10, Kolken
Hudson
Mass





ELEMENTS
OF
NATURAL PHILOSOPHY,
WITH
PRACTICAL EXERCISES,
FOR THE USE OF SCHOOLS.
BY FRANCIS J. GRUND,
Author of an Elementary Treatise on Plane and Solid Geometry, translator of the
Arithmetical and Algebraic Problems, of Meier Hirsch, &c.
BOSTON:
PUBLISHED BY CARTER AND HENDEE,
AND
RICHARDSON, LORD AND HOLBROOK.
1832.

ENTERED according to Act of Congress, in the year 1832,
BY FRANCIS J. GRUND,
in the Clerk's office of the District Court of Massachusetts.
BOSTON
CLASSIC
PRESS.
I.
R.
BUT T S.

PREFACE.
THE general want of a suitable text-book on Natural
Philosophy, adapted to young pupils, and, at the same time,
to the progress of instruction in this country, has, for a long
time past, been the subject of complaint with many of the
most experienced teachers. In the following treatise, the
author has made an attempt, so far as his abilities permitted,
to supply this deficiency. He has, for this reason, endeavor-
ed not only to preserve his work from some of the gross errors,
with which it is common to find elementary treatises on this
science charged, but has enlarged it also with the most re-
cent discoveries in electricity, galvanism, and magnetism.
The authorities, and the sources from which he has drawn,
have been carefully indicated; and the subjects on which
the opinions of philosophers are divided, treated of in a man-
ner to leave both teacher and pupil at liberty to adhere
either to one or the other hypothesis. As regards the gene-
ral plan and arrangement of the work, it will suffice to say,
that the inductive method has been pursued, as far as it
was practicable in a treatise of this nature. The whole is
divided into ten chapters, treating separately of the General
Properties of Matter, of the Phenomena of Cohesion and

iv
PREFACE.
Adhesion, of the Laws of Motion, of Hydrostatics and
Ærostatics, of the Mechanical Properties of the Atmosphere,
of Heat, Light, Electricity, Galvanism, and Magnetism.
Each chapter is again divided into sections, which are num-
bered, and consist of short sentences, for the sake of being
more easily referred to, and to assist the memory of young
pupils. The mathematical part has been separated from the
text, and is thrown into the notes, not to interrupt the pro-
gress of those who are not yet familiar with mathematical
reasoning. The appendix contains nothing but exercises
for the pupils, which are divided into as many chapters and
sections as the text; each chapter referring to the same
chapter in the text, and each section to that section of the
book which is preceded by the same number.
The astronomical part has been omitted, for the obvious
reason of its making no part of Natural Philosophy. Astro-
nomy is a science sufficiently important of itself to be treated
of separately, as has been done by authors of distinction,
whose works are already extensively introduced into com-
mon schools. The study of Astronomy, when united to that
of Natural Philosophy, tends, in most cases, only to divide
the attention of the learner, and to impede his progress.
It is more intimately connected with Mathematics, and
forms a far better sequel to Geometry, than any branch of
the natural sciences.
Having thus brought his treatise on Natural Philosophy
to its proper limits, the author intends to have it followed by
an elementary treatise on Chemistry, which will be execu-
ted on the same plan, and form a necessary sequel to this
work.
Boston, March 28, 1832.

DIRECTIONS TO TEACHERS.
To every section of the book there is a question in
the appendix, under the head of the same chapter, and
preceded by the same sectional number as that of the
text. The sentences in italics are to be committed to
memory, and constitute the answers to the questions
in the appendix, which are likewise printed in italics.
The questions which, in the appendix, are printed
in smaller type, refer to the remarks in the text, which
are intended for more advanced pupils, and may be
omitted until reviewing the book.
The questions in the notes refer to the mathematical
part contained in the notes to the text. They are to
be required only of those pupils who have had some
instruction in Mathematics. They are all of so simple
a nature, that any one who has acquainted himself
with the elements of Geometry will be ready to answer
them.

ERRATA
66
66
66
6
66
(6
65
Page 80, 10th line from top, for “gravity’read' elasticity.'
105, 9th bottom, for ' reduced by mechan-
ical pressure 'read “ reduced, or by mechanical
pressure.'
111, 12th line from bottom, for density 'read 'inten-
sity
66 112, 13th
for • phenomena' read
phenomenon.
7th
for § 226' read ' § 225.
121, 9th
top, for Table IV' read “Ta-
ble V.
168, 16th
bottom, for circle' read cir-
cuit.'
169, 4th
for in the 'read in its.'
184, 4th
top, for continue read 'in-
crease.'
185, 10th
for thus' read then.'
195, 3d
CC
66
66
CG
66
CG
66
56
66
66
bottom, for line of deviation,
read line of no deviation.'
66

TABLE OF CONTENTS.
CHAPTER I.
OF THE GENERAL PROPERTIES OF MATTER
Page.
1
CHAPTER II.
OF THE PHENOMENA OF COHESION, ATTRACTION,
AND AFFINITY
13
.
19
22
28
CHAPTER III.
THE LAWS OF MOTION.
A. Uniform Motion
B. Accelerated Motion. — Gravity
C. Decomposition of Forces. — Compound
Motion
D. Application of the foregoing Theory to
Curvilinear Motion
E. Motion on an Inclined Plane
F. Oscillation of a Pendulum
G. Of the Lever
H. Of the Centre of Gravity
I. Laws of Percussion
1. Percussion of Unelastic Bodies
2. Percussion of Elastic Bodies
K. Vibrating Motion. — Acoustics
L. Obstacles or Hindrances of Motion
CHAPTER IV.
LAWS OF MOTION OF FLUIDS.
A. Pressure, Weight, and Equilibrium of
Liquids (Hydrostatics)
30
32
36
40
45
47
48
49
53
64
68

viii
CONTENTS.
73
Application of the foregoing Laws to the
Determination of the Specific Gravities
of Bodies
B. Pressure, Weight, and Equilibrium of
Elastic Fluids (Ærostatics)
CHAPTER V.
MECHANICAL PROPERTIES OF THE ATMOSPHERE
77
81
rors
CHAPTER VI.
OF HEAT
92
Means of producing Heat
93
Different Capacities for Heat
98
Propagation of Heat
101
CHAPTER VII.
OF LIGHT
109
Reflection of Light
113
A. Reflection of Light from Plane Mirrors 114
B. Reflection of Light from Spherical Mir-
115
C. Refraction of Light.
1. General Observation
120
2. Refraction of Light in a Body bound-
ed by Plane and Parallel Surfaces 121
3. Refraction of Light through Bodies
bounded by Spherical Surfaces (Lens-
es)
125
D. Theory of Colors (Acromatics)
131
E. Of Vision.
1. The Eye
137
2. Of Vision
139
F. Optical Instruments
142
CHAPTER VIII.
OF ELECTRICITY.
A. Phenomena
150
B. Opposite Electricity
154
C. Theory of Electricity
157

CONTENTS.
ix
D. Electrical Instruments
160
E. Motion of Accumulated Electricity 167
F. Effects of Electricity upon Bodies
169
G. Electricity of the Atmosphere
170
CHAPTER IX.
OF GALVANISM
173
Theory of Galvanic Electricity and the Vol-
taic Pile
181
Organic-Electric Phenomena
185
CHAPTER X.
OF MAGNETISM
186
A. Relation of Native Magnet to unmagnetic
Iron
187
B. Relation of Magnet to itself and to an-
other Magnet
189
Imparting of Magnetism
190
Of the Variation and Dip of the Magnetic
Needle
195
Magnetism of the Earth
198
Intensity of Magnetism
200
Modern Discoveries in Magnetism
201
APPENDIX,
CONTAINING QUESTIONS FOR THE EXERCISE OF THE
PUPILS.
EXERCISES IN CHAPTER I.
On the General Properties of Matter
203
EXERCISES IN CHAPTER II.
Of the Phenomena of Cohesion, Attraction, and
Affinity
209

X
CONTENTS.
EXERCISES IN CHAPTER III.
On the Laws of Motion.
A. Uniform Motion
211
B. Accelerated Motion. -- Gravity 213
C. Decomposition of Forces. — Compound
Motion
214
D. Application of the foregoing Theory to
Curvilinear Motion
215
E. Motion on an Inclined Plane
216
F. Oscillations of a Pendulum
217
G. Of the Lever
217
H. Of the Centre of Gravity
218
I. Laws of Percussion
219
1. Percussion of unelastic Bodies 220
2. Percussion of elastic Bodies 220
K. Vibrating Motion. - · Acoustics
221
L. Obstacles or Hindrances of Motion 225
EXERCISES IN CHAPTER IV.
Laws of Motion of Fluids.
A. Pressure, Weight, and Equilibrium of
Liquids (Hydrostatics)
227
Application of the foregoing Laws to the
Determination of the Specific, Gravi-
ties of Bodies
B. Pressure, Weight, and Equilibrium of
Elastic Fluids (Ærostatics)
231
229
EXERCISES IN CHAPTER V.
Mechanical Properties of the Atmosphere
233
EXERCISES IN CHAPTER VI.
Of Heat
Means of producing Heat
Different Capacities for Heat
Propagation of Heat
236
236
237
239

CONTENTS.
X1
EXERCISES IN CHAFTER VII.
rors
Of Light
244
Reflection of Light
245
A. Reflection of Light from Plane Mirrors 246
B. Reflection of Light from Spherical Mir-
246
C. Refraction of Light.
1. General Observations
247
2. Refraction of Light in a Body
bounded by Plane and Parallel
Surfaces
248
3. Refraction of Light through Bodies
bounded by Sperical Surfaces
(Lenses)
248
D. Theory of Colors
249
E. Of Vision
251
1. The Eye
251
2. Vision
252
F. Optical Instruments
253
EXERCISES IN CHAPTER VIII,
Of Electricity.
A. Phenomena
B. Opposite Electricity
C. Theory of Electricity
D. Electrical Instruments
E. Motion of Accumulated Electricity
F. Effect of Electricity on Bodies
G. Electricity of the Atmosphere
254
256
257
257
260
261
262
EXERCISES IN CHAPTER IX.
Of Galvanism
263
Theory of Galvanic Electricity and the
Voltaic Pile
265
Organic-Electric Phenomena.
266

xii
CONTENTS.
EXERCISES IN CHAPTER X.
268
Of Magnetism
266
A. Relation of native Magnets to unmag-
netic Iron
267
B. Relation of a Magnet to itself, and to
another Magnet
Imparting of Magnetism
269
Of the Variation and Dip of the Magnetic
Needle
270
Magnetism of the Earth
272
Intensity of Magnetism
272
Modern Discoveries in Magnetism . 273
TABLES.
TABLE I. Specific Gravities of Bodies, compared
to Distilled Water
275
TABLE II. Exhibiting the Specific Caloric con-
tained in some substances, compared to the
Quantity of Caloric in an equal Weight of
Water
276
TABLE III. Boiling-Points
276
TABLE IV. Exhibiting the Degree of Tempera-
ture at which various Liquids congeal, or
freeze
277
TABLE V. Showing the Refractive Power of
several Substances; that of atmospheric
air being taken for Unity
277

NATURAL PHILOSOPHY.
CHAPTER I.
ON THE GENERAL PROPERTIES OF MATTER.
space.
$1. EVERYTHING which may become an object Time and
of our senses must exist in time and space. Time
and space are not things of themselves, but are
merely the conditions under which we can become
conversant with them.*
$ 2. That which fills space is called matter. Matter.
Any portion of this within fixed limits is called a
physical body. The extension of a body, or the
space which it apparently fills, is termed its
volume; and the quantity or bulk of matter which Volume and
it contains, its mass.
mass of bod-
ies.
* The terms, time and space, are here taken in their
mathematical sense. All phenomena in nature cannot
occur at once; they follow each other with a succession of
intervals, the length or duration of which, we are capable
of comparing and measuring. This constitutes our idea of
time. Neither is it possible for us, to imagine two bodies to
be, at the same time, in the same place. Each body exists
within certain limits inaccessible to others, the extent of
which, however, is subject to variation, and is, therefore,
again capable of being compared and measured. This con-
stitutes the idea of space.
1

2
GENERAL PROPERTIES OF MATTER.
Divisibility
of matter.
Interstices of
bodies.
3. Geometry teaches us how to divide and
subdivide space.
The same may be done with
the matter which fills it. Thus we say, matter is
divisible.*
$ 4. The space which physical bodies occupy
is not throughout filled with their own substance,
In a piece of wood, for instance, there are places
which, at least, are not filled with particles of
wood. These are called interstices or pores.
It is not necessary to suppose that these are vacui,
that is, entirely void of matter. When water or other
fluids enter the pores of bodies, it may be by expel-
ling another substance previously contained in them.
(This is done, for instance, when a sponge is filled
with water; the air contained in it is then expelled.).
REMARK. The pores of bodies, and the cellular
texture of plants and animals, explain the influence
of the atmosphere upon them, the operation of salves,
plasters, &c.
§ 5. Our senses tell us that all bodies have
not the same plıysical properties, or do not affect
us in the same manner. Even in the same body,
(as in granite), we discover dissimilar particles.
Water, gold, quicksilver, &c, though composed
of similar particles, are heterogeneous substances
with regard to each other. Hence the different
appellations of substances, the difference in color,
taste, sound, &c.
Difference of
matter.
* We prove in Geometry that space is divisible ad infini-
tum. The same, however, cannot be supposed to be the
case with matter. For although the division of some sub-
stances, for instance, of gold, silver, &c, can be carried to
surprising minuteness, yet the particles thus obtained will
finally become so small as actually not to admit of any fur-
ther separation.

GENERAL PROPERTIES OF MATTER.
3
$ 6. If the whole volume of a body were en- Density of
tirely filled with its own matter, that is, if there
were no interstices, it would be perfectly dense.
As there is no such body in nature, we call a
body more or less dense in comparison with
another, when it has fewer interstices, or, which
is the same thing, when it contains a greater
quantity of matter in the same space.
$7. We say a body is compressed, when some Compressi-
exterior force compels it to occupy less space, bodies.
without diminishing its mass; and expanded, ,
when the matter of which it is composed is
obliged to take up apparently more space. All
bodies are more or less compressible, because all
have pores.
A perfectly dense body would be incompressible;
for one body cannot enter upon the substance of an-
other and fill the space already occupied.
§ 8. Some bodies are easily compressed; oth-
ers with more, and some only with the greatest Mobility of
difficulty. In general, we meet with more or less of matter.
resistance, whenever we wish to change the form
of a body. This must be occasioned by the greater
or smaller capacity which its particles have to
change their relative position; for without such
a mobility of its particles, there could be neither
compression nor expansion, and consequently no
change in the forms of bodies.
9. The resistance which we meet in chang-
ing the forms of bodies, and the degree of force Power of co-
which is required to separate their particles, con-
vince us of the existence of a certain power by
which they are held together, and in their relative

GENERAL PROPERTIES OF MATTER.
Mechanical
division of
bodies,
position. This is called the power of cohesion ;
and the adhesion of the particles of the same body
to each other is called the attraction of cohesion.
§ 10. When the particles of a body are sepa-
rated by the application of some exterior force,
then the body is said to be mechanically divided.
To this kind of division belong cutting, grinding,
pounding, wire drawing, the pouring out of liquids,
&c.
The parts or particles thus obtained, have apparently
yet the same properties which they had before the
separation; and for this reason they are called integral
Integral parts : because they differ from each other and the
parts of mat-
body from which they are obtained, merely in magni-
tude, and not in substance.
$11. We know from experience that some
bodies may also be divided in such a manner,
that the parts differ in their properties from each
other, and the body from which they are obtained.
The body is then said to be decomposed into its
chemical compounds or ingredients. These phe-
compounds.
nomena are treated of in chemistry. Those sub-
stances which have not, as yet, becn decomposed
into compounds, are termed elements.
Adhesion. $ 12. When particles obtained by mechanical
division are brought near each other, they evince
ter.
Chemical
Elements.
* This is to be considered as a mere definition. The
phenomenon itself cannot be explained. We do not know
in what manner the power of cohesion produces the adhe-
sion of the particles of matter to each other. The hypothe-
ses of Des Cartes and others are far from being satisfactory.
+ Here the teacher might mention the great number of
bodies that have been decomposed within the last fifty
years, the decomposition of water into hydrogen, oxygen,
&c.

GENERAL PROPERTIES OF MATTER.
5
a disposition to unite again. In many cases,
however, they adhere stronger to other substances.
Two drops of water unite in one, as soon as they
are brought in contact; but a drop of the same fluid
spreads on wood or glass; and when these substances
are immersed in water and then withdrawn, they be-
come wet, which shows, that the particles of water
sooner adhere to them, than remain united with each
other. So do water and many other fluids enter the
interstices of wood, paper, sugar, &c. which could
not be if the mutual attraction among the particles of
these fluids were stronger than their adhesion to those
substances.
§ 13. Some bodies show a disposition of ap- Attraction.
proaching and uniting with each other at a con-
siderable distance. Magnet attracts iron at a
visible distance, and little pieces of cork-wood
fly to a rubbed glass tube from a distance of
several inches.
The phenomenon of gravity, or the disposition which Terrestrial
all bodies evince to approach the surface of the earth;
gravity.
and, when prevented from doing so, the manifestation
of this disposition by pressure, weight, &c, is caused
by a power of attraction which operates even at a
distance of several miles. Finally, the celestial bodies
themselves, the planets, the sun, and the stars, attract
each other, and would unite into one huge mass, if
they were not kept in their orbits by other forces,
which we shall speak of hereafter. This inexplicable
phenomenon of mutual attraction, which is inherent
in matter, is the principal cause of all motion by which
nature is animated. It is the main source of all
changes in the form and substance of bodies; it es-
tablishes a mutual relation and dependency among
all natural objects, not only upon our globe, but also
among the planets of our solar system, and the most
distant spheres and worlds.
§ 14. In many cases bodies and their particles
separate or seem to be repulsed from each other.
But these phenomena alone do not justify the
1*

6
GENERAL PROPERTIES OF MATTER.
Attraction of
supposition that there is a primitive repulsive
power in nature, as they may be easily explained
by attractions in opposite directions. (See Tobias
Repulsion. Mayer's Elements of Nat. Phil. ;* also Green's
Journal of Nat. Phil., Vol. VII.)
$ 15. One of the most remarkable phenomena
gravity.
of attraction is, as we have said before, the attrac-
tion of gravity, or the disposition which all
bodies exhibit, to approach the surface of the
earth--the falling of bodies -- if they are not pre-
vented from doing so, by some other cause. This
phenomenon is often explained by attributing to
the earth the power of attracting bodies. But
we know gravity only from its effects, and know
nothing of its nature and the manner in which it
operates.
§ 16. The direction in which a falling body
gravity.
approaches the surface of the earth, when not
solicited by any other power, is termed a vertical
Vertical, hor-
izontal, and line, and may be exhibited by any heavy sub-
stance, suspended by a string. Lines or planes
at right angles with the direction of gravity are
said to be horizontal. Inclined planes form ob-
lique angles with the direction of gravity.
The direction
of gravity
If the earth is a sphere, then the direction of gravity
must everywhere go through its centre, because it is
through the everywhere perpendicular to its surface.f Hills and
mountains differ from plains, inasmuch as their sur-
faces form oblique angles with the direction of gravity.
Direction of
inclined di-
cretions.
passes
earth's cou-
tre.
Anfangsgründe der Naturlehre von Tobias Mayer.
Göttingen, 1820.
At small distances from each other we consider two
vertical lines a parallel, on account of the comparatively
great remoteness of the centre of the earth.

GENERAL PROPERTIES OF MATTER.
7
§ 17. The pressure which a body exercises Absolute
weight of
upon a horizontal plane which prevents it from bodies.
falling, or the degree of force with which it pulls
a string by which it is suspended, is called its
absolute weight.
There is a great difference between gravity and
weight. Gravity is in all substances alike ; that is,
all substances are equally, and in the same direction,
attracted to the centre of the earth. But all particles
of matter being alike attracted, it follows that the
pressure resulting from them, is in proportion to their
number; that is, the absolute weight of bodies is in
proportion to their masses.
§ 18. By specific gravity of a body we under- Specific grav-
ity.
stand its absolute weight compared to that of
another body of the same volume. Hence the spe-
cific gravities of bodies are in direct proportion to
their absolute weight, and inversely as their cubic
contents; that is, among bodies of equal volume,
that is specifically heaviest whose absolute weight
is greatest; and of bodies whose absolute weights
are equal, the specific gravity of that is greatest,
whose volume is smallest.
Determina-
§ 19. In order to determine the absolute
weight of bodies, we make use of a certain weight weight of
as unity of measure. This may be a pound, an
bodies
ounce, a drachm, &c.
For different bodies we use different units of meas-
ure, according to the degree of exactness required.
Thus we have avoirdupois weight, Troy weight,
apothecary's weight, &c. When we say a body
weighs three pounds, we mean that its pressure upon
a horizontal plane is equal to the united pressure of
three units of measure (here pounds).
The balance and other instruments for determining
the weight of bodies, will be spoken of in the theory of
the lever.
tion of the
absolute

8
GENERAL PROPERTIES OF MATTER.
Absolute
place.
Situation,
Inotion of
bodies.
Hence we say,
§ 20. Every body exists somewhere in space.
This is called its absolute place or position. By
comparing it to the place of other bodies, we
are led to the idea of situation or relative position.
A successive change in the position of a body or
its particles is called motion.
Absolute motion cannot be perceived through the
medium of our senses; we merely conclude that a
motion has taken place, when a body has changed its
position with regard to others.
Way, orbit. $ 21. When a body is in motion, we consider
it abstractedly as a mere point, which approaches
others, or removes from them.
the
body describes a line, which is its way or orbit.
This may be a straight or a curve line, according
as the moving body continues in the same direc-
tion or changes it continually.
$ 22. Every kind of motion requires time;
because a body cannot, at once, be in two points
of its orbit. We measure time by years, months,
weeks, days, hours, minutes, &c.
Velocity. § 23. When we compare the time which a
body needs to move from one place to another to the
distance which is between them, we form the idea
of velocity, which is estimated by the space which a
body goes through in a certain time, (a minute, a
second, &c.) Of two bodies which are in motion,
that is said to have the greater velocity, which,
in the same time, passes through a greater space.
Uniform, ac- 24. When considering the velocities of
selerated and
retardod mo- bodies, we call their motion uniform, accelerated,
or retarded, according as the spaces gone through,
in equal times, are equal, or become successively
greater or smaller.
Time.
tion.

GENERAL PROPERTIES OF MATTER.
Vis inertia.
reaction of
bodies.
$ 25. Every motion, as well as every change
of it, in velocity or direction, must proceed from
a cause or power, which, by soliciting the body,
produces this effect.
Without such a cause every body in nature would
remain in the state of rest or motion once assumed.
This universal principle, evident of itsel:, is termed
vis inertia. It originates in the difference which
we make in our minds, between what is moveable or
moved, and the power which puts it in motion. This,
however, is no proof that matter and power are neces-
sarily distinct from each other; for the moving power
may also be inherent in bodies, as is, for instance,
the case in animals.
♡ 26. When a body A, is in motion, it has the action and
power of moving another body B, which is in its
way, or at least to change its motion. When this
takes place, we say the body A has imparted
motion to the body B. While it is thus soliciting
B, a part of its own force or motion is destroyed.
This is called the reaction of the body B upon A,
Now, as the force of the body A can be diminished
only as far as it finds resistance in B, it follows that
action and reaction are equal to one another ;
that is, A loses as much of its own force as it
imparts to B.
$ 27. The imparting of motion requires time. Time requir-
This may be shown by a variety of experiments. parting mo-
tion,
One of the simplest is to place a heavy substance,
say a piece of copper, on a smooth horizontal surface,
which covers a vessel of sufficient diameter. When
the cover is suddenly removed, without changing its
horizontal direction, the copper will fall into the vessel ;
which could not be if the motion communicated to the
cover were, at the same time, transmitted to the copper.
$ 28. The operation of bodies upon one an- Mechanical
other by imparting motion, is called mechanical. operation,
ed for im-

10
GENERAL PROPERTIES OF MATTER.
ies.
But when the attractive powers which are in-
herent in bodies, cause a motion of their particles,
then the operation is called a chemical one.
Organic motion, such as the circulation of the
blood, the secretion of liquids, &c, cannot be
explained either by mechanical or chemical
agencies.
Geometrical
$ 29. It is yet important to distinguish between
and physical the geometrical and physical form of bodies. By
the geometrical form of a body we understand its
dimensions in space; whereas by its physical
form we mean the peculiar properties by which
it distinguishes itself from others of the same
volume. To these properties belong the manner
in which they affect our sense of touch, the power
which we must apply to divide them or to change
their form, &c. Hence the appellations of solid,
hard, soft, ductile, fragile, viscous, smooth, rough,
&c.
Modification
Some bodies are easier divided or split
of attraction in one direction than in another. In this case,
by cohesion.
they consist of filaments or fibres which are not
so intimately connected with each other as the
particles of these fibres themselves. These and
similar modifications of the phenomenon of at-
traction, must be considered as occasioned by the
agency of cohesion ($ 9).
Fluids, li- $ 31. Bodies, whose cohesive powers are so
quids, gases.
small that their particles are with the greatest
ease removed or separated, are called fluids.
There are two kinds of fluids ; such as form
drops — liquids, and others, which are susceptible
of great degrees of compression, and afterwards
reassume their former volume
gases.
$ 30.
of the powers
-

GENERAL PROPERTIES OF MATTER.
11
solid bodies.
It can be mathematically proved, that the agency
of cohesion in a fluid, let its mass be great or small,
is such that it must assume a spherical form, when it is
not prevented from doing so by other powers operating
upon it at the same time. Hence the spherical form
of drops, the convex surface of water and other fluids
in greased vessels, &c. It is well, also, to observe
the infinite variety in the power of cohesion, from the
perfect fluid to the state of absolute solidity.
§ 32. We know from experience that many Melting of
solid substances, when under the influence of
certain degrees of heat, become fluid, and the
reverse, that fluids become solid when exposed to
cold, or to inferior degrees of temperature.
This has led philosophers to suppose, that all bodies
are in their original state fluid, whence they become
solid through the loss of heat. In general it appears
that all matter has at first been in a fluid state, and we
see yet, every day, in all three kingdoms of nature,
solid substances form themselves out of fluids. The
round shape of the heavenly bodies themselves, seems
to agree with this supposition.
§ 33. When liquid substances become solid, Crystalliza-
their particles form regular layers, which give the gelation of
solid body thus forming itself, a determinate
texture, and sometimes a regular geometrical
shape, worthy of the greatest admiration. This
phenomenon is called the crystallization or conge-
lation of bodies.
§ 34. There are bodies whose textures are Elasticity.
such, as to be capable of changing their forms,
when some interior force is applied to them ; as-
sume however their former shape as soon as that
power ceases to operate. This property, which
all bodies possess in a greater or less degree, is
known by the name of elasticity. Some bodies
possess it in an eminent degree, such as steel,
ivory, &c.
tion and con-
bodies.

12
GENERAL PROPERTIES OF MATTER.
Ponderable
and imponde-
form of
bodies.
$ 35. Those fluids which obey the law of
rable fluids. gravity, and whose weight, therefore, can be as-
certained, are called ponderable. To these belong
all aeriform fluids, steam, and vapors. But there
are other fluids, such as light, caloric, electricity,
&c, which are either not at all, or at least so little
affected by gravity, as entirely to escape our ob-
servation, wherefore they are called imponderable
substances.
Aggregate 36. Solids and liquids become frequently
transformed into elastic fluids, and aeriform sub-
stances become again liquid and solid. Ice, for
instance, becomes water, and water steam under
the influence of certain degrees of heat. The
particles of a solid or liquid body, which have
thus been changed into an elastic fluid, are said
to form the ponderable basis of that fluid. Thus
water is the ponderable basis of steam, &c.
§ 37. The three forms of bodies, which we
have just considered, and with regard to which
all bodies are either solid, liquid, or elastic fluid,
are commonly called the three forms or states of
aggregate.
Besides the aggregate forms of bodies, they have
yet an infinite number of other characteristics, by
which we are able to distinguish them from one
another, and to arrange them into classes, some of
which we shall become acquainted with in the
following sections.

13
CHAPTER II.
OF THE PHENOMENA OF COHESION,
ATTRACTION, AND AFFINITY.
of bodies.
$ 38. IF we suspend several cylindrical or Method of
prismatical rods, and attach to their lower ends the cohesion
as much weight as is necessary to tear them
asunder, we determine thereby the cohesive
powers of these substances, of which these rods are
composed. In the same manner we determine
the strength of cords, ropes, &c.
According to Muschenbroek the power of cohesion
in different metals decreases in the following order :
IRON.
JAPAN COPPER.
FINE SILVER.
ENGLISH Tin.
SWEDISH COPPER. ZINC.
FINE GOLD.
ENGLISH LEAD.
The cohesive powers of wood rank in the following
order:
OAK.
ELM.
BIRCH.
PINE.
Silk cords are almost three times as strong as flax
cords of the same thickness. A thread made of human
hair is stronger than one of horse hair of the same
thickness. The tarring of cordage diminishes their
strength considerably ; bleached thread is weaker
than unbleached, &c. The power of cohesion in
metals is sometimes increased by moderate hammering,
rolling, casting, drawing, &c. Some bodies become
stronger when exposed to the atmosphere or to heat.
* See Tobias Mayer's Elements of Nat. Phil. ; also,
Buffon's Expériences sur la Force des Bois; also, Petr. v.
Muschenbroek's Introd. ad cohaerentiam corporum firmo-
rum.
2

14
PHENOMENA OF COHESION.
Adhesive at-
traction.
§ 39.
Shape of li-
quids in ves-
sels.
This is the case when their pores are filled with
liquids which diminish the power of cohesion, and
which evaporate when exposed to the air. A compo-
sition of different metals is in many cases much
stronger than either of the component parts. This we
see in brass, bronze, &c.
When two well polished marble or
glass surfaces are brought in contact, they adhere
to each other the stronger, the greater the number
of points is, in which they actually touch each
other.
This phenomenon explains a number of processes
in the mechanic arts; the gilding, tinning, silvering of
glasses, &c.
$ 40. On account of the spherical form which
every fluid matter necessarily assumes when solely
acted upon by the attraction of cohesion among its
particles, every liquid inclosed in a vessel, ought
to exhibit a convex surface; but as the particles
of the liquid, are at the same time solicited by the
general attraction of gravity ($ 15), the surface
becomes flattened and almost horizontal. If, in
addition to this the liquid is strongly attracted by
the sides of the vessel, above the surface, then it
will rise around those sides, and its surface will
become concave.
This does actually take place with water poured into
glass or metallic vessels, whereas quicksilver in ves-
sels of glass or wood exhibits a convex surface;
because the particles of quicksilver attract each other
more strongly than they adhere to glass or wood, and
are therefore more at liberty to follow the attraction
of cohesion. A convex surface is also exhibited by
water in glass or wooden vessels, when the sides of the
vessel, above the surface of the water are greased with fat
or oil. This seems to prove that the surface of liquids
depends entirely upon the sides of the vessel, and
particularly upon that portion which remains above the

PHENOMENA OF ATTRACTION.
15
liquid ; so that if the cohesion of the liquid is less than
its attraction to the sides of the vessel, the surface will
be concave; while on the contrary it will exhibit a con-
vex surface, when its cohesion is greater than the attrac-
tion to the sides of the vessel. When a vessel is en-
tirely filled with water, so that no portion of its sides
remains above the surface, there being no room for
the liquid being attracted by the sides of the vessel,
and consequently no possibility of its assuming a con-
cave surface, we can always add a small quantity
without making it overflow, and the water being now
solely solicited by the power of cohesion, exhibits again
a convex surface.
REMARK. What has just been said about the sur-
face of fluids, will serve to explain a number of phe-
nomena, some of which it will be easy for the teacher
to show to his pupils. Little balls of corkwood, for
instance, when thrown into a wooden or glass basin,
which is filled with water, are attracted by its sides;
and when these are greased and covered with witch-
meal, they are repulsed by them.
§ 41. When a narrow glass tube, which is open Phenomena
of capillary
at both ends is immersed in water, or in any
other
liquid which strongly adheres to glass, the liquid
in the tube will rise above the surface in the vessel.
The liquid in the tube will, accord-
ing to what has been said, form a
concave surface, that is, it will rise
higher along the sides of the tube,
than at its centre, (see the figure).
Now if the tube is very narrow, (a
capillary tube) then the particles of
the liquid which rise along the sides
are sufficiently near each other for
their cohesive powers to act. AC-
cordingly they flow in one and form
a little column abcd above the sur-
face of the liquid in the vessel. But
as soon as this is completed, the liquid rises again
along the sides of the tube, and by a new confluence
forms a new column cdef; and this process continues
until the weight of the column thus formed is in equi-
librium with the attraction of the liquid to the sides
of the tube.
attraction.
e
c
a
3

16
PHENOMENA OF ATTRACTION.
$ 42. The attraction of a liquid to the sides of
a narrow tube which is immersed in that liquid,
is called capillary attraction. The same phenom-
enon, however, may be produced by bringing the
tube merely in contact with the surface of the liquid.
If directly over a drop of water you place the open
end of a capillary tube, it will not only enter and rise
in the tube, but if its weight is less than that of a
column of water, which by the capillary attraction of
the sides may be raised in the tube when immersed in
water, the whole drop will, as if by suction, be absorbed
by the tube, and continue to remain in it, even when
the tube is moved from its position, contrary to the
laws of gravity.
§ 43. In order that a liquid shall rise in a
capillary tube, the tube must be made of a sub-
stance which attracts the particles of the liquids
stronger than they attract each other. This is the
reason why quicksilver does not rise in a glass
tube ; or water in a tube whose sides are greased
with fat. But quicksilver rises in a capillary tube
made of tin or lead, or in glass tubes which have
been lined with fat or oil.
REMARK. What has been said about capillary at-
traction is sufficient to explain why water and other
liquids enter the interstices of solid substances, such
as wood, sugar, lime, paper &c. Moreover it may be
proved that the phenomena of capillary attraction are
independent of the pressure of the atmosphere, as they
take place, also, under the recipient of an air-pump,
an instrument which will be described hereafter, when
treating of the atmosphere.*
* All natural philosophers do not agree in their mode of
explaining the various phenomena of capillary attraction.
The most complete and mathematical theory of it is given
by La Place, in the supplement to his Mécanique Céleste.
It has since appeared separately as a pamphlet, Théorie de
l'Action capillaire, par M. La Place. Paris, 1807.

PHENOMENA OF ATTRACTION.
17
come.
bodies.
$44. The reason why the particles of a fluid Mobility of
the particles
change so easily their relative position, is because of fluids.
they attract each other equally in all directions.
Thus an animalcule moves about with the greatest
ease in a drop of water, because it has not to overcome
the cohesion of the liquid, but merely to change the
relative position of its particles. It is a different case,
when a drop is actually to be separated from the rest;
because then the cohesion of the liquid must be over-
Hence an animalcule, though moving with
great facility in a drop of water, finds it difficult to rise
above the surface. Aquatic insects, needles, or small
pieces of sheet iron, although heavier than water, do
not sink until they are immersed, that is, until the
cohesion of the liquid is overcome by the separation
of its particles.
$ 45. The solidity of bodies originates in their Solidity of
particles not being equally attracted in all direc-
tions ; for if these attractions were everywhere
the same, they would mutually cancel each other,
and a body might be perfectly dense, and at the
same time perfectly liquid.
In such a body animals and insects might then move
with as much ease as an animalcule in a drop of water.
§ 46. When liquids enter the pores of solid Solution of
substances, it often happens that the cohesion of stances.
the particles of the solid is overcome. They con-
sequently lose their texture, and unite so perfectly
with the liquid as to make with it but one homo-
geneous mass. In this case we say, the solid has
been dissolved. The result of the whole opera-
tion is termed a solution, and the liquid in which
this takes place, its medium. Thus when sugar or
salt are dissolved in water, the latter is called the
medium of the solution.
$ 47. Such an operation evidently requires a
strong mutual attraction between the solid and
2*

18
AFFINITY.
tion.
the liquid ; and this mutual attraction, through
which two heterogeneous substances combine with,
Affinity. or dissolve each other, is called affinity.
Some substances combine more easily with each
than with other substances; some cannot be dissolved
at all, and others only after certain preparations, such
as heating, pounding, powdering, &c. The degrees
of affinity, therefore, vary in different substances; but
experience and observation alone can teach us, which
substances have greater affinity for one another than
others.
Perfect solu- § 48. A solution is perfect, when even the
Saturation. smallest imaginable part of it is homogeneous.
When a liquid has dissolved so much of a sub-
stance that it can dissolve no more of it, the
liquid is said to be saturated with that substance.
The temperature of the medium and of the sub-
stance which is to be dissolved, has great influence
upon the degree of saturation. A remarkable phe-
nomenon is also deserving of our notice : when two
substances combine with each other, the volume of
the combination is generally less than that of the two
compound substances before the solution.
Engagement,
Decomposi-
§ 49. The more a solution is saturated, the
less are we able to distinguish the properties of
its component parts. The two substances which
have thus combined to form a new body, are then
said to be engaged in it; and when, by some pro-
cess or other, one of the component substances is
again separated from the solution, and made to
assume its former state, we say, it has become
free ; and the solution is decomposed.
The theory of these combinations and decomposi-
tions has, for some years back, been considered as a
part of Natural Philosophy ; but it has since become so
complicated and extensive, that it was necessary to
treat of it separately, under the head of Chemistry, as
a distinct branch of the natural sciences.
tion.

