, and reunion of the two fluids with electrical indifference results. If one contained an excess of either fluid, both remain
excited after contact, with that description of electricity which was in
excess; the excess being divided in the ratio of their surfaces.
Electrical currents are either momentary or permanent.-The
first occur when contact is formed between substances oppositely excited by friction or otherwise, and their effects are instantaneous and
transient.
Permanent electric currents arise only from the sustained action of
some continuous cause; as, from the continued motion of the electrical
machine, or, more simply, from the chemical action of unlike substances,
as in the voltaic battery, in which the electrical current is kept up as
long as any chemical action exists.
818. Path and velocity of electric currents.-If several conducting paths are open to an electric current, it will always choose the
shortest, and that in which it meets the least resistance. If the current is powerful, and the conductor inadequately small, its passage will
be marked by light, and perhaps by the combustion and deflagration
of the conductor. The velocity of static electricity, by Wheatstone's
48




538            PHYSICS OF IMPONDERABLE AGENTS.
experiments, over.a copper wire, was found to be 288,000 miles in a
second-nearly half again more than the velocity of light (~ 404).
It appears from Dr. Gould's discussion (Am. Jour. Sci. [2] XI., 161), of the
very numerous telegraphic observations in the United States, made under the
direction of Prof. Bache, for the Coast Survey, and by other astronomers, that
the velocity of a voltaic current, when the earth forms part of the circuit, does
not exceed 16,000 miles per second, and it has been measured as low as 11,000
miles per second; showing a great retarding force in a conductor of 1500 miles
circuit.  In the famous Atlantic cable, the electrical retardation was much
greater than this, being mixed with the accompanying phenomena of induction.
II. LAWS OF ELECTRICAL FORCES AND DISTRIBUTION OF ELECTRICITY UPON
THE SURFACE OF BODIES.
819. Coulomb's  laws.-Coulomb  (died  1806), a  distinguished
French physicist, by the use of the torsion balance, first demonstrated
the following laws of electrical attractions and repulsions:1st. Tuo excited bodies attract and repel each other with a force proportional to the inverse square of their distances from each other.
2d. The distances remaining the same, the attractions and repulsions
are directly as the quantities of electricity possessed by the two bodies.
Coulomb's laws of torsion have already been demonstrated (266).
He happily applied these principles, first established by himself, to the
measurement of electric forces in his tor-               555
sion electrometer.
820. Torsion  electrometer.-This                   ^s
instrument, fig. 558, consists of an exterior glass cage, protecting a slender
needle, no, of gum  lac, suspended by
a fine wire of silver or platinum, centrally attached to the under side of the
cap, e, upon the tube d.
This cap is graduated, and turns like the                I 
cover of a box. The graduation is read at
the vernier, a. A small weight, o, of brass,'II,,,,,1
keeps the wire tense, while through it the         "l,,^
gum lac needle passes. At one end of the                       ll
needle, n, is a small gilded ball of pith, or a  I
disk of tinsel paper. The cover of the glass
case is perforated for the free passage of a                      
glass insulating rod, i, carrying a polished 
brass ball at m. The glass cage is graduated
in a zone at C, into 360 degrees, to measure
the angular spaces traversed by the needle.        -
The zero of the graduation, and of the arc on the cap, are both made to correspond (by revolving the tube, d,) with the normal position of the needle when
at rest, and unexcited. To avoid the loss of electricity, the air in the cage is
kept dry by a little quick-lime, placed in a dish for that purpose, on the bottom.




ELECTRICITY.                        539
821. Demonstration of the first law.-The apparatus being thus
arranged, the insulated rod, i, is withdrawn, and the ball, m, placed in
contact with some excited surface-as the electrical machine. Thus
excited, m is immediately returned to its place by the insulating handle,
taking care that it touches nothing. Forthwith the disk, n, is attracted
to m, is oppositely electrified, and then repelled with a force proportioned to the intensity of m. After a few oscillations, n comes to rest
say at 30 degrees on the graduated circle. This angle then represents
the repellent force of the electricity on m, since the torsion of a wire
is directly as the twisting force. But what would be the force requisite to hold the disk, n, in equilibrium at half this angular distance, or
15~?  Revolving the movable circle, e, in the direction of the arrow,
we find it is necessary to carry it from 0 to 105~, in order that the
needle may point to 15~. The wire is then twisted at top with a force
of 105~, and at bottom with a force of 15~, giving 120~ as the angle
representing the force with which the two electrified bodies repel each
other, at the distance of 15~-or, at half the distance, we have quadruple the force; at one-third the distance, or 7j, the force would be
472~'5 + 7~'5  = 480~, according to the law of inverse squares.
In like manner, reversing the electricities, we prove that the force
with which two electrified bodies attract each other, is inversely proportional to the square of the distance by which they are separated.
822. Demonstration of the second law.-Having repelled the
needle, n o, by the excited ball, m, withdraw the latter, and touch it to
a second metallic ball of the same size, insulated on a glass handle.
The ball, m, parts with half its electricity to the second ball (827).
Now return it to the torsion balance; it will be found that the needle,
n o, is repelled to a distance equal to its former distance multiplied by
the square root of one-half, D' = D1/-. Touch m again to the second
ball, as before, and it will then repel the needle to a distance equal to the
first distance multiplied by the square root of one-fourth, D" = D=1//,
and so on.
Sir Wm. S. Harris, of England, by the use of a bifilar electrometer,
which substitutes the force of gravity for that of torsion, has shown that the'
two laws of Coulomb are not strictly accurate, unless the two excited bodies
have the same size and form, or unless the sections of the opposing parts are
equal. The result of his determinations is, that the attraction is directly proportional to the number of points immediately opposed to each other, and inversely
to the square of their respective distances.
823. Proof-plane.-For the purpose of determining the relative
quantities of electricity that are found on the different parts of the surface of an electrified, conductor, a contrivance called a proof-plane is
used. It is nothing but a small disk of tinsel, or metal, insulated, as in




540            PHYSICS OF IMPONDERABLE AGENTS.
the ball, m, of the torsion balance, fig. 558. This is touched to the
surface whose electricity is to be examined, and receives therefrom  a
quantity of electricity equal to the sum of both of its own surfaces. It
may then be inserted in the balance of torsion, or used on any other
electroscope. The electricity on the body touched is diminished to the
same extent, but when the proof-plane is small, compared with the area
of the excited conductor, no sensible error can arise from this loss.
The most important source of error to be guarded against in the use
of this instrument, arises from the effects of induction, presently to be
explained.
824. Electricity resides only on the outer surfaces of excited
bodies, and not in their substance, or on their interior surfaces. This
fact is attributed in part to the repulsive power of the electric fluid
acting upon the particles of matter interiorly, thus driving the excitement to the outer surface, where it meets the non-conducting air, and
is arrested. It is also due to the inductive influence of the electricity
of surrounding bodies, and of the walls of the room. The following
experiments will illustrate this law.                      559
A. Electrify the metal sphere, a, fig. 559, on an  ^ 
insulating stand, b, and approach to it the two hollow
hemispheres of brass, c c, insulated, and made accu- 
rately to cover the sphere. On removing them, a will 
be found without the least trace of electrical excitement, as may be proved by a delicate electroscope,
while the two hemispheres are fully excited. To remove the enveloping hemispheres is to remove the surface of the sphere,        560
and with them its electricity.
B. Fig. 560 shows an insulated hollow sphere,
with a hole in the top. When this is electri-                  \
fied, the proof-plane may be introduced by the 
opening, and placed in contact with its inner\ 
surface, without acquiring any excitement
(provided care be taken to avoid the inducing 
effect of the edges of the opening, which may                    w
otherwise decompose the neutral electricity of
the gum-lac handle), while from contact with
any point of the outside, the proof-plane acquires abundant excitement.
C. Faraday has described a muslin bag in
the form of a net, fig. 561, sustained on an
insulated ring of wire, and provided at the
point of the cone with two insulated silk
strings, c c', so that it may be turned inside 
out at pleasure, without touching it. When 
this is electrized exteriorl, it may be turned 
inside out by means of the strings, without a 
trace of electricity being found on the inside
(which an instant before was the outside), and this may be repeated several times




ELECTRICITY.                            541
before the electricity is dissipated. lie is in the habit of covering his most delicate electroscopes with muslin bags, to protect them from the influence of excited
electrical machines, with entire           561                   562
success.
Fig. 562 shows a ribbon of 
metallic paper wound around a.......
metallic axis, insulated by the                             r
silk threads rr; two pith-balls, C
e e', are  suspended  by  linen  -
threads, at one end of the ribbon. When the ribbon is wound
up, and the whole is electrized,  
the balls of the electroscopes di-               __
verge powerfully. If the ribbon                                
is now unwound by drawing the
insulating string below, the electroscope balls gradually fall, and finally come
almost in contact; but when the ribbon is again wound up, the balls diverge as
before. This may be repeated several times. This beautifully illustrates the
relation of surface naQ intensity. As the surface is increased, the same quantity of electricity is spread out over a larger surface, and its energy declines, but
is increased again as the surface is diminished by re-winding the ribbon.
D. It appears from these experiments that a ball of wood or pith, covered with
tin foil or gold leaf, can accumulate on its surface as much electricity as if it was
of solid metal.
It is thus proved that all the electricity with which a conducting
body is charged, is disposed on its surface.
825. Distribution of electricity.-The form  of conductors influences the distribution of electricity on their surface. In a sphere, the
distribution is uniform, as would be anticipated from the known properties of the solid. The proof-plane, applied to any part of an excited
sphere, acquires, as tested by the balance,               563
the same power.  In an ellipsoid of revo-          e
lution, like fig. 563, the proof-plane applied at a, gives a much larger angle of
torsion in the balance than at any other
point, while the minimum is in the vicinity
of e; showing a tendency in electrical excitement to accumulate about the extremi.
ties of any solid having unequal axes. 
In cylinders, the concentration of force is within about two inches from each
end, and is feeble at the middle. So in plates, the maximum of accumulation is
about an inch from the edge. The same is true of the edges and solid angles
of prismatic bodies.
826. The power of points (first investigated by Franklin) in concentrating electricity is such that the excitement passes off, as rapidly
as it accumulates, to the nearest bodies, or is diffused into the ambient
air in an electrical brush or pencil, visible in the dark (842 (6) ). This
48*




542            PHYSICS OF IMPONDERABLE AGENTS.
fact follows as a consequence of the tendency of electricity to accumulate at the smaller end of an ellipsoid. The ellipsoid may be so elongated that the electricity escapes-it then becomes a blunt point. These
facts are of the greatest importance in the construction of electrical
machines.
827. The loss of electricity in excited bodies, even when insulated in the best manner, is constant, chiefly from two causes, viz.: 1st,
the moisture of the air; and 2d, the imperfection of the insulation.
The loss from the first cause, in still air of average dryness, is proportioned to the state of electrical tension. Bodies feebly excited, and perfectly well insulated in dry air, retain their state of tension for weeks
or months, while those highly excited, and not carefully preserved, are
soon deprived of all electrical excitement. The rate of loss by imperfect conduction is, of course, dependent on the non-conducting material
used, the perfection of workmanship, and care of the apparatus.
The loss of electricity by an excited conductor, when placed in contact with an unexcited body, insulated from the earth, is in proportion
to the relative surfaces of the two bodies. One gains, the other loses.
Two equal spheres will divide the whole quantity between them.  If
they remain in contact, the distribution is unequal, being least at the
point of contact, and increasing to a maximum  at 20~ to 30~ from  the
point of contact. The proof-plane determines exactly all such questions.
In a vacuum, a high state of electrical tension is impossible, since the restraining power of the air is wanting. But a feeble tension can be preserved in
an exhausted receiver for a long time. The movement of the mercury against
the walls of the tube of a barometer, excites electrical tension, and even luminous electricity, as was shown by Cavendish.
III. INDUCTION OF ELECTRICITY.
828. Electrical influence or induction.-Every electrified body
is surrounded, so to speak, by an atmosphere of influence, analogous to
that surrounding a magnet (783), within which every insulated conductor becomes also excited. Bodies so affected are said to be electrified
by induction, having their neutral electricity decomposed by the tension
of the excited conductor, exercised through the intervening air.
Let the conductor, V, fig. 564, of an electrical machine, be approached within
say six inches of an insulated metallic conductor, A B.  The small electroscopes, a a',           564
suspended beneath its ends, instantly diverge,  j      A             B
and at the same time are respectively attracted   -2i
to V, at A, and repelled from it at B. If V
is - A is -, and the remote end, B, is plus.
The intermediate electroscopes, b b', also diverge, but in a less degree, while those near
the middle, cc', do not diverge at all. If,
while thus excited) A B is withdrawn from V (care being taken not to touch the




ELECTRICITY.                           543
conducting surface), the electroscopes will presently cease to indicate any ex.
citement. The explanation of these facts is, that the neutral fluid of A B has
been decomposed by the influence of V, the + fluid being repelled to B, and the
-- attracted to A, while, near the centre (never exactly in the centre), a neutral
point is found, where no decomposition exists. When V, the disturbing cause,
is withdrawn, the two electricities of A B unite again, and leave the conductor
entirely passive. If, however, the conductor, A B, is made in two parts, joined
at the neutral point, and each on a separate glass leg, when it is inductively
excited, the two parts may be separated, and each part will then be found, when
removed from influence, to possess the same excitement developed in it, under
the inductive power of V.
By means of a glass tube, or stick of resin gently excited, and approached to
one of the electroscopes, it is, of course, easy to determine the description of
excitement in V, which we now assume to be +.
829. The laws of induction may be thus stated:-lst. A body
electrized by induction, possesses no more electricity than before. This
is shown by the fact, that as soon as the inducing influence ceases, the
two fluids reunite in A B, and no trace of excitement remains.
2d. If a conductor, excited by induction, is touched, or made to communicate with the earth in any part of its surface, it parts.with a portion of electricity, always of the satme name with the inducing body,
and it retains the fluid of opposite name. If the inducing cause is
then withdrawn, the insulated conductor remains excited, with the fluid
of opposite name to that of the inducing body.
Thus, we note the important distinctions between a body electrized by induction and by conduction. Induction occasions no transmission of free electricity
to the other body; but only a decomposition of the -i electricities of the insulated conductor. Induction produces dissimilar conduction, similar electricity
to that of the exciting body; and the distance to which electricity of induction
extends, greatly exceeds that to which it can be propagated by conduction,
where absolute contact or very close proximity is required. A strong analogy
exists between electric and magnetic induction. Both magnetism and electricity
by contact, are of the same name with the body touched. By influence, the
neutral fluid of the excited body is decomposed, and the polarities are in accordance with laws already stated.
830. Induction is an act of contiguous particles.-Dr. Faraday
has modified the usual view of induction just stated, by showing that
induction never takes place at a distance, without polarizing the molecules of the intervening non-conductor, causing them to assume a constrained position, which they retain as long as they are under the
influence of the inductive body.
Because air and other non-conductors permit the passage of electrical
influence in this manner, Faraday calls them dielectrics, in distinction
from electrics, or conductors which can become polarized only when
insulated by some dielectric. Dielectrics differ in their specific inductive capacity, air being the lowest in the scale, as follows, viz.: air, I




544             PHYSICS OF IMPONDERABLE AGENTS.
resin, 1'77; pitch, 1'80; wax, 1'86; glass, 1'90; sulphur, 1-93; shellac,
1-95..
The apparatus used by Faraday in determining the relative inductive capacity
of air and other gases, is seen in fig. 565, consisting, essentially, of two metallic
spheres, C and P Q, of unequal diameter, the smaller placed       565
in the centre of the larger, and insulated from it by a stem     B
of shellac or gutta percha, A. The two halves of the outer
sphere join in an air-tight joint, like the Magdeburg hemi-     A 
spheres (257). The space, m n, may be emptied of air by an
air-pump, controlled by a cock in the foot, and filled with
any other gas or fluid. This apparatus resembles the Leyden jar (847), with the advantage of changing the intervening
dielectric at pleasure. The balls, C and B, constitute the
charged conductor, upon the surface of which all the electric
force is resident by virtue of induction. As the medium in
m n may be changed at pleasure, while all other things remain the same, then any changes manifest by the proofplane and torsion balance, will depend on changes made in
the interior. The same end would be reached by having two
exactly similar inductive apparatus, with different insulating
media. When one was charged and measured, the char, \\\\\
being divided with the other, the ultimate conditions of both indicate by the.
torsion balance whether or not the media had any specific differences. (For
further details, see Faraday's Exp. Res. 1197.)
831. The attractions and repulsions of light bodies (811) can
be explained only in view of the phenomena of induction. The excited
tube or resin, decomposes the neutral electricity in the pith-balls or
bits of paper, repelling the electricity of opposite name, and being thus
left of an opposite excitement to the rod or resin, they become attracted
to the exciting body, in obedience to electrical laws. All cases of electrical repulsion are equally referable to attraction under inductive.
influence. Thus the apparent repulsion of the two pith-balls in an
electroscope, is really the effect of the attraction of surrounding bodies,
whose electrical equilibrium is disturbed by the inductive influence of
the exciting cause.
The following experiment illustrates, in an interesting manner, the development of electricity, and the attractions and repulsions of light bodies by induction. Support by its edges a pane of dry and warm window-glass, about an
inch from the table, on two pieces of dry wood, and place beneath it several
pieces of paper or pith-balls. Excite the upper surface by friction with a silk
handkerchief, the electricity of the glass becomes decomposed, its negative fluid
adheres to the silk, and its positive to the upper surface of the glass plate; this,
by induction, acts on the lower surface of the glass, repelling its positive electricity, and attracting its negative, the intervening dielectric being polarized as
explained, and the lower surface of the glass electrified by induction through
its substance, attracts and repels alternately, the light bodies, like the excited
tube (811). (Bird.) Numerous experiments, illustrative of induction, are given
under the electrical machine.




ELECTRICITY.                              545
832. Electrometers.-Cavallo's, Volta's, and Bennett's.-The
electroscopes mentioned in section 813, serve to indicate the presence
and name of the electricity. Electrometers are designed to give approximate measures of the quantity of elec-                  566
tricity.
Fig. 566 shows Cavallo's electrometer-a bell-                          B  
jar with a metallic rod and button, B, sustaining
two pith-balls, m, at the ends of two wires. Volta 
substituted for the two pith-balls, two delicate
blades of straw, p. Bennett replaced these by.                 c
two strips of gold leaf, o, placed face to face.                      -
When the knob, B, receives electricity, the pith-   
balls, straws, or gold leaves, diverge, and by the
degree of their divergence, measured on a graduated are, the intensity of the
electricity is judged of. Two strips of tin foil, c c', are      567
pasted to the inside of the glass bell, to discharge the
diverging leaves, when they are repelled, so as touch the
sides. Otherwise the inside of the glass jar would be electrified by induction, and render the apparatus useless; and
to avoid dampness, the top of the bell is varnished, and the
air within, dried by quick lime. Approaching an excited       i 
body towards B, the gold leaves diverge, because the positive fluid, if the excitant is positive, is driven into them,
while the negative is attracted to B. Touching B with the
finger, the positive fluid passes off to the earth, but on
withdrawing the finger, the leaves diverge under the influence of the negative electricity remaining in the apparatus.
Fig. 567 is a sensitive form of gold leaf electrometer, with
brass condensing plates, ~ 846, and a cup at top to illustrate the effect of evaporation in producing electrical excitement.
Hare's single leaf electrometer, and the condensing electrometer, are mentioned
in section 846, and Bohnenberger's under the dry pile, ~ 873.
IV. ELECTRICAL MACHINES.
833. The electrophorus. —Any apparatus by which electrical phenomena may be obtained at pleasure, is an electrical machine.  The
simplest apparatus of this sort is Volta's electrophorus, or carrier of
electricity, invented in 1775.                   568            569
A cake of resin, or a disk of whalebone- 
india-rubber, or gutta percha, eight or
ten inches in diameter, is excited by a
fur or warm flannel, and a smaller disk of
brass, or tin plate (with rounded edges), is      I    X
placed on it by an insulating handle. Touch
the upper surface of the metallic disk with
the finger (fig. 568), in order to allow the 
escape to the common reservoir (815) of the
negative electricity, resulting from the decomposition of the neutral fluid in the
metallic plate by the excited resin. Now removing the finger, raise the diskby the




546            PHYSICS OF IMPONDERABLE AGENTS.
insulating handle, and approach its edge to any conductor, as the knuckle, fig.
569; immediately a strong spark is seen, due to the free positive electricity
existing in A. Place A on B again, touch it as before, and the same result
may be obtained as often as desired. If A is left in repose upon B, it will remain
charged a long time, even for weeks, and a Leyden jar may be charged with it at
any time: on the table of the laboratory it            570
may be more conveniently used than an ordi- 
nary electrical machine for exploding gases.
The section of the electrophorus, seen in fig.  a  __.
570, shows how the inductive action of the
excited resin acts, in affecting the electrical 
nomenclature of each surface, as indicated by
the signs + and -.
The phenomena involved in the electrophorus are identical with
those explained in ~ 829.  Of course, if the plate, A, were raised
without touching, it would manifest no electrical excitement; the two
luids re-combining as in the insulated conductor, fig. 563.
834. The cylinder electrical machine.-Vhen larger quantities:f electricity are required than can be obtained from the means already
described, resort is had to machines of larger size, and more power, all
Af which, however various in form, consist principally of three parts,
viz.: 1st, a non-conductor, usually of glass, revolving on a horizontal
axis, and producing friction; 2d, a rubber, against which the nonconductor presses. The rubber is a soft, elastic non-conducting body,
as a cushion of leather, usually armed with amalgam, to be described
hereafter. 3d, two conductors, usually of brass, mounted on glass supports, one to receive the + and the other the -  electricity.
In the cylinder machine, fig. 571, a smooth cylinder, M, of glass, insulated
571
-d f     w   p     d  a  i r        I                            
and filled with perfectly dry air, is revolve I by the winch before the rubber (0,




ELECTRICITY.                           547
sustained on the insulated prime conductor, A, and covering about one-eighth
of its surface: an apron of silk is usually attached to the upper edge of the
rubber, and extends as far as the points, P, on the second conductor, B, designed
to receive the +  electricity excited at C. If the connecting rods, E D, are
approached as in the figure, and the cylinder is revolved, and there is no connection with the earth, then the + electricity accumulated on the positive conductor, will reunite with a spark with the - electricity of the negative conductor,
A, again to be decomposed as before at C. If the negative conductor, A, is
connected with the earth by a chain or metallic thread, then, when the machine
is worked, a continuous flow of sparks of positive electricity will pass from the
positive conductor, B, to any conductor near enough to receive them. But if A
is insulated, and B is connected with the earth, then from E, a continuous flow
of negative electricity is obtained. In this case a flow of positive electricity
takes place from the cushion, C, through the conductor, B, to the earth, thus
leaving the conductor A charged with negative electricity. This form of cylinder
machine was designed by an Englishman named Nairne.
Amalgam.-No considerable quantity of electricity can be evolved
from  an electrical machine of glass, unless the rubber is excited with
an amalgam  composed usually of four parts mercury, eight zinc, and
two tin, mixed with some unctuous matter and spread on silk or leather.
The zinc is first melted; the tin is added, and the mixture stirred, and
poured, not too hot, into a wooden box, coated inside with chalk, and
into which the heated mercury has been first poured.  The lid is put
on, and the box violently shaken, until the amalgam  becomes cool.  It
is then finely pulverized in a mortar, and becomes as soft as butter.
835. Ramsden's plate machine, as its name indicates, has a plate
or plates of glass substituted for the cylinder. This form of apparatus
is seen in fig. 572. The plate, F F, is revolved by the winch, M, sustained in a frame, O 0, of baked wood. Two pairs of spring cushions,
a c, armed with amalgam, produce friction. The conductors, C C, collect
the electricity from the glass by the points seen on the inside of their
curved branches, placed near the surface of the plate. Each of the
cushions is connected with the earth by the conductor, D; strips of
tin foil pasted upon the edges of the frame, 0, and shown in   573
the figure unshaded, communicate between the four sets of
cushions and the chain D.
Ramsden's apparatus originally gave only positive electricity.
It was so modified by Von Marum as to obviate this defect. This
form of electrical machine was contrived by Ramsden, of London,
in 1776.
The earliest electrical machine was made by Otto V. Guericke
(who invented the air-pump), and was a globe of sulphur or resin,
driven by a motor wheel, the hand being used for friction. A cone of sulphur,
fig. 573, cast in a wine-glass, and provided with a glass rod as a handle. serves
to illustrate this early electrical apparatus. But hard india-rubber is a more
convenient and certain source of negative electrical excitement.
In the United States, our mechanicians have brought all apparatus




548           PHYSICS OF IMPONDERABLE AGENTS.
for electrical illustrations to a degree of perfection leaving little to be
desired.
572
AK
836. The American  plate electrical machine.-The form  of
plate machine commonly adopted in the United States is seen in fig.
574 (from Ritchie). It is arranged for the exhibition of both electricities at pleasure, and has a prime conductor on a movable stand.
DR. HARE has very ingeniously met the difficulty of obtaining both
electricities from the plate machine by making the plate revolve horizontally, and thus allowing the positive and negative conductors to
stand like arches in two vertical planes at right angles to each other
above the plate. Am. Jour. Sci. [1] VII. 108.)  Dr. Hare was an
ardent supporter of the Franklinian hypothesis, and this apparatus
was contrived to sustain his arguments in favor of that view.
837. Large electrical machine.-Ritchie's double plate ma



ELECTRICITY.                               549
chine.-The largest electrical machine hitherto constructed, so far as we are
advised, is that made for the University of Mississippi, at Oxford, under ths
574
direction of President Barnard, by Ritchie, of Boston. The general construction
of this gigantic electrical apparatus may be understood from fig. 575 (frontispiece), in which, however, the prime conductors are not shown.  These, for
greater convenience of manipulation, are made movable on separate supports.
This machine has two plates of French glass, each six feet in diameter, sustained by an insulated steel axle, upon eight cut-glass supports, on a frame of
rosewood. The plates are excited by four pairs of rubbers, made of brass, and
lined with fine wool felt three-eighths of an inch thick, such as is used for the
dampers of the grand piano. These are covered with firm  India silk, upon
which the amalgam is spread. Rubbers of this construction are found to be far
more efficient thn those in general use. The prime conductors of this machine
expose fifty squre feet of polished brass cylinders in three sections, about one
foot in diameter by seven in length, sustained also on cut-glass insulating pillars. One turn of this machine fills the apartment with an overpowering odor
of ozone. It is so arranged as to afford negative electricity from four rubbers.
One battery for this machine contains one hundred and twenty glass bells,
arranged in detachments, whose coated surfaces expose about ninety square feet
of area. No detailed description of the performance of this superb machine
has yet been mde public. It cost over three thousand dollars without its batteries.
The Tylesian machine.-The largest and most famous plate machine
mentioned in t)ie books before that of Ritchie, of Boston, both on account of its
size and perfcrmance, was made by Cuthbertson for Von Marum in 1755, and
was placed ii <he Tylerian Museum, at Haarlem, in Holland. It was a double
40




550            PHYSICS OF IMPONDERABLE AGENTS.
plate machine, each plate sixty-five inches in diameter, with eight cushions
nearly sixteen inches in length, and twenty-three and a half feet surface in the
conductor. It gave three hundred sparks twenty-four inches long in a minute
forked like lightning, and with rays six or eight inches long, branching from the
angles of the flash. It deflected a thread six feet long, six inches from a perpendicular, at a distance of thirty-eight feet, and the balls of Cavallo's electroscope (832) diverged half an inch asunder when forty feet distant from it. The
prime conductor was supported on three glass pillars sending out collecting
branches between the plates. Two, and sometimes four men, were employed
to turn it. When in full force, a single spark from the conductor sufficed to
burn and dissipate a strip of gold-leaf twenty inches long, and one and a half
lines wide. A pointed wire exhibited the appearance of a luminous star when
held twenty-eight feet from the conductor.
All glass is not equally fit for electrical plates; that which is white, hard, and
free from bubbles, is most esteemed. If too much alkali is used in the composition of the glass, its surface attracts moisture, and soon becomes damp and
rough. Such a plate is worthless. The preference given to old plates is due,
probably, to the fact, that their composition has enabled them to preserve their
properties uninjured.
838. Care and management of electrical machines.-Perfeco
insulation and freedom from dust and roughnesses, are essential to the
good condition of all electrical machines.  For this end, the glass
columns are varnished, to avoid the deposition of moisture, and all the
polished surfaces of metal, as well as the glass, must be kept quite
clean, and free of dust.  If the surface of the cylinder or plate
becomes streaked with amalgam, it must be wholly removed.  It is
better not to put any amalgam  into immlediate contact with the glass,
but to spread it upon the cushion pretty thickly, and then to cover it
with a piece of silk; a sufficient quantity will pass through the silk,
as the machine is worked.
If the glass becomes greasy, it is best washed with rectified camphene, burning fluid, or ether. It is indispensable that the surface of the amalgam should
be in good metallic communication with the earth, which is accomplished by the
use of tin foil, or tinsel. Cushions stuffed with metal filings are preferred by
some, chiefly for this reason. A cushion or rubber made of two or three folds
of cotton-flannel, between which is laid a continuous strip of tin foil, of the
same size with the rubber, works exceedingly well. Ritchie prefers piano felt.
Aurum mussivum (the bisulphuret of tin), a yellow bronzy powder, is an excellent substitute for amalgam. It is supposed to suffer chemical decomposition
when in use, and so to quicken the activity of the machine. Finally, a dry
winter air is indispensable for the best working of an electrical machine; hence,
radiant heat, falling on the machine, or an apartment heated by a dry furnace
air, is especially favorable. In carpeted rooms, it is desirable to connect the
rubber with a gas-fixture, to secure a good communication with the common
reservoir.
839. Electricity from steam.-Armstrong's hydro-electric machine,
fig. 576, is designed to illustrate the development of powerful electrical
eifects from  high steam; a fact well known to all concerned in the




ELECTRICITY.                           551
management of locomotive steam-engines, but first scientifically noticed
in 1840, by Mr. Armstrong, at Newcastle-on-Tyne.  The apparatus
which he contrived to show these effects,               576
is a common high pressure steam  boiler,
about three feet long and twenty inches in
diameter, mounted on insulating pillars, 
and strong enough for a pressure of 200                             I
lbs. to the inch.  The steam is suffered to             SD
escape by jets, A, of a peculiar form, on
the side of the box, B, into which it is admitted by the cock, C.  Faraday, in investigating the electricity of steam, found
that dry steam  gave no excitement, and                      l
that the electricity resulted from  the friction of vesicles of water against the sides
of the orifice.  Hence, B contains a little
water, over which the steam escapes, and is partially condensed. The
jet has an interrupted passage, seen at M, to produce friction, and its
nozzle is lined with dry box or partridge wood.  The vapor escapes
against a plate, P, covered with metallic points, to collect the electricity,
and ending in a brass ball, D, insulated from the earth. The boiler is
negative, and positive electricity is collected at D, provided the water
is pure and free from grease.  Turpentine, and other volatile essences,
reverse the polarity, while grease, or steam from acid, or saline water,
destroys all excitement. If the nozzle of the jet ends in ivory or metal,
there is also no excitement. A boiler, such as is described, will develop
in a given time, as much electricity as four plate machines forty inches
in diameter, making sixty turns a minute; a truly surprising result.
840. Other sources of electrical excitement.-1. The bands of
leather, India-rubber, or gutta-percha, used to drive machinery, sometimes become powerful sources of resinous electrical excitement, giving
sparks of negative electricity over twenty inches in length.
In cotton-mills, so much electricity is thus set free, that it becomes necessary
to let steam into the carding and roving rooms, to avoid inconvenience from the
repulsions and attractions of the cotton. A leathern band, mentioned by Mr.
Bachelder (Am. Jour. Sci. [2] III., 250), gave sparks to the finger at three feet,
and a luminous brush, to a steel point, at seven feet. The discharge from leather,
as from all bad conductors, is local, or danger would attend it.
Dr. Franklin, in a letter to Bowdoin, suggested, for a portable electrical machine, a crossed band of stuffed leather, moved by a winch over drums.
2. The friction of shoe-leather on woollen carpets, in houses warmed
by hot-air furnaces, or steam, in cold weather, is a fertile and curious
source of negative electrical excitement.




552            PHYSICS OF IMPONDERABLE AGENTS.
The young people in the author's house find an unfailing source of amusement in cold weather, in giving eloctrical shocks, by kisses and otherwise, to
unwary people, or in lighting the gas by a spark from the finger, or a keyhandle, after running briskly over the carpet. Prof. Loomis has noticed these
effects in detail in the Am. Jour. Sci. [2] X., 821, and XXVI., 586. They
appear to be unknown in Europe, owing probably to the fact that European
houses are seldom warmed and dried by hot-air furnaces.
841. Theory of the electrical machine.-The phenomena of the
electrical machine may be explained, either on the theory of one or two
fluids.  The explanations of induction (828), already given, apply
equally to the development of free electricity, upon the prime conductors of electrical machines.  When the machine is turned, the neutral
electricity of the rubber is decomposed, the positive fluid follows the
glass, until coming opposite the points on the prime conductor, the
negative electricity of the conductor flows out, to unite with the positive of the glass, while the positive fluid of the conductor is repelled to
the other end, thus leaving the prime conductor powerfully positive.
Reaching the rubber, the neutral fluid of the glass is there decomposed,
its negative portion seeks the common reservoir, and the positive follows the revolving glass to the points as before. The conductor does
not acquire positive electricity from the plate, but gives its negative
thereto, thus becoming itself positive.
It is still an open question whether the action of the amalgam is chemical or
mechanical (834). It is certain that an amalgam of silver, or gold, does not act
to excite electricity, like amalgams of oxydizable metals; and Dr. Wollaston
demonstrated, that the latter did not act in an atmosphere of carbonic acid or
nitrogen, free of oxygen.
In all cases, the discharge of an electrical conductor, by a spark or otherwise,
is accompanied by the induction of an opposite excitement in the body receiving
the shock, whose opposite electricity, uniting with that of the conductor by a
forcible disruption of the intervening dielectric, produces the sound and flash
of the electric discharge.
842. Experimental illustrations of electrical attractions and
repulsions.-A  multitude of instructive and amusing experiments
may be made with the electrical machine, illustrating the law of attraction.  A few must suffice.                              577
1. The insulating stool is a bench with
glass legs, fig. 577 (a board on four black bottles
answers perfectly), on which a person may stand
or sit, while in communication with the electrical machine. Being thus insulated, the free
electricity can escape only through the sur- 
rounding air,-approaching the knuckle to any 
part of the person or dress of one so situated,
a strong spark is received. Except for the hair being repelled, the person
charged is not conscious of any change from an ordinary state. A doll's head,
with paper hair, set upon one of the conductors, is a common electrical toy.




ELECTRICITI.                              553
2. Henley's electroscope, fig. 578, serves to mark the degree of tension
in the machine by the repulsion of a pith-ball at the end of a straw: it is
mounted on one of the conductors, and in dry   578                579
weather remains extended a long time, but in
damp weather falls immediately, when the ma-.chine stops.
3. Electrical bells, fig. 579; the bells, A
and B, are suspended by a metallic thread, from
the ends of a cross-bar of metal hung on the
machine; the bell, C, and the two clappers, are
hung by insulating threads. C is connected with            A \    
the earth; and when the machine is worked, A and  -\
B become positive, and by induction C becomes
negative, and the little clappers being alternately
attracted and repelled, a constant ringing is kept up as long as the excitement
lasts. If the machine is too active, luminous sparks pass, and the bells remain still.
The bells may be conveniently arranged on an independent foot, as in fig. 580.
4. Volta's hail-storm  is a contrivance designed to show bow (in Volta's
view) hail might be produced. It is a larger way of             581
showing the same facts already explained in ~ 811.  A
glass bell communicates with            580
the machine, fig. 581, above,
and rests on a metal plate in
communication with the earth. 
When the machine is worked, 
the pith-balls on the plate are
violently agitated, being drawn
up and repelled again actively, 
while the excitement lasts. A              II'
simple bell-glass, or large tum-                             ~ ~  
bier, electrized by contact of its'
interior surface with the con-  "
ductor of an electrical machine,
answers quite as well, and may
be placed over a heap of pithballs on the table; they are
violently thrown about as long
as the excitement continues. The dance of puppets, fig. 582, is only a substitution of little figures of dancing peasants, made of cork or      582
pith, and placed between two metallic plates.
5. The  electrical wheel is composed of several
points fixed in a centre, so balanced as to rest on an upright, 
sustained on one of the conductors, fig. 583; as the machine
is worked, the escape of the electricity from the points reacts
on the air with sufficient force to revolve the wheel with acti- 
vity.  The existence of such a current of air, caused by the
escape of electricity from points, is further shown:- 
6. By a candle flame; a candle, fig. 584, held before
the point, has its flame blown aside by the rush of air accompanying the electricity. If the candle is placed as a conductor,
and a point is held out to it, the direction of the flame is altered by the reveioe
duid induced'u the point, fig. 585.
49*




554            PHYSICS OF IMPONDERABLE AGENTS.
This experiment has been called the electrical blow-pipe. The rush of air from
the points may be so energetic from an active machine, as to extinguish the
flame. In the dark, all points on an electrical          583
machine emit a stream of light, called the electrical brush. Of course        584
no sparks can be drawn
585
from points, but a Leyden jar may be silently charged from them. Masts and
yards of ships are often seen thus tipped with fire (called St. Elmo's fire) in a
thunder storm. If the point is covered with a ball an inch or two in diameter,
its peculiar action ceases, and the ball emits sparks.
7. Franklin's spider, Ellicott's electrical water-pot, the inclined plane, and the
electrical planisphere, are other well-known forms of apparatus, designed to
show the same principle. The catalogues of all leading instrument-makers,
contain numerous additional illustrations to the same end.
V. ACCUMULATED ELECTRICITY AND ITS EFFECTS.
843. Disguised or latent electricity.-The phenomena of induction, already explained, have a curious and most important extension
in the subject of this chapter. When two equal and insulated conductors, equally excited by the two opposite electricities, are separated
from each other by only a thin plate of glass, or other dielectric material, no signs whatever of any electrical excitement are communicated
by either to an electroscope connected with them. The dielectric prevents the union of the opposing electricities, but not their mutual
inductive action, whereby their presence is entirely masked to surrounding bodies.
Removed to some distance from each other, each manifests free electricity, by the divergence of its electroscope. But if they are once
more brought together, this evidence of excitement again disappears,
and so on, until the imperfect ins lation of the air gradually neutralizes all free electricity.
When so situated, the electricities are said to be latent or disguised,paralyzed by their mutual attractions.
844. The condenser of AEpinus.-The phenomena of disguise,
electricity are illustrated by the use of various condensers, consisting
essentially of two extended metallic surfaces, and an insulating -ne



ELECTRICITY                               555
dium.  They are sometimes adapted to a cumulate electricity of high
tension, and sometimes their aid is invoked to render sensible, quantities of electricity otherwise insensible.
The condenser of AEpinus, figs. 586, 587, is designed for the former purpose.
rwo polished metallic surfaces, AC, with    586               587
electroscopes, a b, and an intermediate
thin  glass plate, B, fig. 587, are  all  
mounted on insulating glass pillars, and       c                     a
slide in a groove cut in the base. In fig.  
586, the two disks are placed in close
contact with the intervening dielectric,           
B, while, by the chain, n, positive electricity flows into A, from  the excited
conductor of an electrical machine.
Did A stand alone, it could only receive so much electricity as would raise its
surface to the same tension with the prime conductor of the machine. But this
condition is wholly changed by the presence of the second plate, C, cut off from
actual contact with A, by the dielectric, B, but entirely within its inductive infuence. A part of the natural fluid of C is at once decomposed by this influence of A, attracting its negative fluid to the inner surface of C, and holding it
there, while the corresponding positive fluid from C, is expelled by the conductor, m, to the earth.  No free electricity would remain if it were possible for B
to exist and act as a dielectric without thickness: but, as this is evidently impossible, it happens that a little less negative fluid is drawn to the surface of C,
than exists of positive on A, by reason of the thickness of B. Consequently,
the electroscope on A remains slightly elevated (residual charge), even after
some time, while that on C continues wholly passive.
But the neutralization of A's positive fluid by the decomposition of an equivalent of natural electricity in C, results in diminishing the tension of A, to the
low degree corresponding to its residual free electricity. Hence, A can receive
a fresh charge from the machine, raising its tension to its first condition, and
inducing the decomposition of a fresh portion of neutral electricity in C as
before, and thus the action proceeds, until the whole of the natural fluid of both
plates is decomposed and disguised, or rendered latent, excepting that small
portion which at each instant constitutes the fiee electricity, equivalent to the
difference due to the thickness of B, and which, as we have seen, would be null,
if B could be conceived of as having no thickness. It is this small residue
which constitutes the residual charge in the Leyden jar.
In performing this experiment, the knuckle may serve as a conductor to the
earth, in place of i, when a rapid series of sparks will be received (positive
electricity), constantly diminishing, and ceasing with the maximum charge of
A and C. This point of maximum  charge is dependent on, 1st, the extent of
surface in A B; 2d, on the tension of the prime conductor; and 3d, on the
thickness of B.
When the point of saturation in A and B is reached, and all the electricities
possible are disguised in the condenser, the pendulum on A still shows only a
feeble excitement, although both A and B are in a state of extreme tension.
Withdraw, now, A and C from B, as shown in fig. 587; now, the electroscopes,
A and B, both show high excitement: restore the plate again as at first, and b
becomes again entirely passive, while a shows the same feeble excitement as
before. The opposing fluids on A and C are wholly occupied with their mutual




556           PHYSICS (I IMPONDERABLE AGENTS.
attractions, and only the small excess of + fluid is free, as already explained
to affect the electroscope, B. The plates, A and C, are now fully charged witi
disguised electricity, rendered latent by mutual inductions, and the polarization
of the dielectric B. Although apparently passive, they are actually in a state
of high tension, as may be proved by their discharge.
845. The discharge of the condenser may happen in three
ways:-lst, insensibly; by the imperfect insulation of the supports,
especially if the air is damp; but always gradually.
2d, by the disruptive discharge.  If the plate, B, is too thin in reference to the extent of surface in A and C, the tension of the opposing
fluids will overcome the cohesion of the glass, B, and it will be shivered
in pieces, with a loud explosion, and brilliant spark.  The same spark
and explosion may take place without destroying the dielectric, if we
use a discharging rod, to effect communication between A and C. This
apparatus is either single, as in fig.  588              589
588, or double, as in fig. 589. If
this rod is provided with glass insulating handles (as in the figures), 
the experimenter feels no sensation;                           l
but otherwise, or if A and C are 
brought into  connection  by the
naked hands, then a powerful shock 
is experienced, oonvulsing the whole 
frame.  The same sensation, in a
feeble degree, is felt when  the
knuckle receives the sparks of an excited machine.
3d, and lastly, the charged plates may be slowly discharged by alternate connection with the earth. While the condenser is in the condition
indicated by fig. 586, touch C with the finger; no effect follows; touch
A, and a feeble spark is received; the electroscope, a, falls, while, at
the same instant, that on C is raised to the same degree, showing that
what A has lost in free positive electricity, C has gained in free negative fluid. Touch C; a slight shock, a feeble spark, and the fall of the
electroscope, B, ensue, while the electroscope on A again manifests its
original excitement. Thus, by the alternate discharge of A and C, the
whole of their disguised fluids are gradually set free and discharged.
846. Volta's condensing  electroscope.-This instrument de
pends on the principles just explained, and if used to render sensible
by condensation, electricity of too feeble a.tension to affect the ordinary
gold-leaf electrometer.
The plate A. fig. 590, is covered with waxed silk, slightly larger than the
disks; this takes the place of the dielectric, B, fig. 586. When the instrument
is used, the upper plate is placed in the position shown in fig. 591, and its sur



ELECTRICITY.                           557
face is touched with the body whose excitement we would measure; e. g. a
crystal of tourmaline.  At the same time, the under         590
surface of the lower plate            591
(in connection with the gold
leaves), is touched by the  
moistened finger of the other 
hand. The influence of the ex- 
cited electric acts in this case
exactly as has been already
explained in the condenser of 
AEpinus.  No divergence is
seen in the gold leaves, until                         I
the upper plate of the conden- 
ser is raised, as in fig. 590,
when the gold leaves promptly
diverge: this  action  being
heightened by the inductive
influence of two little balls of
polished brass, rising within
the glass as high as the lower
edge of the gold leaves.                _ 
Dr. Hare's single gold-        -     - -
leaf  electrometer.-In 
this instrument, a single gold leaf, about three inches long, by one-third
of an inch broad, is hung by a brass rod from the top of a bell or globe,
as in the last instrument. Immediately opposite to the lower end of
the leaf, a similar rod of metal passes through an opening in the side
ofthe vessel carrying a gilded disk of wood or paper half an inch in
diameter. This lateral rod is graduated to measure small distances.
To use this instrument, the lateral rod is put in communication with
the earth, and an electric is brought in contact with the upper disk,
when, if the distance between the leaf and the lower disk is small, the
most minute attractive force is detected.  In the original     592
instrument, Dr. Hare employed a plate of zinc, on an
insulating handle, and one of copper on the instrument 
arranged  as in Volta's electrometer, when the simple
separation of these two disks would evince a tenfold deli-     - 
cacy of action compared to Volta's condenser.*
847. The Leyden jar.-Accident led to the discovery   i
of this remarkable piece of apparatus, long before its  il
principles were made clear by the condenser of 2Epinus,'il lI1
and the explanations of Franklin. It consists of a thin         l1
glass jar, fig. 592, coated inside and outside with tin foil,   1i' — S
as far as the bend of the neck.  The inner surface is extended by the
* Hare's Mechanical Electricity, Philadelphia, 1835, p. 29.




558            PHYSICS OF IMPONDERABLE AGENTS.
wire, carrying a brass knob at top, touching the inner coating by a
piece of chain or wire, and sustained in its place by passing through
a non-conducting cover of dry wood.
The relations of the jar and the two metallic coatings, will be seen by fig. 593,
showing in section a Leyden jar, the parts of which are separable, and its wire bent
conveniently into a hook, to suspend it on the machine. It will be seen at a glance
that this arrangement is identical in principle with the condenser of Epinus, and
the electrical plates of Franklin. If the knob, b, of the Leyden jar, insulated
upon a stand, fig. 594, is presented to the conductor, a, of the electrical machine
in action, only a single spark or so, will enter it, unless     594
a way is provided, as by the conductor, c, for the escape of   
the similar electricity from the exterior coating,  593
while its opposite is then fixed as in C, fig. 587.
The charging of the jar then proceeds, and for
every spark which darts from a to b, a corresponding one of similar electricity, is seen to escape 
from the outer coating to c. When it is held in 
the hand, the same effect follows through the arm,
accompanied by a slight twinge in the nerves.
Presently the point of saturation is reached, and the two decomposed electricities
are latent. Either coating may be fearlessly touched alone, but as soon as by the
discharger or otherwise, communication is made between them, a loud snap and
brilliant spark follow with a violent shock.
The invention of the Leyden jar, or vial, is commonly attributed to Cunsus
or Muschenbroek of Leyden, in 1746. Von Kleist, dean of the chapter at Comin,
in Pomerania, also independently discovered this important instrument by a
similar accident.
With a view to fix electricity in some insulated substance, Cunseus, in 1746,
led electricity into a small vial containing water, by a bent nail thrust through
the cork, and hung upon the prime conductor. Endeavoring, in one of these
trials, to detach the vial and nail from the electrical machine, Cunseus, to his
great amazement, received a violent shock. Von Kleist, in the course of a
valuable series of experiments (1745) on electricity, led the fluid by a brass
wire or pin into a bottle containing mercury.  "As soon," he says, "as this
little glass, with the pin, is removed from the electrical machine, a flaming
pencil issues from it so long, that I have been able to walk sixty paces in the
room with this little burning machine; and if the finger or a piece of money be
held against the electrified pin, the stroke coming out is so strong that both
arms and shoulders are shaken thereby."
This discovery of so wonderful a power in nature, before unsuspected, created
immense excitement over the civilized world, and it was precisely at this time
that Franklin immortalized himself by his contributions to the new science. He
explains the action of the Leyden vial by his single fluid hypothesis, in his
"' Observations and Experiments on Electricity," in a manner which must ever
win for him the reputation of a profound philo-           595
sopher.
848. Electricity in the Leyden jar                                  I D
resides on the glass.-In fig. 595, the
Jar, A, is composed of the three separable
pieces; B, the glass, C, its outer, and D,_ =
its inner metallic coatings.  When this jar is charged, and set on an




ELECTRICITY.                           559
insulating surface, it may be separated into its three parts without
being discharged; but C and D will then be found by the electroscope
entirely free from excitement, while B remains strongly excited.  Putting the parts together again as in A, the jar will be found charged as
at first, if the air is dry, and too much time has not passed.
849. The electric battery.-As the charge of the Leyden jar is,
other things being equal, directly as its surface, large jars are plainly
of more power than small ones.  But a limit of size is soon reached,
which the thickness of glass required for strength, and other circumstances, render it unprofitable to pass. Hence several coated jars, of
moderate size, are united by joining all their inner coatings by metallic
rods, and all their outer coatings by a common conducting base, as
shown in fig. 596. Such an arrangement                 596
is called  an  electrical battery.  When  
charged from a common source, and discharged in the usual way, they all act as
one great jar, the result being not quite      U S
in the ratio of the number of jars, but
nearly so.  Hence, the smaller the num- I  
ber, the thinner the glass, and greater the j.
size of the jars, the better, and several
batteries of seven and nine jars, united to the charging rods of the
central jars, are preferable to more extended single series.  They are
charged by connecting the interior with the prime conductor by t,
and the exterior with the earth.  If the battery is extensive, and the
machine powerful, great caution  is requisite to avoid receiving its
shock; an accident which might be serious in its consequences.
The battery used by Von Marurn, with the machine already noticed (837), embraced one hundred jars, each thirteen inches in diameter and two feet high. The
coated surface was five hundred and fifty square feet (five and a half feet to each
jar). When fully charged, its force was irresistible. A bar of steel nine inches
long, half an inch wide, and one-twelfth of an inch thick, was rendered powerfully magnetic by the discharge. A small iron wire, twenty-five feet long, was
deflagrated, and various metals were dissipated and raised in vapor, when
placed in the circuit of discharge. A book of 200 pages was pierced by it, and
blocks of hard wood, four inches square, split into fragments.
850. Discharge in cascade.-A series of two or three Leyden jars
may be placed horizontally upon insulating stands, so that the interior
of each succeeding one may receive the spark from the outer coatings
of the one preceding.
This mode cf charging cannot be carried beyond two or three jars, owing to
the accumulate.d resistance soon vitiating the result. But Mr. Baggs, of London,
has very ingeniously contrived an electric battery, the jars of which are charged
together, but are discharged consecutively. Each jar is supported in a horizontal
position on a vertical spindle, their kno'ps, while being charged, pointing out



s60            PHYSICS OF IMPONDERABLE AGENTS.
ward, like the radii of a circle, and when the battery is to be discharged, the
knobs, by a quarter revolution, are brought opposite, each to the bottom of the
next jar. In this way the disruptive power or intensity of the spark is multiplied as the jars, the quantity remaining the same. Mr. Boggs is said to have
discharged his battery of twelve jars through a space of three feet.  (Am.
Jour. Sci. [2] VII. 418.)
851. The universal discharger.-Various contrivances are in use
for regulating or measuring the discharge of the electric battery, and
the single jar. Of these, Henley's                  597
universal discharger, fi,. 597, is, O                            a 
perhaps, the  most useful.  By 
means of this simple apparatus,                          e
the electrical fluid may be made to 
pass through any substance placed
upon the table, t.  Two rods, sliding in the joints a a', end in balls,
c c, covering points which can be       ll
exposed by their removal.  The rod, a', connects with the positive side
of the battery, for example, while by the discharging rod, fig. 589,
communication can be made at pleasure between a and the negative
side of the battery, by a chain or metallic thread.
The charge of the battery may be prevented from passing a given limit, by
using the discharging electrometers of Lane or Cuthbertson, in which a ball is
sustained at such a distance from the discharging knob of the battery, that when
its charge reaches the proper tension, it discharges itself.
A beautiful illustration of the slow discharge of a charged jar is
seen in fig. 598, where a charged Leyden jar, with a small bell in
place of the knob, is set upon a board,                 598
near to a little brass ball, hung from a
silken thread, upon a wire, carrying a
second bell in connection with the earth
by AB.  The effect is, that the + electricity of the jar attracts the little ball, 
lut after striking the bell, the ball is repelled, until, coining in contact with the
other bell, it is discharged, and so on for     A 
many hours, this little chime is rung by
the electrical pendulum.
852. The electric spark.-The electric light and spark result from  the reunion of the two electricities in the air.
In a vacuum there is no spark (fig. 601). 
The zigzag path of the spark and of lightning is due to the resistance
of the air  Every electrical discharge produces expansion of the air,




ELECTRICITY.                          561
and the form  and color of the spark are materially influenced by the
density and chemical composition of the gaseous medium  through
which it passes. The character of the sparks depends also on the form,
area, and electrical intensity of the discharging surfaces, likewise on
the kind of electricity on the conductor in which the spark originates;
from the negative conductor the sparks are far less dense and powerful
than those from positive electricity.                         599
Kinnersley's thermometer, fig. 599, shows the
agitation and expansion of the air following an electrical
explosion. A portion of water in the larger vessel, which
is air-tight, communicates freely with the small open tube, 
attached to the foot, and ending in a narrow glass tube. 
When an electrical discharge takes place through the apparatus, the consequent expansion of the air violently raises
the column in the smaller tube, but, after the commotion is
over, the fluid gradually regains its original level, as the
air in the larger vessel cools. The electrical mortar discharges its ball by the force of air expanded at the moment
of the electrical discharge.
The color of the electrical spark.-Faraday
observed that in air, oxygen, and dry chlorohydric          
acid gas, the spark was white, with a light bluish
shade, especially  in air.  In  the heavy thunderstorms common in an American summer, the light
of a powerful flash of lightning is distinctly purple,
and sometimes violet.  In nitrogen  it is blue or
purple, and gives a remarkable sound; in hydrogen
it is crimson, and disappears when the gas is rarefied; in carbonic acid the color is green, and the form of spark very
irregular; in oxyd of carbon it is sometimes green and sometimes red;
in chlorine it is green.                            600
The little apparatus, fig. 600, is 
well calculated to show these effects  al  a/ 
by contrast at one view. The three 
tubes, a a' a", are respectively filled
with various gases and sealed. Each                
tube has two short platinum wires, nn,
soldered into its sides, through which 
the electric spark from b must pass
on its way to the ground by c.
The electrical discharge in
a vacuum, becomes an ovoidali
tuft of light, uniting the conductors.  The apparatus, fig. 601, is designed to show these effects.
A  large egg-shaped glass vessel is mounted at the lower extremity
with a stop-cock, for attaching it to the air-pump, in order to re50




]62           PHYSICS OF  IMPONDERABLE AGENTS.
move the whole or a part of the air, or to replace it by vapor of
alcohol, ether, or any other gas not acting on         601
brass. By the rod, A, connection is established    A
with the electrical machine, while the distance 
between the electrical poles, B C, may be              B
adjusted by sliding the upper rod in its air- 
tight socket.  This apparatus is called the
electrical or philosophical egg.  The rarer the
air, the more globular becomes the spheroid,
and, at the same time, less brilliant.  The
auroral tube is only a modification of the same
apparatus.
This apparatus is also used with splendid effect
with the Induction coil.
Difference between the positive and
negative  spark.-The tuft of light from
positive electricity is far more beautiful than
that from negative, as seen from     602               l
the ends of two points.  Thus,
while positive electricity gives an
opening sheaf of light, negative
electricity gives only a small star,   +
fig. 602. In rarefied  air, these 
differences are much less appa-        I            -
rent. Faraday suggests that they are due, chiefly, to the greater facility
with which negative electricity escapes in air, than       603
positive, as conductors negatively charged, lose their
excitement sooner than those positively charged.
The diamond jar.-To show that the coatings of
the jar convey the electricity collected on the glass
to the point where it meets the cause of discharge, a
jar may be coated with metallic filings, fig. 603, or
patches of tin-foil, fig. 604, cut in lozenges   604
(a diamond jar). The wire of the jar is
bent over, as in fig. 603, so as to bring the
ball near the outer coating, which connects
b)y a chain with the earth.  When the ma- 
chine (on whose arm this jar is hung) is
worked, a brilliant spark is seen at intervals to dart from  the knob to the outer
coating, and thence to spread in zigzag 
courses over the whole surface.
Scintillating tube and magic squares.
-Every collection of electrical apparatus contains these familiar pieces




ELECTRICITY.                           563
of apparatus, illustrative of the phenomena of the electric spark.  The
scintillating tube, fig. 605, like the jar, fig. 604, has rows of lozenge605
shaped pieces of tin-foil pasted on its interior, usually in a spiral, and,
when held by the hand, as shown in the figure, the electricity flashes
from point to point at the same apparent instant, producing a most
agreeable effect.                                  606
The magic squares are panes of
glass on which are interrupted strips
of tin foil, cut to represent some
design, to be made visible only when
a spark passes. These squares are
mounted on a foot, in connection
with the earth, and are set near the
ball of the prime conductor. By
scattering metallic filings over a
varnished surface of glass, the same
effect is produced as upon the jar,
fig. 603.
853. Effects of the electric  -        t        b.        s
discharge.-The effects of the
electric discharge  are chiefly,
1st, physiological; 2d, physical; 3d, mechanical; 4th, chemical.  The passage of the electricities through bodies, is sometimes
impeded by their bad conducting power, or by want of proper dimensions; and, in either case, a powerful electric discharge manifests itself
in one of those modes.
854. Physiological effects.-These are seen in the shock experienced by all living beings, in the passage of electricity through any
of their members.  Any number of persons, joined hand to hand, will
receive, at the same instant, the shock of an electric battery. Abb6
Nollet imparted it to over six hundred persons in his convent at one
time-those in the middle of the chain being little less affected than
those near the conductors.
A person charged on the insulating stool, feels a prickly heat and glow of the
skio, resulting in perspiration. Many useful applications have been devised of




564            PHYSICS OF IMPONDERABLE AGENTS.
this agent in medicine.* It needs hardly to be said, that the full shock of a
powerful battery will destroy life in man. Sparks, fifteen or eighteen inches
long, begin to be unsafe, if from large surfaces. Small animals, as birds, are
easily killed by a moderate discharge, on the table of the universal discharger.
Fig. 597.
855. Inflammation of combustibles.-Although no sense of heat
is felt when the knuckle receives strong sparks from an active machine,
yet the smallest spark serves to inflame ether, whether from a Leyden
jar, from the finger, or, more strikingly, from an icicle held in the
fingers of one mounted on an insulating                    607
stool.
The ether is placed in a metallic cup, and the
spark should be drawn on its edge moistened with
ether, fig. 607. Gunpowder placed on the table
of the universal discharger, over the poitts of  +
the rods, a a', fig. 597, is simply thrown about,
without being fired; but if a wet string, in 
place of one of the conducting wires, forms part 
of the connection, its retarding power is such as
to fire the powder. The lighting of gas from
the finger of one charged by running on a carpet, has already been mentioned (840, (2)) Lycopodium, alcohol, a newly
extinguished candle, and many other combustibles, are also easily inflamed by
the spark. Gold leaf confined between two glass plates with the edges hanging out, will burn with the explosion of the glass, and, if held between cards,
will stain them with purple oxyd of gold. Silhouette likenesses of Franklin
are thus printed: a powerful current from a battery is needed for this.
856. Chemical union effected  by electricity.-A  mixture of
hydrogen two volumes, and of oxygen one volume, or of hydrogen with
seven or eight times its volume of common air, is exploded by a spark
passing through the containing vessel, e. g.               609
the tin air-pistol, called "Volta's pistol," 
fig. 608, is provided with an insulated conductor, ending near the inner       608 
surface of the pistol at B.
Its mouth is closed tightly
by a cork, and the spark _ 
caused to pass by holding
it near the prime conductor,
fig. 609, or to the electro- 
phorus.  The cork is then
violently expelled, by the expansion of steam, with a loud explosion.
* Consult Garratt's Electro-physiology, Boston, 1860, 8vo., pp. 708; or Channing's Medical Electricity.




ELECTRICITY.                             565
Volta's electrical lamp.-A self-regulating hydrogen apparatus is
seen in fig. 610, similar in its action to the common hydrogen lamp,
with platinum sponge. In its base drawer                  610
is an electrophorus, r P, the plate, P, of 
which is always charged. A  silk cord
connects the upper plate P, with the gas  v
cock, R, in such a way that when the gas 
in T is drawn, the communication is ef-              X
fected at o, with the insulated wire, t/,                            o
and the electricity thus finds its way in
a spark between the buttons at 0, and              r i 
escapes to the earth by t.  As the hydro-  
gen is flowing at that moment from  the           _   __
jet, it is inflamed, and kindles a little 
candle standing in its path.  Every time                         --
the cock, R, is moved, the plate, P, rises,
and communicates a spark.  With care,
this instrument remains in action for weeks, from a single excitement.
857. The mechanical effects of the electrical discharge.-Any
thin non-conducting substance placed between the balls of the universal discharger, is either pierced or broken where the fluid passes. The
phenomena attending these experiments are curious and instructive in
point of theory.
When a thin piece of glass, v, is placed in the position seen in fig. 611,
between the points of the conductors, a b, a small hole will be made through
the glass, as if with a drill, provided the effect of the fluid is concentrated by
placing a drop of oil at the point to be pierced. The hole is circular, starred,
and its edges smooth, and sometimes it remains filled with the powdered
glass in fine dust, easily removed. It requires a powerful battery to pierce
glass one-twelfth of an inch thick.                               612
If a card is placed in the path of the fluid, it is pierced with
a raised edge (burr) on both sides of         611             a
the hole. When the card is placed 
obliquely, as seen in fig. 612, between  D       b:='   +b
the points, a c, of the insulating holderI
the hole is made in the place and direction seen at o in the section; that
is, nearer the negative pole, its edges 
being raised, or thickened, a circum-      v  
stance due, probably, to the decompo-                    
sition of the neutral fluid in the card, 
occasioning a rush of electricity in both 
directions. This has been esteemed a 
fact inexplicable on the single fluid hypothesis, while the position of the hole,
always near to the negative pole, indicates that the negative fluid passes lees
readily through the air than the positive. Many other examples of the frac50*




566           PIYSICS OF IMPONDERABLE AGENTS.
ture, or dispersion of non-conducting bodies, may be gathered from the larger
treatises.
858. The chemical effects of statical electricity are generally feeble. Besides those before alluded to (856), Wollaston, with very fine
points of gold wire immersed in water, decomposed water in very
small quantity. A paper moistened with iodid or bromid of potassium,
is stained brown by the electrical discharge when it is laid upon the
scintillating square (fig. 606). Olefiant gas, sulphuric acid, chlorohydric acid, ammonia, and nitrous oxyd, are decomposed by the electric
discharge, with the separation of their constituent elements, and carbonic acid is decomposed into oxygen, and oxyd of carbon. The elements of the air unite under a prolonged series of sparks (Priestley),
to form nitric acid (Cavendish), and lightning in the atmosphere forms
the same compound, as the analysis of rain-water has shown (Liebig).
Numerous other evidences of the chemical effects of electricity have
been recorded; perhaps the most important of these, is that atmospheric effect, called ozone.
859. Ozone.-This term is derived from the Greek, in allusion to
the peculiar odor which is always perceived after an electrical discharge
or excitation of a machine, and sometimes improperly compared to the
odor of sulphur, which it does not at all resemble. It is due to a remarkable state or condition induced in oxygen gas by electricity (and
by several other causes also). Mr. Schonbein, of Basle, has devoted
himself to the study of the curious properties of this singular product,
the record of which belongs rather to Chemistry than to Physics.
VI. ATMOSPHERIC ELECTRICITY.
86G. Franklin's kite.-We owe to Dr. Franklin the demonstration
that the phenomena of a thunder-storm are due to electricity, identical
with that excited in electrical experiments. He proposed two modes,
in 1749, by which he supposed electricity might be drawn from the
clouds. Dalibard, at his suggestion, erected in the open air near Paris,
in 1752, a pointed and insulated iron rod, 40 feet long. On the 10th
of May, 1752, electrical sparks were obtained from this rod, with the
usual snapping sound. In June of the same year, Franklin, tired of
waiting for the erection of a tall spire in Philadelphia on which to
place his pointed conductor, conceived the idea of reaching the higher
regions of the air by a kite. This he formed of a silk handkerchief
stretched over two light cedar sticks. It had a pointed wire at top,
and a silken cord insulated the hempen string, at the lower end of which
he tied an iron key.
Watching the approach of a thunder-storm, he raised the kite, and
soon had the satisfaction of seeing the fibres of the hempen string




ELECTRICITY.                             567
bristle and repel each other, and finally when the rain had rendered
the string sufficiently a conductor, he enjoyed the unspeakable satisfac.
tion of seeing long electrical sparks dart from the iron key. Thus was
realized by actual experiment one of the boldest conceptions and most
interesting discoveries in the history of science.
Efforts have been made to rob Franklin of the honor of this discovery, but it
is one thing to suggest that two phenomena may be identical, and quite another
thing to prove it. Dalibard's experiments were undertaken at Franklin's sug
gestions and hardly preceded his own in date.
These experiments were everywhere repeated, and it soon became evident that
they were far from being free from danger. Romas, in June, 1753, during a
thunder-storm in France, drew flashes of electrical fire ten feet long, from a kite
r.ised by a string 550 feet long. The experiment was accompanied by every
evidence of intense electrical tension in the attraction of straws, the sensation
of spiders' webs over the faces of the spectators, and in the loud reports and
roaring sounds, similar to the noise of a large bellows. In August, 1753, Prof.
Richmann, of St. Petersburgh, lost his life while engaged in similar experiments.
Cavallo, in London, in 1777, obtained enormous quantities of atmospheric electricity by an electrical kite, and noticed that it frequently changed its character
as the kite passed through different layers of the air. In telegraph offices during
a thunder-storm, vivid sparks, often very inconvenient and not without danger,
are constantly flowing from the receiving instruments, being induced on the
telepraph wires from  the atmosphere, during thunder-storms. (Henry, Am.
Jour. Sci. [2] III. 25.)
861. Free electricity in the atmosphere.-That the atmosphere,
besides the combined electricity proper to it, contains also at all times
free electricity, is proved by raising an insulated conductor a few feet
into the air, as by a long fishing-rod, and connecting it with the condenser of the electrometer, the leaves of which will diverge sensibly
when there is no sign of any thunder-storm. Near the earth (say within
three or four feet), no evidence of free electricity can be detected, but
as we rise in the air, its force constantly increases.  Becquerel and
Breschet, sent up arrows, attached to a tinsel cord ninety yards long,
from  the top of the Great St. Bernard, while the other end was connected with the condenser of an electrometer; they found that the gold
leaves diverged in proportion as the arrow rose higher.
It appears from experiments like tlese and others made chiefly by Ronalds,
of Kew, that the atmospheric electricity increases and decreases daily, twice in
twenty-four hours, and the following general results are established.
1st. The electricity of the air is always positive-is fullest at night-increases
after sunrise-diminishes towards noon-increases again towards sunset, and
then decreases towards night, after which it again increases.
2d. The electrical state of the apparatus is disturbed by fogs, rain, hail, sleet,
or snow. It is negative when these approach, and then changes frequently to
positive, with subsequent continued changes every three or four minutes.
3d. Clouds also, as they approach, disturb the apparatus in a similar way,
and produce sparks from the insulated conductor in rapid succession, so that
an explosive stream of electricity rushes to the receiving pole, which should be




568           PHYSICS OF IMPONDERABLE AGENTS.
passed off to the earth. Similarly powerful effects frequently attend a driving
fog and heavy rain.
Crosse, of England, had over a mile of insulated wire sustained on poles one
hundred feet high above the tall trees of his park, connecting by pointed conductors with his laboratory, where he has frequently collected, during a heavy fog,
electricity enough to charge and discharge a battery of fifty jars, and seventythree square feet of coated surface, twenty times in a minute, with a report as
loud as that of a cannon.
Numerous hypotheses have been put forward to account for what has
been considered the free electricity of the atmosphere. Prof. Henry,
after an attentive study of the whole subject, feels compelled to reject
them, all as insufficient except that of Peltier, which refers these phenomena not to the excitement of the air, but to the inductive action of the
earth on its non-conducting aerial envelope. This view involves the
assumption that the earth was in some way primarily electrified. It is
a fact that the earth is always in a state of negative excitement, as was
shown by Volta, who for this purpose received the spray from a cascade
on the balls of a sensitive electrometer, when the leaves diverged with
negative electricity.  (See an able article on Atmospheric Electricity
by Prof. Henry, Patent Office Report, Agriculture, 1859, p. 485.)
The subject of atmospheric electricity, especially the description of
electric meteors, is more properly referred to Meteorology.
Q 3. Dynamical Electricity.
I. GALVANISM AND VOLTAISM.
862. Discovery of galvanism.-In 1786, Luigi Galvani, professor
of anatomy in the University of Bologna, while engaged upon a long
series of observations on the effects of atmospheric electricity upon
animal organisms, noticed that the legs of some frogs, prepared for
experiments, became convulsed, although dead and mutilated-when
the vertebrae, with portions of the lumbar nerves, were pressed against
the iron railing of the window balcony where they          613
were placed, awaiting the use for which they had
been designed.  Repeating this novel and curious
observation in various ways, he soon found that  
the convulsions were strongest when he made connection by means of two metals between the lumbar
nerves, and the exterior muscles denuded of the          C 
skin, as shown in fig. 613, where rods of copper and
zinc, being thus held, convulse the leg into the
position shown by the dotted line. But contact of
metals with the animal tissues he found not to be
essential to produce these convulsions, since they occur also by contact
of the exterior mucous with the interior nervous surface.




ELECTRICITY.                              569
To repeat Galvani's experiment, strip the skin from the legs of a vigorous
frog and cut the animal in two, an inch above the thighs. Expose the lumbar
nerves within and on either side of the backbone, by pushing aside the muscles
with the finger, so that the point of an arc of the two metals may touch the
nerves; then bring the other metal rod into contact with any portion of the
outer surface, and strong twitchings will be developed as if the animal was
alive, both on touching and removing the rod, even some hours after death.
The galvanic fluid.-Galvani regarded the convulsions of the frog
as excited by a nervous or vital fluid, which passed from  the nerves to
the muscles by way of the exterior communication established between
them: this fluid, in his view, existed in the nerves, it traversed the
metallic arc, and falling on the muscles, it contracted them, like the
electric discharge..
Galvani was an anatomist and physiologist, and not a chemist or physicist.
He did not work out all the teachings of his own discovery, being more interested in demonstrating, as he did, the existence of a true animal electricity,
developed between the outer surface and the nerves. The physical branch of
the subject he left to others, and chiefly to VOLTA, devoting the few remaining
years of his life to the study of animal electricity. Volta's doctrines Galvani
never accepted, and died in 1798, before the Voltaic Pile was given to the world.
In the department of vital electricity, Galvani's labors have been justly appreciated only in our time, having been naturally eclipsed in his own by the splendid
discovery of the Voltaic Pile, and the crowd of wonders following in its train.
The story usually found in text books, of the accidental discovery, in 1790,
of the new science by the twitching of frogs' legs, prepared for the repast of
Madam Galvani, is a fabrication of Alibert, an Italian writer of no repute.
Galvani had then been for eleven years engaged upon a laborious series of
electro-physiological experiments, using frogs' legs as electroscropes.  No great
truth was ever discovered by accident, and years of laborious research had prepared the way for this discovery. It is undoubtedly true that what we find is
often more important than what we seek, but it is research and not accident
which makes the discovery. Every hypothesis is good which bears fruit in discovery; but to accept the discovery and reject the hypothesis when no longer
fruitful, requires all the self-denial of the highest philosophy, and is a noble
attribute of the greatest minds.
863. Origin of Volta's discovery.-Contact theory.-Adopting
at the outset with the greatest enthusiasm the vitalist hypothesis of
Galvani, Volta came, after no long time, to the conviction that the
electrical effects attributed by Galvani to the animal electricity of the
frog, were really due to the contact of dissimilar substances, and that
the frogs' limbs were only the sensitive electroscope, adapted to indicate
the electrical current developed by the two unlike metals. Each discoverer saw but half the truth. Thus originated his celebrated " contact
theory;" a view of the source of dynamic electricity, that long held
almost universal sway over scientific opinion until gradually supplanted
by the electro-chemical theory, which refers these phenomena to chemical
action.




570            PHYSICS OF IMPONDERABLE AGENTS.
By the use of his condensing electrometer (846), Volta sought to establish the
contact theory by a great number of well-devised experiments. Being assured
of the passive state of the electrometer, he established communication between
the earth and the upper plate by the moistened fingers, while at the same time
a bit of zinc plate held also in the moistened fingers of the other hand is placed.
in contact with the lower plate; after a single instant, contact is broken, and
on raising the upper plate, the gold leaves diverge. Whence the electricity?
Volta replied, "from the contact of the two unlike substances," overlooking the
fact that there was a chemical action, due to the effect of the moist fingers on
the zinc. As the plate touched by the zinc became positive, and the copper
negative, he assumed that there was an " electromotive force" capable of developing these electrical states in the two metals as a result of simple contact.  This
experiment was repeated with conductors of every sort, and always, when one
of them was an alterable substance, with the same results. He divided conducting bodies into two classes; the first class, including the metals, metallic ores,
and carbon, he calls electromotors; the second class contains liquids, saline solutions, animal tissues, &c. He found that a double combination of three elements,
so arranged that their order was reversed, neutralized each other, and produced
no spasm in the frog's legs, which he uniformly used as an electroscope. This
was in 1796, four years in advance of the date usually assigned as that of the
invention of the Voltaic pile.
Passing over the long controversy between Volta and his cotemporaries, we
come to the essential fundamental fact of Volta's discovery, viz.: thmrt certain
metals, and particularly the oxydizable metals, disengage electricity and charge
the condenser, when placed in the conditions just described.
This discovery immediately led to the second, and by far the most
celebrated of Volta's discoveries, viz., the Voltaic pile, or battery.
864. Volta's pile, or the Voltaic battery.-Every form of apparatus designed to produce a current of dynamic electricity is called a
battery or pile. Volta's original apparatus was, as its name implies, a
pile of alternate silver and zinc disks, laid up as in fig. 614, with disks
of paper or cloth between them, moistened with brine, or acid water.
This arrangement was more commonly made with alternate disks of
copper (C) and zinc (Z), care being taken always to observe the order,
copper-cloth-zinc.  The terminal disks were provided with ears for
the convenient attachment of wires.  Thus arranged, the following
characteristic results are observed. 1st. The pile being insulated by
glass or resin, touch Z with the plate of the condenser (covered with
silk), while the finger rests on C, and then apply the plate to the condenser; the gold leaves will indicate strong vitreous electricity. 2d.
Reverse this order, touching C with the plate while the finger is on Z,
and a strong charge of resinous electricity is received.
The pile may be regarded as a Leyden jar, or electrical battery, perpetually charged, and capable of re-charging itself as long as the given
conditions are maintained.
Thse results may be repeated an indefinite number of times, as long




ELECTRICITY.                        571
as the cloths remain moist, and the intensity of the action is directly as
the number of plates in the pile.
Each touching couplet of copper and zinc may be soldered together,
and is then called a couple, pair, or voltaic element. Any two metals
of unlike properties may be substituted for the        614
zinc and copper, with the same results.
The end of the pile which yields vitreous
electricity is called its positive pole, and that 
which yields resinous electricity is called the
negativepole; a name also applied to the wires
or conductors connecting the two poles. 
Arranged as in fig. 614, the pile, when its
poles are joined, gives a decided shock, similar                4
to, but less intense than, that from, statical
electricity. On breaking contact between thel 
poles, a brilliant spark of voltaic electricity is 
seen; and if the wires end in points of gold or
platinum, inserted in water, without mutual
contact, a flow of gas bubbles from  them, aniounces the decomposition of the water. We
thus classify the effects of the pile into physiological, physical, and chemical phenomena.
The discovery of the pile, Volta announced in
March, 1800, to Sir Joseph Banks, both in the 
form just described and also the crown of cups 
(Couronne des tasses), a series of twenty glass 
goblets arranged in a circle, with wires connecting the + and - elements of each cup to
the opposite of the next.
This last is the type of all modern batteries
with separate cells. He classified its effects, but made no mention
of its power of chemical decomposition, a property he had not then
observed. This last power was immediately discovered by Nicholson
and Carlisle, in London, on the 2d of May, 1800. Aside from Volta's
theoretical notions, history will ever assign him a high place as a
philosopher, and as having by his genius blessed the world by one of
the greatest and most fruitful discoveries in science.
Distinction between Voltaism and Galvanism.-It will be seen
that Voltaism and the Voltaic pile are terms properly applied only to the
discoveries of Volta, and that the term galvanic battery is a misnomer, Galvani never having seen such an irstrument. The term Galvanicfluid is
justly applied to animal electricity, which Galvani was the first to discover.




572            PHYSICS OF IMPONDERABLE AGENTS.
865. Quantity and intensity.-There is a very marked difference
between the tension of the electricity from the Voltaic pile, and that of
friction.  No sensation follows the touch of either pole of a Voltaic
battery singly: both poles must be touched simultaneously in order to
perceive the shock.  The projectile force in Voltaic electricity is so
nearly null, that in the most energetic and extensive series of cells, the
terminal points must be brought indefinitely near, or into actual contact, before any current is established, unless in vacuo. The intensity
of the battery is however, under some circumstances, increased by reduplicating the number of couples of a given size (see 1 881).  The
quantity of electricity set in motion in the Voltaic battery depends not
on the number of the series, but on the extent of surface brought into
action in each pair, the conducting power of the interposed liquid, and
also upon the external resistance.
The views formerly expressed by most authors on the subject of quantity and
intensity have been modified in important respects by the application of the
"law of Ohm;" for a discussion of which compare j 881.
866. Simple Voltaic couple.-Whenever two unlike substances,
moistened by, or immersed in, an acid or saline fluid are brought into
contact, a Voltaic circuit is established. The earliest recorded observation on this subject (Sulzer's), was the familiar experiment of a silver
and copper coin, or bit of zinc, placed on the opposite sides of the tongue,
and the edges brought together, when a sharp, prickly sensation and
twinge is felt, and if the eyes are closed, a mild flash of light is also
seen.  In this case, the saliva is the saline fluid, exciting a Voltaic
current due to its chemical effect on the zinc or copper; and the nerves
of sense are the electroscope.  The action depends on contact, and
ceases, or is renewed, as often as this is broken or made.
In fig. 615, we have the simplest form of Voltaic battery, a slip of amalgamated zinc, Z, and another of copper, C, immersed in a glass of water, acidulated
by sulphuric acid. When these strips touch (either within or   615
without the fluid), an electrical current is set up, passing from
the zinc to the copper in the fluid, and from the copper to the
zinc in the air, as shown by the arrows. The polarity of the
ends in the air is the reverse of that in the acid, as shown by
the signs plus and minus. This is analogous to the decomposition of neutral electricity in a rod of glass or of wax. While 
contact is maintained, either directly or by conducting wires,
evidence of chemical action is seen in the constant flow of gas    -
bubbles (hydrogen) from the zinc to the copper, from the surface of which they are given off. This action ceases at any
moment when contact ceases, and if the separation of the metals takes place in
the dark, a minute spark is seen at the moment of breaking contact in the air.
The direction of the Voltaic current depends entirely on the nature
of the chemical action producing it. Thus if in the arrangement just




ELECTRICITY.                          573
described, strong ammonia water was used in place of the dilute acid,
all the electrical relations of the metals and the fluid would be reversed:
since the action would then be on the side of the copper, and the zinc
would be relatively the electro-negative metal.
867. Electro-positive and electro-negative are relative terms,
designed to express the mutual relations of two or more elements in
reference to each other. Thus zinc, being a metal very easily acted on
by all acid and many saline solutions, becomes electro-positive to whatever other element it may be associated with, unless, as in the last
section, the other element is acted on, and the zinc is not, when it
becomes electro-negative. Oxygen is an element which acts upon every
other, and is therefore the type of electro-negative substances; gold,
platinum, and silver, being among the least easily oxydized metals,
become electro-negative substances to all others more easily acted on
than themselves, and therefore these are fit substances for the negative
element of Voltaic couples. In chemical works, tables will be found
in which all the elements are grouped in this relative order of electropositive and electro-negative power.
868. Amalgamation.-Commercial zinc is seldom  or never pure
and the foreign substances which it contains are such as to stand in an
electro-negative relation to the zinc. A slip of common rolled zinc,
immersed in dilute sulphuric acid, is actively corroded with the escape
of abundance of hydrogen, while if a strip of chemically pure zinc was
used, no action would happen. (De la Rive.) This action of common
zinc is called a local action, implying the existence of as many small
local Voltaic circuits as there are particles of foreign electro-negative
substances on its surface; each of which constitutes, with the contiguous particles of zinc, a minute battery, and thus the whole surface is
presently corroded and roughened, and the power of the whole couple
reduced just in proportion to the extent of this local action.
Rub the freshly corroded surface of such a piece of commercial zinc
with a little mercury, when instantly it combines with and brightens
the whole surface, covering it with a uniform coating of zinc amalgam.
This perfectly protects the zinc from local action by covering up the
electro-negative points, and makes the whole surface of one electrical
name.  Zinc, thus amalgamated, may be left indefinitely long in acid
water, without injury, and when brought into contact with the electronegative element of a Voltaic couple, it becomes a much more energetic
source of electricity than before.
The discovery of this property (due to Mr. Kempt) is hardly less
important than the discovery of the battery, for without it, sustained
and manageable batteries are impossible.
51




574           PHYSICS OF IMPONDERABLE AGENTS.
II. BATTERIES WITH ONE FLUID.
8G9. Voltaic batteries are constructed for use either with one or
with two fluids.
The first embraces the original crown of cups (864), and all batteries with one
fluid and a single cell. The batteries with two fluids and two cells, of whatever
name, involve a double chemical decomposition, and are, hence, more complicated, but also, generally, more efficient; we will consider these separately,
remarking, that the interest attached to the first class, with a single exception,
is now chiefly historical.
870. Trough batteries.-The inconvenience of Volta's original
form of the pile, fig. 614, led to placing the elements in a trough, as
seen in fig. 616, called, from the               616
inventor, Cruickshank's trough.
Each compound couple of zinc
and copper was cemented water \  Siii 
tight into a groove, all the zincs 
facing in one direction.  The filling of these cells with dilute acid was
a tedious operation, with extended series, and as the zincs were not
amalgamated, the best force of the apparatus was spent before it could
be filled.  Davy and Nicholson greatly improved the trough by attaching the couples to a bar of wood                  617
by straps, conm, as in fig. 617,
and Dr. Wollaston surrounded each              -  
zinc, z, with the copper, on both 
sides, thus doubling the effective
surface. Thus arranged, the wlole
series could be plunged at one
movement into class cells, aa, or
into a porcelain trough divided
into cells.  The famous battery of the London Royal Institution, (first
used in May or June, 1810,) was a series of 2000 couples of this construction, arranged in 200 glass or porcelain troughs, ten couples in
each trough, each plate having an effective surface of twenty-two square
inches. This battery was placed in the vaults under the Royal Institution, where its hydrogen and acid vapors did not annoy the experimenter, and its power was led up by conductors to the laboratory above.
The battery with which Davy made his immortal discovery of the
metallic bases of the alkalies (October, 1807), contained 250 pairs of
plates, made in 1803.  [See Am. Jour. Sci. [2], XXVIII., 279.]
Hare's calorimotor consisted of twenty plates each, of copper and zinc,
nineteen inches square, and so combined in a cubical box as to form but two
large elements of fifty square. feet each, or two hundred square feet of active
surface in both members, all plunged by one movement in a vat of acid.




ELECTRICITY.                             575
The deflagrators of Dr. Hare, as originally constructed, were formed
of spirals of copper and zinc, rolled with a narrow space between them, and the
opposing metals held from contact by wooden strips. Each zinc was 9 X  6 in.,
and each copper 14 X 6 in.; so that every part of the zinc was opposed to the
copper surface; eighty of these coils were so arranged on bars of wood as to
plunge by an easy mechanism into glass cylinders containing the acid. The
facility of immersion and removal of these coils in contact of the acid liquor,
made Hare's deflagrators as much superior to the early trough batteries as the
batteries of two fluids are superior to Hare's. In a very efficient form of Hare's
deflagrator, the members were connected in a box, suspended, to revolve on an
axle having another box placed at right angles to the first, so that a quarter
revolution of the apparatus turned on or off the exciting acid at pleasure, without deranging the connections, which were established through the axis of revolution.
A battery constructed for Prof. Silliman, in Boston, in 1836, on the plan of
Wollaston and Hare combined, contained nine hundred couples of copper and zinc
(10 X 4 in. each), exposing five hundred and six square feet of available surface,
arranged in twelve parallel series, capable of being used consecutively as nine
hundred couples, or in three series of three hundred each. One plunge immersed
the whole battery, and when this instrument was new, the arch of flame between
its poles measured over six inches.
Mr. Crosse, and also Mr. Gassiot, have constructed very extended series of
trough batteries for physiological experiments; the former had twenty-four
hundred pairs of plates, the cells well insulated; the latter put up three thousand
five hundred and twenty cylindrical pairs, placed in cells of varnished glass,
and insulated by glass pillars varnished. The batteries were excited by water
only. Except for the purposes of low intensity and long-continued action, batteries of this description are now no longer constructed.
The want of sustained and regular action in all batteries of the original form,
has led to the contrivance of other and more scientific batteries; some of the
most valuable of which we will now describe.
871. Smee's battery is formed of silver and amagalmated zinc, and
needs but one cell and one fluid to excite it.  The             618
silver plate, S, fig. 618, is prepared by washing in
nitric acid to roughen it, and then coating its surface
with platinum, thrown down on it by a voltaic cur- 
rent, in that state of fine division, known as platinum-black.  This is to prevent the adhesion of the 
liberated hydrogen to the polished silver.  Any sur- 
face of polished metal retains a film  of gas with
singular obstinacy, thus preventing, in a measure,
the contact between the fluid and the plate.  The                     l
roughened surface produced from the deposit of platinum-black, entirely prevents this. The zinc plates,
zz, in this battery, are well amalgamated, and face both sides of the
silver. The three plates are held in position by a clamp, b, at top,
while the interposition of a bar of dry wood, w, prevents the passage




576             PHYSICS OF IMPONDERABLE AGENTS.
of a current from  plate to plate.  Water acidulated with one-seventh
its bulk of oil of vitriol, or, for less activity, with one-sixteenth, is the
exciting fluid.
The surface of the negative plate is kept clean in daily use by occasional immersion in chlorid of iron, which removes all foreign substances
deposited on it. For large sized batteries, the silver plates are made by
electro-casting, to secure entirely plane surfaces. (Mathiot.)
The quantity of electricity excited in this battery is very great, but the intensity is not so great as in the compound batteries presently to be described; This
battery is nearly constant, does not act until the poles are joined, and, without
any attention, will maintain a uniform flow of power for days together. A thick
plate of lead, well silvered, and then coated with platinum-black, will answer
equally well, and, indeed, better than a thin plate of pure silver. This battery
is recommended over every other for the student, as comprising the great requisites of cheapness, simplicity, and constancy. This is the battery generally
employed in electro-metallurgy. Chester has patented an improved form of this
battery, much used by the telegraph companies. It is the only single fluid bat.
tery now much used in physical experiments.
Mathiot has described the form of Smee's batteries used in the large electrotyping operations of the United States Coast Survey Office.  See Am. Jour.
Sci. [2], XV., 303.                                            619
872. The sulphate of copper battery is designed to
use a solution of sulphate of copper in dilute sulphuric
acid, the copper element being made to contain the exciting fluid. This battery, fig. G19, is used for electromagnetic experiments, and although, it soon becomes           ii
encumbered with a pulp of metallic copper thrown 
down on the zinc, its cheapness and constancy will always render it a
valuable instrument.
III. DRY PILES.
873. Dry piles of Zamboni and DeLuc.-These piles are constructed of disks of metallic paper, as of copper and zinc (called gold
and silver papers), placed back to back, and alternating, as in the pile
of Volta, fig. 614, all the coppers facing in one direction. Sometimes zinc paper gilded on one side; or zinc paper smeared with
black oxyd of manganese and honey on the other side, is used,
and with more marked effects.  Some-hundreds, and even thousands
of these disks, as large as a quarter dollar, are crowded into a glass
tube, just large enough to receive them, varnished within and without.
Screw caps of metal compress and retain the disks, forming at the same
time metallic connections with the outer pairs to propagate the electrical effect. A feeble current is thus set up, which may last for years;




ELECTRICITY.                             577
but, if the paper has been artificially dried, so as to free it from  all
absorbed moisture, no current exists.                               620
Zamboni (1812), and DeLuc (1810), who first constructed piles
of this sort, arranged them in pairs to ring bells by the vibration of a small electric pendulum (fig. 598), alternately attracted
and repelled between the columns, which are in the condition of
a perpetually-charged Leyden jar of low tension. A set of these 
bells rang in Yale College laboratory for six or eight years
unceasingly.
Bohnenberger's electroscope is constructed on this              -      l
principle. B and C, fig. 620, are the poles of two dry piles, between which hangs a single gold leaf, ending in the knob, D. 
When any feebly electric body is approached to D, the gold leaf _,  lu,
at once declares its electrical name, by being attracted to its
opposite. This is undoubtedly one of the most delicate clectroscopes known.
IV. BATTERIES WITH TWO FLUIDS.
874. Daniells oonstant battery.-This truly philosophical instrument was invented in 1836; up to which time the improvements in the
original Voltaic pile had been only mechanical.  Prof. J. F. Daniell]
of London, first discovered and applied an effectual means of preserving
the power and continuing the action of the apparatus for a length of
time. All other batteries with two fluids are only modifications of his
original instrument.                                               621
It consists of an exterior circular cell of copper, C, fig. 621,  i
which serves both as a containing vessel and as a negative element; a porous cylindrical cup of earthenware, P (or the gullet
of an ox tied into a bag), is placed within the copper cell, and a
solid cylinder of amalgamated zinc, Z, within the porous cup.
The outer cell, C, is charged by a mixture of eight parts of water
and one of oil of vitriol, saturated with blue vitriol (sulphate of
copper). Some of the solid sulphate is also suspended on a perforated shelf, or in a gauze bag, to keep up the saturation. The
inner cell is filled with the same acid water, but without the cop- 
per salt. For the most constant results, he used a saturated solution of blue vitriol, made slightly acid for the outer cell, and for 
the zinc, twenty parts water to one of sulphuric acid. Eight or 
ten hours is about the limit of its constancy. Any number of
cells so arranged are easily connected together by binding screws,  iB
the C of one pair to the Z of the next, and so on.
The hydrogen from  the decomposed water in this instrument is not
given off in bubbles on the copper side, as it is in all forms of the
simple circuit of zinc and copper; but the sulphate of copper there
present is decomposed in the circuit, atom for atom, with the decomposed water, and the hydrogen  takes the atom  of oxyd of copper,
appropriating its oxygen to form water again, while metallic copper is
deposited on the outer cell. If the zinc is well amalgamated, no action
51*




578           PHYSICS OF IMPONDERABLE AGENTS.
of any sort results in this battery until the poles arc joined, and it gives
off no fumes.  Ten or twelve such cells form a very active, constant,
and economical battery, and twenty or thirty are ample for most uses.
Hot solutions increase its power, while the extent of zinc surface, and
not the diameter of the copper, limits the amount of electrical effect.
875. Grove's nitric acid battery.-Mr. Grove, of London, has
successfully applied the principle of Daniell's battery, to produce the
most powerful and intense sustaining battery            623
known. The fluids used are strong nitric acid
and dilute sulphuric acid, kept apart by a
porous jar.  The metals are amal-    622
ganated zinc, placed in the sulphuric acid of the outer vessel,  
and platinum in the porous vessel:
fig. 623 shows this arrangement   _BT   I
complete, while the platinum  element, P, is seen isolated in fig. 622. p III  +
The cover, c, upon the vase, V, fig. 
623, tends to keep down the strong
vapors of nitrous acid  evolved
when the battery is in action.  tlll
The binding screws, ab, serve to                  --
unite the elements of separate pairs.  The zinc here surrounds the
platinum, because both that metal and the nitric acid are to be economized as much as possible, being the costly parts of the arrangement.
From six to ten parts of water are used in A, to one of acid
The action of this battery is intense and splendid. The hydrogen is
immediately engaged by the nitric acid, which it decomposes very
readily. There is therefore a double chemical action, and an increased
flow of electricity, since no part of-the power is lost in combination.
The fumes of nitrous acid are partly absorbed by the nitric acid,
turning it at last intensely green; but enough are evolved to render it
important to set the apparatus in a clear space, or good draught. Four
cells, with platinum  three inches long by half inch wide, decompose
water rapidly; and twenty such cells form a battery giving intense
effects of light.
Platinum, in the nitric acid battery, is estimated as sixteen or eighteen times
more powerful than copper in Daniell's battery; that is, six square inches of
platinum is as efficacious as one hundred square inches of copper; and Peschel
found that three hundred and forty times "3 much surface of copper was needed
in a" spiral battery on Hare's construction, as of platinum in Grove's, to insure
equal effects.
A Grove's battery, constructed by Jacobi, of St. Petersburgh, contains sixty



ELECTRICITY.                             579
four platinum plates, each tmnrty-six square inches surface, or combined, sixteen
square feet. This would be, by comparison, equal to a Daniell's battery of two
hundred and sixty-six square feet, or a Hare's battery of about five thousand
five hundred square feet. Grove's battery is rather costly, and very troublesome to manage, as are all batteries with double cells and porous cups, although
the trouble involved in their use is not to be compared with the vexation involved
in the earlier single fluid batteries.
876. Carbon battery.-The great cost of large members and extensive series of Grove's platinum  battery, led               624
Prof. Bunsen, of Marburg, to use the carbon
of gas coke as a substitute for the platinum.  
Prof. Silliman, Jr., in  1842, described a
battery (see Am. Jour. Sci. [1], XLIII.,
393, and XLIV., 180), in which. natural                       
plumbago was used in place of the plati- 
num  of Grove's arrangement.  This was
before Bunsen's apparatus was known of 
in this country.
Fig. 624 shows the original form of Bunsen's 
cells. Where the carbon, C, is contained in an
exterior vase, V, of nitric acid, the amalgamated  -
zinc is in a porous cup, P, of dilute sulphuric -___          IIi
acid. The objection to this arrangement is the    - -_      ~~_ ___
large consumption of nitric acid and smallness
of the zinc. In the Author's plan, afterwards adopted essentially by M. Deleuil,
the carbon was in the porous cup, surrounded by the zinc. In fig. 625, this
625                                   626
arrangement is shown in detail.  P, is the pile complete.  F, is the jar of hard
pottery to contain the zinc, Z, and the dilute sulphuric acid; V is the porous
vase, to contain the carbon, C, with its nitric acid. The attachment of a conductor to the carbon is accomplished by a conical hole in the centre, into which
a plug of hammered copper is crowded with a wrenching motion. If prisms of
the hard carbon of the gas retorts are used (and this kind of carbon is unquestionably the best), a copper band is attached to the top by electro-galvanic soldering. The carbon of Bunsen's cells is prepared by pulverizing, and baking
in moulds, the coke of bituminous coal. Fig. 626 shows a series of ten cups of
the carbon battery arranged for use, the alternate members being joined by
binding screws, as made by Deleuil, of Paris, each zinc being twenty-two centimetres (eight and three-quarter inches) high. As the electro-motive energy of
the battery depends on size as well as number, these large members have great




580            PHYSICS OF IMPONDERABLE AGENTS.
advantages. The Author demonstrated, in 1842 (loc. cit.), that carbon was
nearly if not quite as good as platinum, surface for surface. A battery of fifty
cells, like fig. 626, costs fifty-five dollars in Paris, and, with such a series, all the
most splendid effects of the electric light, deflagrations, and chemical decompositions can be very satisfactorily shown.
877. Other forms of Voltaic battery exist in great variety, but
involving no principle not already explained. Some have special adaptation to a particular use, like Chester's form of Smee's battery for
telegraphic use; Farmer's copper battery; the battery of Bagration,
of zinc and copper in moist earth; or Grove's oxygen and hydrogen
gas battery, so instruotive theoretically. But further descriptions are
excluded by want of space.
V. POLARITY, RETARDING POWER, AND NOMENCLATURE OF THE VOLTAIC
PILE.
878. Polarity of the compound circuit.-In batteries of two or
more couples, connection is formed, not as in the single couple, between
members of the same cell, but between those of different names in contiguous cells, as in fig. 627, where the copper of 1 joins the zinc of 2,
and so on. The current flows from the zinc to the copper in the fluid,
but from the copper to the zinc in the air (fig. 628), both in simple and
627
sg+       A         rc628
1     2      3      4:                1    2    3    4        5
compound circuits.  This is important to be remembered, since the
zinc is called the electro-positive element of the series, although out of
the fluid it is negative. Consequently, in voltaic decompositions, the
element which goes to the zinc pole is called the electro-positive, and,
for the same reason, that which goes to the copper, is the electro-negative element. The terminal plates, Z and C, in 1 and 5, fig. 627, are
not concerned  in  the  electrical                  629
effect, being in fact only conduc-            ~
tors of the electricity, and hence
they may be removed as in fig.
628, without altering the power or
nature of the battery.  They serve, 
in fact, merely as a convenient mode    1      2    3      4 
of joining the poles, as in fig. 629. The apparent polarity of the simple
circuit is, therefore, the reverse of that of the compound circuit; but,




ELECTRICITY.                            581
an attentive observation of these explanations, and of the figures, will
prevent all confusion on this point.
879. Grouping the elements of a pile, in various numerical relations, is an important means of modifying its power, and the character
of its effects, already explained.
Take, for example, six cups, as in fig. 630, arranged in consecutive order, and
we have, owing to the resistance to the elec-           630
tric flow, the maximum intense effects possible with such number. Changed to two -
groups of three each, the quantity is doubled,
with half of the intensity, fig. 631. In fig.
631            632
632, are three groups of two cups each, so
arranged as to present three times the sur-        a
face in 630, with a proportionate loss of intensity. Lastly, in fig. 633, each zinc, and
each copper, joins one common conductor,
each on its own side, throwing the six           S
couples into one surface of six-fold extent
to fig. 630. The arrangement may be ex-                 6.3
pressed, assuming the resistance of a single
cup as unity, thus: 1.    = 1-5.     =  0-666. 
= 0-166, and so for any number of couples.
880. Electrical retarding  power
of the battery.-Ohm's law.-A certain resistance  to the passage of a voltaic current is offered by
every additional element placed in the circuit as well as by increased
length of conductor.  The new properties thus acquired by the compound circuit have been already alluded to (865).
Ohm, of Berlin, in 1827, first demonstrated mathematically the law
regulating the flow of electricity in the compound battery. As the apparatus is composed solely of conductors of different retarding power,
the electric current must proceed, not only along the connecting wire,
from pole to pole, but also through tMe whole apparatus; the resistance
offered to the passage of the current consists therefore of two parts, one
exterior to, and one within, the apparatus.
Let the ring, a b c, in fig. 634, represent a homogeneous conductor, and let a
source of electricity exist at A. From this source the electricity will diffuse
itself over both halves of the ring, the positive passing in the   634
direction a, the negative in b, and both fluids meeting at c. Now,
it follows, if the ring is homogeneous, that equal quantities of'
electricity pass through all sections of the ring in the same time.
Assuming that the passage of the fluid from one cross section of
the ring to another, is due to the difference of electrical tension at
these points, anil that the quantity which passes is proportional
to this difference of tension, the consequence is, that the two fluids 
proceeding from A, must decrease in tension the farther they recede from the
starting point.
This decreasing tension may be represented by a diagram. Suppose the ring




582             PHYSICS  OF IMPONDERABLE  AGENTS.
in fig. 635, to be stretched out to the line A A'. Let the ordinate A B rei resent the
tension of positive electricity at A, and A' B' the nega-       635
tive tension at A', then the line B B' will express the 
tension for all parts of the circuit by the varying lengths
of the ordinates A B, A' B', at every point of A c or c A'.
E                         A              _
Hence Ohm's formula F == ~, where Frepresents the                  
strength of the current, E the electro-motive force of 
the battery, or the attraction of zinc for oxygen, and R
the resistance. Therefore, the greater the length of the circuit, the less will be
the amount of electricity which passes through any cross section in a given time.
In exact terms, this law states that the strength of the current is inrersely proportional to the resistance of the circuit, and directly as the electro-motive force.
In the simplest Voltaic current, we have not a homogeneous conductor,
but several of various powers.  To illustrate this, let the conductor, A A', fig.
636, consist of two portions having different cross sec-         636
tions.  For example, let the cross section Ald be. n'
times that of d A'; then, if equal quantities pass  \ 
through all sections in equal times, and if through a A                       A
given length of the thicker wire no more fluid passes 
than through the thinner wire, the difference of tension 
at both ends of this unit of length of the thicker wire
1
must be only -th of what it is in the latter. Thus, "the electric fall," as Ohm
calls it, will be less in the case of the thick wire than of the thinner, as shown
by the line B c in the figure. The result is expressed in the law that the "electric
fall" is directly as the specific resistances of the conductors, and inrersetly as their
cross sections. Hence, the greater the resistance offered by the conductor, the
greater the fall. The very simplest circuit must therefore present a series of
gradients expressive of the tension of its various points-as one for the connecting wire, one for the zinc, one for the fluid, and one for the copper. The
electro-motive force of a voltaic couple (" E" of Ohm's formula) may be experimentally determined, and is proportional to the electric tension at the ends of
the newly broken circuit.
881. Formulae of electric piles.-It follows, from what has been
stated, that the intensity, 1, of a current, united by a homogeneous
wire whose length is L, may be represented by the formula
E
L+  r'
in which r designates a length of wire representing the resistance of
the pile or its reduced length, and E the electro-motive force measured
by the tension at the poles when the circuit is broken.
If the resistance of the pile is nothing, or an insensible quantity, as
in the case of a thermo-electric couple of great surface, the formula
E
becomes I-=  L.  That is, the intensity of the current is in the inverse
atio of the length of the homogeneous wire joining the poles of tho




ELECTRICITY.                          583
battery. If, however; the pile itself offers sensible resistance, as is the
case with hydro-electric piles composed of many couples, the formula
shows that the intensity of the current is in the inverse ratio of the length
of the connecting wire increased by a constant quantity, r, which represents the resistance of the pile itself.
In the case of many different sources of resistance, interposed in the
circuit of the connecting wire, L represents the sum of the reduced
lengths equivalent to these resistances.
E
Intensity given by many couples.-In the formula, I== 
L -r'
let E be the electro-motive force, and r the resistance of a single couple,
L and r being always reckoned as lengths of the same kind of wire
taken as a standard of comparison; we may then consider many
couples united one to another in a series as shown in fig. 630. Ohm
considers that each couple produces an electric current which traverses
the pile as if that couple was alone, so that the electro-motive force of
the series, or the tension at the poles which measures it,will be the sum
of the electro-motive forces, E + E  + E  - +-..., of all the couples
in the series. In the same manner the current, produced by each couple
traversing all the others, meets with a resistance equal to the sum,
r + r' + r" +.., of the resistances of all the couples; hence,
E+  E' + E" +...
L +  -r + + r'  r+...
If the couples are all equal to each other, and 7. represents their numnE
ber, the formula becomes I =  L     n. This shows that the intensity
of the current, from a series arranged one by one, is proportional to
the sum of the electro-motive forces of all the couples, and inversely as
the total resistance of the circuit including the pile itself.
If we designate by c, 1, s the conductibility, the length, and the section
of a wire; and by c', 1', s' the same quantities for a second wire, it
follows from the principles already established, and from the fact that
the resistance of a wire is in the inverse ratio of its conducting power,
that two wires will produce equal diminution of the intensity of the
same electric current when:
I     1'                            sc
s -  -s- or, ls'c' = 1/', or, I = V/
The third equation expresses the length of a wire whose section is s,
and conductibility c, that will produce the same effect upon the current
as another wire whose length is V1, section s', and conductibility c'.