19
CHAPTER III.
THE LAWS OF MOTION.
tion.
A. Uniform Motion.
950. It has been stated before (Chap. 1, § 24) Uniform mo-
that a body is said to be in uniform motion, when
it passes through equal spaces, in equal intervals
of time. From this definition it follows, that the
spaces described by two bodies in uniform motion,
are in proportion to their velocities when the times
are the same, and in proportion to the times, when
their velocities are equal. Thus of two bodies in
uniform motion during the same number of
minutes or seconds, that which has the greatest
velocity will pass over the greatest quantity of
space; and if the velocities are equal, that will
describe the greatest space, which moves during
the greatest number of minutes.
9 51. The space described by a body in uniform Space de-
motion, may be found by multiplying the number body in uni-
of minutes, seconds, 8c, it has been in motion, by form motion
its velocity, expressed in number of miles, rods,
feet, doc, it passes over in a unit of time. To
give an example: If a body has been in uniform
motion during 15 seconds, with a velocity of 3
rods per second, none will doubt, that the space
over which it passed is equal to three times 15, or
45 rods.
$ 52. The immediate inference which we
draw from this principle is this : The spaces

20
UNIFORM MOTION.
described by two bodies in uniform motion are in
proportion to the product of the times, multiplied
by the velocities ; for these products give the
spaces over which they passed.
$ 53. The second inference which we draw
from this principle is that the velocities of two
bodies in uniform motion are in proportion to the
spaces, divided by the times. A body which has
passed, in uniform motion, over a space of 20 rods
in 5 seconds, has evidently had the velocity of 4
rods in 1 second ; which is the quotient of 20
divided by 5; and another, which has passed over
60 rods in 10 seconds, has moved with the velocity
of 6 rods in a second, which is the quotient of
60 by 10 : consequently the velocities of these
two bodies are as 5 to 6, or, which is the same, as
20
is to
4 10
$ 54. Every body in motion has the power of
communicating motion to another body (Chap. I,
26). The degree of that power must necessa-
sarily depend upon its mass and velocity. Of two
bodies which move with the same velocity, the
greatest power will be exercised by the one which
has the greatest mass or bulk of matter; and if
60 *
*
IfS, V, T, respectively, denote the space, velocity, and
time of one body, and s, v, t, respectively, denote the space,
velocity, and time of another; then we have the proportion
S:s=TXV:tXv,
and dividing the first and third terms of this proportion by
T, and the second and fourth by t, we obtain easily :
S
V:v=
T t'
(See Grund's Plane Geometry, Theory of Proportions.)
s
:

UNIFORM MOTION.
21
Momentum.
their masses are the same, the greatest effect must
be produced by that whose velocity is the greatest.
$ 55. From this principle we infer, that the power
of a body in motion is measured by the products
of its mass into its velocity. This product is gen-
erally called the momentum of the body. For an
illustration of this principle, let us compare the
power of a cannon-ball weighing 24 lbs. and whose
velocity is 96 feet per second, to that of an 18
pounder whose velocity is 120 feet per second.
The momentum of the former is 96 multiplied
by 24=2304, while that of the latter is 120 by
18 = 2160 ; consequently the effect produced by
these balls are in the ratio of 2034 to 2160, or
which is the same, as 16 to 15.
The above example shows the surprising influence
of velocity upon the momentum of a body. A still
more striking instance of that influence is the fact,
that it is possible, with a tallow candle, to shoot
through a board of considerable thickness.
$ 56. From what has been said, we may like-
wise infer, that the power which is requisite to
impart to a body a certain velocity, must be in
proportion to the momentum, that is, to the product
of the mass of the body, by the required velocity,
Thus a power equal to 2000 lbs. is required to
impart to a mass of 100 lbs. the velocity 20; be.
cause 100 times 20= 2000; or, in other words,
the power which would impart to a mass of 1 lb.
the velocity 2000, will impart to a mass of 100
Ibs. only the velocity 20.
$ 57. In order that a body should move with
uniform velocity, it is necessary that the power
which sets in motion, should cease to operate the

22
GRAVITY.
ACCELERATED MOTION.
-
moment it has imparted that velocity. Then, ac-
cording to the law of inertia (see $ 25, page 9),
the body would continue to move in a straight
line, with the same velocity, until, by the opera-
tion of some
new cause, its motion is either
changed or entirely arrested.
B. Accelerated Motion. — Gravity.
Definition of
$ 58. If the power which sets a body in
an accelerat- motion continues to operate, in the same direction,
ing power.
during the following intervals of time, it must
necessarily continue to increase its velocity.
Such a power is then called an accelerating
power ; and the motion resulting from it, an ac-
celerate motion.
59. If the velocities thus imparted increase
in proportion to the times, that is, if an equal
increase of velocity corresponds to equal intervals
of time, then there will result an uniformly accel-
erated motion ; and the power which produces it
is termed a uniformly accelerating power.
$ 60. The most remarkable uniformly accele-
rating power, and that which more or less in-
fluences all mechanical operations in nature, is
gravity (see y 13, page 5). It will be proper,
therefore, to begin with investigating its laws, it
being understood, that the same principles will
hold true with regard to any other uniformly
accelerating power we may find in nature.
Gravity is a $ 61. To satisfy yourself that gravity is really
uniformly
operating a continually operating power, you need only take
power.
à stone, or any other heavy substance, and place

ACCELERATED MOTION.
23
GRAVITY.
it upon your hand; you will not feel any succes-
sive jerks, but one continued pressure. Besides,
even if there were intervals in the operation of
gravity, they could not, on account of their ex-
treme minuteness, affect its laws; much less
become the object of our senses.
§ 62. The four principal laws of falling bodies, Laws of fall-
and which are applicable also to every other
uniformly accelerated motion, are these :
1. The final velocities are in proportion to the
times, that is, if the velocity at the beginning of the
first second is 1, it will be 2 at the beginning of
the second, three at the beginning of the third, and
so on; because if the increase of velocity did not
correspond to the increase of time the motion
would not be uniformly accelerated.
2. The space described by a free falling body
in a certain time, is always equal to the space
through which it would have passed, had it moved
uniformly with half the final velocity. Thus if a
falling body has, at the end of a certain time, the
velocity 6, then the space through which it has
fallen, is equal to that, through which it would
have gone, had it all that time had the uniform
velocity 3.

24
GRAVITY
ACCELERATED MOTION.
-
To understand this principle, we need only
consider that every increase of velocity causes
IA also the falling through a proportionally greater
space. Moreover, it is easily perceived that,
at the end of half a given interval of time,
the velocity of the falling body will only be half
as great as at the end of the whole interval.
(See principle 1.) Now although the body
does not throughout fall with half the final
16 velocity, yet the effect is the same; for what
during the first half interval it needs towards it,
is made up by the successive gains during the
·c
second half interval, which propels the body as
much beyond the middle velocity, as, during
ed the first half interval, it fell short of it. For
an illustration, let us suppose that a body has
fallen from A to B (see the figure). Then,
according to what has been said, its velocity,
when arrived at the point. C (half of A B), will
be one half of what it is in B; and when ar-
B
rived at d, it will be as much greater than at
C, as in b it was less than the middle velocity;
because b and d are equally distant from the
centre C.
3. The spaces through which a falling body
passes, in a succession of equal intervals, are in
proportion to the odd numbers, 1, 3, 5, 7, 9, foc.
Thus, if a body falls, during the first second,
through 16 perpendicular feet, it will fall in the
2d second, through 3 times 16 = 48; in the 3d
second through 5 times 16 = 80 feet, and so on.
To understand this, let us suppose a falling body
had, at the beginning of the first second, the velocity
1. Then, according to principle 1st, its velocity must
be 2, at the beginning of the 2d second ; consequently,
if the solicitation of gravity ceased at this moment, it
would go on with the velocity 2, which it has now ac-
quired, during the whole of the 2d second. But at
the beginning of the 2d second, it receives a new im-
pulse, = 1 from gravity; so that its velocity is now 3
times as great as it was at the beginning of the first
second. Again, at the end of the 2d second, the

ACCELERATED MOTION.
25
GRAVITY.
velocity of the falling body is double of what it is at the
end of the first second ; having been 2 at the end of
the first second, it will be 4 at the end of the 2d, and
receiving a new impulse = 1 from gravity, its velocity
will, at the beginning of the third second, be 5; and
continuing this mode of reasoning, we shall find the
velocity, at the beginning of the following 4th, 5th,
and 6th seconds, to correspond to the odd numbers
7, 9, 11, &c. But if the velocities increase as the
numbers 1, 3, 5, 7, &c, the spaces described by them,
must be in the same ratio.
4. The whole spaces passed through, are propor-
tional to the squares of the whole times. Thus, if a
body fall 16 feet in 1 second, it will fall 4 times
16 = 64 in 2 seconds, 9 times 16 = 144 feet in
3 seconds, and so on; because 1, 4, 9, 16, &c,
are the squares of 1, 2, 3, 4, &c.
This law follows immediately from the preceding
one (see principle 3d). For, if the space fallen
through in the 1st second is 1, and in the 2d 3, then
the whole space of the two first seconds is 1+3=4
If to this we add the space described in the third
second, which is 5, we have 1+3+5=9, for the space
described in the three first seconds; the same reason-
ing will give us 1+3+5+7=16 for that in the four
first seconds, and so on.
$ 63. With the assistance of these laws we Application
can find the space through which a body falls in of gravity.
a given number of seconds, if the space through
which it falls in 1 second is known. This is,
according to the nicest calculation, 16 feet and
1 inch = 193.09 inches, in the latitude of Lon-
* The truth of these laws has been established, also, by
the beautiful and most ingenious experiments of Mr George
Atwood. (See George Adams' Lectures on Natural and
Experimental Philosophy. London, 1794. E. G. Fischer's
Simplification of Atwood's Falling Machine. Also, Library
of Useful Knowledge, Treatise of Mechanics, page 19.)
3

26
ACCELERATED MOTION. GRAVITY.
don ;
but for most calculations we may call it 16
feet, which is sufficiently near the truth.
Suppose we knew a body had fallen freely during
the time of 5 seconds, we should find its perpendicular
descent by multiplying 16 by the square of 5, thus,-
16X 25=400 feet. In general, we obtain a body's per-
pendicular descent, by multiplying the number 16 by the
square of the time, expressed in seconds. Again, if the
space fallen through is known, we can find the time by
dividing that space by 16, and extracting the square root
of the quotient. Thus, if a body had fallen through
400 feet, by dividing 400 by 16, and extracting the
square root of the quotient, which is 25, we should ob-
tain V25=5 seconds, for the time of its descent.
The laws of $ 64. The mass of a body has no influence
gravity are
independent upon, and does in no way modify the laws of falling
bodies. This is self-evident. A number of balls
of the same substance, let fall at the same time,
from the same height, will at the same time arrive
at the surface of the earth, whether they be let
fall one by one, or connected together in a single
mass; because every particle of matter is equally
attracted by gravity.
Experiments have shown that the falling of all
bodies is equally accelerated by gravity, and that all
differences in time and velocity are solely attributable
to the resistance of the atmosphere, which a smaller
mass (whose momentum is consequently smaller also),
is less capable of overcoming, than a body of more
• bulk.
of the mass of
bodies.
* Let S represent the space through which a body falls
in a given time; g, the space fallen through in 1 second;
and T, the time of its falling, expressed in seconds; and we
shall have
S=g T2
S
s
T2=- and T=V-
g

ACCELERATED MOTION.
27
GRAVITY.
$ 65.
For the same reason that gravity accele- Law of mo-
tion of a per-
rates the velocity of a FALLING body, it retards that pendicular
ascending
of a perpendicularly ASCENDING one, in every succes- body.
sive moment of its ascent, until it becomes zero ;
then the body will return to the earth, and receive
during its fall the same velocity which it had at
the first moment of its ascent.
B В
od
6
f
g
e
C
motion of
bodies
§ 66. If a body is thrown up in a direction Curvilinear
AB (see the figure), making with the horizontal
line AG (see 16, page 6), any angle you please, thrown up at
it cannot continue its way in the same direction; gles with a
because it is, in every moment of its rise, attracted line.
downwards by gravity; it must therefore describe
a curve line, which in mathematics is termed a
parabola.
Suppose the velocity imparted at the point of start-
ing impels the body through a space Ab in 1 sec-
ond. Then, if it were not acted upon by any other
power, it would, at the end of the 2d second be in c;
at the end of the 3d second in d; and so on (taking:
ab, bc, cd, &c, to be all equal to one another). But
being, in every moment of its motion solicited by
gravity, it will, at the end of the 1st second, be as
many perpendicular feet below the point b, as it would
have freely fallen through in that time, namely 16;
at the end of the 2d second, it will be 4 times 16 =

28
COMPOUND MOTION.
64 feet below the point c; at the end of the third 9
times 16 = 144 feet below d; &c. Thus, the body
describes a curve line, which, when geometrically exam-
ined, is found to be a parabola.*
C. Decomposition of Forces.
Compound Motion.
Equilibrium
of forces.
Difference of
§ 67. A body solicited at the same time by two
equal opposite forces, remains in the state of rest;
forces in op- the two forces cancel each other, and are said to
posite direc-
tions.
be in equilibrium. If the two forces which operate
upon the body, at the same time are unequal, then
it will follow the impulse of the greater, and re-
ceive a velocity equal to the difference of the two
forces.
$ 68. If the directions of the two forces which
diagonal
solicit the body at the same time, make an angle
with each other, then the body will describe the
diagonal of a parallelogram, whose sides are pro-
portional to the spaces through which the body
would have passed in the same time, following the
simple impulses of each of these forces.
Lateral and
force.
P Р
B
M
А
С C
To comprehend this, we need only consider, that
when the body is in M, it is actually as far from the
* Because the squares of the ordinates are in proportion
to the abscissa.

COMPOUND MOTION.
29
direction OP of the force P, as the force O has im-
pelled it; because BM is equal to AC; and it is, at
the same time, as far from the direction AO of the
force 0, as the power P alone, would have impelled
it, because CM=AB; therefore, in describing the
diagonal AM, it has followed the impulse of both
forces - which was to be proved.
B
C
Go
А,
D
g
The following experiment agrees perfectly with the
above reasoning. Take a level table in the form of a
parallelogram, and provide it with a ledge to prevent
a ball from rolling off; and let two spring guns, G, g,
be placed in A, so that when G strikes the ball, it
shall move along the side AD, in a certain time, and
when g strikes it, it shall move in the same time along
AB. Now, if both guns strike the ball at the same
instant, it will move along the diagonal AC, in exactly
the same time, as, by the impulse of each gun sepa-
rately, it moved along the sides.*
§ 69. The motion which we have just de-
scribed is called a compound motion. AP and AO
(see the figure before the last) are called lateral
forces (sometimes, also, lateral velocities), and
AM is termed the mean force or velocity. A
single force, namely, equal to AM, would carry
the body, in the same time, as far as the two forces
P and O together. This principle enables us to
find, by decomposition, the lateral forces AP and Decomposi-
tion of forces.
AQ, when the diagonal force AM is known, an
vice versa.
* See Library of Useful Knowledge, Mechanics.
3*

30
CURVILINEAR MOTION.
REMARK. The above principle may be applied to
the decomposition of a diagonal force into three, four,
and more lateral forces, and vice versa.
To illustrate this theory, the teacher may give ex-
amples, such as the sailing of a ship, steering in one
direction, and carried in another by the wind; the
motion of a boat in crossing a river, where the oars
impel it in one direction, and the current in another ;
the flying of kites, attracted perpendicularly by gravity,
and horizontally by the string, &c.
D. Application of the foregoing Theory to Cur-
vilinear Motion in general.
Centripetal
$70. When the body A (Fig. 1.) receives an
and centrifu- impulse in the direction AP, it ought, according
to the law of inertia (see $ 25, page, 9), continue
to move in that direction, and describe the straight
line AP. But if, at the same time, there is a
Fig. II.
Fig. 1.
А
P Р
C
D
A.
-P
B
F
G
H.
I
K
M
il
L
S
N
s
power in S, attracting the body A in the direction
AS, then, according to what has been said ($ 69),

CURVILINEAR MOTION.
31
the body A will describe a diagonal, AD, whose
sides, AC and AB, are in proportion to the two
forces P and S, and would continue in the direc-
tion ADM, if it were not again solicited by either
of these forces. If in D the attractive force s
urges the body again towards S; then the body
will describe a new diagonal, DG, whose sides
are now in proportion to the forces which urge
the body in the two directions, DM and DS. If
the force S is again operating in G, then the body
will describe a new diagonal, GK; and in the
same manner may a fourth, fifth, and sixth diago-
nal be described. The smaller the intervals are,
with which the attractive force S acts on the body
A, the smaller will be the diagonals, AD, DG, GK,
&c; finally, when the force S operates continually,
the body A will, in every moment of its motion,
be turned from its direction, and describe a curve
line, which is represented in Fig, II.
$71. A force which attracts a body contin-
ually towards one and the same point, is called a
centripetal force ; and that which incessantly urges
it, to remove from that point, in a straight line, is
termed a centrifugal or tangential force ; both
forces together, are termed CENTRAL FORCES. If, Central
at any time, one of those powers ceased to operate,
the body would solely obey the impulse of the
other. Supposing, for instance, that this takes
place when the body is in T (Fig. II.), then if
the centripetal force remains, the body will move
to the point S, and its motion will be a uniformly
accelerated one, similar to that of a falling body ;
but if the centrifugal force remains, then the
9 forces.

32
MOTION ON AN INCLINED PLANE.
body would remove from the point S, and go on
forever, in the straight line Tu,
REMARK. The nature of the curve line, resulting
from the joint action of central forces, depends upon
the ratio which the centripetal bears to the centrifugal
force. If the impulses of the centripetal force are
inversely as the squares of those of the centrifugal
force, then the body describes an ellipsis. This is the
case with the planets of our solar system, which, in
consequence of their being continually attracted by
the sun, are forced to describe elliptical orbits. In
the same manner does the moon gravitate round the
earth, and every satellite round its planet, by which
it is attracted.
The whole theory of central forces may be illus-
trated by the centrifugal machine.*
E. Motion on an Inclined Plane.
inclined
$ 72. An inclined plane, AN, is one which
makes with an horizontal plane any angle at
Motion on an
pleasure. If upon this plane you place a heavy
plane.
body, A, it will be prevented from falling in a
vertical direction, AC, but is obliged to slide
down the plane MN.
M ABK
P
De
H
N
$ 73. The law of motion on an inclined plane,
is analogous to that of a free falling body; that
* See Ferguson's Astronomy.

MOTION ON AN INCLINED FLANE.
33
is, the motion of a body on an inclined plane, is
like that of a free falling body, uniformly accele-
rated; the only difference consists in the velocity,
which, on an inclined plane, is naturally smaller
than at the perpendicular fall; (because AB is less
than AC, BK less than CO, &c.)
Supposing the body A had, in the first second; fallen
through a space
AC, then the space described by
its motion on the inclined plane is equal to AB; be-
cause AC may be considered as the diagonal of two
lateral forces ($ 69, page 29), one of which (AB) urges
the body down the plane MN, and the other AE,
which exercises upon that plane a perpendicular pres-
sure. During the 2d second, the body A would have
fallen through a space CO, three times as great as
AC ( 62, 3dly); hence, the corresponding space BK,
described on the inclined plane is three times as great
as AB. In like manner, because the body A would,
during the third second, have fallen through a space
five times as great as AC, its motion on the inclined
plane will be five times AB; and so on.
The velocity of a body moving on an in- Velocity on
clined plane, depends on the angle of elevation. plane.
(ANH) which the plane MN makes with the hori- Angle of ele-
zontal plane HN. The greater this angle is, the
more will the velocity on the plane resemble that
of a free falling body ; finally, when the angle of
elevation becomes a right angle HNP (see the
figure) the plane will be perpendicular to the
horizon, and the motion will be that of a free
falling body. The reverse takes place, when the
angle of elevation is zero, that is, when the plane
MN is parallel to the horizon ; because then the
whole weight of the body is supported, and no moc
tion takes place
§ 74.
vation.

34
MOTION ON AN INCLINED PLANE.
M M
NO
B
C
$ 75. To prevent the motion of a body on
an inclined plane, it is necessary that it should
be urged in the opposite direction, with a force
which is to the weight of the body, as AB is to
AC; consequently, with a less force than is re-
quired to prevent the perpendicular fall of bodies
(AB being less than AC); because part of the
body's weight is supported by the plane. — Thus
2 a pound in B will be in equilibrium with 1 lb.
in M, when AB is half of AC, } lb. is in equili-
brium with 1 lb. in M, when AB is one third of
AC; in short, the more the situation of the plane
AC approaches that of the horizontal plane BC,
the more is the body's weight supported by it, the
less force, consequently, is required to prevent its
reaction. This may be shown by an experiment.*
A
B
(с
H
N
* Those who have studied Geometry will easily perceive
that the triangle ABC is similar to the whole triangle AHN,
(having the angle at A common, and both being right

MOTION ON AN INCLINED PLANE.
35
REMARK. The whole theory of motion on an in-
clined plane, and consequently, also, that of free falling
bodies, to which it is analogous, may be illustrated by
an instrument, which, on account of its simplicity and
cheapness, may form part of a common school appara-
tus. "It consists of an inclined plane, provided with
ledges, to prevent the ball from rolling off, or moving
down otherwise than in a straight line. The whole of
this plane is divided into equal parts, which are
marked. At the 1st, 4th, 9th, 16th, &c, of these di-
visions are bells, with mechanical contrivances, which
angled, the one in B, and the other in H); therefore we
have the proportion:
AB : AC=AH : AN; that is,
The motion on the inclined plane is to that of a free falling
body, as the side AH of the right angled triangle, AHN,
is to the hypothenuse AN. From this proportion it follows,
that a body needs as much time to move down the hypothe-
nuse of a right angled triangle, as it needs for the perpen-
dièular fall through one of its sides.
Α.
с
E
D
B
Another remarkable inference which we may draw from
this principle is, that a body descends either of the cords,
AC, AE, AD, in exactly the same time which it would
need to fall perpendicularly through the diameter AB;
because ACB, AEB, ADB, &c, are right angled triangles,
having for their common hypothenuse the diameter AB.
(See Grund's Plane Geometry, Section V. Remark to Prob-
lem XVII.)

36
OSCILLATION OF A PENDULUM.
cause them to be struck, when the ball arrives at these
points, without impeding its velocity. Now, if the
plane receives an inclination which makes it pass
through the first of these divisions in the 1st second,
then it will pass through the three next divisions in
the 2d second, through the five next in the 3d, and so
on; so that the balls are struck regularly at the end
of the 2d, 3d, and 4th second; which proves the prin-
cipal law of accelerated motion, namely, that the whole
spaces, described from the beginning of the motion, are
as the squares of the times. Thus, if the times are
1, 2, 3, 4, &c, the spaces are 1, 4, 9, 16, &c, (the di-
visions on the plane being made accordingly).
F. Oscillation of a Pendulum.
Oscillation of
a pendulum.
$ 76. If a heavy body B is suspended in such
a manner that it can freely move round the point
of suspension A, it receives the name of a pendu-
lum. A simple pendulum is imagined to have but
one heavy point, which is suspended by an inflex-
ible straight line. A heavy mass suspended by a
very fine thread or by a hair, may, for most pur-
poses, be considered a simple pendulum.
A
Do
bo
M
N
I
B
$77. If the heavy body, B (see the last figure,
is raised from its perpendicular direction AB, to

OSCILLATION OF A PENDULUM.
37
the inclined position, AC, and afterwards let free,
then, because gravity attracts it downwards, in
the perpendicular direction, CE, and the string
AC prevents it from following that impulse, it
will begin to swing in circular arcs (CBD), and
would continue to do so, if no obstacle came in
its way, to impede or stop its motion. The angle
BAC, by which the pendulum at first departs
from the perpendicular direction AB, is called the
angle of oscillation, or elongation.
The heavy body B, will at first describe the arc CB,
with accelerated velocity; because, in every moment
of its descent, gravity operates upon it.* When the
body has arrived at the point B, its velocity, which
has now arrived at its maximum, does not suffer it to
remain there, but forces it, according to the law of
inertia) to rise on the other side, and to describe a
new arc BD, which, if nothing impedes the body's
motion, must be equal to the arc CB, through which
it first descended. When the body is in D, its veloci-
ty, which, during its ascent from B to D, has been
diminished by gravity, in the same manner in which
it was increased during its descent from C to B, is
now in precisely the same situation in which it was
at first, in the point C; it will therefore return, and
describe a new arc, DBC ; and then, again, another
arc, CBD: and so on. In this manner, the oscillations
ought to continue forever ; but the resistance of the
* These accelerations cannot be uniform ; because the
nearer the heavy body approaches to the point B, the
less does its position vary from the horizontal plane, MN.
The whole of the arc BC, namely, may be considered
as consisting of a great number of inclined planes, which,
having different inclinations to the horizontal plane, MN,
must, of course, change the law of motion of the swing-
ing body, in every moment of its descent. Thus, although
the velocity continues to increase, yet the increase is not
uniform.
4

38
OSCILLATION OF A PENDULUM.
atmosphere, friction, and the small force which is
required to bend the string by which the heavy body
is suspended, gradually reduce the arc of oscillation,
until the pendulum finally stands still.
Remarkable
$ 78. The most remarkable property of a pen-
property of a
pendulum.
dulum consists in the equal duration of its oscilla-
tions, although, from the circumstances alluded
to, the arc of oscillation is continually diminish-
ing; for the duration of one of its oscillations is
but very little influenced by the magnitude of the
arc; so that if this be small, one oscillation will
last as long as another.
The time which is needed for each oscil-
lation depends upon the length of the pendulum.
With regard to this dependency there exists the
following law : The lengths of any two pendulums
are in proportions to the squares of the times needed
for one of their respective oscillations. Thus, of
two pendulums the twice longer will swing four
times slower; because it will need four times as
much time to perform one oscillation ; the three
times longer will swing nine times slower ; the four
times times longer, 16 times slower, &c. This
may be shown by experiments.*
Time eded
for each os-
cillation.
$ 79.
* If T, t, respectively, represent the times needed for
one oscillation, and L, 1, the respective lengths of the pen.
dulums, then we have the proportion:
T2 : t2=L:1;
whence,
T:t=VL:V1.
The theory of the pendulum proves difficult, even to those
well versed in the higher branches of Mathematics. The
most difficult pioblems are the finding of the time in which

OSCILLATION OF A PENDULUM.
39
$ 80. The uses of the pendulum consist - Uses of the
pendulum.
1st. In exhibiting the direction of gravity
(when the pendulum is in the state of rest).
2dly. It shows that great masses influence the
attraction of gravity ; because, in the neighbor-
hood of large mountains, the direction of a pen-
dulum differs from a vertical line.
3dly. The pendulum proves that all bodies are
equally attracted by gravity ; because pendulums
made of different substances, when equally long,
swing equally fast.
4thly. The pendulum shows that the attraction
of gravity is less near the equator than near the
poles ; because a pendulum of the same length
swings slower near the equator than near the
poles.
5thly. The pendulum is the best regulator of a
clock; because the duration of its oscillations are
as nearly as possible equal to one another.
*V
the heavy body describes a given portion of the arc, and the
determination of the centre of oscillation.
The whole duration of an oscillation is nearly equal to
2
seconds;
g
where a stands for the number 3,1415926, L for the length
of the pendulum, expressed in feet, and g for the number
of feet through which a free falling body falls in the 1st
second. This formula enables us to find the space through
which a body falls in the 1st second, if the length of the
pendulum and the time of its oscillation are known.

40
OF THE LEVER.
G. Of the Lever.
The lever.
Definition of
the lever.
$ 81. An inflexible, straight bar, AB, support-
ed in one of its points, and capable of moving
round that point, is called a lever. The point in
which it is supported is called the prop or ful-
crum ; and the parts, AC, CB, of the bar, which
extend on each side of the prop, are termed the
arms of the lever.
A
В
с
A
$ 82.
Power,
weight.
When two forces act upon the lever, in
order to distinguish them from one another, we
call the one power, and the other weight.
$ 83. There are three kinds of levers.
The first has the fulcrum between the power
and the weight. (Fig. I.)
Fig. I.
Kinds of
lever.
A
The second has the weight between the fulcrum
and the power. (Fig. II.)
Fig. II.

OF THE LEVER.
41
The third has the power between the fulcrum
and the weight. (Fig. III.)
Fig. III.
$ 84.
lever
The principal law of the lever is this : Law of the
The power is to the weight inversely as the dis-
tances from the fulcrum; that is, the smaller the
power is, which shall be in equilibrium with the
weight, the greater must be its distance from the
fulcrum. Thus, a power of 1 lb. is in equilibrium
with a weight of 2 lbs. when its distance from the
fulcrum is double the distance of the weight; if
its distance is three times as great as that of the
weight, it will be in equilibrium with 3 lbs. and
This may be clearly shown by experi-
ments. The product of the power or the weight
by the distance of the fulcrum is called moment.
Hence the above law may also be expressed in
this manner. The power is in equilibrium with the
weight, when its moment is equal to the moment of
the weight.
(The following demonstration is intended for
those only who are acquainted with Geometry;
other pupils may omit it.)
So on.
4*

42
OF THE LEVER.
A
M
R
D A
C
B
P
To understand why this is so, let us at first consider
a straight line AB, supported at its lower end B, in
such a manner that it may move round that point,
either to the right or left. Upon the point A (and in
the same plane), let act two powers, P and Q, one
urging the line AB in the direction AP, and the other
at the same time urging it in the direction AQ. Let
AN and AM represent these impulses, then it is
easily perceived, that in order to prevent the line AB
from being moved in either direction, it is necessary
that the force P should be to the force Q, as the side
AM is to AN, or, which is the same, as BM is to BN
(BM being equal to AN, and BN to AM); for, in this
case, the line AB itself is the diagonal resulting from
the lateral forces AM and AN (see § 69, page 29);
This being supported in B, no motion whatever can
take place, and the line AB will remain in the state of
rest. If instead of the line AB we imagine the whole
parallelogram AMBN supported in B, then it will
make no difference whether the two forces P and Q
act upon the point A, or in M and N; provided their
directions AP and AQ are not changed. Now, if you
drop the perpendiculars BR, BS, to the directions AP,
BR respectively, the two similar triangles BMR and
BMS, will have their two sides, BR and BS, in the
same ratio in which BM and BN are; consequently,
the parallelogram AMBN is still in equilibrium, when
the two forces P and Q are in proportion to their
distances, BR and BS, from the fulcrum B. The same
will take place, if, instead of the parallelogram,
ABMN, we had only the inflexible angle MBN;
finally, if, instead of an angle we take a straight line,
DBC, supported in B, the two arms AB, CB will them-
selves mark the distances of the forces P and Q from

OF THE LEVER.
43
the fulcrum; and the two forces P and Q will be in
equilibrium, if P is to Q as the distance BC is to the
distance DB.*
Fig. I.
$ 85. When there are several powers and
weights operating upon the lever, then they will be
in equilibrium when the sum of the moments of the
weights equal to the sum of the moments of the
powers. If some of those powers or weights
are acting in opposite directions (see Fig. II),
then, instead of adding their moments, they are
to be subtracted.
Fig. II.
lever.
$ 86. Use of the lever. The lever serves to Use of the
raise heavy weights by small powers. There are
infinite applications of the lever. Among these
* This proportion is expressed
P:Q=BC: AB;
whence
Q X BC=P X AB:
(See Grund's Plane Geometry, Theory of Proportions.)

44
OF THE LEVER.
it may suffice to mention the crow-bar and hand-
spike; a poker to raise fuel in a grate; scissors,
shears, pincers, nippers, consist each of two
levers. The brake of a pump, the oars of a boat,
the rudder of a ship, chipping-knives, nut-crack-
ers, wheel-barrows, &c, are all instances of levers.
All weighing machines — balances and steel-yards
are founded upon the theory of the lever. Finally,
the limbs of animals and men are levers, of which
the socket of the bone is the fulcrum.
$ 87. The lever and the inclined plane are
sometimes called prime movers. The pulley is
nothing but a lever with two equal arms (Fig. I).
The wedge and the screw are likewise applications
of the inclined plane. Their theory, together
with the further extension of the theory of the
lever, form the subject of a distinct branch of
Mathematics.
Prime
movers.
Fig. I.
Fig. II.
Fig. III.

OF THE CENTRE OF GRAVITY.
45
H. Of the Centre of Gravity.
$ 88.
$ 90.
The point in which an inflexible bar or
a lever (see the figure page 40), charged with
several weights, must be supported in order that it
shall neither move in one way or another, is called
its centre of gravity. It may easily be found
from the above law of the lever, (section 84, page
41.)
The
pressure
which such a bar exercises
upon
the
prop which supports it, is equal to the sum
of all the weights with which it is charged. Thus,
if the sum of all the weights is 100 lbs. their
pressure upon the prop is equal to that produced
by a single weight of 100 lbs.
91. Every heavy body may be considered as
an assemblage of small weights, held together by the
attraction of cohesion, as by straight lines. Let
us, at first, consider two of these weights, A and B
(see the figure); their centre of gravity will be
$
A CB
FD
OE
somewhere between A and B, say in C. If with
this we combine a new weight E, then the centre of
gravity will be somewhere in D (between C and
E). In the same manner we may combine this
new centre with a new weight, G, which would

46
OF THE CENTRE OF GRAVITY.
bring the centre of gravity somewhere in F; and
it is easily perceived, that by continuing to reason
in this way, we shall be able to find a point in
which the whole weight of the body, consisting of
ever so many heavy points, A, B, E, G, &c, is
concentrated, and which is therefore called the
centre of gravity.
$ 92. A vertical line drawn through the
centre of gravity is called the direction of the
body's weight, or simply the line of direction. If
this line is in any point supported or fixed, the
body will remain motionless. Such a point may
be found by trials, by balancing the body on a
sharp point, or by suspending it; the direction
of the cord, which is then one and the same with
the direction of gravity ($ 16, page 6), will al-
ways pass through the centre of gravity.
93. When a body is placed upon a basis, its
stability depends upon the relative position of the
line of direction (S 92). If the line of direction
falls within that basis, it will stand the firmer, the
nearer that line falls to the centre ; and will be
liable to turn over when it falls near the edge of
the basis ; finally, when the direction of gravity
falls without the basis, the body must turn over
that edge, which is nearest the line of direction.
REMARK. What has been said about the centre
of gravity will serve to explain a number of phe-
nomena, among which we will only mention a few;
the teacher may give more examples. A large table
cannot stand firm on a single leg, unless that leg ter-
minates in a tripod. The feats of rope-dancers are
greatly facilitated by holding a heavy pole; because
the centre of gravity of the dancer and pole together is
then brought near the centre of the pole, which the

LAWS OF PERCUSSION.
47
dancer holds in his hand. When a man walks, he
throws his body a little forward, in order to make the.
centre of gravity fall in the direction of his toes, and
assist thereby the muscular action, which propels the
body in the same direction. — A quadruped never
raises two feet on the same side ; because the centre
of gravity would then cease to be supported. — When
a porter carries a load on his back, he throws his body
forward, to bring the centre of gravity (of his body
and the load), within the basis of his feet. If he car-
ries the load on his head he will go erect, and when
carrying it in his arms he leans backwards. -- For the
same reason does a man incline forward, when ascend-
ing a hill, and backward in descending it. When a
person wishes to rise from a chair which has no back,
it cannot be done without inclining the body forward,
so as to bring the centre of gravity in the direction of
the feet; or drawing back the feet, so as to bring them
under the centre of gravity.
I. Laws of Percussion.
$ 93. When a moving body meets another on Central and
eccentric per-
its way, it will strike that body with a force pro- cussion.
portional to its moment. If the line in which the Laws of, &c.
centre of the striking body moves, passes also
through the centre of the body on which it strikes,
then the percussion or stroke is called central ;
otherwise it is termed eccentric.
$ 95. Among the numerous cases of percus-
sion that can take place, but few can be made the
subjects of elementary investigation.
Among
these we will mention the following three : Per-
cussion of two unelastic bodies ; percussion of an
elastic body with an unelastic body; and finally,
percussion of two elastic bodies.

48
LAWS OF PERCUSSION.
1. PERCUSSION OF UNELASTIC BODIES.
Percussion of
unelastic
bodies.
§ 96. When two unelastic bodies strike
against
each other, three cases can occur : the two bodies
may move against each other, and have equal mo-
ments ; or they may move against each other, and
have unequal moments; or they may move in the
same direction, and have unequal velocities, so that
the one which moves behind must overtake the other.
1. In the first of these cases, the motions of both
bodies will be entirely destroyed.
2. In the second case, the motion of the body
whose moment was less before the stroke will not only
be destroyed, but it will be compelled to move in the
opposite direction, following the impulse of the
greater moment. Both bodies may then be con-
sidered as one mass, moving with a velocity cor-
responding to the difference between the original
movements.
3. In the third case, the striking body loses as
much of its moment as the other gains; both bodies
will continue to move in the same direction.
To illustrate these laws, let us, in the first place,
suppose that the two balls A, B (Figure I), have
Fig. I.
A
с
D
E
B
equal masses and velocities, but opposite directions.
Then it is easily perceived, that at the stroke in C,
both motions will be destroyed, and the two bodies
will reinain in the respective positions, D and E.

LAWS OF PERCUSSION:
49
To illustrate the second case, let us suppose the
two bodies A and B (see Fig. II), are again moving
Fig. II.
A
D
E
B
M
against each other; but A with the velocity 6, and B
with the velocity 4. Then B will lose its whole velo-
city by the stroke, A only 4; and the remainder, 2,
will be divided between A and B. Both bodies will
now move with the velocity 1, in the direction from
D to M.
The third case may be exemplified by two bodies,
A and B, moving in the same direction. Let A's
Fig. III.
А
B
с
D
E
M
velocity be 6, and B's 4 (the masses being equal);
then A will overtake B, and during the stroke commu-
nicate to it as much motion as will equalize their ve-
locities. Both bodies will continue to move in the same
direction with the velocity 5; A will have lost 1, and
B received an addition of 1 to its velocity.
2. PERCUSSION OF ELASTIC BODIES.
97
When the two bodies are both perfectly Percussion of
elastic, then the reaction of each of them upon the
.
5

50
LAWS OF PERCUSSION.
other must be equal to the loss or gain which it
receives from the other. Thus, if the one gives
the other the impulse 5, it receives, by the elas-
ticity of the other, the same impulse 5 back again,
in the opposite direction.
Laws of per
$ 98. The law just named will enable us to
cussion, &c; determine the three principal cases, that may
occur in the percussion of elastic bodies :
1. When the two bodies (whose masses we will
again suppose to be equal), move against each
other.
2. When the one stands still, and the other
strikes upon it; and
3. When both move in the same direction, but
the one which moves behind, with a greater ve-
locity, so as to overtake the other.
In the first case, they will exchange velocities,
and move in the opposite directions to those they had
before the stroke.
In the second case, the body which stood still
will receive the velocity of the striking body, and
the striking body will remain in the place of the
other.
In the third case, they will again exchange velo-
cities, but continue to move in the same direction.
If the two bodies A and B move against each other,
A with the velocity 5, and B with the velocity 3, then
after the stroke, A will return with the velocity 3, and
A
D
E
B
一年
​
LAWS OF PERCUSSION.
31
B with the velocity 5. During the stroke, A lost 3 of
its velocity, in the direction from A to B (because 3 is
the velocity of B); but by the reaction of the elastic
body B, it receives the whole impulse 5 back again,
in the direction from D to A ; which not only cancels
the velocity 2, remaining after the stroke, but impels
it backwards with the velocity 3. In the same man-
ner it may be shown that B must return from A to B,
with the velocity 5.
A
D
B
M
If B stands still, and A strikes upon it with a certain
velocity, say 4, then the body B will be impelled from
B to M with the velocity 4, which A had before the
stroke, and A will receive B's velocity, which was 0;
that is, it will remain in D. This is frequently seen
at a billiard table, when the balls are perfectly elastic,
and is only a modification of the first case.
A
B
E
Finally, let both move in the same direction, A with
the velocity 5, and B with the velocity 3. After the
stroke their velocities will be exchanged ; A will move
with the velocity 3, and B the velocity 5. This may
be explained in the following manner. During the
stroke, A and B’s velocities become equalized. A's
surplus of velocity being 2, it will give 1 to B. This,
and an additional 1, which A loses by the reaction of
B, reduce its velocity to 3; while the velocity of B,
by the gain of 1, and an additional 1, in consequence
of the reaction of A, will have increased to 5. The
directions will remain the same as before the stroke.

52
LAWS OF PERCUSSION.
$99. When an elastic body impinges against
an unelastic, firm plane; or an unelastic body
against an elastic, firm plane, then it will rebound
from it in such a way that the angle of incidence is
equal to the angle of reflection. Thus, if the body
Fig. I.
A
D
С
MAS
a
M
6
B
N
E
A strikes the plane MN in the direction AB, then
it will rebound in the direction BC, making the
angle a equal to the angle õ.
If the angle of incidence is a right angle, it
will rebound in the direction BA (Fig. II), with
the same velocity as it struck the plane MN.
Fig. II,
A
M
B
-N
The force AB (see Fig. I), may be decomposed into
the two lateral forces, AD and AE, of which the
former is parallel to the plane MN, and the latter per-
pendicular to it. When the body has arrived in B, it
may again be considered as receiving two impulses,
one to move along the plane BN, with a force equal
to EB, and another to rebound at right angles, with
the velocity BD. The diagonal force BC, therefore,

ACOUSTICS.
53
must make the same angle with the plane MN, which
AB made with it. This may be illustrated by an ex-
periment on a billiard table.
$ 100. When several elastic balls, of equal
magnitude, are suspended in such a way that
their centres lie all in the same straight line (see
the figure), then, when the first
is raised from its position and
let fall again, so as to strike
upon the second, the motion
will transmit itself through all
the balls, which will remain in
the state of rest, and only the last will bound off,
with a velocity equal to that with which the first
ball struck upon them. The explanation this
phenomenon follows from the 2d case, page 51.
K. Vibrating Motion. Acoustics.
sound.
$ 101. When a body is put in a vibrating mo- Vibrations,
tion, and the vibrations are going on with a cer-
tain velocity, they are productive of sound; and
the reverse is also observed, namely, that every
body which shall produce sound, must first be put
in a vibrating motion.
These vibrations may be noticed on a sounding bell,
by suspending a little ball of cork or sealing-wax, so
that it touches the bell exteriorly. As long as the
bell is sounding, the ball will be tossed to and fro like
a pendulum. I)ust or quicksand will be thrown off
from a sounding body. Small pieces of paper hanging
on a violin string are thrown off when the bow is
drawn. When the sound is very powerful, such as is
produced by the ringing of several bells, or by the
5*

54
ACOUSTICS.
Propagation
of sound,
hearing
Medium of
propagation.
firing of cannon, then these vibrations shake even
walls and houses ; which proves that they communi-
cate themselves also to other bodies.
$ 102. If these vibrations are any ways prop-
agated, so as to reach our ear, we hear the sound,
and denote by the word 'hearing the sensation
which the sounding body produces in our ear.
The different modifications of sound, its highness or
graveness, its power or feebleness, the variety of
human and animal voices, the different sounds of mu-
sical instruments, produce each a distinct sensation in
our ear, incapable of being described. The description
of the human ear &c, belongs properly to Phy-
siology.*
§ 103. The medium through which sound is
commonly propagated, is the atmosphere. All
other bodies, however, whether solid or liquid, are
capable of doing the same in a greater or less
degree.
This may be shown by experiments. The ticking of
a watch is heard at a distance of several feet, when the
watch is held at one end of a board or pole, and the
ear at the other. The sound from a diving-bell is
heard through the water, &c.
$ 104. The vibrations which a sounding body
produces in the surrounding atmosphere, resemble
the undulations of waves, and consist in expan-
sions and contractions, without communicating to
the atmosphere a progressive motion.
Vibrations
produced in
the atmos-
phere.
* Those teachers who wish to be informed about it, will
find it in Blumenbach's Physiology, translated by Charles
Caldwell. Phil. 1795. Also, in Scarpa anatomicæ disquisi-
tiones de Auditu et Olfactu. 1789. Sömmering Abbildun.
gen des menschlichen Hörorgans. Franckfurt, 1806,

ACOUSTICS.
55
a sonorous
This is the reason why a sounding body produces
no wind, does not blow out a candle, &c. It explains,
also, why we can hear several musical sounds at the
same time; because the vibrations produced in the
atmosphere may intersect each other in various direc-
tions, without disturbing each other's motion, like the
undulations produced on the surface of water by
throwing stones into it.
105. In order that a body shall be capable Requisites of
of producing sound, it is necessary that it should
body.
be elastic, for a body without elasticity cannot be
put in a vibrating motion, and consequently pro-
duce no sound ( 101, p. 55). The capacity of
a body for sound increases with its elasticity.
§ 106. When a sonorous body vibrates, there
remain always certain points or lines in its sur-
face, which remain in the state of rest. In the
same manner does a vibrating cord frequently
divide itself into aliquot parts. (This discovery
was first made by Dr Chladni, of Wittenberg. *)
The points and lines which remain in the state of rest,
while the remainder of the sonorous body is vibrating,
may be exhibited to the scholars by one of Chladni's
simplest experiments: Take a circular or square pane of
common window-glass, cover it thinly with pulverized
alabaster, and hold it in such a manner, between your
thumb and finger, that only the ends of them actually
touch it. Then draw a violin bow across its edge, until
it produces a clear sound. The moment that this
takes place, the powdered alabaster is partly thrown
off the pane, but remains in certain fixed places, form-
ing, in most cases, a regular symmetrical figure. If
the bow be afterwards drawn in a different place, this
figure will immediately change; the higher the tone
is which is thus produced, the more complicated is the
figure; the lowest sounds produce the simplest figures.
* See Chladni's Acoustics. Leipzig, 1802.

56
ACOUSTICS.
Another experiment, which is still more simple, is this.
Take a tumbler half filled with water, and draw a
violin bow or a wet finger across its edge, until it
produces a clear sound. The surface of the water in
the tumbler will, at the same moment, be thrown into
an undulating motion ; but it will be easy to perceive
that the undulations proceed only from certain regular
places, while there are others in which the water re-
mains entirely in the state of rest.
107. If the places which are exempt from
the vibrations of a sonorous body, are touched
with the finger, the sound is not only not prevent-
ed, but not even modified; while, on the contrary,
all sound ceases, or is at least weakened and
changed, when one of the vibrating parts is
brought in contact with some other body.*
This is the reason why the tongue of a bell must
immediately recede from it, after striking ; why a
fractured bell does not produce a clear sound, &c.
The sound of
108.
The height or depth (acuteness or
on the length, gravity) of sound produced by cords, depends
and tension upon the length of the cords, their densities and
of the cord their thicknesses.
The theory of vibrating cords may be reduced to
that of the oscillations of a pendulum ; and it may be
proved mathematically, that the number of vibrations,
and consequently, also, the acuteness of sound, is in
direct proportion to the square-roots of the tensions, and
in the inverse ratio of the lengths and thicknesses of the
cords.t
* See Discoveries about the Theory of Sound, by
Ernest Fl. Fr. Chladni.'
# If L, I, respectively, stand for the lengths of two cords,
P, p, for their tensions, or the degree of force with which
they are stretched; T, t, for their thicknesses; and N, 1,

ACOUSTICS.
57
§ 109. If the thicknesses and densities are
the same, then the number of vibrations is in the
inverse ratio of the length; that is, the shorter
cord will give the higher tone.
This we know from experience, and it may be proved
by a variety of experiments.
110. When two cords are stretched to such a Unison.
degree, and have such lengths and thicknesses,
that they make the same number of vibrations in
the same time, then they will also give the same
tone, and are therefore said to be in unison (uni-
sono). If the cords are made of different sub-
stances, then there will be a specific difference in
the tone, but none with regard to height or depth.
Whenever a cord is struck, an exercised ear will,
besides the principal tone, hear several others, sound-
ing with it. This phenomenon probably originates in
the cord being more stretched at the two ends than in
the middle. A tone is the clearer the fewer of these
sounds are heard. This consideration is unimportant
for the perfection of musical instruments.
$111. When a cord c makes, in the same Octave,
time twice as many vibrations as another cord, C, Tedrachurd.
then it is called the next higher octave of C; when
a còrd, G, makes three vibrations, while C makes
two, then G is the quint of C; and when c makes
4 vibrations to G's 3, then c is the quart of G.
for the number of vibrations each makes in the same time;
then we shall have the following proportions:
N :n=1:L.
N :nst:T.
N:n=VP: Vp.

58
ACOUSTICS.
3 to 4
Gamut.
Diatonic
scale.
Numerical
value of
notes.
Thus, the ratio of the first (which is called
the fundamental tone C) to its next higher
octave, is as
1 to 2
That of the quint G to the fundamental
tone C, as
3 to 2
And that of the quint G to its quart, C,
which is at the same time the octave of C, as
These three notes form the simplest scale, and are
supposed by some to have formed the Tedrachord of
Hermes.
$ 112. There are seven principal tones or
notes in an octave from C to c; these are
C, D, E, F, G, A, B, C;
of which C is called the fundamental tone, D the
second, E the tierce, F the quart, G the quint,
A the sext, and B the septima, of the fundamental
tone, C. These seven tones are what in music is
called the gamut, or Diatonic scale.
§ 113. By the numerical value of a tone or
note, we mean the number of vibrations which it
makes, while the fundamental tone makes 1 vi-
bration. Thus, if the fundamental tone is 1, the
value of the next higher octave is 2 ; that of the
next lower octave, ; that of the next higher
quint, î; that of the next lower quint, { ; that of
the next higher quart, $; and that of the next
lower quart, å
The numerical values of the seven tones or notes of
the Diatonic scale, derived from these, are nearly as
follow:
C, D, E, F, G, A, B, C.
1, , 81, , , 47, 15, 2.
§ 114. The ratio of one tone to another, for
instance, that of the fundamental tone to the
second, which is 1 to g, is, in music, termed the
interval between C and D,
Interval.

ACOUSTICS.
59
of musical
$ 115. The successive intervals between the Inequalities
seven tones of the Diatonic scale, are not equal to intervals.
one another. The ratio of the fundamental tone
C to D, for instance, is not the same as that of E
to F, or a to B. Thus, although E is the tierce
of C, F is not the tierce of D, G not the tierce of
E, &c.
scale.
§ 116. On this account, the Diatonic scale Chromatie
does not satisfy the demands of modern music,
and in its stead is used the Chromatic scale,
which has 5 additional semi-tones, inserted be-
tween C and D, D and E, F and G, G and A,
A and B
19
243
2 562
27
329
3
4)
The numerical values of these notes are as follow:
C, C sharp, D,
D sharp,
E.
E F,
考​,
or, expressed in decimals,
1.0000, 0.9492, 0.8888, 0.8437, 0.8000 0.7500,
Fsharp, G,
G sharp,
A,
A sharp,
B,
3 125,
,
0,7111, 0.6666, 0,6328, 0.5963, 0.5625, 0.5333,
161
2709
8
152
c.
1
0.5000.
Here the numerical values of A and E differ a little
from those given in the Diatonic or natural scale.
This impurity, however, was nécessary, in order to
make the intervals as nearly as possible equal to one
another. It is particularly indispensable with instru-
ments which have but 12 notes in an octave. No
musical instrument, namely, can give every interval
as clear and distinct as the human voice. The most
perfect of all, and that which approaches nearest to it,
in purity and variety of tone, is the organ.

60
ACOUSTICS.
Harmony.
Discord.
In the first case,
Melody
There are yet other scales, used by composers of
music. In Germany, for instance, the equally tem-
perate scale (Gleichschwebende Temperatur). The
chromatic scale, however, is generally preferred.
§ 117. When several notes are sounded to-
gether, they either produce an agreeable or a dis-
agreeable sensation in our ears.
they are said to form harmony or concord, and in
the second case, discord, or dissonance. To give
an example : the fundamental tone and the quint
always produce concord, the second and septima
always discord ; the fundamental tone C, the
tierce G, the quint A, and the octave c, give a
perfect accord.
9 118. Melody consists in a succession of
simple and suitable notes, following each other in
regular intervals of time. In the choice and
arrangement of these notes, and in the regulation
of the time in which they are to follow each other,
consists the difficulty, and, at the same time, the
beauty of musical compositions.
The reason why the striking of several notes at the
same time, is in some cases agreeable and in others
disagreeable to the ear, cannot be satisfactorily ex-
plained, and forms a proper subject for physiology.
Dissonances in a melody frequencly serve to enhance
the beauty of the following harmony. Mozart's com-
positions, which may serve as models to all ages, afford
striking instances of such artificial dissonances.
§ 119. Very high or very low tones are no
longer audible. Five or six octaves probably
comprise the whole system of notes fit for music
$ 120. Very remarkable is the sound produced
on a common violin string, by drawing the bow

ACOUSTICS.
61
discord on the
under a very acute angle. The cords, instead of Remarkable
making transversal vibrations, will then vibrate violin.
longitudinally (lengthwise). The sound thus pro-
duced is exceedingly disagreeable to the ear, and
is frequently from 3 to 5 octaves higher than the
natural tone produced by the cord's vibrating
transversely.
The height or acuteness of the sound thus produced
does not depend upon the thickness or tension of the
cord, but solely upon its length. The phenomenon
just described explains, in some degree, why the dis-
cords on the violin are more disagreeable than those
on any other instrument.
$ 121. The velocity with which the vibrations Propagation,
velocity of
of a sounding body are propagated through the sound.
air, is from 1036 to 1040 Parisian feet, or from
about 1105 to 1110 feet, English measure,* in a
second of time.
Different densities in the atmosphere - dampness,
heat, winds, &c, — modify the propagation of sound
through the air, which is the reason why its velocity
varies from 1105 to 1110 feet in a second. A loud
sound can be heard farther than a low one, because
greater vibrations of the sonorous body communicate
more motion to a greater number of particles of air.
The propagation of sound through the medium of
other bodies, has not, as yet, been sufficiently investi-
gated. Chladni's experiments, however, show that
* See Tobias Mayer's Practical Geometry, Vol. I. page 51.
(Practische Geometrie von Tob. Mayer. Iter Theil, Seite
51.)
Chladni's Acoustics. Leipzig, 1802. (Since translated
into French, by the author, upon a demand of the late em-
peror Napoleon.)
Perolle, in Gilbert's Annals of Nat. Phil. Vol. II.
Biot, Traité de Physique expérimental, Tom. II.
6

62
ACOUSTICS.
Rays of
sound.
solid bodies propagate the sound better and quicker
than air. Biot and Hasenfratz found the same by
experiments.
§ 122. The vibrations which every sonorous
point causes in the surrounding atmosphere, may
be considered as rays of sound, emanating, in all
directions, from the sounding body, (see the
figure), and making regular pulsations in a, b, c,
d, e, &c, where the air is compressed.
A A
a b c d e f
Since these rays are nearer together in the
neighborhood of the sonorous body, than further
from it, it is evident that the sound will be heard
better near it than at a distance; and it may be
proved mathematically, that the intensity of sound
decreases in the inverse ratio of the square of the
distance. Thus, at 2 rods' distance the sound is
4 times weaker than at 1 rod's distance; at 3
rods' distance, it is 9 times weaker, &c.
Until now but few experiments have been made on
this subject; yet the truth of the mathematical theory,
which is founded on the known property of the sec-
tions made parallel to the basis of a cone,* cannot be
doubted.
§ 123. We know, from experience, that when
a ray of sound strikes on a firm plane it is reflected
from it, according to the law of percussion of
Reflection of
sound, echo.
* See Grund's Solid Geometry, Sect. III. Of Cones, 2d
Consequence to Query II.

ACOUSTICS.
63
ments,
elastic bodies (see 99, page 52); and the angle
of incidence is equal to the angle of reflection.
Only the last pulsation, that is, only the few parti-
cles of air, which in their vibration strike the plane,
are really reflected ; but these immediately create
new pulsations in the air, and form what is called the
ray of reflection. This explains the phenomena of the
echo, the operation of the acoustic tube (which is so
constructed that the sound which strikes its inner
sides is reflected in parallel rays), the use of the
speaking trumpet, &c.
§ 124. When air is blown into flutes, trum- Wind instru-
pets, horns, or other wind instruments, it first
vibrates longitudinally (lengthwise), but the sound
thereby produced is modified by the different re-
flections from the sides of the instrument. By
the opening or closing of the holes or keys, the
length of the vibrating column of air is either
extended or diminished, and by that means the
different notes are obtained.
The reason why the sound is not prevented, by
touching these instruments with the hand, is because
it is not the substance of these instruments - for in-
stance, in trumpets, not the brass of which they are
made — but the column of air which is vibrating in it,
which produces the sound ; and these vibrations are
not checked by touching the instrument outside. It
is quite the reverse with cords or bells, which by their
own elasticity are productive of sound. Bassoons and
flutes must be made of wood, and not of metal; be-
cause metallic substances being more elastic, the vi-
brations of the air would communicate themselves to
the instrument, and thereby destroy the purity of its
tone. For the same reason are very elastic metals,
such as silver, brass, &c, unfit for the building of
organs. Speaking trumpets convey the articulated
voice less distinctly (although further) than those made
of wood, or even paste-board,

64
OBSTACLES TO MOTION.
REMARK. The description of the human speaking
organs belongs to Physiology, and may be given by
the teacher. (See Caldwell's translation of Blumen-
bach's Physiology, Vol. I. Sect. XII, Qf Voice and
Speech.)
L. Obstacles or Hindrances of Motion.
Hindrances of
Inotion.
pores, catch
Laws of fric-
tion.
§ 125. No body has a perfectly smooth and
even surface, even if it appear so to our senses ;
because all bodies have pores or interstices ($ 2,
page 4). Thus, when two bodies, ever so well
polished, move upon one another, the little prom-
inences and cavities caused by their
into each other, and thereby resist or retard their
motion. This resistance, which is commonly
termed friction, is one of the greatest hindrances
of motion.
§ 126. The laws of friction cannot very well
be fixed ; because we have no precise measure of
it. Nevertheless we are enabled by experience to
lay down the following principles :
1. The velocity of the body has but little influ-
ence on its friction.
When a body moves swiftly, it will, in less time,
meet with more protuberances and cavities; but at
the same time have more force to glide over or over-
come them.
2. If the pressure of the mass of a body is
throughout the same, then the friction does not
increase with the magnitude of its surface.
When a greater surface is presented, more particles
are rubbed against each other, but the pressure upon

OBSTACLES TO MOTION.
65
any particular part of the larger surface, is smaller,
than when the same pressure is exercised upon a
smaller surface.
3. The more uneven a surface is, the greater
is the friction, supposing everything else to re-
main the same.
Very even and polished surfaces increase friction,
because polishing favors their mutual attraction, by
allowing them to touch each other in more points.
(See § 39, page 14.)
4. The amount of friction is seldom more than
one third of the pressure,
Sometimes it is only one fourth, one fifth, one tenth,
and even a less part of the pressure of the bodies,
which are rubbed against each other.
5. The friction of woods and metals is greatest
upon wood and metals of the same kind. Thus
the friction of wood on wood is greater than of
that of wood on brass ; and the friction of brass
on brass greater than that of brass on steel, or on
wood.
6. The friction of wood is less when moved
lengthwise (parallel to its fibres), than when
moved transversal (against the grain).
7. The friction of metals is increased by heat,
that of wood by dampness.
$ 127. When a heavy body is placed upon an
horizontal plane, which supports its whole weight,
then the least impulse parallel to the plane ought
*
* Tob. Mayer, Nat. Phil. page
160.
Coulombe, Sur la Théorie des Machines simples, en
ayant egard au Frottement. 1781.
6*

66
OBSTACLES TO MOTION.
Means of
to set it in motion. Nevertheless, the friction on
its surface presents considerable obstacles to the
smallest change of its place. It is friction, also,
which prevents the falling of a body on a mode-
rately inclined plane; which enables us to climb
up mountains, ascend or descend on inclined
planes, &c.
A cask may be moved more easily than a box; be-
cause by the rolling of a cask the friction is overcome
in a manner similar to the pulley ($ 87, page 44).
§ 128. Since friction retards motion, it must
avoiding fric- be avoided, as much as possible, in machinery.
This is effected three ways:
1. By bringing only such bodies in contact
with each other, whose friction, we know from
experience, is comparatively small.
2. By diminishing the points of contact.
3. By overspreading their surfaces with oil, tar,
soap, fat, or any other substance, which we know
diminishes friction.
$ 129. Another obstacle of motion is the resist-
ance of the atmosphere. The greater the velocity
phere.
of the body, and the surface which is presented to
the air, the more particles of air will it have to
remove on its way; the greater, therefore, will be
the resistance of the atmosphere.
$ 130. The resistance of the atmosphere in-
creases as the square of the velocity of the moving
body.
For when a body moves with double the velocity, it
has to remove twice as many particles of air, with
double the speed; the resistance of the atmosphere,
is therefore twice 2, = 4; if moving with 3 times the
Resistance of
the atmos-
Laws of Re-
sistance &c.

OBSTACLES TO MOTION.
67
velocity, it will have to remove 3 times more particles,
3 times more swiftly; the resistance is then 9; and
so on.*
Resistance of
water.
§ 131. The resistance of water to a moving
body is greater than that of the atmosphere ;
water being less elastic, and its particles being not
so easily removed as those of the atmosphere.
Without this resistance there would be neither
swimming, nor stirring, nor, in short, any volun-
tary motion, neither in water nor in the air.
Here it would be easy to explain the principles of
swimming of men, animals, and fishes; the flying of
birds, &c.
§ 132. If a stone, or cannon-ball impinges
under a very acute angle on a sheet of water, it
will be reflected from it, without entering, and
the angle of reflection will be equal to the angle
of incidence ($ 99, page 52).
$ 133. Through friction and the resistance of
the atmosphere, every body which is in motion,
must finally be brought to rest.
$ 134. If the infinite space in which all celes-
tial bodies move, and in which our earth itself
performs its orbit, is filled with a thin, subtile
fluid, then the resistance of this fluid must neces-
sarily modify their motion. The existence of
such a fluid is more than probable. †
** See Prof. Prechtle's experiments, in the Annals of the
Polytechnic School in Vienna.
+ Tob. Mayer's Nat. Phil. page 168. Also, Schröter
on Comets. (Neueste Beiträge zur Erweiterung der Stern-
kunde, von Hier Dr Schröter. Göttingen, 1800.)
Also, Schröter on the Comet of 1807.

68
CHAPTER IV.
LAWS OF MOTION OF FLUIDS.
A. Pressure, Weight, and Equilibrium of Liquids.
(Hydrostatics.)
Laws.
-
$ 135.
Fundamental law. A liquid in a ves
sel cannot rest, until its surface is perfectly hori-
zontal and level. For if any part of the fluid is
placed higher than the rest, and then left to itself,
it will, on account of the extreme mobility of its
particles, descend as on an inclined plane, and
thereby raise the lower parts, until its surface is
perfectly even
U13
$ 136. Water, or any other liquid which com-
municates with water or the same liquid, by
means of canals, tubes or pipes, stands equally high
in both places. Thus, water stands equally high
in the two legs of a syphon (see the figure.)

HYDROSTATICS.
69
Fig. 1.
Fig. II.
Α.
А
This may be shown by experiments, and explained
in this way: When the surface of a liquid is once hor-
izontal, every part of it must be at rest. Now, if the
part A, for instance, is taken away, the neighboring
part must flow in its place. This, however, is
rendered impossible, if some hard impenetrable body
of the same bulk and shape is substituted for it. The
remaining liquid will then continue in its horizontal
position. And it makes no difference whether A is
in the middle of the basin (as in Fig. I.) or on one of
its sides (Fig. II.), or if there are three, four, and more
places, in which, instead of the liquid, a solid hindrance
is placed, to prevent the confluence of the liquid.
$ 137. If one of the legs of a syphon is shorter
than the other, and provided with an orifice in B,
1
B
then the liquid sallies forth from this orifice ; and
if the stream is directed perpendicularly upwards,
it is thrown nearly as high as the surface of the
liquid in the other leg.
The reason why, in reality, it does not reach the
same height as the surface of the liquid in the other
leg, is because the resistance of the atmosphere and
the friction of the orifice impede its velocity.

70
HYDROSTATICS.
$ 138. If, instead of providing an orifice, it is
closed with an horizontal plane, AB, then the
с
D
А)
B В
pressure of the liquid upon that plane (upwards)
is equal to the column ABCD of the liquid,
which, when placed upon AB, establishes the
equilibrium.
Thus, if AB is closed with a bladder, it is necessary
to place upon it as much weight as is equal to the
column ABCD, which would be in equilibrium in the
other leg. This may be shown by experiments. A
small quantity of water in one leg, can thus exercise
an enormous pressure upon an horizontal surface, AB.
Count Real's filtering press is established upon this
principle.
Pressure of § 139. The pressure of water or any other
on the
bottom of a liquid upon the bottom of a vessel A, is equal to the
vessel.
Fig. I.
m
m
n
az
Fig. III.
Fig. II.
cd
а е
c
.
AL
b
7
6
a
a
weight of the perpendicular column a b c d, of
the same liquid, which has for its basis the bottom
of the vessel. It is therefore less than the weight
of the whole liquid, if the vessel grows wider near
the top ; greater than the weight of the whole

HYDROSTATICS.
71
liquid, when the vessel grows narrower near the
top; and equal to the whole weight of the liquid,
when the vessel is throughout of the same diame-
ter. Thus, the pressure upon the bottom of each
of the three vessels represented in Figs. I. II. III.
is the same, if the bottoms of these vessels are
equal, and the liquid stands equally high in all.
This law takes its origin in the disposition of all
fluids to expand themselves horizontally in all direc-
tions. For it has been said before (9 136), and it can
be proved also by experiments, that the liquid must
stand equally high in both legs of two communicating
tubes, whatever be their shape ; consequently, it makes
no difference whether one of the legs grows narrower
or wider at the top. In both cases, the liquid rises as
high in one leg as in the other; which proves that the
pressure upon the plane ab is always the same;
namely, equal to the perpendicular column abcd, which
of itself would be in equilibrium with the liquid in the
other leg.
А.
clefla
elen
СІ
$ 140.
From what has gone before, it follows, Lateral pres-
that the pressure upon any point in the side of a sure of li-
vessel, depends upon the height of the liquid above
that point. The deeper, therefore, this point is
situated under the surface of water, the greater is
the pressure upon it. Moreover it may be mathe-
matically proved that the velocity with which the
water spouts from different orifices in the sides of
a vessel, is proportional to the square root of the

72
HYDROSTATICS.
perpendicular distance of that point from the sur-
face of the liquid in the vessel.
Upon this lateral pressure depends the reaction of
water on pipes through which it flows. If a suspended
vessel be provided with several such pipes, it will turn
in the opposite direction to that in which the water
runs out by the pipes.
$ 141. Liquids of different specific gravities
(see § 18, page 7), do not stand equally high in
communicating vessels or tubes; but the specific
heavier will stand as many times lower than the
other, as its specific gravity is greater than that
of the liquid in the other tube.
This inay be proved by experiments, and is suffi-
ciently evident from the law given in § 138, page 70.
If the two liquids are quicksilver and water, the water
will stand nearly 14 times higher than the quicksilver.
$ 142. When the surface of a liquid in a ves-
sel is perfectly horizontal, then every portion of
it is kept in its place or held up by the pressure
of the surrounding parts. The same pressure is
exercised upon any solid body immersed in it,
which is therefore held, or pressed upwards with
the same force as an equal portion of the liquid.
From this we derive the following general.law:
A body immersed in water or in any other fluid,
loses as much weight as an equal bulk of the fluid
weighs; and the fluid gains the same weight.
$143. According to this law, a body immersed
in a liquid of the same specific gravity must rest
in the place where it is put. But a body of greater
specific gravity will sink, and one of less specific
gravity will rise to the top and float.

HYDROSTATICS.
73
In the first case, namely, it loses all its weight,
and its pressure downwards being everywhere the
same as that of an equal portion of the liquid ; there
is no power, neither upwards nor downwards, to put
the body out of its place. In the second case, the
pressure downwards is greater than the pressure of
the liquid upwards; therefore the body must follow
the impulse of the greater force, and sink ($ 67). Fi-
nally, in the third case, the pressure of the liquid
upward is greater; consequently, the body must rise
and float. *
$ 144. The law just given with regard to solid
bodies applies equally to liquids of different spe-
cific gravities. Thus, if several fluids (which
have no chemical affinityt for each other), be
poured together in the same vessel ; the specific
heaviest will descend to the bottom, and the spe-
cific lightest will rise to the top.
It sometimes happens that a specific heavier body
rests on the surface of a lighter fluid. But this takes
place only
1st. When the lower fluid can nowhere give way
to the upper fluid, and at the same time the sides of
the vessel are strong enough to resist their united
pressure.
2d. When the pressure of the upper fluid is in every
point the same.
Application of the foregoing Laws to the Determi-
nation of the specific Gravities of Bodies.
$ 145. For this purpose we need an instru- Specific grav-
ment called a hydrostatic balance; whose differ-
ities.
* The weight of the immersed body is always =G-g,
where G is the absolute weight of the body, and g the
weight of an equal bulk of the liquid.
† See $ 47, page 18.
7

74
HYDROSTATICS.
ence from a common balance consists chiefly in
one of its scales being shorter than the other (see
the figure), and provided with a hook, by which
the heavy body that is to be weighed is sus-
pended. The body is first weighed out of
water; then it is immersed, and its loss of weight
ascertained, which (according to § 142), is the
weight of an equal bulk of the fluid. If the
specific gravity of distilled water is taken for unity
of measure, then we need only divide the absolute
weight of the body by its loss, when immersed in
distilled water ; the answer will be the specific
gravity of the body.
§ 146. The principal cases that can occur in
the determination of specific gravities, are the
following:
Determina- 1st CASE. When the body is heavier than water.
tion of speci-
fic gravities. Weigh it first out of water, then ascertain its loss
in water, and divide the one by the other; the
answer is the specific gravity of the body.
Example. Let the body weigh 3 lbs. out of
water, its loss in water 2 lbs. ; then its specific
gravity is =1.5.
2d Case. When a body is lighter than water.
Annex to it a piece of a heavier body, whose weight

HYDROSTATICS.
75
and loss in water has been previously ascertained ;
so that it will sink. From the loss of the com-
pounded mass subtract the loss of the heavy body
alone; the difference is the loss of the body whose
specific gravity is to be ascertained. Its absolute
weight divided by this loss will then be its specific
gravity.
Example. Suppose a piece of elm weighs
15 lbs. out of water; and a piece of copper,
which weighs 18 lbs. loses 2 lbs. when immersed
in water; let the compound mass lose 27 lbs.;
then 27 less 2= 25, is the loss of the elm alone,
which divided into the absolute weight of 15 lbs.
gives 15 =, or 0.6, for the specific gravity of
elm.
3d Case. For a fluid. Find the loss of weight
of one and the same body in water and in the fluid
whose specific gravity is to be ascertained; divide
the loss in the fluid by that in water ; the answer
is the specific gravity of the fluid.
Example. Suppose a piece of iron* loses in
distilled water Ibs. and in sea-water 3 lbs.
Then the specific gravity of sea-water is di-
vided by 3 == 1.03 nearly.
$ 147. Bodies whose specific gravities are less Floating and
immersing of
than that of water, must float on its surface, or bodies.
immerse only as far as will make the weight of
the whole body equal to the weight of a bulk of
water of the magnitude and shape of the immersed
1
* For this purpose a piece of glass is generally used;
particularly in ascertaining the specific gravity of acids,
whịch affect metals chemically.

76
HYDROSTATICS.
part. If such a body is forced down deeper, and
let free, it will rise again to the same height.
This may be shown by numerous experiments on
woods.
Wine and
beer scales.
§ 148. It follows from this, that the same body
cannot be equally deep immersed in liquids of
different specific gravities, and that it will immerse
deepest in the specific lightest fluid.
Upon this principle is founded the construction of
wine, beer, and brandy scales; the construction of
Nicholson's aræometer, &c, which the teacher, if at
hand, may show and explain to his pupils, from the
laws laid down in the last five paragraphs.
Swimming.
S 149.
Bodies of greater specific gravities
than water, can be made to float, by making them
hollow, or compounding them with lighter sub-
stances, so that the weight of an equal volume of
water is still greater than that of the compound
mass.
Hereupon is founded the floating of empty bottles,
of vessels, &c. The rising of balloons filled with a
lighter fluid than air, &c. The swimming by means
of bladders, &c. The specific gravity of the human
body averages 1,12. There are, however, men whose
specific gravity is less than water. These are natural
swimmers. Very fat men are generally good swim-
mers ; because, by displacing a greater quantity of
water, they lose more of their own weight.
$ 150. The position of a floating body depends
floating body.
on its centre of gravity, and on the centre of
gravity of the bulk of water which is displaced by
the immersed part of the body. Both centres of
gravity must lie in the same vertical line; other-
wise the body cannot remain in its position. The
deeper the body is immersed, the safer is it
Position of a

ÆROSTATICS.
77
water.
from turning over. In general; the centre of
gravity of a swimming body ought at least to be
under the surface of the water. *
$ 151. When the weight of a cubic inch or Absolute
foot of distilled water is known, we can find the cubic foot of
absolute weight of a cubic foot of any substance,
by multiplying the specific gravity of that substance
by the weight of a cubic foot of distilled water,
Hutton, in his course of Mathematics, makes a cubic
foot of water equal to 1000 ounces avoirdupois weight.
This, however, disagrees somewhat with the state-
ments of others. In the same manner do the specific
gravities in his table disagree with those formed by
some of the best chemists. Lavoisier and Brissont
found a cubic foot of rain water equal to 70 lbs. Paris
weight. (See the table of specific gravities at the end
of the book.)
B. Pressure, Weight, and Equilibrium of Elastic
Fluids. (Ærostatics.)
$ 152. Fundamental Law. When an elastic
fluid is shut up in a vessel, it will press its sides Laws of &c.
equally in all directions, with a force proportional
to the elasticity of the enclosed fluid.
§ 153. If the sides of the vessel are not strong
enough to resist this pressure, then the fluid will
*
Benjamin Franklin's Letters on Philosophical Subjects.
London, 1769. Euler's Naval Science. Petersburgh, 1749.
† Pésanteur specific des Corps utile à l'Histoire Natu-
relle, &c. Par Brisson. Paris, 1787.

78
ÆROSTATICS..
a
burst through them ; or if the vessel be provided
with an orifice, the fluid will pass through it;
until its expansive power is exhausted.
$ 154. An elastic fluid cannot escape from
vessel, when the elasticity, and consequently the
pressure, of an elastic fluid without, is equal to
the
pressure
of the fluid within the vessel. If the
pressure of the elastic fluid without is greater than
that of the elastic fluid within, and the vessel is
provided with an orifice, then the fluid from with-
out will enter the vessel ; or if the pressure of the
inner fluid is greatest, it will escape through the
orifice, until the elasticities of both fluids are in
equilibrium.
Compressi- $ 155. Every elastic fluid can by pressure be
bility of elas-
tic fluids.
forced into a smaller bulk. Its elasticity and
density are then found to increase in proportion
to the force or weight which compresses it. The
elasticity and density of elastic fluids are also in-
creased by compressing greater quantities of them
in the same space.
Both modes of compression
must have their limits, when the fluid has reached
its greatest density.*
Degree of § 156. The degree to which an elastic fluid
compressibil-
ity of, &c. may be compressed varies. Some of them lose
by great pressure their elastic form, and become
liquid; as is, for instance, the case with steam.
Others are permanently elastic, at least as far as
our experience goes, by the greatest pressure until
now applied to them.
* Tobias Mayer's Nat. Phil. page 197.

ÆROSTATICS.
79
ids.
Probably all elastic fluids would become liquid, if it
were possible to compress them sufficiently for this
purpose.
$ 157. We distinguish yet between absolute Absolute and
and specific elasticity of fluids. By absolute elas- ticity of flu-
ticity we mean the degree with which - it resists
pressure or compression ; by specific elasticity we
understand the degree with which an elastic fluid
of the same density, resists pressure. Thus, of
two elastic fluids, which resist pressure with the
same force, the specific elasticity of the thinner
fluid is the greater.
Fluids of the most different
specific elasticities, may yet have the same abso-
lute elasticity, and therefore be in equilibrium
with each other.
$ 158. When an elastic fluid is attracted by a Formation of
atmospheres.
solid or liquid body, it must form around it an
atmosphere, whose density will be greater near
the body than farther from it; because the layers
which are next to the body are pressed by the
gravitation of those above them. Every body in
nature may, in this manner, be surrounded by an
atmosphere.
$ 159.
When such an atmosphere is in the Equilibrium
state of rest, then every part of it is, by its elas- ids.
ticity, in equilibrium with the pressure of the
gravitating parts above. It will, therefore, neither
give way to that pressure, nor cause any motion
in the surrounding particles.
$ 160. But if, by some mechanical or chem-
ical cause, either the elasticity or the density of elastic flaide.
,
the layers, or even the pressure of the surrounding
particles, is changed, then a motion of the fluid,
of elastic flu-
Motion of

80
AEROSTATICS.
or at least of a portion of it, must necessarily take
place, and continue until the conditions of its
equilibrium ($ 159, page 79) are again established.
Upon this principle depends the whole theory of
winds.
$ 161. All elastic fluids are expanded by heat,
and compressed by cold. In the first case, they
exercise, with much less density, the same pres-
sure as before with greater density. Thus, heat
increases the specific gravity of elastic fluids.
This we know from experience; the power of
steam, for instance, increases with the heat.
closed warm room, the pressure of air often becomes
insufferable, when we may expose ourselves to the
same or even a greater degree of heat, without suffer-
ing any inconvenience from it, when there is a draft
or an aperture for the inner air to pass through, and
establish the equilibrium with the air without. A
bladder filled with air, will burst, when exposed to
heat, &c.
When two or more elastic fluids are placed
upon one another, the specific heaviest will de-
scend, and the specific lightest will rise to the
top. In such cases, the laws of hydrostatics
($ 143, page 72) apply to elastic fluids.
In a

81
CHAPTER V. •
MECHANICAL PROPERTIES OF THE
ATMOSPHERE.
§ 163. Our earth is everywhere surrounded Existence of
atmospheric
by a thin invisible fluid, which is termed the air.
atmosphere (158), of whose existence every
day's experience furnishes sufficient proof.
Here the teacher may give some examples; the
rapid motion of the hand productive of wind; a tum-
bler or a bottle, with the bottom uppermost, held per-
pendicularly under water, are only partly filled with
it, but when held obliquely air departs from them in
bubbles. The same is the case with a diving-bell,
&c.
164. The height of the atmosphere above Height of the
the surface of the earth is not yet exactly ascer-
atmosphere
tained; but it is yet found at the top of the high-
est mountains, and it is evident from calculation
(of its pressure), that it must yet extend many
miles above them.
§ 165. Air is an elastic fluid; because it is
Gravity of
compressible, and expands itself again, when left air.
free, to its original volume.
This may be shown by experiments. In a hollow
cylinder closed at one end, the air may be compressed
by a piston ; but as soon as the piston is left to itself,
the air in the cylinder will push it back again. When
a bladder is filled with air, it will be susceptible of
changing its shape by the least pressure ; but imme-
diately reestablishes its shape, when the pressure is
removede

82
MECHANICAL PROPERTIES
$ 166. Air is a heavy fluid, and as such obeys
the laws of gravity, (§ 15, page 6.)
To show this by an experiment, take
А
a tube, AB, closed at the end A, and
after having filled it with quicksilver, in-
C vert it, so that the under end may be
unsupported. The quicksilver will not
run out; because the pressure of the air,
acting at B, in opposition to the quick-
silver, supports it in the tube. If an
aperture be made in A, the quicksilver
immediately descends; the air which is
admitted by the new aperture then acts
equally from above; which shows that
when the tube was close at top, it was the
external air which supported the quick-
B В
silver.
The ancients, to whom this property of air was un-
known, explained this phenomenon by the horror which
they supposed nature had against empty space (horror
vacui).
§ 167. When the closed tube, AB, is three or
four feet long, then part of the quicksilver will
indeed run from the aperture B, but the tube will
always remain filled to the height of about 28
inches. Hence we infer, that the pressure of the
atmosphere upon a surface, is equal to the weight
of a quicksilver-column of 28 inches, having that
surface for its basis.
* Euler's Letters to a German Princess, translated by
Hunter. London, 1802, Vol. I.

OF THE ATMOSPHERE.
83
The space AC, between the quicksilver and the end
of the tube, is a real vacuum, which, from its author,
Torricelli, is termed Torricelli's Vacuum.*
$ 168. If, instead of quicksilver, the tube is
filled with water, then the pressure of the air will
support a column of nearly 14 times the length of
that of quicksilver ; which agrees perfectly with
the hydrostatic law, given in § 141, page 72.
Thus, the height of a column of a water is 14 X 28
= 392 inches, or about 33 feet. This experiment has
actually been made by Mr Sturm, in Germany, with
a tube of that height.
$ 169. The above described property of the
air explains the phenomenon of the sucking
pump. This consists chiefly of a hollow cylinder,
and a piston or sucker, E, fixed
to a rod, which is moved up and
F
down by the lever, F: The
piston is made hollow, or is per-
forated in E, and provided with
மடி a valve opening upwards. A
plug is fixed in the lower part
of the barrel, also perforated
DI
and provided with a valve, open-
ing upwards. When the piston
descends, the air that is con-
tained between E and D opens
the valve N, and escapes into the barrel above
the piston; then, when the piston is raised again,
the external atmosphere keeps the valve N shut,
M
* Torricelli, a pupil of Galileo, first made this experi-
ment, in 1643.