5r84          PHYSICS OF IMPONDERABLE AGENTS.
This value of I is called the reduced length of the first wire as compared with the second.
If we have a series of wires united together by their ends as a
compound conductor, the equivalent length of the first wire will be
expressed by the formula:-,          71//  + "///       i...   SC      -r      +   ///
sc    M s  sc                                 1~       V \
s'c'   s-Cc" +    sc" +   -    scs  s-c" + s" c"' )/
Effect of increasing the number of couples in a battery.The consideration of the formulae given above shows that,
1. The intensity of the current increases with the number of couples.
E
Dividing both terms of the fraction by n, it becomes I =  L, this
n
shows that the value of I increases with increase of n, or the number
of couples.
2. The increased intensity of the current, by increasing the number
of couples, is more evident when L is great in comparison with r, or
when the external resistance to be overcome is much greater than the
L
resistance of the battery. If on the contrary L is very small, - is also
very small, and the intensity of the current changes but very little with
any increase of the number of couples.
nE  E
3. If there is no exterior resistance, or, L = 0, I ==.  In
nr    r
this case the intensity is not varied by varying the number of couples,
or one couple gives as great intensity as any number of couples.
4. The intensity is not increased by increasing the number of couples
when each couple added is accompanied by an exterior resistance equal
to L; or. in other words, when the exterior resistance increases in the
same ratio as the number of couples, since on that supposition the
nE         E
formula becomes          I     n-.
nL + nr   L - r
5. If the exterior resistance, L, is very great, I is very small, unless
n is made very great.  This shows that it is necessary to employ a
great number of couples when a great amount of resistance is to be
overcome, as in the voltaic arch, and in the electrolysis of bodies that
are imperfect conductors, or in sending an impulse through a long
telegraphic circuit.
Effect of enlarging the plates of a battery.-If, instead of
uniting many couples in a series, we unite a number of couples, m, by
poles of the same name a. in fig. 633, it will be equivalent to enlarging




ELECTRICITY.                          585
the dimensions of the plates of a single couple, the resistance of the
r                                  E
battery will be -, and the formula becomes I =. We thus see
rm'                                    r
In
that if L, the exterior resistance, is very great in proportion to r, the
resistance of the battery, the intensity will be but little increased by
uniting the couples by poles of the same name. If L is very small in proportion to r, the intensity will he much increased by this method, and if L
is so small that it may be neglected, the intensity will be proportional to
the extent of surface acting as a single couple.  We know indeed that,
when chemical action is exerted over a large surface, the quantity of
electricity which traverses the connecting wire is also very great.
Effect of enlarging  the  couples and increasing  their number. -
If the number and dimensions of the couples are both increased at
nE         E
the same time, the formula becomes I=         -. This
L +  -      L +  r
nm   n  m
shows that increasing the number of couples produces the same effect
as diminishing in the same proportion the resistance of the exterior
circuit, and increasing the surface of each couple has the same effect as
diminishing the resistance of the pile. Hence:If L, the resistance of the exterior circuit, is great, it will he most
advantageous to unite many couples in a single series: But if the resistance of the exterior circuit is small, greater advantage may be obtained by
uniting the couples by poles of the same name, in such a manner as to
form couples of large extent of surface.
A most interesting application of these principles to the practical
construction and use of batteries will be found in a paper by Mr. G.
Mathiot, Electrotypist of the United States Coast Survey. (Am. Jour.
Sci. [2] XV. 305.)
882. Faraday's nomenclature.-Faraday has introduced certain
terms into the language of electrical science, which are generally adopted
for their convenience, and their absence of assumed or theoretical notions.
Electrode is used in place of pole, to which latter term, meaning the
terminal wires of a battery, Davy and others seemed to attach a sense
as if it possessed a certain attractive force, like the pole of a magnet.Electrode (from  riArx-pov, and o6oq, a way), means simply the way or
door by which a Voltaic current enters or leaves a substance.
Anode is that surface of a body receiving the current, or the positive
side of the series, from ava, upwards (as the sun rises), and 68oq, a way.
Cathode is that surface of a body from which a current flows out
towards the negative side of the series, from xara, downwards, as the sun
52




586            PHYSICS OF IMPONDERABLE AGENTS.
sets, and 68o;, a way). The observer is supposed to face the north, with
the positive of the battery on his right hand, and its negative on his left.
Electrolyte is any substance capable of separation into its constituents by the influence of a Voltaic series (from rj2cxTrpov, and A6o,
to sec loose). rlectrolysis, the act of decomposition. Electrolyzed, and
electrolyzable, are obvious derivatives from the same words.
Ions (from'ov, neuter of elJq., to go), are the elements into which an
electrolyte is resolved by the current.  These are either anions, elements found at the anode, or catons, ions found at the cathode.
Hereafter we shall employ these terms when they are appropriate.
VI. THE EFFECTS OF TIE VOLTAIC PILE.
1. Physical effects.
883. The Voltaic spark  and arch.-In  1809, Davy, with the
extensive series of two thousand couples at the Royal Institution, first
demonstrated the full splendors of the Voltaic arch between electrodes
of well-burned charcoal.  However powerful the series may be, no
effect is seen, in the air, until the points of the carbon electrodes are
brought into actual contact, or at least insensibly near.  Herschel
noticed that an electrical spark from  a Leyden           637
jar, sent through the carbon points, when near 
each other, established the flow of the Voltaic
current, by projection no doubt of material particles. When the spark
passes, then the electrodes may be withdrawn, as in fig.      68
637, and the arch of electric flame connects them with a
white and violet light of intolerable brightness; several
inches in length if the pile is very powerful.  This arch
of seeming flame is not produced by the combustion of
the carbon electrodes, since it exists, with even greater
brilliancy, in a vacuum, or in an atmosphere of nitrogen
or carbonic acid.  Despretz states that in vacuo with a
powerful pile, the Voltaic arch may he formed at some
centimetres distance, without contact. - Fig. 638, shows a
convenient apparatus for this experiment, in vacuo, or in
various gases, as in Davy's original experiments.  The
Voltaic arch is accompanied by a loud hissing or rushing
sound, due to the mechanical removal and transportation
of particles of carbon from  the positive to the negative
electrode, by which the former is diminished in length, or
made cup-shaped, while the latter is sensibly elongated,
as frst noticed and described by Prof. Silliman, in 1822
(Am. Jour. Sci. [1] V. 108), in the use of a powerful deflagrator constructed by Dr. Hare.




ELEJTRICITY.                              587
Through colored glasses, these particles of carbon can be conveniently observed
apparently moving slowly from pole to pole, and giving unquestionably that oval
form to the arch, seen in fig. 639, when the electrodes are vertical, and the negative carbon is uppermost. There is also distinctly to be seen, a certain structure
in zones, or bands of different brilliancy. When the image of the carbon electrodes
is projected on a screen, fig. 640, as was first done by Foucault with the electric
lantern, the growth of the negative              640                  641
and the decrease of the positive electrode is easily observed, without injury to the eyes. The negative carbon
is seen to glow first, as    639 
if the light originated
there, but as the experiment advances, the posi-  /
tive carbon becon'es the 
most briliant, and main- 
tains this superiority du- l\
ring the experiment; be-  
coming at the same time
cup-shaped.
The Voltaic arch is magnetic, or capable of influencing the magnet, by the
approach of which it is deflected, as seen in fig. 641, or it is made to revolve
with a loud hissing noise; a fact first               642
observed by Davy, but since carefiully
studied by De la Rive, Quet, and Dospretz. This fact is far more conspicuous
in the arc from the induction coil,. 933. 
884. Regulators of the electric light.-Since  the introduc- 
tion of powerful constant batteries, o
it has been possible to use the elec- 
tric light for scientific and econo-       i     lifll
mical purposes.  For this purpose
regulators have  been devised  to
render the light constant, by approaching the electrodes in  proportion as they are consumed.
In fig. 642, is shown that of Delenil,
of Paris, and its details, in fig. 643. The
two carbon points, P and N, are held
in position by two vertical rods, of
which the lower one, P, is moved up- 
wards by the mechanism in fig. 643;                    -
while the upper one, N, passes through
the ball, D, with friction. The flow of
the current is shown by the arrows
arriving at G, and departing at II. L 
The frame of the apparatus is of cast- 
iron. The slightly concave mirror, R, is for certain purposes replaced by a large
parabolic mirror. When the zinc electrode is connected with G, and the carbon




588            PHYSICS OF IMPONDERABLE AGENTS.
with H, communication is established by depressing N with the hand. As the
current in its circuit passes through a coil of wire surrounding the electromagnet, E, fig. 643, the soft iron armature, m, on   643         644
the lever A, is drawn up to E, so long as the current flows, but if it is interrupted, then m falls,
and the lever A is drawn upwards by the spring,
B, acting against the fulcrum, L: the effect of that 
motion is to raise the electrode, P, by a tooth,
t, catching  in
notches on the                -
upright, K. In....
this way  con-.'       
nection is again 1  ll
established with S                             3 
the battery; and  
when this sim-  m
pie  mechanism   s
is once adjusted, it will act for hours with great certainty,
maintaining the light constant.
Duboscq's photo-electric lantern is seen in fig.  
644.  This instrument is used to replace the sun in
all optical experiments requiring a strong white light. 
The poles S and I are preserved at the same distance by
the action of an electro-magnet in the foot E, upon a soft -
iron bar F F in connection with an endless screw V, moving,4
the pulleys P P', which are connected by cords with the poles 
S and I. The contact of S and I induces magnetism in the
electro-magnet E, while the springs R L regulate the motion] 
of the machinery. The apparatus is simple and portable, 
and its effect is to make the electrical light so steady and 
constant that it may be used for all optical experiments..     L
The positive pole consumes much more rapidly than the
negative, both from  a more intense action upon it and 
because its particles are carried over and deposited on the
negative pole, elongating the point of the latter.  To pro-       i
vide for this difference, the pulley P' is variable, and carries  l i
the pole I up proportionably faster, so that the focal posi- 
tion of the light remains unchanged.
885. Properties of the electric light.-Like the
solar light, it is unpolarized. It explodes a mixture of hydrogen and
chlorine, and acts on chloride of silver, and other photographic preparations, like the sun. Bodies made phosphorescent by the sun, are
similarly affected by the electric light. In 1842, Silliman took daguerreotypes with it (Am. Jour. Sci. [1] XLIII. 185), and it is now used in
preference to solar light, for the purpose of taking microscopic photographs. (Duboscq.)
Fizeau and Foucault, have compared, by photometric measurement, the light
from ninety-two carbon couples, arranged in two series of forty-six (879), with




ELECTRICITY.                              589
the solar-team, and also with the oxyhydrogen or Drummond light. In a clear
August day, with the sun two hours high, the electric light, assuming the sun
as unity, bore to it the ratio of 2-59:1, i. e., the sun was twice and a half more
powerful: while the Drummond light was only the one one hundred and fortysixth that of the sun. Bunsen found the light from forty-eight elements of carbon,
equal to five hundred and seventy-two candles. The intensity of the electric light
depends far more on the size of the individual members of the pile than on their
number. The effect from forty large sized couples was found by Fizeau and Foucault to be about the same as that from double the number, when the eighty
were arranged consecutively, as in fig. 630, while, with the same elements in
two parallel series, there was a very great increase of effect. Fraunhofer showed
that the spectrum of the electric light was distinguished from that of the sun
by a very bright line in the green, and a somewhat less luminous one in the
orange (461). Dove has lately shown (Poggendorff's Annalen, 1857, No. 6) that
this light has two distinct sources: 1st, the ignition or incandescence of the
translated particles, passing in the course of the discharge: 2d, the proper
electric light itself. On the contrary, Draper has shown that the. pectrum from
a glowing platinum wire heated by the battery, contains no dark lines, so that,
unlike the electric light, it is strictly white (Am. Jour. Sci. [2] VIII., 340). It
is not only particles of carbon which pass in the Voltaic arch, but of whatever
conductor may form the positive electrode, as platinum, or any metal, and the light
varies in its optical properties with every change of the electrode. (Wheatstone.)
886. Heat of the Voltaic arch.-Deflagration. —When the positive electrode is fashioned into a small crucible of carbon,    645
as in fig. 645, gold, silver, platinum, mercury, and other
substances,-are speedily fused, deflagrated, or volatilized, 
with various-colored lights. 
The fusion of platinum (like wax in a candle) before the Voltaic 
arch is significant of its intense heat, and still more, the volatiliza-  
tion and fusion of carbon, a result first announced by Prof. Silliman
in 1822, and since confirmed by Despretz, who, by the union of the
heat of six hundred carbon couples arranged in numerous parallel series, and
conjoined with the jet of an oxyhydrogen blow-pipe, and the heat of the midday sun, focalized by a powerful burning-glass, succeeded in volatilizing the
diamond, fusing magnesia and silica, and softening anthracite. The diamond
is also softened, and converted into a black spongy mass resembling coke, or,
more nearly, the black diamond found in the Brazilian mines.
A delicate stream of mercury being allowed to flow from a narrow elongated
funnel (the negative electrode), upon a surface of mercury in a glass vase forming the positive electrode, is deflagrated with transcendent splendor. Many
yards of number twenty platinum  wire, held between the electrodes, may be
kept in the full glow of white heat for a long time. The teacher can devise
many pleasing additional experiments, as drawing the arch beneath water, oil,
and other liquids, from points of carbon, or from platinum and steel wires.
When a fine platinum wire is made the positive electrode, and a solution of
chlorid of calcium, or any other metallic chlorid, is made the negative electrode, on touching the surface of the liquid with the point of the fine wire, if
the series is powerful the wire is fused on the surface of the liquid, evolving a
light of surpassing beauty, whose color is that appropriate to the metal in solution; e. g., from calcium salts, violet-red; from sodium, yellow; from barium,
52 *




590            PHYSICS OF IMPONDERABLE AGENTS.
reddish-yellow; from potassium, violet; from strontium, red, &c. These beau.
tiful facts were first noticed by Dr. Hare.
Dr. Page has described a singular motion imparted by the current to globules
of pure mercury, placed in a shallow dish, and covered by acidulated water: the
globules elongate to ovoids and move actively about, one end, that towards the
+  pole, being clouded by escaping gas-bubbles. If the mercury contains zinc,
the position of the clouded end is reversed. (Am. Jour. Sci. [2], XI., 192.)
887. Measurement of the heat of the Voltaic current.-By
means of a long wire coiled into a close spiral, and enclosed in a calorimeter of glass, containing water, Becquerel and others have established
the laws regulating the flow of heat in the electric current, by its effect
in elevating the temperature of the water. A coil of platinum wire
contained in the bulb of a Sanctorio's thermometer, becomes a means
of estimating the heat of currents too feeble to be otherwise measured.
The results are, that when a Voltaic current traverses a homogeneous
wire, the quantity of heat in a unit of time is proportional:1. To the resistance which the wire opposes to the passage of the electricity:
2. To the square of the intensity of the current.  The intensity of a
current is measured by the quantity of water which it will decompose
in a given time.
For a given quantity of electricity, the elevation of temperature at
different points on a conducting wire, is in the inverse ratio of the
fourth power of its diameter.
Draper has applied the coefficient of expansion to determine the
degree of heat corresponding to a particular color (585).
2. Chemical effects of the pile.
888. Historical.-The chemical effects of the pile are most wonderful,
and the present advanced state of chemical science is largely attributable to the flood of light shed by the researches of Davy and Faraday
upon the electrical relations of the elements and the decomposition of
compounds by the Voltaic circuit.
In 1800, immediately after Volta's announcement to Sir Joseph Banks of his
discovery of the pile, Messrs. Nicholson and Carlisle constructed the first pile
in England, consisting of thirty-six half crowns, with as many discs of zinc and
pasteboard soaked in salt water (864). Observing gas-babbles arise when the
wires of this pile were immersed in water, Nicholson covered them with a glass
tube filled with water, and, on the 2d of May, 1800, completed the splendid discovery, that the Voltaic current had the power to decompose water and other
chemical compounds. Stimulated by so fine a result, chemists and physicists
everywhere repeated the experiment, perfecting the methods of obtaining the
oxygen and hydrogen gases in a separate condition. The chemical theory of
the pile, originally advanced by Fabbroni, a countryman of Volta's, some years
before, was taken up and ardently advocated by Davy, who, in 1801, had succeeded to a place in the laboratory of the Royal Institution: where, on the 6th




ELECTRICITY.                           591
of October, 1807, he made, by the Voltaic pile, the memorable discovery of
potassium, the metallic base of potassa, before regarded as a simple substance;
and soon after established the startling truth, that all the earths and alkalies,
until then esteemed simple substances-the whole crust of the globe, in factwere oxyds of metals, whose existence had hitherto been unsuspected.
889. Electrolysis of water.-Voltameter.-The Voltaic decomposition, or electrolysis of water, is the finest possible illustration of
the chemical power of the pile.  Water is a compound of oxygen and
hydrogen gases, in the proportions of one measure of the former to twQ
of the latter.  When two gold or platinum wires are connected with
the opposite ends of the battery, and held a short distance asunder in
a cup of water, a train of gas-bubbles will be seen rising from eacly
and escaping at the surface. If the electrodes are not        647
of gold or platinum, the oxygen combines with one of
them, and only hydrogen escapes, as in Nicholson's ori- 
ginal experiment. With two glass tubes placed over the
platinum poles, fig. 646, we can collect      646
these bubbles as they rise.  The gas 
(hydrogen) given off from the negative
electrode is twice the volume of that
obtained from the positive.  When the
tubes are of the same size, this difference becomes at once evident to the.    -.~'eye.  By examining these gases, we
shall find them, respectively, pure hy- 
drogen and oxygen, in the proportion   \ +
of two volumes of the former to one of
the latter.  Agreeably to principles
already explained, the oxygen (electro-negative) appears at the + electrode, and the hydrogen (electro-positive) appears at the - electrode.
The rapidity of the decomposition is greater when the water is made a
better conductor, by adding a few  drops of sulphuric acid; and for
rapid electrolysis the number of couples in the series should be in.
creased to overcome, by superior tension, the low con-         648
ducting power and chemical affinity of the electrolyte.  If a single tube only covers both electrodes, as
in fig. 647, the total electrical effect is easily measured
by the graduation of the tube, the quantity of gases
given off in a unit of time being directly as the current.
The contents of this tube will explode if a lighted
match is applied to them, or if an electric spark passes
through them.  Such an instrument is a Voltameter. 
A convenient form of this instrument is seen in fig. 648, made of a common
bottle, filled with acid water; the platinum electrodes pass through the cork and




592           PHYSICS OF IMPONDERABLE AGENTS.
end in two plates of platinum, while a bent gas tube of glass conveys off the
accumulating gases as fast as they are evolved by the electrolysis.
890. Laws of electrolysis.-From  a great number of elaborate
experiments, the accuracy of which remains unshaken, Faraday has
deduced the following general laws of electrolysis.
1st. The quantity of any given electrolyte, resolved into its constituents by a current of electricity, depends solely on the amount of electricity passing through it, and is independent of the form of apparatus
used, the size or dimensions of the electrodes, the strength of the solution, or any other circumstance.  Hence, the amount of water decomposed in a given time in the Voltameter, is an exact measure of the
quantity of electricity set in motion.
2d. In every case of electrolysis, the elements are separated in
equivalent or atomic proportions, and when the same current passes in
succession through several electrolytes in the same circuit, the whole
series of elements set free are also in atomic proportions to each other.
It follows, therefore, that the amount of electricity required to resolve
a chemical combination, is in constant proportion to the force of chemical affinity by which its elements are united.
3d. The oxydation of an atom  of zinc in the battery, generates
exactly so much electricity as is required to resolve an atom of water
into its elements. Thus, 8'45 grains of zinc dissolved in the battery,
occasions the electrolysis of 2'35 grains of water. But these numbers
are in the ratio of 325: 9 the equivalents, respectively, of zinc and of
water.  tence follow these corollaries:-First, The source of Voltaic
electricity in the pile is chemical action solely. Second, The Jorces termed
chemical affinity and electricity, are one and the same.
One or two additional illustrations of these laws will suffice in this
place, referring the student to chemical             649
treatises for a fuller discussion of this
very important topic.                             B   A
891. Electrolysis of salts.-In the
bent tube, B A, fig. 649, put a solution
of any neutral salt; i. e., sulphate of
soda, and diffuse the blue solution from
a purple cabbage in the liquid.  Let the    -                    +  
current of a Voltaic pile communicate 
with this saline solution by two platinum
wires, dipping into the legs of the tube —
presently the blue color of the solution 
is changed on the positive side for red, and on the negative for green,
indicating the presence of an acid set free in A, and of an alkali in B




ELECTRICITY.                             593
If the action is kept up, the whole of the blue liquid is changed to red
and green.  Transpose, then, the + and -  wires, so as to reverse the
direction of the current; presently, the red and green change back to
blue, and, in a short time, that which was red becomes green, and vice
versa.  This is a case of electrolysis in which the electrolyte (sulphate
of soda) is changed, not into its ultimate elements, but only into the
acid and alkali, which may be called its proximate constituents; any
other saline fluid may be substituted with similar results. If an alkaline chloride is used, i. e., common salt, the free chlorine evolved on
the +  side, discharges all color, while the soda produces on the -
side its appropriate green tint. If a metallic salt, e. g., sulphate of
copper, or acetate of lead, is used in A B, then, on the - side, metallic
copper or lead is evolved; while, on the + side, is the free acid before
in combination in the salt.
A more surprising example of the apparent transfer of elements under the
power of the Voltaic current, is illustrated in fig. 650, where in B, the centre glass.
of the three wine-glasses, A B C, is a                650
solution of sulphate of soda, while A        A         B         c
and C contain only pure water, blued 
with cabbage solution. Filaments of
moist cotton wick connect the three                       
glasses, and the electrodes are intro-  
duced into A and C, when the same                        
series of changes, already described in
fig. 649, takes place, with the same reversals when the electrodes are transferred. B remains apparently unchanged, while C is reddened, and A becomes
green, or vice versa. There is, in fact, nothing more wonderful in this case than
in the last, only the dissection of the process into three parts, makes the result
still more striking. In place of A B C, any number of glasses, with different
salts and compounds, may, with a powerful series of Bunsen, be substituted,
with results conformable to the law in. 890.
892. Electro-metallurgy.-The  electrotype.-The cold casting
of metals by the Voltaic current, is a fine example of          651
the rich gifts made by abstract science to the practical
arts of life.  Every Daniell's battery is, in fact, an
electro-metallic bath, in which metallic copper of a
firm  and flexible texture is constantly thrown down
from solution.
The very simple apparatus required to show these results
experimentally, is represented in the fig. 651. It is nothing, 
in fact, but a single cell of Daniell's batttery. A glas tum- 
bler, S, a common lamp-chimney, P, with a bladder-skin
tied over the lower end and filled with dilute sulphuric acid, 
is all the apparatus required. A strong solution of sLlphate ^  Ill Ii.
of copper is put into the tumbler, and a zinc rod, Z, is inserted in P; the moulds,
or casts, m m, are suspended by wires attached to the binding screw of Z. Thus




594             PHYSICS OF IMPONDERABLE AGENTS.
arranged, the copper solution is slowly decomposed, and the metal is evenly and
firmly deposited on mm. A perfect reverse copy of ni is thus obtained in solid
malleable copper. The back of m is protected by varnish, to prevent the adhesion of the metallic copper to it. In this manner the most elaborate and costly
medals are easily multiplied, and in the most accurate manner. In practice,
reverse casts of the object to be copied are first made in fusible metal or wax. The
art is now extensively applied to plating in gold and silver from their solutions;
the metals thus deposited adhering perfectly to the metallic surface on which
they are deposited, provided these be quite clean and bright.
Even alloys, as bronze, brass, and German silver, may be deposited according
to electrolytic law.
The positive electrodes should be of the same metal as that in solution, and
as large as the surfaces to be coated, and these should not be larger than the
plates of the battery furnishing the current. The arrangement of apparatus
commonly used in this art, is seen in fig. 652, where the metallic solution is held
652
in a separate bath, over which are extended two stout rods; B, carrying the
objects, m, in connection with the negative side of the battery; and with the positive side, the rod D, on which is suspended a plate of the metal proposed to be
deposited, to maintain the uniform strength of the solution, which is preferably
kept at a somewhat higher temperature than that of the air. Wood-cuts and
printers' types are thus copied in copper, the moulds taken in wax from them
being made conductors by dusting over the surface with extremely fine plumbago. All the copper-plates for the charts of the United States Coast Survey,
are reproduced by the electrotype —the originals never being used in the press,
but only the copies; and any required number of these may be produced at
small expense. For an instructive account of these extensive electrotype operations, the student is referred to a paper by the Electrotypist of the Coast Survey, Mr. G. Mathiot (Amer. Jour. Sci. [2], XV., 305\.
893. Crystallization  from  the action  of feeble currents.-It
was known to the alchemists, very early in chemical history, that certain metals, as gold, silver, copper, lead, tin, &c., were deposited in a
pure, or "reguline" condition, from their solutions, when another metal
was present, or even sometimes without that condition.  Thus the lead
tree (arbor Saturnce), the tin tree (arbor Jovis), the silver tree (arbor
Diance), were so called by the alchemists, from  the apparent growth




ELECTRICITY.                             595
of theso metals out of their solutions, and in tree-like forms.  This
growth we now know to be due to Voltaic crystalline deposition.
Examples.-A solution of chlorid of gold in ether, by slow change, deposits
spontaneously, crystals of fine gold, in elegant moss-like growths; and Liebig has
shown us how to prepare a silver solution, which, by the aid of an essential oil as a
reducing agent, will coat glass with a film of silver so thin as to be transparent,
and still so brilliant as to reflect light more perfectly than the best mercurial
mirrors.
A dilute solution of acetate of lead (half an ounce to a quart of rain water),
surrenders all its lead to a strip of zinc hung in the containing bottle, in elegant
crystalline plates (the arbor Saturslce); this, and the next case, are true Voltaic
circuits, while in the first two cases, hydrogen appears to supply the want of the
second element of Voltaic couple. In like manner, a dilute solution of nitrate
of silver, placed over mercury, soon deposits all its silver in an arborescent form
(arbor Diance) on the mercury.
But the most instructive case of this kind is when a bar of pure tin is placed
upright in a tall vessel, the lower half of which is filled with a saturated solution
of protochlorid of tin, while above it rests a dilute solution of the same salt.
The bar is therefore in two solutions chemically identical, but physically unlike.
The result is a Voltaic current, by which metallic tin, in beautiful brilliant plates,
is deposited upon the upper part of the bar, while the lower part is correspondingly dissolved by the free electro-negative element of this electrolysis.
The earliest recorded experiments with this species of Voltaic circuit are those
of Bucholz (1807), whence this slow-acting pile is sometimes called the " Buckolzpile." Becquerel has greatly extended our knowledge of the actions thus produced, forming thereby many non-metallic crystalline products. Cross thus
formed crystals of carbonate of lime in two days in the light, or in six days in the
dark. Mallett thus produced crystals of copper, and of red oxyd of copper, in
a single night from the nitric solution. (Am. Jour. Sci. [2] XXX. 253.)
894. Deposit of metallic oxyds and Nobili's rings.-Becquerel
has shown that oxyd of lead and oxyd of iron may be deposited in
a thin film on the surface of oxydizable metals by using an alkaline
solution of the metallic oxyd, and making the plate to be oxydized the
negative electrode of a constant battery; a deep brown coating of the
oxyd is thus deposited in a few minutes so firmly as to withstand the
action of the burnisher, and perfectly protect the iron or steel from
atmospheric action.
If the film of oxyd of lead is very thin, it presents, over a surface
of polished silver or steel, a most pleasing exhibition of colored rings,
analogous to the colored rings of Newton from thin plates (530). For
this purpose the negative electrode is made of a thin platinum wire,
protected from the solution by a glass tube, except at the extremity,
where a mere point is presented.  A rim of wax on the edges of the
plate retains the solution of potassa, saturated with oxyd of lead, while
it is connected on the positive pole, and the negative point is held for a
few seconds within a line of the polished surface. These colored rings
were first noticed by Mr. Nobili, whence their name.




596            PHYSICS OF IMPONDERABLE AGENTS.
3. Physiological effects of the pile.
895. The physiological effects of the Voltaic pile. —Galvani's
original experiment, and the earlier observations of Swammerdam and
Sulzer, of two metals on the tongue, deserve to be remembered as being
our earliest knowledge of this subject. From a single cell, or even a small
number of pairs, the dry hands, grasping the electrodes, receive no sensation; number, and not size of elements, is requisite for the physiological effect. Thus, from a column of fifty elements, or still more from
fifty cups of Bunsen, or a Cruickshank's trough (870), a smart twinge is
felt, reaching to the elbows, or if the hands are moistened with saline
or acid water, the shock will be felt in the shoulders. This shock is
unlike the sharp and sudden commotion from statical electricity, being
a more continued sensation, accompanied, during the continuance of the
current, by a sense of prickly heat on the surface. But it is only at
the making and breaking of contact that a shock is felt. If the battery
contains some hundreds of couples actively excited, the shock becomes
painful, or even fatal.  It may be passed through any number of persons whose moistened hands are firmly joined, but it is sensibly less
acute at the middle of such a circuit than to those at the electrodes.
Even after death, this power produces spasmodic muscular contractions, efforts to rise, and contortions of the features frightful to behold.*
Persons in whom  animation was suspended, have been restored by the
influence of the hydro-electric current on the nervous system.
The senses of sight, hearing, and taste, are all affected by a Voltaic current;
a flash of light, a roaring sound, and a sub-metallic savor being received when
the shock of a small battery is passed, successively, through the eyes, the ears,
and the tongue.
From the experiments of Becquerel, it appears that seeds subjected to a
gentle electric current, germinate sooner than otherwise. Von Marum observed
that plants with a milky juice, like the Eupiorbiacece, do not bleed after a
powerful electrical shock, owing, he suggests, to the loss of contractile power in
the plant.
For a detailed account of the application of electricity to medical uses, consult the works of Dr. G. Bird (of London), W. F. Channing (of Boston), and the
late elaborate volume of Dr. Garrett.
The magnetic effects of the pile belong to electro-dynamics,
while its electrical effects have already been considered in ~ 863, 864.
VII. THEORY OF THE PILE.
896. Three views.-1. It has already been stated (863), that Volta
and his school ascribed the effects of the pile to the simple contact of
unlike metals, each decomposing the neutral electricity of the other.
* See a notice of Dr. Ure's experiments on a newly executed criminal, at
Glasgow, in 1818. HARRIS, Galvanism, 123, J. Weale.




ELECTRICITY.                        597
He argued that the chemical action of the battery was requisite only
to afford conductors for the electricity, while the metallic substances
remaining in every way unchanged, they are supposed to discharge
into each other. According to this hypothesis, the two metals are in
opposite electrical states, one being positive, the other negative; these
states becoming at once destroyed by the intervening fluid. This theory
assumed that the whole effect of the apparatus is but a disturbance
and reproduction of electrical equilibrium.  This view, however, cannot be maintained, since it involves an impossibility:-the production
of a continual current, flowing on against a constant resistance, without any consumption of the generating force.
2. On the other hand, Fabbroni, Davy, Wollaston, and, above all, in
our day, Faraday, De la Rive, and Becquerel have sought to establish
that the Voltaic excitement was only the reciprocal of the chemical
action; and as this was more intense, and properly directed, so was
the pile more powerful. In addition to the statements and arguments
already adduced, it is proper here to consider the ground of these two
views, and somewhat more in detail.
3. A third view or theory of the pile has been advanced by Peschel,
which he calls the molecular theory, and which rests on a sort of middle
ground between the contact and the chemical theories.
897. Volta's contact theory.-The advocates of this mode of explaining the action of the pile (embracing nearly the whole body of the
German physicists), contend that they have experimentally established
the following points in support of Volta's theory, viz.: 1st, That Volta's
original experiments demonstrate the fact beyond question, that the
simple contact of heterogeneous metals does produce an electrical current (846). 2d, That in some cases, when a purely chemical action
exists between a fluid and one of the two metals immersed in it, the
contact of the metals arrests this action, and an opposite action commences. 3d, That there are even cases of hydro-electric combinations,
in which electrical action exists, without any chemical action whatever
on the electromotors. 4th, The advocates of this view further contend
that chemical action is never the primitive cause of electrical excitement; although some do not question the influence of chemical action
in promoting and increasing the excitement originally due to contact.
Since scarcely any chemical action, or none at all, occurs in a constant battery without contact, it is, with reason, urged that contact of
the heterogeneous metals is the one indispensable prior cause of the
Voltaic current. Hence the real difficulty seems to be, to decide what
share chemical influence really has in exciting the electrical action.
Want df space prevents our giving the evidence in detail upon which
53




698            PHYSICS (OF IMPONDERABLE AGENTS.
the advocates of the contact theory rely for the support of the above
propositions.
898. The chemical theory assumes the electrical current to be the
reciprocal of the chemical action in the cells of the battery, and that
chemical action is essential to the production of such a current.
De la Rive demonstrated this latter point in the following manner:
A pair, formed of two plates, one of gold, the other of platinum, was
plunged into pure nitric acid, without the development of any current;
by the addition to the nitric acid of a single drop of chlorohydric acid,
a very decided current was obtained from  the gold to the platinum
through the liquid. In the first case there was no chemical action; in
the second case, the gold was attacked, and the platinum was not, or
more feebly.
The laws of electrolysis, first demonstrated by Faraday, as already
stated (890), lend the evidence of mathematical certainty to the chemical theory of the pile. Since we thus reach the unavoidable conclusion
that an equivalent of electricity is a chemical equivalent, and so bring
the discussion down to the rigid test of the balance, the ultima ratio
of chemists and physicists.
In addition to the laws of Faraday, already rehearsed, are the following:Laws of the disengagement of electricity by chemical action,
first stated by M. Becquerel:1st. In the combination of oxygen with other bodies, the oxygen takes the
electro-positive substance, and the combustible the electro-negative.
2d. In the combination of an acid with a base, or with bodies that act as such,
the first takes the positive electricity, and the second the negative electricity.
3d. When an acid acts chemically on a metal, the acid is electrified positively,
and the metal negatively: this is a consequence of the second law.
4th. In decompositions, the electrical effects are the reverse of the preceding.
5th. In double decompositions, the equilibrium of the electrical forces is not
disturbed.
The quantity  of electricity  required to produce chemical
action is enormous, compared with the amount of statical electricity
disturbed by the common frictional machine.  Faraday has, in his
masterly way, demonstrated this fact by simple experiment.
He has shown that the quantity of Voltaic electricity requisite for decomposing
one grain of water, would be sufficient to maintain at a red heat a wire of platinum about one one-hundredth of an inch (T-14) in diameter, during three minutes
forty-five seconds, the time requisite to effect the perfect decomposition of the
grain of water. The quantity of frictional electricity required to produce the
same effect, would be that furnished by eight hundred thousand discharges of a
battery of Leyden jars, exposing three thousand five hundred square inches of
surface, charged with thirty turns of a powerful electrical machine.
Beequerel, by a different mode of experiment, arrived at nearly the same




ELECTRICITY.                            599
result. Therefore, to decon pose a grain of water. requires an amount of electricity equal to that furnished by the discharge of an electric pane having a
surface of thirty-two acres. "Equal to a very powerful flash of lightning."
" This view of the subject gives an almost overwhelming idea of the extraordinary quantity of electric power which naturally belongs to the particles of
matter." (Faraday Expt. Res., 853-861.)
899. Polarization and transfer of the elements of a liquid.The electro-chemical theory has been much expanded by the researches
of De la Rive; he explains the phenomena of polarization and the
transfer of the elements of a liquid in the following manner:Iis theory assumes that every atom has two poles, contrary, but of the same
force. The different kinds of atoms differ from each other in that some have a
more powerful polarity than others. When two insulated atoms are brought
near each other, they attract each other by their opposite poles; the positive
pole of that which has the strongest polarity unites with the negative pole of
that which has the feeblest polarity. A compound atom, when insulated, has
therefore two contrary polarities between the poles of a pile; for example, the
atom is so arranged that its + pole is turned to the platinum (or - side) of
the pile, and the - pole is turned to the zinc (or + side) of the pile. This
same action occurs with other atoms, so that there is produced a chain of polarized particles between the poles of the pile.
The oxygen of the particle of water nearest the zinc becomes negative,
because of its affinity for the zinc, and the hydrogen becomes positive. The
other particles of water become similarly electrified by induction, but the
platinum has become negative by induction from the zinc, and therefore is in a
condition to take up the positive electricity from the zinc of the contiguous
hydrogen. The action now rises high enough for the zinc and the oxygen to
combine chemically with each other. The oxyd of zinc thus formed dissolves
in the liquid (dilute sulphuric acid), and is thus removed. But the particle of
hydrogen nearest the zinc, now seizes the oppositely electrified oxygen of the
adjacent particle, producing a fresh atom of water. The particle of hydrogen
which terminates the flow is electrically neutralized by the platinum, to which it
imparts its excess of positive electricity, and escapes in the form of gas; and
other particles of water are continually produced, to supply the place of those
decomposed, and thus continuous action is maintained. These changes, continually taking place, furnish an uninterrupted flow of electricity, which is
conveniently termed a Voltaic current.
Other instances of electrolysis are explained in a similar way.
900. Chemical affinity and molecular attraction-distinguished.
-According to De la Rive, and in support of the view of the polarity
of atoms, the distinction between chemical affinity and molecular
attraction is as follows: chemical affinity is the attraction of atoms,
operating by their contrary electric poles, which come into contact,
while physical attraction results from the mutual attractive action that
the atoms exercise over each other in virtue of their masses. This last
attraction is never able to produce contact, because of the repulsive force
of the ether which envelops the atom, and which increases in proportion
as the sphere which separates the attracted atoms diminishes (146).
901. Peschell's molecular theory of the pile.-Resting upon the




600            PHYSICS OF IMPONDERABLE AGENTS.
opinion long held by many chemists, that those forces which lie at the
basis of adhesion, and those which cause chemical affinity are not essentially different, Peschel holds that- When electricity is generated in any
Voltaic arrangement, it results from  a molecular change, brought about
in the touching bodies by the adhesive force which subsists between them.
This theory possesses the advantage, that no new power need be assumed to
exist, whereas the contact theory demands the existence of an "electro-motive
force," of which we know nothing. It also accounts for the production of electricity, apart from aqy chemical action. In common with the chemical hypothesis, it deduces the phenomena of the single battery from the molecular forces;
it considers the fluid not merely as a conductor of electricity, but as engaged in
its production, and that the elements of the battery, by the physical changes
which they undergo, are the actual sources of electricity; that their contact
renders this change possible, and it is, therefore, the occasion, and not the generating cause, by which the electricity is produced. By this view, the chemical
hypothesis is only a special case of the molecular. The simultaneous commencement of chemical action with the development of electricity, and the
circumstance that the chemical intensity of a simple Voltaic arrangement
increases and decreases as the chemical action on the fluid conductor, and on
the elements of the battery is greater or less, fully accords with the statements
of this theory. It follows, hence, that the electrical and molecular forces are one
and the same, and that the latter appears as electricity whenever it passes from
one mode of operation into the other, as, e. g., when it ceases to hold the elements
of the water, and so oxydizes the zinc.
g 4. Electro-Dynamics.
I. ELECTRO-MAGNETISM.
902. General laws.-Electro-dynamics is that department of physics
devoted to the mutual action of Volta-electric currents.  These are
distinct from  the phenomena of static electricity.  The phenomena of
electro-dynamics may all be arranged  under the following general
propositions.
1. Every conductor, conveying a current of electricity, affects a free
needle as a magnet would do.
2. Electric currents affect each other like magnets.
3. A magnet acts upon an electric current as a second current would
have done.
4. Electric currents in conductors excite similar currents in other conductors within their influence.
5. Magnets excite electric currents, and all the electrical effects depending upon them.
Hence, when magnetism  is excited by electric currents, it is called
electro-magnetism: and inversely, when electrical currents result from
magnetism, they are called magneto-electrical currents.
It is impossible, in our narrow limits of space, to consider each of these propositions in full detail. We shall endeavor, however, to present those phaiomena and their applications which are of most general interest.




ELECTRICITY.                          601
903. Mrsted's discovery.-In 1819-20, Prof. Hlans Christian CErsted, of Copenhagen, in a course of researches upon the relation of the
Voltaic apparatus to the magnet, made the discovery of the fundamental
fact of electro-magnetism, stated in the first of the foregoing propositions.  Many physicists had before sought to evolve the phenomena
of magnetism from the battery; but in vain, because they proceeded
without connecting the poles by a conductor, in which case, of course
(as we now clearly see), the power of the apparatus is dormant, like
stagnant statical electricity in an unexcited conductor.  (Ersted closed
the battery circuit by a conductor; and therein rests his discovery.  He
found when such a conjunctive wire was approached to a free needle,
that the needle was influenced by it, as if he had used a second magnet: in other words, the conducting wire, of whatsoever metal it might
happen to be, had itself become a magnet.
If positive electricity flows from south to north over a horizontal
conducting wire, placed in the magnetic meridian, then a free magnetic
needle, b a, fig. 653, would have its north end, b, deflected to the west,
653                                654
if it is placed below the conducting wire, and to the east if it is placed
above the wire. If the needle is placed on the east side of such a conductor, its north end is depressed, if on the west side of the wire, the
north end of tfie needle is raised. Reversing the direction of the current, reverses all these movements.
The rectangle, fig. 654, surrounding the magnetic needle, has three
connections, by the use of which the current may, at pleasure, be sent
above or below the needle.
(Ersted also found that only needles of steel or iron were thus affected, and
not those of brass, lac, and other non-magnetic substances. He called the conductor a "conjunctive wire," and he describes the effect of the electric current
(or the "electric conflict," as he calls it), as resembling a helix; and that it is
not confined to the wire, but radiates an influence at some distance.
The effect of (Ersted's discovery was remarkable. The scientific world was
ripe for it, and the truth he thus struck out was instantly seized upon by Arago,
53*




602            PHYSICS OF IMPONDERABLE AGENTS.
Ampere, Davy, and a crowd of philosophers in all countries. The activity with
which this new field of research has been cultivated, has never relaxed, even to
this hour; while it has borne fruit in a multitude of important theoretical and
practical truths, among which is the ELECTRO-MAGNETIC TELEGRAPH, one of the
great features of this age.
904. The electro-magnetic current moves at right angles
to  the  course  of the  conjunctive  wire.-Let a current flow
over a conductor in the direction of the arrow, fig. 655, from + to -;
a small bar of soft iron, or a steel sewing-              655
needle, held vertically before this wire, be-             N
comes instantly a magnet, with its N. pole
toward the earth-place the rod of iron on the  -                      +
opposite side of the conjunctive wire, and its
polarity is instantly reversed, as in the figure. Revolve it in either position in a vertical plane at right angles to the conjunctive wire, and the
induced poles will retain their relation to the current in every position;
i. e., the end marked N. in the figure, will remain north at every point
of the revolution. If a steel needle is used, it retains polarity after
the current ceases to act on it. If the bar or needle be laid parallel to
the conjunctive wire, then the two sides of the needle or bar have opposite polarities.
Hence, it follows, that a free magnetic needle tends to place itself at right
angles to the path of an electro-magnetic current traversing a conjunctive wire,
and were the needle free from the directive tendency of terrestrial magnetism,
it would so place itself. The electro-magnetic current is, therefore, a tangential
force, and acts tangentially upon a free needle.
Simple as is the relation between the electric current on a wire, and the order
of polarity induced by it in a needle, its corre-t expression is always difficult.
To aid its exact statement by some simple formula, Ampere lays down the
following rule:The north pole of a magnet is invariably deflected to the left of the
current which passes between the needle and the observer, who is to have
his face towards the needle, the electric current being supposed to enter.
from his feet and pass out of his head.
A verification of these cardinal principles by actual experiment, is
the only way in which the student can obtain a vivid and lasting impression of them.
905. Galvanometers or multipliers.-If the conjunctive wire is
bent into a rectangle, fig. 656, so as to carry            656
the current once, or many times, around the
needle, then the effect of the same force on the
needle is multiplied in proportion to the number of convolutions.  Thus Schweigger contrived his multiplier, fig. 656, composed of a
flat spool of fine insulated copper wire within which the needle was




ELECTRICITY.                             603
suspended. By this means a very feeble current became quite sensible.
For ordinary purposes, a few turns, or, it may be, three hundred or
four hundred convolutions suffice; but, for particular purposes, and
where the cur-              657                           658
rent is very feeble, many thousand feet of very
fine  wire   are                         n -1 lf
used.                    e 
In Nobili's dou-        9z a'
ble galvanometer,
an astatic needle i.            l
(787), is used, in 
which the needles, a b, b' a', fig. 657, are not
quite equal, leaving a very slight directive
force only. Fig. 658 shows this delicate instrument in its most perfect form, as used
in determining the laws of transmission of
heat, as well as for other purposes demanding a very sensitive instrument.  Only the
lower and stronger needle is enclosed in the
helix, D, while the system is suspended by
a fibre of raw silk, beneath a glass shade, 
leveled by three screw feet, C. The ends
of the spool are seen at R K, while by the
head, F, the whole instrument may be revolved so as to bring the wires of the spool
parallel to the suspended needle at rest,
which is the position of greatest sensitive- 
ness. The sensitiveness of such an arrangement is very great. Suppose, for example,
there are five hundred revolutions in the
coil, then the lower needle is acted on one 
thousand times, and the upper one five hundred times by any given current; or
the original force of the current is multiplied fifteen hundred times. But the
directing force of the earth's magnetism  on a              659
given needle is proportional to the squares of the
vibrations it makes (795). Now, assuming that
the needles alone made sixty vibrations in a          4
minute, and as astatic needles only ten, then                     i ~~
we have 3600: 100 as the numbers representingi    
the effect of terrestrial magnetism  in the two                    i
cases; or it is thirty-six times less in the astatic
system than in the simple needles, and, consequently, the electril current will affect them
thirty-six times more than if they were not astatic. The deflecting power of the current in
question will, therefore, be increased by such a 
galvanometer, 1500 X 36 - 54,000 times.
A less expensive form of galvanometer is seen in fig. 659.




604             PHYSICS OF IMPONDERABLE  AGENTS
906. The  tangents  or sine  compass  galvanometer. -This
instrument, invented by Pouillet, is designed to measure currents of
greater intensity than can be measured by the common galvanometer.
It depends on the established principle, that the intensity of a current is proportional to the sine of the angular deviation of the needle.
The angle of deviation being known, and                     660
consequently its sine, tho intensity of the
current is expressed in terms of the sine. 
Fig. 660 shows the arrangement of this instrument, in which the current, entering by the conductors, b a, through the ivory piece, E, circulates a
few times only, sometimes only once, over the vertical circle, M, placed in the magnetic meridian.
The magnetic needle, m, is deflected upon the hori- 
zontal circle, N, in proportion to the force of the 
current in M, and a silver index needle, n, serves
to record the angular deviation of in from its neutral point. When the needle is at rest, the vertical
circle, M, is revolved upon the standard, 0, by the 
button, A, until its plane coincides with the plane
of deviation of m, and this angular distance is
then read off by the vernier, C, upon the lower
graduated circle, H.  This galvanometer, or a
simpler modification of it, is the form of instrument generally used in electromagnetic researches.
907. Rheostat.-This simple contrivance of Wheatstone's serves to
introduce a longer or shorter conducting wire into any circuit, the intensity of which it is proposed to measure by the galvanometer.
Since the intensity of the current is inversely as the length of the circuit (880),
we may, by increasing or diminishing that
length, produce from  any current a determinate deviation (say 300), on the galvanometer. Fig. 661 shows this arrangement,
composed of two equal and parallel cylinders, one of wood, B, and the other of brass,
A, supported in a frame-work and revolving   _
on their centres. B is provided with a spiral groove, in which the turns of a copper
conducting wire may be laid. One end of
this wire is at a, in connection with the current pole, o. The wire may all be wound
on B, in which case the current passes
through its whole length, and escapes at,, _
through the metallic connection of its end,
e, with A. If it is desired to shorten the
conductor, the handle, d, is put on the axis, c, and A is revolved from left to
right, until, as in the cut, one-half, for example, of the conductor, is wound on
A. But A, being a metallic conductor, the current passes to n by the shortest
course, and the only part of the wire in action is what remains wound on B,




ELECTuICITY.                           605
and this quantity is read off by an index and graduation engraved on the farther
ends of the cylinders. This apparatus is indispensable in exact observations.
908. Ampere's electro-magnetic discoveries and theory.-Immediately after the first announcement of (Ersted's discovery of the
magnetic powers of a conjunctive wire, Ampere, one of the most renowned of the French physicists (born 1755-died 1836), commenced a
series of experiments (September, 1820) to determine the laws concerned in these curious phenomena. Of three principal hypothesis
which he framed to this end, he finally accepted and demonstrated the
following, viz.:A  magnet is composed of independent elements or molecules, which
ict as if a closed electric circuit existed within each of them: in other
words, each of these magnetic molecules may be replaced by a conjunctive
wire bent on itself, in which a constant current of electricity is maintained,
as from a Voltaic circuit.
This hypothesis he maintained by singularly ingenious experiments, many of
which were the direct suggestion of the hypothesis itself, and he brought all,
by his power of mathematical analysis, into exact conformity with his theory.
This theory recognises only such forces as are common to mechanical physics,
and often called "push and pull" forces. These forces are mutual, and belong
to all electric currents. In permanent magnets, the minute circular and parallel
currents, pertaining, by this theory, to each magnetic molecule, all act at right
angles to the magnetic axis or line of force. Hence, as in (Ersted's experiment
(903), the magnetic needle strives to place itself at right angles to the path of
the current on the conjunctive wire, it follows, that currents in the magnet seek
a parallelism to that in the conjunctive wire. Granting this to be true, it follows, as a corollary from the premises,1st. That two free conducting wires must attract or repel each other, according
to the direction of the currents in them.
2d. That a conjunctire wire may be made in all respects to simnulate a magnet.
909. Mutual action of electric currents.-Parallel currents attract
each other when they flow in the same direction. Thus, in fig. 662, where
the arrows and the signs -  and -  indicate the flow of the currents to
662                              663
-+      +
_          __                           -4 —-_
be identical, there is attraction, while, in fig. 663, the same signs show
the currents to be reversed, in conformity to the law that:-Parallel
currents repel each other when their directions are opposite. To illustrate
these laws experimentally, one of the conductors should be fixed,
and the other movable.  The following simple apparatus also illustrates these laws, and several other points of interest presently to be
noticed.




606             PHYSICS OF I5MPONDERABLE AGENTS.
De La Rive's floating current, fig. 664, is a little battery of amalgamated zinc, z, and copper, c, or zinc and platinum, set afloat by a disc of cork,
a b, whose poles +  and - are connected by a conjunctive        664
wire, 8 t. When this little float is placed in a vessel of acidu-  s  >
lated water (water with one-twentieth sulphuric acdi), an
electric current flows in the direction of the arrow. Then a   -
join the poles of a single cell of Grove's or Smee's battery 
by a conjunctive wire of convenient length, and stretching 
the wire between the two hands, approach it parallel to s t;
if the current is flowing in the same direction, the float will be attracted to the
wire in the hands; if otherwise, repulsion is seen. If the two wires are not
parallel to each other, then the movable current seeks to take up a position of
parallelism, or one in which the two currents have a similar direction. A little
rectangular frame of wood 3 X 6 in., may be wound with ten or twelve turns of
fine copper wire, covered by silk in the manner of a          665
galvanometer, and its free ends connected with a battery will give a stronger current. By simply turning   
the frame in the hand, the direction of the current is
reversed.
Roget's oscillating spiral, fig. 665, also illustrates the law of attraction of parallel conductors. Here
the conductor is coiled into a spiral, which is suspended \__/, 
from the top of an upright metallic standard in con- 
nection with one pole of a battery, while the other end          -
dips into mercury in the glass, in connection with the 
other pole, K. When the poles are joined, each turn of            -..
the spiral attracts flee next turn, shortening the spiral,
and breaking the mercurial connection, with a spark. The weight of the spiral
then restores the connection, and thus a continuous oscillating movement is
kept up.
We add the following general propositions on this subject.
1. Two currents following each other in the same direction, as also
different parts of the same current, repel each other.
2. Two fixed currents of equal intensity, flowing near and parallel
to each other in opposite directions (as when the same wire returns on
itself without contact), exert no influence on a fixed current running
near them: in other words, they exactly neutralize each other, and
their effect is null.
The rotation of electric conductors about magnets, and the reverse;
the rotation of a magnet on its own axis by an electric current, and the
rotation of electrical conductors about each other, are all points most
curious and instructive to trace, did space permit. The student will
find these principles very neatly illustrated by appropriate apparatus
in Davis's Manual of Magnetism. The researches of Henry, Page, and
other American physicists, have made very important additions to this
department of physics.
910. Helix, solenoid, or electro-dynamic spiral.-By winding




ELECTRICITY.                          607
the conjunctive wire into a helix, as in fig. 666, and carrying the wire
back again through the axis of this                666
spiral, C B, the effects of the current 
from A to B, will be neutralized by              xI  
its return from B to C, and there will
remain only the effect due to its spiral revolution about C B. Ampbre
called this form of the wire a solenoid. The effect of the helix thus
wound, is reduced solely to the influence of a series of equal and
parallel circular currents. By winding the silk-covered wire in the
manner shown in fig. 667, the two ends of the coil are returned to the
centre of gravity, and being pointed               667
with steel, the whole system  can be
conveniently suspended, as in fig. 668,
upon what is called an AmpBre's
frame, in which the arrows show the
course of the current from the battery B;
to the helix or solenoid thus suspended.
When the current is established, the axis of the solenoid, A B, swings
into the magnetic meridian, while its several spires are in the plane of
the magnetic equator. This position               668
it assumes in obedience to the soli-  
citation of terrestrial magnetism; 
consequently it simulates in all respects the character of a magnetic
needle, although possessing not a
particle of iron or steel in its structure.  If a second helix, b, through     _
which also a current passes, is now 
presented to the first, as in fig. 668, all the phenomena of attraction
and repulsion will be seen, the action of the two helices or solenoids
being to each other exactly like those of two            669
magnets.
De La Rive's floating current, already explained in ~ 909, is also well adapted to illustrate
the attractive and repulsive influence of a magnet 
on a free conjunctive wire, as well also as its obe- 
dience to the solicitations of terrestrial magnetism. For this purpose the conjunctive wire is
wound, as in fig. 669, into a helix. Left to itself,
this apparatus will act just as the solenoid on the frame, fig. 668, and
will obey the impulses of a magnetic bar, or of another solenoid.