84
MECHANICAL PROPERTIES
pipe M.
and the air in the barrel being thus exhausted, is
no longer in equilibrium with the pressure of the
outer air on the surface of the water in the well.
This is therefore forced up, and through the valve
O enters the barrel of the pump. When the
piston is pushed down again, into the water,
which is now in the barrel between E and D,
the valve N will be opened by this water, which
will now come to stand above the piston, and by
the next motion upwards it must flow from the
A number of other phenomena are
equally well explained by the pressure of the
atmosphere.
To these belong the sucking, drinking, smoking, the
use of bung-holes in casks, &c.
§ 170. From the elasticity and gravity of at-
mospheric air, it follows, that its pressure near
the surface of the earth must be greater than
further from it; and in general that its pressure
decreases in proportion as we ascend. (See $ 159,
page 79.)
This is proved, also, by the height of a column of
quicksilver, which the pressure of air supports in a
tube. For the quicksilver in the Torricellian tube
stands lower at the top of a high mountain, than at
its foot. It is also evident that the pressure of air, in
a room which communicates with the atmosphere,
must be the same as that of the open air; because
the elasticity of the air in the room must be in equi-
librium with that of the air without (§ 154).
§ 171. We know from experience that air is
Expansion of
a ir by heat. expanded by heat and contracted again by cold.
If, therefore, it be shut up in a vessel, so as to
be unable to expand itself, it will press against

OF THE ATMOSPHERE.
85
the sides of the vessel more than before ; if the
vessel has an aperture, the heated air will pass
through it, until the remaining part of it is in
equilibrium with the denser air without.
In this manner nearly all the air can be expelled
from a vessel ; but as soon as it grows cold, the air
will again rush into it; or if the aperture of the vessel
be immersed in water, the water will be forced up into
the vacuum.
$ 172. Air which is expanded by heat, must
rise above the denser, and consequently specific
heavier air, which surrounds it. This is evident
from hydrostatic principles. (See S 142.)
This explains the draft, in grates, and stoves, in
astral lamps; the wind which generally accompanies
conflagrations; the rising of a balloon filled with
heated air, &c.
$ 173. It has been stated (155), that all
elastic fluids, and consequently, also, atmospheric
air, may be compressed by forcing a greater bulk
Condensing
into the same space. This is done by the con- machine.
densing machine.
This consists principally of a cylinder made of
metal, ABCD (see the figure), provided at O with a
valve opening inwards. The piston is also
provided with a valve opening inwards.
When the piston is moved down, the pres-
1D
sure of the air between E and G shuts the
valve N, while the compressed air enters
the valve 0, in the cavity ABGH. When the
piston recedes, the pressure of the air in the
E F cavity ABGH shuts the valve O, so that there
remains a vacuum between E and G, to fill
N
which the air without enters through N.
As soon as the cavity EFGH is filled with
G H
air, the piston is moved down again, and a
new portion of air forced through the valve
AB 0, and so may the condensation be carried
on as long as the sides of the cylinder are
T
0
8

86
MECHANICAL PROPERTIES
strong enough to resist the pressure of the compressed
air in the cavity ABGH ; and we shall always find, that
the density of the compressed air increases in proportion
to the force of the compressing power.
Upon the compressibility of air depends the theory
of the air-gun — which it will now be easy for the
teacher to show or explain to his pupils.
$174. Another remarkable and useful experi-
ment, which may be equally well explained from
the pressure of the atmosphere, is the siphon,
Siphon.
which consists in a bent tube, having its two legs
either of equal or unequal length. If it is filled
with water and then inverted, with the two open
ends downwards, and held level in this position.
The water will remain suspended in it when the
legs are equal; but if these be unequal, or the
siphon is inclined, so that the orifice of the one
end is lower than that of the other, then the
equilibrium will be destroyed, and the water will
descend by the lower end and rise in the higher.
For in the first case, if the legs are not over 33 or
34 feet high, the pressure of the atmosphere is a coun-
terpoise to that of the water in the legs ($ 168, page
83). In the second case, if one of the legs be longer
than the other, the air presses equally on both orifices;
but the weight of water in the two legs being unequal
,
a motion must take place where the power is greatest,
and continue till the water has run out by the lower
end.

OF THE ATMOSPHERE.
87
If the shorter leg is immersed in a basin of water,
and the water be set a running from the longer leg
which may be done by suction, then the water in the
basin is by the pressure of the air forced up into the
siphon, and continues to run out of the longer leg,
until the surface in the basin is at a level with the
orifice of the other leg. The whole basin may thus
be drained, by making the leg B sufficiently long for
the orifice to be below the bottom of the basin.
The theory of the siphon explains some of the most
remarkable phenomena in nature. Among them we
will mention the conducting of water over steep hills;
the drying of pumps after a heavy rain; and above all,
the remarkable phenomenon of the Lake of Cirknitz,
in Karinthia. This lake is sometimes entirely drained,
and then filled again. The canal in the province of
Languedoc, in France, is founded upon the theory of
the siphon.
$. 175. We know from experience that the Barometer
pressure of the atmosphere is not always the
same; because it does not always support a
column of quicksilver of the same height in the
Torricellian tube ( 166). Upon this is founded
the theory of the barometer, which is an instru-
ment for measuring the pressure and elasticity of
air, at any time. It is made of a glass tube,
nearly 3 feet long, and filled with mer-
cury, like that of Torricelli ; but the
lower end is bent upwards again, and
ends in a small open basin (see the
figure). The column of quicksilver
supported in the tube is commonly
from 28 to 31 inches, leaving an en-
tire vacuum in the upper end of the
tube above the mercury. The upper
3 inches (from 28 to 31), have a scale attached to
them, for measuring the length of the column at

88
MECHANICAL PROPERTIES
all times, by observing which division of the scale
the top of the quicksilver is opposite to; as it
ascends and descends within these limits, accord-
ing to the state of the atmosphere.
The weight of the column of quicksilver in the tube,
which is equal to the pressure of the atmosphere, may
at all times be computed, being nearly at the rate of
12% of a pound avoirdupois weight, for every inch of
quicksilver in the tube, on every square inch of base.
Consequently, when the barometer stands at 30 inches,
which is nearly the medium of the standard height,
the whole pressure of the atmosphere is equal to 143
lbs. on every square inch of base; and in the same
proportion for other heights. From this the
pressure
of the atmosphere on the surface of bodies and ani-
mals may easily be calculated. The reason why we
do not feel this pressure is because it is equal on all
sides, and counterbalanced by the fluids in our bodies,
with which it is in equilibrium.
§ 176. To illustrate the different mechanical
properties of air, and indeed only these can come
within the limits of this treatise, we make use of
the air-pump, an instrument invented by Otto von
Quericke, in the 17th century.* It is similar in
construction and operation to the water-pump,
described in $169, consisting principally of a brass
barrel, bored and polished, truly cylindrical, and
exactly fitted to a turned piston, and furnished
with a valve, opening upwards. The end of the
* He performed his first experiment at Regensburg, be-
fore Emperor Ferdinand III. in 1654.

OF THE ATMOSPHERE.
89
LIL!
D
с C
B
barrel communicates, by means of a narrow tube,
with the receiver, C. In B is another valve,
opening upwards. By lifting up the piston, there
is a vacuum between B and D, to fill which the
air from the receiver opens the valve B, and ex-
pands itself into the barrel, occupying more space
than before, when it filled the receiver alone, and
being consequently rarefied. The piston is now
moved down, when the air in the barrel closes the
valve B, and escapes through the other valve, D;
another stroke of the piston exhausts another
barrel of the already rarefied air in the receiver.
And so may the rarefaction of the air in the re-
ceiver be carried on to nearly sdo of its original
density.*
It is evident that the vacuum created in this manner,
in the receiver C, is not so perfect as that in the
Torricellian tube (p. 83); for let the air in C be ever so
much rarefied, a small portion of it will always remain.
It is customary to place a small barometer under the
* The further description of this instrument, and the
ontrivances made to facilitate its use, does not belong to a
text book. It is better explained verbally by the instructer,
when exhibiting the apparatus.

90
MECHANICAL PROPERTIES
receiver, to measure the diminished pressure, and con-
sequently the degree of rarefaction of the air in C, by
the falling of the quicksilver. The plate on which
the receiver stands is provided with a cock to let in
the air from without, when the experiment is finished.
177. With a good air-pump the following
remarkable experiments may be made :
1. A closed bladder, only partly filled with air,
expands itself in the rarefied air of the receiver.
2. A thin glass bottle, shut air-tight and placed
under the receiver, is burst by the elasticity of the
air which is inclosed in it.
3. A bladder, but little filled with air, and at-
tached to a piece of lead, which makes it sink in
water, expands itself, and rises again to the sur-
face.
4. The air escapes from a vessel whose orifice
is placed under water and the liquid enters into
it, when the air from without is let into the re-
ceiver.
5. Water ceases to run from a siphon.
6. The falling of a feather and of a piece of
lead, or any other substance, is equally accelerated
by gravity ($ 64, page 26).
7. Corkwood and lead, which are in equili-
brium in a balance, are no longer so in rarefied
air.
8. A ball from which the air has been pumped,
weighs less than one that is filled with it.
Thereby the specific gravity of air has been ascer-
tained, which is about 0.008, taking that of distilled
water = 1.

OF THE ATMOSPHERE,
91
9. The sound of a bell or of a cord becomes
weaker in rarefied air, and finally ceases entirely.
10. An animal suffocates in very rarefied air ;
a 'candle is extinguished; flint ceases to strike
sparks from steel, &c.
11. Ether, and other subtile fluids evaporate
when the pressure of the atmosphere is removed. *
* The teacher may now ask the pupils to explain some
of these phenomena, from the principles learned in the pre-
ceding, and in this Chapter.

92
CHAPTER VI.
OF HEAT.
Heat.
$ 178. In the vicinity of certain bodies, or in
contact with them, we feel either heat or cold, and
designate by these words sensations which do not
admit of any further description.
It is customary, also, to call the bodies which pro-
duce these sensations, cold or warm; but it is certain,
that we cannot tell what body is absolutely cold or
warm, and that our sensations tell us only what body
feels so in comparison to another.
$ 179. The principle by which all bodies are
more or less capable of producing the infinite
degrees of sensation of heat, or, in other words,
the primitive cause of all phenomena of heat and
cold, is as yet perfectly unknown. Most modern
philosophers, however, are of opinion that they
proceed from a certain imponderable, exceedingly
subtile substance, termed calorie, which pene-
trates all bodies, and, on account of its elasticity,
endeavors incessantly to be everywhere in perfect
equilibrium.*
* Professor Meissner, of the Polytechnic School of Vien-
na, has endeavored to show, by a series of brilliant experi-
ments, that caloric is actually a ponderable substance. (See
his Elements of Chemistry. Vienna, 1816.) But the
expansion of all bodies by heat, and the consequent diminu-
tion of their absolute weight, by displacing a greater bulk

OF HEAT.
93
Means of producing Heat.
of heat.
$ 180. There are four principal means of pro- Production
ducing heat:-
1. By friction.
Hence the heat produced by the boring, filing, or
hammering of metals; by wire-drawing, by turning,
&c. These phenomena take place, also, under the
receiver of an air-pump.
2. By chemical operations ($ 28, page 9); such
as solutions, fermentations, putrefactions, &c.
Instances of this kind are, all solutions of metals in
acids, iron and water, lime-stone and water, &c.
Dung, flour, malt, and wet hay, cause, under certain
circumstances, spontaneous combustion. Finally, the
heat produced in the animal and human body, by the
process of respiration and digestion.
of air, may not, perhaps, have been sufficiently taken notice
of. Most French chemists, the most celebrated philosophers
in Germany, and, above all, the greatest chemist now
living, Berzelius, in Sweden, are for the existence of calorie.
The greatest opponents to this system are Count Rumford
and Sir Humphry Davy. William Henry, of Manchester,
has shown that the arguments of the latter against a self-
existing, heat-producing principle, are fallacious, or at least,
as far as they go, insufficient. — For further information,
see Gilbert's Annals of Nat. Philosophy, Vol. XII. p. 546.
Gehler's Physical Dictionary; article, Heat. A. Lorenz'
Chemical and Physical Investigation of Fire. Copenhagen,
1789. Also, Tobias Mayer's Nat. Philosophy. (Gilbert's
Annalen der Physick: Gehler's Physicalisches Wörter-
buch ; A. Lorenz, Chemisch-Physicalische Untersuchungen
über das Feuer. Copenhagen and Leipzig, 1789,

94
OF HEAT.
3. By exposing a body to the light of the sun,
which is the principal source of all heat upon our
earth.
Hence the immense heat produced by the reflection
of sunbeams from a concave mirror.
4. By bringing colder bodies in contact with
heated ones. In this case, the heat of the one
will communicate itself to the other, until it is in
both in perfect equilibrium.
Heat expands $ 181. All bodies are expanded by heat, and
all bodies.
assume again their former bulk, when exposed to
cold.
Unequal ex-
pansion of
heat.
This may be shown by numerous experiments. A
heated iron ball passes no longer through a hole,
through which it went when cold ; a bladder only
partly filled with air, is expanded over a coal fire; a
hollow glass ball, which floats upon cold water, sinks
to the bottom when the water is heated, &c. Wood
shrinks when exposed to heat, through the evaporation
of the fluids contained in its pores. The same takes
place with clay in the manufacturing of bricks, &c.
$ 182. Heat does not expand all bodies in the
same degree; air is expanded quicker than liquids,
and liquids quicker than solid bodies.
§ 183. The expansion of liquids or solid
bodies, is found, by experiment, not to be propor-
tional to the degree of heat; that is, equal de-
grees of heat do not occasion in them equal
degrees of expansion. Elastic fluids differ in their
expansion from liquids and solids, their expansion
being proportional to the successive degrees of
heat applied to them.

OF HEAT
95
ones.
The cohesive attraction in solids and liquids being
greater than in air, the first portions of heat applied
to them, find more resistance than the following
Moreover, we have to consider, that both
liquids and solid bodies, when under the influence of
certain degrees of heat, begin to change their aggre-
gate fomrs ($ 36, page 12). Thus, when water is
very nearly heated to a certain degree, it becomes
transformed into vapor, and is therefore expanded
much quicker than at inferior degrees. When once
transformed into vapor, its expansions are, like those
of other elastic fluids, proportional to the degree of
heat applied to it.
$ 184. The expansion of bodies by heat, and Thermome-
their contraction by cold, afford the means of
measuring degrees of temperature. The instru-
ment used for this purpose is called a thermometer.
ter.

96
OF HEAT.
50
It is made of a hollow glass tube,
which, having a hollow ball at
the bottom, is nearly half filled
with quicksilver.* When this
210
200
is done, the whole is heated
190
until the quicksilver rises quite
180
170
to the top. The top is then
160
150
hermetically sealed; that is, so
140 as perfectly to exclude all com-
130
120 munication with the outward
110
air. Then, in cooling, the
100
90
quicksilver contracts, and con-
80
70
sequently its surface descends
60
in the tube, until it comes to a
point which corresponds to the
30
temperature of the air. When
10
the atmosphere becomes warm-
o
10
er, the quicksilver expands, and
20
rises in the tube, and contracts
and descends again, when the
atmosphere becomes cooler. By
the side of the tube is placed a
scale, which is prepared thus : -- The thermome-
ter is brought into the temperature of freezing,
by immersing the ball in water just freezing, or
in ice just thawing, and the scale is marked where
the quicksilver then stands, for the point of freez-
ing. Then it is immersed in boiling water, and
the scale again marked, where the surface of the
LILIT
40
20
I
...
* This fluid is now generally used for thermometers, it
being very susceptible to the different degrees of heat;
enduring great heat before it becomes transformed into
vapor, and great cold before it becomes solid.

OF HEAT.
97
quicksilver then stands. The distance between
these two points is divided into 180 equal divis-
ions, or degrees, and the same degrees are con-
tinued to 32 degrees further below, which point is
then called zero; and as much below zero and
above the boiling point, as is convenient; so that
there are 212 degrees from the boiling point down
to zero.
Fahrenheit found that the quicksilver always de-
scended to 0 (namely, to the point which he called
zero), by placing the ball in a mixture of equal parts
of snow and salammoniac. From him the above di-
vision of the scale is called Fahrenheits. Fiftyfive
degrees of this division mark the mean temperature of
this country; and it is in this temperature, and in an
atmosphere which sustains a column of 30 inches of
quicksilver in the barometer, that the specific gravities
of bodies are ascertained.*
Besides the scale just described, there are others,
which are particularly used on the continent of Europe.
Among them are Reaumur's, dividing the space from
the freezing point (which he calls zero), to the boiling
point, into 80 degrees; and De L'Isle's, on which the
degrees are counted downwards, dividing the space
from the boiling to the freezing point into 150 equal
parts ; and Celsius's, or the centesimal scale, in which
the distance between the boiling point and the freez-
ing point, is divided into 100 equal parts. It is ex-
ceedingly easy to deduce the degrees of one division
from those of the other. Thus, 24 degrees Fahren-
heit making one degree of Reaumur's scale, we can
change Fahrenheit's degrees into Reaumur's, by sub-
tracting 32 from their number, and dividing the
remainder by 24. There are also thermometers in
which air is the fluid through whose expansion the
degrees of heat are ascertained ; but they require so
many corrections and precautions in practice, that
they are almost entirely out of use.
* See Hutton's Mathematics, edited by Robert Adrian.
Vol. II. page 234.
9

98
OF HEAT.
To indicate great degrees of heat, Wedgewood
made use of pure clay, which contracts to about one
fourth of its bulk, from the time it acquires a red heat
until vitrification. It is to be regretted, that the clay-
cylinders, or parallelopipeds, which are used for this
purpose, change, in course of time, which makes them
incapable of indicating great degrees of heat. On
this account, Wedgewood himself does no longer
manufacture them.*
Different Capacities for. Heat.
Capacity for
heat.
§ 185. We know-from experience, that the
same quantity of heat, imparted to two different
substances, produces in them unequal degrees of
temperature, when measured with the thermome-
ter. This we ascribe to the greater or less
capacity which these substances have for absorb-
ing heat, and call the capacity for heat greater in
that body which requires a greater quantity of heat
than another to produce the same degree of tempe-
rature. Thus, the capacity of water is greater
than that of quicksilver, because, when exposed,
during the same time, to the same degree of heat,
quicksilver exhibits a greater degree of tempera-
ture, by the thermometer, than water ; which
shows that water absorbs more heat.
§ 186. There are various ways to ascertain
the
capacities of bodies for heat. One is, to bring
Manner of
ascertaining
the capacity
for heat.
* A full description of this instrument, and the degrees
of heat indicated by it, compared to Fahrenheit's scale, may
be found in the Library of Useful Knowledge; article,
Heat, page 19.

OF HEAT.
99
equal portions of different substances in contact
with each other. It is then found that the mix-
ture never exhibits the mean temperature between
them. A pound of water, for instance, heated to
156 degrees, and mixed with a pound of quick-
silver, at 40 degrees, produces a common temper-
ture of 152, instead of 98, the exact mean.
In this experiment, the water lost 4 degrees, and
the quicksilver gained 112; which proves that the
quantity of heat which is required to raise one pound
of quicksilver from 40 to 152 degrees, is equal to that
which is required to raise one pound of water from 152
to 156. Thus, the capacity of water for heat is to that
of quicksilver as 112 to 4, or, which is the same, as
28 to 1.
§ 187. In a similar manner to that we have
just described, have some philosophers (particu-
larly Crawford, Wilcke, Kirwan, and Gadolin)
determined the capacities for heat of many dif-
ferent substances, and compared them to that of
water. These comparative capacities for heat
they then called specific capacities, or specific
caloric. (See Table II. at the end of the book.)
$ 188.
From what we have said it is easily Different
perceived, that if there be such a self-existing Culoric in
quantities of
substance as caloric, it does not exist in equal equal temper-
quantities and densities in different bodies, al- atures.
though they may show the same degree of tempe-
rature on a thermometer.
$189. Every change in the relative position
of the particles and interstices of bodies, changes
also their capacities for heat. This is particularly
the case, when solid bodies become changed into
liquids, or liquids into elastic fluids. They then

100
OF HEAT.
and disen-
gagement of
heat.
absorb great quantities of heat, without showing
any increase of temperature by the thermometer.
Engagement Heat is then said to be engaged in these bodies.
And it also frequently happens, that bodies be-
come changed from the fluid state into the liquid,
or from the latter into the solid state, in which
cases their temperature is increased, without any
new addition of heat. Heat is then said to become
disengaged or free.
Hence the cold felt when air or vapors expand
themselves rapidly (because in this state they absorb
caloric); the quantity of heat which must enter into
metals before they melt ; the quantity of heat requisite
to change water into steam, &c.
190.
When two or more substances are
mixed together, their chemical affinities ($ 47,
page 18) frequently change the mean sum of
their capacity for heat. In this case, the mixture
absorbs more heat (caloric), and causes the sen-
sation of cold.
This takes place, for instance, when salts are dis-
solved in water; when snow is mixed with muriate of
soda, or water with diluted spirit of wine, or nitrate of
ammonia ; when snow is melted in water, or mixed
with muriate of lime, &c.
Influence of
191. It is not improbable, that light, by
light on heat. striking upon bodies, changes their capacity for
heat, and thereby disengages caloric. This seems
to be corroborated by the circumstance, that those
bodies through which light passes easiest, or which
reflect light most, are least heated by it ; whereas
dark and opaque bodies become sooner warm.
White bodies, glass, water, &c, are not easily heated
by sun-light. A thermometer held in the sun rises
higher when the ball is made black. Strips of cloth of

OF HEAT.
101
different colors, placed upon snow, sink the deeper the
darker the color is.* Dark cloths are warmer than
white ones, &c.
Propagation of Heat.
heat.
192. Heat does not pass through all bodies Velocity of
with the same degree of velocity. When thin
cylinders, of silver, glass, and wood, are held with
one end in the flame of a candle, the silver will
soon be too hot to hold; while the glass will be
much longer in being heated, and the wood will
burn at one end, before the least sensation of heat.
is felt at the other. Those substances which
become hot soonest at the furthest end from the
fame, are said to be the best conductors of heat.
193. The densest bodies, consequently met-
als, are the best conductors of heat. Earthy sub-
stances are in this respect inferior to metals; wood
is still more so, and atmospheric air, when not in
motion, is accounted to be the worst conductor
of heat. Among solid substances, the coverings
(skins) of animals have the least conducting
power.
The worst conductors among these are hare's fur
and eider down; and this property is probably owing
to the bulk of air which is contained among the parts
of which they consist. For the same reason are the
warmest articles of clothing those which have the
longest nap, fur, or down, and the imperfect conduct-
ing power of snow arises probably from the same
cause. It is stated, that in Siberia, while the tempe-
rature of the air has been 70 degrees below the freez-
* These experiments were first made by Dr Franklin,
and are described in his Letters on Philosophical Subjects.
9*

102
OF HEAT.
fect conduct-
ing point (38 degrees below zero, of Fahrenheit's
scale), the surface of the earth, protected by a covering
of snow, has rarely been 32 degrees (zero of Fahren-
heit's scale).*
Use of imper- § 194. The imperfect power of conducting
ors of heat. heat, in some substances, is taken advantage of
,
for the purpose of confining heat. Furnaces are
surrounded by coats of clay, trees by straw;
double windows are used in winter, throughout
Germany and the North of Europe, in order to
prevent the escape of heat from the rooms, by a
column of air inclosed between the windows, &c.
§ 195. The same substances which prevent
the escape of heat, are equally effectual in prevent-
ing its admission. Hence the air under a thatched
roof, although warmer in winter, is cooler in
summer, than the air under a roof of tile or slate.
Straw, which keeps a fig-tree from freezing in the
winter, keeps the heat from an ice-house in sum-
mer, &c.
Different sen-
sations of
heat produc-
ed by differ-
ent bodies of
§ 196. The different sensations we have on
touching different substances, although of the
same temperature by the thermometer, must be
the same tem- ascribed to their different powers of conducting
perature.
heat. The best conductors must feel coldest to
the touch ; because they absorb the heat from the
hand quicker than imperfect conductors of heat.
It is for this reason that iron feels colder than
glass, and the latter colder than wood, although
they be all in the same room, and of the same
degree of temperature.
* See Library of Useful Knowledge; article, Heat, p.23.

OF HEAT.
103
197. It is yet to be observed, that solid sub- Latent heat.
stances conduct heat in all directions — upwards,
downwards, and sideways — with nearly the same
facility. On this account, the heat which they
conduct is called latent.
$ 198. But it has been found by experiments,
that heated bodies, when exposed to the air, lose
part of their heat, also, by radiation ; that is, by
part of their heat flying off in right lines, from
every point in their surface.
The principal experiment on this subject is made
with two concave reflectors of tiñ-plate, placed at a
distance of several feet, exactly opposite each other.
Then, by placing a heated iron ball, which shall not
be red, in the focus of the one, and the ball of a mer-
curial thermometer in the focus of the other, the
mercury in the thermometer will instantly rise, even
if a transparent glass plate be placed between it and
either of the reflectors. Any other hot substance used
instead of iron, produces the same effect.
§ 199. Some natural philosophers are of
opinion, that radiant heat moves with a velocity
equal to that of light. But this seems to be more
than doubtful. All we know about it from ex-
periments is, that radiant heat moves with such
a velocity as to require no perceptible interval of
time to traverse the space of 69 feet.*
Whether the phenomena of radiant heat-are really
produced by projections of caloric, emanating from
every point in the surface of a heated body, or whether
they are occasioned by expansions and contractions
of heated particles of atmosphere, like the rays of
sound ($ 122, page 62), is not yet decided among phi-
losphers. Professor Leslie of Edinburgh is of the
See Pictet's Experiments on Fire.

104
OF HEAT.
Fusion of sol-
ids.
latter opinion, and has made a series of brilliant and
interesting experiments, eminently calculated to cor-
roborate his hypothesis.
$ 200. When solid bodies are for some time
exposed to great degrees of heat, their cohesive
powers are overcome, they lose their texture, and
consequently become liquid (546, page 17).
This is called the melting or fusion of solid bodies.
When still greater degrees of heat are applied,
then solid and liquid substances become trans-
formed into steam, or vapors, which process is
Evaporation.
called the evaporation of bodies.
Ń 201. The degree of heat, at which solid
bodies melt, or liquids evaporate, varies in differ-
ent substances, and seems to depend, in some
measure, on the cohesive power of their particles.
Some substances appear to us liquid or as elastic
fluids, at the lowest stages of temperature, and
there are others which require great degrees of
heat, to be exhibited in this form. Most solid
bodies have been converted into liquids, and
the greater part of these into vapors, by the in-
tense heat produced by modern ingenuity,
$.202. Liquids may become transformed into
liquids.
steam so quickly as to be thrown into an undu-
lating motion, which is called the boiling of li-
quids. . The portion of air which is generally
contained in them, is, by this process, expelled;
wherefore the boiling of liquids is a means of
purifying them.
203. Some bodies boil at very low degrees
of heat (for instance, ether and spirits of wine),
particularly when the pressure of the atmosphere is
Boiling of

OF HEAT
105
removed. (See Table III. at the end of the book.) Pressure is an
In general we may lay down this principle, that boiling of li-
quids.
the pressure of the atmosphere, and pressure in gen-
eral, is an obstacle to the boiling of liquids.
This is the reason why liquids boil sooner upon the
top of high mountains, and under the receiver of an
air-pump, than under the pressure of the whole at-
mosphere. Without this pressure of the atmosphere,
it is probable that many fluids would not be known
otherwise than in the elastic state.
$ 204. When a liquid boils, it ceases to assume
a higher degree of heat. All heat that is further
added, is employed in the formation of steam.
But when the vessel is closed in such a manner,
that the steam is prevented from passing off, then
the liquid can assume a degree of heat far sur-
passing the boiling point. The steam which is
thus shut up, is capable of exercising an immense
pressure, which is now universally employed in
machinery.
Here the teacher might give a description of the
steam-engine, and its application. (An excellent and
cheap model of it has lately been prepared by Mr
Claxton, a skilful mechanic of Boston.)
§ 205. When the degree of temperature is Deco nposi-
reduced by mechanical pressure, steam loses its
elasticity, and returns to its liquid state. This
process is called the decomposition of steam.
$ 206. No formation of steam or vapor can take Absorption of
place without absorption of heat ($ 189, page 100).
Hence the surrounding bodies must lose a portion
of their heat, and become cooler. This serves to
explain a number of phenomena : the cooling of
rooms in summer, by sprinkling them with water;
tion of steam.
heat by steam.

106
OF HEAT.
the sensation of cold, experienced by wetting the
hand with spirits of wine or ether, and suffering
these substances to evaporate upon it ; the re-
freshing coolness felt-in summer after a bath, &c.
Fog, mist.
$. 207. When steam, either by a diminution
of heat, or by pressure, begins to be decomposed,
it forms a great number of exceedingly little
drops, whose specific gravity is not sufficiently
great to overcome the resistance of air, and which
remain, therefore, suspended in the atmosphere.
In this state they are visible, and form what is
commonly called a fog, or mist. Such a mist or
fog is almost always formed, when the steam from
a boiling liquid escapes into a cooler atmosphere.
§ 208. Atmospheric air changes continually,
Evaporation,
exhalation. and at all degrees of temperature, a certain por-
tion of water into steam. This process, which is
carried on much slower than the formation of
steam by intense heat, receives the name of
evaporation, or exhalation. Our atmosphere is in
this manner constantly filled with an immense
quantity of steam and vapor, which, as long as
they are perfectly elastic, are dry and pellucid;
but when they separate again from the atmos-
phere, by being either cooled down or condensed,
they appear as fog, mist, or clouds, and finally
descend as rain or snow.
$ 209. Steam and vapors which are not per-
fectly dissolved in the atmosphere, frequently
adhere to other substances, and thereby damp
and wet them. In this state they are often sucked
in by the adhesive attraction of these bodies,
Rain and
SNOW.

OF HEAT.
107
which, by the degree of their subsequent expan-
sion, indicate the dampness of the atmosphere.
Upon this principle is founded the theory of the hy- Hygrometer.
grometer, which is an instrument for measuring the
dampness of the atmosphere. The hygrometrical sub-
stance is either a human hair (Saussure's), or a cat-gut
(Lamberts), or it is a whale-bone (De Luc's). They
are all too imperfect and variable to give any results
to be relied upon, and deserve, therefore, as yet, no
place in a text-book.
§ 210.
When liquids are exposed to certain Congelation,
freezing.
degrees of cold (which is either done by bringing
them in contact with colder bodies, or by exposing
them to the influence of a colder atmosphere),
they congeal and become solid. This is called
the congelation or freezing of liquids. All liquids,
with the exception of alcohol, have been reduced
to the solid state ; but very different degrees of
cold are required for this purpose, in different
substances. (See Table IV. at the end of the
book.)
§ 211. When the process of congelation is
going on slowly, so that the particles of the liquids
have time to follow their mutual cohesive attrac-
tion, they assume regular geometrical forms, and
the solids thence obtained are termed crystals
(see $ 33, page 11).
§ 212. When water is changed into ice, it
receives a regular texture, and becomes porous.
On this account, its volume is greater than that
of the water from which it is obtained, the ratio
being nearly as 9 to 8.
This explains why glass and other vessels burst,
when water freezes in them; why trees and rocks

108
OF HEAT.
burst in severe winters, &c. But so long as water
remains liquid, it contracts by cold, and reaches its
greatest density a few degrees above the freezing
point.
$213. It remains to be observed, that heat is
a powerful chemical agent. All chemical combi-
nations, namely, take place sooner, when the
bodies are brought to a certain degree of tempe-
rature; and there is hardly any chemical process,
which is not more or less accompanied with an
absorption or disengagement of heat.
These
phenomena, however, form no part of Natural
Philosophy, and are more properly treated of in
Chemistry

109
CHAPTER VI.
OF LIGHT.
$ 214. Light is one of the most powerful Nature of
light.
agents in the whole material world. Its nature
has not yet been ascertained. Two very opposite
opinions, however, have been maintained by phi-
losophers, with regard to its origin and its propa-
gation. Some suppose it to consist of material
particles, emanating from the luminous body, with
immense velocity, and in all directions (Sir Isaac
Newton's hypothesis); while there are others
(Huygens, Euler, Young, &c,) who believe it to be
a fluid diffused through all nature, and in which
vibrations and undulations are produced by the
action of the luminous body, which are then prop-
agated through the air, in a manner similar to
sound.
We shall adhere neither to the one nor the other
hypothesis, but treat only of the laws and motion of
light, which are perfectly demonstrable by mathemati-
cal science,
§ 215. The operation of light or of luminous Seeing.
bodies
upon the
is accompanied by a sensa-
tion which is called the seeing of bodies; and
throagh it we become conscious of the situation,
figure, magnitude, and motion of the luminous
body.
eye,
10

110
OF LIGHT.
Luminous
and illumine
bodies.
Reflected
light.
$ 216. With respect to light, all bodies are
either of themselves luminous, or they are illu-
mined (receive light from others), so that we can
see them.
Among the luminous bodies we count the sun,
the
fixed stars, phosphorus, some fishes, and insects, the
flame of candles, lamps, &c. Light may also be pro-
.duced by pressure, friction, putrefaction, and other
chemical processes. Sometimes a luminous body is
not seen when near another, of a more intense light.
$ 217. When the light which dark bodies re-
ceive from luminous bodies, is reflected by them
into our eyes, then they become visible, and we
say that we see them. The light thus received,
is termed reflected light.
$218. Some bodies, instead of reflecting light,
Transparen-
cy, opacity. suffer a great quantity of it to pass through them.
These are called transparent, or pellucid; while
those which do not possess this property, are
termed opaque bodies.
Most liquids and crystals are transparent. Polished
metals, being the best reflectors, suffer no light to
pass through them, except when hammered out into
very thin plates.
8 219. A third kind of bodies, which of
Light-mag-
themselves possess no light, have the faculty of
becoming luminous, when exposed to sunshine,
or to the intense light of a flame or candle, and
continue afterwards to throw out light in the
dark, for a considerable length of time. These
are by some called light-magnets or absorbers of
light.
Instances of this kind are the diamond, phosphor
of Canton, &c. Snow and ice probably belong to the
same class of bodies.
nets.

OF LIGHT.
111
220. All the light which falls upon dark Black and
white bodies.
bodies is not reflected by them. A portion of it
is absorbed, or at least not reflected into our eyes.
Those which absorb light most are called black ;
those which reflect it most are termed white
bodies.
$ 221. Light is propagated in straight lines, Propagation
of light.
with a prodigious velocity of about 195,000 miles
in a second.
The first of these assertions (that light moves in
straight lines), is proved by the fact that bodies cannot
be seen through bent tubes, and it may also be infer-
red from the shadow which dark bodies cast. For the
discovery of the velocity of light, we are indebted to
Römer and Bradley, who have proved, from observing
the eclipses of Jupiter's satellites, that light needs but
7 minutes to travel from the sun to the earth. From
this immense velocity of light, it is plain that the velo-
city with which it traverses the greatest possible
terrestrial distance, can neither be measured nor
observed, with the nicest time-keepers; as it would
need but one twentyfourth part of a second to travel
from one point of the earth to the other.
5 222. Iflight is propagated in rays or straight Density of
lines, its density decreases in proportion to the light.
squares of the distances, from the luminous body.
This law is established on the same principle, on
which we established a similar law for the propagation
of sound ($ 122, page 62), and applies equally well to
all propagation of motion or matter in form of rays.
When a beam of light passes through Refraction of
a transparent body, it is first bent or broken from light.
its direction, on its passage through that body,
and then bent again on emerging from it. This
is called the refraction of light; and its degree
yaries in different substances.
$ 223.

112
OF LIGHT.
This may be illustrated by an experiment. Let
PQ be a vessel, in one of whose sides is a small hole,
P
A
D
F
B C
Inflection of
light.
0. Place a lighted candle at a distance of two or
three feet from it, so that its flame is in A. A ray of
light proceeding from it, will pass through the hole o,
in a straight line AB, and strike the bottom of the
vessel at B, where it will form a small circle of light.
But when the vessel is filled with water, up to EF, this
circle of light, instead of being in B, will fall upon C,
the beam of light being bent in the point D, where it
strikes the water. These phenomena we shall notice
more particularly hereafter.
$ 224. We know, also, from experience, that
light is changed from its direction, when passing
near the surface, edges, or corners of bodies, in
which case it is said to be inflected.
This phenomena, in the opinion of some philoso-
phers, speaks for the materiality of light; inasmuch
as they seek the cause of it in the chemical affinity
which the substance of light has for these bodies, by
the attraction of which, it seems to be bent from its
original direction.
$ 226. When light falls upon an opaque body
,
the latter casts a shade behind it, whose magni-
tude, shape, and position depend upon the maga
nitude and shape of the opaque body, upon its
distance from the luminous body, and the direction
of the light which strikes upon it. Its further
theory belongs to Mathematics and the fine arts,
Shade.

OF LIGHT.
113
Let us now consider separately, the three prin-
cipal phenomena in the propagation of light:-
reflection, refraction, and the formation of colors.
1. REFLECTION OF LIGHT.
$ 226.
When @ray of light falls upon a pol-
ished surface, either plane or curved, it follows the
laws of elastic bodies (§. 99, page 52), and is con-
sequently reflected in such a way, that the angle of
incidence is equal to the angle of reflection.
This may be shown by an experiment; (reflecting
the light of the sun or of a candle, from a looking-
glass).
$
227. Bodies which are commonly used to Mirrors.
reflect light, are called mirrors. They are made
either of metal or glass, having their surface
highly polished. Mirrors are either plane, con-
Plane, con-
cave, or convex, according as their surfaces are cave, and
plane, or spherical (the curvature turned inward, rors.
or outward).
Glass mirrors must be quicksilvered on one side, in
order to reflect more light. Metallic mirrors are the
best reflectors; those of platinum admitting of the high-
est polish.
convex mir
10*

114
OF LIGHT.
A. Reflection of Light from Plane Mirrors,
§ 228.
Law. - A luminous point before the
mirror, appears to the eye as if proceeding from a
point situated exactly as far behind the mirror, as
the luminous point is before it.
M
AL
S
A
D
N
Let A (see the figure) be a luminous point; AB a ray
of light striking the plane mirror, MN; BC the same
beam AB, reflected from the mirror MN; then by ex-
tending the reflected ray BC, in the direction Ba, it will
cut the perpendicular Aa, in such a manner, that the
distance as, is equal to AS. In the same manner will
every other ray, emanating from the same luminous
point A, be reflected as if coming from the point a be-
hind the mirror: an eye in 0, therefore, will receive the
reflected rays, AB, AS, AR, &c, as if proceeding from
the point a, which is exactly as far behind the mirror as
the luminous point A is before it.
§ 229. The point a behind the mirror, from
which the rays of light seem to proceed, is called

OF LIGHT.
115
the image of the luminous point A, before it.
The law just found for a luminous point, applies
equally to a whole object, which will therefore ap-
pear behind the mirror, at the same distance, and
have the same situation and magnitude, which it
has before the mirror.
B. Reflection of Light from Spherical Mirrors.
$ 230. Law. — The image a, of a luminous
point A, before a spherical concave mirror PQ,
lies always in a straight line, AB, drawn from the
luminous point through the centre, C, of the circle
PQ, of which the mirror makes a part. This
straight line is called the axis of the mirror.
M
B
А
N
TOMT
Let C be the centre of the spherical mirror PQ;
CM its radius ; A the luminous point before the mir-
ror; AB a straight line from A through the centre C;
AM a ray emanating from A. Then the angle of in-
cidence, AMC, being equal to the angle of reflection,
CMa, it follows that Ma is the reflected ray; and in
a similar manner it may be shown, that every other
ray proceeding from the luminous point A is likewise

116
OF LIGHT.
reflected to the point a'; wherefore a will be the im-
age of A. And if the point A is situated differently
with regard to the concave mirror PQ, it will still be
found, that its image lies in a straight line, drawn from
the point A, through the centre of the mirror.* If a
were the luminous point, then aM would be em-
anating ray, MA the reflected ray, and the point A the
image of a. This is sufficiently plain from inspection.
(See the figure.)
$ 231. When parallel rays strike upon a spher-
ical concave mirror, they are reflected in a point,
which lies exactly in the nviddle, between the mirror
and the centre C of the arc PQ. This is the case
when the rays of the sun strike upon it, which,
on account of the great distance of the sun, may
be considered as parallel. The point in which
these rays are reflected is called the burning point,
or focus ; because an indefinite degree of heat
may be produced there, by the concentration of
the sun-beams. Diverging rays are collected in a
point, which is as much nearer the focus as the
luminous point is remote from the mirror.
$ 232. The distance of the image from the
mirror depends upon the distance of the luminous
point before the mirror. With regard to this we
have the following law : The nearer the object
approaches the focus, the greater will be the distance
of the image before the mirror. When the object A
is in the focus itself (Fig. I.), then there will be no
Focus, or
burning
point.
-
* When the mirror is an arc of more than 10 degrees,
there will be some incorrectness in the reflection of rays,
and the image in a will not be distinct.

OF LIGHT.
117
Fig. 1.
A
image at all, because the rays will then be reflect-
ed parallel to one another. Lastly, when the ob-
ject A is between the focus and the mirror (Fig. II.),
Fig. II.
AF
a
-B
the reflected rays will be diverging, and the image
will be behind the mirror, in a point, a, which, to
distinguish it from the real focus, before the
mirror, is called the geometrical or virtual focus.
Geometrical
focus.

118
OF LIGHT.
233. If MN is a whole object before the mir-
ror (Fig. III.) then the image of the point M, will
Fig. III.
M
Tin
P
ry 꿔
​N
be in m, in the axis MO ($ 230); and the image
of the point n, in n, in the axis NP; consequently
every other point of the object MN, will have its
image between m and n; so that mn is the whole
image of the object MN.
$ 234. When the object is further from the
mirror than the focus, the image is inverted (as is
the case in the last figure), but when the object
is between the mirror and the focus, the image
will be upright, and grow larger in proportion as
the object is placed nearer the mirror.
The truth of these assertions may all be proved by
simple drawings; observing always to make the angle
of incidence, made by the striking ray and the radius
of the mirror, equal to the angle of reflection, made by
the radius and the reflected ray. The whole may be
illustrated by the simple experiment of placing the
flame of a candle nearer or further from the focus, or
in the focus itself,

OF LIGHT.
119
M
P
m
N
n
$ 235. How the image is formed with a con- Convex mir-
vex mirror, may likewise be shown by drawing rors,
(see the figure), whereby it will be easy to per-
ceive, that the image appears always upright, and
behind the mirror (see the figure); that it will
recede from the mirror, and be smaller in propor-
tion as the object (MN) recedes from it ; finally,
that a convex mirror of a smaller radius, repre-
sents the same object, held at the same distance
from it, smaller than one of a greater radius.
All these assertions may be easily verified by ex-
periments with the flame of a candle.
$ 236. What has been said of spherical mir- Conical and
rors, will serve to explain the phenomena of mirrors.
cylindrical and conical .mirrors.
Both give a
perfect image of the object in length, but the
transversal dimensions appear smaller, and are,
in conical mirrors, diminishing from the basis to
the vertex of the cone.
Upon this property of cylindrical and conical mir-
rors, is founded the art of making certain distorted
drawings and paintings, which become regular when
viewed through such a mirror (catoptrical anamor-
phoses).

120
OF LIGHT.
C. Refraction of Light.
1. General Observations.
Ratio of re-
fraction.
$ 237. It has been observed ($ 223, page 111),
that a ray of light, AB, passing from one medium
into another, is refracted ; and it has been shown,
also, by experiments, that the angle of incidence,
x, formed by the ray AB, and the perpendicular,
P
А,
S
B
PBQ, bears a certain constant ratio to the angle
of refraction y, made by the same perpendicular
PBQ, with the refracted ray Bu; that is, a ratio,
which, for the same two mediums, remains uni-
formly the same,* whatever may be the position
of the
ray
with
respect to the surface.
* Mathematically speaking this constant ratio does not
exist between the angles, but between their sines, which
are obtained by describing a circle from the centre B, and
dropping from r and u, the perpendiculars rs and uv, to the
line PQ. When the angles are small, then the ratio of
their sines may be taken for that of the angles x and y.

OF LIGAT.
121
Thus, the ratio of the angle of incidence to the
angle of refraction, is nearly as 4 to 3, between air
and water; as 100 to 65 between air and common
glass, &c.
$ 238. The smaller the angle of refraction, Refracting
the greater is said to be the refracting power of bodies.
the transparent body. In this manner the refract-
ing power of many bodies has been determined.
(See Table IV. at the end of the book.)
Heretofore a belief existed, that the refracting
power of bodies is in proportion to their densities; but
experiments have since proved that the refracting
power is greater in combustible substances, independ-
ently of their densities.
2. Refraction of Light in a Body bounded by plane and
parallel Surfaces.
$ 239. When a ray of light falls perpendicu-
larly upon a transparent body, bounded by plane
and parallel surfaces, then no refraction takes
place, and the emerging part, CD, has yet the
same direction as the incidental ray, AB (sce
Fig. I.)
Fig. 1.
A
B В
c
D
11

122
OF LIGHT.
$ 240. When parallel rays (see Fig. II.) fall
obliquely upon a transparent body, bounded as
before mentioned, the emerging rays will again
be parallel ; because, upon entering the body, the
rays will be refracted as much towards the per-
pendiculars, as upon emerging from it, they are
refracted from them.
Fig. II.
If the emerging rays pass through a second or third
transparent body, the emerging rays will still be par-
allel to each other, provided the refracting surfaces
are themselves parallel to each other. This is, for
instance, case with the rays of the sun, when
refracted through several parallel panes of a window,
&c.

OF LIGHT.
123
$.241. When diverging rays fall upon a trans-
parent body of the same description, then the
emerging rays, cD, FG, will be less diverging than
Fig. III.
А.
B В
TE
G
K
H
the incidental rays, ABK, AEH, when the trans-
parent body possesses a greater refracting power,
($ 238, page 121), than the air, and more diverg-
ing when the reverse takes place. (Fig. III.
represents the first case, and Fig. IV. the second.)
Fig. Iy
Ti-.


124
OF LIGHT.
These principles will serve to explain a variety
of phenomena, viz:- why, through the refraction of
light in the atmosphere, the stars appear higher than
they really are; because the different strata of air,
becoming more dense in proportion as they approach
the surface of the earth, a ray of passing through
them, is continually refracted, and describes an arc
AO, so that the spectator's eye in O sees the star A in
(The distance between A and a is termed the
a.
а
A
parallax, and is of the greatest importance in astrono-
my):— why a body, placed under water, appears
nearer the surface : why a rod, partly immersed in
water, appears broken: why an atmosphere, charged
with fog or mist, exhibits different optical deceptions,
particularly in the vicinity of lakes, and other large
bodies of water (the futa morgana, near the city of
Reggio, in Italy), &c.*
Among those who have particularly distinguished
themselves in this department of Natural Philosophy, are
Dr Brewster and Dr Wollaston, in England; Messrs Biot,
Arrago, and Malus, in France; and Tobias Mayer, and
Prof. Wünsch, in Germany. - See Gilbert's Annals of Nat.
Philosophy; Gehler's Dictionary of Nat. Philosophy, newly
edited by Dr Brandes.

OF LIGHT
125
3. Refraction of Light through Bodies bounded by
spherical Surfaces (Lenses).
Lenses.
$ 242. A piece of glass having on one or both
sides a spherical form, is called a lens.* There
are seven different kinds of lenses.
A
B
с
D
E F
G
M
HD
IN
1. A spherical lens, A (see the figure), having
every point in its surface at the same distance
from a common centre.
2. A double convex lens, (B), bounded by two
spherical sections.
3. A plano-convex lens (C); bounded by a plane
on one side, and a spherical section on the other.
4. A double concave lens (D), bounded by two
concave spherical sections.
5. A plano-concave lens (E), bounded by a
plane on one side, and a concave spherical section
on the other.
6. A meniscus (F), bounded by a concave and
a convex spherical surface"; the radius of the
convex surface being smaller than that of the con-
cave surface.
* From the Latin lentil, a small kind of bean.
11*


126
OF LIGHT.
7. A concavo-convex lens (G), bounded by a
concave and convex surface, but the radius of the
concave surface being smaller than that of the
convex surface.
The line MN, in which the centres of these
spherical surfaces are situated, and to which these
lenses are perpendicular, is called their axis.
Properties of
$ 243. All convex lenses have the following
convex lenses.
properties :-
1. Parallel rays (Fig. I.), or rays proceeding
Fig. 1.
F
from a distant object A, (Fig. II.), are refracted
Fig. II.
A
F
by them in such a manner, that they unite again
in a certain point, F, behind the lens. This point
is called the image of A. (Compare this to the
laws of reflection, $ 230.)
2. The image lies always in a straight line,
drawn from the object to the centre of the lens
(compare $ 230). Hence it follows that --
3. The images of the objects before the lens,
appear inverted behind it, as is the case with the
image produced by concave mirrors ($ 234).

OF LIGHT.
127
4. When the object is the sun, then the re-
fracted rays meet in a point, which is called the
focus, or burning point of the lens; because the
heat produced in that point by the condensation
of the sun-beams is capable of igniting combustible
substances.
5. There is a focus or burning point on either
side of the lens, according as one or the other side
is turned towards the sun.
6. The distance of the focus from the lens is
called the focal distance, and may be found by
experiments.*
7. The nearer an object approaches the one
focus of the lens; the further will its image fall
beyond the focus on the other side.
8. When the object is placed in the focus itself,
then there is no image whatever formed on the
other side of the lens; because the emerging rays
will be parallel to one another (compare $ 232).
But when
9. The object approaches still nearer, so as
to be between the focus and the lens, then the
emerging rays are diverging, and seem to proceed
from a point before the lens, which is called the
focus of the diverging rays.
* In a double and equally convex lens, the focal distance
is generally equal to the radius of the sphere. If the lens is
unequally convex, the focal distance is found by the follow-
ing rule:- Multiply the two radii of its sections, and divide
twice that product by the sum of the radii; the quotient is
the focal distance required.

128
OF LIGHT.
Figures III. IV. and V. represent the last three
When the image is in A (Fig. III.), beyond
cases.
Fig. III.
A
а
the focus F, then the image is in a, beyond the focus
f, on the other side. When the object is in the focus
F (Fig. IV.) then no image is formed; and the emerg-
Fig. IV.
M
N
F
P
ing rays MN, OP, are parallel to each other. Finally,
when the object is between the focus F, and the lens
Fig. V.
M
S
N
R
(Fig. V.), the emerging rays MQ, NR, are diverg-
ing, and seem to emanate from the point S, before the
lens.
10. The further the image is made to recede
from the lens, the more will the object appear
magnified. Moreover, the image must be inverted
(Fig. VI.), as is the case with the image pro-

OF LIGHT.
129
Fig. VI.
duced by refraction from a concave mirror
($ 234).
11. The greater the focal distance of the lens,
the greater are the images of one and the same
object, at the sanie distance from the lens; or, in
other words, the magnifying power of the lens in-
creases with the focal distance.
All these principles may easily be proved by draw-
ings or simple experiments. Their rigorous demon-
stration belongs to Mathematics.
$ 244.
The phenomena produced by concave Phenomena of
lenses are the following: -
1. When parallel rays, AB ID (Fig. I.), fall
concavo
lenses.
Fig. I.
в с
A
M
N
I
DE
#
upon a concave lens, the emerging rays COEH,
are diverging, and seem to proceed from a point
F, which is called the virtual or principal focus
of the lens.

130
OF LIGHT
2. When diverging rays, AB, AC, &c, (Fig.
II.) (proceeding from any point beyond the focus),
Fig. II.
В.
А
fall upon a concave lens, then the emerging rays
are still more diverging, and seem to proceed
om a point a, between A and the centre of the
lens. As the object A approaches the lens, the
point a will also grow near it.
3. Converging rays are either made less con-
verging, or parallel, or even diverging, according
as they proceed from a point beyond the focus, or
from the focus, or from a point within the focus
and the lens. Hence it is evident that concave
lenses are unfit for the formation of images,
§ 245. The effect of a meniscus (§ 242), is
the same as that of a convex lens, of the same
focal distance; and that of a concavo-convex lens,
is likewise the same as that of a convex lens, of
the same focal distance.
REMARK. It is well to distinguish between Dioptric
and Catoptric images. The images produced by lenses
are called Dioptric images; while those produced by
the refraction of light from mirrors are termed Catop-
tric images.

OF LIGHT.
131
D. Theory of Colors (Achromatics).
r
M M
S
B
A.
Violet.
Indigo.
Blue.
Green.
Yellow.
Orange.
Rod.
c
N
G
220
»
spectrum.
§ 246. When a small opening is made in the Prismatie
window-shutter of a dark room, and a triangular
glass prism be placed behind it, in such a manner
that the rays of the sun may enter and leave the
prism at equal angles ; then the rays, after being
refracted by the prism, will disperse, and form
upon a screen MN, an oblong image PT, contain-
ing the seven colors which are enumerated in the
figure; the red being least and the violet most re-
fracted, from the original direction of the beam of
solar light, AB. This oblong image PT is called
the solar, or also the prismatic spectrum.
$ 247. The magnitude of the spectrum varies
according to the different substances chosen for
the refracting prism. These substances, there-
fore, are said to possess different dispersive powers.

132
OF LIGHT.
Simple and
compound
colors.
§ 248. When a hole is made in the screen
MN, opposite any of these colors, and a beam of
colored light is let fall separately upon a second
prism, it will be found that the light of each
of these colors is alike refracted; because the
second prism cannot separate them again into an
oblong image, or into any other colors. For this
reason, the above-mentioned seven colors are
called simple, or homogeneous; and the white
light, from which it is obtained, is call compound,
or heterogeneous.
§ 249. If the prismatic spectrum is made to
fall upon a lens or concave mirror, then the seven
colors refracted into the focus, appear again white,
as the solar beam AB, before being refracted by
the prism.
$ 250. Another prism, ACB, formed like the
prism ABC, and made of the same substance,
when brought in contact with it as represented
in the figure), destroys, likewise, the spectrum PT,
by refracting all the rays separated by the prism
ABC, to the same point Y, where, by their mix-
ture, they form again white light.
$251. But when the angle of the prism A Cb is
not equal to the angle of the prism ABC, then the
second prism does neither correct the refraction of
the first, nor prevent the dispersion of the colors,
and a short spectrum is formed in Y', a little above
Y, when the angle of the prism ACb is less than
the angle of the prism ABC, or below Y, when
the angle of the prism ABD is greater than that of
the prism ABC.

OF LIGHT.
133
$ 252. From these and other experiments,
first made by Sir Isaac Newton,* and afterwards
repeated and extended by Euler, Young, Brewster,
Dollond, Leslie, Arrago, Biot, Tobias Mayer,
Wünsch, &c, we are entitled to the following
conclusions :
1. That white solar light is compounded of col-
ored rays, and is capable of being decomposed into
seven primitive colors.
2. That the seven colors have each the same
capacity for being refracted, or, in other words,
that they have all the same refrangibility.
3. That their mixture produces again white light.
4. That there is no refraction of light without
dispersion of colors.
5. That different substances possess different dis-
persive powers.
$ 253. If light (according to Sir Isaac New-
ton) is material, and emanating from the luminous
body, then we can explain these phenomena two
ways; 1st, by supposing that light is composed
of heterogeneous particles, which of course affect
our eyes different ways, and thereby produce the
different sensations of colors; or, 2dly, by sup-
posing the particles of light to be homogeneous,
but differing from each other in magnitude, and
*
Optics, by Sir Isaac Newton. London, 1701. Optice
sive de Reflexionibus, Refractionibus, Inflexionibus, et
Coloribus Lucis, Libri III. auct. Is. Newtono ; lat. redd.
Samuel Clarke. Lond. 1706. Leonh. Euleri nova Theoria
Lucis et Colorum, in the first volume of his Opusc. varii
argumenti.
12

134
OF LIGHT.
producing different sensations in our eyes, on
account of having different velocities.
According to Young and Leonhard Euler, who
believe light to consist in vibrations, similar to
those which are productive of sound, the seven
simple colors are to the eye, what the seven tones
of the Diatonic scale are to the ear; resulting
from the quicker or slower tremulations of the
luminous body. White light is then for the eye
what a mixture of sounds is for the ear — noise
without harmony. The different shades and gra-
dations of the seven simple colors, are analagous
to the different octaves in music.
The phenomena just described explain a number
of phenomena in nature:- the appearance of the rain-
bow, produced by the dispersion of colors, when solar
light passes through drops of rain; the colors perceived
in a soap-bubble; the colored fringe, seen when look-
ing through a cut glass, &c.
Herschel, a celebrated English philosopher, pretends
to have discovered invisible rays of solar light, beyond
the red color of the spectrum, possessing a greater
degree of heat than any of the colors of the spectrum.
Other experiments, however, made by Beckman, in
Carlsruhe, and Leslie, in Edinburgh, do not seem to
corroborate this statement.
$ 254. It is important to observe the difference
between refraction of light and dispersion of col-
For a certain transparent medium may
retract light more than another, and yet have a
less dispersive power. Upon this principle is
founded the construction of achromatic prisms
and lenses, which refract light without decom-
posing it into colors.
John Dolland, of England, first found by experi-
ment, that flint-glass (the white glass of which drink-
ars.

OF LIGHT.
135
Fig. 1. ing glasses are made), and crown-glass
(the glass with which windows are glazed),
а А have different dispersive powers. By
combining flint and crown-glass in a lens
(as is shown in Fig. I. where AB re-
presents a concave lens of crown-glass,
and ab a convex lens of flint-glass), the
dispersive power of the flint lens corrects,
to a considerable degree, that of the crown
BB lens. By a concave lens of muriatic acid,
with a metallic solution, between two lenses
of glass (see Fig. II.), the rays of different
Fig. II,
colors are bent from their rectilinear course,
with nearly the same regularity as by the
reflection from metallic mirrors. This is
an invention of Dr Blair. *
$ 255. It remains for us to explain Variety of
the infinite variety of colors exhibited
by different bodies, when exposed to
solar light, or the rays of any other
luminous substance. This may be explained,
according to Sir Isaac Newton's theory, by sup-
posing these bodies to possess different chemical
properties ($ 28), in consequence of which they
decompose the white solar light, absorbing some
of its simple colors, and reflecting the rest.
Were
we to adhere to Euler's theory, we should have
to seek the reason of the variety of colors in the
shape and elasticity of the surface which is pre-
sented to the light; for on these would depend
the angle of refraction, and the quickuess of the
vibrations of the refracted colors.
* Euler proved the possibility of combining two sub-
stances whose dispersive powers might mutually correct
each other, long before the experiments of Dolland, by the
simple force of mathematical reasoning. (See Euler's
Dioptrica.)

136
OF LIGHT.
$256. Some bodies suffer part of the light to
which they are exposed, to pass through them,
and absorb or reflect the rest. This property ex-
plains the blue hue of the atmosphere, the effect
of colored glasses, &c.* Other bodies become
transparent when their pores are filled with a
transparent fluid.
Paper becomes transparent
when it absorbs a quantity of oil ; the stone called
hydrophane, when dipped in water, &c.
$ 257. The chemical properties of bodies may
be so changed, that they act differently upon
light from what they did before. In this case,
they must also exhibit a different color. Instances
of this kind are daily furnished in chemistry; or
we may also cover the surface of a body with a
substance (pigment), which operates differently
upon light, and thereby produces a change of
color. Hereupon depends the process of dyeing,
painting, &c.
* Goethe, in his Acromatics (Goethe's Farbenlehre,
Tubingen, 1810), explains the variety of colors in a manner
diametrically opposite to that of Sir Isaac Newton. But his
work is better adapted to painters and artists, as the whole
subject is treated in particular reference to the fine arts.

OF VISION,
137
E. Of Vision.
1. The Eye.
$ 258. The human eye (of which Fig. I. is
a front view, and Fig. II, a vertical section), is
nearly of a globular form, with a slight elongation
Fig. 1.
Fig. II.
al
M
7
7
a
N
r
a
M
7OFA
al
or projection in front. It consists of four coats,
or membranes, - the sclerotic, the cornea, the
choroid, and the retina :— of two fluids, the
aqueous and the vitreous ; —and of the crystalline
lens.
$ 259. The sclerotic coat, aaaa (Fig. I. and
II.), the outer and strongest coat, (commonly
called the white of the eye), to which are attached
the muscles for giving it motion. Joined to it, is
the cornea, bb, which is the clear and transparent
membrane through which we see. The cornea
consists of several layers, to give it strength, and
to defend the delicate part within from external
12*

138
OF VISION
injury. On the inner surface of the sclerotic
coat, is the choroid coat, covered with a black
pigment. The innermost coat is the retina, rrrr,
formed from the expansion of the optic nerve,
which enters the eye at 0. In the centre of the
retina is a small hole, with a yellow margin ;
properly speaking, it is but a transparent spot,
free of the pulpy matter of which the retina con-
sists.
260. The interior part of the globe of the
eye is divided into two very unequal segments, by
a flat, circular membrane, ef, called the iris. It
is of different colors in different persons, and we
are in a habit of calling a person black-eyed,
blue-eyed, &c, according as the iris of his eyes is
black, blue, &c. The iris has a circular opening
d (Fig. I. and II.) in its centre, called the pupil,
which expands when the light which enters
through it is diminished, and contracts when the
light is increased. The space before the iris,
which is called the anterior chamber of the eye,
contains the aqueous humor, from its resemblance
to pure water; and the space behind the iris is
called the posterior chamber, and contains the
crystalline lens, ll, and the vitreous humor, which
fills all the rest of the eye.
§ 261. The crystalline lens is suspended in a
transparent capsule, or bag, by what are called
the ciliary processes, gg. This lens is more con-
vex behind than in front (as shown in the figure),
and consists of concentric coats, which are again
composed of fibres. The lens is destined to con-
vey the rays, after refraction, to the retina, there

OF VISION.
139
to form the image of the object before the eye.
The vitreous humor MMN, which occupies the
largest portion of the eye, lies immediately behind
the crystalline lens, and fills the whole space be-
tween it and the retina, rrrr.*
2. Vision.
$262. The crystalline lens and the retina,
are by far the most important parts of the eye,
and on them depends chiefly the process of seeing.
The
rays of light which enter the eye through the
pupil, after being refracted through the crystalline
lens, and the other aqueous and vitreous humors
of the eye, impress the retina with a distinct im-
age of the object before the eye see the figure),
* The above description of the eye is chiefly taken from
the excellent treatise on optics, in the Library of Useful
Knowledge. Those teachers who wish for a more detailed
description of the eye, and the functions of each of its mem-
branes, will find it in the first volume of Caldwell's transla-
tion of Blumenbach's Physiology ; Sect. XXI. on Vision.
Philadelphia, 1795.
For a more minute description of the crystalline lens, and
its muscular properties, see Prof. Reil's Dissertation, in
Gren's Journal of Natural Philosophy. Vol. VIII. page
325.

140
OF VISION.
in a manner similar to the formation of images by
convex lenses ($ 243, page 126). We see an ob-
ject the clearer the more distinctly the retina is
impressed with its image.
§ 263. The different humors of the eye seem
to be destined to correct the dispersion of colors
by the crystalline lens; otherwise we should see
all things embroidered with colors and fringes, as
they appear when seen through a prism.
$ 264. The eye cannot see clearly a distant
object and a near one, at the same time ; because
the image of the more remote object, will be
nearer the crystalline lens than that of the object
which is at a shorter distance ($ 243, page 127,
7thly); consequently, when the image of the one
is distinct on the retina, that of the other will be
less so.
§ 265. Some persons cannot see well at a
distance, while others cannot see clearly an object
which is near them. The former are called near-
sighted, and the latter long-sighted. In a near-
sighted person, the image of a distant object falls
always between the retina and the crystalline
lens; in a far-sighted person, the image of a near
object falls beyond the retina. Hence the inven-
tion and use of spectacles. Near-sighted persons
need concave glasses; far-sighted persons use
convex glasses, to produce a distinct image on
the retina.
266. The images of the objects before the
eye appear inverted on the retina (§ 243, 3dly).
Several images, however, have, with regard to

OF VISION
141
each other, the same relative position which the
objects themselves have, and this is the reason
why we do not see them inverted. We do not
even become conscious of this inversion of the
images upon the retina, and do not judge, from
the position of the image in the eye, of what
is above or below, to the right or left of an
object.*
§ 267. Two lines (see the figure), drawn
from the two extremities of an object to the
middle of the crystalline lens, form what is called
the visual angle, and the image of the object
itself is formed upon the retina, within the ex-
tended legs of this angle. The greater the
angle is, the greater is the image on the retina ;
the greater, therefore, appears the object itself.
When the visual angle is very small, then the
object, which appears to diminish to a simple
point, can no longer be perceived, unless it be
* This is a matter of physiological speculation. The eye
seems to be merely the medium through which the optic
nerve receives impressions from the objects before the eye.
But in what manner the optic nerve propagates these im-
pressions through the brain, and how thence the mind itself
becomes conscious of them, is totally unknown to the anat-
omist and the physiologist,

142
OF VISION
very intensely illumined. This is the case with the
fixed stars, which we cannot perceive in daylight.
268. The further an object is from the eye,
the smaller is the visual angle (see the last figure).
Of the distance itself, however, we do not become
conscious by mere vision.
On the contrary, we know that children, and persons
who have had cataracts removed, had no idea of dis-
tance, but had to acquire it by experience. Thus,
we judge of the distance of an object by comparing
its apparent magnitude to its known size ; by the
weakness or intensity of the light in which it appears;
by the number of things which are seen between the
object and the eye, &c.
F. Optical Instruments.
$ 269. The following are some of the principal
instruments now in use.
1. The camera obscura, or darkened chamber.
פיינטס
Camera ob-
darkened
chamber.
A
D
B
If through the window-shutter of a darkened
room, a small circular hole be made, and provided
with a double convex lens, the images of external
objects, such as trees, houses, men, &c, will be
seen upon a screen, or piece of white paper,
placed before the aperture,

OF VISION.
143
The same phenomena may be witnessed, also, with-
out a lens: but then the colors will be less bright.
The images appear inverted (see the figure), because
the rays which proceed from the top A of the object,
will fall upon D, the foot of the image; whereas the
ray BC, proceeding from the foot of the object, will
form the top of the image.
Another modification of the same instrument
which is frequently used by painters, to delineate
a landscape, may be seen from the following
figure. It consists of a small house, with a plane
reflector, inclined at 45 degrees with the hori-
zon, and a plano-concave lens (see the figure),
through which the rays reflected from the mirror
are so refracted as to form a perfect image of the
object without, upon a piece of paper, upon which
the painter may sketch it. The utility of this
instrument is manifest from its construction.

144
OF VISION.
2. The camera lucida, invented by Dr Wollas-
ton. It consists in a quadrangular prism, at-
BERRIEN
B
tached to a small metallic rod, which may receive
any inclination you please, with the table to which
it is fixed. The rays proceeding from a distant
object are refracted by a prism, in such a man-
ner, that, to an eye in O, the image appears
upright on the horizontal table AB. This instru-
ment may likewise be used for delineating a land-
scape.
3. The single microscope. This consists in a
double convex lens, or in a small globe of glass,
made by melting the ends of a few threads of
spun glass in the flame of a candle. Its magnify-
ing effect, when held between the object and the
eye, may easily be understood, from the properties
of convex lenses ($ 243, page 126).

OF VISION
145
4. The compound microscope: It is composed
of two lenses (see the figure), fixed in a tube,
А
с
B
D
ABCD, in such a way that an image of the object
P is formed within the tube, and afterwards seen
magnified through the other lens, AB. The object
is commonly placed a little beyond the focus of the
smaller lens, CD, which is called the object-glass ;
while the lens AB is called the eye-glass.
5. The astronomical telescope; which consists
A
M
P D
K
B В
N
of two convex lenses, of unequal focal lengths (§
243, 6th), and placed at a distance from each
other, equal to the sum of their focal lengths. The
lens of greater focal length forms the object-glass ;
the other lens forms the eye-glass. The rays MA,
NB, which come from a very distant object, for
instance from a star (and which may, therefore,
be considered as parallel to each other), are by
the object-glass collected into an image, K. This
image is then seen as many times magnified
through the eye-glass DC, as the focal length of
13

146
OF VISION
this eye-glass is contained in the focal length of
the object-glass. Thus, if the focal length of the
eye-glass DC be 100 times contained in that of
the object-glass AB, the star will be seen 100
times magnified. That the object is seen invert-
ed, is casily perceived from the figure. The ray
AM will, after refraction, be seen in the direction
CO, and the ray NB in the direction DP.
6. The terrestrial telescope, for such purposes
P
А
E
см
Ο Η!
DN
Q
B
as ship and spy-glasses. This is a refracting
telescope, with two additional eye-glasses of the
same size and shape, placed at equal distances
from each other, and in such a manner that the
focus of the one meets that of the next lens.
These two additional eye-glasses, EF, GH, are
introduced for the purpose of collecting the rays
proceeding from the inverted image, MN, into a
new, upright image, between GH and EF, which
is then seen through the last eye-glass, GH, under
the visual angle, POQ.
The image of the object, seen through a refracting
telescope, is never so clear and perfect as that obtain-
ed by the reflecting telescope (first projected by
Kepler); because the dispersion of colors which every
lens more or less produces, renders the image dull
and indistinct, in proportion to the number of lenses
employed.

OF VISION.
147
7. The reflecting telescope (see the figure). It
A
7
7
g
G
2
B
consists of a large tube, containing two concave
metallic mirrors, AB, and c, with two plano-convex
eye-glasses. The mirrors are placed at a little
more than the sum of their focal distance from
each other. The effeet produced by it is this:
The parallel rays, rr, rr, coming from a distant
object, are by the mirror AB reflected to a focus
g, where an inverted image of the object is
formed. The diverging rays proceeding from this
image are by the small mirror c again reflected,
and received, by the eye-glass F, through a hole in
the middle of the mirror AB. The eye-glass F
collects these reflected rays into a new image,
and this image, which is now upright, is seen
magnified, through the second eye-glass, G.
The reflecting telescope just described was invented
by Dr Gregory. Its advantage over a refracting tel-
escope is considerable ; because admitting of an eye-
glass of a shorter focal distance, an object may be
seen through it, much more magnified; and as in the
reflection from the mirrors there is no dispersion of
colors, the image is by far more distinct than it can
ever be produced by the best coml on of lenses.
Besides the telescope just described, there are others,
varying a little from it in their construction. Gregory's

148
OF VISION.
telescope, however, is most frequently used for as-
tronomical purposes.*
8. The solar microscope. This consists of two
А.
lenses, C and D (see the figure), and a plane mir-
ror, AB. The two lenses are contained in a
tube, which is fixed in such a manner, to one of
the window-shutters of a darkened room, that the
only light which enters the room passes through
the lens C. This lens is called the condenser.
The mirror AB, remaining without, and the con-
denser C, are destined to throw the greatest pos-
sible light on the object, which is placed a little
beyond the focus of the lens C. The rays which
depart from this object are refracted by the convex
lens, D, and form behind it a magnified image,
whose dimensions are the greater the nearer the
object approaches the principal focus of the lens
C. This image is received upon a screen, as in
the camera obscura,
at
* The most remarkable reflecting telescopes, besides the
Gregorian, are Sir Isaac Newton's telescope, the Cassegra-
nian reflector, and Herschel's large telescope, now
Greenwich, in England. For a minute description of these
instruments, see Library of Useful Knowledge, treatise on
Optical Instruments. Part I. pages 11–19.

OF VISION
149
The solar microscope serves to magnify little in-
sects, animalculæ of infusion, &c; but the most beau-
tiful experiment that can be made with it, is to witness
the formation of crystals, when, instead of the object,
a solution of sulphate of soda is placed near the prin-
cipal focus. In a few minutes the liquid evaporates,
and the process of crystallization may be followed in
all its details.* Any other saline solution will pro-
duce a similar effect.
9. The magic lantern, which is constructed
on the same principle as the solar microscope.
A
L
с
D
B
But instead of the light of the sun, the fame of a
candle or some other luminous body is used,
When this light is of itself not intense enough, a
concave mirror, AB (see the figure), is substituted
for the plane mirror (in the last figure), and a
lens, CD, is used for a condenser. The effect is
the same as that produced by the solar micro-
scope ; only proportionally weaker, as may be sup-
posed from the less intense illumination of the
object.
* See Biot's Précis Elementaire de Physique. Tom. II.
page 358.
13*

150
CHAPTER VIII.
OF ELECTRICITY.
A. Phenomena.
Phenomena
$ 270. When a piece of sealing-wax, or a
of electricity. smooth surface of glass is briskly rubbed with a
dry woollen cloth, and immediately afterwards
held towards light and small bodies, such as
pieces of paper, thread, cork, feathers, &c, these
bodies will first fly to the surface which has thus
been rubbed, and adhere to it for a short time,
after which they are repelled again. But as soon
as they have touched the table, they are again
attracted, and this process continues for a consid-
erable time. This property, which some bodies
Electrical at- acquire by being rubbed, is called electric attrac-
traction and tion and repulsion ; the surface which acquires
this attractive and repulsive power is said to be ex-
cited; the bodies themselves, which produce these
phenomena, are called electrics; and the agent or
cause to which we ascribe these phenomena, is
termed electricity.*
The principal electrics are amber, glass, resin,
sealing-wax, the fur of most quadrupeds, feathers, dry
air, dry wood, paper, silk, and perfect ice, at 13 de-
grees below zero, of Fahrenheit's thermometer. Most
* From the Greek word electron (amber); because the
ancients knew this property of amber.

OF ELECTRICITY.
151
bodies exhibit more or less the same phenomena, un-
der favorable circumstances; wherefore the division
of bodies into electrics and non-electrics is hardly any
longer practicable.*
§ 271. If the experiment just described is
performed in a dark room, flashes of light, of a
bluish color, are perceived, during the friction,
extending over the whole surface rubbed, and
sparks, attended with a snapping sound, are seen
to dart around it in all directions. If a round
metallic ball, or a knuckle, be presented to the
surface, a spark will be drawn, accompanied by
a prickling sensation, and if the face be brought
near, a feeling will be excited in the skin, as if it
were covered with a cob-web.
§ 272. When a metallic tube, perfectly round Electricity
on all sides, and either suspended by silk cords, and transfer.
or supported by a piece of glass or sealing-wax,
is brought near, or in contact with an excited
surface, then the whole of that tube will exhibit the
same phenomena as the excited surface itself, and
is therefore, in the first case, said to be electrified
by induction ; or, in the second case, by a transfer
of electricity from the excited surface. But when
glass, silk, or sealing-wax are in the same manner
brought near, or in contact with the excited sur-
face, they exhibit no such influence.
$273. From this and similar experiments, we
are led to infer that some bodies readily receive
* The science of electricity is of modern date, and but of
the seventeenth century. William Gilbert, Otto von Que-
ricke, Robert Boyle, Hauksbee, Gray, Du Fay, and Frank-
lin, have most contributed to its advancement.

152
OF ELECTRICITY.
and non-con-
ductors.
Conductors and convey electricity, while there are others
which seem to possess no such conducting power.
The former are called conductors of electricity,
and the latter non-conductors.
The principal conductors of electricity are the met-
als, water, and the human body. The principal non-
conductors are glass, resin, silk, and sealing-wax.
Insulation. § 274. When a body which is capable of con-
ducting electricity, is on all sides surrounded by
non-conductors, it is said to be insulated.
The great difference between a conductor and a
non-conductor, consists chiefly in this: When an
insulated conductor touches an excited surface, its
whole surface becomes electric; and when, in this
state, it is again touched by a non-insulated conductor,
it loses at once its electricity. A non-conductor, on
the contrary, shows the electric phenomena only in
the point which has been touched by the excited
surface; and when electrified by rubbing, and touched
by a conductor, it loses its electricity only in the point
of contact.
§ 275. It is important to observe, that all
non-electrics.
electrics are non-conductors; and that, on the
contrary, the best conductors are non-electrics, –
or, in other words, that the power of producing
electricity increases in all bodies in proportion as
their power of conveying this influence dimin-
ishes, and vice versa.
$ 276. When a metallic body is insulated, and
becomes electrified by transfer from an excited
surface, its electricity is for a considerable time
permanent ; but when it is touched with the
hand, or brought in contact with conducting
bodies, which communicate with the earth, then
its electricity is lost by diffusion into the mass of
Electrics and

OF ELECTRICITY.
153
the earth, which is an inexhaustible source for
the absorption and supply of electricity.
$ 277. In order that a body shall contain Proper shape
for retaining
electricity for a considerable time, it is neces- electricity.
sary that its form should be as nearly as possible
spherical (a sphere, a spheroid, or a cylinder ter-
minated on both sides by a hemisphere). For it
has been found by experiments that electricity es-
capes most readily from bodies of a pointed figure,
in proportion as the points project from the sur-
face.
$ 278. To perform electric experiments with Electrical
greater ease and facility, we make use of what is
called an electrical machine. It consists chiefly
machine.
С
of four parts, viz. - the electric, the rubber, the
conductor, and the insulator,

154
OF ELECTRICITY.
tance.
The best machine for this purpose consists of a
circular glass plate, A,* turning on an axis. (See the
figure.) It is rubbed by two pair of cushions, fixed at
opposite parts of the circumference, by elastic frames of
wood. A hollow brass tube, C (the prime conductor),
supported by glass columns (the insulator), is fixed to
the machine in such a manner, that its branched ex-
tremities, which are commonly furnished with pointed
wire, nearly meet the plate.
$ 279. By means of this machine, the above
Single spark.
Striking dis- described electrical phenomena may be witnessed
much more distinctly, than by rubbing the electric
with the hand. If a round conductor, or the
knuckle, is presented to the conductor of the
machine, a vivid spark proceeds from it, which is
called the single spark. The greatest distance at
which this spark may be drawn, is called the
striking distance of the machine.
To produce these phenomena to their fullest extent,
it is necessary that the rubber should communicate
with the earth. Very near the conductor, the sparks
are smaller than at a greater distance from it.
B. Opposite Electricity.
Opposite
electricity.
$ 280. For the discovery of opposite electricity
we are indebted to Du Fay. It is established on
the following phenomena and experiments.
1. If a glass tube and a piece of sealing-wax
are both suspended by silk cords, and an excited
surface (for instance, a piece of rubbed glass), is
* See Biot's Traité de Physique. Tome I. page 545,

OF ELECTRICITY.
155
presented to them, then this surface attracts both
the suspended glass tube and the sealing-wax.
The same takes place when the excited surface
is a piece of sealing-wax.
2. When the suspended sealing-wax and glass-
tube are themselves electrified, and a rubbed piece
of glass is presented to each of them as before,
then the electrified sealing-wax is attracted by it,
and the electrified glass tube is repelled.
3. But if an excited piece of sealing-wax is
used instead of the excited piece of glass, then
the electrified glass tube will be attracted, and
the electrified sealing-wax will be repelled.
§ 281. These experiments establish the fol-
lowing laws.
1. An un-electrified body is always attracted by Laws of op-
posite elec-
an excited electric, whatever be its nature.
tricity.
2. The electricity produced by rubbing a piece
of sealing-wax, is essentially different from that
produced by rubbing a piece of glass. And such
is the nature of these two kinds of electricity,
that bodies under the influence of the same electri-
city repel each other, while those acted upon by
different electricities evince a mutual attraction.
§ 282.
To distinguish these two kinds of Positive and
electricity, Du Fay, called that which is excited tricity.
negative elec-
by rubbing glass, the vitreous or positive electri-
city; and that which is produced by rubbing a
piece of sealing-wax, the resinous or negative
clectricity. If we denote the vitreous electricity

156
OF ELECTRICITY.
-
-
by + E, and the resinous electricity by — E,
we shall have the following table:
+ E repels + E.
E repels — E.
+ E attracts - E.
E attracts + E.
When the rubber of an electrical machine is also
provided with a conductor, then this conductor exhibits
the phenomena of resinous electricity, or
E; and
the prime conductor exhibits those of the vitreous
electricity, or + E.
§ 283. This law holds, not only of excited
electricity, but also of that which is transferred
from an excited surface to another body.
This may be shown by two little pith-balls. When
both receive + E, or both — E, from an excited sur-
face, they will, in both cases, repel each other. But
when the one receives + E, and the other — E, then
they attract each other. (For the purpose of perform-
ing this experiment, the pith-balls had better be
suspended by flax or silk cords.)
$ 294. Upon the repulsive power which one
ter, and elec- electrified body exercises upon another, which is
troscopes.
under the influence of the same electricity, is
founded the construction of electrometers or elec-
troscopes. These are instruments for measuring
or indicating the degree of electricity with which
a body is charged.
d
One of the simplest contrivances of
this kind is Henley's electrometer,
(see the figure), but it is by no means
an exact measure of electricity. It
consists of a slender rod of light wood,
capable of revolving round its axis C,
and terminating in a small pith-ball a.
This rod is the index of the instru-
ment; dfe is an ivory semicircle, for
Electrome-

OF ELECTRICITY.
157
the purpose of showing the degree of elevation of the
moveable index ca. The whole is fixed to a wooden
stem, which may be fitted to a hole in the upper
surface of the conductor of an electrical machine.
The number of degrees described by the moveable
index is then the evidence of the quantity of electricity
with which the apparatus is charged.
The repulsive and attractive power between the
two kinds of electricity, is also taken advantage of
in some electric toys; such as the dancing of small
figures cut out of paper or cork-wood, between two
metallic plates, of which one communicates with the
earth, and the other with the conductor of the ma-
chine — the flying feather, the electrical spider, &c.
285. When a piece of metal, shaped in the
form of an S, and pointed at both ends, is placed
upon a pointed wire, which communicates with
either of the conductors of an electrical machine
(s 277), then it will move round with great ve-
locity while the machine is turning. If the ex-
periment is performed in the dark, then a circle
of light is seen, and a current of air is felt to
proceed from the points of the metal; which,
however, is generally noticed when electricity
escapes from a pointed surface.
C. Theory of Electricity.
$286. To explain the above described phe- Theory.
nomena of electricity, two theories have been
established; one by Du Fay, and the other by
Dr Franklin.
14

158
OF ELECTRICITY.
I. According to Du Fay's theory, there exist two
very subtile and highly elastic fluids, which per-
vade the earth and all bodies, but are void of any
perceptible degree of gravity. These two fluids
possess the following properties :-
a. They move with various degrees of facility,
through different substances : in conductors, or
non-electrics, such as metals, the human body,
&c, without the least perceptible obstruction ;
but in non-conductors, or electrics, such as glass,
resin, &c, they move apparently with great diffi-
culty.
6. Both fluids possess the same general proper-
ties; but in relation to one another, their natures
are essentially different, and so completely oppo-
site to each other, that when combined they
neutralize and balance each other, and all visible
action ceases.
c. By friction, or other causes, the union in
which these fluids exist in all bodies, is dissolved;
the vitreous electricity is impelled in one direc-
tion, and the resinous electricity in the opposite
one.
Thus when a piece of glass is rubbed, the vitreous
electricity accumulates on the surface of the glass,
and the resinous electricity passes over to the rubber.
d. The particles of one fluid have a strong
attraction for those of the other ; but the particles
of the same fluid repel each other (on account of
their perfect elasticity), with a force which is in
the inverse ratio of the square of the distances.