608            PHYSICS OF IMPONDERABLE AGENTS.
911. Directive action of the earth.-These effects are expressed
in the following law:Terrestrial magnetism  acts upon electric currents just as if the entire
globe was encircled with electric currents from E. to W. in lines parallel
to the magnetic equator.
The direction in which these currents are supposed to move is the
same with the apparent motion of the sun, and the one in which the
earth's surface receives its advancing rays; and since it is now known
that electrical currents generated by heat exert precisely the same
influence on the magnetic needle as Voltaic currents do, therefore it
has been inferred that the thermal action of the sun is the generating
and maintaining cause of the currents of terrestrial magnetism (801).
912. Magnetizing by the helix.-We have already (805) described
a mode of producing magnets from  an electrical current.  The explanation of this, after all that has been said, is easy. As each volute of
the helix, carrying an electric current, is itself an active magnet, it is
easy to conceive that under the united influence of a great number of
such circular and parallel currents, the coercitive force of a steel bar,
or bar of soft iron, should be decomposed, and active magnetism be
thus induced, permanent or transient, according as steel or iron is the
subject of experiment.  Even a series of sparks from an excited electrical machine, passed through a helix, will magnetize a steel needle.
The position of the poles in a bar so situated will depend on the right-handed
or left-handed twist of the spire. If the current flows from +  to -, and the
wire, as in fig. 670, turns from                670
left to right (like the hands of
a watch), then the north pole --
of the magnet is toward the
left; but if the spire turns, as.ti
in fig. 671, from right to left,
or opposite to the hands of
a watch, then the poles are                     
reversed. The following sim- 
pie formula, by Faraday, will
always enable the student to                     671
obtain definite notions of the polarity of the helix: —" Let a person," observes
Faraday, " imagine that he is looking down upon the dipping needle, or north
magnetic pole of the earth, and then let him think upon the direction of the
motion of the hand of a watch, or of a screw moving direct; currents in that
direction would create such a magnet as the dipping-needle."
If the helix is wound on a tube of glass, paper, or wood, these substances
offer no resistance to the passage of the power; but if a tube of copper or other
metal were employed, the magnetizing power of the current on the enclosed bar
would be destroyed.
If the same helix is wound in two opposite directions, as in fig. 672, then, according to the direction of the current, there will be a pair of north polos at the




ELECTRICITY.                           609
point of reversal in the centre (or a pair of south ones), and the two ends will
have the same name. A bar of steel placed in such a helix     672
will remain permanently an anomalous magnet (779). Reversing the position of the bar in the helix, or reversing the
position of the electrodes in the binding cups, will reverse
its polarity.
Arago's original experiment.-If a short conjunctive wire of copper, or any non-conducting metal, is strewn
with iron filings, they will arrange themselves as seen in
fig. 673, not bristling as in the magnetic phantom, with
opposite polarities (777), but in close concentric rings, disposed over the whole
length of the conductor. This fact was observed         673
by Arago, in 1824, and by others, before the
application of the helix to the induction of
magnetism in soft iron.
When the helix is closely wound with many 
turns of insulated wire, and excited by a battery of considerable quantity, a cylinder of
soft iron, as a b, in fig. 674, will be drawn into    llllll
it from the position seen in the figure, with great power, and, after several
oscillations, will come to rest in the middle of its length, in  674
opposition to gravity, realizing the fable of Mahomet's coffin,
suspended in mid air without visible support. This axial        He
movement is availed of in the electro-magnetic engine.
913. Electro-magnets.-Electro-magnets are masses
of soft iron wound with coils of closely packed and insu          I 
lated copper wire, varying in size and length, according
to the use to be made of them.  Fig. 675 shows the
usual form of those designed to sustain great weights.
The spools, A and B, are virtually continuations of one spool, the direction of the whorl being apparently reversed by the bend of the horseshoe. If a lever of the third order (113) is used as a steelyard, the
lumber of heavy weights is avoided in the use of these instruments,
and the power of the apparatus is easily tested.
Electro-magnets develop their surprising power only when the armature is in contact with the poles, a fact due to induction; without their
armatures, they sustain not a tenth part of their maximum load. They
are capable of over-saturation by an excess of battery power, and after
that has been cut off, they retain a remarkable residual force so long
as the keeper is in place, but as soon as the armature is detached, the
whole of this residual magnetism  is lost.  Their polarity is instantaneously reversed by reversing the poles of the battery.  This complete
and immediate paralysis and reversal of power, renders these magnets
of inestimable value in experimental researches.
Sturgeon, of England, in 1825, appears to have been the first to produce soft
54




610            PHYSICS OF IMPONDERABLE AGENTS.
iron electro-magnets. Prof. Henry, and Dr.. Ten Eyck, in 1830, produced the
first electro-magnets of great power, by a new mode of winding the inducing
coil. (Am. Jour. Sci. [1] XIX. 400.)
Prof. Henry, on a soft iron bar of fifty-nine lbs. weight, used twenty-six coils
of wire, thirteen on each leg, all.675
joined to a common conductor by
their opposite ends, and having. dil
an aggregate length of seven hundred and twenty-eight feet. This
apparatus, with a battery of four
and seven-ninths feet of surface,
sustained two thousand and sixty-    I
three pounds avoirdupois: with a
little larger battery surface it sus-l
tained twenty-five hundred lbs.
This  electro-magnet was  constructed for Yale College Laboratory, in 1831, and is still among
Mr. J. P. Joule (Annals of
Electricity, V. 187), in 1840,
constructed soft iron electromagnets of peculiar form, being in fact tubes with  very
hhick walls cut away on one
side lengthwise, and wound in 
the direction of the length; I
one of which, weighing 15 lbs., -                        __v d
held 2090 lbs., equal to nearly
L40 times its own weight.  It: —
was wound with 4 covered copper wires, tr inch diameter, and each 23 feet long only, the length of the
soft iron being 8 inches, and its outer diameter three inches. Another
magnet weighing 1057 grains supported twelve pounds, or 1286 times
its own weight; and a very minute one, which weighed only 63-3 grains,
carried on one occasion 1417 grains, or 2834 times its own weight. The
last is more than eleven times the proportionate load of the celebrated
magnet of Sir Isaac Newton, & 806.
914. Page's revolving electro-magnet, fig. 676, affords satisfactory
evidence of the great rapidity with which a mass of soft iron may receive and
part with magnetism, having its polarity reversed also by a change of position.
In this instrument, a permanent U-magnet has a vertical spindle in its axis, on
the upper end of which is placed a mass of soft iron, destined to receive induced
magnetism through the covered wire with which it is wound, and whose ends are
represented by the two s recw cups, one on each side. By a simple contrivance,




ELECTRICITY.                          611
called an interrupter, or break-piece (formed by sawing a silver ferrule on the
axis into two parts by vertical slits), the continuity   676
of the current is interrupted twice in every revolution, when the position of the armature is as seen
in the figure. The effect of this arrangement is to 
paralyze the magnetic force at the right instant to
permit the momentum of the mass to carry the
armature by the poles of the fixed magnet, when 
the battery connection is again completed, new
magnetism induced, and the motion continued as
before. Such a little magnetic engine may revolve 
with a velocity of 2000 times a minute, equal to
4000 reversals of polarity,-each reversal being
accompanied by a passive interval, when the soft
iron is no magnet.
915. Power of electro-magnets —The
power of electro-magnets depends, 1st, on the 
intensity of the current; 2d, on the number
of whorls in the helix; 3d, on the kind and
shape of the iron bar; 4th, on the fonrm and size of the keeper or armature.  These points have been studied by Lenz and Jacobi, and many
others, of whom the results of Dub are the most recent. Dub distinguishes between magnetism, attraction, and sustaining power, in electromagnets, confining the terim magnetism to the magnetic excitation due
to the Voltaic current. Lenz and Jacobi measured this by means of the
induced current excited by the vanishing of the magnetism to which it
is proportional. When a second bar of soft iron is caused to approach
the first, this also becomes magnetic (by induction), and by n-fold magnetism, n2 times the attraction is produced; until actual contact happens, when this ratio is no longer maintained.
Dub gives the following summary of his results:1. The attraction of U-shaped electro-magnets, with an equal number
of windings, is proportional to the squares of the magnetizing current
force.
2. The attraction of U magnets is, with equal currents, proportional
to the squareof the number of windings of the magnetizing spirals.
3. The attraction of U magnets is proportional to the square of the
current force multiplied by the square of the number of windings.
[This is true alike for attraction and sustaining force, both in straight
and in U magnets.]
4. The magnetism  of massive cylinders of iron of equal length,
magnetized by Voltaic currents of equal force, and by spirals of an
equal number of windings, closely surrounding the core, is accurately
proportional to the square roots of the diameters of these cylinders.
5. For the particular case in which the surface of contact does not




612           PHYSICS OF IMPONDERABLE AGENTS.
disturb the result, the attraction and sustaining force are, with equal
magnetizing forces, proportional to the diameters of the bar or Umagnets.
6. The attraction of bar and U-shaped electro-magnets with equal
magnetizing forces, increases the nearer the whole of the windings are
to the poles.
7. The attraction, like the sustaining force of U electro-magnetsother things being equal-remains the same, whatever be the distance
of the branches of the magnet.
8. The length of the branches of a U-shaped electro-magnet has no
influence on its attractive or sustaining force, if the windings of the
spiral surround its whole length.
In addition to these laws, the author has found that the attraction
which a helix or spiral exerts upon a soft iron bar placed in its axis,
follows the same law as an electro-magnet; hence it follows, that:9. The attraction of a spiral is proportional to the square of the magnetizing current, multiplied by the square of the number of windings.*
The sustaining power of an electro-magnet increases with the mass
of the armature up to a certain point, not exceeding the mass of the
electro-magnet itself; and, moreover, Liais has shown that an arma,
ture whose face of contact is not over one-third the breadth of the
poles to which it is applied, gives a maximum effect.
For some curious results with circular and trifurcate electro-magnets,
and the applications of this force to "break up" railway trains, consult the papers of Prof. Nickles (Am. Jour. Sci. [2], XV., 104 and 380;
and XVI., 110 and 337).
916. Vibrations and musical tones from induced magnetism.Dr. Page, in 1837, noticed the production of a musical sound from a magnet,
between the poles of which a flat spiral was placed. The sound was heard
whenever contact was made or broken between the coil and the battery. Two
notes were distinguished, one the proper musical tone of the magnet, and the
other an octave higher. De la Rive, Delezenne, and others, have confirmed
and extended these curious observations. The existence of molecular disturbance in receiving and parting with magnetic induction, has been farther illustrated by the same ingenious observer, by the vibrations imparted to Trevellyan's
bars by the current from two or three cells of Grove's battery. (Am. Jour. Sci.
[2], IX., 105.) Trevellyan's bars are prismatic bars of brass, hollow on one
side, so as to rest by sharp edges on blocks of lead. When these are gently
warmed, and then laid upon the leaden blocks, the unequal expansion and contraction of the two metals gives the brass bars a slight motion of vibration,
due to molecular disturbance by heat. A Voltaic current, according to Dr.
Page's observation, produces the same effect as heat, but more remarkably.
917. Electro-magnetic motions and mechanical power.-The
*Am. Jour. Sci. [2], XVII., 424.




ELECTRCIITY.                           613
facility with which masses of soft iron may be endued with enormous
magnetic power by currents of Voltaic electricity, and again discharged,
or reversed, in polarity, has led to numberless contrivances to use this
power as a mechanical agent. A great variety of pleasing and instructive models of such machines, with the use both of permanent magnets
and of electro-magnetic armatures, or of electro-magnets only, are
described in Davis's Manual of Magnetism. The revolving armature,
fig. 676, is one of these.
We annex a figure of an electro-magnetic engine, similar to one by
which Dr. Page obtained a useful effect of ten horse-power, in driving
machinery, and transporting a railway train. A and B, fig. 677, are
677
^ ill^"1111!lll"l"l^lllIIIlI^ l Ii~\ l lll l   ll i a lil  11 1    lllilllillll
two very powerful helices of insulated copper wire, within which are
two heavy cylinders of soft iron, C D, counter-balanced on the ends of
a beam, G F I, like the working beam of a steam-engine. By the movement of an eccentric, L, on the main shaft of the fly-wheel, the poles
are changed, at the moment, to magnetize and de-magnetize, alternately, the two helices, drawing into them the two soft iron cylinders,
by a force of many hundred pounds.  Prof. W. R. Johnson tested the
force of an engine of this kind built by Dr. Page, in 1850, and found
it to give about six and a half horse-power.  (Am. Jour. Sci. [2], X.,
472.)
M. Jacobi, of St. Petersburgh, has studied this subject very carefully, and
has contrived an effective form of rotating machine, very similar to that of
Cook and Davenport, so well known in the United States in 1837. Froment,
of Paris, has also constructed a powerful apparatus of this sort, in which armatures of soft iron on the periphery of a wheel are drawn towards electro-magnet
placed radially.
In all these machines, it is heat developed by chemical action that is transformed, in the form of magnetic attraction, into mechanical work (761!. As
the result of a great many experiments, Mr. Joule has shown that the best theoretical result from the heat, equivalent to the solution of a grain of zinc in a
64*




614             PHYSICS OF IMPONDERABLE AGENTS.
battery, is eighty lbs. raised one foot high. But a grain of coal burned in a
Cornish boiler, raises one hundred and forty-three lbs. one foot, and the price of
the coal is to that of the zinc as 9d. per cwt. to 2161. per cwt. Therefore, under
the best conditions (which are never reached in practice), the magnetic force is
25 times dearer than that of steam. Until, therefore, zinc is cheaper than coal,
in the proportion of 80 to 143, coal will probably be burned in atmospheric air,
preferably to the combustion of zinc in sulphuric acid, to produce mechanical
work.
918. Conversion of magnetism  into heat.-Foucault has shown that
the magnetism induced in a disc of copper revolving between the poles of an electro-magnet, is converted into heat.                 678
For this purpose, a powerful electro-magnet is supported upon a
basement, fig. 678; two pieces of
soft iron are attached to the poles 
of the magnet, so that they con- 
centrate, upon the two faces of a
metallic disc, their magnetism of
induction. This disc of copper
receives, by means of pulleys, a                                       _
rapid revolution, which will con- 
tinue for a long time, if no current exists in the electro-magnet;
but if a current from a battery
of two or three cells is passed
through the wire, the disc is
almost immediately stopped; if, however, against this resistance the disc is forced
to revolve, the expense of force is converted into heat, and the temperature of
the disc is rapidly raised.
II. DIAMAGNETISM.
919. Action of magnetism on light.-Fig. 679 shows the appa679
ratus designed by Ruhmkorff, in illustration of Faraday's magnetic
rau    eindlyRhmo            nilsrto   of Fa adysmgei




ELECTRICITY.                        615
rotatory polarization of light already spoken of under Optics (560).
Two powerful inducing coils, N and M, surround two hollow cylinders
of soft iron, S and Q. The current enters the bobbins by A, and following the direction of the arrows, returns by B. The two coils slide
in the groove in the base, K, on the two supports, 0 0, so that they
may be approached or withdrawn at pleasure by turning the screws,
m m. A commutator, or interrupter of the current, is arranged at 1 n.
At a and b are two Nicol's prisms (553), of which a has a vernier or
index, reading the degrees on the, graduated circle, P. To make the
experiment, a piece of heavy glass, or silicious-borate of lead, c, is
placed on a support between the poles S and Q. A ray of light from
the candle, polarized by the prism, b, is transmitted through the glass
in the axis of the poles. When the current is applied, the ray of light
appears to be revolved, similarly to the effect produced on polarized light
by quartz, or oil of turpentine (556). A great number of other solids and
liquids are found to act in a like manner, but to a less degree, than in
the case of " heavy glass." As no rotation of the ray takes place unless
there is some medium  on which the magnetism  may act, it has been
argued with some force by Becquerel and others, that the action is
wholly due to a molecular change in the solid under experiment. A
reversal, however, of the direction in which the ray travels, reverses
the direction of rotation in the polarized ray, a circumstance not found
in bodies in the natural state. This apparatus also serves to illustrate
the phenomena of diamagnetism.
920. Diamagnetism.-We have already (799) alluded to the action
of magnetism  upon all bodies, discovered by Dr. Faraday, in 1846, a
discovery which alone would place its author in the highest rank of
modern philosophers. By the use of the apparatus, fig. 680, he proved
that every substance which he tried, solid,            680
fluid, or gaseous, was sub-      681                  B
jectto magnetic influence, 
assuming either the equatorial or axial position,
according to its nature.
For solids, and some flu- 
ids, fig. 681 shows the arrangement.  Two  bluntly
rounded polar pieces of soft   
iron are fitted into the openings of the spools, S and Q, while between them are suspended on a silk fibre
cubes, iw, or short bars of the various magnetic metals, bismuth, antimony, copper, lead, tin, &c. If the cube is spinning about when the current passes, the
induced magnetism arrests its motion in whatever position it may be; and if




616            PHYSICS OF IMPONDERABLE AGENTS.
the metal has the form of a little bar, it rests athwart the axis like a cross. If
non-magnetic liquids, alcohol, water, and most saline solutions, are confined in
little narrow bottles (like homoeopathic vials), hung like m, fig. 681, these are
similarly affected. If they are filled, however, with magnetic solutions, the salts
of iron, nickel, or cobalt, they then arrange themselves axially.
PlUcker has shown that if these magnetic solutions are placed in watchglasses upon the poles, S Q, as in fig. 680, according as the poles are nearer or
farther asunder, these liquids are heaped up in one or two elevations, as in A
and B.
The flame of a candle placed between the poles, S Q, fig. 682, is strongly repelled, a fact first observed by Father Bancalari, of Genoa,   682
and the flames of combustible gas from various sources
are differently affected, both by the nature of the com-  
bustible and by the nearness of the poles. The flame         S   o
from turpentine is most curiously affected, being thrown 
into the form of a parabola, whose two arms stretch upward
a great distance, and are each crowned by a spiral of
smoke. Oxygen, which, in the air, is powerfully magnetic
(799), becomes, when heated, diamagnetic. A coil of platinum wire, heated by a current of Voltaic electricity, and
placed beneath the poles of Faraday's apparatus, occasions a powerful upward current of air, but, when magnetism is induced, the ascending current
divides, and a descending current flows down between the upward currents.
The following list expresses the order of some of the most common paramagnetic substances, viz.: iron, nickel, cobalt, manganese, palladium, crown-glass.
platinum, osmium. The zero is vacuum. The diamagnetics are arranged in the
inverse order, commencing with the most neutral: arsenic, ether, alcohol, gold,
water, mercury, flint-glass, tin, "heavy glass," antimony, phosphorus, bismuth.
Plucker has further demonstrated the important fact, that the optic axis of
Iceland spar is repelled by the magnet-a fact probably true of many crystalsin some of which the magnetic axis is parallel to the longer axis of crystallization. Thus, a piece of kyanite will, under the influence even of the earth's
magnetism, arrange itself like a magnetic needle.
III. ELECTRIC TELEGRAPH.
921. Historical.-The thought of making telegraphic communications by electricity appears to have suggested itself as soon as it was
known that an electrical current passed over a conducting wire without sensible loss of time. The following brief summary of well-known
historical facts, will serve at once to show how impossible it is justly to
bestow the exclusive merit of the electric telegraph upon any inventor,
while at the same time it strikingly illustrates what is true of every
important invention, that final success rescues from oblivion many
schemes that had hardly vitality enough in their day to find a place
in the records of history.
In 1747, Dr. J. WATSON erected a telegraph from the rooms of the Royal
Society, in London, for two miles or more, over the chimney tops, using frictional electricity on a single wire, with the earth for a return circuit. In 1748,
Dr. FRANKLIN set fire to spirits of wine by a current of electricity sent across




ELECTRICITY.                             617
the Schuylkill on a wire, and returning by the river and the earth. In 1774,
LE SAGE, a Frenchman, established at Geneva an electric telegraph, in which
he used twenty-four wires insulated in glass tubes buried in the earth, each
wire communicating with an electroscope, and corresponding to a letter of the
alphabet, and excited by an electrical machine. (MOGNIO TraitS, 59.) In 1787,
BETANCOURT, in Spain, made an effort to employ electricity for telegraphing by
passing signals from a Leyden vial over wires connecting Madrid with Aranjuez, a distance of twenty-six miles. SALVA, in 1796, also presented to the
Academy of Madrid, a plan of an electric telegraph of his own invention, which
received the patronage of the Prince of Peace. In 1800, the public announcement of VOLTA'S discovery of the pile supplied a new means for telegraphing,
far more certain than frictional electricity, and accordingly we find, that in
1811, Prof. SOEMMERING, of Munich, proposed to the Academy in that city a
complete plan, with details, for an electro-chemical telegraph, in which he used
thirty-five wires (twenty-five for the German alphabet, and ten for the numerals),.tipped with gold and covered by the same number of glass tubes filled with water,
to be decomposed whenever the corresponding letter or numeral was touched by
the battery wire on a key-board at the other end. This is the type of all electrochemical telegraphs. Dr. J. REDMAN COXE, of Philadelphia, in 1816, in Thompson's Annals of Philosophy, apparently without knowledge of Soemmering's plan,
proposes a similar one by the use of Voltaic electricity. In 1819-20, (ERSTED'S
discovery of electro-magnetism, and AMPERE'S development of the subject, opened
the way to electro-magnetic telegraphy. (Ersted first, and then Ampere, proposed
the plan of a telegraph, using the deflections of a magnetic needle for signals; the
type of Wheatstone's needle telegraph; but their suggestions were never put in
practice. In 1823, Dr. F. RONALDS, of England, published a volume detailing
the plan upon which he had previously constructed eight miles of electric telegraph, and in which he used a movable disc, carrying the letters, the type of all
dial telegraphs. In 1825, WILLIAM STURGEON, of Woolwich, England, made the
first electro-magnet of soft iron, without which, further progress in the electromagnetic telegraph was impossible. Prof. JOSEPH HENRY, in 1830, described a
mode of giving greater power to electro-magnets, and the same philosopher, in
1831, devised the first reciprocating electro-magnet and vibrating armature,
including also the principle of the relay magnet, so indispensable an auxiliary in
the Morse system. (Am. Jour. Sci. [1] XX. 340.) In 1834, Messrs. WEBBER
and GAUSS established an electro-magnetic telegraph at Gottingen, between the
Observatory and the Physical Cabinet of the University, and used it for all the
purposes of scientific communication.
In 1836, Prof. J. F. DANIELL invented the constant battery (874), without
whien any mode of electric telegraph would have been futile.
In 1837-a year ever memorable in telegraphic history for the first general and
successful introduction of the electro-magnetic telegraph-and almost at the same
time appeared MORSE, in the U. S.; STEINHEIL, at Munich; and WHEATSTONE
and COOKE, in England; as distinct and independent claimants for the honor of
this discovery. Prof. J. D. Forbes, the able historian of the Physical Sciences,
in the eighth edition of the Encyclopedia Brit. America, speaking of these
inventions, says: "the telegralh of the two last (Steinheil and Wheatstone)
resembles in principle (Ersted's and Gauss's: that of the first (MORSE) is entirely
original, and consists in making a ribbon of paper move by clock-work, whilst
interrupted marks are impressed upon it by a pen," &c. - "  " The ttlegraphs
of Morse have the inestimable advantage, that they preserve a permanent record




618            PHYSICS OF IMPONDERABLE AGENTS.
of the despatches which they convey." This advantage, it is but just to say,
they share with Bain's electro-chemical telegraph.
922. The  earth  circuit.-Although  Drs. Watson  ard Franklin
(1747-8) used the earth as the return circuit in their telegraphic experiments, it was considered essential in the use of Voltaic electricity to employ at least two wires, until Steinheil, in 1837, in the construction of his
telegraph at Munich, dispensed with the whole resistance of the return
wire by burying a large plate of copper at each station, with which the
circuit wire communicated. This certainly must be esteemed one of the
most important discoveries in connection with the telegraph; but from
some cause or other it obtained for some years but little publicity,
although described at length in the Conptes-Rendus, of Sept. 10, 1838.
Bain re-discovered the same fact some years later, and Matteucci, of
Pisa, in 1843, made experiments which convinced the most incredulous
of the truth of this important fact.
Fig. 683 illustrates the mode of using the earth circuit, now universal in all
telegraphs. S and S' are two distant stations, with their batteries, b b', and magnets m m'. A wire passing over insulating posts, through the air, connects S and
S'. One pole of each battery is connected with the earth through the magnets,
683
"endig in pls of copp. N    er batery wil, howeer, act, uess 
ending in plates of copper, P P'. Neither battery will, however, act, unless one
of the breaks, or finger-keys, S or S', is depressed. If the finger-key, S, is
depressed, the circuit consequently is completed through the earth, for the battery, b, while that of b' remains open. The arrows show the course of the
current, and this will be reversed when the circuit at S is closed. The explanation of this curious fact appears to be, not that the electricity is conducted back
by the earth to its origin at the battery, buttthat the molecular disturbance in
which the polarity of the circuit consists, is effectually relieved by communication with the common reservoir of neutral electricity (815), and so conduction
proceeds without interruption. Any number of parallel currents may thus coexist without interference. This simple device saves not only half the expense




ELECTRICITY.                          619
of constructing lines, but it more than doubles their power of electrical transmission. For the rapidity of the current, refer to j 818.
923. Varieties of electro-telegraphic communication.-There
are essentially but two modes of electro-telegraphic communication,
viz.: the electro-mechanical and the electro-chemical. Various and seemingly unlike as are the numerous ingenious contrivances for this purpose,
they all fall under one of these two divisions.
The electro-mechanical form of telegraphic apparatus, embraces
the needle telegraph, the dial telegraphs, and the electro-magnetic, or
recording telegraphs: both those which, like Morse's, use a cipher, and
those, like Iouse's, which print in legible characters.
The electro-chemical telegraphs (having their type in Soemmering's original contrivance) depend on the production of a visible and
permanent effect, as the result of some chemical decomposition at the
remote station; of these, Bain's is the best known.
This is not the place, had we time, to give all the details of the wellknown machines in use for telegraphic purposes. A few words, stating
the principles on which they all depend, with a notice of two or three
of those most used in the United States, must suffice.
As the needle telegraph of Messrs. Wheatstone and Cooke (depending on the deflection of a needle by a galvanometer coil) has never been
used in this country, and cannot compete with either of the systems
adopted here, it is needless to describe it. It requires one operator to
read the movements of the needle, and another to record the message,
and its average capacity is not over ten or twelve words per minute.
The dial telegraph of Froment, and others, is open to the same objections.
924. Morse's recording telegraph.-Every electro-telegraphic apparatus implies the use of at least two instruments, one for recording,
and one for transmitting the message. Besides these, in most cases
there is need of a relay magnet, which receives the circuit current and
acts to bring into use the power of a local battery, by which the work
of recording is performed. This is requisite because the circuit current
is usually too feeble to do more than establish a communication with
the local battery. Every recording instrument has a clock-work, or
some similar mechanical movement, to carry forward the paper fillet on
which the record is impressed, at a regular rate of motion. Fig. 684
shows the Morse recording instrument.
It consists, essentially, of a simple lever, A, with a soft iron armature, D,
over the electro-magnets, E F, by which the electrical impulses are propagated
to the pen or stylus, o. A weight, P, gives motion to a train of wheels, K C, by
which the fillet of paper, pp,'s carried over the rollers, G H, in the direction of




620              PHYSICS OF IMPONDERABLE AGENTS.
the arrows. A feeble spring, r, withdraws the point, o, and armature, D, when
the electricity ceases, and the motion of the pen-lever is farther adjusted by two
684

regulating screws, m M, that can be set at pleasure.  The battery current enters
the apparatus at the binding screws, a b.
The message is recorded by a cipher of dots and dashes, made on the moving
fillet by the point of the pen-lever. The lever moves in obedience to the impulses
of the operator at the transmitting station, who presses the "finger- key," for a
longer or shorter instant, according to what he would transmit. Every motion
of the pen-lever gives a sound, corresponding to the letter communicated; and
to a practiced operator, this sound becomes a definite language, which his ear
interprets with unfailing certainty,                  685
so that he literally hears the message and translates it without the
necessity of looking at the record.
Fig. 685 shows the spring finger-key ],
by which messages are transmitted.
The Morse instrument has the ad- 
vantage of great mechanical simplicity, so that it requires but little K
skill to manage it, and its record      l
being permanent and  sufficiently 
rapid for all ordinary purposes, it 1         1 11 1
has come into more general use in
the United States than any other, and over the continent of Europe has also been
very generally adopted. Mr. Morse conceived this plan of telegraphic transmission in 1833, but it was only in 1837 he applied for his first patent, and in
1844 the first line was built in the United States, from Washington to Baltimore.
925. House's electro-printing telegraph.-This most ingenious
instrument records its message in plain printed characters, and, as a
mechanism, must be regarded as one of the most wonderful results of




ELECTRIOITY.                             621
inventive genius.  A  drawing of its chief parts, some of the details
being omitted, is seen in fig. 686.
Its chief parts are a key-board, marked with the letters of the alphabet; a
6S6
type-wheel, o, on which the letters of the alphabet are engraved; ahelical coil
of fine wire in the cylinder, A, in connection with the circuit, and which operates to open a valve for the emission of a blast of air, compressed by a pump
under the table into a reservoir, B. The purpose of this blast is to work the
escapement regulating the motions of the type-wheel, o.  This is the only
function of the electricity in the recording machine; every other motion is a
mechanical one. The electricity, by opening and closing the air-valve, regulates
the motion of the type-wheel, arresting it at the pleasure of the operator at the
distant station, who, by touching on his key-board the letter he would transmit, arrests the type-wheel of the recording instrument at that letter; a simple
mechanism then presses the fillet of paper on the face of the type, and moves
it forward to receive the next impression.  Its actions are quicker than
thought, and, owing to the exact duality of the two machines in every part, and
the perfect equality of their motion, the operator transmitting is as conscious as
him receiving, if there is any error, aided as he is by a tell-tale above the typewheel, showing, in our design, the letter A. It is impossible, without many
pages of detail, and minute drawings of the parts, to render this marvel of
mechanical art perfectly intelligibl. But the general thought of the inventor
is clear enough, to place the recording apparatus at the control of the transmitting operator, through the agency of compressed air, controlled by the electric
current, and controlling, in its turn, the escapements of the recording apparatus.
It prints about one hundred letters per minute, on a circuit of one hundred and
fifty miles.
926. The electro-chemical telegraph depends on the decomposition, by the electrical current, of a salt of iron with which the paper
fillet is saturated, and the production of a blue or red stain upon it.
The same clock-work movement used by Morse, carries forward the
paper over a metallic cylinder, which is one pole of the circuit, while
65




6 2*       PHYSICS OF IMPONDERABLE AGENTS.
a steel pen (if a blue mark is intended, or copper, if red is intended),
in connection with the other pole, bears steadily upon the paper; the
least transit of electric force decomposes the prussiate of potassa with
which the paper is charged, producing a stain. To insure the dampness in the fillet requisite for electrical conduction, Maison-Neuve has
proposed to charge it with a solution of nitrate of ammonia, a salt
whose attraction for moisture is such that the paper remains always
damp.  To avoid errors, as well as to insure greater rapidity, Bain,
who was the author of this system, proposed to prepare the messages,
on fillets of paper, punched with holes by a machine called a compositor
or multiplier. Humaston has lately so improved the mechanism of this
compositor, that it is possible, by combining this apparatus with the
Bain system of reading, to transmit not less than three thousand signals
per minute, equal to six hundred letters, or one hundred and twentyfive words of five letters each. The punched fillets take the place of
the finger-key as a circuit breaker for the transmission of the message.
Autograph telegraphic messages can be transmitted by the electro-chemical method, by writing upon the transmitting cylinder, with
solution of hardened wax, and then causing a tracing point to traverse
the cylinder with a close spiral from end to end. The result is, the
interruption of the current where the wax is, and a corresponding
blank space left on the paper at the receiving station.  The union of
these white spaces gives what was written in wax, as a white character
on a dark ground.
927. Submarine telegraphs-the Atlantic cable.-The first submarine telegraphic cable was successfully sunk in August, 1851, connecting Dover, in England, with France, at Cape Griz Nez. Since that
time, numerous other submarine cables have been laid, of which that
through the Black Sea was the longest, until the placing of the Atlantic
cable was accomplished, on the 5th of August, 1858.  The failure of
this great enterprise is now believed to be attributable to injuries received
by the cable before submergence.  Its failure was gradual,-over 400
messages being transmitted before it became totally inactive.
Fig. 687 shows the size and mode of construction of this cable. The conducting wire is formed of seven strands of No.         687
32 copper, twisted into a cord, and buried in
refined gutta percha, laid on by. machinery in
three coatings, over whiLc are placed several
strands of tarred cord. The whole is encased
in seventeen strands of iron wire, each strand
formed of seven No. 30 iron wires. It weighs
about two thousand lbs. to the nautical mile, and about two thousand miles of
it lie submerged between Valentia Bay, Ireland, and Trinity Bay, Newfoundland. The shore end is formed of ten miles of much stronger cable, enclosing,
however, the same conductor.




ELECTRICITY.                           623
The problem of scientific as well as practical interest in long cables, is the
possibility of transmitting signals through them with sufficient rapidity for
useful purposes. Faraday has shown (Ept. Res. vol. 3d, p. 507-523 and 575),
that a gutta-percha covered wire is, when submerged in water, in very different
electrical conditions from what it is in air. In the water it simulates the character of the electrical condenser, or Leyden vial, and when thus charged by induction, must be discharged before a second wave can be transmitted through it;
and when the electric pulses are frequent, as in telegraphic communications, the
effect of the electric conflict, as (Ersted originally termed it, is to produce a
tremor in place of sharp and decided beats. Those who would know the'history
of the telegraph more in detail, will consult Schaffner's Telegraphic Manual,
and Prescott's History and Practice of the Electric Telegraph, Boston, 1860.
928. Electrical clocks and astronomical records.-If a clock
pendulum  is, by any mechanical device, made to open and close the
circuit in a telegraphic arrangement, it is obvious, that if the clock
beats seconds, these will appear recorded as dots at equal intervals
upon the paper fillet. An astronomer, watching the transit of a star
across the wires of his telescope, with his hand upon the finger-key of
the same circuit, closes it at the exact instant of time, and the record
of the passage of the star is fixed with unerring certainty between the
beats of the clock and upon the same fillet which bears record of the
time in seconds and their subdivisions. This beautiful system is wholly
and peculiarly American, as the clear records of science show, and
offers incomparably the best possible mode of determining longitude
differences. The names of Bache, Bond, Gould, Locke, Mitchel, Saxton, Walker, Wilkes, and others, are inseparably connected with the
history of this important application of the telegraph, for-the details
of which the student is referred to the American Journal of Science,
the proceedings of the American Association for the advancement of
Science, and the reports of the United States Coast Survey.
Bain, it is believed, constructed the first electrical clock (in 1842), which was
moved by a current from a large copper and zinc plate buried in the earth, or,
better, to a zinc plate buried in charcoal. By any simple mechanical arrangement, the motion of the pendulum reverses or breaks the current at every beat,
and by the aid of a stationary magnet, the vibratory movement due to the electric current is strengthened and perpetuated. It is possible to transmit the
same electric current to any number of clocks, in the same place, or in different
places, and thus secure exact equality of time.
Fire-alarm.-Boston, Philadelphia, and some other cities are provided
with a telegraphic system due to Dr. Channing and Mr. Farmer, by which a
fire-alarm is sounded simultaneously in every district: a detailed description of
which will be found in Am. Jour. Sci. [2], XIII., 58.
5. Electro-dynamic Induction.
I. INDUCED CURRENTS.
929. Currents induced from other currents.-Volta-electric




624           PHYSICS OF IMPONDERABLE AGENTS.
induction.-The phenomena, of electro-magnetism  seem to point, as
an almost necessary consequence, to the discovery made by Faraday, in
1831-2, of induced currents, as well as of magneto-electricity. Faraday
argued thus:1st. That as a wire carrying a current acts like a magnet, therefore it
ought, by induction, to excite a current in another wire near it.
2d. That, as magnetism  is induced by electric currents, so magnets
ought also, under proper conditions, to excite electric currents.
The first of these theses Faraday sustained thus: Let a double helix,
or bobbin, be wound of two parallel silk-covered wires, about a cylinder of wood (which being withdrawn afterwards, leaves the helix hollow), in close contact, but perfectly insulated, so that the two wires
run side by side through their whole course. Let the ends, a b, fig. 688,
of one wire be connected with a                 688
galvanometer, or magnetizing spiral, while a battery current enters      i 
out by d.  When contact is made  
between c and the battery, the 
galvanometer needle is deflected                             e
by a current moving in the same 
direction with the battery or primary current. This deflection, however, is only for a brief instant.
After a few vibrations, the needle comes to rest, although the battery
current still flows. Break now the contact between the wire, c, and
the battery, and the galvanometer needle is again deflected by a secondary or induced current; but this time it moves in the opposite direction
to the first. These are called secondary or induced currents. They are
momentary, but are renewed with every interruption of the battery
circuit, and their strength is always proportional to the strength of the
primary or inducing current.  If a mass of soft iron (or, better, a
bundle of soft iron wires) is placed in the core of the helix, the force
of the induced currents is greatly increased. This action of a current
from a Voltaic battery, Faraday called Volta-electric induction.
The phenomena of influence (828) in electricity present a strong
analogy to these facts, and support the probability that the secondary
currents in the case of Voltaic induction, are also due to decomposition of the natural electricity of the second wire, by the current on
the first. In fact, a current of statical electricity may be substituted
for the Voltaic current with similar results, as was shown by Henry,
in 1838 (Trajs. Am. Phil. Soc., vol. 6, N. S., and Am. Jour. Sci. [1],




ELECTRICITY.                          625
XXXVIII., 209). Fig. 689 is a convenient form of apparatus designed
by Matteucci, for this experiment. Two coils of insulated wire, A B,
are sustained on movable feet, ad-                 689
mitting of near approach.  When                        A
the charge of a Leyden jar, D, is            ^
passed through the coil c d on A, a
person whose hands grasp the con-               S              D
ductors, ih, of the coil, B, will re-  J 
ceive a shock, the violence of which        a
increases with the closer approach     
of A and B. The direction of the current in B, is the reverse of that
in A. If a galvanometer is inserted in the circuit ih, its needle is
deflected, or, if a magnetizing spiral is used, needles may be magnetized
by it.
930. Induced currents of different orders.-By using a series of
flat spirals of copper ribbon alternating with helices of fine insulated
copper wire, arranged as in fig. 690, Prof. Henry (in 1838) demonstrated
690
\W              --  B    f
that secondary or induced currents produced other induced currents of
the second, third, fourth, and so on, as far as the ninth order. Thus, the
flat spiral, A, receiving the battery current, induces, at every rupture
of that current, a secondary intense current of opposite name in B,
while the second flat spiral, C, receives from B a quantity current,
inducing a tertiary intense current in the second fine wire spiral, W,
and so on. The signs + and -  alternate after the first remove from
the battery current, as is easily demonstrated by inserting magnetizing
spirals in the conducting wires, and using steel sewing-needles as tests.
A screen or disc of metal introduced between any two of      691
these coils, cuts off the inductive influence.  But if the
screen has a slit, a b, cut from the centre to the circum-  ^ 
ference, as in fig. 691, the induction is the same as if no
screen were present. Discs or screens of wood, glass, paper, or other
non-conductors, offer no impediment to this induction.
55 *




626          PHYSICS OF IMPONDERABLE AGENTb-.
930. Extra-current, or the induction of a current on itself.The effect of a long and stout conductor in giving a vivid spark and
shocks from a single cell (which alone, or with a short conductor, gives
neither sparks nor shocks), was first noticed in 1832 by Prof. Henry.
(Am. Jour. Sci. [1], XXII., 404.) This fact was afterwards the subject
of investigation by Faraday, in December, 1834, and also by Henry,
in January, 1835. The arrangement used by Prof. Henry is seen in
fig. 692. A small battery, L, is connected with the flat spiral of cop692
per ribbon, A, by wires from the battery cups, Z and C; when this
communication is broken by drawing the end of one of the battery
wires, Z, over the rasp, a brilliant spark is seen at the instant of breaking contact. No spark is drawn on making contact. Moreover, if a
fine wire coil, W, is placed in the relation to,A shown in the figure,
there is only a feeble spark seen on breaking the battery contact, —
while the powerful. secondary current already named is set up in W,
violently convulsing the hands which grasp its terminals. The strong
spark from the large flat coil or single wire in the first case, is then the
equivalent of the current which would be produced in the second case,
if such current were permitted. This reflux current induced on a conductor, and the outflow or recoil of which produces vivid sparks, is
what Faraday calls the extra current. In powerful coils, this extra
current produces sparks, the report of which resembles the explosion
of a pistol, especially under the inductive influence of a powerful electro-magnet, as in the engine of Dr. Page, already noticed. The heavy
coils of this apparatus produced sparks from the extra current from
two to six inches in length, and having the same rotative action as the
conductor itself. (Am. Jour. Sci. [2], XI., 191.) Many forms of electro-magnetic apparatus, in which two coils are combined, show the
extra current in a striking manner, as in:931. Page's vibrating armature and electrotome.-In this apparatus, fig. 693, the flow of the battery current is interrupted by the
movements of the bent wire, P W 0.  At M  is a bundle of soft iron




ELECTRICITY.                         627
wires, forming the core of the inducing coil. Becoming magnetic, these
attract a small mass of iron on the end of P to M. This movement
raises the other end out of the mercury in the cup, C, with a brilliant
spark, due to the flow of the                   693
extra current, the magnetism
having disappeared by the            A  )
break  of the battery flow.
Gravity then restores the wire    P    I( 
to its original position, thus
renewing the battery current
and the magnetism, and with
it the spark in C. A fine wire                     ~ ~._ -
induction coil of two thousand
or three thousand feet, wound about the inducing coil, develops the
secondary currents already noticed, with powerful physiological and
other inductive effects, resembling statical electricity.
932. Induced currents from the earth's magnetism.-The earth's
magnetism also induces electrical currents in metallic bodies in movement; another of the discoveries of Faraday. For this purpose, a helix
in the form of a ring is made to revolve with its axis at right angles to
the magnetic meridian, and, consequently, each point of the ring describes circles parallel to the plane of this meridian. A pole changer
on the axis is so arranged as to keep the induced current moving always
in the same direction; when so arranged, and its terminal wires are connected with a galvanometer, a deviation of the needle indicates the flow
of a current to the east or the west, according to the direction of the
rotation.
933. Conversion of dynamic into static electricity.-The induction coil.-By careful insulation of the secondary coil of fine wire
-as well in itself as from the primary or magnetizing wire-electricity
of high tension is produced, surpassing, in energy and abundance, that
from machines of the greatest power.  Masson, in 1842, first succeeded
in obtaining these results, but in a very feeble manner compared with
those we now know. Ruhmkosff, of Paris, in 1851, constructed the
coils which bear his name.  By careful insulation of the fine wire
coil, he succeeded in producing sparks of about two inches in length
between the electrodes, charging and discharging a Leyden jar wift
astonishing rapidity. No electrical instrument has, in modern times,
been more celebrated.
Ritchie, of Boston, has so vastly improved this apparatus, as to deserve the highest praise from all interested in physical research.
Ritchie's form of the induction coil is shown in fig. 694. The cause




628            PHYSICS OF IMPONDERABLE AGENTS.
of the superiority in the American apparatus is due chiefly to the
mode of winding the fine wire coil, by which it is possible to use with
success a wire of eighty thousand feet in length, while the limit in the
instruments made by Ruhmkorff was about ten thousand feet.  The
extreme length of spark obtained by the European instruments, was,
for the French, about two inches (Jean's); and for the English, four
inches (Hearder's); the American instruments have projected a torrent
of sparks over sixteen inches in free air; while the one shown in fig. 694,
is limited to about nine inches.
The chief parts of this apparatus are the two coils, an interruptor to the primary circuit, and the condenser.               6
In the instrument here figured,
over sixty-eight thousand feet
of silk-covered  copper wire,
the softest and purest possible,
twelve thousandths of an inch
in diameter (No. 32 of the wire  
gauge), is wound upon the exterior bobbin, C. About two
hundred feet of wire, oneseventh of an inch in diameter 
(No. 9), forms the inducing
wire, whose ends + and - are
visible in the binding screws
on the base. A heavy glass 
bell, a, insulates the coils from   e
each other, and its foot is = 
turned outwards by a flange as
wide as the thickness of the
coil. The induction coil, for 
more perfect insulation, is also 
encased in thick gutta percha. The ends of this coil are carried by gutta-percha covered conductors, to two glass insulating stands (only one of which is
visible in our figure), where they end in sliding rods pointed with platinum at
one end, and having balls of brass at the other. The interrupter devised by
Mr. Ritchie, is the toothed wheel, b, which raises a spring hammer, the blows
of which fall upon the anvil, o, breaking contact between two stout pieces of
platinum. fhe European machines are provided with a self-acting breakpiece; but experience has shown, by comparative trials, that there is an
advantage in varying the rapidity of the interruptions, according to the class
of effects to be produced, and that a certain time is requisite for the complete
charge and discharge of the soft iron wires (which form the core of the battery
circuit), longer than the automatic break-piece allows.
The object of the condenser (which is due to Mr. Fizeau) is to destroy, by
induction, the greater part of the force of the extra current, which, owing to the
very powerful magnetism developed in the core of soft iron within the battery
coil, would otherwise greatly impair the power of the apparatus, as it moves in
i direction opposite to the primary current (931). The condenser consists, in.he instrument figured, of one hundred and forty square feet of tin-foil, divided




ELECTRICITY.                         629
into three sections (two of 50, and one of 40 feet), whose termini are at e. The
tin-foil of the condenser is carefully insulated by triple folds of oiled silk, and
laid away in the base of the instrument, in a cell. prepared for it, quite out of
view.
The batteryforce needed to excite this apparatus, is only two or three largesized cells of Bunsen's battery.
934. Effects of the induction coil.-The physiological effects are
so distressing and even dangerous, that too great care cannot be taken
to avoid them. M. Quet was confined to his bed for some time, after
having accidentally received the shock. Small animals are instantly
killed by its discharge.
The luminous effects.-When a series of sparks passes between
the points of platinum, or between the balls, they are of a zigzag form,
and accompanied by a loud noise and a strong odor of ozone. Their
color is violet and yellowish, or greenish yellow. If the points are
within an inch or two, the stream of sparks appears to be continuous,
a fourth of an inch broad, surrounded by a violet areola, and crossed
by numerous lines at right angles to its path. If it is blown by the
breath, or by a bellows, it is deflected into a curve, and a bright flame
is seen projected for some distance beyond the purple or violet stream
of electric light. The color of the flame varies with the nature of the
electrodes (885). If one of the electrodes is covered by a small glass
flask, the power of the induction is such that a stream of violet electricity is seen, as it were, to pass directly through the glass, while the
ball of the flask is covered with a magnificent net-work of violet light,
spread out like the blood-vessels upon the eye-ball.
If an AEpinus condenser, or a Leyden jar, is put in the path of
the current, the length of the spark is much diminished, but its
intensity and splendor are increased twenty-fold. The electric light
then becomes intensely white, and the sound of the explosion of the
successive sparks, when these are drawn by a slow movement of the
break-piece, is like the snap of fulminating mercury, or the sound of a
pistol, while the electric stream appears continuous. If a Newton's
chromatic disc is caused to revolve before it, each sparks causes the
colors of the revolving disc to appear stationary, although without this
evidence of an intermittent character, the stream of electricity would
appear to be unbroken.
Splendid phenomena of fluorescence with canary-colored glass-chemical
decompositions, deflagrations of the leaf metals, discharges of flashes of lightning over the surface of a metallic mirror, a gilded board, or wet table, and
numerous other most beautiful and instructive experiments, are made with this
apparatus. Indeed, nearly all the phenomena of static electricity are shown by
it, and some of them with a power which no frictional apparatus can approach.
It iu curious to observe, that the sparks of this kind of electricity pass freely




630           PHYSICS OF IMPONDERABLE AGENTS.
from pointed wires (826). If two fine iron wires are used as the electrodes, the
negative wire alone reddens and burns, unless the current is very energetic. All
the apparatus used for showing the luminous effects of machine electricity,
g 852, may be employed with this apparatus with vastly greater brilliancy.
The chemical effects of the induction coil are shown in the decomposition of water, &c., while a stream of sparks from it, passed through
a tube containing air, soon causes the production of reddish vapors due
to the formation of hyponitric acid from the union of the elements of
the air.  Mr. Gassiot has lately shown (Phil. Mag. Aug. 18G0) that the
intensity of the coil is such as to transmit electrolytic effects across
glass, or apparently through the walls of a Florence flask.
935. Light of these currents in a vacuum.-The difference between the light from the positive and the negative electrodes has
already been noticed. Owing to the absence of intense effects of heat
in the currents from  the induction coil, they           695
are particularly adapted to illustrate this difference, especially in vacuo.
In a vacuum tube, or the electrical egg well
exhausted, a torrent of rosy or violet fire falls,
from  the positive electrode above, toward the
negative, which is surrounded with a blue and  
white light, extending down the stem, with
splendid fluorescence (533). If the vacuum  is
made.upon vapor of turpentine, or of phosphorus
in the egg, or in an auroral tube, a most wonderful phenomena shows itself; the stratification
of the electrical light in alternate bands of light
and darkness, surrounding and depending from
the positive pole, as indicated in fig. 695. This
curious phenomenon was first observed by Mr.
Grove.  Vapor of alcohol, wood-naptha, biclorid
of tin, or bisulphid of carbon, may be used, each
with a different effect.
Mr. Gassiot has studied with great care the
character of the spark in vacuums formed on 
various gases and vapors, and has established
the curious fact, that in a perfect Torricellian
vacuum, the spark will not pass, showing that -- 
an extremely tenuous vapor is essential to its passage.  These facts
bear in an important manner on the phenomena of the Aurora Borealis.
Gassiot's cascade in vacuo.-If we place in a vacuum  a goblet
coated with tin-foil in the manner of a Leyden jar, and carry the indue



ELECTRICITY.                         631
tion current to its bottom by means of a wire passing through the cap
of the air-bell, as in fig. 696, the other electrode being in communication
with the air-pump plate on which the whole appa-         696
ratus stands, we are delighted to see, when the current is established from the induction coil, the vase
overflow like a fountain with a gentle cascade of
light, wavy and gauze-like, falling like an auroral
vapor on the metallic base. This experiment re-1
quires a very good vacuum, and is certainly one 
of the most beautiful exhibitions in luminous electricity.
936. Rotation  of the electric light about
a magnet.-We here recall the early observation of Davy, ~ 883, on the influence of a magnet rl
on the Voltaic arc. If an electro-magnet is enclosed in the electrical egg, and a very perfect vacuum  is made within it, when the
induction current is caused to flow, the electrical      697
stream is seen to revolve in a steady and easy man-       +
ner about the magnet, the direction of its motion
corresponding to the polarity of the magnet. In
fig. 697 is shown such an apparatus.  The magnet
here is a bundle of soft iron wires enclosed in a
glass tube, and passing through the foot, so that    j 
when the instrument is placed on one pole of an  
electro-magnet, the mass of wires may be magnetized 
inductively. Two platinum wires + and -  pass in 
glass tubes hermetically through the walls of the 
vessel, into the vacuum and form the points of attach-  1
ment for the electrodes.
937. Applications have been made of the induction current for firing blasts and sub-aqueous magazines, and also for lighting simultaneously all the gas burners in a large
audience room or theatre.
Electrical blasting by Ruhmkorff's coil is easily accomplished by the
use of Stateham's fuse, fig.                  698
698, which is only a gutta-per- (    +"  A
cha covered conductor, A B,  
in which the discharge is interrupted at points, a b, buried
in the gunpowder, producing 
its combu tion, even at a dis-  B
tance of many miles, and in many distinct mines, or blast holes, sue




632           PHYSICS OF IMPONDERABLE AGENTS.
cessively, but almost at the same instant. Dr. Iare first employed his
calorimotors for electrical blasting ii 1831. (Am. Jour. Sci. [1] XXI.
139.) But the use of an extended battery, and all uncertainty, is
avoided by using the induction coil. Ruhmkorff, in experiments made
at Villette, inflamed gunpowder with this coil through about sixteen
miles. In excavating the Napoleon docks at Cherbourg, lately, over
65,000 cubic yards of rock were thrown out by one series of blasts fired
in this way.
II. MAGNETO-ELECTRICITY.
938. Currents induced by magnets.-If the helix in fig. 699 is
connected with a galvanometer, and a bar magnet is quickly thrust
into, and suddenly withdrawn from it,             699
the needle of the galvanometer indicates the movement of a current of
electricity opposite in the two cases,
and whose direction in each case is
opposite to that of a current which, on 
Ampbre's theory, would produce a
magnet like the one employed. It is
hardly needful to say that reversing
the ends of the bar magnet, reverses the movements of the galvanometer. This is a case of magnetic electric induction.
This fact is also illustrated in other modes, viz.:a. By revolving a circular plate of copper between the poles of a
horse-shoe magnet (arranged in general like fig. 678), the axis of the
700
copper being in connection with one pole, and the edge with the other,
a series of sparks may be obtained, as in Faraday's original experiment,
some device being inserted to interrupt the current during the revolution.




ELECTRICITY.                            633
b. By a helix on the armature of a magnet, the ends of the helix being
connected with the poles respectively, on suddenly sliding the armature
from the poles of the magnet, a spark is seen, and if the fingers grasp the
wires at the same time, a shock follows. This fact was first announced
in December, 1831, by Srs. Nobili and Antinori.  Saxton constructed
the first magneto-electric machine in which the armature, wound with
a helix, was made to revolve in front of the poles of a magnet, and so to
reproduce all the phenomena of static and voltaic electricity from permanent magnets.  Fig. 700 shows an improved form of Saxton's apparatus, where the double inducing coil revolves by means of a motor
wheel and band between the poles of two powerful magnetic batteries.
The magnetic-electric-induction is interrupted by the little crown-wheel
seen on the upper end of the axis of the revolving coils.
Clarke's magneto-electric apparatus.-This apparatus is a modification of Saxton's, and consists of a                701
powerful magnetic battery, A, fig. 701,
clamped on the upright board, PR, by the
clamp C. The wheel, F, puts in motion
two helices, H G, wound upon a rotating                111
armature of soft iron. The electrical current induced in the coils is interrupted by
the spring, or hook, Q, which rubs on the
interrupted back piece, H, while the circuit!
is completed by the hook, 0, passing upon 
the continuous part of the spindle, R. A
stout wire, T, movable at pleasure, con-                        Hll
nects the two sides, M and N, otherwise
insulated by the piece of dry wood, L. 
When the coils are rapidly rotated before
the poles of the magnet, the current is in-  
terrupted twice in every revolution by the
hook, Q, with the production of a brilliant
spark. If the coils are composed of a long
and fine wire, then powerful shocks will be
experienced by one holding the handles R
and S, but capable of a great graduation, by changing the position of the breakpiece, H, with reference to the point of the revolution when it leaves Q. These
shocks may be made quite intolera-                   702
ble.
If the conducting wires of the
intensity coil terminate in a decom- 
posing apparatus, fig. 702, trains 1
of minute gas bubbles are seen to
rise from the platinum points under              
the tubes, showing the production 
cf dynamic from magnetic electricity. Other effects of the intense
class, as the decomposition of iodid
of potassium, may also be produced with it. Substituting a coil of large wire
56




634            PHYSICS OF IMPONDERABLE AGENTS.
not over two hundred feet long, for the small long wire, the quantity armature is
produced, from which brilliant sparks, the deflagration of mercury, and setting
fire to ether, as in fig. 703, may be produced; mercury, in a copper spoon, B, is
touched by the revolving points, A, on the end           703
of the axis, d, and with every disruption of
the circuit, the extra current discharges with
splendid effect. A platinum wire may also be
ignited, and electro-magnets charged by the       A 
same armatures. Thus we see all the effects of  
electricity, physical and physiological, coming
from a magnet.
939. Identity   of  electricity  from 
whatever source.-It follows from  all
that has been said, that the phenomena of
magnetic, static, and dynamic electricity,  pX l
are all capable of being produced each by 
the other; and the conclusion seems war-               I
ranted tha-t electricity, from whatever source, is one and the same
power.
Numerous and instructive forms of apparatus have been devised to demonstrate this point, as well also as to illustrate in detail, the principles we have,
for want of space, been compelled to state in terms too concise. The student
and teacher will find it useful to consult the figures of Davis's Manual of Magnetism for various forms of apparatus, due to the ingenuity of Faraday, Dr. Page,
and many others. For works of standard authority, he is referred to Faraday's
experimental researches, and De La Rive's treatise on electricity, each in three
volumes.
2 6. Other Sources of Electrical Excitement.
940. Universality of electrical excitement.-Every clinne in
the physical or chemical condition of matter, seems to be attended
with  electrical excitement.  This is evident from  the phenomena
attending the cleavage, or.pulverizing, of many minerals and crystallized substances, as sugar, mica, zinc-blende, and numerous other
substances which evolve light when suddenly cleaved. If precautions
are taken to insulate these, as with mica it is easy to do, by sealing
wax, they also show the effects of electrical excitement by the condenser. The production of crystals is often also accompanied by electrical light.
Combustion, evaporation, the escape of gas attending chemical transformations, chemical decompositions and combinations, have all been
known to evolve electricity when properly observed; but in most such
cases, the phenomena are too complicated to render it clear to which,
if indeed to any single action of those enumerated, the excitement is
due.




ELECTRICITY.                         635
The electrical currents set up by heat (thermo-electricity), and those
arising from the phenomena of life (animal electricity), are the most
important of all sources of electricity not before dwelt on, and to them
we will now briefly advert.
I. TIERMO-ELECTRICITY.
941. Thermo-electricity.-The discovery of this source of electrical currents is due to Seebeek, of Berlin, in 1821. He found that
if two metals of unlike crystalline texture and conducting power are
united by solder, and the point of junction is either heated or cooled,
an electrical current is excited, which in general flows from the point
of junction to that metal which is the poorer conductor. Fig. 705
shows such an arrangement of two little bars of bismuth and antimony. When the junction, e,              704                705
is heated, a current of positive   
electricity flows from  the bismuth, b, to the antimony, a. If
the form of a rectangle is given                                 \\_
to this arrangement, as in fig.  __ 
704, an instrument resembling  /  
Schweigger's multiplier is form-.~."                     -
ed (905), by which the magnetic needle is deflected. A twisted wire
also produces a thermo-electric current when the twisted portion is
gently heated, and, besides metals, other solids, and even fluids, give
rise to this species of electricity. The order in which the metals stand
in reference to this power is wholly unlike the Voltaic series, and
appears related to no other known property of these elements. The
rank of the principal metals in the thermo-electric series is as follows,
as determined by Becquerel: —The numbers prefixed give the order of
each metal in the table of specific heats as determined by Regnault.
Those having the highest specific heat, as a general rule, being first in
positive power (+) in the thermo-electric magnet: 6 antimony; 1 iron;
2 zinc; 4 silver; 7 gold; 3 copper; 5 tin; 9 lead; 8 platinum; 10
silver.
When the junction of any pair of these is heated, the current passes
from that which is highest, to that which is lowest in the list, the extremes affording the most powerful combination.
Becquerel has found the intensity of the current in a thermo-electric
combination to be proportional to the difference of temperature in the
solderings up to 100~ or 120~ F., one of the points being at 32~. Above
this limit, the increase of intensity is less and less, with an increase of




636           PHYSICS OF,IMPONDERABLE AGENTS.
heat. In a couple of copper and iron, the increase of current was in.
sensible near 570~ F.
In a compound thermo-electric series, intense effects, analogous to
those of the Voltaic pile, are obtained only when half   706
the solderings are heated, the alternates being
cooled.
Thermo-electric motions.-If a compound ring
of brass and German-silver is suspended within the
poles of a magnet, as in fig. 706, when the soldering
of the ring is heated, a revolution is set up, through
the influence of the magnet on the electric current,
quite analogous to similar electro-magnetic motions.
Cold produced by electrical currents.-If we
pass a feeble current of electricity through a pair of
antimony and bismuth, the temperature of the system
rises, if the current passes from the former to the
latter; but if from the bismuth to the antimony, cold is produced in
the compound bar. If the reduction of temperature is slightly aided
artificially, water contained in a cavity in one of the bars may be frozen.
Thus we see that, as a change of temperature disturbs the electrical
equilibrium, so, conversely, the disturbance of the latter produces the
former.
942. Melloni's thermo-multiplier.-We have already alluded to
this delicate metallic thermometer, ] 588, and have shown its application in the phenomena of dia-          708               707
thermancy (642). This instru- 
ment consists of a series of  
small bars of antimony and bis-.         -
muth, a and b, fig. 707, soldered                         
together at their alternate ends.    I' " I
Two wires connect the opposite. 
members, n and m, fig. 708, of   6this battery, with a galvanometer. The needle of the galvanometer is suspended over a graduated circle, and moves in exact
accordance with a thermo-electric current produced by the battery.
The least difference in temperature between the opposite faces of this
battery, produces a thermo-electric current, deflecting the needle of
the galvanometer, fig. 658, as already explained in ] 642.
It. ANIMAL ELECTRICITY.
943. The galvanic current.-We have already spoken of the di.




ELECTRICITY.                         637
covery by Galvani of electrical currents in animals, living, or recently
dead, flowing from the outer or cutaneous, to the inner or    709
mucous surface.  Thus, when contact is made between the
muscles of the thigh and the lumbar nerves, by bending
the legs of a vigorous frog, fig. 709, contractions immediately follow. Aldini, who was a zealous advocate of
Galvani's views, during the controversy between the followers of Galvani and Volta, demonstrated the existence
of such a current in other animals by the legs of a frog used
as a galvanoscope.  For this purpose, he brought the
lumbar nerve of a frog, held as in fig. 710, in contact with
the tongue of an ox lately killed, while the hand of the operator, wet
with salt water, grasped an ear of the ani-          710
mal to complete the circuit.  The legs were
then convulsed as often as the nerves touch
the mucous surface of the tongue. The same
delicate electroscope also shows similar excitement when its pendulous ischiatic nerves
touch the human tongue,-the toe of the
frog being  held between  the moistened   I 
thumb and finger of the experimenter.
Matteucci, of Pisa, in 1837 (forty years
after Galvani's result was obtained), has the -/    -
merit of reviving Galvani's original and correct opinion as to the vital source of this -     
electricity. IIe demonstrated, that a current of positive electricity is
always circulating from the interior to the exterior of a muscle, and that,
although the quantity is exceedingly small, yet, by arranging a series of
muscles, having their exterior and interior surfaces alternately connected, he produced suffi               711                   712
cient electricity to cause
decided effects. By a series  (        4 
of half thighs of frogs, 
arranged as in fig. 711, he 
decomposed the iodid of
potassium, deflected a galvanometer needle to 900, and, by
a condenser, caused the gold leaves of an electroscope to
diverge. The irritable muscles of the frog's legs form  an
electroscope fifty-six thousand times more delicate than the
most delicate gold-leaf electrometer. When the pendulous
nerve of a single leg, arranged in a glass tube, as in fig. 712,
is touched in the places where electrical excitement is suspected, the
56 




638           PHYSICS OF IMPONDERABLE AGENTS.
muscles in the tube are instantly convulsed.  Dil Bois Raymond, of
Vienna, has demonstrated the existence of these currents, in his own
person, by the use of the galvanometer, for which purpose the muscles
of the hands and arms are alternately contracted on a metallic bar in
connection with a galvanometer.
944. Electrical animals.-In some marine and fresh-water animals, a special apparatus exists, adapted to produce, at pleasure, powerful currents of statical electricity, either as a means of defence, or of
capturing their prey. Of these, the electrical eel, of Surinam, first
described by Humboldt, and the cramp-fish, or torpedo, a flat fish found
on our own coast, are the most remarkable.  They have an alternate
arrangement of cellular tissue and nervous matter in thin slates of a
polygonal form, constituting a perpetually charged electrical battery,
arranged in the manner of a pile. By touching their opposite surfaces,
a very violent shock is received, such as to disable a very rowerful
man, or even a horse. Prof. Matteucci has shown us how to charge a
Leyden jar, by placing the torpedo between two plates, arranged like
the plates of a condenser; and Faraday has published an interesting
account of his experiments with the eels of Surinam, from which he
not only obtained shocks, but made magnets, deflected the galvanometer, produced chemical decompositions, evolved heat and electrical
sparks. (Expt. Res. 1749-1795.) The student is also referred to Prof.
Mattfucci's interesting " Lectures on Living Beings," for further details
on this very interesting subject, and to a memoir, on the American
Torpedo (Dr. D. H. Storer, Am. Jour. Sci. [1], XLV., 164).
945. Electricity of plants.-Pouillet, in his researches on the
origin of atmospheric electricity, made the interesting discovery of the
disengagement of negative electricity during the germination of seeds,
and the growth of plants. This observer estimates that a surface of
100 square yards covered with vegetation disengages, in a day, more
electricity than is required to charge the most powerful Leyden battery.
Currents of electricity have also been detected in fruits, and in the
bark, roots, and leaves of growing plants; the roots, and all internal
parts of plants filled with juice, being, according to Buff, negative with
relation to the exterior or less humid parts.
[For Problems on Electricity, see end of Meteorology.]




APPENDIX.
CHAPTER I.
METEOROLOGY.
946. Meteorology is that branch of natural philosophy which treats
of the atmosphere and its phenomena. The subject may properly be
divided into —st, Climatology; 2d, Aerial phenomena, comprehending
winds, hurricanes, and water-spouts; 3d, Aqueous phenomena, including fogs, clouds, rains, dew, snow, and hail; 4th, Luminous and electrical phenomena, as lightning, rainbows, and aurora borealis.
Our narrow limits of space restrict our remarks on this interesting
subject to a very inadequate rehearsal of its principles. The student
will refer to the works of Espy and Blodget, and the papers of Coffin,
Henry, Loomis, Redfield and others, in the transactions of the American Philosophical Society, publications of the Smithsonian Institution,
the United States Patent Office, andtle American Journal of Science,
for an exhibition of the American results in this science.
2 1. Climatology.
947. Climates, seasons.-By climate is meant the condition of a
place in relation to the various phenomena of the atmosphere, as temperature, moisture, &c. Thus, we speak of a warm  climate, a dry
climate, &c.
A season is one of the four divisions of the year, spring, summer,
autumn, and winter. Astronomical seasons are regulated according to
the march of the sun. In meteorology it is sought to divide them
according to the march of temperature. Winter being the most rigorous of seasons, it is so arranged that its coldest days (about January
15th) fall in the middle of the season. Hence, winter consists of December, January, and February; spring of March, April, and May,
&c. Few meteorologists have regard to the astronomical divisions,
which make winter begin December 21st.
948. Influence of the sun.-The sun is the principal cause that
regulates variations in temperature. In proportion as this luminary
rises above the horizon, the heat increases; it diminishes as soon as it
sets. The temperature, also, depends on the time it remains above the
horizon. The sun, in winter, sends its rays obliquely upon the earth,
and at this season, therefore, less heat is received than in summer,
when its rays are more nearly perpendicular. Mathematicians have
(639)




b40                          APPENDIX.
in vain endeavored to deduce the temperature of days and seasons
from the height of the sun above the horizon. This failure is owing
to many accidental and local causes, which modify the result,-as elevation above the ocean, inclination of the surface, vicinity of seas, lakes,
or mountains, prevalent winds, &c.
949. Meteorological observations, to be compared with each
other, especially when made in different locations, should be made at
certain fixed hours of the day. The hours regarded as most suitable
for this purpose, are 6 A. M., 2 p. M., and 10 P. m. To these hours are
sometimes added 9 A. M., and 6 r. M.
950. Mean temperature.-T'le mean or average daily temperature is commonly obtained by observing the standard thermometer at
stated times during the day, and then dividing the sum of these temperatures, respectively, by the number of observations. It has been
ascertained, that the mean temperature deduced from  observations
taken at 6 A. M., 2 P. M., and 10 P. M., corresponds almost exactly with
the mean obtained from  observations taken every hour in the 24;
hence the three hours named are considered the proper hours for
taking observations. The lowest temperature of the day occurs shortly
before sunrise; the highest a few hours after noon. The mean daily
temperature, at Philadelphia, is found to be one degree above the temperature at 9 A. M.
By taking the average of all the mean daily temperatures throughout
the year, the mean annual temperature is obtained.
951. Monthly variations in temperature.-In the successive months
of the year, there is a regular variation in temperature. From the
middle of January, the temperature rises, at first slowly, in April and
May rapidly, then less rapidly to the end of July, when it attains its
maximum.  It falls first slowly in August, rapidly in September and
October, and reaches the minimum about the middle of January.
In the United States, the monthly variations of temperature are nearly as
follows. (The figures attached to the signs + and - by the side of each month,
signify the number of degrees colder or warmer it is than the one immediately
preceding.)
January, the coldest; February, +2~ to 4~; March, 8~ to 10~; April, 10~;
May, 9~ to 12 0; June, 7~ to 9~; July, 4~ to 6~; August, — 1~ to 3~; September,
-5~ to 8~; October, -8~ to 10~; November, — 10~ to 14~; December, -10~ to
15~. The coldest days are generally about the 15th of January; the warmest,
near the 25th of July. The means of the months of April and October, are
very near the annual mean.
952. The range of temperature during the year, is due to variations
in the length of days and nights, and the height of the sun above the
horizon at noon.
In January, when the days begin to increase in length, the sun acts with more
force, because its angular height is greater, and because it remains longer above




METEOROLOGY.                             641
the horizon. This change is slow at first, and it is only towards the vernal
equinox that the increase in temperature is considerable. The days being then
longer than the nights, the earth receives more heat than it loses by radiation.
The temperature increases more slowly as the summer solstice is approached,
because the changes in the height of the sun and length of the day, are small.
After the solstice, the temperature continues to increase, until about July 25th;
the heat received through the day being still greater than the quantity lost
during the night. As the days decrease in length, and the sun approaches the
equator, the temperature falls, and attains its minimum near the middle of
January. For the extremes of natural temperature, compare section 744.
953. Variations of temperature in latitude.-The mean temperature of different places on the same latitude, varies according to
the height of the sun at mid-day above the horizon at these points.
The highest temperature is, therefore, found at the equator; it diminishes either way to the poles.
The mean summer temperature of regions midway between the poles and the
equator, may be as high as at the equator, because the sun is above the horizon
a greater number of hours. At the poles, however, where the sun is above the
horizon during six months of the year, the rays are directed so obliquely that
their calorific action is very feeble.
The temperature is not the same for places in the same latitude in
the two hemispheres, as is seen in the following table:Places.      Latitude.  Temp.       Places.       Latitude.  Temp.
Falkland Isles,. 51~ S.    470~23  London,...   51~ 31'N.  50~72
Buenos Ayres,.34~ 36' S. 62~'6   Savannah,.         320 05..64~058
Rio Janeiro,.. 22" 56' S. 73~096  Calcutta,..22~ 35'N. 780.44
This variation is owing to a variety of local causes, such as the elevation and form of the land, proximity to large bodies of water, the
general direction of winds, &c.
954. Variations of temperature in altitude.-The average diminution in temperature in ascending from the sea level is 1~ F. for every 300 feet.
Supposing the average temperature of the air at the level of the sea, near the
equator, to be 80~, and toward the poles 0~, the figures in the second and third
column of the following table will express approximately the temperature at different elevations. (From Daniell.)
DECREASE OF TEMPERATURE IN THE ATMOSPHERE FROM ELEVATION.
Altitude in feet.    Equatorial tmpra-   Arctic temperature.
ture.
0-              80~                  0~
5,000'        64~04            -  180'5
10,000-              48~04            -  37~'8
15,000-              31~04            -  58~-8
20,000'              120~8            -  82~1
25,000'       -  70~6            -1090.1
30,000'       — 30~07            -140~'3 




642                            APPENDIX.
955. Limit of perpetual snow.-It follows from  what has just
been stated, that in every latitude, at a certain elevation, there must
be a point where moisture once frozen must ever remain congealed.
The lowest point at which this is attained is called the limit of perpetual snow, or the snow-line. This point is generally highelst near the
equator, and sinks towards either pole. There are, howevelr, numerous
exceptions to this rule.
LIMIT OF PERPETUAL SNOW  AT DIFFERENT PLACES.
Places.                   Latitude.          Snow-lines.
Straits of Magellan,.....          54 S.                 3760 feet
Chili,..........                     41~ S.                6009 "
Quito,....        00~                 15,807 "
Himalaya, North side,.,            30~ 15' N.          16,719 "
Alps,.......           42~ N.               8220 "
W. Cordilleras,..                    14~ 30' S.          18,631 
Mexico,...                       19~ N.              14,763 "
IEtna,......      37~ 30' N.            9531 "
Katltschatka,.......                 56~ 40' N.           5248 "
It has been observed that the different heights of perpetual frost decrease
very slowly as we recede from the equator until we reach the limit of the torrid
zone, when they decrease more rapidly. The average difference for every 5~ of
latitude in the temperate zone is 1318 feet, while from the equator to 30~ the
average is only 664 feet, and from 60~ to 80~ of latitude it is only 891 feet. The
limit of perpetual snow presents remarkable and inexplicable phenomena at
different points: thus it is much higher in the Himalayas, latitude 14~ 15' N.,
than at the equator. Humboldt remarks that the limit is not due alone to
geographical latitude, that it is owing to a combination of many causes, such as
differences in the temperature of each season, the direction of the winds, the
habitual dryness or humidity of the atmosphere, the form of the mountain, its
vicinity to other peaks, &c.
956. Isothermal lines.-If all the points whose mean temperature
is the same are connected by lines, a series of curves are obtained,
which Humboldt was the first to trace on charts, and which he has
named isothermes, or isothermal lines (from  i~'o, equal, and Olppr,
heat). The latitude and longitude are the principal conditions which
determine the temperature of any point upon the earth's surface, but the
influence of these conditions is greatly modified by numerous accidental
and local influences: hence, the isothermal lines present numerous
sinuosities instead of passing around the earth parallel to any degree
of latitude. The introduction of isothermes formed an important epoch
in meteorological science, for by it have been established the great laws
of the distribution of heat over the surface of the earth for the four




METEOROLOGY.                            643
seasons.  The chart of isoclinal lines, fig. 543, serves also to illustrate
the general direction, and place of isothermal lines.
2 2. Aerial Phenomena.
957. General consideration of winds.-Wind is air in motion.
Winds are generally caused by variations in the temperature of the
earth, produced in part by the alternation of day and night, and the
change of the seasons.  The air in contact with the hotter portion of
the earth becomes heated, and being lighter than before, rises, while
the surrounding air rushes in below to supply its place. The revolution
of the earth on its axis, also comes in as an important modifying cause
of the thermal conditions.  Winds are also, sometimes, caused by the
sudden displacement of large volumes of air, as in the fall of an avalanche.  Winds are named from  the points of the horizon from which
they blow.
958. Propagation of winds.-Whether a wind is first felt in the
countryfrom which it comcs, or in that to which it is directed, is still
an unsettled question. It would.seem, however, that often at least it is
first felt in the region to which it is directed.
It has already been said that winds are caused by inequalities in the temperature of the air. If the air above a certain region, as in the tropics, becomes
heated, it rises, and the air in the vicinity rushes into the space abandoned by the
ascending column. This air becomes rarefied, and this rarefaction is communicated from point to point, just as the waves of sound expand. The wind is thus
propagated in a direction opposite to that in which it blows. Such winds are
called winds of aspiration. Winds which are propagated in the same direction
from which they blow are called winds of instfflation. Franklin made some
interesting observations on winds of aspiration. He noticed that a violent northeast wind, which arose about 7 o'clock, p. M, in Philadelphia, was not felt at
Boston until 11 o'clock in the evening. Again, a violent south-west wind blew
first at Albany, and afterwards at New York. But the existence of winds of
insufflation is not less well proven. The terrible hurricane from the south-west,
on the 29th of November, 1836, arrived at London at 10 o'clock in the morning, at the Hague at 1 o'clock in the afternoon, at Amsterdam at 1~, at Hamburg
at 6, at Lubeck at 7, and at Stettin at half-past 9 o'clock in the evening.
959. Anemoscopes.-The direction of currents of air blowing at
great heights may often be determined by the direction in which the
clouds move. The direction in which surface winds move is determined
by means of anemoscopes (from  alvsp.oq, wind, and axowros, one who
watches).
The ordinary vane is the simplest anemoscope. From its position on the top
of an edifice, observations of it are extremely inconvenient, and as ordinarily
constructed, it is not sufficiently delicate to move with slight agitations of the
air. Anemoscopes, suitable for accurate observation, are variously constructed.
They may consist of two or more fan-wheels, whose axis supported horizontally
is in connection with a vertical bar. The lower end of this bar is delicately




644                            APPENDIX.
supported, and has a needle attached to it at right angles, moving over a comr
pass dial-plate. The needle points upon the dial the direction of the wind.
960. Anemometers (from  av/lo;, wind, and /ulrpov, measure) are
instruments designed to measure the velocity of winds.
The velocity of winds is indicated by the force with which they move, i. e.,
the pressure they exert. Some anemometers are constructed so as to exhibit the
amount of pressure excited by a wind upon a plate placed perpendicular to its
own direction. This plate may be supported on a spiral spring, the extent of
its compression indicating the force of the wind. Fig. 713 represents a simple
form of this class of instruments.  Other               713
anemometers indicate the velocity of the
wind by the number of revolutions given Pl 1F
to a fan-wheel in a given time. Such an  l
one is Woltmann's anemometer. It con- llj
sists essentially of a small wind-mill, to 
which is attached an index marking the  1 
number of revolutions per minute. The
stronger the wind, the greater the number of revolutions made. The necessary
data for ascertaining correctly with this instrument the velocities of winds are
easily obtained as follows:-Nothing more is necessary, than on a calm day, to
travel with the apparatus on a carriage or rail car, observing the number of revolutions made in going any known distance in a given time. The effect will
be the same as if the air was in motion. A table is then constructed, indicating
the velocity of a wind which turns the sails forty, fifty, sixty, or more times per
minute.
Anemometers of very various forms have been designed. No one.yet constructed indicates the velocity of winds with absolute precision.
961. The velocity of winds varies from that which scarcely moves
a leaf to that which overthrows the staunchest oak.
VELOCITY AND POWER OF WINDS (Sineaton).
Velocity of the wind.    Perpendicular force on one  Common appellation of such
Miles per hour.     sq. ft. in lbs. avoirdupois.      winds.
1'005           Hardly perceptible.
5                       123              Gentle wind.
10'492
15                     1 07             } Pleasant brisk gale.
20                      1'968
25                        75              Very brisk.
30                     4-429
35                     6027             } High wind.
40                      7-873           Very high.
50                     12300            Storm.
60                    17 715            Great storm.
80                     31-490           Hurricane.
100                    49-200            Violent hurricane.
Formulae.-The following formula for determining the velocity of




METEOROLOGY.                             645
winds from the observed pressures, have been deduced from Smeaton's
table given above:If Vrepresents the velocity per hour in miles, and P represents the pressure
an a square foot of surface at right angles to the direction of the wind:V _           2== l_~_,_ or V=  14.257/ P.
The pressure in pounds avoirdupois, on a square foot of surface, when the wind
moves one mile an hour, being = 0-00492 lbs.
To obtain the velocity per second in feet, we multiply by 5280 (the number of feet
in a mile), and divide by 3600, the number of seconds in an hour, and we have
5280    5280
v    VX 3-00  3600 X 14-257v P =  20-91 /P
Winds are divided into three classes, viz., regular, periodical and
variable.
962. Regular winds are those which blow continuously in a nearly
constant direction, as the trade winds.
Trade winds occur in the equatorial regions, on both sides of the
equator to about 30~ of latitude.  Those in the northern hemisphere
blow from the north-east to the south-west; those in the southern hemisphere from the south-east to the north-west.
These winds are produced by the unequal distribution of heat upon the surface
of the earth, and by the rotation of the earth on its axis. From the vertical
position of the sun, the equatorial regions are intensely heated, the temperature
gradually diminishing towards the poles. The heated air, above the equator,
rises and blows off in the upper regions of the atmosphere towards either pole.
At the same time, currents are established on the surface of the earth to supply
to the equatorial regions the air which the upper currents have carried off. If
the earth were at rest, these winds would blow due north and south. But the
earth is revolving on its axis, from west to east, at the equ.ator; therefore, the
eastern velocity is greatest, but it gradually diminishes towards the poles. In
consequence of this, the wind blowing from the north pole, towards the equatqr,
acquires a westerly direction, and seems to come from the north-east, and for
the same reason, the wind blowing from the south pole towards the equator, also
acquires a westerly direction, and seems to come from the south-east.
These trade winds are not stationary, moving to the north in the summer of
the northern hemisphere, and south as the sun withdraws to the southern tropic.
The general direction of these trade winds is no more altered by the form of
continents, their elevation and headlands, than is the general course of the
waters in a river by rocks in its bed, though abrading surfaces and irregularities may produce a thousand eddies in the main stream.
963. Periodical winds are those which blow regularly in the same
direction, at the same seasons of the year, or hours of the day.  The
most interesting winds of this class are the monsoons, and the land and
the sea breezes.
The monsoons occur within, or near the tropics; they blow from a certain
quarter about one-half of the year, and from an opposite point during the other
half. The cause of the monsoons is found in the effect produced by the sun in
57




646                            APPENDIX.
his annual progress from one tropic to another, successively heating the land on
either side of the equator. The simoon is a periodical wind which blows over
the deserts of Asia and Africa; it is noted for its high temperature, and the
sand which it raises in the atmosphere, and carries along with it. This wind
from the Great Sahara desert blows over Algeria and Italy, and reaches even
the north shores of the Mediterranean, where it receives the name of sirocco.
On the coasts and islands within the tropics, and to some extent in temperate
regions, a sea breeze daily occurs flowing from the sea to the land during the
day; as it gradually subsides, it is succeeded by a land breeze, flowing from the
land to the sea. In some places these breezes are scarcely perceptible beyond
the shore; in others, they extend inland for miles.
The causes of the land and sea breezes are very apparent. During the day,
while the sun shines, the land acquires a higher temperature than the water of the
surrounding ocean. The air, above the land, becomes heated, and rises. To
supply the place of that which has risen, air flows in from the sea, constituting
the sea breeze. But when the sun descends, the land rapidly loses its beat, by
radiation, while the temperature of the ocean is scarcely changed. In consequence of this, the air above the land becomes cooled, and therefore more dense,
and flows towards the water, constituting the land breeze. At the same time, in
the higher regions of the atmosphere, air flows in from the sea to the land.
964. Variable winds are those which blow sometimes in one direction, sometimes in another. The direction of winds is influenced by
numerous causes, as the nature and form of the surface of the earth,
the proximity of large bodies of water, &c. In these latitudes, the direction of the prevailing winds is from the north-west to the south-east.
965. General direction of winds in the higher latitudes.-In
the table given below, the relative frequency of different winds is
given. The total number of winds in each country is represented by
1000; the figures in the table represent their relative frequency.
FREQUENCY OF DIFFERENT WINDS.
Countries.      N.   N. E.   E.   S. E.   S.   S. W.   W,  N. W.
England,...   82   111    99    81   111   225   171   120
France,...  126   140    84    76   117   192   155   110
Germany,... 84    98   119    87    97   185   198   132
Denmark,... 65    98   100   129    92   198   161   156
Sweden,.  102   104    80   110   128   210   159   106
Russia,..          99   191    81   130    98   143   166   192
North America,. 96   116    49   108   123   197   101   210
In these countries there is a predominance of south-west winds, with the
exception of Russia, where the greater proportion are from the north-west. In
all the northern hemisphere there is a predominance of westerly winds. This is
shown by the fact that the average length of the voyage from New York to
Liverpool by packet is but 23 days, while that of the return voyage is 40. In
the high southern latitudes the same thing is observed. Lieut. Maury remarks
that at Cape Horn there are three times as many westerly as easterly winds.




METEOROLOGY.                            647
966. Physical properties of winds. —Winds are hot, cold, dry,
or moist, according to the direction from which they come, and the
kind of surface over which they pass.
If they come over the sea, from lower latitudes, they are warm and
moist; if across the land, and from the north, they are cold and dry.
Our north-east winds are cold and moist, because they come from the
north, over the Atlantic Ocean.  South winds are here warm  and
humid; north winds cold and dry.
967. Hot winds.-Over the deserts of Asia and Africa, an intensely
hot wind occasionally prevails. In Arabia, it is called simoon, signifying poisonous: in Egypt, khamsin, because it blows forty days. In
the western part of the Great Desert, and in Guinea, it bears the name
of harmattan.
The soil of these countries is uniformly covered with a fine reddish sand,
which becomes prodigiously heated by the sun's rays. As the wind passes ovei
this surface, it becomes intensely heated; the fine particles of sand are raised in
the air, giving a reddish or purplish tinge to the atmosphere; the sky becomes
obscured, the sun loses its brilliancy, as the winds blow from the desert. The
barometer falls very low, plants dry up, and evaporation takes place with great
rapidity from the surface of the skin, giving rise to the greatest suffering.
Whole caravans have been known to perish, the prey of a consuming thirst.
968. Hurricanes, or cyclones, are terrific storms, often attended
by thunder and lightning; they are distinguished from every other
tempest by their extent, their power, and the sudden changes in their
direction.  From numerous observations, "it appears that hurricanes
are storms of wind, which revolve around an axis, upright or inclined
to the horizon, while, at the same time, the body of the storm has a
progressive motion over the surface of the earth."  This law has been
established by Redfield and Reid. Their progressive velocity varies
from ten to thirty or forty miles per hour; the rotatory velocity is
sometimes as much as a hundred miles per hour.  The diameter of a
hurricane is from a hundred to five hundred miles, though sometimes,
as in the Cuban hurricanes, it is much more.
Fig. 714 shows the origin, rotation, and general course of hurricanes in both
the northern and southern hemispheres. These terrible storms have never been
known to sweep across the equator, although, in one case, similar hurricanes were
raging at the same time, on both sides of the equator.
A northern hurricane commences with a violent rotary motion, as shown by
the arrows at a, in latitude 10~ or 150 north of the equator, corresponding very
nearly with the sun's northern declination, and extending over an area of from
50 to 200 or 300 miles, the rotary motion of the storm tending inwards towards
its centre. At the same time the general progress of the storm is obliquely
west and northward until it reaches the limit of the north-east trade winds, where
it sweeps around, taking a north-easterly direction, the vortex enlarging as it
progresses, spreading over an area of 500 or 1000 miles, until at last it moves




648                           APPENDIX.
in a nearly easterly direction, and- exhausts its force by its excessive enlarge.
ment, in latitude 40~ or 50~ N.                            714
Southern hurricanes pursue a similar course in                       N.L
the southern hemisphere, as shown in the lower....        45o
part of the figure. The circular arrows show the 
rotation of the air in the area of the cyclone, and    /I'".  - 40~
the arrows in the parabolic curve, a b c, show the,-.'-           3.o
general course of the moving storm.                         N  E T     30o
The arrow, NET, shows the region of the,,D- a250
north-east trade winds, and the parallel of lati-    -"  200
tude, L NE T, shows their northern limit. The,. 0  15~
arrow, S E T, and line, L S E T, also show the...       -i10o
region and limit of the south-east trades.      JUL. TO OCT..       50
Between the northern and southern hurricane   Zone of Varin;le \Windls.
regions, is the zone of variable winds, which the                       50
hurricanes are not known to pass. On either side                       100
of the zone of variable winds lie the zones of                   -'
expansion, in which hurricanes originate. The   /                      200,
letters, D D, indicate the most dangerous portion  /-.     25
r i ii'''~  L S E T  - 250
of the hurricane track.                                
It is now well ascertained that, in both                            - 350
hemispheres, the air in a cyclone or hurri-                             400
cane rotates in a direction contrary to that                           450
of the course of' the sun.  Thus, in  the JAN.TO APR.                  S.L.
northern hemisphere, the course of the sun is from the east around to
the south, then to the west and north, and the movement of the air in
the hurricane is in the opposite direction; i. e., from the north, by the
west, south, and east, or in a direction contrary to the motion of the
hands of a watch, lying with the face upward. In the southern hemisphere, the course of the sun is from the east, by north, west, and south,
and that of the cyclone is from the north, by east, south, and west, or
in the direction of the hands of a watch. East winds are, in both
hemispheres, characteristic of a commencing hurricane (i. e., an east
wind is always found on the front of the advancing storm, as shown in
the figure); while, in general, west winds occur only in the latter part
of the storm, as decreasing winds; hence, in the northern hemisphere,
the most dangerous part of a hurricane is in the advancing border of
the right hand semicircle, or about the line D D; while, in the southern hemisphere, the dangerous limit, D D, is the advancing quadrant
of the left hand semicircle.
The effect of the rotary movement of the hurricane is to accumulate
the air around its outer margin, with a pressure increasing as it recedes
from the centre; consequently, the barometer is lowest at the middle
of a storm, and highest at its extremity. The barometer oscillates
before and during a hurricane, rising and falling rapidly, owing to the




METEOROLOGY.                             649
inequality of the pressure which causes the storm; so that:-.Great
barometric oscillations generally announce the approach of a tempest.
By careful observation of the barometer, the mariner anticipates the
approach of a hurricane, or other dangerous storm. So, also, by careful attention to the course of the winds, and the sailing directions,
based on the researches of Redfield, Reid, and Maury, he knows how
to sail out of the track of a hurricane after it has commenced.
969. Tornadoes or whirlwinds are distinguished from hurricanes,
chiefly in their extent and continuance. They are rarely more than a
few hundred rods in breadth, and their whole track is seldom more
than twenty-five miles in length. The continuance of tornadoes is but
a few seconds at any one place. They are oftentimes of great energy,
uprooting trees, overturning buildings, and destroying crops.
970. Water-spouts differ from whirlwinds in no other respect than
that water, or vapor of water, is subjected to their action, instead of
bodies upon the surface of the land.
Water-spouts first appear as an inverted cone, extending downward from a
dark cloud. As the cone approaches the water, the latter becomes agitated, the
spray rises higher and higher, and finally, both uniting, there is formed a continuous column from the cloud to the water, usually bent as in fig. 715, but some715
t1,ucs erect. After a little time, the column breaks, and the phenomena disappbar. As to the origin of water-spouts, philosophers are divided. Kaemtz, a
distinguished German meteorologist, assumes that they are due principally to
two opposite winds, which pass side by side, or when a very brisk wind prevails
in the higher regions of the atmosphere, while it is clear below. Peltier, and
other physicists, ascribe water-spouts to an electrical cause.
Water-spouts are, in great part, formed of atmospheric water, as is shown by
the fact, that the water escaping from them is not salt, even in the open sea.
57*




650                          APPENDIX.
If the atmosphere is not moist, there is-no condensation of vapor, and the only
noticeable phenomenon is the violence of the wind and its rotatory motion.
971. General laws of storms.-Great storms, in temperate climates,
are governed by general laws, presenting more or less analogy to the
movements of hurricanes. As a general thing, the great storms which
pass over North America have no connection with the storms of Europe;
and the storms of both continents are modified in their course and
~general phenomena by the configuration and elevation of the land.
Great storms of rain and snow, and also lesser storms, which prevail
in the United States from  November to March, are governed by the
following general laws, which have been condensed from the researches
of Professors Espy (Reports to United States Senate), and Loomis
(Smithsonian Contributions, 1860).
1. Storms travel from the region of the Mississippi eastward as far
as the Gulf of St. Lawrence, and disappear in the Atlantic Ocean.
2. They are accompanied with a depression of the barometer, often
amounting to an inch or more below the mean height, along a line of
great extent from north to south, the line being curved with its convexity
eastward. In the front and rear of the storm, there is a rise of the
barometer, which, in some places, is more than an inch above the mean.
3. Great storms travel from the Mississippi to the Connecticut River
in twenty-four hours; and from the Connecticut to Newfoundland in
nearly the same time, or about thirty-six miles an hour; though sometimes they appear to remain nearly stationary for four or five days.
4. The area covered by a storm  is nearly circular, often of great
extent; frequently 1000 miles from east to west, and 2000 or 3000
miles from north to south.
5. For several hundred miles, on each side of the centre of a violent
storm, the wind inclines inwards towards the area of least pressure,
and, at the same time, it circulates around the centre in a direction
contrary to the motion of the hands of a watch. Compare 6 968.
6. On the borders of the storm, near the line of maximum pressure,
the wind has but little force, and tends outwards from the line of greatest pressure.
7. The wind uniformly tends from an area of high barometer towards
an area of low barometer.
8. In the northern parts of the United States, the wind generally, in
great storms, sets in from the north of east, and terminates from the
north of west; and in the southern states, the wind generally sets in
from the south of east, and terminates from the south of west.
9. During the passage of storms, the wind generally veers from the
iatward around by the south, and then towards the west.




METEOROLOGY.                            651
10. In a great storm, the area of high thermometer frequently does
not coincide with the area of low barometer, or with the centre of rain
and snow. But in the United States, on the north-east side of a storm,
at a distance of 500 miles from the area of rain and snow, the thermometer sometimes rises as much as twenty degrees above its mean
height.
11. In Europe, storms are often modified and controlled by the Alps
of Switzerland, which appear, for days together, to serve as the centre
of great storms.
For the connection of barometric changes with changes of weather, see section 271; and for fuller discussions of the theory and laws of storms, see the
works already referred to above, and also ~ 946, 968.. 3. Aqueous Phenomena.
972. Humidity of the air.-Vapor of water is always contained in
the air. This may be demonstrated by placing a vessel filled with ice
or a freezing mixture in the atmosphere; in a little time the vapor
from the air will be condensed on the walls of the vessel, in the form
of minute drops of water.
Air is said to be saturated with moisture, when it contains as much of the
vapor of water as it is capable of holding up at a given temperature. That the
capacity for moisture is greater as the temperature increases, is shown in the
following table:A body of air can absorb
At 320 F., the 160th part of its own weight of watery vapor.
it 590  "'  80th         "      "         "       "
"  860 ~     "  40th     i"      "         "       "
" 1130 "      20th        "      "         "       "
It will be noticed that for every 27~ of temperature above 32~, the capacity
of air for moisture is doubled. From this it follows, that, while the temperature of the air advances in an arithmetical series, its capacity for moisture is
accelerated in a geometrical series.
Table XXI., Appendix, shows the weight of aqueous vapor in a cubic
foot of saturated air, at temperatures from 0~ to 100~ F.
Absolute  humidity,-relative  humidity.-The  term  absolute
humidity of the air has reference to the quantity of moisture contained
in a given volume. Relative humidity refers to the dampness, or its
proximity to saturation with aqueous vapor.
The absolute humidity is greatest in the equinoctial regions, and diminishes
towards either pole; it diminishes, also, with the altitude, but the true ratio is
not fully known. The absolute humidity is also greater on coasts than inland,
in summer than in winter, and less in the morning than about midday.
Relative humidity is dependent upon the mutual influence of absolute humidity
and temperature. The atmosphere is considered dry when water rapidly evaporates, or a wet substance quickly dries. The expressions wet and dry convey
simply an idea of the relative humidity of the atmosphere, and have no refer



652                            APPENDIX.
ence to the absolute quantity of moisture present; for a damp air is rendered dry
by raising its temperature, and a dry air damp by cooling it.
Near great bodies of water, the atmosphere generally contains a greater
amount of moisture, both absolute and relative, than at inland places, or over
arid plains and deserts.
973. Hygrometers are instruments by which the humidity of the
atmosphere is determined.  They are of various kinds, and may be
classified as follows:-chemical hygrometers, absorption hygrometers,
condensation hygrometers, and psychrometers.
All hygroscopic substances (viz., those which have an affinity for water) are
chemical hygrometers. The amount of moisture in the air is determined with
these substances, by filling a tube with chlorid of calcium, for example, and
passing a known volume of air through it; the increase in weight of the tube,
after the experiment, indicates the weight of moisture present in the air. This
method yields the best results, but is difficult of execution.
Saussure's hygrometer depends upon the elongation and contraction of a hair by increase or diminution of relative humidity; but such
instruments afford no means of accurate comparison.
Daniell's hygrometer depends upon the condensation of moisture
by means of artificial cold.
It consists of a glass tube, bent twice at right angles, having a bulb at either
extremity. The bulb, A, fig. 716, is partly filled with ether, into which is inserted
the ball of a delicate thermometer, enclosed in the          716
stem of the instrument. The tube is filled with the
vapor of ether, the air having been driven out. The
bulb, B, is covered with fine muslin. Upon the sup- 
porting pillar, a second thermometer is placed. In
order to determine the dew point, or hygrometric
state of the atmosphere, by this instrument, a few
drops of ether are allowed to fall upon the muslin-.
covered bulb, evaporation of the ether takes place,
the bulb is cooled, and condenses the ethereal vapor
within. In conseqtence of this effect, the ether in   _1
A evaporates, causing a reduction of temperature,
indicated by the internal thermometer. At a certain 
point, the atmospheric moisture.begins to form in a ring of dew upon the bulb
A. The difference at this moment between the degrees indicated by the two
thermometers, denotes the relative humidity of the atmosphere; the dryer the
air, the greater is this difference.
August's psychrometer or hygrometer of evaporation depends
for its action upon the rapidity of evaporation in the open air.  It consists of two similar thermometers, t', placed side by side, fig. 717,
supported on a frame. The bulb of t' is covered with fine muslin, the
lower end of which dips into a small vessel, v, like a bird-glats, containing water; by this arrangement, the bulb is kept continually moist.
Evaporation takes place from the moistened bulb, with a rapidity varying with the humidity of the atmosphere, and a corresponding depression




METEOROLOGY.                         653
in the temperature of the thermometer is produced. The hygrometric
state of the atmosphere is determined from the observed difference in the
two thermometers by the use of tables prepared for the purpose. (Meteorological and Physical Tables, Smithsonian Collection.)    717
This is a very convenient instrument to determine the
condition of the air in dwellings heated by different.
methods. Observations with this instrument show how -,I
much our comfort and health depend upon preservingthe proper state of humidity or dryness in our dwellings,
or in the sick-room.
974. Fogs, or mists, are visible vapors that float in  
the atmosphere, near the surface of the earth. Fogs are -     -
produced by the union of a body of cool air with one that 
is warmer and humid. Many philosophers, as Saussure             -
and Kratzenstein, consider that the globules or vesicles of
which a fog is composed, are hollow, the water serving only
as an envelope; it is probable this is true, in some cases:
there are probably also mixed with the vesicles many mi- -
nute drops containing no free air. According to Kaemtz,    
the average diameter of fog globules does not exceed oti    o
TrA  of an inch. Maille, of Paris, has computed that it t'j  L   t
would require 200,000,000 fog globules to make a drop
of rain -y of an inch in diameter..
975. Dew  is the moisture of the air condensed by
coming in contact with bodies cooler than itself. The temperature
at which this deposition of moisture commences, is called the dew
point (674). The dew point varies according to the hygrometric state
of the atmosphere; being nearer the temperature of the air, the more
completely the air is saturated with moisture. In this climate, in summer, the dew point is often 30~ or more below the temperature of the
atmosphere. In India, it has been known to be as much as 610.
Cause of dew.-Dr. Wells, of London (born in South Carolina),
determined, by his researches, the cause of dew. It may be given
briefly as follows: —During the day, the surface of the earth becomes
heated by the sun, and the air is warmed by it. When the sun goes
down, the earth continues to radiate heat without receiving any in
return, and thus its temperature diminishes. The air loses its heat
more slowly, and is cooled only when it comes in contact with the
cooler earth. If this cooling reaches the dew point of the air, moisture
is condensed in the form of small drops upon cold objects (good radiators), as the soil or vegetation.
Circumstances influencing  the  production  of dew.-The




654                        APPENDIX.
amount of lew deposited in a given time depends upon the humidity,
tranquility, and serenity al the air. Since dew is the moisture of the
atmosphere condensed, it is evident it must be affected by the amount
the air contains. On a windy night, the air in contact with cold objects
is so quickly changed, that it is not cooled down to the dew point; but
gentle agitation of the air favors the production of dew, bringing more
moist air to furnish dew to cold objects. The most copious deposits of
dew take place on cool, clear nights. For, when there are clouds, these
radiate back the heat which has escaped from the earth, and thus prevent its cooling, and therefore no dew is deposited. If the clouds separate only for a short time, dew is rapidly deposited.
Straw, mats, boards, &c., used by gardeners to protect delicate plants
from freezing, act in the same manner as clouds, to prevent the deposit
of dew or frost. See Fig. 718.
976. Substances upon which dew falls.-Dew does not fall upon
all substances alike; in consequence of differences in radiating and
conducting power, certain substances cool quicker and more perfectly
than others. The dusty road, the rocks, and barren soil, cool slowly,
receiving heat from the earth by conduction, and therefore on them but
little dew falls. Trees, shrubs, grasses, and vegetation of every kind,
radiate heat easily, and, on account of their peculiar structure, they
receive but little heat from the earth, or other objects, by conduction;
hence they become rapidly cooled, and abundance of dew is deposited
upon them.
977. Frost is frozen dew. When the temperature of the earth sinks
in the night to the freezing point, the aqueous vapor then deposited
congeals in the form of sparkling crystals, known as hoarfrost. Fig.
718, from Stoeckhardt, in which the arrows indicate the movements of
718
5? 4 E'IY 
50  \6           3     I\  39,orDr
heat, and the numerals the temperature of the air, will render the phenomena of dew and frost more intelligible.
The sun's rays in winter, may, in the day, warm the soil to 530, as
in the figure, while the air above the ground is 50~. At night, the ra