OF ELECTRICITY.
159
Hence the attraction which is manifest between two
insulated bodies, charged with different electricities,
and the repulsion between two insulated bodies, under
the influence of the same electricity.
II. Dr Franklin ascribes all electric phenomena
to the agency of a single highly elastic fluid,
which is dispersed through the pores of all bodies,
and, from some cause or other, moves through
them with various degrees of velocity, according
as these bodies are conductors or non-conductors
of electricity
The electric phenomena are then explained
thus :
a. When the attraction which every body has
for the electric fluid is equal to the degree of
force with which the particles of this fluid repel
each other, then no electric phenomena will take
place, and the electric fluid is said to be in equi-
librium.
b. When a body is excited, the electric equi-
librium is destroyed ; one part of the excited
body contains more, and the other part less than
its ordinary share of electricity. That part which
contains more than its natural share of electricity,
is said to be positively electrified ; the other,
which has less than the ordinary share, is said
to be negatively electrified.
An insulated conductor of electricity,
brought in contact with a positively excited sur-
face, receives from it part of its surplus of electri-
city, and becomes therefore itself positively elec-
trified. If on the contrary, the same conductor is
c.

160
OF ELECTRICITY.
made to touch a negatively excited surface, it will
lose part of its own electricity, and thereby become
negatively electric.
d. When a positively electrified conductor,
and another which is negatively electrified, are
brought near each other, the surplus of electricity
of the one rushes violently over to the negative
conductor, and restores the electric equilibrium.
This is generally accompanied by a flash of light
(a spark), and the other phenomena described
($ 270, 271, pages 150, 151).
REMARK. Dr Franklin's theory explains all electric
phenomena full as well as Du Fay's. The only appa-
rent difficulty seems to be in the repulsion of two
negatively electrified bodies; for which purpose we
must assume that the particles of a body which are
void of electricity repel each other, in the same man-
ner as those which are actually charged with the fluid.
It is on this account, and because, according to Dr
Franklin, the electric fluid must have the same attrac-
tion for all bodies, that some modern philosophers
(such as Biot, Berzelius, Meissner, Strommeyer,
Tobias Mayer, &c,) still adhere to Du Fay's theory,
although Dr Franklin's theory, on account of its sim-
plicity and elegance, is, and justly deserves to be,
preferred by most electricians.
D. Electrical Instruments.
§ 287. Besides the electrical machine ($ 277,
page 153), there are yet a variety of other instru-
ments for the purpose of exhibiting the electric
phenomena. Among those we will merely men-
tion the following three : the electric jar, or Leyden

OF ELECTRICITY.
161
phial, the electrical battery, the electrophorus, and
the condenser.
§ 288. The electric jar, or Leyden phial,* for Electric jar.
ФА.
the purpose of accumulating large quantities of
electricity. It consists of a jar or bottle, provided
on both sides with a coating of tin-foil ; leaving,
however, a sufficient space uncovered at its upper
part, to prevent a spontaneous discharge (which
might occur, if the two coatings were not entirely
separated from each other). A metallic rod,
rising two or three inches above the jar, and
ending in a brass ball, A, called the knob of the
jar, extends through the cover, and is in contact
with the interior coating. The outer coating
communicates with the ground.
$ 289. When the knob is brought in contact,
or communicates with the prime conductor of an
electrical machine, then the positive electricity
* So called, because Cunæus and Muschenbroek, in Ley-
den, first constructed these phials, in 1745. The discovery
was made accidentally, by Von Kleist, the 11th of October,
1745.
14*

162
OF ELECTRICITY.
(282), which is accumulated at the surface of
the conductor passes through the knob to the
interior coating, whence its escape is prevented by
the interval of uncovered glass (a non-conductor);
while the outer coating becomes, at the same
time, negatively electrified. In this state the
phial is said to be charged.
The phial may also be charged by connecting the
knob with the negative conductor of the machine (the
conductor of the electricity of the rubber); but then
the inner coating will be negatively, and the outer
coating, positively, electrified. If the knob, instead
of touching the conductor of the machine, is brought
within its striking distance (§ 279), then a succession
of sparks will pass from the conductor to the knob ;
and if the phial is insulated, and the knuckle, or any
round conductor be presented to the outer coating,
the same number of sparks will be drawn from it,
simultaneously with those of the conductor. An insu-
lated phial cannot be charged.
$ 290.
When several electric jars or phials
are connected together, a prodigious quantity of
electricity may be accumulated. They then re-
ceive the name of an electric battery (see the
figure). For this purpose, the inner coating must
Electric bat-
tery.

OF ELECTRICITY.
163
communicate with each other by metallic rods,
and the outer coatings must have a similar com-
munication with each other, which is commonly
established by placing the phials with their cover-
ed bottoms on a sheet of tin-foil. When this is
done, the whole battery may be charged, like a
single phial.
$ 291. For the purpose of discharging an elec-
tric jar or battery, which is done by establishing
a direct communication between the inner and
outer coating (between the positive and negative
electricity (282), we make use of an instrument
called the discharging rod, or jointed discharger.
It consists of two bent metallic rods (see the
figure), terminating in two brass balls, and fixed
in such a manner to a glass handle, that they may
be closed or separated like a pair of compasses.
When one ball touches the exterior coating, and
the other is quickly turned toward the knob of
the phial or battery, then a discharge is effected,
accompanied by a much greater spark and shock
than can be obtained from the conductor of an
electrical machine. The glass handle (which is

164
OF ELECTRICITY.
Electric cir-
cuit.
a non-conductor) secures the person who holds
the discharger from the effect of the shock.
$ 292. To convey a whole charge of electricity
through any substance or person, we must form
an electric circuit, that is, we must place that
substance or person between two conductors, of
which one communicates with the inner, and the
other with the outer coating of the phial.
A number of persons may receive the electric shock
at the same time, by taking hold of each other's hands,
the last on one side cummunicating with the inner,
and the last on the other side with the outer coating.
$293. An excellent instrument for directing a
discharger. charge of electricity with certainty and precision,
is Henley's universal discharger. It consists of
Universal
c
A
B В
two moveable wires or metallic rods, terminating
in little brass balls, and insulated by two glass
columns, A and B (see the figure). When one
of the wires is brought in contact with the outer
coating, while the other is made to touch the
knob of the phial, then a direct charge is sent
through the body, which is placed upon a little
insulating table, C, between the extremities of the
two wires. With this instrument a charge may
be directed through any part of a body with the
greatest accuracy.

OF ELECTRICITY.
165
B, is
$ 294. The electrophorus (invented by Volta, Electropho-
in 1775*) is an apparatus for collect-rus.
ing weak electricities. It consists
B
principally of three parts, the electric,
the sole, and the cover. The electric
A is à cake of some resinous substance,
such as sulphur, sealing-wax, pitch,
&c. This is melted upon the sole, A (see the
figure), which is a conducting plate, provided
with a rim to contain the cake. The cover,
a round metallic plate, with an insulating handle.t
All parts of the electrophorus must be smooth and
well rounded, to prevent the escape of electricity.
$ 295. The cake of the electrophorus is first Effects and
excited, by rubbing it with a woollen cloth or fur ; of the elec-
its electricity (according to what has been said trophorus.
(5282), will be resinous, or negative. Then the
cover, held by its insulating handle, is placed
upon it; in which state the cover does not actu-
ally touch the cake, but is yet sufficiently near it
to acquire, at its lower surface, the opposite (that
is, the positive), and at its upper surface the
same (that is, the negative) electricity. When
in this situation the upper negative surface of the
cover is touched with the knuckle, or any metallic
conductor that communicates with the earth, a
te
Wilke made use of a similar instrument previous to
Volta. (See Memoirs of the Swedish Academy, Vol.
XXIII.)
† Instead of an insulating glass handle, the cover may be
raised and placed upon the cake by three silk cords, which
answer the purpose equally well,

166
OF ELECTRICITY.
spark will pass from this conductor to the cover,
to establish the electric equilibrium. If the
cover is now removed by its insulating handle,
it is found to be positively charged, and its elec-
tricity may be imparted to an insulated conductor,
or a Leyden phial. This operation may be re-
peated a great number of times; for the negative
electricity of the cake continues sometimes undi-
minished for several months.
If the cover is raised without previously receiving a
spark from some conducting substance, then it will
exhibit no sign of electricity ; for in this case it will
actually have received none, its electric state having
been caused only by the vicinity of an electrified sub-
stance (9272). If the sole be insulated, a spark may be
drawn from it when the cake is excited; and if, when
the cover is on the cake, the cover be touched with
one finger and the sole with another, a shock will be
felt, similar in effect, though of course weaker, than
that obtained from a Leyden phial.
§ 296. The condenser is another instrument
OG
AB
for collecting weak electricity, from a large sur-
face into a small body. This was likewise in-
vented by Volta (1775). It consists of a small
plate, A (see the figure), which is connected

OF ELECTRICITY.
167
with the substance whose electricity we wish to
examine. This is brought within a very small
distance of another metallic plate, B, which com-
municates with the earth. The small electricity
of the substance connected with the plate A,
excites by induction (§ 272) the opposite state of
electricity in B. The plate B reacts now upon
the plate A, and increases its capacity for receiv-
ing electricity from the substance connected with
it. Thus a new quantity of electricity is accu-
mulated in A, which again reacts upon the plate
B; and so does this mutual action and reaction
continue, until an electric equilibrium is estab-
lished. If the plate A is now separated from the
electrified substance, and, thus insulated, removed
from B, it is found by the electrometer to be
charged with positive electricity.
The condenser and electrophorus have received
various shapes, and have been modified according to
the different tastes of electricians; but the principle
on which these instruments are established, is the
same as that we have stated.
E. Of the Motion of Accumulated Electricity.
§ 297. The electric fluid chooses on its pas-
sage always the best conductors, although they
be more circuitous; but when different passages
are opened to it through equally good conductors,
then it always chooses that which is the shortest.

168
OF ELECTRICITY.
Thus, if a person holding a wire between his hands,
discharges a jar by means of it, the whole of the fluid
will pass through the wire, without affecting him; but
if a piece of dry wood be substituted for the wire, he
will feel a shock; for the wood being a worse con-
ductor than his own body, the charge will pass through
the latter, as being the easiest, although the longest
passage. During its passage through the human body,
the shock is felt only in those parts which are situated
in the direct line of communication ; and if the charge
is made through a number of persons who take each
other by the hand, each will feel the electric shock, in
the same manner and at the same instant, the sensa-
tion reaching from hand to hand directly across the
breast. By varying the point of contact, the shock
may be made to pass in different directions; and this
may either be confined to a small part of a limb, or
be made to traverse the whole length of the body,
from head to foot.
§ 298. The velocity with which electricity
moves through a conductor has not yet been
ascertained. In an electric circle of four miles
in extent, the shock is felt with the same intensity,
and in every point simultaneously.
These experiments have been made in England,
France, and Germany. But they are far from being
satisfactory, and have not as yet led to any conclusion
as to the manner in which electricity moves, nor the
velocity with which its particles are propelled.
299. When the electric fluid meets with an
impediment to its passage, either in a bad con-
ductor, or the inadequate size of it, then both its
velocity and its effect are diminished in proportion
to the degree of obstruction. In this case, the
electric fluid is often seen to deviate from its
circuit, and to fly off to better conductors, which
it may find in the vicinity of its passage.

OF ELECTRICITY.
169
$ 300. When the metallic passage offered to
a stream of electricity is interrupted by small
pieces of glass, or other non-conducting sub-
stances, small sparks are seen to pass through all
the interruptions of the conducting substance,
resembling, through its whole extent, a continued
stream of light.
This peculiarity in the motion of electricity explains
a number of experiments; such as the formation of
words and figures on a piece of glass on which frag-
ments of tin-foil are pasted, sufficiently near each other
for the electric fluid to pass between them; the chain
of light, and other electrical toys.
F. Effects of Electricity upon Bodies.
mulation.
$ 301. The simple accumulation of electricity Simple accu-
in bodies does not produce the least sensible
change in their properties.
A person standing on an insulating stool (with glass
legs), may be charged with any quantity of electricity
from a machine without being anywise affected by it,
until the electric equilibrium is destroyed by drawing a
spark from him. Moreover, the electric fluid is accu-
mulated only on the surface, and leaves the rest of
the body in a state of perfect neutrality.
$302. The uninterrupted passage of electri- Charge sent
city through a conductor of sufficient size, does
through a
not produce the least perceptible change in the of.
mechanical properties. But when a charge of
electricity is sent through a non-conductor, or
through à conductor of insufficient magnitude,
non-conduct-
>
15

170
OF ELECTRICITY.
Mechanical
effects of
then the body is often burst or rent by the im-
mense rapidity with which the electric fluid
passes
through it.
9 303. The mechanical effects of electricity
electricity on on non-conductors which are in the line of its
course, are similar to those produced by a sharp
instrument driven with great violence and velocity
through the substance of a body. Many of the
effects of electricity, however, seem to be the
effect of expansion, produced by heat, which, more
or less, accompanies all electrical phenomena.
non-conduct-
ors.
G. Of the Electricity of the Atmosphere.
Electricity of $ 304. Our atmosphere is almost continually
the air.
charged with electricity, although varying in quan-
tity and intensity, and frequently changing from
the positive to the negative state.
It is stronger
in daytime than during the night; increasing
from sunrise till about 9 o'clock, and is weakest
from 12 till 4 o'clock in the afternoon.
§ 305. The electricity of the air is generally
positive, particularly in clear weather. On the
approach of fog, rain, snow, or hail, it changes
often from positive to negative; but afterwards
undergoes new transitions to opposite states. On
the approach of a thunderstorm these alternate
states of electricity follow each other with sur-
prising rapidity.

OF ELECTRICITY.
171
cloud,
To discover the electricity with which the air is Method of
charged, a metallic rod may be employed, raised to some ascertaining
eminence above the ground. When its lower end is ty of the at-
insulated, it will show its electrical state by affecting mosphere.
an electrometer, with which it must be connected.
To investigate the electricity of higher strata of air, a
kite may be used, having in its string a slender piece
of wire interwoven.
$ 306. The analogy between the discharge of Analogy of
a Leyden phial, and the electricity of a thunder- ty of a Ley-
cloud was already observed by several philosophers, with that of
particularly by Abbé Nollet; but it was reserved a thunder-
for the immortal Franklin to prove, by actual ex-
periment, the identity of the electric fluid with that
of lightning
On an approaching storm, in June, 1752, he raised a
kite, attached a key to the lower end of the hempen
string, and insulated the whole by a silk cord. After
waiting for some time, Dr Franklin observed the
bristling up of some of the fibres of the hempen string,
and on presenting the knuckle to the key, he obtained
a spark.* Dr Franklin's discovery is by far the most
important and practical application of the whole
science of electricity. It led him to the invention of
the lightning rod for the protection of buildings and
vessels from one of the most dreaded agents in nature,
and explained at once the most interesting phenome-
non of meteorology.
§ 307. To secure buildings from the effect of Method of
lightning, pointed metallic rods should be placed building
at least two or three feet above the highest part effects{ of
they are to protect. Their thickness must not be
lightning.
less than half an inch, and they ought to be con-
tinued, without interruption, into the ground
* The same experiment was made by Dallibard and De
Lors, but only in consequence of Dr Franklin's sugges-
tion,

172
OF ELECTRICITY.
below the foundation of the house, until it reaches
either water or a moist stratum of earth.
For the construction of lightning rods, copper is
preferable to iron; copper being a better conductor of
electricity and less liable to rust. The points of the
lightning rod ought to be gilt, or be made of platina, to
secure them from corrosion. Large buildings require
several rods ; for it has been found by experiments, that
each rod protects only a circle whose radius is twice
the height of the rod above the building.

173
CHAPTER IX.
OF GALVANISM.
$ 308.
ALTHOUGH friction is the principal Electricity
means of exciting electricity, yet we know from produced by
experience, that there are other causes equally heat, &c.
productive of electric phenomena, though more
feeble in degree than those we have treated of in
the last chapter. Among these we reckon heat,
chemical affinity, and the heat which is produced
by contact.
Different degrees of heat affect the conducting
power of water, and it has been said before (§ 270),
that ice at 13° Fahrenheit is an electric; conse-
quently, a non-conductor of electricity. Late ex-
periments have proved that changes of temperature
produce similar effects in other substances. Glass,
when red-hot, is no longer an electric, but becomes
a conductor of electricity. The most striking in-
stance of this kind is exhibited by the Tourmaline.
This is a stone hard enough to scratch glass, of
various colors and forms, transparent when viewed
across its thickness, and perfectly opaque in the oppo-
site direction. It becomes electric by heat, and when
in this state affects iron-foil and other metals, in a
manner similar to that of the load-stone. (See Chap.
X. On Magnetism.) The electric phenomena pro-
duced by chemical agency, belong to a different branch
of the natural sciences.
§ 309. The electric phenomena produced by Explanation
contact are so numerous and complicated, and have Galvanism.
15*

174
OF GALVANISM,
Facts on
which the
theory of
Galvanism
depends.
given rise to so many theories and conjectures,
that it has become necessary to treat of them as a
distinct science, which from its author, Aloysius
Galvani,* is termed Galvanism.
§ 310. The two principal facts on which the
whole theory of galvanism is established, are
these :
1. The contact of two metals produces in the
one an accumulation of positive electricity, or
+ E, and in the other negative electricity, or - E
(see § 282).
* Dr Aloysius Galvani, Professor of Anatomy in Bologna
(born 1737, died Dec. 5, 1798), was led accidentally to this
discovery in 1790. One of his pupils happened to touch the
bare nerve of a frog that had been recently skinned, with
the blade of a knife, while another was turning an electrical
machine in its immediate neighborhood. The convulsion into
which the leg of the frog was suddenly thrown, and other
similar experiments, afterwards made by Galvani, and re-
peated by others, led him to the idea that every muscle of the
animal body resembled in its operation an electric battery;
that the different fibres of which it consists are so many elec-
tric jars, which are continually charged with electricity from
the brain, through the conducting powers of the nerves, &c.
But this theory was soon afterwards exploded by Professor
Volta, of Pavia, who proved by experiment that the same
convulsions in the legs of frogs and other animals, may be
occasioned by touching the nerve alone with two different
metals, as soon as these metals themselves are brought in
contact with each other. Modern philosophers have gone
further, and produced the same phenomena with homoge-
neous metals, by giving each a different form or polish, or
varying their temperature. Baron von Humboldt produced
sudden convulsions in the leg of a frog, with two pieces of
metal of the same kind, by the inere breath of his mouth.
See his interesting work “ Über die gereizte Muskel und
Nervenfaser.” Berlin and Posen, 1797.

OF GALVANISM.
175
duced on the
2. All living bodies are, through the medium of
the nerves, more or less affected, when brought
in contact with two heterogeneous metals.
311. Among the effects produced on the Effects pro-
human body by galvanism, it will suffice to men- human body.
tion the following three,
1. When any wounded place is touched by two
different metals, a very acute pain is felt as soon
as these metals are brought in contact with each
other.
2. If a piece of silver is placed upon the wet
end of the tongue, and a piece of zinc is placed
under the tongue, and the zinc is brought in con-
tact with the silver, an acid taste is felt; and when
the order in which the metals are placed is re-
versed, the taste becomes of a more burning and
pungent nature.
3. When one of the metals is placed against
the moist corner of the eye, while the other
touches the
gum of the lower jaw, then, the
moment the two metals are joined, a sensation of
light is felt in the eye, as if proceeding from dis-
tant lightning
This sensation of lightning is purely physiological :
as it is only felt by the individual who is performing
the experiment, and not by those who are near him.
The phenomena just described explain, in some meas-
ure, why certain liquids, such as beer, ale, wine, &c,
taste differently when drank out of metallic vessels,
from what they do when drank out of glasses; why
food prepared and served up in metallic vessels or
plates, tastes not so pure as when prepared in earthen
vessels, and served up on china, &c.

176
OF GALVANISM.
§ 312. The influence of galvanic electricity
on the bare nerves and muscles of dead animals,
is manifest by the sudden convulsions into which
they are thrown, when touched by different metals,
which are themselves brought in contact with
each other. Cold-blooded animals, particularly
those which are amphibious, are more affected by
galvanic electricity than quadrupeds or birds.
Galvani's experiment with the bare leg of a frog
(see the note to page 174), can easily be repeated, by
forming a chain of conducting substances between
the outside of the muscles and the crural nerve; or by
placing a piece of zinc under the nerve of the leg, and
a piece of silver (for which purpose a small coin may
be used) upon the muscle. The moment the zinc and
the silver are connected by a conductor, say a piece
of bent wire, the whole of the leg is thrown into violent
convulsions ; but if the connecting substance be a
non-conductor, for instance, a piece of bent glass, no
such phenomenon will take place.
$ 313. The electricity produced by contact
can be much increased, and its effects be rendered
more visible, by an apparatus which, from its
illustrious inventor (Professor Volta), is called the
Voltaic pile. Voltaic pile. It consists of a number of silver
z
s
W
Z
s
W
Z
S
W
z
S
W
Z
S
coins (of the size of a dollar), and an equal num-
ber of pieces of zinc, of the same form and di-

OF GALVANISM.
177
mensions. Between each pair of these metals, is
placed a piece of wet card or cloth (a conductor),
of somewhat less dimensions than the metallic
plates. Great care must be taken to preserve
throughout the same order, viz, silver, zinc, we
cloth — silver, zinc, wet cloth, &c, so that the
two extremities of the column may contain differ-
ent metals; one end silver and the other zinc, as
may be seen from the figure (S, Z, respectively
stand for silver and zinc, and W for wet cloth or
card). These ends are called the poles of the Poles of the
Voltaic pile.
pile; one is called the silver pole, and the other
the zinc pole.
Instead of silver copper may be used, by which
means the pile becomes less expensive. If the pile
is to produce the desired effect, there ought not to be
less than 50 pairs of plates, and the cloth or card ought
to be wet in a solution of salt, which greatly increases
its conducting power.
$314. Several Voltaic piles may be connected Voltaic bat-
with each other, so as to form a Voltaic battery.
tery.
А.
B В
This is done by establishing a direct metallic
communication between the last plate of the one
and the first of the next; this is connected in the
same manner with the third, and so on, observing
always the same order of succession in the plates,

178
OF GALVANISM.
Experiments
made with
the Voltaic
pile.
as represented in the figure. (The dark lines
represent the silver or copper plates, and the light
lines the zinc plates.) The two extremities, A
and B, of the battery are again called the silver
and zinc pole of the battery.
§ 315. The most remarkable experiments that
can be made with the Voltaic pile or battery are
the following.
1. If each end of the pile is provided with a
piece of wire, and both seized, one with the
right, and the other with the left hand, an invol-
untary trembling motion is felt, which coutinues
as long as both wires are held.
The effect of the Voltaic pile upon the nerves may
be much increased by wetting both hands, or by con-
ducting each wire into a separate basin of water, and
putting the hands into the basins.
2. When the silver or copper pole (§ 313),
communicates with the earth, and the zinc pole is
connected with a good electrometer ($ 284), it
shows positive electricity, or + E; but when the
zinc pole communicates with the earth, and the
copper pole is connected with the electrometer,
then this will show negative electricity, or -- E.
For this reason is the zinc pole called the positive
pole, and the copper or silver pole is called the
negative pole of the pile.
3. A small electric jar ($ 288) may be charged
with positive or negative electricity, according as
the zinc or copper pole is connected with the
knob, while the other communicates with the
earth,

OF GALVANISM.
179
4. A condenserº (296) may be charged with
either electricity
5. When the wire of the zinc pole is brought
in contact with the wire of the copper pole, an
electric spark is obtained, of sufficient intensity
to ignite phosphorus or sulphur, or to consume a
small piece of gold-leaf.
6. When both wires (which for this purpose
must be of platina or fine gold), are conducted
into a glass tube, which is filled with distilled
water, the water becomes decomposed into its
chemical compounds ($ 11, page 4); the silver
or copper pole disengages hydrogen, and the zinc
pole, oxygen.
In general, it may be remarked, that the chemical
operations of the Voltaic pile are greater and more
intense than its mechanical operation; wherefore the
whole subject of galvanic electricity forms one of the
most important parts of chemistry.
$ 316. Among the modern discoveries on the Modern dis-
subject of galvanic electricity, the most remarka- coveries.
ble is, that the effects of the Voltaic pile on the
animal body depend chiefly on the number of
plates that are employed ; but the intensity of
the spark, and its chemical agencies, increase
more with the size of the plates, than with their
number.

180
OF GALVANISM.
Instead of separating each pair of plates of the
Voltaic pile, by a piece of wet card or cloth, a liquid
(commonly a saline solution), may be employed for
that purpose. Such an apparatus receives, then the
Trough bat- name of a Trough Battery. There are various forms
and ways of constructing it. One is represented in
the following figure. A, represents a trough, made of
tery:
B
Α.
hard wood, or wedge-wood, with partitions of glass,
which divide it into several cells. The plates, B, are
fitted to these cells, and are connected together by a
slip of wood, so as to admit of being let down and
lifted up together. An apparatus of this kind is in its
chemical operations, far more powerful than a simple
galvanic pile; but its uses and applications cannot
form part of an elementary treatise on natural philos-
ophy.*
Attempts have been made to construct Voltaic piles
without the assistance of liquids, by means of layers of
gold and silver paper.f The effect of such piles re-
mains undiminished for several years; but their chem-
ical operation continues weak.
* Its most remarkable phenomena are described in Ber-
zelius' Chemistry, Vol. I. page 106.
† By Zomboni, Prof. Bohnenberger, and De Luc.

OF GALVANISM.
181
Advantage has been taken of these piles to con-
struct a sort of electric perpetuum mobile. It consists
Α.
B
of two piles (see the figure), whose poles are inverted,
so that if the positive pole of the first pile is at the
top, it is, in the other pile, at the bottom; and in a
similar manner are the negative poles disposed of.
Between the two piles is a pendulum, suspended
nearly in its centre of gravity, and provided on both
ends with little pith-balls. When the pendulum is
set in motion, both balls are at first attracted by the
two positive poles, A and D (which situation is repre-
sented in the figure). But as soon as both balls have
the same (positive) electricity, they are repulsed and
attracted by the negative poles of the piles; from
these they are again repulsed and attracted by the
positive poles and so on.
(Such an electric pendulum is in the Polytechnic
school of Vienna, and it has been known to continue
its operation without interruption for several years.*)
Theory of Galvanic Electricity, and the Voltaic
Pile.
(It is to be observed, that the phenomena of the
Voltaic pile, and the trough battery, are as yet far
from being satisfactorily explained. The opinions of
* See Prof Neuman's Treatise on Natural Philosophy,
Vol. I. § 878—881. (Neuman's Lehrbuch der Physik.
Wien bey Gerold.)
16

182
or GALVANISM.
Theory of
the Voltaic
pile.
the best chemists and philosophers of our time, are in
this respect at variance with each other. There are
consequently but few general facts acceded to by all
parties and only these can form part of an elementary
treatise.)
§ 317. There are evidently two kinds of con-
ductors of electricity.
1. Exciters; which, although they oppose no
obstacles to the passage of electricity, disturb the
electric equilibrium, when brought in contact with
one another, so that, in this case, one becomes
always charged with+E, while the other receives
the opposite electricity, or — E.
2. Mere conductors ; such as afford a passage
to electricity, without disturbing its equilibrium.
Metals are the principal exciters of electricity.
The following table shows their galvanic relation
to each other. Each metal, namely, combined
with one that precedes it in the series, receives
+ E; but when combined with one that comes
after it, then it receives E.
-
SILVER.
TIN.
COPPER.
LEAD.
IRON.
ZINC.
Prof. Erman, of Berlin; has lately discovered a third
kind of conductor, which he has called uni-palar con-
ductors. They conduct only one kind of electricity,
and insulate the other. Dry soap, for instance, con-
ducts + E, and insulates — E. The flame of phosphorus
conducts - E, but insulates + E. With such a con-
ductor no galvanic pile can be discharged; but they
are capable of conducting the electricity of one pole
to any body capable of receiving it.*
* Berzelius's Chemistry, Vol. I. p. 124.

OF GALVANISM.
183
$. 319. The different properties of exciters
- and mere conductors of electricity, stated in the
preceding section, will enable us to explain the
operation of the Voltaic pile in the following
manner.
1. When there is but one pair of non-insulated.
metals, say zinc and copper (the copper below,
and the zinc above), then the zinc will receive
+ E, and the copper · E, from the contact.
2. If a mere conductor (such as wet card or
cloth) be now placed upon the zinc plate, and a
new pair of plates upon this conductor, then the
wet conductor will afford a passage to the + E
contained in the zinc plate of the first pair.
Hence the second zinc plate, which, in contact
with copper, must receive a surplus of + E, will
contain a greater quantity of positive electricity,
than the first zinc plate'; while the second copper
plate, in consequence of an accession of + E
from the wet conductor, will have less negative
electricity than the first copper plate. In the
same manner the pile may be continued, and it is
easy to show, that each following zinc plate must
contain a greater quantity of positive electricity
than its immediately preceding one, whereas the
negative electricity diminishes from the bottom,
upwards, so that the lowest copper plate contains
the most E, and the highest zinc plate the
greatest quantity of + E. It is for this reason
the two extremities of the piles are called its poles
($ 313, page 177).

184
OF GALVANISM.
3. If the lowest copper plate communicates
with the floor (as we have supposed in our ex-
planation), then the electricity of the pile will
continue by a continued accession of electricity
from the earth. If, on the contrary, the pile is
insulated, then the quantity of electricity does
not increase, but the greatest positive electricity
will be condensed at the top, and the greatest
negative electricity is at the bottom.
4. When both poles of the pile communicate
with the earth, then a continued motion of elec-
tricity must ensue, from the bottom of the pile
upwards to the zinc pole, whence it is again
conducted to the earth.
5. If the two poles of the pile communicate
with each other by some conducting substance,
for instance, a piece of wire, then a galvanic
circle is formed; that is, the positive electricity
passes from the bottom of the pile to the zinc
pole, and thence by means of the conducting sub-
stance, again to the bottom of the pile, then again
to the zinc pole, and so on.
Those who believe in the existence of two distinct
electric fluids ($ 286, page 159), are of opinion that two
'separate electric streams produce the phenomena of the
Voltaic pile; that these streams take opposite directions,
the positive fluid moving upwards through the zinc pole,
and the negative fluid downwards through the copper
pole, both streams meeting each other, in the circle.
Whichever of the two theories may be the correct
one, it is certain that the phenomena of the Voltaic
pile cannot be satisfactorily accounted for, by the mere
laws of electricity. A great deal seems to depend
upon the conducting liquid, which by the agency of
the pile becomes decomposed. It is also worthy of
notice, that the plates of which the pile is composed,
Galvanic
circle.

OF GALVANISM,
185
become themselves oxidated, and that the effects of
the pile become more energetic in proportion as the
process of oxidation is going on more rapidly.
The further extension of this theory belongs to
chemistry.
Organic-Electric Phenomena.
$. 319. A peculiar electric effect is produced
by a certain kind of fish, when they are touched
at two different places of their bodies. The
shocks thus felt are similar to those obtained from
a Leyden phial, or an electric battery (§ 288,
and 290. They do not, however, affect an elec-
trometer, neither has it as yet been possible to
elicit sparks from them.
To this kind of fish belong :
The Gymnotus Electricus, or Electric Eel.
The Raja Torpedo.
The Silurus Electricus.
The Trichiurus Indicus.
$ 320. When these fishes are placed upon
metallic dishes, or touched on two sides of their
bodies by pieces of metal, they lose the power of
producing shocks, because the discharge of elec-
tricity follows the best conductor, namely, the
metal (see 297):*
* See Berzelius's Chemistry, Vol. I. page 132.
16*

186
CHAPTER X.
OF MAGNETISM.
nets, load-
stones.
Artificial
§ 321. Among the black iron ores which con-
tain iron in a feeble degree of oxidation, there
are pieces which possess the wonderful power
of attracting metallic iron, sometimes in con-
Native mag- siderable masses. These are called native mag-
nets, or load-stones. The same power, however,
may be communicated to iron and steel, by a
variety of processes, which we shall become ac-
quainted with hereafter. These are then called
maguets.
artificial magnets,
§ 322. Besides iron, there are yet two other
metals, nickel and cobalt, which participate the
magnetic properties; and according to the latest
discoveries (made by Coulomb), all solid bodies
are susceptible of magnetic influence, but in so
feeble a degree that it is perceptible only by the
nicest experiments.*
Native magnets are found in various parts of the
world, particularly in the iron mines of Sweden and
Norway, in different parts of Arabia, China, Siam,
and the Philippine Islands ; more seldom, and in
smaller masses, in England and Germany,
* See Gilbert's Annals of Nat. Philosophy, Vol. IV. page
1; Vol, v, p. 384; Vol. XI. p. 367; Vol. XII. p. 194;
Vol. LXIV. p. 395.

OF MAGNETISM.
187
A. Relation of native Magnets to unmagnetic
Iron.
§ 323. Metallic iron and black iron oxid (none Relation of
magnet to
other) adhere to native magnets with considerable iron.
force.
This power, which may be measured by weight,
does not depend on the size, and is variable in one
and the same magnet.
§ 324. The magnetic power does not operate Poles of the
with equal intensity in all points of the surface.
There are in every magnet two places, in which
its attractive power is greatest. These are called
the poles of the magnet.
They may be made visible by laying the magnet
in iron-filings, which will adhere stronger to the poles
than to any other place (see the figure). A thin piece
magnet.
of iron will adhere perpendicularly to the surface of
the poles; in any other place it will have a position
inclined to the poles ; and in the middle (the point
which is equally distant from both poles), it will re-
main horizontal, that is, parallel with the magnet.
$ 325. When both poles are made to operate
at the same time on a piece of iron, the magnetic
attraction is increased.

188
OF MAGNETISM.
Hence it is customary to give artificial magnets the
shape represented in the following figure. The two
А
B
D
W
Law of mag-
netic attrac-
tion,
poles of the magnet are then in the same horizontal
line AB. Upon these is placed a piece of malleable
iron (commonly called the armature of the magnet),
which may then be charged with as many weights as
the magnet will draw.
$ 326. The attractive power of the magnet
manifests itself not only in contact, but also at
considerable distances, and it has been proved,
that the general law for the attraction of gravity,
the propagation of sound, of heat, and light, holds
true, also, with regard to the magnet; that is,
the magnetic power is in the inverse ratio of the
squares of the distances.*
$ 327. When a native magnet is placed under
a plate of glass, wood, pasteboard, or even metal,
which is thinly covered with iron filings, these
filings will form themselves into curve lines, which
will appear to emanate from one pole, and to
enter into the other.
* See Coulomb's Experiments with the Magnetic Balance,
in Gren's Journal of Natural Philosophy; Fisher's Me-
chanical Philosophy ; Hauy's Physique; Biot, Essai de
Physique, exp. et math. Vol. III.; Gilbert's Annals of
Philosophy, Vol. LXIV.

OF MAGNETISM.
189
This experiment proves, that the magnetic influ-
ence is not destroyed by the interposition of another
substance, with the exception of iron, which, accord-
ing to its position, either increases or diminishes the
operation of the magnet.
$ 328. The power of a magnet is preserved,
and even increased by letting it continually draw
as much weight as it is capable of bearing.
Small load-stones may be kept in iron-filings.
Oxidation diminishes the attractive powers of the
magnet. Great heat destroys it.
B. Relation of Magnet to itself, and to another
Magnet.
§ 329. When a magnet is so situated that it Polarity of
magnets.
can move freely in an horizontal position, then it
will always place itself in a determined direction,
one of its poles pointing to the north, and the
other to the south. This wonderful property is
called the polarity of the magnet.
Upon this property of the magnet is founded the
construction of the mariner's compass, which, on ac-
çount of its utility in navigation, is of universal interest
to mankind. Its inventor has not as yet been precisely
ascertained, but it is certain that its invention and
use can be traced back to the thirteenth and four-
teenth century. The ancients knew only the attractive
power of the magnet.
$ 330. One magnet attracts another magnet Relation of
stronger than it does iron, but in certain points to another
they seem mutually to repel each other; and it is
found by experiments, that the north pole of one
magnet attracts the south pole of another, and vice

190
OF MAGNETISM.
versa ; but that the two north poles or the two
south poles repel cach other.
This law may be easily exhibited by placing a
magnet nearly horizontally upon a pivot, so that it
can freely move upon it. In this situation, its south
N
S N
S
pole will follow the north pole of another magnet, but
recede from its south pole. The two poles which thus
mutually attract each other, are by some philosophers
called the friendly poles, while those which seem to
repel each other, are called the inimical poles of the
magnet.
Imparting of Magnetism.
$331. Methods of making artificial magnets
of iron or steel. This is done in three ways; by
the single touch, by the double touch, and by per-
cussion.
Single touch. $ 332. Method by single touch.
1. For this purpose a bar of iron is laid flat on
M
N
A
B

OF MAGNETISM.
191
a table, and a magnet at right angles slid several
times along its surface. In this operation care
should be taken to slide the magnet always in the
same direction.
2. When two magnets are employed, the effect
is still more powerful. The two magnets are
placed with their dissimilar poles in contact, upon
the middle of the bar, C, that is to be magnetized
(see the figure). They are then drawn in oppo-
S N
A
B
С
site directions (one towards B, and the other
towards A). When arrived at the two extremities
of the bar they should be perpendicularly re-
moved to a considerable distance, then again
joined with their dissimilar poles, and placed upon
the middle of the bar. This operation must be
repeated several times on both sides of the bar.
3. A third method of communicating magnetism
by the single touch, and the most effectual of all,
is to place two bars which are to be magnetised,
parallel to each other, and to connect them by two
shorter pieces of soft iron, I, i, so that the whole
forms an oblong (see the figure). The north and
S
N
NS
I
i

192
OF MAGNETISM.
south poles of the magnets are again brought in
contact over the middle of the bar, and inclined
so as to make a right angle with each other. The
remainder of the operation is then similar to that
described in No. 2.*
§ 333. Method by double touch.
The bars,
A, B, C, D, E, which are to be magnetised, must
M
mi
А В
C D E
be of equal size, and are placed in a straight liné,
in contact with each other (see the figure). Two
magnets, or parcels of strongly magnetised bars,
M, m, with their poles reversed, are fixed parallel
to each other at a distance of about a quarter of an
inch. These are placed perpendicular to the line
of bars, and in this situation slid backwards and
forwards on both sides of the bars, until a suffi-
cient effect is obtained.
This method, which was first published by Mitchel,
of Cambridge, in 1750, has since been improved by
Canton, Aepinus, Biot, Coulomb, and others. The
principle is nearly the same in all.
$ 334. Method by percussion. In this case,
the steel bars are best formed into parallelopipeds,
or right-angled prisms. They are then inclined
nearly vertically, the lower end deviating to the
* This process was devised by M. Duhamel, in conjunc-
tion with M. Authcaume, both of the French Academy of
Sciences.

OF MAGNETISM.
193
north, and in this position struck several times
with a hammer, by which means it will acquire
all the properties of a magnet
When in this manner, the steel bars are hammered
upon soft iron or steel, their magnetic power is found
to be much greater than if they are hammered on
wood or any other substance.
$ 335. The general law, which is observed in Laws.
making artificial magnets, by any method what-
ever, is this : Each extremity of the magnetic
bar becomes the opposite pole to that with which
it is last touched. Thus the extremity of the bar
which is touched by the south pole of the mag-
net, becomes the north pole of the artificial mag-
net; while that extremity which is last touched
by the north pole of the magnet, becomes the
south pole of the bar.
Soft iron is sooner magnetised than steel; but the
magnetic power communicated to steel is more per-
manent than in iron.
336.
The magnet which is employed in
magnetising a steel bar, loses little or nothing of
its own power. Thus with one magnet a number
of bars may be magnetised, and then combined
together, by which means their power may be
indefinitely increased. Such an apparatus is then
Magnetic
magazine.
called a magnetic magazine.
$ 337. Communication of magnetism by induc- Induction of
tion.
magnetism.
As long as a piece of iron is attached to a
magnet, it is itself magnetic, and attracts other
iron or steel. In this case, the iron is said to be
magnetic only by induction; and it is to be ob-
served, that this magnetic power disappears almost
17

194
OF MAGNETISM.
entirely as soon as the magnet is removed from
the iron.
$ 338. The law of magnetic induction is sim-
ilar to that of electricity (5 272). And it is easy
to prove with a magnetic needle, that the south
pole of the magnet excites the north pole, in that
end of an iron bar which is in its immediate
neighborhood, and the north pole at the other
extremity, which is most remote from it, so that
each pole of the magnet communicates the oppo-
site state of magnetism to the neighboring iron.
339. This law being perfectly similar to
that of electricity, has led some philosophers to
think that magnetism and electricity originate
from the same cause, or are at least manifesta-
tions of the same power in nature, although
Franklin and others seem to have been of a differ-
ent opinion. *
Aepinus supposed all magnetic phenomena to pro-
ceed from a single fluid, whose particles mutually
repel each other, but have a strong attraction for iron
and steel. This fluid is everywhere in perfect equi-
librium. Iron, and black iron oxid are filled with it,
but the fluid is throughout equally distributed in them.
In magnet, on the contrary, there is a surplus of the
fluid on one side, and a deficiency on the other. The
surplus of magnetism he calls + M, and the deficiency
or want of it he calls — M, &c. The whole theory is
analogous to Dr Franklin's theory of electricity (see
§ 286, page 159).
Wilke and Brugman believe in the existence of two
magnetic fluids, which have great attraction for each
other, but the particles of either fluid repel each other.
* See Franklin's letter, in Sigăud de la Fond Précis
historique et experimental des Phenomènes électriques,
Paris, 1781.

OF MAGNETISM.
195
In iron they are combined together, and in this state
produce no magnetic phenomena. In magnets, on
the contrary, they are separated; one fluid accumu-
lates at the north pole, and the other at the south
pole, &c. (Compare this theory with Du Fay's theory
of electricity.)
of the Variation and Dip of the Magnetic
Needle.
and variation
$340, When an unmagnetic iron needle is
poised in its centre, upon a sharp point, so that
its position is perfectly horizontal, and it is after-
wards magnetised, then, in most places, it will
not exactly point to the north, neither will it re-
main in its horizontal position ; but its acquired
south pole will considerably incline to the horizon,
forming generally an angle of about 7 degrees.
The deviation from due north, is by mariners Declination
called the declination or variation of the compass ; of the mag-
netic needle.
the inclination to the horizon is called the dip of
the magnetic needle.
$ 341. Variation of the compass. The north Variation of
pole of the compass deviates in England and
throughout Europe, from about 16 to 18 degrees
westward. These deviations become smaller the
further we go to the west; and through America
and the Gulf of Mexico goes a line, in which the
compass points exactly north. This line is called
the line of no variation. Beyond this line the de- Line of no
viation is to the eastward.
The line of deviation seems to form a great circle,
beginning westward of Baffin's Bay, crossing the
United States, and passing along the Gulf of Mexico,
the compass.
variation.

196
OF MAGNETISM.
Variation of
the compass
Brazils, and the South Atlantic Ocean, towards the
south pole. It reappears in the western hemisphere,
south of Van Dieman's Land, passes across the west-
ern part of the Australian continent, and divides in the
Indian Archipelago into two branches; one crossing
the Indian Sea, Asia, Hindostan, Persia, Western
Siberia, Lapland, and the Northern Sea; the other,
taking a more northern course, traversing China,
Chinese Tartary, and Eastern Siberia, whence it loses
itself in the Arctic Seas. The whole earth seems by
this line divided into two great hemispheres ; one
embracing Europe, Africa, and the western part of
Asia, the other comprising nearly the whole of the
American continent, the entire Pacific Ocean, and a
portion of Eastern Asia. In the first hemisphere, the
deviation of the compass is to the west ; in the second
it is to the east. The best map of this kind has lately
been published by Hansteen, Professor of Natural
Philosophy, in Christiana, Norway.
§ 342. The most remarkable phenomenon
at the same accompanying the variation of the compass, is
place,
that the deviation from the north is not always the
same, at the same place, The western deviations
increase, until they amount to about 19 degrees;
they then diminish, until they become zero, finally
deviate to the east, until a certain maximum,
whence they recede again to the westward.
The line of no deviation, which now passes through
America, went in the seventeenth century through
Europe. The successive but slow deviation of the
compass to the westward and eastward, resemble in
some respects the oscillations of a large pendulum.
Its laws, however, are far from being satisfactorily
determined, and will probably need centuries of ob-
servation and experiment before they can be relied
upon.
Daily varia- § 343.
Another remarkable phenomenon,
which deserves to be noticed, is the daily variation
needle.
of the magnetic needle, at one and the same
tion of the

OF MAGNETISM.
197
place.
In the forenoon the magnetic needle
moves slowly westward, but returns, during the
whole of the remaining time, with a slow easterly
motion
This gradual motion of the compass was firs dis-
covered by Graham, in 1722. Wargerlin and Canton
have made similar experiments, and have shown that
heat has a considerable influence upon this motion.
For this experiment very long and nice needles must
be used; otherwise the motion of the needle will es-
cape observation.
$ 344. Dip of the magnetic needle. The dip Dip of the
of the magnetic needle, like its variations, differs needle.
in different parts of the globe. As a general rule,
which, however, is not without exceptious, we
may say, it diminishes near the equator, and in-
creases towards the poles, until finally, at the
poles themselves, the needle is perpendicular to
the horizon. Those places at which there is no
dip — those, namely, where the needle is per-
fectly horizontal are in a line, which encircles
the earth, and is on that account called the mag- .
netic equator.
5 345. The magnetic equator does not coin- Difference
cide with the equator of the earth, but may be between the
considered as a great circle, inclined to the earth's terrestrial
equator, at an angle of about 12 degrees.
It cuts
the terrestrial equator in four points, assuming
17*

198
OF MAGNETISM.
somewhat the shape represented in the following
figure, where the line EE denotes the terrestrial,
and MMM the magnetic equator.
M.
TT
E
M
M
Magnetism of the Earth.
Magnetism of
§ 346. To explain the above described phe-
the earth.
nomena of the magnetic needle, many philosophers
of eminence (among whom are Kepler, Hadley,
Euler, Bernouilli, Tobias Mayer, &c,) considered
our whole globe as one great magnet, because it
operates upon the magnetic needle, as one magnet
does upon another.
To illustrate familiarly the operations of terrestrial
magnetism, draw a circle upon a board, placed hori-
zontally, and provide its centre with a small magnet.
A small magnetic needle carried round its circum-
ference, will assume nearly the same situation with
regard to the circle, as an inclined magnetic needle
does to the earth.
§ 347. It is neither necessary to suppose in
theory, nor is it at all probable in reality, that a
fixed, limited magnet exists in the centre of the
earth, which causes the magnetic phenomena.
It is very probable, on the contrary, that there are
large masses of magnets scattered in the interior
of our globe, whose axes and poles must, on ac-

OF MAGNETISM.
199
count of the common law of magnetic attraction
(see 5 324), be nearly parallel to each other, by
which means their united virtue is similar to that
of a single magnetic bar.
The combined effect of all these masses must al-
ways be more or less influenced by the locality of the
place.* This is the reason why the variations of the
compass appear more irregular, the further we carry
our research, and the more accurate the instruments
are, which are employed for that purpose.
§ 348. If our earth contains large magnetic
masses in its centre, then it may be easily con-
ceived, that all the iron in their vicinity must, in
course of time become itself magnetic, which
would naturally enough explain the successive
changes in the variation and inclination of the
magnetic needle.
This is the way in which Tobias Mayer, Professor
of Natural Philosophy in Göttingen, explains the
variation and changes in the dip of the magnetic
needle ; which, according to his supposition, must con-
tinue, until all the iron which our globe contains is
converted into magnet.
$ 349. Among the effects of terrestrial mag- Effects of ter-
netism, we must count the fact, that iron bars restrial mag-
become magnetic, without using any other means
than exposing them to the atmosphere, in the di-
rection of the dip of the needle (340). The
magnetism thus acquired is, like that produced
by induction, of short duration.
Iron instruments may become magnetic, also, by a
variety of other means, such as filing, boring, cutting,
netism
* This is so far true, that the experiments with a magnetic
needle, made in a room or building, seldom agree with
those made in the open atmosphere.

200
OF MAGNETISM.
sawing, hammering, &c. This explains, in some
measure, the magnetism acquired by tools used for such
purposes, the magnetism of pokers, tongs, and other
utensils, which remain for a long time in a vertical
position, &c.
Intensity of Magnetism.
Intensity of
magnetism,
$ 350. When the magnetic needle is brought
out of its natural direction (329), and let free
again, it will vibrate in a manner similar to the
oscillations of a pendulum, until it has again
assumed its original position. The velocity of
these vibrations furnishes us with a correct means
of estimating the intensity of the magnetic force,
as the oscillations of the pendulum are the only
safe means of calculating the velocity of falling
bodies, and the diminution of gravity on the
equator (see 80, 4thly).
La Place has proved mathematically, that the whole
theory of the pendulum not only perfectly applies to
the vibrations of the magnetic needle, but also that
the intensities of the magnetic power in two different
places, are in proportion to the squares of the number
of vibrations, which the needle makes in each of these
places. Hereupon he has founded a method of finding
the dip of the magnetic needle, by the mere observa-
tion of its vibrations.
$ 351. Another remarkable fact, strongly cor-
roborating the hypothesis of terrestrial magnetism,
results from the observations of Alexander von
Humboldt. He found that the magnetic power
is stronger on the equator, and diminishes without
interruption, as we proceed to the south or north
of it.

OF MAGNETISM.
201
From the same observations it appears, also, that
the intensity of the magnetism is far less subjected to
local disturbances than the dip of the needle.
Modern Discoveries in Magnetism.
$ 352. The intimate relation of magnetism to Faets rela-
electricity and heat, has long ago fixed the atten- theory of
magnetism.
tion of philosophers; modern discoveries have put
the identity of electricity and magnetism almost
beyond a doubt.
The following facts will serve to establish the
truth of this assertion.
1. The conducting wires of the Voltaic pile pro-
duce deviations in the magnetic needle.*
2. The electricity of the conducting wire im-
parts permanent magnetism to a steel needle.
3. Magnetism can be imparted, also, by com-
mon electricity, by means of an electric spark.
Arago and Savary found that the magnetism com-
municated in this manner to a needle, does not increase
with the number of sparks, and that its maximum de-
pended on the quality of the steel.
$ 353.
The influence of heat upon magnetism Influence of
has already been spoken of ($ 328). We will
now mention the remarkable experiments first
made on that subject by Prof. Seebeck, in 1822.
If a piece of bismuth is connected with a piece of
brass or copper, so that the whole forms a ring,
heat.
* This discovery was made in 1820, by Prof. Aerstadt.
† Gilbert's Annals of Natural Philosophy, Vol. LXXII,

202
OF MAGNETISM.
Influence of
light.
and one end of the bismuth is suddenly heated,
then a magnetic needle in its vicinity will deviate
from its direction in the same manner as when
affected by the zinc pole of a Voltaic battery
(page 180). If instead of bismuth antimonium be
taken, then the result will be exactly the reverse,
that is, the needle will deviate in the opposite
direction.
Bismuth and antimonium are not the only metals
which, combined with copper and then heated, produce
deviations of the magnetic needle. They produce this
effect only in a greater degree.
$ 354. It remains for us to notice the influ-
ence of light on the development of magnetism.
Marochini, in Rome, found that steel needles
became magnetic when exposed for a length of
time to the violet rays of the prismatic spectrum
(F246). Lady Somerville, in London, and
Baumgärtner, in Germany, made similar experi-
mients, and obtained the same result.
The red, orange, and yellow rays are without effect;
the green, blue, and violet rays producé magnetic
polarity; green the least, violet the most. The needle
must for this purpose be half covered, and exposed,
for at least two hours, to the influence of the rays.
In the focus of a burning-glass the same result is ob-
tained in 20 minutes. The part which is exposed to
the violet rays, becomes the north pole. The light of
the moon or of a lamp produces no such effects.

203
APPENDIX,
CONTAINING QUESTIONS, FOR THE EXERCISE
OF THE PUPILS.
EXERCISES IN CHAPTER I.
ON THE GENERAL PROPERTIES OF MATTER.
[The questions printed in italics, refer to the text printed
in italics, which is to be committed to memory. The ques-
tions printed in small type are intended only for more
advanced pupils, and may be omitted until reviewing the
book. The sections of the questions refer to the same sec-
tions in the text.]
ES 1.] What do you understand by time and
space ?
[S2] What do you call that which fills space?
What is matter ? What do you call any portion
of matter within fixed limits? What do you un-
derstand by the volume of a body? What by its
mass ?
[$ 3.] What do you understand by matter
being divisible ?
[$ 4.] Is the space occupied by physical
bodies filled throughout with their own substance?
What are those places which are not filled with a
body's own matter called ?

204
CHAPTER I.
APPENDIX.
-
Is it necessary to suppose that the pores of bodies
are vacui, or void of matter? How can you explain
water and other fluids entering the interstices of
bodies? What phenomena are explained by the pores
of bodies ? By the cellular texture of plants and an-
imals ?
[$ 5.] Do all physical bodies affect us in the
same manner, or have all bodies the same phy-
sical qualities? Give instances of heterogeneous
substances; and of substances composed of dis-
similar particles.
[S 6.] When do you call a body perfectly
dense ? Is there such a body in nature ? When
do you call a body more or less dense, in com-
parison to another?
[$ 7.] When do you say a body is compress-
ed? when expanded ?
Could a perfectly dense body be expanded? Why
not?
[$ 8.] Are all bodies alike easily compressed ?
How do you explain the greater or less resistance
we meet with whenever we wish to change the
form of a body?
[9.] What do you understand by the power
of cohesion? How are we convinced of its ex-
istence ? What do you call the attraction of
cohesion?
[$ 10.] When do you call a body mechanically
divided ? Give instances of this kind of division.
What do you understand by the integral parts of
matter? Why are they called so ?
[§ 11.] Is mechanical division the only man-
ner in which bodies can be divided ? When do
you call a body decomposed into its chemical

EXERCISES IN CHAPTER I.
205
compounds, or ingredients? What do you call an
element ?
[§ 12.] What disposition do the particles ob-
tained by mechanical division evince, with regard
to each other, and with regard to other substances ?
Give examples.
[$ 13.] Is the general disposition of bodies to
approach and unite with each other, confined to
the contact ? Give instances where it operates
at a distance ?
Give instances of mutual attraction operating at a
still greater distance.
[§ 14.] In many cases bodies seem to repel
each other : is this a proof that there is a primitive
repulsive power in nature? How then may these
phenomena be explained ?
[$ 15.] What do
you
understund by the attrac-
tion of gravity ? How is this phenomenon gen-
erally explained?
[$ 16.] What is the direction in which a fall-
ing body approaches the surface of the earth
called ? How can you exhibit a vertical line ?
What do you call lines and planes at right angles
with the direction of gravity? What, lines and
planes forming oblique angles with the direction
of gravity ?
If the earth is a sphere, why must the direction of
gravity go through its centre? In what respect do
plains differ from hills and mountains ?
[8 17.] What do you understand by the abso-
lute weight of a body?
Tell me the difference between gravity and weight.
What proportion does the absolute weight of a body
bear to its mass?
18

206
EXERCISES IN CHAPTER 1.
[$ 18.] What do you understand by the spe-
cific gravity of a body ? What proportion do the
specific gravities of bodies bear to their absolute
weights?
[$ 19.] How is the absolute weight of a body
determined ?
Is the same unit of measure employed for ascertain-
ing the weight of all bodies ? What do you under-
stand when it is said, a body weighs 3 lbs. 4 lbs. 5 lbs.
&c.?
[S 20.] What do you call the absolute space
or position of a body? How are we led to the
idea of situation or relative position of bodies?
What do you call motion ?
Can absolute motion be perceived by your senses ?
In what cases do we conclude that a motion has taken
place?
[S 21.] What do you understand by a body's
describing a line ? or by its way or orbit? When
is the orbit of a body a straight, when a curve
line ?
[$ 22.] Why does every kind of motion require
time? How is time measured ?
[$ 23.] How are we led to the idea of veloci-
ty? How is the velocity of a body estimated ?
[8 24.] What do you understand by uniform,
accelerate, and retarded motion ?
[S 25.] What must every motion and every
change of it in velocity or direction proceed from?
What do you understand by vis inertia ? In what
does the idea of it originate ? Must matter and power
necessarily be distinct from each other? May power
not inhere in bodies? Give instances of this kind.

EXERCISES IN CHAPTER I.
207
[8 26.] What is meant by saying, the body
A has imparted motion to B? What do you un-
derstand by action and reaction of a body? Why
are action and reaction always equal to one another ?
[$ 27.] Can motion be imparted without an
interval of time?
Can you tell me an experiment which proves that
the imparting of motion requires time?
[S 28.] What do you understand by the me-
chanical operation of one body upon another?
What do you understand by a chemical opera-
tion? Can you explain organic motion from
either principle?
[$ 29.] What is meant by the geometrical, and
what by the physical form of bodies? What
properties of bodies belong to their physical form?
[$ 30.] In what cases are bodies divided or
split easier in one direction than in another ? To
what power do we ascribe these modifications in
the phenomena of attraction ?
[$ 31.] What do you call fluids? How many
different kinds of fluids are there? What are
liquids ? what gases?
What form must every fluid mass assume, when
solely acted upon by its cohesive powers ? Give ex-
amples. Is the power of cohesion equally strong in
all liquids ?
[$ 32.] What change does heat produce on a
solid body? What changes does a liquid undergo
when exposed to cold or an inferior degree of tem-
perature?
What ideas have these phenomena given rise to?
By what circumstances are they corroborated ?

208
EXERCISES IN CHAPTER I.
[$ 33.] What do you understand by the crys-
tallization or congelation of bodies?
[§ 34.] What do you call that property of
bodies, which enables them to change their form,
when some exterior force is applied to them, and
to reestablish their former shape when that power
ceases to operate ? Do all bodies possess this
property in the same degree?
[$ 35.] What fluids do you call ponderable ?
What are those fluids called, which are either not
at all, or at least so little affected by gravity, as to
escape our observation ?
Give instances of pon-
derable and imponderable fluids?
[$ 36.] What changes does heat frequently
produce on solid and liquid bodies? When a
liquid or solid substance becomes transformed
into an elastic fluid, what are its particles said to
form ? Give an example.
[$ 37.] What do you understand by the aggre-
gate forms of bodies? How many of these aggre-
gate forms are there? Are the aggregate forms
of bodies the only characteristic by which we are
able to distinguish them from one another?

EXERCISES IN CHAPTER II.
209
EXERCISES IN CHAPTER II.
OF THE PHENOMENA OF COHESION, ATTRACTION, AND
AFFINITY
[$ 38.] How is the cohesive power of solid
substances determined ? How that of cords,
ropes, &c.?
Can you tell me the order in which the power of co-
hesion decreases in the principal metals? Can you tell
the same order with regard to wood ? Which of two
cords of equal thickness is stronger, one made of silk,
or one made of flax? Does the tarring of cordage
increase or diminish their strength ? Is bleached
thread as strong as unbleached thread? What means
have we to increase the power of cohesion in metals?
In what cases do bodies become stronger when ex-
posed to the atmosphere, or to heat ?
[$ 39.] What takes place when two well pol-
ished surfaces are brought in contact with each
other ? What processes in the mechanic arts
does this phenomenon explain ?
[$ 40.] What ought to be the shape of every
liquid contained in a vessel ? Why? But what
will be the surface of a liquid in a vessel to whose
sides it is strongly attracted ? Why?
When does water actually exhibit a concave surface ?
When does water exhibit a convex surface? What
principle do these phenomena seem to establish ?
[§ 41.] What does take place, when a narrow
glass tube, which is open at both ends, is immersed
in water, or in any other liquid which strongly
adheres to glass?
18*

210
EXERCISES IN CHAPTER II.
How is this phenomenon explained ? (Let the
pupil draw the figure.)
[$ 42] What do you call the attraction of a
liquid to the sides of a narrow tube, which is im-
mersed in that liquid? Is the actual immersion
of the tube in the liquid necessary to produce
the phenomena of capillary attraction? By what
other means may the same phenomenon be
pro-
duced ?
Give an example.
[§ 43.] What is necessary in order that a
liquid shall rise in a capillary tube? Why does
not quicksilver rise in glass tubes? Why does
it rise in tubes made of tin or lead ?
What phenomena are explained by the theory of
capillary attraction ? Are the phenomena of capillary
attraction dependant on the pressure of the atmos-
phere?
[S 44.] Why do the particles of a liquid.
change so easily their relative position ?
Why does an animalcule find it easy to move in a
drop of water ? Why is it difficult for an animalcule to
rise above the surface ? How happens it that aquatic
insects, needles, small pieces of sheet iron, &c, remain
on the surface of the water ?
[$ 45] In what does the solidity of bodies ori-
ginate?
Is it possible for a body to be perfectly dense, and
yet perfectly liquid?
[S 46.] When do you call a solid body dis-
solved in a liquid ? What do you call the result of
such an operation? What do you call the liquid
in which this takes place? Give an example.

EXERCISES IN CHAPTER III.
211
[$ 47.] What do you call the mutual attraction,
through which two heterogeneous bodies combine
with or dissolve each other ?
What means are employed to facilitate the solution
of solid bodies ? Are the degrees of affinity the same
in all substances ?
[$ 48.] When do you call a solution perfect ?
When do you call a liquid saturated with a sub-
stance ?
[$ 49.] What do you call the two substances
which have combined with each other, to form a
new body? When is a solution said to be de-
composed ?
EXERCISES IN CHAPTER III.
ON THE LAWS OF MOTION.
A. Uniform Motion.
[$ 50.] When is a body said to be in uniform
motion ? What general law follows from this
definition? Of two bodies in uniform motion,
during the same number of seconds, which is said
to have the greatest velocity? If the times are
unequal, which of two bodies, of the same velocity,
will describe the greatest space ?
[$ 51.] How do you calculate the space de-
scribed by a body in uniform motion? Give an
example. What is the space described by a body
in uniform motion, during 12 seconds, with a
velocity, of 5 rods per second? What that of a

212
EXERCISES IN CHAPTER III.
body in uniform motion during 10 minutes, with
a velocity of 3 miles per minute ?
[$ 52.] What proportion do the spaces described
by two bodies in uniform motion bear to each other?
Why?
[S 53.] What proportion do the velocities of
two bodies in uniform motion bear to each other ?
Give an example ?
[$ 54.] What power has every body in motion,
with regard to another body which it finds on its
way? On what does the degree of this power
depend? Which of two bodies, which move with
the same velocity, will exercise the greatest
power? Which of two bodies, whose masses are
equal, will produce the greatest effect? *
[S 55.] How is the power of a body in motion
measured? What do you call the product of the
mass into the velocity of a body? What is the
momentum or moment of a body whose mass weighs
40 lbs. and whose velocity is 40 feet per second?
What that of a body whose mass is 100 lbs. and
whose velocity is 10 feet per second ? What that
of a body whose mass is 200 lbs. and velocity 4
feet? Which of these moments is the greatest ?
[$ 56.] What other principles can you infer
from the one last established ? Give examples.
[S 57.] What is required in order that a body
shall move with uniform velocity? How long
then would the body continue in motion ?
* Those pupils who are acquainted with algebra or geom-
etry, may state the proportions, in the note to page 20.

EXERCISES IN CHAPTER III.
213
B. Accelerated Motion.
Gravity.
[§ 58.] What kind of motion does a power
produce, which, after having communicated mo-
tion, continues to operate in the same direction,
during the following intervals of time? What do
you call the power itself?
[§ 59.] What kind of motion takes place, if
the velocities imparted, are in proportion to the
times ? What is the power which produces such
a motion called ?
[S 60.] Which is the most remarkable uni-
formly accelerating power in nature ?
[S 61.] How can you satisfy yourself that
gravity is really a uniformly accelerating power ?
Would it make any material difference, if there
were intervals in the operation of gravity? Why
not ?
[S 62.] Which are the four principal laws of
falling bodies?
How can you prove, that the space described by a
free falling body, in a certain time, is always equal to
the space through which it would have passed, had it
moved uniformly with half the final velocity ?
How can you prove that the spaces through which
a falling body passes, in a succession of equal inter-
vals, are in proportion to the odd numbers, 1, 3, 5, 7,
&c.?
How can you prove that the whole spaces passed
through from the beginning, are proportional to the
squares of the whole times ?
[$ 63.] Through how many feet does a free
falling body pass in the first second ?
Supposing you knew a body had freely fallen during
the time of 5 seconds, how should you calculate its

214
EXERCISES IN CHAPTER III.
perpendicular descent?
What rule is there for ob-
taining a body's perpendicular descent ? If the space
through which a body has fallen is known, how can
you find the time? Supposing the body had fallen
through a space of 400 feet, what would have been the
whole time of its fall? What time would a body need
to fall through the space of 576 feet? What time to
fall through 1024 feet? What, to fall through 16000
feet?
[S 64.] Has the mass of a body any influence,
or does it in any way modify the laws of falling
bodies? Why not?
Is the falling of all bodies equally accelerated by
gravity? What are all differences in time and velocity
solely attributable to ? *
[$ 65.] How does gravity affect the motion of
a perpendicularly ascending body?
[$ 66.] If a body is thrown up in a direction
making an oblique angle with the horizon, what
kind of line will it describe ? Why would it not
continue in the same direction ?
How can you show this by an example ?
(Here the teacher ought to require the pupil to draw
the figure, page 27.)
What is the name of the curve line which the body
then describes ?
C. Decomposition of Forces. — Compound Motion.
[§ 67.] If a body is at the same time solicited
by two equal opposite forces, what must necessa-
rily take place? What are these forces said to
Those pupils who have studied algebra or geometry,
may now give the formulæ given in the note to page 26,

EXERCISES IN CHAPTER III.
215
be? If the two forces which act upon the body
in opposite directions are unequal, what will then
be the result ?
[$ 68.] If the directions of the forces which
solicit the body, make an angle with each other,
what direction will the body then follow?
How can you explain this by reasoning ? How can
you verify it by an experiment ?
[$ 69.] What is the motion which you have
just described, called? What do you understand
by the lateral forces ? What do you call the mean
force, or velocity?
D. Application of the foregoing Theory to curvi-
linear Motion ?
[S 70.] When a body receives an impulse in
one direction, and is at the same time continually
attracted by another force, what kind of motion
will then take place ?
Ans. The body will then, in every moment of
its motion, be turned from its direction, and de-
scribe a curve line.
Quest. How can you show this?
[$ 71.] What is the name of a force which
attracts a body continually toward one and the
same point ? What is the name of that force
which urges it continually to remove from that point
in a straight line? How are both forces called ?
If at any time one of these forces should cease to
operate, in what direction would the body con-

216
EXERCISES IN CHAPTER III.
tinue to move ? What motion would take place,
if the centripetal force remained? What, if the
centrifugal force remained ?
E. Motion on an Inclined Plane.
[S 72.] What do you understand by an in-
clined plane? What takes place if a heavy body
is placed upon it?
[§ 73.]
What is the law of motion on an in-
clined plane?
How can you here apply the law of the decompo-
sition of forces ?
[$ 74.] On what does the velocity of a body,
moving on an inclined plane, depend? What
law is there respecting the angle of elevation ?
What motion takes place, when the angle of eleva-
tion is a right angle? What takes place when
the angle of elevation is zero, that is, when the
plane is parallel to the horizon?
[$ 75.] What power is required to stop the
motion of a body on an inclined plane ?*
* Those who understand geometry may give the geomet-
rical demonstration of this law, given in the note to page
34; and also the remarkable inference which may be drawn
from the principle laid down in the note to page 35.

EXERCISES IN CHAPTER III.
217
F. Oscillations of a Pendulum.
[$ 76.] What do you call a pendulum ? What
a simple pendulum ? What may be considered a
simple pendulum?
[$ 77.] When a pendulum is raised from its
perpendicular, to an inclined position, and then
let free again, what will take place? What do
you call the angle by which the inclined position
of the pendulum (to which it is raised) differs
from the perpendicular direction ?
How can you explain the operation of the pendu-
lum?
Why does the pendulum not continue to swing for-
ever?
[S 78.] What is the most remarkable property
of the pendulum ? Is the duration of the oscilla-
tions of a pendulum influenced by the length of the
arc which it describes ?
[$ 79.] On what does the time which is needed
for one oscillation depend? What law is there
with regard to this dependency? Give examples
of the application of this law.*
[$ 80.] What are the uses of the pendulum ?
G. Of the Lever.
[81.] What do you understand by a lever ?
What do you call the point in which the lever is
* Those who understand geometry ought to state the pro-
portion given in the notes to pages 38 and 39.
19

218
EXERCISES IN CHAPTER III.
supported? What do you understand by the arms
of the lever ?
[$ 82.] What do you call weight and power
on the lever ?
[$ 83.] How many different kinds of levers are
there? Which are they?
[$ 84.] What is the principal law of the lever ?
Give examples of its application. What do you
call the product of the power into the distance
from the fulcrum ? When is the power in equi-
librium with the weight?
[$ 85.] When are several powers and weights,
operating on the lever, in equilibrium with each
other? What must be done if some of these
powers or weights are pulling in opposite direc-
tions ?
[$ 86.] Wherein does the principal use of the
lever consist ? Tell me some of the simplest
applications of the lever.
[$ 87.] What are the lever and the inclined
plane sometimes called ? What is a pulley ?
What a wedge? a screw ?
H. Of the Centre of Gravity.
[$ 88.] What do you call the point in which
an inflexible bar or lever, charged with several
weights, must be supported, in order that it shall
neither move in one way nor another?

EXERCISES IN CHAPTER III.
219
[S 90.] What is the pressure, which such a
bar exercises upon the prop which supports it,
equal to ? Give examples.
[S 91.] What may every heavy body be taken
for ? How can you convince me that in every
heavy body there is a point in which its whole
weight is active ?
[S 92.] What is the name of a vertical line,
drawn through the centre of gravity of a body?
What must take place if this line is in any point
supported or fixed ? How can you find such a
point ?
[S 93.] When a body is placed upon a basis,
on what does its stability depend? If the line of
direction falls within the basis, when will it stand
firm, and when will it be liable to turn over?
What will occur when the line of direction falls
beyond the basis?
What phenomena can be explained from the theory
of the centre of gravity ?
I. Laws of Percussion.
[$ 94.] When a moving body meets another
on its way, what must necessarily take place? If
the line in which the centre of the striking body
moves, passes also through the centre of the body
on which it strikes, what is the stroke or percus-
sion called? What is it called, when this line
does not pass through the centre of the body
which is struck ?

220
EXERCISES IN CHAPTER III.
[$ 95.] Which are the three principal cases,
which can occur in the percussion of bodies !
1. Percussion of Unelastic Bodies.
(S 96.] How many cases can there occur in
the percussion of unelastic bodies? Which are
they? What will take place in the first of these
cases ? What in the second ? What in the
third ?
How can you illustrate these laws ?
2. Percussion of Elastic Bodies.
[$ 97.] What is the principal law in the per-
cussion of elastic bodies ?
Give examples.
[$ 98.] How many different cases can there
occur in the percussion of elastic bodies? Which
are they? What must take place in the first
case? What in the second ? What in the third ?
How can you illustrate these three cases?
[$ 99.] What law is there for the case in
which an elastic body impinges against an elastic
firm plane? or an unelastic body against an elas-
tic firm plane? What will occur when the angle
of incidence is a right angle?
How can you prove this law by the decomposition
of forces ?
[$ 100.] When several elastic balls, of equal
size, are suspended in such a way that their

EXERCISES IN CHAPTER III.
221
centres lie all in the same straight line, and the
first is raised from its position, and let fall again,
so as to strike upon the second, what will then
take place? Can you explain this phenomenon
from the laws of percussion of elastic bodies ?*
K. Vibrating Motion. — Acoustics.
[§ 101.] How is sound produced ; and what
is necessary in order that a body shall produce
sound ?
How may the vibrations which are productive of
sound be made visible ? What do these experiments
prove?
[$ 102.] What is necessary in order that we
shall hear the sound of sonorous bodies? What
do we denote by the word hearing ?
[$ 103.] What is the medium through which
sound is generally propagated ? What other
bodies are capable of propagating sound?
How may this be shown by experiments ?
[S 104.] What do the vibrations which a
sounding body produces in the surrounding at-
mosphere consist in ?
What phenomena are thereby explained ?
1$ 105.) What property must a body possess,
in order that it shall be capable of producing
sound? Why can a body without elasticity pro-
duce no sound ? With what does the capacity
of a body for sound increase ?
* Let the pupil recur to the second case.
19*

222
EXERCISES IN CHAPTER III.
[$ 106.] Is the whole uninterrupted surface of
a sonorous body thrown into a vibrating motion,
or are there certain points or lines which remain
in a state of rest? What does frequently take
place when a cord vibrates ?
By what experiments may the points and lines which
remain in the state of rest, while the rest of the sono-
rous body is vibrating, be exhibited ? By whom was
this discovery first made ?
[§ 107.] Is the sound prevented or modified
when the places which are exempt from the vibra-
tions of a sonorous body, are touched with the
finger? What takes place when a sonorous body
is touched in any other place, or brought in con-
tact with some other body?
What phenomena does this explain ?
[§ 108.] On what does the height or depth
(acuteness or gravity) of sound depend ?
To what theory may the oscillation of a pendulum
be reduced? What proportion does the acuteness of
sound bear to the tensions, the lengths and the thick-
nesses of the cords.*
[§ 109.] If the thicknesses and tensions are
the same, on what does the number of vibrations
then depend?
[$ 110.] When will two cords produce the
same tone ?
What are two cords which give
the same tone said to be ?
When a cord is struck, what does an experienced
ear always distinguish, besides the principal tone ?
In what does this phenomenon probably originate?
* The pupils who have studied geometry ought to state
the proportions, in the note to page 57.

EXERCISES IN CHAPTER III.
223
[§ 111.] When a cord c makes, in the same
time, twice as many vibrations as another cord,
C, what is it called ? What is a cord G called,
which makes three vibrations, while C makes two ?
What is the name of a cord c, which makes three
vibrations to the cord G's making three?
What is the ratio of the fundamental tone to its
next higher octave? What that of the quint to the
fundamental tone ? What that of the quint to its
quart, which is at the same time the octave of the fun-
damental tone? What do these three notes form?
What are they said to have formed ?
[§ 112.] How many principal tones are there
in an octave? By what letters are they desig-
nated, and what are they called ? What are
these seven tones called in music ?
[$ 113.] What do you understand by the nu-
merical value of a tone or note ? If the funda-
mental tone is 1, what is the value of the next
higher octave ? What that of the next higher
quint? What that of the next lower quint?
What that of the next higher quart? What that
of the next lower quart ?
What are the numerical values of the seven tones
of the Diatonic scale, derived from those just given?
[S 114.] What is the ratio of one tone to
another called ?
[$ 115.] Are the successive intervals between
the seven tones of the Diatonic scale equal to one
another? Give instances where they are un-
equal ?
[§ 116.] Does the Diatonic scale satisfy the
demands of modern music? What scale is used
in its stead? Wherein does the Chromatic scale
differ from the Diatonic scale ?

224
EXERCISES IN CHAPTER III.
What are the 5 additional semi-tones called, which,
in the Chromatic scale, are inserted between C and
D, D and E, F and G, G and A, and A and B ?
What are the numerical values of these notes ?*
The numerical values of the notes A and E in the
Chromatic scale, differ a little from those which these
notes have in the Diatonic scale; what was this impu-
rity of sound introduced for? Where is it absolutely
indispensable? Is there any instrument which can
give every interval as clear and perfect as the human
voice? Which is the most perfect of all?
[$ 117.] What do you understand by harmony,
or concord? What, by discord or dissonance ?
Give examples of both.
[S 118.] What does melody consist in?
Wherein consists the difficulty and beauty of mu-
sical composition ?
[$ 119] Are very high or very low tones still
audible? How many octaves comprise nearly the
whole system of notes fit for music?
[$ 120.] What kind of vibrations does a com-
mon violin string make when the bow is drawn
under a very acute angle? What sensation does
such a sound produce in the ear? Is the sound
higher or lower than the natural tone of the cord,
produced by transversal vibrations ?
Does the height or acuteness of the sound thus pro-
duced depend upon the thickness or tension of the
cords ? On what then does it depend? What does
this phenomenon explain ?
[$ 121.] Can you tell the velocity with which
sound is propagated through the air ?
By what is the propagation of sound through air
modified? Why can a loud sound be heard further
* This question the teacher may put or omit at pleasure ?

EXERCISES IN CHAPTER III.
225
than a low one? What do you know about the prop-
agation of sound through solid bodies ?
[§ 122.] As what may the vibrations which
every sonorous body causes in the surrounding
atmosphere be considered ?
Why is the sound
heard better in the neighborhood of the sonorous
body, than at a distance from it? What law is
there with regard to the intensity of sound? Give
an example.
[S 123.] What takes place when a ray of
sound strikes on a firm plane?
Is the whole ray of sound reflected, or only the few
particles which in their vibrations strike the plane ?
What remarkable phenomenon is thereby explained?
What instrument does it show the utility of? How
is the acoustic tube constructed ?
[ 124.] How does the air vibrate, which is
blown into flutes, trumpets, horns, or other wind
instruments ? By what means are the different
notes obtained from these instruments ?
What is the reason that the sound is not prevented,
when these instruments are touched with the hand?
Why is it not so with cords or bells? Why can bas-
soons and flutes not be made of metal ? Why are
highly elastic metals, such as silver and brass, unfit
for the building of organs? Why do speaking trum-
pets made of brass convey the articulated voice less
distinctly than those made of pasteboard or wood?
L. Obstacles or Hindrances of Motion.
[$ 125.] Is there a body in nature that has a
perfectly smooth and even surface? What does
always take place when two bodies, ever so well

220
EXERCISES IN CHAPTER III.
What do you
polished, move upon one another ?
call this resistance ?
[§ 126.] Can the laws of friction be fixed with
precision? Why not? What principles, how-
ever, are we enabled to lay down from experience ?
[S 127.] What obstacle does every body,
whose weight is wholly supported by an horizon-
tal plane, present to the least change of place?
What other phenomena are explained by friction ?
Why is a cask moved more easily than a box? Can
you now perceive the use of the pulley ?
IS 128.] By what means can friction be
avoided in machinery ?
[S 129.] What other obstacle to motion is
there besides friction ? On what does the resist-
ance of the atmosphere principally depend ? and
in what proportion does it increase ?
[$ 130.] What proportion is there respecting
the resistance of the atmosphere, and the velocity
of the moving body?
How can you convince me of the correctness of this
law?
[S 131.] Why is the resistance of water to a
moving body, greater than that of the atmosphere?
What processes are by the resistance of water
rendered possible?
[S 132.] What does take place, if a stone or
cannon-ball impinges under a very acute angle?
[$ 133.] What is the final effect of friction,
and the resistance of the atmosphere on every body
which is in motion ?