METEOROLOGY.                             655
diation into a cloudless sky, will reduce the temperature of the ground
to 43~, or even 33~, while the air above the same points is 46~ or 39~.
But a cloud resting above the earth prevents radiation, and reflects the
heat back to the earth. So dew or frost will be deposited on the upper
surface of a platform when radiation takes place freely, while boards,
like the cloud, reflect back the heat coming from the ground.
978. Clouds are masses of vapor that float in the upper regions of
the atmosphere.  They are distinguished from  fogs only by their altitude; they always result from  the partial condensation of the vapors
that rise from the earth.  As clouds often float in regions whose temperature is many degrees below the freezing point, they are sometimes,
no doubt, composed of frozen particles.
Clouds being condensed moisture, are heavier than the air, and have a tendency to fall to the earth. They are kept suspended in the air, 1. By ascending
currents during the day, the warmer air dissolving the cloud as fast as it falls
into it. Such clouds are more elevated at midday than in the morning, and
they descend towards the earth at evening.
2. Horizontal currents also oppose the fall of clouds. The minite vesicles or
globules, whichever they may be, are carried forward and dissolved by the drier
air on the advancing side of the cloud, while on the windward side of the cloud,
vapor is constantly precipitated.
3. The resistance of the air opposes the rapid descent of clouds. This resistance is in the inverse proportion to the dimensions of the particles. For this
reason, considerable time would be required for vapor to descend even a few
hundred feet. If, as many writers suppose, the water of clouds exists in the
form of minute vesicles containing air, the expansion of the enclosed air by
heat would at once account for the buoyancy of clouds; for they would float like
balloons in air of their own aggregate density, and every increase of heat would
increase their buoyancy.
979. Classification of clouds.-Clouds are generally divided into
four great classes, viz.: the nimbus, the cumulus, the stratus, and the
cirrus, as shown in the diagram, fig. 719.
Intermediate forms of clouds are distinguished by the names of cirrostratus, cirro-cumulus, and cumulo-stratus.
The cirrus (cirrus, curl) usually resembles a disheveled lock of hair, being
composed of streaks or feathery filaments, assuming every variety of figure.
The cirrus floats at a higher elevation than other clouds, and probably is often
composed of snow-flakes. It is among the cirri that halos and parhelia are
formed.
The cumulus (cumulus, heap) appears often in the form of a hemisphere,
resting on a horizontal base; sometimes in detached masses, gathered in one
vast cloud, near the horizon. When lighted up by the sun, they present the
appearance of mountains of snow. The cumulus is the cloud of day; in the
fine days of summer it is most perfect.
The name of cirro-cumulus is given to little rounded clouds.
The cumuli owe their existence to ascending currents; their height varies
greatly, but it is always less than that of the cirri.
The stratus (stratus, covering) ccnsists of sheets of cloud, or layers of vapor,




656                              APPENDIX.
stretching along and resting upon the horizon. It forms about sunset, increases
710
tion above the earth.
The cirro-stratus partakes of the character of the cirrus and stratus. It is
remarkable for its length and thickness. It appears, sometimes, as a long and
narrow band; at other times, as composed of small rows of clouds or bars of
vapor.  Cumuli, heaped together, pass into the condition of cumulo-stratus,
which consists of a horizontal stratum of vapor, from which rise masses of
cumuli. " These often assume, at the horizon, a dark tint, and pass into the
nimbus state.
The nimbus, or rain-cloud (nimbus, storm). This has a characteristic stormlike form; it is distinguished from others by its uniform gray or blackish tint,
and its edges fringed with light.
980. Rain is the vapor of clouds, or of the air, precipitated to the
earth in drops. Rain is generally produced by the rapid union of two
or more volumes of humid air, differing considerably in temperature;
the several portions, when mingled, being incapable of absorbing the
same amount of moisture that each would retain if they had not united.
If the excess is great, it falls as rain; if it is of slight amount, it
appears as cloud. The production of rain is the result of the law, that
the capacity of air for moisture decreases in a higher ratio than the
temperature.
Rain-gauges.-Instruments for determining the quantity of rain, are
called rain-gauges, ombrometers, h1yctometers, &c.  They are of very
various construction.
One of the simplest rain-gauges consists of a cylindrical copper vessel, furnished with a float; the rain falling into the vessel, the float rises. The stem




METEOROLOGY.                              657
of the float is accurately graduated, so that an increase in the depth of the water
of one one-hundredth of an inch, is easily measured.
Another rain-gauge, a section of which is represented in fig. 720, consists of
a cylindrical copper vessel, M, closed by a cover, B, shaped    720
like a funnel, with an aperture in the centre, through
which the water passes into the interior. This cover pre- 
vents loss by evaporation. A lateral glass tube, A, carefully graduated, rises from the base of the vessel. The
water rises in the tube to the same height as in the copper  
cylinder. If the apparatus has been placed in an exposed    lllll   l 
situation, for a certain time, as a month, and the gauge
shows three inches of water, this indicates that the rain 
that has fallen during the interval would cover the earth 
to the depth of three inches, if it were not diminished by
evaporation, or infiltration.
From a series of experiments made at the Smithsonian
Institution, and continued for several years, it is found
that a small cylindrical gauge, of 2 inches in diameter, and about six inches in
length, connected with a tube of half the diameter, to retain and measure the
water, gives the most accurate results. In still weather, it indicates the same
amount of water as the larger gauges; but when the wind is high, it receives
more rain; for, on account of its small size, the force of the eddy which is produced, is much less in proportion to the drops of water. This gauge may be
still further improved by cutting a hole of the size of the cylinder, in a circular plate of tin, of 4 or 5 inches in diameter, and soldering this to the cylinder,
like the rim of an inverted hat, three or four inches below the orifice of the
gauge.
981. Distribution  of rain.-Rain is not equally distributed over
the surface of the earth.  As a general rule, it may be stated that, the
higher the average temperature of a country, the greater will be the
amount of rain that falls upon it.  Local causes, however, produce
remarkable departures from this rule.
In the tropics, the average yearly rain fall is ninety-five inches; in the temperate zone it is thirty-five inches. Within the tropics, the greatest quantity of
rain falls when the sun is at its zenith, that is, in the season corresponding to
our summer. North of the tropics it rains more abundantly in winter.
In certain regions there is a periodical season, when rain is very abundant
for six months, called the rainy season. During the remainder of the year,
called the dry season, it seldom rains.
Many regions are destitute of rain.  In Egypt, it scarcely ever rains.
Along the coast of Peru, is a long strip of land upon which no rain ever
descends. A similar destitution of rain occurs on the coast of Africa, and
some parts of North America; the intervals between the showers being six or
seven years.
In Guiana it rains during a great part of the year; this is also the case,
according to Davison, at the Straits of Magellan. In the Island of Chiloe (S.
lat. 43~), there is a proverbial saying, tha. it rains six days of the week, and is
cloudy on the seventh.
982. Days of rain.-The rainy days are more numerous in high
than in low latitudes, as is seen in the following table, although the
68




658                            PAPPENDIX.
annual amount of rain which falls is smaller.  Consequently, the ordinary rains of the tropical regions are more powerful than those of the
temperate regions.
N. latitude.                Mean annual number of rainy days.
From 12~ to 430                               78
it  43~ " 46~                              103
I  46~, 50~                               134
"  50~ " 600                               161
In the northern part of the United States there are, on the average,
about 134 rainy days in the year; in the southern part, about 103.
983. Annual depth of rain.-The greatest annual depth of rain
occurs at San Luis, Maranham, 280 inches; the next in order are Vera
Cruz, 278; Grenada, 126; Cape Francois, 120; Calcutta, 81; Rome,
39; London, 25; Uttenberg, 12-5. In our country, the annual average
fall is 39-23 inches; at Hanover, N. II., 38; New York State, 36; Ohio,
42; Missouri, 38-265.
984. Snow is the frozen moisture that descends from the atmosphere,
when the temperature of the air at the surface of the earth is near, or
below, the freezing point.  The largest flakes of snow  are produced
when the atmosphere is loaded with moisture, and the temperature of
the air is about 32~; as the cold increases, the flakes become smaller.
The bulk of recently fallen snow is ten or twelve times greater than that of the
water obtained from it. Snow flakes are crystals of various forms. Scoresby ha.s
enumerated six hundred forms, and figured                721
ninety-six. Kaemtz has met with at least
twenty forms not figured by Scoresby. Crystals of snow are not solid, else they would be
transparent as ice; they contain air. It is
to the reflection of light from the assemblage of crystals, that its brilliant whiteness
is due.  Snow crystals are produced with
most regularity during calm weather, without
fog. Fig. 721 represents a few of the beautiful forms assumed by snow crystals.
985. Colored snow  is mentioned by Pliny.  It occurs under two
very different circumstances,-either while the snow is falling, or some
time after its descent.
In 1808, rose-colored snow fell in the Tyrol and in Carinthia. Its color was
owing to an earthy powder, composed of iron, silex, and alumina. Of a similar
composition was a red snow that fell on the mountain of Toual, in Italy, in
1816. These facts provi conclusively that, at times, snow tinged with mineral
ingredients, falls upon the earth. That the color is sometimes (and generally)
produced by the presence of minute organisms, is no less conclusively demonstrated.  Captain Ross, in 1819, discovered a crimson snow clothing the sides
of the mountains at Baffin's Bay. It has been observed on the Pyr6nees, Alps,
and Apennines; in Scotland, Sweden, Norway, &c. Certain French meteorologists, at Spitzbergen, in 1838, passed over a field covered with snow, which




METEOROLOGY.                            659
appeared of a green hue, whenever pressed upon by the foot. Agassiz regards
these colors as animal products, believing them to be the ova of a rotiferous
animalcule. The more common belief is, that (generally, at least) these hues
are owing to the presence of a certain class of microscopic plants, the different
colors representing different stages of development. Martini gives, perhaps,
the correct explanation: that this product is a vegetable cell, enclosing fluid, in
which multitudes of infusoria find a nidus and support.
986. Hail is the moisture of the air frozen into globules of ice.
Hail-stones are generally pear-shaped; they are formed of alternate
layers of ice and snow, around a white, snowy nucleus. It is necessary
for the production of hail, that a warm, humid body of air, mingle
with another so extremely cold, that, after uniting, the temperature
shall be below the freezing point. The difficulty of explaining the
phenomena of hail-storms, consists in accounting for this great degree
of cold.
Hail-storms are most frequent in temperate climates. They rarely occur in
the tropics, except near high mountains, whose summits are above the snowline. It is in great part during the summer, and in the hottest part of the day,
that hail falls. Hail-storms rarely occur at night. Hail-stones are often of
considerable size; the largest are frequently an aggregation of several frozen
together. Sleet is frozen rain; it occurs only in cold weather; it falls only
during gales, and when the weather is variable.
@ 4. Electrical Phenomena.
987. Free electricity of air.-The general laws of atmospheric
electricity have been considered in a previous paragraph (861).
It is common to refer the free atmospheric electricity to several
causes, always at work on the earth's surface, as, 1. Evaporation,
especially of impure water; 2. Condensation; 3. Vegetation  (945);
4. Combustion; and, 5. Friction; without doubt these are all causes
of electrical excitement in the air.  But far more important than them
all is the powerful inductive influence of the negatively excited earth
upon its gaseous envelope.  The dense air near the earth's surface
is like the dielectric of the AEpinus condenser, and the constant presence of positive electricity in the air is a fact not explicable on any
other hypothesis than that of induction from the negative earth.
In addition to the laws already announced in & 861, may be added
the fact that atmospheric electricity is more abundant in summer than
in winter.
988. Thunder-storms are most frequent and violent in the equatorial regions.  They decrease in frequency towards either pole, and are
more frequent in the summer than in the winter months, and after midday than in the morning.  They are produced in the same manner as
ordinary storms; but they differ from  them  in their local character,




660                         APPENDIX.
in the rapidity and extent of the condensation of the atmospheric vapor,
and in the accumulation of electricity.
Thunder-storms are usually attended by an alteration in the direction of the
wind. Of one hundred and sixteen thunder-storms recorded in the Meteorological Register of the Connecticut Academy, ninety-nine were either preceded or
followed by an alteration in the direction of the wind.
Thunder-storms generally prevail in the lower regions of the atmosphere.  They are, however, not unfrequently observed at great elevations. Kaemtz notices one on the mountains of Switzerland which
rose to the height of more than 10,000 feet.
The geographical distribution of thunder-storms has been lately
discussed by Prof. Loomis (Am. Jour. Sci. [2] XXX. 94), whose results
confirm the general statement already made with reference to latitude,
thus:Between latitude 0~ and latitude 300                    51.6
i"     "   30   "   "    50    The average number   19-9
9"    i"  50  "   "   60           of thunder-storms l 14-9
it     "   60  "   "   70          annually is         4Beyond    "   70                                         0
Maury's storm and rain charts, however, show that the frequency
of lightning depends on other circumstances than simply latitude, since
throughout the western half of the Atlantic Ocean lightning is three
times as frequent as over the eastern half of that ocean, and two and a
half times as frequent in the North Atlantic as in the South Atlantic.
The origin of thunder-clouds appears, by both theory and observation to be due, in this country, to the rushing up of the lighter air
to restore the normal equilibrium of the atmosphere, which had been
disturbed or rendered unstable by the gradual introduction, next to
the ground, of a stratum  of warm and moist air.  The upper end of
such an ascending column of air, on the principle of Peltier (861).
must be negatively electrized, as its lower end receives positive induction from  the negative earth. As, by the principles established by
Espy, the excess of watery vapor in such a cloud will be precipitated
as it rises, it follows, that the ascending column becomes a conductor, and a series of electrical discharges will take place between the
upper and lower parts of the cloud. The hour-glass form, which the
aeronaut Wise asserts is the shape of a thunder-cloud, when seen from
one side, in a balloon, confirms this view. (Consult Professor Henry's
paper on Meteorology, in the Report of the Patent Office for 1859,
Agriculture. )
989. Thunder.-As lightning passes through the air with amazing
velocity, it violently displaces it, leaving void a space into which the air
rushes with a loud report; this is thunder.




METEOROLOGY.                              661
The rolling of thunder is generally ascribed to the reverberation of the sound
from clouds and adjacent mountains. It is also considered that as the lightning
darts to a great distance with immense velocity, thunder must be produced at
every point along its course, and the sounds not reaching the ear at the same
time that elapses between lightning and its thunder, we are enabled to calculate
the distance of the former. According to Mr. Earnshaw, the sound of a thunder
clan is propagated with much greater velocity than ordinary sounds. See
Appendix, p. 668.
990. Lightning.-It has already been stated, that air subjected to
compression emits a spark.  The production of lightning is by some
attributed to the energetic condensation of the atmosphere before the
electric fluid, in its rapid progress from point to point. When lightning
is emitted near the earth, the flashes are of a brilliant white color; when
the storm is higher, and therefore in a rarefied atmosphere, their color
approaches to violet. Clouds appear to collect and retain electricity.
When a cloud overcharged with electricity approaches another less
charged, the electric fluid rushes from the former to the latter. In the
same manner the electric fluid may pass from the clouds to the earth.
In such cases, elevated objects, as trees, high buildings, church steeples,
&c., often govern its direction.  It is unnecessary to dwell upon the
powerful and destructive effects of lightning.
991. Classes of lightning.-Lightning has been divided by Arago
into three classes, viz.: zigzag or chain lightning, sheet lightning, and
ball lightning. We may add heat lightning and volcanic lightning. This
classification is convenient, and is universally adopted.
Zigzag or chain lightning is supposed to owe its form to the resistance
of the air compressed before it. The lightning takes the path of least resistance; then moves forward until it meets with a like opposition, and so continues
glancing from side to side until it meets the object it seeks. Sometimes the
flashes divide into two, and sometimes into three branches; it is then called
forked lightning.
Sheet lightning appears during a storm as a diffuse glow of light illuminating the borders of the clouds, and occasionally breaking out from the central
part.
Heat lightning as it is called, appears often in serene weather during
summer, near the horizon; it is generally, if not always, unattended with
thunder; heat lightning is the reflection in the atmosphere of lightning very
remote, or not distinctly visible. By many, this phenomenon is supposed to be
occasioned by the feeble play of electricity when the air is rarefied, and the
pressure upon the clouds is so much diminished that the electric fluid cannot
accumulate upon their surface beyond a certain point, and escapes in noiseless
flashes to the earth.
Ball lightning appears in the form of globular masses, sometimes remaining stationary, often moving slowly, and which in a little time explode with great
violence. This form of lightning is of very rare occurrence, and philosophers
have not as yet been able to account for it.
5b *




662                           APPENDIX.
Volcanic lightning.-The clouds of dust, ashes, and vapor, that issue
from active volcanoes, are often the scene of terrific lightning and thunder.
Volcanic lightning is probably caused by rapid condensation of the vast volumes
of heated vapor thrown into the air.
The rapidity of lightning of the first two classes is probably not less
than two hundred and fifty thousand miles per second.  Arago has
demonstrated that the duration of a flash of lightning does not exceed
the millionth part of a second. The waving trees illuminated at night
by a single flash of lightning during a storm  appear motionless; the
duration of the flash is so short, that, during its continuance, the trees
have not sensibly moved.
992. Return stroke.-When a highly charged thunder-cloud approaches the earth, it induces the opposite kind of electricity upon the
ground below, and repels that of the same kind.  If the cloud is
extended, and comes within  striking  distance of the earth, or of
another cloud, a flash at one extremity is often followed by a flash
at the other. This latter is called the return stroke, and sometimes
is of such violence as to prove fatal, even at a distance of several miles
from the point of the first discharge.
993. Lightning-rods were first introduced by Dr. Franklin.  He
was induced to recommend their adoption as a means of protection to
buildings, from the effects of lightning, by observing that electricity
could be quietly and gradually withdrawn from an excited surface by
means of a good conductor, pointed at its extremity (826).
Lightning-rods are ordinarily made of wrought iron; but copper is preferable, being a better conductor of electricity, and less easily corroded. The size
of the rod, if of iron, should not be less than three-quarter inch in diameter.
The upper extremity of the rod should be pointed. Three points is the usual
number used in the United States, but one is sufficient. The points should be
tipped with silver, gold, or platinum, or copper gilded by electricity; these
metals being unaffected by the air, which would corrode the copper or iron, and
render them poorer conductors. The rod should be continuous from top to
bottom, and securely fastened to the building. Glass or wooden insulators are
often recommended, but when once wet by a shower, there is but little advantage
in them over metallic supports. When there are surfaces of metal about the
building, as gutters, pipes, &c., these should be connected with the conductor by
strips of metal, as first recommended by Prof. Henry. The lower part of the
rod, where it enters the ground, should be divided into two or three branches,
and bent away from the building, penetrating so far below the surface of the
earth as to reach water, or permanently moist soil. Charcoal is recommended
to fill the hole in the centre as a means of effecting a better conduction. In a
church, in New Haven, the lightning has twice penetrated a twenty inch brick
wall at a point opposite a gas-pipe, 20 feet above the earth, through which the
discharge has escaped to the earth, although the conductor of three-quarter inch
iron was well mounted, but its connection with the earth was less perfect than
that of the gas-pipe.




METEOROLOGY.                            663
Protective power.-According to Mr. Charles, a lightning-rod protects a space around it; whose radius is equal to twice its height above
the building. Thus, if a conductor extend ten feet above the houses it
affords protection to a circular space forty feet in diameter, the rod
being in the centre.
Conductors do not attract the lightning toward the building upon which they
are placed. They simply direct the course and facilitate the passage of the
electricity to the earth, which otherwise might have been effected in a powerful
and destructive discharge through the building. It is indeed considered by
Arago, that "lightning-rods not only render strokes of lightning inoffensive,
but considerably diminish the chance of their being struck at all."
994. Aurora borealis.-Under this name are comprised the luminous
phenomena seen frequently in the northern sky; and also, although
more rarely, in the neighborhood of the south pole; they are then called
aurora australis. They present, when in full display, a spectacle of
surpassing splendor and beauty. The cause of the aurora borealis is yet
involved in obscurity. Although it is, evidently, intimately connected
with terrestrial magnetic electricity, it is impossible at present to say
exactly what this connection is. It has been ascribed to the passage
of electrical currents through the upper regions of the atmosphere, the
different colors being manifested by the passage of the electricity
through air of different densities.
Appearance of auroras.-Before the aurora appears, the sky in the
northern hemisphere usually assumes a darkish hue, which gradually
deepens, until a circular segment of greater or less size is formed. This
dark segment is bounded by a luminous arc, of a brilliant white color,
approaching to blue.
The lower edge of this are is cleat defined; its upper edge gradually blends
with the sky. When this luminous arc is formed, it frequently remains visible
for many hours, but it is always in motion. It rises, falls, and breaks in
various places. Clouds of light are suddenly disengaged, separating into rays,
which stream upwards like tongues of fire, moving backwards and forwards.
When the luminous rays are numerous, and their palpitating lights pass to the
zenith, they form a brilliant mass of light, called the corona or crown, whose
centre is the point towards which the dipping-needle at the place is directed.
The aurora is then seen in its greatest splendor; the sky resembles a fiery dome,
supported by waving columns of different colors. When the rays are darted
less visibly, the aurora soon disappears, the lights momentarily increase, then
diminish, and finally disappear. It is asserted that sounds, like the rustling of
silk, often accompany the display of auroras, but this is extremely problematical; the most celebrated polar navigators never heard any noises which they
could certainly ascribe to the auroras.
995. Remarkable auroras.-The aurora is not a local phenomenon;
it is often seen simultaneously in places far apart, as in Europe and
America.




6G6                              APPENDIX.
In 1796, a beautiful aurora was observed simultaneously in Pennsylvania and
France.  The aurora of January 7th, 1831, was observed in all central and
northern Europe, and at Lake Erie. The aurora of November 17th, 1848, is one
722
Auroral display, seen at Bossekop, 700 N., 1838-9.
of the most remarkable previously recorded. It was seen from Odessa, on the
Black Sea, lat. 46~ 35', long. 30~ 35' E. to San Francisco (California), 38~ N. lat,
122~ W. long., and as far south as Cuba. It seems everywhere to have had a
prevailing red hue, mistaken in many places for a conflagration.  (Am. Jour.
ici. [2] VII. 203.)
More remarkable than all, however, was the aurora of August 28th to September 4th, 1859, for the great extent of teritory over which it was seen, for its
long duration, and for the brilliancy of its cfors, the intensity of its illumination,
and the rapidity of its changes. It was equally remarkable for the accompanying magnetic disturbances, recorded not only by the usual magnetic instruments,
but over the whole system of telegraph wires both in America and Europe.
This aurora was seen as far west as the Sandwich Islands, lat. 20~, long. 157~
W., and east as far as Barnaul, Russia, long. 83~ 27' E., a circuit of 240~ about
the earth. The observations seem to justify the inference that it was as vivid
in the southern as in the northern hemisphere. It was seen off Cape Horn and
in Australia, in the southern hemisphere, up to Concepcion, Chili (lat. 36~ 46' S.),
and from about lat. 60~ N., in North America, to San Salvador in 13~ 18' N.
For full details of this aurora, see Am. Jour. Sci. [2] Vols. XXVIII., XXIX.,
and XXX.
996. Height of auroras.-Many  astronomers have endeavored to
determine the height of auroras, but the results of their calculations
are not certain. Earlier philosophers computed their altitude at several
hundred miles; a lower limit is assigned by later observers. A brilliant auroral arch was observed in the Northern  and Middle States,




METEOROLOGY.                             665
April 7th, 1847; from  the observations made at Iartford and New
Haven, Conn., its height was computed by Mr. E. C. Herrick, of the
latter place, to be nearly one hundred and ten miles. Another, seen
April 29th, 1859, is by the same observer estimated approximately at
much over 100 miles in height. (Am. Jour. Sci. [2] XXVIII. 154.)
Prof. Loomis calculates the height of the base of the auroral curtain,
August 28th, 1849, as about forty miles, but the same observer estimates the height of the belts of this aurora in other places as over one
hundred and fifty miles.
Frequency of auroras.-Auroras are perhaps rather more frequently seen in winter than in summer; but this circumstance does
not indicate that during the former season there are actually a greater
number, for the increased length of night would render a greater number visible, even if they were equally distributed throughout the year.
During the summer of 1860, auroras have been uncommonly frequent
in the N. United States. About the period of the equinoxes they appear
to be more frequent than at other times.*
In addition to the annual period, there appears to be another, a secular period,
extending through a number of years. One of these periods was comprised between 1717 and 1790; its maximum was obtained in 1752. An increase in the
frequency of auroras began again in 1820. Prof. Olmsted, in an important paper
on this subject, in the Contrib. of Smithson. Inst., vol. 8, selects one of these
secular periods between August 27th, 1827, and November, 1848, or a little later.
The number of auroras, observed for a period of about sixteen years, at New
Haven, by Mr. E. C. Herrick, is given in the following table:AURORAS OBSERVED AT NEW  HAVEN DURING SIXTEEN YEARS.
Number of auroras.                  Number of auroras.
April 1837 to April 1838,   42        April 1845 to April 1846,   21
"  1838 "   "   1839,   34           "  1846"   "   1847,   25
"  1839"   "   1840,   43            "  1847 "   "   1848,   30
"  1840 "   "   1841,   48           "  1848 "   "   1849,   42
"  1841 "       1842,   29           "  1849 "   "   1850,   18
"  1842     "   1843,    9           "  1850 "March 1851,   15
"  1843 i   "   1844,    7          Oct. 1851 " Oct. 1852,   33
"  1844"   "   1845,   10             "  1852      "   1853,   24
997. Geographical distribution  of auroras.-Prof. Loomis has
lately (Am. Jour. Sci. [2], XXX., 89) published a chart showing the
distribution of auroras in the northern hemisphere. He shows from a
tabular comparison of record ed observations, that near the parallel of
40~ N., on the meridian of Washington, there are only 10 auroras
annually; nearly 42~ N., the average is 20 annually; near 45~ it is
* See a paper on Huxham's Observations (Am. Jour. Sci. [1], XXXIII., 301),
showing that the A. B. is as abundant in summer as in winter.




666                          APPENDIX.
40; and near the parallel of 50~ it is 80 annually. Between this and
the parallel of 62~, auroras are seen almost every night, appearing
high in the heavens, and as often to the south as to the north. Above
62~ they are seldom seen, except in the south, and from this point they
diminish in frequency and brilliancy as we advance towards the pole.
On the meridian of St. Petersburg a similar comparison gives a like
result, except that the auroral region is situated further north than it
is in America, the zone of 80 auroras annually being from 66~ to 75~ N.
Prof. Loomis's chart (loc. cit.) shows that the region of greatest auroral
activity is an elliptical belt, having one focus near the north pole, and
the other near the pole of magnetism, and whose major axis crosses the
meridian of Washington, near lat. 56~, and the meridian of St. Petersburgh, in lat. 71~. Accordingly, auroras are more frequent in the
United States than in the same latitudes of Europe. Thus, on the line
of 500, we find in North America 40 auroras annually, but in Europe
less than 10 on the same parallel.
998. Magnetic disturbances during auroral displays.-During
the prevalence of auroras, all the magnetic elements show great disturbance, simultaneously, at the most distant stations. This statement
is confirmed by comparing the observations at Toronto, Canada West,
lat. 43~ 59' 35" N., long. 79~ 21' 30" W., with those at St. Petersburgh,
Russia, lat. 59~ 56' 30" N., Ion. 30~ 19' E., on the 2d and 3d of September, 1859, during the great aurora already described, when, on
several occasions, the magnets in the several instruments oscillated
completely beyond their scales-equal to a total deflection of over 5~~
of arc. (Am. Jour. Sci. [2], XXVIII., 390, and XXX., 80.)
The magnetic oscillations sympathize with the auroral streamers;
when the arc is quiet, the needle rests.  During the grand aurora of
November 14, 1837, the range of oscillation, as observed at New Haven
by Messrs. Herrick and Haile, was 6~.
999. Effect of the aurora on telegraphic wires. —This phenomenon, already alluded to (994), is entirely distinct from the induction
of static electricity during thunder-storms from the atmosphere (860).
During the aurora of August-September, 1859, several of the telegraphic
lines in the United States were worked, for hours together, entirely by
the magnetic current induced from  the aurora, the batteries being
detached.  Chemical decompositions, and powerful heating and luminous effects, have been often observed from the currents induced during
auroral disturbances.  These facts were first noticed by Mr. G. B.
Prescott, at New Haven, in 1847. In Europe, during the great aurora
of 1859, the same disturbances of the telegraphic lines were observed
as in this country.




METEOROLOGY.                             667
While all the lines were more or less affected, whatever their direction, it appears that the disturbances were more marked on the north
and south going lines, than on those going east and west: and in
Tuscany, Prof. Matteucci observed, that where there were several parallel lines, one above the other, the upper wires were most affected,
and those nearest the earth, least; and that the inductive effects were
stronger on the longest lines.
1000. Reversal of polarity in the auroral current.-Mr. Prescott
first determined, by observation on the aurora of July 19, 1852, that
the auroral current invariably changes its polarity with every wave.
First, a positive current, producing, on Bain's system, a deep blue
mark, light at first, and then stronger, until, having attained the intensity of at least 200 Grove's cups, it subsided, and was followed by a
current of reverse polarity, which bleached instead of coloring the
paper. Sometimes a flame of fire followed the steel stylus, and burned
through a dozen thicknesses of the prepared paper.  Free or atmospheric electricity, when it is induced on the telegraph wires, produces
no color on the paper. (Am. Jour. Sci. [2], XXIX., 92 and 391.)
Problems on Electricity.
243. Compare the force of electricity on two similar balls, of which one repels
the needle of the torsion electrometer 45~ and the other 100~.
244. The extreme plates of a voltaic battery, being placed in contact, there
was no exterior resistance, and the electro-motive force manifested by the evolution of hydrogen was reckoned as unity, or, E =  1, r =  1,. 881. A pair
of electrodes having then been united to the poles, and the bath arranged for
electrotyping, the gas evolved was found to be only one-twentieth as much as
before. Calculate the relative value of r and L, and also the intensity of the
battery.
245. In the case of a Voltaic battery, so constructed that, when in use, the
exterior resistance L is equal to nineteen times the resistance of the battery r,
what would be the effect of doubling, trebling, and quadrupling the dimensions
of all the plates in the battery?
246. With the same conditions as in the preceding case, L =  19r, how would
the intensity of the current be changed by doubling the number of couples in
the battery?
247. In a battery in which L =  r, or the external resistance is equal to the
resistance of the battery, how will the intensity vary by doubling the number
of couples of the same dimensions in the battery?
248. When L =  4,-, what advantage would be gained by uniting two similar
batteries in a single series?
249. If in the use of a Voltaic battery of 100 pairs of plates, arranged in a
series, the exterior resistance, L, is found to be six times the resistance of the
battery, r, what change of intensity will be produced by so uniting the couples
as to form only four groups, each having twenty-five times the previous extent
of surface?




668                            APPENDIX.
ADDENDA.
NOTE TO ~ 369.-Uniform  musical pitch.-A general congress, called
together by the Society of Arts, at London, June 8, 1860, of musicians, amateurs, and otkers interested in music, have accepted the report of a committee
appointed in 1859, to consider the subject of uniform musical pitch. This committee recommend a pitch of 528 full vibrations for C' =-  440 for A, basing their
calculations on 33 single vibrations of an organ pipe 32 feet high, in place of 32
vibrations, the actual number. The following is the scale at this pitch-the
only one yet proposed which gives all the sounds in whole numbers:C    D    E    F    G    A    B    C'
264  297  330  352  396  440  495  528
This pitch is but 16 vibrations per second higher than the normal Diapason,
C' == 512, or "Stuttgard pitch," and 18 vibrations lower than the present pitch
of 546. It is therefore nearly half way between the two, being a quarter tone
above one, and the same quantity below the other.
The commission recently appointed to report on the pitch in France have
advised the following scale:C     D     E     F      G     A     B    C'
261  2981  326    348  3911  435  4891  522
The following is a list of the several pitches considered in this report:Handel's Tuning Fork (C. 1740) A at 416     C at 499k
Theoretical Pitch              A " 426 =  C " 512
Philharmonic Society (1812-42) A " 433 =  C " 5181
Diapason Normal (Paris, 1859) A " 435        C " 522
Stuttgard Congress (1834)      A "440 -  C " 528
Italian Opera, London (1859)   A "455 =-C " 546
(Journal of the Society of Arts, June 8, 1860.)
NOTE TO ~ 343.-The velocity of all sounds not the same.-Rev.
E. S. Earnshaw, of Sheffield, England, lately brings good evidence, both mathematical and physical, to show that the accepted views stated in 0 343 are correct
only for sounds having no very great difference of intensity. Every note in music
may be formed by two kinds of vibrations of the same rapidity, but differing in
wave-length and velocity of transmission. Only one variety of these waves is
supposed in general to be sensible by human ears. The velocity of sounds of
all kinds is a certain function depending upon the rapidity and length of vibration. In the case of violent thunder the numerical value of this function becomes
much greater than for ordinary sounds. These and other remarkable conclusions are sustained by mathematical reasoning. The author of the memoirs also
cites evidence to show that the crash of violent thunder-claps has been often
heard almost simultaneously with the flash of lightning, although the stroke
fell several miles distant. (London, Edinburgh, and Dublin Phil. Mgag., June,
July, Sept. 1860.)
NOTE TO g 392.-Sounds produced by insects.-Burmeister has shown
that the usual opinion of naturalists (expressed in ~ 392) is erroneous, and that the
sounds produced by insects are formed by the expansion and contraction of their
air tubes, the sound being formed by the passage of air through the orifices of
the tubes, which act like a whistle. ( Taylor's Scientific lMemnoirs, Vol. 1., p. 377.)




CHAPTER II.
PHYSICAL TABLES.
TABLE I.
MEASURES AND WEIGHTS.
ENGLISH MEASURES.
Measures of Length.
THE inch is the smallest lineal integer now used.  For mechanical
purposes it is divided either duodecimally or by continual bisection; but
for scientific purposes it is most convenient to divide it decimally. The
larger units are thus related to it:Mile. Furlongs. Chains. Rods. Fathoms.   Yards.    Feet.  Links.    Inches.
1= 8   80   320 = 880         1760  - 5280   = 8000  = 63360
1 —10=  40 —-110           220  -  660   = 1000  =  7920
1-   4-   11   =   22  -   66    - 100  -   792
1=   2-75       5-5    16-5        25  =   198
1         2  =    6   =       91=    72
1  =     3   =     46=    36
1         1- la     12
*000125-   00101 —01    04=.11= — 22-    0-66-    1  =           7-92
Measures of Surface.
Acre.      Roods.  Square Chains. Square Yards.  Square Feet.
1    =     4    =    10       -   4840   =    43,560
1    -      2-5    -   1210   =   10,865
1    =      484   =      4,356
1    =        9
Measures of Volume.
Cubic Yard.   Cubic Feet.  Cubic Inches.
=-    27    --    46,656
I    -       1,728
59                                                (669)




670                           APPENDIX.
Imperial Measure.
The Imperial Standard Gallon contains ten pounds avoirdupois weight
of distilled water, weighed in air at 62~ Fahr. and 30 in. Barom., or 12
pounds, 1 ounce, 16 pennyweights, and 16 grains Troy, = 70,000 grains'
weight of distilled water.  A  cubic inch of distilled water weighs
252'458 grains, and the imperial gallon contains 277'274 cubic inches.
Distilled Water..
Grains.   Avoir. lb.   Cubic Inches.   Pint.  Quart. Galls. Pecks. Bush. Qr.
8,750      1-25 -      34659  1
17,500 =    2-5  =      69318 -    2 _-    1
70,000 =  10  277-274 -    8 =    4=   1
140,000 -  20   -    554548 =  16 =    8 =   2 -   1
560,000 — 80   -   2,218-192- 64=   32     8 -  4   1
4,480,000 = 640   =  17,745-536    512 =  256 =  64 =  32 = 8 -  1
Apolhecaries' Measure.
The gallon of the former wine measure and of the present Apothecaries' measure contains 58,333-31 grains' weight of distilled water, or
231 cubic inches, the ratio to the imperial gallon being nearly as 5 to 6,
or as 0'8331 to 1.
Gallon. Pints.  Ounces.  Drachms.    Minims.   Gr.ofDist. Wat. Cub. Inch.
1 =   8 =   128  =   1024         61,440  -   58,333-31 =   231
1 =    16  =    128  =    7,680  =    7,291-66 =    28-8
g1 =         8 =       480 =       455.72 =       1-8
3 1          60  56-96  =              0-2
ENGLISH WEIGHTS.
Avoirdupois Weight.
Pound.          Ounces.           Drachms.              Grains.
I1              16       =        256       =        7000
1       =        16       -         437-6
1      =          27-34375
Apothecaries' l-oy Weight.
Pound.       Ounces.        Drachms.       Scruples.        Grains.
1     =      12      =      96     _       288     =       5760
1     =       8      =       24              480
1     -           3             60
1     -         20




PHYSICAL TABLES.                           671
FRENCH MEASURES.
Measures of Length.
1 Kilometre   =   1000 Metres. i 1 Metre           -   1 000 Metre.
1 Hectometre  =    100   "          I Decimetre   -   0.100   "
1 Decametre   =       10   "         1 Centimetre  =   0.010   "
1 Metre        -       1   "  1 Millimetre   -   0-001 
1 Kilometre   =   0-6214 Mile.    1 Centimetre  =- 0-3937 Inch.
1 Metre        =   3 2809 Feet.  2-539954 c. m.               1 I nch.
Comparison of Standard Measures.
1 Metre =  3-28089917 English Feet, =   3-28070878 American Feet.
1 Metre -  3-07844400 Paris Feet,  =  39-36850535 American Inches.
Measures of Volume.
1 Cubic Metre      =  1000-000 Litres.    1 Litre = 0-22017 Gallon.
1 Cubic Decimetre -       1 000   "        1 Litre -- 0-88066 Quart.
1 Cubic Centimetre -      0001   "         I Litre =  1-76133 Pints.
1 Cubic Metre       =   35-31660 Cubic Feet.
1 Cubic Decimetre  =   61-02709 Cubic Inches.
1 Cubic Centimetre -    0.06103 
FRENCH WEIGHTS.
1 Kilogramme  =  1000 Grammes.  1 Gramme              =  1-000 Gramme.
1 Hectogramme =   100         "          1 Decigramme  =  0-100'
1 Decagramme  =       10      "       1 Centigramme =  0-010 
1 Gramme        =       1     "       1 Milligramme =  0-001 
1 Kilogramme = 2-67951 Pounds (Troy), = 2-20485 Pounds (Avoirdupois).
1 Gramme    - 15 44242 Grains.
To convert French metrical quantities into English measures and
weights consult Table II.
To convert Grains into Grammes.
Log. Grains +  (- 2-8115680) =  Log. Grammes.
Tb convert Cubic Inches into Cubic Centimetres.
Log. Cubic Inches + 1-2144993 =  Log. Cubic Centimetres.
To convert Inches into Millimetres.
Log. Inches -t 1-4048337 =  Log. Millimetres.




TABLE II. 
FOR CONVERTING FRENCH DECIMAL MEASURES AND WEIGHTS INTO ENGLISH MEASURES AND WEIGHTS.
A.-MEASURES OF LENGTH.
1_2                 3          4          5          6           7          8           9
METRE,
English yards    1-09363   2-18727   3 28090   4-37453    5-46816    6-56180    7-65543    8-74906    9 84270
English feet.   3-28090   6-56180   984270  13-12360   16.40450   19-68539   22-96629   26-24719   29-52809
English inches  39 37080  78-74158 1111136 157-48315  196-85394  236-22473  275-59552  314-96630  354-33709
DECIMETRE,
Feet...   032809   0.65618   0-98427   1-31236    1-64045    1-96854    2-29663    2-62472    2-95281
Inches...   393708   7.87416  11-81124  15-74832   19-68539   23-62247   27-55955   31-49663   35-43371 
CENTIMETRE,
Inches...   0 39371   0-78742   1-18112   1-57483    1-96854    2-36225    2-75596    3-14966    3.54337 
MILLIMETRE, 
Inches...   0-03937   0-07874   0-11811   0-15748    0-19685    0-23623    0-27560    0-31497    0-35434
B.  MEASURES OF CAPACITY.
I_ 1  -   2      _  3          4          5          67                      8          9
CUBIC CENTIMETRE,
Cubic inch..   0-06103   012205   018308   0-24411    0-30514    0-36616    0-42719    0-48822    0-54924
LITRE,
Eng. imp. galls.  0-22017   0-44033   0.66050   0-88066    1-10083    1-32100    1-54116    1-76133    1-98149
Eng. imp. qts.   0.88066   1-76133   2.64199   3 52266    4-40332    5-28398    6-16465    7-04531    7-92598
Eng. imp. pints   1 76133   2-52266   5.28399   7-04531    8-80664   10-56797   12-32930   14-09062   15-85195
STERE,  
Gallons... 220-16643 440-33287 660-49930 880-66574 1100-83217 1320-99860 1541-16504 1761-33147 1981-49791
I   __ ___ _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_ _ ___~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~




TABLE II.-( Continued.)
FOR CONVERTING. FRENCH DECIMAL MEASURES AND WEIGHTS INTO ENGLISH MEASURES AND WEIGHTS.
C.-WEIGHTS.,_1                     1    2          3          4           5           6            7           8            9
KILOGRAMME,
Cwt....   0'01970   0-03939   0.05909   0.07879    009848    0-11818    0-13788    0-15758    0-17727
Pound (Avoird.)I 2-20486   4-40971   6-61457   8-81943   11-02428   13-22914   15-43400   17-63886   19-84371
KILOGRAMME,           
Pound (Troy). 2-67951   5-35903   8-03854  10-71805i  13-39757   16-07708   18-75659   21 43610   24-11562
GRAMME,
Grains..  15-44242  30-88484  46.32726  61 76968   77-21210   92-65352  108-09694  123-53936. 138-98178
DECIGIAMMIE,   >
Grains..  1-54424   3.08848   4-63273   6-17697    7-72121               9-26535   10-80969   12-35394   13-89818
CENTIGRAMME, 
Grains...   015442   0-30885   0-46327   0-61770    0-77212    0-92654    1.08097    1-235391   1-38982 
MILLIGRAMME,                                                                                                                       M
Grains...   001544   0-03089   0-04633   0-06177    0-07721    0-09265    0-10810    0-12354    0-13898
The following example will illustrate the method of using this table:Let it be required to find how many grains are equal to 87-435 grammes.
By column 8, line 4, of Table C, we find:      80 grammes        =  1235-3936 grains.
7, "  4,    "             ("             7     "  108-0969   "
4, "  5,' "    ".4   "        =       61770   "
" 3,    f,           "       ".03  "        -       0 4633 
" 5, "  7,    "   "    ".005"         -=      00772   "
87-435 grammes -   1350-2080 grains.
co




674                            APPENDIX.
TABLE III.
EXPANSION OF SOLIDS.
1,000,000 parts at 320 F.    At 2120 F.  Expansion.
part at 3        become     In length.   In bulk.     Authority
English Flint Glass. 1,000,811   1 in 1248- 1 in  316       Lavoisier
& Laplace.
Glass tube (French). 1,000,861   1 in 1148   1 in  382    Dulong &
Platinum.... 1,000,884   1 in 1131   1 in  377           Petit.
Palladium... 1,001,000   1 in 1000   1 in  333    Wollaston.
Tempered Steel.. 1,001,079   1 in  926   1 in  309          Lavoisier
& Laplace.
Antimony....   1,001,083   1 in  923  1 in  307    Smeaton.
Iron.....  1,001,182   1 in  846  1 in  282    Dulong &
Petit.
Bismuth.... 1,001,392   1 in  718   1 in  239              Smeaton.
Gold... 1,001,466   1 in  682   1 in  227  1
Copper....1,001,718   1 in  582   1 in  194
Brass.... 1,001,866   1 in  536  1 in  179            Lavoisier
Silver... 1,001,909   1 in  524   1 in  175    & Laplace.
Tin.....    1,001,937   1 in  516   1 in  172
Lead...... 1,002,848   1 in  351   1 in  117 
Zinc.....   1,002,942   1 in  340   1 in  113              Smeaton.
INCREASE OF MEAN EXPANSION BY HEAT.
Expansion for each degree F.
Between      Between      Between
32~ and 212~.  32~ and 392~. 32~ and 572~.
Glass...    1 in 69660   1 in 65340   1 in 59220
Platinum......             in 67860.....  1 in 65340
Iron........   1 in 50760....  1 in 40860
Copper...                  1 in 34920....  1 in 21060
Mercury.....           I in  9990   I in  9965   I in  9518
1,000,000 parts at 62~ F.  At 212~ F.   At 662c F.  At Freezing Point.
Black lead ware.  1,000,244  1,000,703
Wedgewood ware.  1,000,735  1,002,995
{ 1,009,926 maximum, but
Platinum...  1,000,735  1,002,995  {1  not fused.
Cast iron..     1,000,893  1,003,943    1,016,389
Wrought iron..  1,000,984  1,004,483  {,08, t  f               n
point of cast iron.
Copper....   1,001,430  1,006,347    1,0.24,376
Silver..     1,001,626  1,006,886    1,020,640
Zinc...   1,002,480  1,008,527    1,012,621
Lead...     1,002,323                1,009,072
Tin..     1,001,472               1,037,980
ok ]                   _ 




PHYSICAL TABLES.                            675
TABLE IV.
EXPANSION OF LIQUIDS.
BETWEEN 32~ AND 212~ F.
1,000,000 parts mercury become.. 1,018,153  1 in 55   Regnault.. "  pure water become. 1,046,600  1 in 21-3  Dalton.
"  "  sulphuric acid become    1,058,823 1 in 17   Dalton.
"      "  chlorohydricacid become 1,058,823  1 in 17   Dalton.
"      "  oil turpentine become    1,071,428  1 in 14   Dalton.
"    "  sulphuric ether become  1,071,428  1 in 14   Dalton.
"      "  fixed oils become.. 1,080,000 1 in 12-5 Dalton.. " calcohol become...1,111,000 1 in  9   Dalton.
"      "  nitric acid become.. 1,111,000 1 in  9   Dalton.
EXPANSION OF LIQUIDS OF SIMILAR CHEMICAL COMPOSITION.
Aldehyde.           Butyric Acid.        Acetate of Ethyl.
CJll402.             C01Hs04.               CeIIsO4.
0C.     Pierre.    Kopp.      Pierre.    Kopp.      Pierre.    Kopp.
(B. P. 220.)  (20-8~.)    (1630.)    (1570.)    (74110.)    (743~.)
0     10000      10000      10000      10000      10000      10000
10      9817       9830       9872       9867       9846       9843
25      9567       9596       9688       9667       9629       9622
45      9284                  9453       9439       9359       9352
60      9094                  9288       9271       9172       9165
75                            9128       9112       8996       8988
110                            8781       8765       8633
Chlorid Monochlo- Monochlo- Bichlori- Formiate of Ethyl.
of    rinated  rinated   nated                   Acetate of Methyl.
Ethylene. Chlorid  Chlo. of Chlorid  C11604.
C4114C12. of Ethyl. Ethvlene. of Ethyl. 
O'GiCr.      C4H14C12. C4HI3C13. C4HSCIS3.
Pierre.  Pierre.   Pierre.  Pierre.  Pierre.   Kopp.   Pierre.   Kopp.
(84-90.)  (64-80.)  (114-20.)  (74-90.)  (52-90.)  (54-90.)  (59.50)  (56-30.)
0   10000   10000   10000   10000  10000   10000   10000   10000
25    9667    9669    9693    9648    9632    9631    9633    9631.
55    9331    9300    9350    9267    9241    9243    9243    9243
80    9068    9003    9090    8988    8953                8955




676                           APPENDIX
TABLE V.
EXPANSION OF GASES.
EXPANSION FOR A CONSTANT VOLUME.*
Air.                            Carbonic Acid.
Pressure at  Pressure at Expansion for  Pressure at  Pressure at Expansion for
320 F.     2120 F.     1800 F.      320 F.      2120 F.    1800 F.
m.m,       m. m.                     m. m.      m.m.
109-72     149 31      0-36482      758-47    1034-54    0-36856
174-36     237-17      0-36513      901-09    1230-37    0-36943
266-06     395-07      0-36542     1742-93    2387-72    0-37523
374-67     510-35      0-36587     3589-07    4759-03    0'38598
375-23     510 95      0-36572
760-00                s0-36650
1678-40    2286-09      0-36760
1692 53    2306-23      0-36800
2144.18    2924-04      0-36894
3655.66    4992-09      0-37091
EXPANSION FROM 32~ TO 212~ F. AT A CONSTANT PRESSURE.*
Hydrogen.!      Air.          Carbonic Acid.       Sulphurous Acid.
m.mM.m.m.                           m..               mm..
60      661760 06613  0  036706     760  0-37099     760   0-3902
2545  0-36616    2525  0-36944   2520  0-38455         980   0 3980
2620  0-36964
TABLE VI.
RADIATING POWER ACCORDING TO PROVOSTAY-E, DESAINS,
AND MELLONI.
Lampblack being... 100         Rough silver (deposited on 
Pure rolled silver...   300     copper)..... 536
Pure burnished silver.      2-50   Burnished silver (pure).. 225
Rolled platinum...  10-80  Burnished platinum.. 950
Gold in leaf.....   4-28  Sheet copper...             490
* Cours de Physique. Par M. J. Jamin. Tome ii. p. 70.




PHYSICAL  TABLES.                            677
TABLE VII.
CONDUCTING POWER OF METALS AND BUILDING MATERIALS.
A.-CONDUCTING POWER OF METALS.
Name of Metal.              Despretz.   Wiedeman    Becquerel.
Gold........    1000-0        1000      1000
Platinum........                     981.0        158        124-91
Silver.........                       973 0       1880      1451-37
Copper.                                898-2       1383      1383 61
Brass........                        444
Steel........                                      218
Iron.........                       374 3        224        188-3
Zinc.........                        363 0                  375*3
Tin...                         303-9        273       212-09
Lead......                           1796         160        128 65
Palladium.....                  118       217-08
Bismuth........                                    34
Marble.........                       23 6
Porcelain.......       12-2
Brick clay.                            11-4
B.-CONDUCTING POWER OF BUILDING MATERIALS.
Conducting                           Conducting
Name of Substance.    power referred  Name of Substance.    power referred
to slate = 100.                      to slate = 100.
Plaster and sand..    18-70        Bath stone...          61-08
Keene's cement.  19-01              Fire brick.               61 70
Plaster of Paris..    20-26       Paniswick stone, H. P.      71-36
Roman cement.  20 88               Malen brick...       72-92
Lath and plaster..    25-55        Portland stone..  75-10
Fir wood...     27-61          Lunelle marble..       75-41
Oak wood.                33-66      Balsover stone, H. P.       76-35
Asphalt...          45-19      Norfal stone, H. P..       95 36
Chalk (soft)..     56-38      Slate.....                100-00
Napoleon marble..    58-27           Yorkshire flag...   110-94
Stack brick...    60-14     Lead...   521 34
__




678                           APPENDIX.
TABLE VIII.
ABSORPTIVE POWER OF DIFFERENT BODIES.
Names.                       Absorptive   Reflective
Power.     Power.
Smoke blackened surface.......                   100           0
Carbonate of lead.......         100           0
Writing paper.........                           98           2
Glass.............  90  10
China ink.                                        85          15
Gum lac...                               72          28
Silver foil on glass......          27          73
Cast iron, polished..                           25          75
Wrought iron, polished....       23          77
Mercury..........                 23         77
Zinc, polished...                             19          81
Steel.......                        17          83
Platinum, thick coat, imperfectly polished.       24          76
"     on copper......          17          83
"     leaves....  17                                    83
Tin...                                         14          80
Metallic mirrors, a little tarnished...       17          83.. "    nearly polished...              14          86
Brass, cast, imperfectly polished...           11          89'   hammered, imperfectly polished.             9         91
"."      highly polished...             7         93
"   cast,         "       ".           7         93
Copper, coated on iron...                      7          93
varnished..                              14          86
"    hammered or cast..                       7          93
Gold plating......                              5          95
Gold deposited on polished steel...             3          97
Silver, hammered, and well polished...          3          97
Silver, cast, and well polished.....          3          97
TABLE  IX.
ABSORPTIVE POWER FOR HEAT FROM DIFFERENT SOURCES.
Name of Substance.       Incandescent  Copper at   Copper at
Nameoubstance.     |Platinum.      400~.       1000.
Lampblack...              100         100         100
Carbonate of lead...                 56          89        100
China ink.                             95         87          85
Isinglass.......               54         64          91
Lac.                                   47         70          72
Metallic surface.....        13-5       13          13




PHYSICAL TABLES.                             679
TABLE X.
DIATHERMANCY OF DIFFERENT LIQUIDS.
row"~
Of 100 incident rays.
Trans-                               Transmitted                               mitted
Bisulphid of carbon (cclorless) 63   Ether.....                  21
Bichlorid ofsulph. (redbrown) 62   Sulphuric acid (colorless)         17
Terchlorid of phosphorus.  62   Sulphuric acid (brown).           17
Essence of turpentine...31   Nitric acid......  14
Colza oil (yellow)....  30   Alcohol..... 15
Olive oil (greenish)...  30   Distilled water...     11
TABLE XI.
[Ratio of Specific Heat to Atomic Weight.]
SPECIFIC HEAT.
A.-SOLIDS.
Water = 1.00.
Names.              Specific Heats. Atomic Weights.   Product,
C.             p.          CXp.
Aluminum.......          02143          13-7           2-94
Sulphur.......                    02026          16             3-24
Iron........                      0-1138         28             3.19
Cobalt.......                    0-1070         29-5           3-16
Nickel....                       0'1086         29-6           3-21
Copper.......                     00952          31-7           3-02
Zinc.....                         0-0956         32-6           3-12
Selenium......                  0-0762         40             3-04
Tin.........                    00562          59             3-31
Platinum......                0-0324         98-7           3-20
Lead........                      00314         103-7           3-26
Phosphorus....          0-1887         31             5-85
Arsenic.......                    00814          75             6-10
Silver......                  0-0570        108             6-16
Iodine........         0 0541        127             6-87
Antimony...          00508         120-3           6-11
Gold........                      0-0324        197             6-38
Bismuth.....                    0-0308        208             6-41
B.-LIQUIDS.
Mercury (liquid)....           0-03331        100            3-33
Mercury (solid)....         0-03241       100             3 24
Bromine (liquid)....       011094          80
Bromine (solid) 28~ C..       008432          80            6-74
L~~~~~~~~_~~8        6'74




680                           APPENDIX.
TABLE XI.-(Continued.)
SPECIFIC HEAT.
C.-GASES AND VAPORS.
Capacity for    Capacity for
Name of Substance.      equal weights. equal volumes.
Water of equal Specific Gravity.
Water - 1.  weightbeing=l. 
Atmospheric air*....           0-2379                      1-0000
Oxygen.......                   0-2182        0-2412        1-1056
Nitrogen......                02440         0-2370        0-9713
Hydrogen......                 3-4046        0-2356       0-0692
Chlorine......                0-1214        0-2967       2-4400
Bromine......                 00552         0-2992       5 3900
Nitrous oxyd...               02238         0-3413        1-5250
Nitric oxyd.....             0-2315        0-2406        1-0390
Carbonic oxyd...      0-2479        0-2399       0-9674
Carbonic acid....         5-2164        0-3308       1-5290
Sulphid of carbon                0-1575        0-4146       2-6325
Sulphurous acid..      0-1553        0-3489       2-2470
Ammonia gas...                 0-5080        0-2994        0-5894
Olefiant gas....           0-3694        0-3572       0-9672
Water vapor....           0-4750        0.2950       0-6210
Alcohol vapor....      04513         0.7171       1-5890
Ether vapor....           0-4810        1-2296       2 5563
Chloroform...           0-1568        0-8310       5-3000
Vapor of mercury...                                     6-9760
Vapor of Iodine....                                     87160
TABLE XII.
FREEZING MIXTURES.
|Substances.            Weight.    Cooling in Degrees F.
Sulphate of soda...8. 
Hydrochloric acid...            from + 50 to   00
Snow or ice........    2)
Common salt.......                 1 
Sulphate of soda.....    3                   + 500       3
Dilute nitric acid...      2J.            50     " - 
Sulphate of soda.....    6
Nitrate of ammonia....    5                 - + 500 ~ -14~
Dilute nitric acid..    4
Snow or ice.....           3            + 200      140
Chloride of calcium.... 4.                     - 20 " - 14  
* De la Roche and Berard.




PHYSICAL TABLES.                              681
TABLE XIII.
DIATHERMANCY OF DIFFERENT SOLIDS.
Substance of Screens.                    Sources of Heat.
[Each plate was 2-62 m. m. (0-1 in.) in thick.]  Naked    Ignited    Coppe  Copper
Flame.  Platinum.  750 F.   2120 F.
Rock salt (limpid).....                        3      92        923  9  92  92
Silician sulphur (yellow)...   74              77        60        54
Fluor spar (limpid)....    72           69        42        53
Rock-salt (cloudy)....              5        65        65        65
Beryl (greenish yellow)...    46           38        24        20
Iceland spar (limpid)....   39              28         6         0
Plate glass....... 39                     24         6         0
Quartz (limpid)......   38           28          6         3
Quartz (smoky)......   37                 28         6         3
White topaz.......   33                24         4          0
Tourmaline (dark green)...         18         16         3         0
Citric acid....... 11                     2         0         0
Alum.........                  9         2         0         0
Sugar candy (limpid)....                         1         0         0
TABLE XIV
TENSION OF VAPORS AT EQUAL DISTANCES ABOVE AND BELOW
THE BOILING  POINTS OF THEIR RESPECTIVE LIQUIDS.
Regnault.      Ure.         Ure.       Marx.        Avogadro.
Number of de-               Alcohol.
grees above or  Water.                    Ether.   Sulph't Carbon.   Mercury.  I
below boiling.
Temp. Pressure Temp. Pressure. Pressure Temp. Pressure Temp. Press ure
OF.  inches.  oF.  inches.  OF.  inches.  OF.  inches.  oF. inches.
+ 40~        252  63-14 
+ 200        232  44-06                124  42-64  137  40-19
Boilingp't. 212  30-00  173  30-00  104 13000  117  29-87  680  30-00
-~20~        192  19-87  153  19-30   84:20-90   97  20-65
-  40~       172  12-78  133  11-601 64  13 00   77  13-89  630  19-85
-~60~        152   7-94  113   6-70   44   8-101 57   9-07
-80~         132   4-67   93   3-67                   37   5-73 590  14-08
60




682                            APPENDIX.
TABLE XV.
MELTING POINTS AND LATENT HEAT OF FUSI)N OF DIFFERENT
BODIES.
Bii  PSubstances.  B Melting Point.  Latenter Heat.
Substances.OF.                          OF.        Water --- 1.
Mercury......                   39           5-11         0035
Oil of vitriol.....     -  30
Bromine......                  -   4
Water......                       1421           1.000
Phosphorus...            +111        808         0-056
Potassium (about)...           131
Yellow wax.....          143          78-32         0551
Sodium......          190
Iodine.......                     224
Sulphur......            239          1651         0116
Tin........                       455          25-74        0180
Bismuth......          518          2230         0156
Lead.......                      630           9-27        0 065
Zinc......                 761          49-43        0-347
Antimony......                    963
Silver.......                    1873          37-92        0-265
Copper.......        2143
Gold...                   2016
Cast iron (above)...         2786
Wrought iron.                  3280
Platinum......           4591
Nitrate of soda....         591         113-36          -797
Nitrate of potash...         642          83-12          584
Nitrate of silver....                     1334           -704
TABLE XVI.
BOILING POINT OF WATER UNDER DIFFERENT PRESSURES.
Boiling Point.     Barometer.        Boiling Point.      Barometer.
~F.             Inches.              ~F.              Inches.
184              16-676              200              23-454
186              17-421              202              24-441
188              18-196              204              25-468
190              18-992              206              26-529
192             19-822               208              27-614
194              20-687              210              28-744
196              21-576              212              29-922
198              22-498              214              31-120
* The numbers in this column may be considered as the number of pounds of
water that could be raised 1~ F. by the heat emitted during the congelation of
one pound of each of the substances included in the table.
t Plattner.




PHYSICAL TABLES.                           683
TABLE XVII.
BOILING POINTS OF LIQUIDS.
Temperature.                         Temperature.
OF.                                  oF.
Sulphurous acid.       17.6      Nitric acid, sp. gr. 1-42    248-0
Chlorid of ethyl.      51.9      Bichlorid of tin..      240-2
Aldehide...          69-4      Fousel oil....         269-8
Ether....              94-8      Terchlorid of arsenic     230-0
Bisulphid of carbon      118-5      Butyric acid...        314-6
Terchlorid of silicon    138-2      Naptha....         320-0
Ammonia, sp. gr. 0-945   140-0      Sulphurous ether.       320-0
Bromine....          145-4      Phosphorus...         554-0
Wood spirit...        149-9      Oil of turpentine.     568-5
Alcohol..            173-1      Linseed oil...        597-0
Dutch liquid...        184.7      Sulp. acid, sp. gr. 1-843    620-0
Water....     212.0      Mercury....           662-0
TABLE  XVIII.
BOILING POINT OF WATER AT DIFFERENT PLACES AND THEIR
ELEVATION ABOVE TIIE SEA.
Above (or be- Mean height
Names of Places.          low) the level   of the   Thermometer.
of the sea.  Barometer.
Feet.     Inches.     Degrees.
Donkia (Himalaya)..            -.     17,337  15-442    179-90
Donkia Pass (Himalaya)...          16,621    15-489       181-40
Farm of Antisana, S. A...      13,455     17-870      187-30
Micuipampa (Peru)....            11,870     19-020      190-20
Quito........                 9,541    20-750       194-20
Mexico.                               7,471     22-520      198-10
Hospice of St. Gothard..           6,808     23.070      199-20
Black Mountain, N. C. (highest            702    22 502        19967
point in the eastern U. S.)*.                 -
Mount Washington, N. H...           6,290    22-905    t200-43
Madrid........                        1,995    27-720       208-00
Salzburg.......       1,483     28-270      209-10
Plombieres.......                   1,381    28-390       209-30
Moscow.......                         984    28-820       210-20
Vienna.........                         436    29-410       211-10
Rome.......            151    29-760       211-60
Dead Sea (below Mediterranean   1316-7    31496    t214-44
Sea).... 
* Guyot.                   t Estimated by Forbes' coefficient.




684                            APPENDIX.
TABLE XIX.
BOILING POINT OF WATER AT DIFFERENT ATMOSPHERIC
PRESSURES.-REGNAULT.
Pressure in atmo-   iling Point of   Pressure in atmo-    Boilin- Point of
spheres of 30 inches   Water.        spheres of 30 inches       ^
mercury..            mercury               ater.
1             212  OF.              11              364-2 OF.
2             249-5                 12              371-1
3             273-3                 13              377-8
4             291-2                 14              384
5             306-0                 15              390
6             318-2                 16              395-4
7             329-6                 17              400-8
8             339-5                 18              405-9
9             348-4                 19              410-8
10             356-6                 20              415-4
TABLE XX.
LIQUEFACTION AND SOLIDIFICATION OF GASES.
Melting       Pressure in Atmospheres.
Names of the Gases.       Point.
OF.    At 32~ F.  At 60~ F.     OF.
Sulphurous acid..   -1050    1-53        2-54    5-16 at 1000
Cyanogen..                   30      2-37             4-00 at 63
Hydriodic acid..         -   60      3-97     5-86
Ammonia.....  103  4-4     6-90    10-00 at 83
Sulphuretted hydrogen        -- 122    10                  14-60 at 52
Protoxid nitrogen.           150    32                33 40 at 35
Carbonic acid....           70   38-5
Euchlorine...     65
Hydrobromic acid..           124
Fluorid of silicon...       220
(Chlorine..                             8'95    13-19
I Arseniuretted hydrogen
Phosphuretted hydrogen
1 Olefiant gas..                                        26-90 at   0~i
Fluorid of boron...                                 11-54 at  62HLydrochloric acid..                26-20             40    at  50
/ I   I       I




lo
TABLE XXI.
AQUEOUS VAPOR IN A CUBIC FOOT OF SATURATED AIR AT DIFFERENT TEMPERATURES.
Degrees Fahrenheit.
Degrees
Fahrenheit.   -
00       10         2       3         40       50        60        70       80        9
~E-4^  ~Grains.   Grains.   Grains.   Grains.   Grains.   Grains.   Grains.   Grains.   Grains.   Grains.
00    0545    0-569    0-595    0-621    0.649    0-678    0-708    0-739    0-772    0-806
~                 10~     0 841    0-878    0-916    0-957    0-999    1-043    1.090    1-138    1-190    1-243
vU     ~     20~      1-298    1-355    1.415    1-476    1-540    1-606    1-674    1-745    1-817    1-892
mn     1     930~     1-969    2-046    2-126    2-208    2-292    2-319    2-469    2-563    2-659    2-759
>            1^40~    2-862    2-967    3-076    3-180    3-306    3-426    3.550    3-679    3-811    3-948
P                 50~     4-089    4-234    4.383    4-537    4-696    4-860    5-028    5 202    5-381    5 562
60~     5-756    5-952    6-154    6-361    6-575    6-795    7-021    7-253    7-493    7.739
70~     7-992    8-252    8-521    8-797    9-081    9.372    9-670    9-977   10.292   10-616
80~    10-949   11-291   11-643   12-005   12-376   12.756   13-146   13-546   13-957   14-378
90~   14-810   15-254   15-709   16-176   16-654   17-145   17-648   18-164   18-693   19-235
100~   19-790   20-357   20-938   21-535   22-145   22-771   23-411   24-069   24-742   25-429




686                                APPENDIX.
TABLE XXII.-LATENT AND SENSIBLE HEAT OF STEAM.
Temp.   Latwit HeatanduSnsibleHeat. Temp.   Latent Heat.  Sum of Latent
and Sensible Heat.                        and Sensible Ileat.. -
Temp.   Latent Heat.   S                Latent           Heatnd Sensible  eat.320     1092.6~        1124-6~         248~        939-6~        1187-6
68       1067-4         1135-4          284         914-4         1198-4
86       1054-8         1140-8           320        889-2         1209-2
104        1042-2         1146-2          338        874-8         1212-8
140       1017-0          1157-0          374        849-6         1223-6
194         979-2        1173-2           410        822-6         1232-6
212         966-6        1178-6           446         795-6         12416
REGNAULT'S RESULTS.  ~ 683.
Pressure in Atmo-                                             Sum of Latent and
spheres.          Temperature.         Latent Heat.         Sensie at
0-0014                  0~               1114-0~              1114-00
0-006                  32                1091-7               1123-7
1 000                212                  966-6               1178-6
8.000                339                   877-3               1216-8
L
TABLE XXIII.-SPECIFIC GRAVITY OF SOLIDS AND LIQUIDS.
Substances.         Sp. Gravity.          Substances.         Sp. Gravity.
Platinum....    21-          Sulphate of lime..       2-32
Gold.....                  19-24        Sulphur...           203
Tungsten....        17           Bone......   1'8-1'99
Mercury.                   1360         Ivory.....      192
Rhodium and Palladium         1           Caoutchouc...         0989
Silver......                1047         Sodium.....           097
Bismuth..  9-82                   Wax......                 097
Copper....               8-78        Gutta-percha...        0966
Arsenic.....             860         Ice.......                  09175
Steel......                 781         Pumice-stone..        092
Iron......                 7-78        Potassium...       0-86
Meteoric iron..       7-26-7-79       Pine wood...       066
Cast iron....          7-21       Cypress wood..             0-60
Zinc......                 6-86        Cedar wood...         0-56
Antimony...              6-71        Common poplar.            038
Iodine......                 4-95       Lombardy poplar..            0-36
Heavy spar...             4-43        Cork....  024
Oriental ruby..            4-28               LIQUIDS.
Topaz......                  356        Sulphuric acid...         184
Diamond....               3-50       Nitrous acid...         1-55
English flint-glass           3-33       Water from Dead Sea           1-24
Parian marble..          2-84       Nitric acid....'22
Emerald...       2-77        Milk......                103
Pearl......                  275         Wine.....                  099
Iceland spar..           2-72        Linseed oil...          0-94
Common marble..           270         Spirits turpentine.         087
Coral.....    2-68        Absolute alcohol..       079
Quartz.....       265        Naphtha, "light oil".         0-733
Agate....   261         Sulphuric ether.          072
St. (Gobain's glass.  2 49               Eupion...        0-65
_..'4.9                    _           A,      A




PHYSICAL TABLES.                          687
TABLE XXIV.
VOLUME AND DENSITY OF WATER.-BY KOPP.
Temperature. Volume of Water ~p Gr. of Water Volume of Water Sp. Gr. of Water
C.       (at 0~-= 1).    (at 0~ = 1).    (at 40 = 1).    (at 40 - 1).
0        1-00000       1-000000       1-00012       0-999877
1        0-99995       1-000053       1-00007       0-999930
2        0-99991       1-000092       1.00003       0-999969
3        0-99989       1 000115       1 00001       0-999992
4        0-99988       1-000123       1.00000       1-000000
5        0-99988       1-000117       1.00001       0-999994
6        0-99990       1-000097       1-00003       0-999973
7        0-99994       1-000062       1-00006       0-99939
8        0-99999       1-000014       1-00011       0-999890
9        1-00005       0-999952       1-00017       0-999829
10        1-00012       0-999876       1 00025       0-999753
11        1-00021       0-999785       1-00034       0-999664
12        1-00031       0-99968q       1-00044       0-999562
13        1-00043       0-999572       1-00055       0-999449
14        1-00056       0-999445       1-00068       0-999322
15        1-00070       0-999306       1-00082       0-999183
16        1 00085       0-999155       1-00097       0-999032
17        1.00101       0-998992       1-00113       0-998869
18        1-00118       0-998817       1-00131       0'998695
19        1-00137       0-998631       1-00149       0-998509
20        1-00157       0-998435       1-00169       0-998312
21        1-00178       0-998228       1-00190       0-998104
22        1-00200       0-998010       1-00212       0-997886
23        1-00223       0-997780       1 00235       0-997657
24        1-00247       0-997541       1-00259       0-997419<
25        1-00271       0-997293       1-00284       0-997170
26        1-00295       0.997035       1-00310       0-996912
27        1-00319       0-996767       1-00337       0-996644
28        1-00347       0-996489       1-00365       0-996367
29        1-00376       0-996202       1-00393       0-996082
30        1-00406       0-995908       1 00423       -0995787
35        1 00570
40        1-00753
45        1-00954
50        1-01177
55        1-01410
60        1-01659
65        1-01930
70        1-02225
75        1-02541
80        1-02858
85        1-03189
90        1-03540
95        1-03909
100        1-04299
6': ~ effpv,




688                          APPENDIX.
TABLE XXV.
COMPARISON OF THE DEGREES OF BEAUME'S HYDROMETER WITH
THE REAL SPECIFIC GRAVITY.
A.-FOR LIQUIDS HEAVIER THAN WATER.
Specific          Specific          pecific  Degrees.  Specific
Degrees.  ravity.                  Degrees. Gravity.    gree.   ravity.
Gravity.          Gravity.         Gravity.          Gravity.
0     1-000     20      1-152     40      1-357     60      1-652
1     1-007     21      1-160     41      1-369     61      1-670
2     1-013     22      1-169     42      1'381     62      1-689
3     1-020     23      1178      43      1-395     63      1-708
4     1-027     24      1-188     44      1-407     64      1-727
5     1 034     25      1 197     45      1-420     65      1-747
6     1-041     26      1-206     46      1-434     66      1-767
7     1-048     27      1-216     47      1-448     67      1-788
8     1-056     28      1-225     48      1-462     68      1.809
9     1-063     29      1-235     49      1-476     69      1-831
10     1-070     30      1-245     50      1-490     70      1-854
11     1-078     31      1-256     51      1-495     71      1-877
12     1-085     32      1-267     52     1-520      72      1-900
13     1-094     33      1-277     53  1-535         73      1-924
14     1-101     34      1-288     54      1-551     74     1-949
15     1-109     35      1-299     55      1-567     75      1-974
16     1-118     36      1310      56      1-583     76     2 000
17     1-126     37      1321      57      1-600
18     1-134     38      1-333     58      1-617
19     1143      39      1345      59      1-634
B.-FOR LIQUIDS LIGHTER THAN WATER.
De.  Specifi   Degrees.  Specific  Degrees.  Specific  c
Gravityegrees.            Gravity.                   Degreesavity.  Gravity.Degrees.
10     1 000     23       -918     36       -89      49       789
11      -993     24       -913     37       -844     50       -785
12      -986     25       907      38       -839     61       -781
13      -980     26       -901     39       -834     52       *777
14      -973     27       -896     40.-830     53       773
15      -967     28       -890     41       -825     54       *768
16      -960     29       -885     42       -820     55       -764
17      -954     30       *880     43       -816     56       -760
18      -948     31       -874     44       -811     57.757
19      -942     32       -869     45       -807     58       *753
20      -936     33       -864     46       -802     59       -749'21      -930     34       -859     47       -798     60       *745
22      -924     35        854     48       -794




PHYSICAL TABLES.                           689
TABLE XXVI.
TENSION, VOLUME, AND DENSITY OF AQUEOUS VAPOR.
Temperature I                   Tension        Volume       Weight of a
of Vapor.    Tension of Vapor   expressed by   occupied by a    cubic metre of
Degrees      expressed in    a column of  kilogramme of  Aqueous Vapor
Centigrade.   Atmospheres.      mercury    vapor, in cubic  in kilogrammes.
in metres.     metres.
0~          o T 00 or     06    0-00460    2 05-222400  0-00487266
17-86         or 0-0200      0-01520      66-144960      0-01512517
29-37   1    or 0'0400       0 03040      34-364490      0-02909000
33-30     aor 0-0500         0-03800      27-852530      0-03590307
37-38.or 0-0625       0-04750      22-578310      0-04430600
42-66     1or 00833          0'06330      17-232270      0-05803375
46-25     1 or 0-1000        0-07600      14-515640      0-06892666
50-60         or 0-1250      00900        119500 1-95 0008495800
53-35         or 0-1428      0-10857      10-391950      0-09622000
56-63         or 0-1666      0-12666       8-996440      0-11119230
60-40         or 0-2000      0-15184       7-582970      0-13185937
65-36      i or 0-2500       0-19000       6-156670      0-16240770
81-72         or 0-5000      0-38000       3-227120      0-30983570
92-18       4 or 07500       0-57000       2-215120      045141000
100'    1  or 1-0000         0-76000       1-696000      0-59130000
106-33    1  or 1-2500       0-95000       1-380541      0-72430000
111-83     1~ or 1-5000       1-14000       1-167228      0-85670000
116-50     1 or 1-7500        1-33000       1-012619      0-98752500
120-64     2  or 2 0000       1-52000       0-895462      1 11571700
124-39     21 or 2-2500       1-72000       0-798033      1-25305700
127-83     21 or 2-5000       1-90000       0-729463      1-37087500
130-98     23 or 2-7500       2-09000       0-668363      1-49620700
133-91     3 or 3-0000        2-28000       0-616697      1-62038400
136-72     31 or 3-2500       2-47000       0-573576      1-74340000
139-29     31 or 3-5000       2-66000       0-534694      1-86582600
141-72     33 or 3-7500       2-85000       0-503167      1-98731800
144-       4  or 4-0000       3-04000       0-474320      2-10828500
146-28     4- or 4-2500       3'23000       0-448860      2-22780000
148-44     41 or 4-5000       3-42000       0-426093      2-34683300
150-35     41 or 4-7500       3-61000       0-405507      2-46605500
152-26     5  or 5-0000       3-80000       0-386960      2-58417600
154-15     51 or 5-2500       3-99000       0-370170      2-70135200
155-94     5~ or 5-5000       4-18000       0-354778      2-81225050
157-64     53 or 5-7500       4-37000       0-340669      2-93460000
159-25     6  or 6-0000       4-56000       0-327779      3 05078500
165-40     7  or 7-0000     532000          0-284938      3-50930700
170-84     8  or 8-0000       6 08000       0-252423      3-97063600
175-77     9  or 9'0000       6-84000       0-226771      4-40770000
180-30     10 or 10-0000      7-60000       0-206248      4-84844400
184-60     11 or 11-0000      8-36000       0,189189      5-28325000
188-54     12 or 12-0000      9-12000       0-174952      5-71425000
190-             12-4250      9'44300       0-169437      5-91142800
195-             13-8160    10-52000        0-153660      6-50428600
200.             15-3560    11-68900        0-138717      7-31716600
230.             27-5340    20-92600        0-083115    1203722000
_, ~~,_______~  __________ _   _______       __ _I _ _




IvMo-r I S i^t 




ANSWERS TO PROBLEMS.
Prob. 1. Ans. (a.) 147640-46 yds.; (b.) 1-021 inches; (c.) 0-03937079 inch;
(d.) 1-1811237.
Prob. 2. Ans. (a.) 1-39697 metres; (b.) 1131-5495 metres; (c.) 20-921 kilometres; (d.) 4-57 metres.
Prob. 3. Ans. (a.) I litre and 703-258 cubic centimetres; (b.) 11 gallons;
(c.) 31-7936 litres; (d.) 0-01232931 pint.
Prob. 4. Ans. (a.) 0-63499 metre; (b.) 54-7286 Amer. inches; (c.) 22-86
metres; (d.) 5468-48 Amer. yards.
Prob. 5. Ans. (a.) 4258-1458 cubic centimetres; (b.) 45419-4486 cubic centimetres; (c.) 0-1618 gallon.
Prob. 6. Ans. 0-1515 foot per second.
Prob. 7. Ans. 60 X  - feet.
Prob. 8. Ans. Unit of time =  0-3896 second.
Prob. 9. Ans. At an angle of 36~ 52' 12" with the component 4, and with a
velocity =  5.
Prob. 10. Ans. Speed of A        8=   ~ of speed of B.
Prob. 11. Ans. Velocity =  180 feet per second; distance = 1800 yards.
Prob. 12. Ans. 20 feet per second.
Prob. 13. Ans. Retardation =  25 feet per second; distance =  3121 feet.
Prob. 14. Ans. 251426 lbs.
Prob. 15. Ans. 31,250 feet per second or 5.9 miles.
Prob. 16. Ans. It would not.
Prob. 17. Ans. 144 feet, 9 inches.
Prob. 18. Ans. 3 seconds.
Prob. 19. Ans. If h represent the height of the tower, the velocity required =   /gh.
Prob. 20. Ans. If v represents the vertical velocity of the balloon, the
height =    - (gt -  v).
Prob. 21. Ans. The height        X  (t + -       
8          gt I
Prob. 22. Ans. 396-03 feet.
Prob. 23. Ans. 641 feet.
Prob. 24.  Ans. Height of bridge =  100-52 feet; time required =  2-4 seconds.
(691)




692                      ANSWERS TO PROBLEMS.
Prob. 25. Ans. 402TZ feet.
Prob. 26. Ans. Velocity -= 1l9  X  t seconds of ascent and return.
Prob. 27. Ans. 208-44 feet.
Prob. 28. Ans. 6-2 seconds.
Prob. 29. Ans. 96-75 feet.
Prob. 30. Ans. 103-37 miles per hour.
Prob. 31. Ans. The train cannot ascend such a grade without more steam. It
would require an initial velocity of 54.69 miles per hour to overcome such a grade.
Prob. 32. Ans. 265-099 lbs.
Prob. 33.  Ans. 3-3256 lbs.
Prob. 34.  Ans. Twelve times its present velocity.
Prob. 35.  Ans. 8-45 revolutions per second.
Prob. 36.  Ans. 1-74 seconds.
Prob. 37.  Ans. 311 feet.
Prob. 38. Ans. 0-88 second.
Prob. 39.  Ans. 1-003 seconds.
Prob. 40.  Ans. At New York g =   21l =  32-155399 feet.
At Cape Horn g =  7r21 =  32-205083 feet.
At Boston g =  32-17076 (1 -000259 cos. 2X) =  32-163064 ft.*
At New Orleans g =  "           "   "  "     =  32-125757 ft.*
At Stockholm g =    "             " "        =  32-131002 ft.*
Prob. 41.  Ans. g' == -Tg'
Prob. 42. Ans. 13916-25 feet =  2-64 miles.
Prob. 43. Ans. 31088 feet -  5-89 miles.
Prob. 44. Ans. 24-87 seconds.
Prob. 45. Ans. 35~ 19' 43"-5 or 54~ 40' 16"-5.
Prob. 46. Ans. 736-35 feet per second.
Prob. 47. Ans. 4!l times greater.
Prob. 48. Ans. 21-21 miles per hour.
Prob. 49. Ans. As 1 to 21.
Prob. 50. Ans. 50 feet.
Prob. 51. Ans. As I to 7:.
Prob. 52. Ans. 24 feet from the smaller weight.
Prob. 53. Ans. Under the weight 7.
Prob. 54. Ans. 125 lbs. and 75 lbs.
Prob. 55.  Ans. At one point 9~ cwt., at the other 20~ cwt.
Prob. 56. Ans. Pressure on A =-  104 cwt.; pressure on B -  17'6 cwt.
Prob. 57. Ans. 40 lbs.
Prob. 58. Ans. Diameter of axle 2]6 inches.
Prob. 59. Ans. 92-4 lbs.
Prob. 60. Ans. 156 cwt.
Prob. 61. Ans. 1382-4 tons.
Prob. 62. Ans. 4970 lbs.
Prob. 63. Ans. 31 cwt.
Prob. 64. Ans. 60 lbs.
Prob. 65. Ans. 12 cwt.
Prob. 66. Ans. A power equal to 8 cwt. would balance the train, but some
additional force is required to impart motion independent of friction, which is
not considered.
Prob. 07.  Ans. 67858-56 lbs.
" Approximate values.  See 4 90.




ANSWERS TO PROBLEMS.                                693
Prob. 68. Ans. 79-58 lbs.
Prob. 69. Ans. 10 lbs.
Prob. 70. Ans. A force of 18 cwt. in both cases.
Prob. 71. Ans. 476-22 horse-power.
Prob. 72. Ans. 1-5874 times greater.
Prob. 73.  Ans. 11-94 miles per hour.
Prob. 74. Ans. At 140, 12321-53 kilogrammes; at 50~, 12925-69  kilogrammes; at 2120, 13885.42 kilogrammes; at 392~, 12291.67 kilogrammes.
Prob. 75. Ans. At 50~ a rod having a section of one square millimetre would
be elongated one-fourth of an inch.
Prob. 76. Ans. Double the weight in the first case.
Prob. 77.  Ans. Sixteen times as much as if the beam were secured at one
end and the weight applied at the other extremity.
Prob. 78. Ans. Tempered steel, 5634-95 to 7546-76 lbs.; untempered steel,
5433-5 to 6238-7 lbs.
Prob. 79.  Ans. 0-07 inch.
Prob. 80.  Ans. 3498-86 lbs. to 8724-71 lbs.
Prob. 81. Ans. 15-474 tons to 18-548 tons of 2000 lbs.
Prob. 82.  Ans. Considering the ends secured by union with the entire structure, the breaking weight =  2990-18 tons; considering the ends not secured,
but merely supported on the piers, the breaking weight = 1495-09 tons.
Prob. 83.  Ans. If the ends are securely fastened the working load =  532-69
tons; but if the ends are merely supported the working load =  233'67 tons.
Prob. 84. Ans. 280-69 tons. Since the entire structure forms a continuous
tube, the ends of the middle span are securely fastened.
Prob. 85. Ans. 59-43 tons.
Prob. 86. Ans. v -  5-85579 feet per second; v' =  8'67579 feet per second;
=-  6-1  feet per second.
Prob. 87. Ans. m -=  7Am'.
Prob. 88. Ans. e -- 06.
Prob. 89. Ans. 153 feet.
1
Prob. 90. Ans. r          -
2n-1
Prob. 91. Ans. 25-6 feet.
Prob. 92. Ans. 84-3 feet per second.
Prob. 93. Ans. Condensation =  0-001006; specific gravity =  1-001007.
Prob. 94. Ans. Specific gravity =  1-0487.
Prob. 95.  Ans. 0.5723 of a cubic inch.
B2
Prob. 96.  Ans. The pressure =  P X.
Prob. 97. Ans. Pressure: Power -4050: 1.
Prob. 98. Ans. Pressure on the bottom =  the weight of the liquid =  half
the sum of the pressures on the four sides.
Prob. 99. Ans. 0-5773 a, 0-2392 a, and 0-1835 a.
Prob. 100. Ans. P: P' =1: 2.
Prob. 101. Ans. As the height of the cylinder to its radius.
Prob. 102. Ans. Pressure of water =   1101-3 lbs.; pressure of mercury
=  748888 tons.
Prob. 103. Ans. Let R =  pressure on the triangles, the pressure on the
4c              /     4c2
)base being reckoned as unity.  Then:-R =  i  i  + -   -- +i A        1 --.
61                            2Z




694                      ANSWERS TO PROBLEMS.
Prob. 104. Ans. 7138-1 grs. =  1-0197 lbs.
Prob. 105. Ans. 1-83823 feet.
Prob. 106.  Ans. 14-4 inches.
Prob. 107. Ans. 500 lbs.
Prob. 108. Ans. 0-03789 X  given weight of the iron.
Prob. 109. Ans. 11-50228 ounces.
Prob. 110. Ans. Gold =  13-8102 ounces, silver =  8-1898 ounces.
Prob. 111. Ans. The addition of 10 lbs. of lead weights under water to produce
equilibrium shows that 209-5 lbs. of iron are concealed in the commercial lead.
Prob. 112. Ans. 5-0752 lbs.
Prob. 113. Ans. 0-6028 diameter.
Prob. 114. Ans. 138-637 cubic inches.
Prob. 115.  Ans. 64-1832 cubic feet.
Prob. 116.  Ans. 473-538 tons.
Prob. 117.  Ans. 67-698 tons.
Prob. 118. Ans. 0-9825 feet.
Prob. 119.  Ans. Volume of B =  4795-34 cubic inches =  2-775 cubic feet;
(both cases assume a depth of twenty feet below the surface).
Prob. 120.  Ans. Specific gravity =  3-84.
Prob. 121.  Ans. Specific gravity of granulated tin =  7'288.
Prob. 122.  Ans. Specific gravity - 3-8093.
Prob. 123.  Ans. Specific gravity of the first =  2-8; specific gravity of the
second =  1-0946.  The volumes of the two bodies are as I to 14-8.
Prob. 124.  Ans. Specific gravity =  8-13.
Prob. 125.  Ans. Specific gravity =  -832.
Prob. 126.  Ans. 23-385 gallons.  Theoretical discharge, 37-718 gallons.
Prob. 127. Ans. Actual range, 15-187 feet.
Prob. 128. Ans. Actual velocity =  0-3833 theoretical velocity.
Prob. 129. Ans. 10180-217 gallons.
Prob. 130. Ans. 38,450 gallons, or 610 hogsheads.
Note.  In the formula, D =  20S           ~, all the quantities, H, d, and 1,
are to be taken in metres, and the result gives D in cubic metres per second.
Prob. 131. Ans. 97-496 feet.
Prob. 132. Ans. If the actual height of the mercury is I inch, the height of
the alcohol will be 22-68 inches, difference of level 21-68 inches.
Prob. 133.  Ans. 63-68 miles.  This problem involves the principles of. 172.
Prob. 134. Ans. 286-1855 lbs.
Prob. 135. Ans. 1156-3 lbs.
Prob. 136. Ans. 0-0796 grain.
Prob. 137. Ans. 460-00437 grains.
Prob. 138.  Ans. Capacity of the globe =  148-626 cubic feet; specific gravity
of gas = 0-0767.
Prob. 139.  Ans. 31-7576 feet.
Prob. 140. Ans. 68 feet.
Prob. 141.  Ans. 17-98 feet.
Prob. 142.  Ans. 6655-85 feet.
Prob. 143.  Ans. Ascensional force with illuminating  gas, 358-4837 lbs.;
ascensional force with hydrogen, 473-0793 lbs.
Prob. 144.  Ans. The conditions of this problem  require that the weight of
the balloon should be nothing, or that the ballast should have an ascensional




ANSWERS TO PROBLEMS.                                  695
force of its own equal to the weight of the balloon, since, at the height indicated,
if the enclosed gas could not expand, it would of itself be in equilibrium with
the atmosphere. If one-half the gas were liberated the balloon would ascend;
to make it remain stationary an amount of ballast must be added equal to the
weight of the gas liberated, or equal to one-fourth the weight of air which would
fill the balloon at the surface of the earth.
Prob. 145.  Ans. The tube will admit no water by compression of the air.
Prob. 146.  Ans. 0-016 inch.
Prob. 147.  Ans. 45-10735 gramlnes.
Prob. 148.  Ans. 76-306 centimetres.
Prob. 149.  Ans. -613-, /1,  14, ]-81.
Prob. 150.  Ans. 5 lbs. 10 oz.
Prob. 151.  Ans. 009698 inch.
Prob. 152.  Ans. Four times as long.
Prob. 153.  Ans. 8105~ feet, or a little more than 11 miles.
Prob. 154.  Ans. Velocity at 90~ F. =   1150-091 feet per second, and at
-40~ F. =  1007-091 feet per second.
Prob. 155. Ans. 11-2 seconds.
Prob. 156. Ans. In iron, 1-59 seconds; in wood, 1-03 to 1-65 seconds; in
carbonic acid, 21'49 seconds; in hydrogen gas, 4-44 seconds; in vapor of alcohol at 140~ F., 21-44 seconds; in vapor of water at 154~ F., 13-72 seconds.
Prob. 157.  Ans. 27 minutes, 9 seconds.
Prob. 158. Ans. 1677-45 feet in the most favorable position.
Prob. 159.  Ans. 422 feet.
Prob. 160.  Ans. 125-69 miles.
Prob. 161.  Ans. 13 seconds.
Prob. 162.  Ans. Distance =  2294 feet; velocity =  764 feet per second.
Prob. 163.  Ans.'7 of its length.
Prob. 164.  Ans. 101o   vibrations.
Prob. 165. Ans. 3-408 feet.
Prob. 166. Ans. E: D   =  25: 24.
Prob. 167. Ans. 2 048
Prob. 168. Ans. It is higher by a commta.
Prob. 169.  Ans. The chromatic semitone = -1; the grave chromatic semitone =- 2Prob. 170. Ans. 1800 beats per minute.
Prob. 171. Ans. Vibrations per minute for one node, 66-56; for two nodes,
133-13; for three nodes, 199-695; for four nodes, 266-26 vibrations.
Prob. 172.  Ans. 263-57.
Prob. 173.  Ans. Reduce the length of the tube to 9-343 metres.
Prob. 174.  Ans. For C 1, 8-0405 feet; D 1, 7-0939 feet; E 1, 6-3407 feet; F 1,
b-9262 feet; G 1, 5-2214 feet; A 1, 4-6618 feet; B 1, 4-1022 feet; C 2, 3-8326 feet.
Prob. 175.  Ans. 11-39 in., 10-03 in., 8-95 in., 8-38 in., 7-37 in., 659 in., 5-8 in.,
5-45 in.
Prob. 176.  Ans. F 5 (too flat), A 5 (too high by half a semitone), and C 6
(also too high by half a semitone).
nV
The formula N =               gives for
L +  -,B
n =  2         N-  2672-5           while F 5 =  2739 2.
=-  3         N - -  35386        while A 5 =  3424.
o - 4         N-  4223-2            while C 6 =  4108-8.




696                     ANSWERS TO PROBLEMS.
Prob. 177. Ans. 8 minutes, 14-79 seconds.
Prob. 178. Ans. 46 years, 155 days, 10 hours, 8 minutes, and 45 seconds.
Prcb. 179. Ans. As 1 to 21.
Prob. 180. Ans. 90~ per cent.
Prob. 181. Ans. 22-85 candles.
Prob. 182. Ans. 21-43 candles.
Prob. 183. Ans. 60~.
Prob. 184. Ans. 18, including the object itself.
Prob. 185. Ans. 66 inches.
Prob. 186. Ans. 7-2 inches.
Prob. 187.  Ans. u =  -r r/.
Prob. 188. Ans. Once and a half the distance of the object from the first
surface.
Prob. 189. Ans. 39~ 49' 3", when the eye is 5 feet above the water.
Prob. 190. Ans. 6 feet, 8 inches.
Prob. 191. Ans. i =  2.
Prob. 192. Ans. At a distance of 2-571 feet from the refracting surface, and
on the same side as the radiant point.
Prob. 193. Ans. The surface is convex, and r =  7-2 inches.
Prob. 194. Ans. On the opposite side of the lens at a distance of 3-134 inches.
Prob. 195. Ans. r: 8 =  10: 242, the surface of shorter curvature being
turned towards parallel rays.
Prob. 196. Ans. 6-44 inches.
Prob. 197. Ans. A convex lens in which f-  4 inches.
Prob. 198. Ans. A double convex lens of crown glass r =  2-955 inches,
=-  2-667 inches, and a concavo-plane lens of flint glass r- =- 2-667 inches, and
8' = infinity, i. e. the second surface is plane.
Prob. 199. Ans. They must converge toward a point between the lenses and
distant -f from the first.
Prob. 200. Ans. 2 diameters.
Prob. 201. Ans. r =  0-449 inches, s -  - 1-235 inches.
Prob. 202. Ans. 161280 times the light received by the unassisted eye.
Prob. 203. Ans. Illuminating power- 362880; penetrating power =  602-4.
Prob. 204. Ans. Illuminating power =  18225; penetrating power =  135.
Prob. 205. Ans. The illuminating power given by 150~ aperture is 21 times,
and the penetrating power 1I times as great as that given by 100~ aperture.
Prob. 206. Ans. Crown glass, 56~ 43' 40"; plate glass, 56~ 36' 26"; flint
glass, 57~ 30' 18".
Prob. 207.  Ans. Reflected by crown glass, 0-0726; by plate glass, 0-0738;
by flint glass, 0-0869.
Prob. 208. Ans. 1-544.
Prob. 209. Ans. Degrees F.   =  Degrees C. -   Degrees R.
-400~  -= 40 ~                 -=  32o
-4    -    -20                    — 16
+158   =    +70   =    +56
+194      =       +90        =      +72
+-442-4   =      +228       =      +182-4
+771-8   =       +411       += 328S8
+-977   =   +525   =   +420
+1832   =   +1000   =   +800
+9732          - +5388-9           +4311-12




ANSWERS TO PROBLEMS.                                  697
Prob. 210.  Ans. Degrees C.  _   Degrees F.  =    Degrees R.
30~87    =        38~0966  -=      -3096
-40         =      -40                - 32
-10         -=     +14          =     -8
+75   -=  +167    =  +60
+290          =  +554            -  +232
+;60          =    +680          =    +288
Prob. 211.  Ans. 18,9; times.
Prob. 212. Ans.
At 10~ F.           250 F.           75~ F.            1000 F.
Iron... 3 ft. 1-99002 in.  3 ft. 1-99376 in. 3 ft. 2-00623 in. 3 ft. 2-01248 in.
Brass.. 3 ft. 1-98425 in. 3 ft. 1-99016 in. 3 ft. 2-00984 in. 3 ft. 2-01968 in.
Copper. 3 ft. 1-98550 in. 3 ft. 1-99093 in. 3 ft. 2-00906.in. 3 ft. 2-01812 in.
Glass.. 3 ft. 19932 in. 3 ft. 1-99578 in. 3 ft. 2-00403 in. 3 ft. 2-00670 in.
Platinum.3 ft. 1-99253 in. 3 ft. 1-99533 in. 3 ft. 2.00466 in. 3 ft. 2.00933 in.
Silver.. 3 ft. 198387 in. 3 ft. 1-98992 in. 3 ft. 2-01060 in. 3 ft. 2-02014 in.
Prob. 213.  Ans. 1-002672 gallons.
Prob. 214.  Ans. 0-134 inch.
Prob. 215. Ans. 41~-51 Fahrenieit.
Prob. 216.  Ans. 0-04728 in.
Prob. 217. Ans. At London, steel 92-93378 in.; brass 53-79322 in.
At Paris, steel 92-90854 in.; brass 53-77861 in.
At New York, steel 92-84311 in.; brass 53-74073 in.
At St. Petersburgh, steel 93.00482 in.; brass 53-83434 in.
Prob. 218.  Ans. (1.) 30-0757 in.; (2.) 29-42076 in.; (3.) 27-8075 in.; (4.)
28-1778 in.; (5.) 23-158 in.; (6.) 24-581 in.; (7.) 17-4228 in.; (8.) 15-835 in.
Prob. 219. Ans. (1.) 24-0962 in.; (2.) 27-58513 in.; (3.) 28-74528 in.; (4.)
19-539 in.
Prob. 220. Ans. 112-588 grains.  (Calculated by Table XXIV.)
Prob. 221. Ans. 1220-75, 245~05, and 3680~25 above its previous temperature.
Prob. 222.  Ans. 1220-357 cubic feet.
Prob. 223. Ans. Water, 5500 units; sulphur, 724-5 units; charcoal, 9617-7
units; alcohol, 525 units; ether, 922 units of heat.
Note.  Specific heat of charcoal =  0-2415; of alcohol (Sp. Gr. 0-81) =  0-7;
of ether (Sp. Gr. 0-76) =  0-66.
Prob. 224. Ans. 680~529 Fahrenheit.
Prob. 225. Ans. 4{ lbs. at 200~, and 15~ lbs. at 50~ F.
Prob. 226. Ans. 88~039 F.
Prob. 227. Ans. 155~088 F.
Prob. 228.  Ans. 70~-79 F.
Prob. 229. Ans. 10-337 lbs.
Prob. 230.  Ans. 0-62S lb.
Prob. 231.  Ans. 9-26 units of heat (as in Table XV.).
Note.  The temperature of the water was raised to 52~:96 F. instead of 20~076 C.
Prob. 232.  Ans. Required for air, 0-831 unit; for oxygen, 0-843 unit; for
carbonic acid gas, 27-879 units; for hydrogen, 0-8235 unit of heat.
Prob. 233.  Ans. 3993-64 units of heat.  By table on page 451.
Prob. 234.  Ans. 1174-4 units of heat.
Prob. 235.  Ans. 28-088 inches.
61 




698                      ANSWERS TO PROBLEMS.
Prob. 236.  Ans. With alcohol, 26-742 in.; sulphuric acid, 29-00 in.; (at 750 F.
the tension of vapor of sulphuric acid is too little to make any perceptible difference;) oil of-turpentine, 28-79 inches.
Prob. 237.  Ans. Tension of vapor of water at 50~ F. -= 0358 in. mercury;
at 75~ -  0-884 in.; at 1100 =  2-582 in.; at 175 -= 13-673 in.; at 220~ =  35-091
in.; at 2650 =  78-619 in.; at 300' =  136-742 inches of mercury.
Prob. 238. Ans. Boiling points of water at the given pressures =  213~0802,
211~-709, 210~-794, 20S8~679, 207~0608, 200~051 F.  Boiling points of ether at
the same pressures =  95~0786, 93~072, 920-83, 900-83, 89~-83, 810-22.  Boiling
points of alcohol at the same pressures, 174~-33, 172~024, 171~-34, 169~031,
168~-31, 162~-13.
Prob. 239. Ans. If the temperature is not allowed to change, a part of the
steam will be condensed and the tension will remain unchanged. In the second
case the tension will be reduced to one atmosphere.
Prob. 240.  Ans. 457~ F. to 460~ F.  This tension exceeds the limits for
which accurate data are given.
Prob. 241. Ans. 12 flues.
Prob. 242. Ans. 15 flues.
Prob. 243. Ans. The two forces are to each other as I to 10-974.
Prob. 244.  Ans. The intensity equals 21 of its original force; and L -- 19r.
Prob. 245. Ans. The intensities are as 1, 1-026, 1-034 and 1-039.
Prob. 246. Ans. The intensity would be increased 1-9 times.
Prob. 247.  Ans. The intensity is increased by one-third its original amount.
Prob. 248. Ans. The intensity is increased by two-thirds its original amount.
Prob. 249.  Ans. The intensity is increased to 1-16 what it was before.




I N D E X.
fTriE RIEFERENCES ARE TO SECTIONS, NOT TO PAGES.J
ABERRATION, chromatic, 465; of glass covers, Appendix, meteorology, 946; addenda, page
510; of lenses, 454; of mirrors, 437; of    668; physical tables, page 609.
sphericity, 455.                               Application of laws of falling bodies, 73; of
Absolute strength, 170; zero, 666.                 levers, 115; of pendulum  and measure of
Absorptive power for heat, 637.                    time, 84; of polarized light, 563; of reflecAccumulated electricity, 843.                      tion, absorption, and radiation, 640; of
Achromatic microscope, 508, 511; telescopes,    screw, 128; of wedge, 126.
504.                                           Appreciation of colors, 490; of distance, 481.
Achromatism, 466.                                Aqueous phenomena, 972; solutions, maxiAcoustics, 335.                                    mum density, 604.
Acoustic shadow, 350.                            Arago's experiment, 912; polariscope, 557..Action and reaction, 27; of.a falling body, 77. Arlchimedes, theorem  of, 205; demonstrated,
Action of a double convex lens, 447; of heat    206.
on matter, 566; of magnetism on light, 919; Arc/hmledes' screw, 298.
of surfaces upon heat, 635.                    Are, 18.
Actual and theoretical velocities, 144.          Areometers, 212.
Adaptation of eye to distance, 480; of power  Artesian wells, 204.
to weight, 110.                                Artificial magnets, 802; temperature, 727.
Addenda, page 668.                               Ascent of liquids in tubes, 239.
Adhesion distinguished from cohesion, 147.    Astatic needle, 787.
Advantage of friction, 141.                      Astronomical telescope, 499.
Aerial phenomena, 957; waves, 332.               Atlantic cable, 927.
Air, buoyancy of, 258; impenetrability of, 259; Atmosphere, 256; free electricity in, 861.
inertia of, 260; pump, 287; vibrating in  Atmospheric electricity, 860; a source of heat,
tubes, 379.                                      747.
Amalgam, 834.                                    Atmospheric engine, 708; magnetism, 800;
Amalgamation of plates, 88.                        pressure, 257; measure of, 261; refractions,
American electrical machine, 836; turbine,    538.
231.                                           Atoms. 20.
Amorphism, 152.                                  Attraction and repulsion of light bodies. 831.
Ampere, discoveries and theory, 908.             Attraction, electrical, 812; experiments, 842.
Amusement with electricity, 840.                 Attraction, magnetic, 780.
Analogy of light and heat, 765.                  Atwood's apparatus, 72.
Analysis of central forces, 64; of colors, 458; Auditory organs of man, 393.
of light, 456; of light by absorption, 458;  August's hygrometer or psychrometer. 973.
by prisms, 456; of trains of wheel-work,  Auroral current, reversal of polarity in, 1000.
117.                                           Auroras, 994; effect on telegraph wires, 999;
Anemometers, 960.                                  geographical distribution, 997; height and
Anemoscopes, 959.                                  frequency, 996; magnetic disturbance, 998
Aneroid barometer, 164.                            remarkable, 995.
Animal electricity, 943; heat, cause of, 756;
strength, 130.                                 BABBAGE'S experiment on friction, 140.
Annealing, 178.                                  Back-ground, 476.
Anode, 882.                                      Bain's telegraph. 926.
Aplanatic foci, 509.                             Balance, spring, 37.
Apparatus, Atwood's, 72; Bohnenberger's, 55; Ballistic curve, 145; pendulum. 104.
for condensation of gases, 690; for distilla- Balloons, 273.
tion, 687; illustrating barometer, 264; Mel- Barker's mill, 217.
loni's, 642; Morin's, 72.                      Bath, tempering by, 178.
(699)




7(0}0                                     T'INDEx.
Barometer, aneroid, 164; at different alti- Chromatic aberration. 465.
tudes, 265; cistern, 266; construction of, Chromatic diagram, 491.
263; correction for temperature, 599; errors  Chromatic polariscope, 557.
of, 269; Fortin's, 266; Gay Lussac's, 267; Chromatics. 456.
measuring heights, 272; metallic, 163; prin- i Chronometers, compensating balance wheels,
ciples of, illustrated, 264; wheel, 268.        596.
Barometric changes and the weather, 271; Cistern barometer, 266.
height, variations of, 270.                   C larke's magneto-electric apparatus, 938.
Batteries, Smec's, 871; trough, 870; voltaic, Cleavage, 157.
869-881.                                      Climates, climatology, 947.
Beams, flexure of, 162; lateral strength, 172;  Clocks, electrical, 928.
of light, 401.                                 Clothing, relations to heat, 625.
Beating, 376.! Clouds, 978; classification of, 979.
Beaumsn's hydrometer, 212.                      Coexistence of sound waves, 338.
Bellows, 281.                                   Cohesion among solids, 147.
Blasting by electricity, 937.                   Cohesion and repulsion, 146.
Body, defined, 1.                               Cohesion in liquids, gases, and solids, 148.
Bohrlenberger's apparatus, 55.                  Cold, apparent radiation of, 634.
Binocular vision, 484.                          Cold by evaporation, 681.
Boiler for Gold's steam-heater, 733.           i Color blindness, 490.
Boiling point, 569; application in arts. 678;  Color dependent on temperature, 768.
circumstances infiuencing,  i76; heights Colored polarization, 555; rings in crystals, 558.
measured by, 679.                             Colors, analysis of, 458; Chevreul's classificaBourdon's metallic barometer. 163.                tion of, 491; complementary, 459; of grooved
Boyden's American turbine, 231.                   plates, 535; of thin plates, 529; study of. 492.
Brachystochrome, 76.                            Columns, resistance to pressure, 171.
Bramah press, 190.                              Combination of waves, 327.
Breast-wheel, 230.                              Combustion, a source of heat, 749; cause of
Breguet's metallic thermometer, 58t).             heat in, 750.
Brightness of ocular image, 473.                Comparison of different thermometers, 576.
Britannia tubular bridge, 172.                  Compass, mariner's, 787.
Brittleness, 177.                               Compensating balance wheels, 596; penduBronze tempering, 178.                         i  lums, 596.
Bunsen's photometer, 414.                      i Complementary colors, 459.
luoyancy of air, 258.                           Components and resultants. 44.
Bluoyancy of liquids, 205.                      Composition of white-light, 457.
Compound chords, 372; crystals, 156; lenses,
CaMUBRIIuE TELESCOPE, 506.                        450; levers, 114; examples of, 115; microCamera lucida, 518.                               scope, 496; achromatic, 511; motion, 33;
Capillarity. 232; general facts in, 233; a    pendulum, 83; pulleys, 120.
source of heat, 741; influenced by curve of Compressed gases, escape of, 283.
surface, 236; laws of, 237.                   Compressibility, 21; of gases, 274; of liquids,
Capstan, 116.                                     188.
Calorimetry, 650.                               Compressing machine, 2S8.
Camels, 206.                                    Compression a source of heat, 739.
Camera obscura, 517.                            Concave lenses, 448.
Carbon battery, 876.                            Concave mirrors, 426; foci of, 427-431; images
Cartesian devil, 2(6.                             by, 433.
Cathode, 882.                                   Condensation of gases, 689, 690.
Catoptrics, 415.                                Condenser of ~Epinus, 844.
Caustic curves, 437.                            Conductibility, clothing, 625; of crystals, 616;
Centigrade thermometer, 570.                      examples of. 622, 623; of gases, 620; of
Centimetre, 18.                                   liquids, 619; of metals, 615; of powders or
Central forces, analysis, 54.                     fibres, 624; relative, of solids, liquids and
Centre of gravity, 60, 62; in bodies of unequal    gases, 621; of solids, 614, 622; of wood, 617.
density, 68; of regular figures, 64; without Conduction of heat, 613.
the body, 65.                                 Conjugate mirrors, 635.
Centre of hydrostatic pressure, 197.            Constitution of liquid veins, 222.
Centre of oscillation, 83.                      Construction of barometers, 263; of musical
Centrifugal and centripetal forces, 52.           instruments, 385; of thermometers, 568.
Centrifugal drying machine, 53.                 Convection of heat, 626; of heat in liquids, 627.
Centrifugal forces, demonstration. 53.          Convex lenses, 447.
Chain pump, 297.                                Convex mirrors, 426, 433; images by, 435.
Change of density, 169.                         Cooling by radiation, 632.
Chart of magnetic variations, 789.              Copper, tempering. 178.
Chart of isoclinal lines, 794.                  Cords, vibration of, 308. 309.
Chemical affinity and molecular attraction, Corollaries, on centre of gravity, 03.
900; combination, 748; effects of the pile, Coronas, 537.
history, 888; force, 5; sources of heat, 748- Correlation of forces, 758.
757; union by electricity, 856.               Coulomb on rolling friction, 139; on starting
Chemistry, relation of to physics, 9.             friction, 138.
Chevreul's classification of colors, 491.       Cbtlcssnb's eleetrical laws, 819; laws of torsion,
Chimneys. draught in, 717.                       106.




INDEX.                                         701
Couples, 48.                                    Dulboscq's electric lantern, 884.
Cowls, 725.                                     Dub's laws of electro-magnetism, 915.
Crystalization by feeble currents, 893.         Ductility, 175.
Crystalography, 151.                            Duration of visual impressions, 487.
Crystals conduct heat, 616; forms of, 153, 158; Dwellings, supply of fresh air, 726.
positive and negative, 551.                   Dynamical electricity, 862; theory of heat. 762.
Cubical expansion, 590.                         Dynamics, 39; Dynamometers, 37.
Culinary paradox, 677.
Currents, in air and gases, 716; induced by  EAR, 393; sensibility of, 378; trumpet, 359.
magnets, 938; in the ocean, 628; of elec- Earth circuit, 922.
tricity, path and velocity of, 818; produced  Earth's rotation, effect of, upon gravity, 94;
by ice, 724.                                    demonstrated by the pendulum, 86.
Curve, ballistic, 145; influence in capillarity, I Ebullition, 675.
236; of liquid surfaces, 234; of swiftest de- Echo, 353; tone changed by, 355.
scent, 76.                                    Echoes repeated, 354.
Curvilinear motion, 51.                         Effects of centrifugal force, 53.
Cut-off, 712.                                   Elastic balls transmit shock, 185; bodies, imCycloidal pendulum, 85                            pact of, 182; fluids, 252.
Cyclones, 968.                                  Elasticity. limit of, 168; modulus of, 183; of
Cylinder electrical machine, 834.                 flexure, 162; of liquids, 188; of metals, table,
161; of solids, 159; coefficient of, 161; oftenD.AIELL'S constant battery, 874; hygrometer,   sion and compression, 160; of torsion,;65.
973.                                          Electric battery, 849.
Dark lines in spectrum, 461, 462.               Electric currents, induced, 929; light in a
Declination of magnetic needle, 788.              vacuum. 935; mutual action, 909.
Decimetre. 18.                                   Electric discharge, effects of, 853; in vacuum,
Deep-sea thermometer, 581.                        852.
Deflagration, 886.                              Electric light, properties of, 885; regulators of,
De La Rive's floating current, 909.               884; rotation about a magnet, 936.
Demonstration of Torricellian theorem, 220.   Electric spark, color of, 852.
Density, 98; changed by tension, 169; of gases, Electric telegraph, history of, 921; Morse's re611; of the earth estimated by experiment,   cording, 924; varieties of, 923.
102; of vapors, 693.                          Electricity, atmospheric, 860, 861; chemical
Depth of waves, 322.                              effects, 858; chemical union by, 856; classiDepression of mercury in tubes, 238.              fication, 773; conductors of, 814: discharge
Descent on curves, 75; on inclined planes, 74.   in cascade, 850; disguised, 843; distribution
Despretz's experiments, 275.                      of, 825; dynamical, 862; dynamical conDestructive effects of impact, 112.               verted into statical, 933; earth a reservoir
Determination of reflective power, 636.           of, 815; floating "urrent, 909; from  all
Deviation of light twice reflected, 423.          sources identical, 939; from steam, 839; loss
Dew, 975; on what it falls, 976.                  of, in excited bodies. 827; magnetic, 774;
Dew-point, 674.                                   mechanical effects, 857; only on outer surDiamagnetism, 920.                                face, 824; of plants, 945; positive and negaDiamond jar, 852.                                 tive, 813; of the air, 987; physiological
Diapason, 377; natural, 395.                      effects, 854; theories of, 816; theory of
Diathermancy, 641; applications of, 647; causes   voltaic, 863; universal discharger of, 851;
which modify, 645.                              velocity of, 818; vitreous and resinous, 813.
Differential thermometers, 687.                 Electrical amusements, 840; animals, 944;
Diffraction, 532.                                 attraction and repulsion, 812; bells, 842;
Diffused light, 410.                              blasting, 937; cascade in vacuo, 935; clocks,
Dilatation by heat explained, 769.                928; condenser, discharge of, 845; effects,
Dimensions of the earth, 92.                      811; egg, 852.
Dioptrics, 438.                                 Electrical excitement, sources, 810; univerDipping needle, 793.                              sality of, 940; various sources, 840.
Direction of force, 40; of osmotic current, 247; Electrical fire alarm, 928; hail-storm, 842:
of terrestrial attraction, 60; of vibrations of    helix, 910; induction, 828; lamp,Volta's, 856.
light, 541.                                   Electrical machines, 834-838; care of, 838;
Directive action of the earth, 911.               theory of, 841.
Dispersion of light, 406.                       Electrical nomenclature, 882; pendulum, 812;
Displacement of zero-point, 573.                  phenomena, 987; power of points, 826; reDissecting microscope, 495.                       tardation, 880; wheel, 842; tension and curDistance calculated by sound, 346; of distinct    rents, 817.
vision, 478; that sound can be heard, 351.   Electro-chemical telegraph, 926.
Distillation, 686.                              Electrode, electrolyte, 882.
Distilling apparatus, 687.                      Electro-dynamic spiral, 910.
Divisibility, 19.                               Electro-dynamics, general laws, 902.
Double diatonic scale. 373; refraction, 550; Electrolysis, laws of, 890; of salts, 891; of
polarization by, 552; vision, 483.              water, 889.
Downward pressure of liquids, 191.              Electro-magnetic currents, motion of, 904
Draught in chimneys, 717.                       Electro-magnetic motion, 917.
Drops of liquids in conical tubes, 241.         Electro-magnets, 913; Page's revolving, 914;
Dry piles, 873.                                   power of, 915.
Drying machine for laundries, 53.               Electrometers, 832.




7(2                                      INDEX.
Electrometer, gold leaf, 846; torsion, 320.    Fairbanks' s ales, 115.
Electrophorus, 833.                            Falling bodies, laws of, 71.
Electro-positive and electro-negative, 867.    Falling body, action and reaction of, 77; space
Electro-printing telegraph, 925.                 described by, 71.
Electroscopes, 813, 842.                       Faraday's nomenclature, 882.
Electroscope, Bohnenberger's, 873; Volta's  Faraday on liquefaction of gases, 689.
condensing, 846.                             Fire-alarm, electrical, 928.
Electrotype, 892.                              Fire engine, 294.
Emerson's ventilators, 725.                    Fire regulators, 594.
Emissive power for heat, 638.                  Fixed lines in spectra, 461, 462.
Elements are simple bodies, I                  Fixed pulley, 118.
Endless screw, 129.                            Flexure of beams, 162.
Endosmose, 244; of gases, 250; theories of, 251. Floating bodies, 206; equilibrium of, 207.
Endosmometer, 245.                             Floating current, 909.
English and American weights, 101.             Floating docks, 206.
English units of length, 17.                   Flow from capillary tubes, 243.
Eolipile, 704.                                 Flow of liquids, 218.
Epipolic dispersion, 533.                      Flow, theoretical and actual, 216.
Equatorial telescope, 505; Cambridge, 506.    Fluids, 186; resistance of, 143.
Equilibrium, 38; conditicns of, in liquids, 199; Fluorecsence, 533.
neutral, unstable, and stable, 207; of bodies Foci of lenses, compound, 450; concave, 448;
supported in more than one point, 69; of    convex, 447; principles, 445; rules for, 449.
machines, 107.                               Fog-bows, 537.
Equilibrium of liquids, between laminae, 240; Fogs, or mists, 974.
free from gravity, 200; in communicating  Foot-pound a measure of heat, 759.
vessels, 201; of different densities, 202.   Force and heat, relations, 758.
Equilibrium of solids placed upon a horizontal Force, chemical or physical, 5; definition of,
surface, 67; supported by an axis, 66.         35; developed by evaporation, 684; direction
Equilibrium of the lever, 114.                   of, 40; of expansion, 593, 603; of gravity,
Errors of barometer, causes of, 269.             58; unit of, 37.
Escape of compressed gases, 283; of liquids Forces are definite quantities, 36.
through tubes, 223, 224.                     Forces, centrifugal and centripetal, 52; corEssential properties of matter, 12.              relation of, 758; not parallel applied at difEstimation of high temperatures, 586.            ferent points, 49; measure of, 41; paralleloEustachian tube, 393.                            gram of, 45; propositions in regard to, 42;
Evaporating power of fuel, 715.                  resolution of, 50; statical and dynamical,
Evaporation, causes influencing, 673; cold by,   39; system of, 44.
681; mechanical force of, 684.               Forcing pump, 292.
Examples of compound levers, 115.              Forms of crystals, 153; of mirrors, 417; of
Exosmose, 244.                                   vibrations, 307.
Expansibility and compressibility, 610.        Formulae, achromatism, 467.
Expansibility, 22.                                 "      altitudes by barometer, 272.
Expansion, amount of, in solids, 591; apparent     "      apparent expansion of mercury,600.
and absolute, 598; coefficient of, 591; cubical.  "    central forces, 54.
590; curve of, for liquids, 602; force exerted   "      change of volume in gases, 608.
by, 593; increases with temperature, 592;        "      compensating pendulum, 596.
linear, 589; of crystals, 590.'      compound lenses. 450.
Expansion of gases, 253, 605; Regnault's re-       "      concave lenses, 448.
suits, 607.                                      "      concave mirrors, 428.
Expansion of liquids, 597; above boiling, 602;     "      convex lens, 447.
amount of, 601.                                  "      convex mirrors, 432.
Expansion apparent of mercury, 600; of mer-        "      correction of barometric height, 599.
cury, coefficient, 598; of solids, 589; of water,  "    electric piles, 881.
604; phenomena of, 594; unequal, of solids,      "      endless screw. 129.
595.                                             "      escape of liquids, 223, 224.
Experiment a source of knowledge, 2; hydro- I             expansion of liquids, 598.
static pressure, 194.                            "      expansion of solids, 591.
Experiments of Despretz, 275; of Pascal, 194,      "      flexure of beams. 162.
262; of Plateau, 200; of Regnault, 276.          "      flow of liquids, 216.
Experiments on density of the earth, 102; on       "      inclined plane, 122-124.
liquid surfaces, 235.                            "      index of refraction, 440.
Explosions, cause of, 701.                         "      light twice reflected, 423.
Extension, 13.                                     "      magnifying power of lenses, 494.
Extremes of temperature, 744.                      "      microscopes, 513.
Eye, action of, on light, 469; adaptation to       "      motion of projectiles, 103.
distance, 480; a polariscope, 562; structure     "      Newton's, for velocity oisound, 653.
of, 468.                                                optical centre of lenses, 452.
Eye-piece, Tolles' solid, 512.                            pencils of light, refracted at plane
Eye-pieces, 500.                                            surfaces, 443.
"     pencils of light transmitted  by
FACTS (in interference) versus theory, 528.                 plane glass, 444.
Fahrenheits hydrometer, 212; thermometer,          "      pendulum, 81, 82.
570.                                             "      penetrating power of telcscopes,507.




INDEX.                                        708
Formula?, pulley, 119, 120.                      the earth's figure, 91; intensity varies with
"     refraction at spherical surfaces. 445.   latitude, 90; measured by the pendulum,
refraction by parallel media, 442.  i88; varied by altitude, 95.
relation of volume, temperature, Gridiron pendulum, 596.
and pressure in gases, 609.       Grove's battery, 875.
"     screw, 127.                          Gyrascope, 57.
"  specific gravity, 210, 211. 
"     specific heat, 053.                  HADLEY'S sextant, 425.
"     spherical aberration of lenses, 454.   lail, 986.
"     standard thermometer, 577.           Halos, 537.
"  strength of beams, 172.             Hammering, 179.
"     uniform motion, 30.                  Hardening, 178.
"     variable motion, 32.                 Hardness, 176.
variation of gravity by rotation of  Haare's calorimotor, 870; deflagrator, 870;
the earth, 94.                      electrometer, 846.
variation of gravity in altitude, 95. aIrmony, melody, 365.
"     variation of gravity in latitude, 90. Iiar ison's compensating pendulum, 596.
"     velocity after impact, 184.          Hearing, 341; of animals, 396.
"     velocity of discharge, 220.          HIeat, action of, on matter, 566; amount by
"     velocity of light, 404.                chemical action, 751; and force, relations
"     velocity of winds, 961.                of, 758; and light, analogy of, 765: and
"     vibration of air in tubes, 384.        light, by chemical and mechanical action,
"     visual power of telescopes, 507.       768; cause of, in animals, 756; causes which
BTrtin's barometer, 266                          modify emissive, absorbent, and reflective
Foucault's apparatus, 404.                       power, 639; change of state in bodies, 764;
Franklin's kite, 860; pulse glass, 677.          coloration, 646; conclusions, 772; conducFraunhofer's dark lines, 461.                    tion of, 613; convection of, 626; developed
Freezing in red-hot crucibles, C99.              by solidification, 663; diffraction and interFreezing mixtures, 657.                          ference, 649; dynamical theory, 762; expanFreezing point, 569.                             sion of gases by, 606; expansion of liquids
Fresh air in dwellings, 726.                     by, 597; expansion of solids by, 589; from
Fresnel lens, 521.                               magnetism, 918; latent, 655; mechanical
French system of measures, 18; weights, 100.   equivalent, 758, 760; mechanical unit of
Friction, advantage from, 141; during motion,   measurement, 759; nature of, 564; of corn.
138; heat from, 735, 736; sliding, 137; start-   bustion, 749; modes of communication, 612,
ing, 138.                                      of capillarity, 741; of chemical action, 748;
Frictional electricity, 809.                     of compression, 739; of friction, 735-738;
Frost, 977.                                      of fusion, 658; of humid combinations, 754;
Fuel, evaporating power, 715; relative value    of percussion, 740; of voltaic arch, 886; of
of, 753.                                       voltaic currents, 887; origin of terrestrial,
Functions of the ear, 394.                       746; polarization of, 649; quantity and inFurnace blowers, 282.                            tensity, 771; quantity developed by fricFurnaces for hot air, 729.                       tion, 736; quality of, how  changed, 770;
Fusion, laws and heat of, 658; peculiar in    radiation of, 629; reflection of, 635; refracsome solids, 659.                              tion of, 648; relation to cold, 565; specific,
651; transmission of radiant, 641; unit of,
GALVANIC battery a misnomer, 864.                650; universal radiation, 633.
Galvanic current, 943.                         Heating by hot water, 730.
Galvanism, discovery of, 862; contact theory, Height measured by barometer, 272.
863.                                         Heights measured by. boiling water, 679.
Galvanometer, 905; sine compass, 906.          Helix, electrical, 910.
Gamut, 366.                                    Hiero's fountain, 295.
Gas illumination, products of, 721.           HIigh-pressure engine, 711.
Gas jet, musical note, 382.                    High-pressure steam, 680.
Gases, 252; and vapors, identity of, 688; com- Horse-power, 714.
pressibility of, 274-277; conductibility for Horse-power machines, 132.
heat, 620; density of, 611; expansion of. 253; Hot air furnaces, 729.
expansion by heat, 605; laws of expansion, Hot water apparatus, 731.
606; liquid and solid, properties of, 691; House's telegraph, 925.
mechanical condition of,- 254; transmit Humidity of the air, 972.
pressure, 255; relation of volume, tempera- Hurricanes, 968.
ture, and pressure, 609; reduced to liquids, Hydraulic ram, 296.
689; specific heat of, 652, 653; volume of, 608. Hydraulics, 213.
Gassiot's cascade, 935.                        Hydrodynamics, 186.
Gay Lussac's barometer, 267; hydrometer, Hydrometers, 212.
212; laws for expansion 6f gases, 606.       Hydrostatic paradox. 195.
Glass, temper of, 178.                         Hydrostatic press, 190.
Glottis, 388.                                  Hydrostatics, 186.
Gold's steam heaters,'732.                     Hygrometers, 973.
Graduation of thermometers, 569.               Hypothesis defined, 3.
Graham's compensating pendulum, 596.           Hypsometer, 679.
Gravity, 58; a source of motion, 70; affected E
by the earth's rotation, 94; influenced by  ICE, currents produced by, 724.
61




704                                        INDEX.
Ice machine, Twining's, 681.                     Law of cooling by radiation, 632; of Latour,
Illumination of railways, 520.                     692; of universal gravitation, 59.
Illumination, products of, 721.                  Laws of acoustics determine specific heat, 653.
Illumination, sufficiency of, 477.               Laws of Bernoulli, 384; of capillarity, 237;
Illustration of vis viva, 111.                     of capillarity between laminae, 240' of elec.
Images, by concave mirrors, 433; by convex    trical attraction and repulsion, 819-822; of
mirrors, 435; by plane mirrors, 419; by    electrical induction, 829; of electricity and
small apertures, 412; by inclined mirrors,    chemical action, 898; of electrolysis, 890;
422; by two plane mirrors, 421; distortion    of electro-dynamics, 902; of electro-magnetof, 455; formed by lenses, 453; in the eye,   ism, 915; of falling bodies, 71; application,
inverted, 470; multiplied by two surfaces,    73; verification, 72; of fusion, 658; of
420; virtual, 434.                               Ohm, 880; of solidification, 662; of storms,
Impact and its results, 112; as related to vis    971; of tenacity, 170; of torsion, 166.
viva, 112; in relation to momentum, 112; Length of luminous waves, 531.
of elastic bodies, 182.                        Lenses, 438; compound, 450; concave, 448;
Impenetrability, 14.                               convex, 447; images formed by. 453; optical
Impenetrability of air, 259.                       centre of, 452; refraction of oblique pencils
Imponderables, 11.                                 by, 451; rules for foci, 449.
Impressions of light and heat, 766.              Le Roy's dynamometer, 37.
Incandescence, 767.                              Lever, 113; application of, 115; equilibrium
Inch of water, 221.                                of, 114.
Inclination map, isoclinal lines, 794.           Leyden jar, 847; electricity in, 848.
Inclined plane, 121-124.                         Life an unknown power, 10.
Index of refraction, 440.                        Light, action of eye upon, 469; amount ireInduced currents, different orders, 930.           fleeted, 407; and heat, analogy of, 765; and
Induced currents from  earth's magnetism,   heat by chemical and mechanical action,
932.                                             7CS; changed by polarization, 543; color of,
Induction an act of contiguous pnrti'les 830.    depends on temperature, 768; diffused, 410;
Induction coil of Ruhmkorff, 933; effects of,   direction of vibrations, 541; heat and elec934.                                             tricity are forces in nature, 11; in a homoInduction, electro-dynamic, 929; of a current    geneous medium, 403; influenced by magon itself, 930; of electricity, 828; of magnet-    netism, 919; internal reflection, 408; irreguism, 783.                                        lar reflection, 410; length of vibrations, 531;
Inductive philosophy, 4.                           nature of, 398; pencils of, passing through
Inductive power of earth's magnetism, 797.         plane glass, 444; pencils of, refracted at
Inertia, 26; of air, 260.                          plane surfaces, 443; polarized by absorption,
Inflammation by electricity, 855.                  545; polarized by reflection, 546; polarized
Influence of the earth's figure upon gravity, 91.   by refraction, 547, 548; properties of, 406;
Intensity of aerial waves, 332; of light, 413;    total reflection of, 409; rays. pencils, beams,
of luminous, calorific, and chemical rays,   401; refracted by parallel strata, 442; rela463; of many couples, 881; of radiant heat,   tion of bodies to, 400; sources of, 399; trans631.                                             mission of vibrations, 542; velocity of, 404.
Interference colors, 529; of light, 527; of Light-houses, 522, 523.
sound, 349; of waves. 327, 328.                Lightning, 990; classes of, 991; return stroke,
Intermittent fountain, 286; springs, 286; sy-   992.
phon, 285.                                     Lightning-rods, 993.
Internal ear, 393.                               Limits of elasticity, 168; of magnitude, 173.
Internal reflection of light, 408.               Linear expansion, 589.
Interval in music, 371.                          Liquid surfaces, cause of curve, 234.
Ions, 882.                                       Liquid veins, constitution of. 222.
Irregular reflection of light, 410.              Liquids, 186; amount of expansion, 601;
Isochronism of the pendulum, 80.                   ascent in capillary tubes, 239; conditions of
Isochronous vibrations, 303.                       equilibrium, 199; conductibility for heat,
Isodynamic lines, 796.                             619; convection of heat in, 627; curve of exIsogonal lines, 789.                               pansion, 602; downward pressure of, 191;
Isothermal lines, 956.                             elasticity of, 188; equilibrium  of, 199, 200;
equilibrium  of, in communicating vessels,
JETS of water, 225.                                201, 202; expansion  of, 597; expansion
Johnson on strength of materials, 170.             above boiling, 602; force of expansion, 603;
Joule's experiments on heat, 760, 761.             lateral pressure, 193; mechanical condition,
187; repelled by heated surface, 697; spherKALEIDOSCOPE, 424.                                 oidal state, 694; transmit pressure, 189; upKalychromatics, 464.                               ward pressure, 192.
Key-note of nature, 335.                         Liquefaction and solidification, 655; gradual,
Kilometre, 18.                                     656.
Liquefaction of gases, theory, 688; of vapors,
LARYNX, 388.                                       685.
Latent electricity, 843.                         Lister's aplanatic foci, 509.
Latent heat, 655.                                Litre, 18.
Latent heat of fusion, 658; of steam, 682.       Living force, 111.
Lateral strength of beams, 172.                  Lodestone, 774.,atour's law for vapors, 692.                    Looming, 539.
Law, definition of, 3.                           Long-sightedness, 486.




INDEX.                                       705
Low pressure engines, 710.  Metre, 18.
Microscope, achromatic, angular aperture, deMACHINE power and weight, 106.                  fining power, illuminating power, magnifyMachines, 105; equilibrium of, 107.             ing power, penetrating power, visual power,
Magic lantern, 515; squares, 852.               513; compound, 496; object-glasses, 508;
Magnetic attraction and repulsion, 780; curves,   Raspail's dissecting, 495; simple, 495; solar,
777; dip of needle, 791; electricity, 774;   516; stand, 514.
figures, 778; force, distribution, 776; force, Millimetre, 18.
lines of, 799; induction, 783; intensity, 795; Minute division, 19.
meridian, 788; needle, 775, 787; observa- Mirage, 540.
tions, 798; phantom, 777; polarity, 776; Mirrors, 415; forms of, 417.
rotary polarization, 560.                   Mobility, 25.
Magnetism, action upon light, 919; atmos-, Modified forms of crystals, 155.
pheric, 800; coercitive force, 786; by contact, Modulus of elasticity, 183.
781; conversion into heat, 918; different Molecular motion, in heat, 763.
bodies, 782; of steel by solar rays, 807; of Molecules, 20.
the earth, action of, on dipping needle, 792; Momentum, 43.
origin of the earth's, 801; terrestrial, 787;  Monochord, 367.
theories, 784, 785.                         Monthly variations in temperature, 951.
Magnetizing by the helix, 912.                Morin's apparatus, 72.
Magneto-electric apparatus, 938.              Morse's telegraph, 924.
Magneto-electricity, 938.                     Motion and force, composition of, examples, 45.
Magnets, anomalous, 779:; artificial, 775; by  Motion communicated by collision, 181.
electro-magnetism, 805; by touch, 803; com- Motion, compound, 33; curvilinear, 51; of
pound, 806; deprived of power, 808; direc-   projectiles, 103; uniform, 30; uniformly
tive tendency of, 787; horse-shoe, 804; natu-   varied, 32; variable, 31; varieties of, 28.
ral, 774; production of, 802; value how  Mountings for telescopes, 505.
varied, 802.                                Mouth-pipes, 380.
Magnifying glasses, 493.                      Movable pulley, 119.
Magnifying power of lenses, 494.               Movement of drops in tubes, 241.
Magnitude, 13; limits of, 173.                Music halls, 362.
Malleability, 174.                            Music, theory of, 363.
Manometers, 278; with compressed air, 280; Musical instruments, 383.
with free air, 279.                         Musical interval, 371.
Map of isoclinal lines, 794.                  Musical scale, 366; new, 373.
Mariner's compass, 787.                       Musical sounds, 335; quality of, 363.
Mariotte's law, 274.                          Musical tones from magnetism, 916.
Martin's compensating pendulum, 596.
Mathematical pendulum, 78.                    NATURAL diapason, 395.
Matter, 1; accessory properties, 19; changes Natural history, 10.
in, 7; essential properties, 12; general pro- Natural philosophy, 9.
perties, 6; three states of, 15; properties of, Nature, key-note of, 335.
physical or chemical, 8.                     Nearsightedness, 485.
Mass, 41, 96.                                 Negative eye-piece, 500.
Maximum and minimum thermometers, 578.  Negretti &Zambra's thermometer, 578.
Maximum density of aqueous solutions, 604; Neutral equilibrium, 207.
of water, 604.                              New musical scale, 373.
Mean temperature, 950.                        Newton's formulae for velocity of sound, 653:
Measure of forces, 41.                        Newton's rings, 530.
Measures of capacity, 17, 101.                Nicholson's hydrometer, 212.
Mechanical condition of gases, 254; efficiency  Nicol's prism, 553.
of the screw, 128; equivalent of heat, 758; Night glass, 498.
force of evaporation, 684; illustration of Nitric acid battery, 875.
vibrations, 301; sources of heat, 735.      Nobili's galvanometer, 905.
Mechanism of the voice, 389.                  Nobili's rings, 894.
Melloni's apparatus, 642.                     Nodal figures, 317.
Mellosi's thermo-multiplier, 942.             Nodal lines, 313; how delineated, 316; posi
Melody, harmony, 365.                           tion of, 314.
Membranes, vibration of, 318.                 Nodal points, 305.
Men, strength of, 131.                        Noise, 335.
Mercurial rain, 24.                           Nomenclature, Faraday's electrical, 882.
Mercurial thermometer, 568; limits of, 574;
defects of, 576.                            OBJECT-GLASSES for the microscope, 508.
Mercury, depression of, in tubes, 238.        Objectives compound, 509.
Meridian measurements, 91.                    Oblique pencils, 430.
Metacentre, 208.                              Oblique pencils refracted by lenses, 451.
Metallicbarometer, 163.                      Observation and experiment, 2.
Metallic thermometers, 580.                   Ocular image, brightness of, 473.
Metals, change of properties, 180; change of  (Ersted's discovery, 903.
structure, 180, conduct heat, 615.          Ohm's law of retarding power, 880.
Metastatic thermometer, 579.                  Open fire, 728.
Meteorological observations, 940.             Opera-glass, 498.
Meteorology, 946.                             Optic angle, 471.
62




706                                      IND EX.
Optic axis, 471.                               Polarizing instruments, 554.
Optical centre of a lens, 452.                 Poole's musical scale. 373.
Optical instruments, 493.                      Pores, physical, 23; sensible, 24.
Optical toys, 488.                             Porosity, 23.
Optics, 397.                                   Positive and negative crystals, 551.
Organ of Poole and Alley, 375.                 Positive eye-piece, 500.
Organic solutions, osmose in, 248.             Pouillet's galvanometer, 906.
Organs of hearing in animals, 396.             Power of points, electrical, 826.
Origin of terrestrial heat, 746.               Power of steam, 714.
Origin of undulations, 299.                    Power, adaptation to weight, 110.
Oscillation, centre of, 83.                    Power and weight, 106; relation of, 109.
Oscillation defined, 78.                       Press, hydrostatic, 190.
Osmose, 244; conditions of, 246.               Pressure, atmospheric, 257; centre of, 197; of
Osmose of inorganic solutions, 249; of organic   liquid in motion, 226; of liquid downward,
solutions, 248; direction of current, 247.     191; of liquid on side of vessel, 193; of
Overshot wheel, 229.                             liquid upon containing vessel, 214; produced
Ozone, 859.                                      by impact, 112; transmitted by gases, 255;
transmitted by liquids, 189; varies with
PAGE'S revolving magnet, 914.                    Sp. Gr., 198.
Page's vibrating armature, 931.                Primary colors, 456.
Parachute, 273.                                Prime seventh, 373.
Parhelia, 537.                                 Prince Rupert's drops, 178.
Parallel forces, resultant of, 46.             Printing telegraph, 925.
Parallelogram  of forces, 45; of rotations, 56; Prisms and lenses, 438.
of velocities, 34.                           Problems on acoustics, page 289; on elasticity
Pascal's experiments, 194, 262.                  and tenacity of solids, page 146; on elecPassive resistance, 136.                         tricity page 667; on gravitation, page 73; on
Paths of vibration, 311.                         heat, page 506; on hydrodynamics, page 199;
Pencils of light, 401; refracted at plane sur-   on laws of vibrations, page 251; on theory of
faces, 443; at spherical surfaces, 446.        machinery, page 107; on optics, page 392;
Pendulum, 78; applied to measure time, 84;   on pneumatics, page 234; on weights, meaapplied to study of gravity, 87; ballistic,   sures, and motion, page 37.
104; compensating, 596; cycloidal, 85; de- Production of waves, 319.
monstrates rotation of the earth, 86; formu- Products of combustion and respiration, 718.
lae for, 81; isochronism of, 80; length beat- Progressive undulations, 300; in liquids, 320.
ing seconds, 89; physical or compound, 83; Properties of matter, general or specific, 6;
propositions respecting, 82; simple, 79; used    physical or chemical, 8.
to measure force of gravity, 88.             Properties of liquid and solid gases, 691; of
Penetrating power of microscopes, 513; of    solar spectrum, 460; of solids, 149.
telescopes, 507.                             Propositions in regard to forces, 42.
Penumbra, 411.                                 Projectiles, theory and laws of, 103
Percussion a source of heat, 740.              Proof plane, 823.
Perfect concord, 372.                          Pulley, compound, 120; fixed, 118; movable,
Perkins' apparatus, 731.                         119.
Perpetual motion, 135.                         Pumps, 289-293.
Phases of undulations, 304.                    Pyrometers, 589.
Phenomena defined, 2; of expansion. 594.       Pyrometer, Daniell's, 584; Draper's, 585; SaxPhilosophical egg, 852.                          ton's reflecting, 582; Wedgewood's, 583.
Phosphorescence, 399, 534.                     Pyrometrical heating effects, 752.
Photo-electric lantern, 884.
Photography, 519.                              QUALITY of musical sounds, 363.
Photometers, 414.                              Quantity and intensity of electricity, 865.
Physical force, 5; pores, 23; optics, 527; Quantity of heat from friction, 736.
sources of heat, 742; tables, page 669;
theory of music, 363.                        RAIN. 980; annual depth of, 983; days of, 9824
Physics and chemistry, 9.                        distribution of, 981.
Physiological effects of the pile, 895.        Radiant heat, intensity of, 631; partially ab;
Piano strings friable, 180.                      sorbed, 630; transmission of, 641.
Plane glass, refraction by, 441.               Radiating power for heat, 638.
Plants, electricity of. 945.                   Radiation, of cold, 634; of heat, universal, 633;
Plateau's experiment, 200.                       law of cooling by, 632; terrestrial, 745.
Plates, vibration of, 312.                     Radiators, steam, 732.
Platform balance, 115.                         Railway illumination, 520.
Pneumatic ink-bottle, 284.                     R ainbow, 536.
Pneumatics, 252.                                Ramsden's electrical machine. S8.5.
Polarity of compound circuit, 878.             Range of human voice, 390.
Polarization and transfer of elements, 899.    Rays of light, 401.
Polarization, atmospheric, 561; by absorption, Reaction of escaping liquids, 217.
545; by heat and by compression, 559; by  JReaumur's thermometer, 570.
reflection, 546; by  refraction. 547, 548; Recomposition of white light, 457.
colored, 555; of heat, 649; of light, 541; Reed pipes, 381.
partial, 549; rotary, 556.                   Regulators of electric light, 884




INDEX.                                        707
Reflecting telescope, 501.                     Self-registering thermometers, 578.
Reflection at curved surfaces, 426; by plane  Sensible weight varies in different localities,
mirrors, 418; by regular surfaces, 415; of    93.
circular waves, 3-26; of light, 406; of sound, Sensibility of the ear, 378.
352; of waves, 323.                          Septum required for osmose, 246.
Reflective power, how determined, 636.         Series of elastic balls, 185.
Refractory bodies, 660.                        Seventh, harmony of, 373.
Refraction at curved surfaces, 445, 446; at Sextant, Hadley's, 425.
regular surfaces, 438; atmospheric, 538; at Shock transmitted by elastic balls, 185.
plane surfaces, 439; by lenses, 447-451; Silliman's photometer, 414.
by plane glass, 441; by prisms, 439; of heat, Simple microscope, 495.
648; of light, 406; of pencils of light, 443; Simple pendulum, 79.
of sound, 357.                               Simple pendulum, propositions respecting, 82.
Refrigerators, 724.                            Simple vision with two eyes, 482.
Regnault's experiments, 276.                   Siren, 360.
Regnault on expansion of gases by heat, 607.  Sliding friction, 137.
Relation of bodies to light, 400; of power to  Smee's battery, 871.
weight, 109; of specific heat and atomic  Snow, 984; colored, 985; limit of perpetual,
weight, 654.                                   955.
Relative value of fuel, 753.                   Solar microscope, 516.
Repulsion, 146; electrical, 812; magnetic, 780. Solar spectrum, properties of, 460.
Repulsion of light floating bodies, 242.       Solenoid, 910.
Repulsive action of heated surface, 697.       Solid eye-piece, 512.
Resistance of columns, 171; of fluids, 143; Solidification, change of volume by, 664.
passive, 136.                                Solidification liberates heat, 663.
Rest, absolute and relative, 25.               Solidification of gases, theory, 688.
Resultant of opposite parallel forces, 47; of  Solids, characteristics of, 149; conductibility
unequal parallel forces, 46.                   for heat, 614; expansion of, 589; structure
Results of impact, 112.                          of, 150; undulations of, 306; unequal exRevolving imagnet, 914.                          pansion of, 595.
Revolving lights, 523.                         Solution, 661.
Reynir's dynamometer, 37.                     Sonometer, 367.
Rheostat, 907.                                 Sonorous tubes, 379.
Rigidity of ropes, 142.                        Sonorous waves, length of. 370.
Ritchie's electrical machine, 837.             Sound, 335; distances calculated by, 346; in
Roberts' oompensating pendulum, 596.             all elastic bodies, 340; interference of, 349;
RRberval's balance, 115.                        not instantaneous, 342; not propagated in
Rods, vibration of, 310.                         a vacuum, 339; propagated by waves. 337;
Roget's oscillating spiral, 909.                 reflected, 352; refracted, 357; velocity in
Rolling friction, 139.                           air, 344; velocity in gases, 345; velocity in
Ropes, rigidity of, 142.                         liquids, 347; velocity in solids, 348.
Rosse's telescope, 503.                        Sounds of birds, 392; of insects, 392; produced
Rotascope, 57.                                   by animals, 392.
Rotation of electric light about a magnet, 936. Sounding bodies vibrate, 336.
Rotation of the earth demonstrated by the  Source of heat influencing diathermancy, 644.
pendulum, 86.                                Sources of heat, 734-757.
Rotations, parallelogram of, 56; right-handed  Sources of light, 399.
or left-handed, 56.                          Space described by a falling body, 71.
Rotary polarization, 556; magnetic, 560.       Speaking trumpet, 358.
Rotary pump, 293.                              Specific gravity, 209.
Rousseau's hydrometer, 212.                    Specific gravity bottle 211.
Ruhmkorff coil, 933.                           Specific gravity by balance, 210.
Rule for position of images, 436.              Specific heat, 651.
Rumford's photometer, 414; thermoscope, 587. Specific heat and atomic weight related, 654.
Rutherford's thermometer, 578.                 Specific heat determined by laws of acoustics,
653.
SAIGEY'S table of length of pendulum, 90.      Specific heat of gases, 652.
Saturated space, 669.                          Specific weight, 99.
Saturation, 661.                               Spectrum, 456; dark lines in, 461.
Saussure's hygrometer, 973.                    Specula, 416.
Savart's toothed wheel, 361.                   Spherical aberration of lenses, 454; of mirrors,
Savary's steam engine, 706.                      437.
Saxton's deep-sea thermometer, 581; reflecting  Spherical mirrors, 426.
pyrometer, 582.                              Sphericity, aberration of, 455.
Scale beam, 115.                               Spheroidal state, 694; cause of, 698; cause of
Scintillating tube, 852.                         explosions, 701; familiar illustrations, 702;
Screens, diathermanic power of, 643.             remarkable phenomena, 700.
Screw, 127; efficiency of, 128; endless, 129.    Spirit level, 203.
Sea lights, 522.                               Spirit thermometers, 575.
Seasons, 947.                                  Spring balance. 37.
Secondary axes, 430.                           Springs intermittent, 286.
Seconds pendulum, 89; formulae for, 90; table  Stable equilibrium, 207.
of lengths in different latitudes, 90.       Standard thermometer, 577.
61 *




708                                     INDEX.
Starting friction, 138.                       TABLES, Decrease of temperature from elevaStatical and dynamical forces, 39.                      tion, 954.
Statical electricity, 809.                       "    Degree of elasticity, 183.
Statics defined, 39.                             "    Depression of mercury in tubes, 238.
Stationary undulations. 302.                     "    Diathermancy for heat from different
Stationary waves, 321.                                   sources, 645.
Steam  boiler, 713; explosions, 701; Gold's,    "    Diathermancy of different liquids,
733.                                                  App. tab. X.
Steam cylinder, Papin's, 707.                    "    Diathermancy of different solids, App.
Steam, electricity from, 839.                           tab. XIII.
Steam, heat latent and sensible at different    "    Elasticity of metals, 161.
temperatures, 683.                             "    Expansion of gases, 607.
Steam, high pressure, 680.                       "    Expansion of gases, App. tab. V.
Steam, latent heat of, 682.'    Expansion of liquids, App. tab. IV.
Steam, power of, 714.                            "    Expansion of mercury, 598.
Steam-engine, 703; high pressure, 711; low      "    Expansion of solids, App. tab III.
pressure,' 710; Newcomen's, 707; Watt's,    "    Force required to heat a pound of
709.                                                  water 1~ F., 761.
Steam-heaters, 732.                             "    Freezing mixtures, App. tab. XII.
Steam-power. 134.                               "    French decimal measures and weights
Steamboat, the first, 705.                              changed to English measures and
Steelyard, 115.                                         weights, App. tab. II.
Stere, 18.                                       "    Frequency of different winds, 965.
Stereomonoscope, 526.                            "    Frequency of auroras, 996.
Stereoscope, 525.                                "    Friction, 138.
Stone's ventilating shaft, 723.                  "    Hardness, 176.
Storms, general laws, 971.                            H eat of combustion in air. 753.
Stream measurers, 227.                          "    Heat of combustion in oxygen, 751.
Strength, animal, 130; of beams and tubes,    "    Hydrometer degrees and specific gra172; of materials, 170; of men, 131.                  vities, App. tab. XXV.
Structure of human eye, 468.                     "    Hydrostatic  pressure  at  various
Structure of metals changed, 180.                       depths, 196.
Study of colors, 492.                            "    Latent and sensible heat of steam,
Stuttering, 391.                                        App. tab. XXII.
Submarine telegraphs, 927.                       "    Laws of falling bodies, 71.
Substance defined, 1.                            "    Limits of perpetual snow, 955.
Suction and lifting pump, 291.                  "    Liquefaction  and  solidification  of
Suction pumps, 290.                                     gases, App. tab. XX.
Sulphate of copper battery, 872.                 "    Measures and weights, App. tab. I.
Sun, a source of heat, 742; influence of, 948;    "    Melting points and heat of fusion,
quantity of heat from, 743.                           App. tab. XV.
Surface of discharging liquid, 215.              "    Radiating and absorbent power of
Syphon, 285.                                            bodies for heat, 638.
Syphon barometer, 267.                          "    Radiating power, App. tab. VI.
System of forces, 44.                            "    Reflection of light, 407.
System of magnetic observations, 798            "    Specific gravity of solids and liquids,
System of wheels, 117.                                  App. tab. XXIII.
Systems of crystals. 154.                        "    Specific heat, App tab. XI.
"    Specific heat for constant pressure
TABLES, Ascent of liquids in tubes, 239.                and constant volume, 653.
Absorptive power for heat from dif-           Strength of men and animals, 133.
ferent sources; App. tab. IX.         "    Strength of materials, 170.
Absorptive power of different bodies,    "     Temperature in different latitudes,
App. tab. VIII.                               953.
"    Aqueous vapor in a cubic foot of satu-    "    Tension of vapors, App. tab. XIV.
rated air at different temperatures,    "    Velocity of winds, 961.
App. tab. XXI.                        "    Volume and density of water, App.
"    Barometric column at various alti-              tab. XXIV.
tudes, 265.                        Telegraph, 921-928.
"    Boiling point of liquids, App. tab. Telescope, 497; achromatic, 504; equatorial,
XVII.                                505; Galileo's, 498; Lord Rosse's, 503.; re"    Boiling point of water at different   fleeting, 501; Sir William Herschel's, 502.
places, App. tab. XVIII.            Telescopes, penetrating power, 507; visual
"    Boiling point of water at different   power of, 507.
pressures, App. tab. XVI.          Telestereoscope, 524.
Boiling point of water under 1, 2, 3, Temper, 178.
&c., atmospheres, App. tab. XIX.   Temperament in music, 375.
Colors of tempered steel, 178.         Temperature, 565; estimation of high, 586;
"    Comparison of thermometers, 576.        extremes of, 744; mean, 950; monthly
"    Compressibility of gases, 276.          variations, 951; of vaporization, 672; of
"    Compressibility of liquids, 188.        vegetables, 757; variations in altitude. 954 
"    Conductingpowerof metalsand build-   variations in latitude, 953.
ing materials, App. tab. VII.       Tempered steel, colors, 178.




INDEX.                                       709
Tenacity of different substances, 170.        Units of measure, 16.
Tenacity, laws of, 170.                       Universal discharger. 851; gravitation, law of,
Tension, 252; changes density, 169; maximum,   59; radiation of heat, 633.
of vapors, 669; of vapors, Dalton's law, 670; Unstable equilibrium, 207.
of vapors in communicating vessels, 671.    Upward pressure of liquids, 192.
Terrestrial attraction, direction of, 60; point
of application, 61.                         VACUUM, Torricellian, 261; vapors formed in,
Terrestrial eye-piece, 500; heat, origin of, 746;   668.
magnetism, 787; radiation, 745.             Value of fuel, 715.
Thaumatrope, 488.                             Value ofg in pendulum experiments, 89.
Theorem of Archimedes, 205; of Torricelli, 219. Vaporization, 667.
Theoretical and actual flow, 216.             Vaporization, temperature, and limits, 672.
Theories of endosmose, 251; of light, 398; of Vapors, 252; and gases, identity of, 688;
light unsatisfactory, 405.                    density of, 693; formed in a vacuum, 668;
Theory defined, 3; of liquefaction and solidifi-   from  the body, 719; Latour's law, 692;
cation- of gases, 688; of undulations, 299.   liquefaction of, 685; maximum tension, 669.
l'hermochrosy, 646.                           Variable motion, 31.
Thermo-electricity, 941.                      Variation chart, 789.
Thermo-electric motions, 941.                 Variations of barometric height, 270; of magThermometers, 567; air, 587; Breguet's metal-   netic needle, 788; annual, daily, 790.
lic, 580; Centigrade, 570; comparison of  Vegetables, temperature of, 757.
scales of, 571; construction of, 568; defects Velocities, actual and theoretical, 144; parin mercurial, 576; Fahrenheit's, 570; gradu-   allelogram of, 34.
ation of, 569; house, 572; Howard's differ- Velocity after impact, 184; of all sounds the
ential, 587; Kinnersley's, 852; Leslie's dif-   same, 343; of all sounds not the same, page
ferential, 587; limits of mercurial, 574;   668; of aerial waves, 332; of electricity,
metastatic, 579; Negretti & Zambra's maxi-   818; of light, 404; of rivers and streams,
mum, 578; Reaumur's, 570; Rutherford's   227; of sound in air, 344; of sound in liquids,
maximum  and minimum, 578; Saxton's   347; in solids, 348; of sound, Newton's fordeep sea, 581; self-registering, 578; sensi-   mula, 653.
bility of, 572; spirit, 575; standard, 577; Ventilation, 716-726; a practical problem, 722tests of, 572; Walferdin's maximum, 578.      necessity of, 718; quantity of air required,
Thermometric scales compared, 571.              720.
Thermo-multiplier, 588, 942.                  Ventilating shaft, 723.
Thermoscopes, 587.                            Ventilators, 725.
Thilorier and Bianchi's apparatus, 690.       Ventriloquism, 391.
Three states of matter, 15.                   Verification of laws of falling bodies, 72.
Thunder. 989.                                 Vernier, 266.
Thunder-storms, 988.                          Vibrating armature, 931.
Time and velocity, 29.                        Vibrating dams, 386.
Time required for vision, 489.                Vibration of air in tubes, 379, 384; of cords,
Tolles' solid eye-piece, 512.                   308; laws of, of cords, 309; of rods, 310;
Tone, 363; changed by echo, 355.                of membranes, 318; of plates, 312; of plates,
Tornadoes, 969.                                 laws of, 315; paths of, 311.
Torricellian theorem, 219; demonstrated, 220. Vibrations, 299; forms of, 307; from magnetTorricellian vacuum, 261.                       ism, 916; isochronous, 303; of different notes,
Torsion, elasticity of, 165; electrometer, 820;   absolute, 369; relative, 368; of heat and
laws of, 166; of rigid bars, 167.             light, 765; of light, direction, 541; of light,
Total hydrostatic pressure, 196.                length of, 531; of light, transmission of, 542;
Total reflection, 409.                          of light, resolution of, 544.
Trains of wheelwork, 117.                     Victoria tubular bridge, 172.
Transposition in music, 374.                  Virtual focus, 429; images, 434; velocities, 105.
Transverse strength, 172.                     Visible bodies, 402.
Tubes, strength of, 172.                      Vision, 468; conditions of, 475; binocular, 484;
Tubular bridges, 172.                           double, 483; single, 482.
Tuning fork, 377.                             Visual angle, 472.
Turbine wheel, 231.                           Visual impressions require time, 489.
Twining's ice machine, 681.                   Visual power of microscope, 513; of telescopes,
Tylerian electrical machine, 837.               507.
Tympanum, 393.                                Visual rays nearly parallel, 479.
Vis viva, 111.
UMBRA, 411.                                   Vitality, 10.
Undershot wheel, 230.                         Vocal apparatus of man, 388.
Undulation in oceans, &c., 329; of elastic  Voice and speech, 387.
fluids, 330; of liquids, 319.               Voice, mechanism of, 389; range of human,
Undulations of a sphere of air, 331'; of solids,   390.
306; origin of, 299; phases of, 304; progres- Volta-electric induction, 929.
sive, 300; progressive, in liquids, 320; sta- Voltaic arch, heat of, 886.
tionary, 302.                               Voltaic batteries, 869-881; effects in various
Uniform motion, 30.                             forms, 881.
Uniform musical pitch, page 668.              Voltaic circuit, polarity of, 878.
Unison, 364.                                  Voltaic couple, 866.
Unit of force, 37.                            Voltaic currents, heat of, 887.
62*                            3A




710                                     INDEX.
Voltaic electricity, quantity and intensity,    air, interference of, 333; of condensation,
865.                                          330; production of, 319; reflection of, 323;
Voltaic pile or battery, 864; chemical theory,   stationary, 321.
898; grouping elements, 879; physical ef- Weather indicated by barometer, 271.
fects, 883; physiological effects, 895; mag- Wedge, 125; application of, 126.
netic effects, 895; theory of, 896.         Weighing machine, 115.
Voltaic spark and arch, 883.                  Wells, artesian, 204.
Voltaism and galvanism, 864.                  Weight, 37, 97, 106; definition of, 58.
rolta's contact theory, 863, 897.             Weights, French system, 100.
Volta's discovery, origin of, 863.            Weight, specific, 99.
Volta's electrical lamp, 856.                 Weight varies in different localities, 93.
Volta's electroscope, 846.                    Wheel and axle, 116.
Volta's hail storm, 842.                      Wheel barometer, 268.
Voltameter, 889.                              Wheel, breast, 230; overshot, 229; turbine,
Volume changed by solidification, 664.          231; undershot, 230.
Volume of gases, 608.                         Wheelwork, trams of, 117.
Whirlwinds, 969.
WALFERDIN'S thermometer, 578.                 Whispering galleries, 356.
Warming, 727.                                 White light, composition of, 457.
Watches, balance-wheels of, 596.              Winds, cyclones, and hurricanes, 968.
Water bellows, 195.                           Winds, general consideration of, 957; general
Water, effect of unequal expansion, 604; ex-   direction of, 965; hot. 967: periodical, 963;
pansion of 604; freezing of, 665; maximum    propagation of, 958; regular, 962; variable,
density, 604; volume at different tempera-   964; velocity of, 961.
tures, 604.                                 Wollaston's camera lucida, 518.
Water pumps, 289.                             Wood conducts heat, 617.
Waterspouts, 970.
Water-wheels, 228.                            YARD, 17.
Watt's steam engine, 709.
Waves, depth of, 322; from foci of ellipse, 324; ZAMBONI & DE Luc, dry piles, 873.
from focus of parabola, 325; of air velocity  Zero point of therfbmeter, 570; displacement
and intensity of, 332; of condensation illus-   of, 573.
trated, 331; of air expanding freely, 334; of  Zero, absolute, 666.'EE END