EXERCISES IN CHAPTER IV.
227
[S 134.] If the infinite space in which the
celestial bodies move, and in which our globe
itself performs its orbit, is filled with a subtile
fluid, similar to the atmosphere, what effect would
it naturally produce ?
EXERCISES IN CHAPTER IV.
LAWS OF MOTION OF FLUIDS.
A. Pressure, Weight, and Equilibrium of Liquids.
(Hydrostatics.)
[$ 135.] Can you tell me the fundamental law
of hydrostatics? How can you convince me of
its correctness ?
[$ 136.] What law is there with regard to
water, or any other liquid, which communicates
with water or the same liquid ?
How can you explain this principle ?
[$ 137. What takes place when a filled sy-
phon has one of its legs shorter than the other, and
provided with an orifice ?
What is the reason that the liquid which sallies forth
from the orifice of the shorter leg does not reach the
same height as the surface of the liquid in the other
leg?
[$ 138.] If instead of being provided with an
orifice, the shorter leg of the syphon is closed

228
EXERCISES IN CHAPTER IF.
What are
with an horizontal plane, what will the pressure
upon that plane (upwards) be equal to ?
If the shorter end be closed with a bladder, how
much weight must be placed upon it, to be in equili-
brium with the liquid in the other leg ?
we by this law enabled to produce?
[$ 139.] What is the pressure of water or any
other liquid, upon the bottom of a vessel, equal
to? When is this pressure less than the weight
of the whole liquid ? When greater than the
weight of the whole liquid ? When is it equal to
the weight of the whole liquid ?
In what does this law take its origin? How can
you explain it ?
[S 140.]
Upon what does the pressure upon
any point in the side of a vessel depend? What
law exists with regard to the velocity with which
water spouts from different orifices made in the
sides of a vessel ?
What does on this lateral pressure depend? What
phenomena are explained by it ?
[§ 141.] Do liquids of different specific gravi-
ties stand equally high in communicating vessels,
or tubes ? What law, then, is there for such
liquids?
If the two liquids are water and quicksilver, how
much higher will the water stand than the quicksilver ?
[$ 142.] When the surface of a liquid in a
vessel is perfectly horizontal, how is every portion
of it held up, or kept in its place? What pressure
does a liquid exercise upon a solid body immersed
in it? What general law is derived from it?
[$ 143.] How does the law you have just
named apply to a body which is immersed in a

EXERCISES IN CHAPTER IV.
229
liquid of the same specific gravity ? How does it
apply to a body whose specific gravity is greater
than that of the liquid ?: How, to a body whose
specific gravity is less than that of the liquid ?
How can you explain these three cases?
I$ 144.] Does the law you have just given for
solid bodies, apply also to liquids of different spe-
cific gravities? What takes place if several fluids
which have no chemical affinity for each other, be
poured together in the same vessel ?
Is this rule without exception? What are the cases
which are exempt from it?
Application of the foregoing Laws to the Deter-
mination of the Specific Gravities of Bodies.
[$ 145.] What is the name of the instrument
which is used for the determination of the specific
gravities of bodies? What does it consist of?
How is it used ? If the specific gravity of distilled
water is taken for unity of measure, how is the
specific gravity of a body found, when its absolute
weight, and its loss in distilled water, are known?
[§ 146.] Which are the principal cases that
can occur in the determination of specific gravi-
ties? How do you find the specific gravity of the
body in the first case ? How in the second ?
How in the third ? If, in the first case, the body
weighs 3 lbs. out of water, and its loss in water
is 2 lbs., what is its specific gravity? Again, if,
in the second case, a piece of wood weighs 15
lbs. out of water, and a piece of copper weighing
20

230
EXERCISES IN CHAPTER IV.
water 2
18 lbs. loses 2 lbs. when immersed ; if, further,
the compound mass of copper and wood loses 27
lbs. in water, what is the specific gravity of the
wood? Finally, if a piece of iron loses in distilled
2 lb. and in sea-water 37, what is the
specific gravity of the sea-water?*
[$ 147.] To what depth can a body, whose
specific gravity is less than that of water, be im-
mersed ? What takes place when it is forced
down deeper, and then left to itself again?
[$ 148.] Can the same body be immersed
equally deep in liquids of different specific gravi-
ties? In what fluid will it be immersed deepest?
What instruments are constructed on this principle ?
[$ 149.] How can bodies of greater specific
gravity than water, be made to float ?
What phenomena are explained by this principle?
What is the average specific gravity of the human
body? Why are fat men naturally good swimmers ?
[$ 150.] On what does the position of a float-
ing body depend? What is necessary in order
that the body shall remain in its position ? What
must be the position of a floating body, in order
to secure it from turning over ? What position
should the centre of gravity of a swimming body
have with regard to the surface of the water ?
[151.] When the weight of a cubic inch or foot
of distilled water is known, how can you find the
* The teacher may now give as many more examples as
he may think fit, or serviceable to his pupils.

EXERCISES IN CHAPTER IV.
231
absolute weight of a cubic foot of any substance,
when its specific gravity is known ?*
B. Pressure, Weight, and Equilibrium of Elastic
Fluids (Ærostatics.).
[$ 152.] What is the fundamental law for an
elastic fluid shut up in a vessel ?
[$ 153.) What will take place if the sides of
the vessel are not strong enough to resist the
pressure of the fluid within ?
[§ 154.] Can an elastic fluid escape from a
vessel, when the pressure of an elastic fluid with-
out is equal to that of the fluid within? What
will take place if the pressure of the elastic fluid
without is greater than that of the fluid within,
and the vessel is provided with an orifice? What,
if the pressure of the inner fluid is greatest ?
[$ 155.] What can every elastic fluid by pres-
sure be forced into? In what ratio do the density
and elasticity then increase? Is there no other
means of increasing the elasticity and density of
a fluid ? What is it?
[$ 156.] Is the degree to which elastic fluids
may be compressed, the same in all fluids? What
changes do some of them undergo, when com-
pressed ? Give an instance. What are those
fluids called, which, even during the greatest
* The teacher may give his pupils some examples from
the table of specific gravities, at the end of the volume.

232
EXERCISES IN CHAPTER IV.
pressure applied to them, retain their elastic
form?
Is it probable all elastic fluids may become liquid by
pressure ?
[$ 157.] What do you understand by absolute
and specific elasticity of fluids ? Can fluids of
different specific elasticities be in equilibrium
with each other? When does this take place ?
[S 158.] When an elastic fluid is attracted by
a liquid or solid body, what does it form? Why
must the density of the atmosphere be greater
near the attracting body, than further from it ?
[§ 159.] When an atmosphere is in the state
of rest, how is every particle of it kept in its
place?
[S 160.] But what must take place, when,
by some cause or other, either the elasticity or
density of the layers, or even the pressure of
the surrounding particles is changed ?
How do you call this motion, when occurring in our
own atmosphere ?t and what phenomena does it ex-
plain?
[S. 161.] How does heat affect all elastic fluids ?
How does heat affect the specific elasticity of
fluids?
Give examples of such effects produced by heat?
* By its own elasticity, which is in equilibrium with
the gravitating particles above.
† Ans. This motion is then called wind; which, accord-
ing to the direction in which it moves, is called North or
South, West or East wind. The whirl-wind is caused by
two currents of air moving in opposite directions,

EXERCISES IN CHAPTER V.
233
[$ 162.] When two or more elastic fluids are
placed upon one another, what respective positions
will they take? What laws apply here?
(The teacher may here ask his pupils to repeat the
laws of hydrostatics.)
EXERCISES IN CHAPTER V.
MECHANICAL PROPERTIES OF THE ATMOSPHERE.
[$ 163.] By what is our earth everywhere
surrounded ?
What experiments and facts convince you of the
existence of the atmosphere?
[§ 164.] What is the probable height of our
atmosphere? What kind of fluid is the air which
composes our atmosphere? Why is air an elastic
fluid ?
What experiments and facts can you adduce to
prove your assertion ?
[$ 166.] Does air, like the liquids spoken of
in the preceding chapter, obey the laws of gravity ?
What remarkable experiment proves this? and
how do you explain this experiment ?
Was this property of air known to the ancients ?
How then did they explain the phenomenon you
have just described ?
[$ 167.] What takes place if, in the last ex-
periment, the tube is 3 or 4 feet long? What im-
portant law do we derive from it?
What is the space between the quicksilver and the
closed end of the tube called ?
20*

234
EXERCISES IN CHAPTER V.
[$ 168.] If instead of quicksilver the tube be
filled with water, what is the height of the column
supported in the tube by the pressure of the at-
mosphere?
(Here the teacher might require the pupil to repeat
the hydrostatic law of § 141, page 72, and show its
intimate connexion with the law stated in this para-
graph.)
[$ 169.] What remarkable phenomenon does
this property, of air explain? What are the prin-
cipal parts of a sucking-pump? Explain their
operation.
What other phenomena does the same property of
atmospheric air explain?
[$ 170. What law follows from the elasticity
and gravity of the atmosphere ?
How is this law proved? Why is the pressure of
air in a room which communicates with the atmos-
phere, the same as that of the air without ?
(The teacher may again refer to § 158, page 79, and
require the repetition of it from the pupil.
[$ 171.] How does heat affect atmospheric
air ? If a portion of air is shut up in a vessel,
and then heated, is the pressure on the sides of
the vessel diminished or increased? What takes
place, if in this state, the vessel is provided with
an aperture ?
What takes place, if after expelling, in this manner,
a portion of air from a vessel, the vessel is suddenly
cooled down again? What, if the aperture of the
vessel is immersed in water?
[s 172.] Does air which is expanded by heat
remain in its place? What position, then, does
it assume? Why ?*
* See § 142.

EXERCISES IN CHAPTER V.
235
What phenomena can you explain by this principle ?
[$ 173.] By what means may all elastic fluids,
consequently, also, atmospheric air, be compress-
ed? How is this done?
What are the principal parts of a condensing ma-
chine? Explain their operations ? What remarkable
relation is there between the density of the compressed
air, and the degree of the compressing power ?
[$ 174.] What does a syphon consist of? If
a syphon is filled with water, and then inverted,
with the two open ends downwards, and held level
in this position, what takes place, when the legs
are equal ? What when these are unequal, or
when the syphon is inclined ?
Explain each of these cases.
How does the opera-
tion of the syphon affect the surface of a liquid in a
vessel, when the shorter leg of a syphon is immersed
in it, and the liquid is set a running from the other
(longer leg)? How must the syphon be situated, if
the whole basin shall be drained by it? What re-
markable phenomena does the theory of the syphon
explain?
[$ 175.] Is the pressure of the atmosphere
always the same at the same place? What ex-
periments convince us that it is not so? What
kind of instrument is a barometer? What is it
made of? How is it constructed ?
How can you compute the weight of the column of
quicksilver in the tube, which is equal to the pressure
of the atmosphere? What is the reason we do not
feel the pressure of the atmosphere?
[$ 176.] By what instrument can the different
mechanical properties of air be illustrated? What
are the principal parts of an air-pump? Explain
their operation ? How far can the rarefaction
of air in the receiver be carried ?

236
EXERCISES IN CHAPTER VI.
Is the vacuum created in the receiver of an air-pump
as perfect as that in the Torricellian tube? Why
not?
[$ 177.] What are the principal experiments
which can be made with an air-pump?
How can you explain them?
EXERCISES IN CHAPTER VI.
OF HEAT.
[§ 178.] What do the words heat and cold
designate?
What do you call bodies which produce in us the
sensation of heat or cold? Is it possible for us to
tell what body is absolutely cold or warm? What
then do our sensations of cold and warm tell us ?
[$ 179.] Do we know the principle or cause
by which all bodies are more or less capable of
producing degrees of heat? What is the opinion
of modern philosphers on this subject?
Means of Producing Heat.
[$ 180.] What are the four principal means
of producing heat ?
Give instances of heat produced by friction ; of heat
produced by chemical operations, and of great heat
produced by the light of the sun ?
[§ 181.] In what manner does heat affect the
volume of bodies?

EXERCISES IN CHAPTER VI,
237
What experiments can you mention to prove this
universal law ?
[$ 182.] Does heat expand all bodies in the
same degree? Which is expanded quickest, air,
liquids, or solid substances ?
[S 183.] Is the expansion of liquids and solids
proportional to the degrees of heat, or, in other
words, do equal degrees of heat produce equal
degrees of expansion, in liquid and solid sub-
stances ? How do elastic fluids differ, in this
respect, from liquids and solids ?
How can you account for these unequal degrees of
expansion by heat? What influence has the aggre-
gate form of liquids and solids on their expansion by
heat? Do the degrees of expansicn remain unequal,
after the body is transformed into vapor ?
[S 184.] What means have we to measure
degrees of temperature ? What is the instru-
ment used for this purpose called ? How is a
thermometer constructed ?
How many degrees of Fahrenheit's scale mark the
mean temperature of this country? Is Fahrenheit's
scale the only one now in use ? What other scales
are there? How many degrees of Fahrenheit are
equal to 1 degree of Réaumur? Is quicksilver the
only fluid used for the construction of thermometers ?
What means did Wedgewood employ to measure great
degrees of heat ?
Different Capacities for Heat.
[§ 185.] Does the same quantity of heat, im-
parted to two different substances, produce in
them the same degree of heat, when measured

238
EXERCISES IN CHAPTER VI.
with the thermometer ? To what do we ascribe
this difference? When do you call the capacity
of a body for heat greater than that of another
body? Give instances of different capacities for
heat ?
[S 186.] What means have we to ascertain
the different capacities of bodies for heat ? Give
an example?
What ratio does the capacity of water for heat bear
to that of quicksilver?
[S 187.] To what did Wilke, Crawford, Kir-
wan, Gadolin, and others, compare the capacities
of different substances for heat ? What did they
call these capacities?
(Here the teacher may explain or require tbe expla-
nation of Table II.)
[$ 188.] If there be such a self-existing prin-
ciple as caloric, does it exist in equal quantities
and densities in all bodies?
[$ 189.] What does every change in the rela-
tive position of the particles and interstices of a
body necessarily produce ? When is this particu-
larly the case? When a body absorbs great quan-
tities of heat without showing any difference of
temperature on a thermometer, what is the heat
which enters the body said to be? What is heat
said to be, when a body indicates a higher degree
of temperature, without receiving any additional
quantity of heat ?
What phenomena does this principle explain?
[S 190.] When two or more substances are
mixed together, is the resulting capacity of the

EXERCISES IN CHAPTER VI.
239
mixture always equal to the mean sum of their
capacities ?*
Give instances where this does actually take place ?
[S 191.] Is it probable that light, by striking
upon bodies, changes their capacity for heat?
What circumstances
to corroborate this
supposition ?
Give instances of this kind.
seem
Propagation of Heat.
[S 192.] Does heat pass through all bodies
with the same degree of velocity? Can you tell
me of an experiment which proves that heat does
not pass through all bodies with the same velocity ?
What are those substances called, which soonest
become hot when exposed to heat ?
[$ 193.] What bodies are the best conductors
of heat? What bodies (among solids) have the
least conducting power ?
What are the worst conductors among the cover-
ings of animals? What is this property probably
owing to? Why is snow a bad conductor of heat?
What remarkable phenomenon does this explain?
[S 194.] How is the imperfect conducting
power of some substances, taken advantage of ?
Why are furnaces surrounded by clay, trees by
*
By the mean sum is meant the arithmetic medium of
their capacities. Thus, if the capacity for heat is in one
body 3, and in another 5, the mean sum of their capacities
5+3
would be
4. Now if the resulting capacity is
2
more than 4, the mixture will absorb heat, consequently
produce cold.

240
EXERCISES IN CHAPTER VI.
straw, &c?
What is the use of double win-
dows in winter ?
[$ 195.] What bodies most effectually prevent
the admission of heat? What is the reason that
the air, which, under a thatched roof, is warmer
in winter, is yet cooler in summer, than the air
under a roof of tile or slate? Why does straw
keep the heat from an ice-house in summer, when
the same substance prevents a fig-tree from freez-
ing in winter ?
(The answer to the two last questions is the same,
viz. because the same substances which prevent the
escape of heat, are equally effectual in preventing its
admission.')
[$ 196.] How can you account for the different
sensations of heat which we have, when touching
different substances ? How must the best con-
ductors feel to the touch ? Why? Why does
iron feel colder than glass, and the latter colder
than wood, although all be in the same room, and
of the same degree of temperature?
[S 197.] In what direction do solid substances
conduct heat? What is this heat (conducted by
solids) called ?
[$ 198.] In what manner does a heated body
lose its heat, when exposed to the air ? What do
you understand by radiation of heat ?
What remarkable experiment can be made on this
subject ?
[$ 199.] Some natural philosophers are of
opinion that radiant heat moves with a velocity
equal to that of light; is this at all probable ?
What do we know about it with certainty ?

EXERCISES IN CHAPTER VI.
241
Is there no other way to account for the phenomena
of radiant heat, than by supposing them to be produced
by actual projections of caloric? What is Professor
Leslie's opinion on this subject ?
[$ 200.] What changes do solid bodies some-
times undergo, when exposed to great degrees of
heat? What do you understand by the melting
or fusing of solids? What takes place when still
greater degrees of heat are applied to these bodies?
In what consists the process of evaporation ?
[$ 201.] Is the degree of heat at which solid
bodies melt, the same in all substances ? On
what does it seem to depend? What effect does
heat produce on most solid bodies and liquids we
know of?
[S 202.] What do you call that process by
which a liquid is so quickly transformed into
steam, as to be thrown into an undulating motion ?
Why is the boiling of liquids a means of purifying
them ?
[$ 203.] Does the pressure of the atmosphere
facilitate, or is it a hindrance to the boiling of
liquids ? What general law is there with regard
to this pressure ?
What phenomena can you explain from this princi-
ple? What would be the state of many liquids, with-
out the pressure of the atmosphere ?
[S 204.] Can a boiling liquid be made to as-
sume higher degrees of heat? What becomes of
the heat which is further added ? Does the same
rule apply when the vessel is closed in such a
manner that the steam is prevented from passing
off? What is the steam which is thus shut up,
capable of exercising?
21

242
EXERCISES IN CHAPTER VI.
[$ 205.] What becomes of steam when its
temperature is reduced, or when some mechanical
pressure is applied to it? What do you call this
process?
[$ 206.] Can the formation of vapor or steam
take place without absorption of heat? How,
then, does this process affect the surrounding
bodies? What phenomena does this explain?
[S 207.] What does steam, which by a reduc-
tion of temperature, or by mechanical pressure,
begins to be decomposed, form in the surrounding
atmosphere? What name do these visible drops
which remain thus suspended in the atmosphere,
receive? When is such a fog or mist formed ?
[$ 208.] What effect does atmospheric air
continually produce on a certain portion of water ?
What do you call this process ? What is the
difference between it and the formation of steam ?*
Do we feel or perceive the immense quantity of
steam and vapor with which our atmosphere is
continually charged, as long as both are perfectly
elastic? What becomes of them when they are
either cooled down or condensed ?
[$ 209.] In what manner do steam and vapor,
which are not perfectly dissolved in the atmos-
phere, affect other substances? When in this
state they are sucked in or absorbed, what do
these substances, by the degree of their expansion,
indicate ?
* It is carried on much slower than the formation of
steam.

EXERCISES IN CHAPTER VI.
243
What instrument is constructed upon this principle ?
What is the hygrometrical substance in Saussure's
hygrometer? What is it in Lambert's ? What, in
De Luc's ?
[$ 210.] How are liquids affected when ex-
posed to certain degrees of cold? What is this
process called? What liquids have by this means
been reduced to the solid state ? Is the same
degree of cold required for the congelation of all
liquids ?
(Here the teacher ought to explain, or require the
explanation of Table IV. at the end of the book.)
[$ 211.] What takes place, if the process of
congelation is going on slowly, so that the parti-
cles of the liquids have time to follow their mutual
cohesive attraction ? What are the solids, which
are obtained in this manner, called?
[§ 212.] When .water is changed into ice,
what does it always receive ? Does its volume
become greater or smaller by freezing ? In what
ratio does it increase ?
What phenomena does this explain? How is water
affected by cold, as long as it remains liquid ? When
does it reach its greatest density ?
[$ 213.] What effect does heat produce on
chemical combinations ? What is every chemical
combination more or less accompanied with?

244
EXERCISES IN CHAPTER VII.
EXERCISES IN CHAPTER VII.
OF LIGHT.
[$ 214.] What opinions have been entertained
by philosophers, respecting the nature and propa-
gation of light?
[S 215.] What do you call the sensations
which luminous bodies produce in our eyes?
What do we, by these, become conscious of?
[§ 216.] What are all bodies, with regard to
light, divided into ?
What are the principal luminous bodies? What
other means are there of producing light?
[$ 217.] When does a dark body become visi-
ble? What is the light thus received, called ?
[$ 218.] When do you call a body transparent
or pellucid ? What bodies do you call opaque ?
What substances are generally pellucid or trans-
parent?
[§ 219.] What are light-magnets, or absorbers
of light?
Give instances of such bodies.
[$ 220.] Is all the light which falls upon dark
bodies reflected by them? Wbat do you call
those bodies which absorb light most? What
those which reflect it most ?
[$ 221.] How is light propagated ? With
what velocity ?
How can you prove that light is propagated in
straight lines? How has the velocity of light been
ascertained? Can the velocity with which light moves
upon our globe be measured ? Why not?

EXERCISES IN CHAPTER VII.
245
[$ 222.] If light is propagated in straight
lines, in what proportion must its intensity de-
crease ?
On what principle is this law established ?
[§ 223.] What do you understand by the term
refraction of light' ?
By what simple experiment can you illustrate this
principle ?
[S 224.] How is light affected when passing
near the surface, edges, or corners of bodies?
What is light in this case said to be ?
What does this phenomenon seem to prove ?
[S 225.] What takes place when light falls
upon an opaque body? Upon what does the mag.
nitude, shape, and position of the shade which an
opaque body casts behind it, depend?
1. Reflection of Light.
[$ 226.] When a ray of light strikes upon a
polished surface, either plane or curved, what law
does it follow ?
[§ 227.] What are those bodies which are
commonly used to reflect light, called? When
do you call a mirror plane, convex, or concave ?
What are the best reflectors ? Why must glass
mirrors be quicksilvered on one side ?
21*

246
EXERCISES IN CHAPTER VII.
A. Reflection of Light from Plane Mirrors.
[§ 228.] How does a luminous point before
the mirror appear to the eye?
How can you prove this?
[$ 229.] What is the point behind the mirror,
from which the rays of light seem to proceed,
called? Does the law which you have just found
for a luminous point, equally apply to a whole
object? How then will a whole object before the
mirror appear to the eye ?
B. Reflection of Light from Spherical Mirrors.
[$ 230.]. What is the principal law with re-
gard to an image produced by a luminous point
before a spherical concave mirror ? What is the
name of a straight line, drawn from the luminous
point through the centre of the arc of which the
mirror makes a part ?
How can you prove the correctness of this law by a
diagram?
[$ 231.] How are parallel rays reflected from
a concave mirror ?
When does this take place?
What is the point to which the rays of the sun
are reflected from a concare mirror, called? Why
does it receive this name? What law is there
with regard to diverging rays?
[$ 232.] On what does the distance of the
image from the mirror depend? What law can
you lay down respecting it?

EXERCISES IN CHAPTER VII.
247
(The elder pupils may here be required to draw
Figures I. and II. page 117.)
[$ 233.] Does the law, which you have just
found with regard to a luminous point, equally
apply to a whole object? Show me this by a
figure.
[$ 234.] In what case will the image of the
object be inverted ? In what case will it be
upright?
[$ 235,] How is the image produced by reflec-
tion from convex mirrors, situated with regard
to the object? Which of two convex mirrors
represents the same object, held at the same dis-
tance from it, larger than the other ?
[$ 236.] How can you explain the phenomena
of cylindrical and conical mirrors? In what
direction do these mirrors give the correct dimen-
sions of the object? How do the transversal di-
mensions of the object appear through them?
C. Refraction of Light.
1. General Observations.
ES 237.] When a beam of light passes from
one medium into another, what relation does the
angle of incidence bear to the angle of refraction ?
What is the ratio of the angle of incidence to the
angle of refraction between air and water?
[$ 238.] What relation exists between the
angle of refraction and the refracting power of the
transparent body?

248
EXERCISES IN CHAPTER VII.
What belief has heretofore existed, with regard to
the refracting power of bodies? What have modern
experiments proved on this subject?
2. Refraction of Light in a Body bounded by Plane
and Parallel Surfaces.
[§ 239.] What takes place when a ray of light
falls perpendicularly upon a transparent body,
bounded by plane and parallel surfaces?
[$ 240.) What takes place when parallel rays
fall obliquely upon a transparent body?
If the emerging rays pass through a second and
third transparent body, how will the rays then be sit-
uated with regard to each other? Give instances of
this kind ?
[S 241.] What takes place when diverging
rays fall upon a transparent body, bounded as
before?
(The elder pupils may here be required to draw
Figs. I. II. III. and IV. pages 121, 122, and 123.)
What phenomena can you explain from the princi-
ples which you have just advanced ?
3. Refraction of Light through Bodies bounded by
Spherical Surfaces (Lenses).
[S 242.] What do you call a piece of glass,
having on one or both sides a spherical form ?
How many different kinds of lenses are there?
What are they?
[S 243.] What are the principal properties of
convex lenses ?

EXERCISES IN CHAPTER VII.
249
[$ 244.] What are the phenomena produced
by còncave lenses?
[S245.] What are the effects produced by
a meniscus, or a concavo-convex lens, similar to ?
D. Theory of Colors.
[S246.] What do you understand by the solar
or prismatic spectrum ?: By what means is it
obtained ?
[$ 247.] Is the magnitude of the spectrum the
same, whatever be the substance chosen for the
prism? What are these substances, therefore,
said to possess ?
[S 248.] When the light of each color of the
spectrum is separately let fall upon a second
prism, is there any difference found in the degree
of refraction of the seven colors ? Why is there
none ?
What are the abovementioned seven
colors on this account called ? What is the white
light from which they are obtained, called ?
[$ 249.] What takes place when the prismatic
spectrum is made to fall upon a lens or concave
mirror, by which they are refracted into a
focus ?
[S 250.] What takes place when another
prism, formed like the first, and made of the same
substance, is brought in contact with the former ?
[$ 251.] What takes place when the angle of
the second prism is not equal to the angle of the
first prism?

250
EXERCISES IN CHAPTER VII.
[$ 252.] To what conclusions do the experi-
ments you have just described entitle you ?
By whom were these experiments first made ?
[$ 253.] In how many different ways can you
explain these phenomena, according to the theory
of Sir Isaac Newton ? How can you explain the
same phenomena, according to the theory of Young
and Leonhard Euler ?
What phenomena in nature are explained from those
you have just described ?
[S 254.] Is it possible for a certain medium
to refract light more than another, and yet to have
a less dispersive power ? What optical instru-
ments are constructed upon this principle ?
What celebrated English optician first discovered
that flint and crown-glass have different dispersive
powers? What do you call flint-glass? What, crown-
glass? In what manner must flint and crown-glass
be combined together, in order that the dispersive
power of the flint-glass may correct that of the crown-
glass? What other means is there for bending the
rays of different colors with great regularity, and with-
out dispersion from their rectilinear course ?
[S 255.] How can you explain the infinite va-
riety of colors exhibited by different bodies, when
exposed to solar light, according to Sir Isaac
Newton's theory? How can you explain them
according to Euler's theory?
[S 256.] What property, possessed by some
bodies, explains the blue hue of the atmosphere,
the effect of colored glasses, &c? By what other
means can you render bodies transparent? When
does the stone called hydrophane become trans-
parent ?

EXERCISES IN CHAPTER VII.
251
[§ 257.] What must take place when the
chemical properties of a body are so changed, that
it affects light differently from what it did before?
By what other means can you change the color of
bodies ? What processes in the mechanic arts
depend upon this principle ?
E. Of Vision.
1. The Eye.
[S 258.] What is the form of the human eye?
Of how many coats or membranes does it princi-
pally consist ?
What are these ?
[$ 259:] Where is the sclerotic coat situated ?
Where the cornea ? Of what does the cornea
consist? What is it intended for ? Where is the
choroid coat situated? With what is it covered ?
Where is the retina situated ?- What is the centre
of the retina ?
[S 260.] How is the interior part of the globe
of the eye divided ? What is the iris? What is
the pupil of the eye? When does the pupil ex-
pand itself?
When does it contract ? What
does the space before the iris, or the anterior
chamber of the eye, contain ? What is the space
behind the iris called ? What does it contain ?
IS 261.] How is the crystalline lens suspend-
ed? How is this lens shaped ? Of what does it
consist? What is this lens destined for? Where
is the vitreous humor situated ?

252
EXERCISES IN CHAPTER VII.
2. Vision.
[$ 262.] What are the most important parts
of the eye? How is the retina impressed with
the image of the object before the eye? On what
depends the clearness of sight?
[$ 263.] What are the different humors of the
eye destined for? How would we see all things,
without these humors ?
[S 264.] Can the eye see clearly a distant
object and a near one at the same time? Why
not? What then will always take place?
[$ 265.] When do you call a person near-
sighted ? when long-sighted? Where, in a near-
sighted person, is the image of a distant object
situated? What is its situation in a long-sighted
person? What kind of spectacles are suited to
near-sighted persons ? What kind are suited to
long-sighted persons ?
[S. 266.] How do the images of the objects
before the eye appear on the retina ? Does this
alter the relative position of these images? Why
not? Do we become conscious of this inversion
of the images ?
[S_267.] What do you understand by the
visual angle? What relation does the image on
the retina, and consequently, also, the appearance
of the object itself, bear to this visual angle ?
When does an object become invisible ? When
the visual angle is very small, what is necessary,
in order that we may see the object? Give an
instance of this kind ?

EXERCISES IN CHAPTER VII.
253
IS 268.] What relation does the distance of
the object bear to the magnitude of the visual
angle? Do we become conscious of the distance
of an object by mere vision ?
Give instances of this kind. How then do we judge
of the distance of an object?
E. Optical Instruments.
[$ 269.] What are the names of the principal
optical instruments now in use ? Describe the
camera obscura or darkened chamber. Describe
a modification of the same instrument, used by
painters to delineate landscapes ? Describe the
camera lucida, invented by Dr Wollaston. What
does the single microscope consist of? How is
the compound microscope constructed ? Describe
the astronomical telescope; the terrestrial telescope.
What does the reflecting telescope consist of?
By whom was the reflecting telescope, which you
have just described, invented ? Wherein consists the
advantage of the reflecting telescope over the refract-
ing telescope ?
What is the construction of the solar microscope ?
What are the uses of the solar microscope ? How is
the magic lantern constructed ?

254
EXERCISES IN CHAPTER VIII,
EXERCISES IN CHAPTER VIII.
OF ELECTRICITY.
A. Phenomena.
[$ 270.] What takes place when a piece of
sealing-wax or a smooth surface of glass is briskly
rubbed with a dry woollen cloth, and immediately
afterwards held towards light and small bodies,
such as paper, thread, cork, &c? What do you
call this property which some bodies acquire by
being rubbed ?
What do you call the surface,
which thereby acquires an attractive and repulsive
power? What do you call the bodies themselves,
which produce these phenomena? What the
agent to which they are ascribed ?
What are the principal electrics? Why is the
division of bodies into electrics and non-electrics no
longer practicable ?
[$ 271.] What takes place, if the experiments
which you have just described are performed in a
darkened room? What, if the knuckle or a round
metallic ball is presented to the surface? What
kind of feeling is excited in the skin, if the face
is brought near it?
[$ 272.] What takes place, when a metallic
tube, perfectly round on all sides, and either sus-
pended by silk cords, or supported by a piece of
glass or sealing-wax, is brought near or in contact
with an excited surface ? What is the body, in
the first case, said to be? What, in the second
case? Do glass, silk, and sealing-wax, brought
in the same manner near or in contact with the
excited surface, exhibit the same influence ?

EXERCISES IN CHAPTER VIII.
255
[§ 273.] What are we, from this and similar
experiments, led to infer? What are conductors
of electricity ? What, non-conductors ?
What are the principal conductors of electricity ?
What are the principal non-conductors ?
IS 274.] When is a body, which is capable of
conducting electricity, said to be insulated ?
In what does the difference between a conductor
and a non-conductor principally consist ?
[S 275.] What relation exists between elec-
trics and non-electrics, conductors and non-con-
ductors of electricity ?
[$ 276.] Is the electricity communicated by
transfer to an insulated metallic body, for any
considerable time permanent ? What becomes
of its electricity when it is touched by a conduct-
ing body which communicates with the earth?
IS 277.] What is the proper shape for a body
which shall contain electricity for a considerable
time? Why is a pointed figure unfit for this pur-
pose ?
[$ 278.] What are the principal parts of an
electrical machine ?
How is the best machine for this purpose con-
structed ?
[$ 279.] When you present the knuckle or
any round conductor to the conductor of an
electrical machine, what do you obtain? What
do you call this spark? What is the greatest dis-
tance at which a spark may be drawn, called ?
What is necessary to produce these phenomena to
their fullest extent ? Are the sparks near the con-
ductor greater or smaller than further from it ?

256
EXERCISES IN CHAPTER VIII.
B. Opposite Electricity.
[$ 280.] To whom are we indebted for the
discovery of opposite electricity ? On what phe-
nomena and experiments is it established?
[$ 281.] What laws do these experiments estab-
Tish ?
[S 282.] What did Du Fay call these two
kinds of electricity? By what signs is it custom-
ary to denote resinous and vitreous electricity ?
How may the general law of opposite electricity
then be expressed ?
When the rubber of an electrical machine is also
provided with a conductor, what kind of electricity
will this conductor exhibit? What will be the elec-
tricity of the prime conductor ?
[$ 283.] Does the law, which you have just
given, hold only of excited electricity, or does it
also hold true of that electricity which is trans-
ferred from an excited surface to another body?
How may this be shown by little pith-balls ?
w
[S 284.] What are the names of the instru-
ments whose construction is founded upon the
repulsive power which one electrified body exer-
cises upon another, which is under the influence
of the same electricity ?
How is Henley's electrometer constructed? What
other advantage is taken of the attractive and repulsive
power of opposite electricities?
[§ 285.] What takes place when a piece of
metal, shaped in the form of an S, and pointed at
both ends, is placed upon a pointed wire, which
communicates with either of the conductors of an

EXERCISES IN CHAPTER VIII.
257
electrical machine? What is observed when this
experiment is performed in the dark? When are
the electric phenomena generally accompanied by
light?
C. Theory of Electricity.
[$ 286.] How many different theories are there
to account for the various phenomena of elec-
tricity? Who are the authors of these theories !
What is Du Fay's theory? What properties do
the two electric fluids, which according to Du
Fay's theory, pervade the earth and all bodies,
possess ?
How does Du Fay's theory explain the vitreous
electricity, excited by rubbing a piece of glass? How,
the attraction which is manifest between two insulated
bodies, charged with different electricities? How, the
repulsion between two insulated bodies, under the
influence of the same kind of electricity ?
To what agency did Dr Franklin ascribe all
electric phenomena ? How are the electric phe-
nomena then explained?
D. Electrical Instruments.
[$ 287,] Are there any other electrical instru-
ments besides the electrical machine, deserving
of our notice? What are they ?
[$ 288.] What does an electric jar or Leyden
phial consist of? What do you call the knob of
the phial?
22*

258
EXERCISES IN CHAPTER VIII.
[§ 289.] What takes place when the knob is
brought in contact or communicates with the
prime conductor of an electrical machine? What
is the phial in this state said to be ?
Can the phial be charged by connecting the knob
with the negative conductor of the machine ; that is,
with the conductor of the electricity of the rubber
What kind of electricity will thus be imparted to the.
inner coating ? What do you obtain, if the knob, in-
stead of touching the conductor of the machine, is
brought within its striking distance? What, if the
phial is insulated, and the knuckle or any round con-
ductor is presented to the outer coating ? Can an
insulated phial be charged ?
[S 290.] By what means can prodigious quanti-
ties of electricity be accumulated? When several
electric jars or phials are connected together,
what name do they receive? What is necessary
to establish, for this purpose, between the inner
and outer coatings ? When a communication is
established between the inner and outer coatings,
how is the whole battery then charged ?
[$ 291.] How is an electric jar or battery
discharged ? What instrument is used for this
purpose ? What does this instrument (the dis-
charging rod) consist of? How is a discharge of
a phial or battery effected by it? What is this
discharge accompanied by ? What is the use of
the glass handle, with which every discharging
rod is provided ?
[§ 292.] What is necessary in order to con-
vey a whole charge of electricity through any
substance or person ?
By what means can a number of persons receive the
electric shock at the same time?

EXERCISES IN CHAPTER VIII.
259
[§ 293.] By what instrument can a charge
of electricity be directed with the greatest cer-
tainty and precision ? What does Henley's Uni-
versal Discharger consist of? How is a direct
charge. sent through a body by means of this
instrument?
[$ 294.] What is the name of an apparatus
for collecting weak electricities? By whom was it
invented? What are its principal parts? What
is the electric ? How is the electric combined
with the sole ? What does the cover of the elec-
trophorus consist of? How must all parts of the
electrophorus be shaped, in order to prevent the
escape of electricity ?
[S 295.] By what is the cake of the electro-
phorus first excited ?
What kind of electricity
will it by these means receive? What kind of elec-
tricity do the upper and lower surface of the cover
acquire, when placed upon the excited cake ?
What takes place, when in this state the upper
(negative) surface is touched by the knuckle, or
any metallic conductor, that communicates with
the earth ? If the cover is now removed by its
insulating handle, with what kind of electricity is
it found to be charged ? What can be done with
this electricity? How many times may this ope-
ration be repeated ?
How long does the electricity of the cake continue ?
Does the cover exhibit any sign of electricity when
it is raised without previously receiving a spark from
some conducting substance? Why not? In what
case can a spark be drawn from the sole? What is
felt, if, while the cover is on the cake, the sole is
touched with one finger, and the cover with another?

260
EXERCISES IN CHAPTER VIII.
[$ 296.] What kind of instrument is a con-
denser ? By whom was it invented? Of what
does it consist? What is the mutual operation of
the plates, when one of them is connected with
an excited substance? How long does the mutual
action and reaction of the two plates of the con-
denser continue ? If the plate which is connected
with the electrified substance, is now separated
from it, and, thus insulated, removed also from
the other plate, with what is it found to be
charged ?
E. Motion of Accumulated Electricity.
[$ 297.] What kind of bodies does the elec-
tric fluid always choose on its passage? What
passage does it choose, when several passages are
opened to it through equally good conductors ?
Is a person, holding a piece of wire in his hands,
affected by the discharge of a Leyden phial? What
will he feel if a piece of dry wood is substituted for
the wire? When accumulated electric fluid passes
through the human body, is the shock felt in the
whole body, or only 'in certain parts? In what line
are the parts, affected by the shock, situated ? If a
charge of electricity is sent through a number of
persons, who take each other by the hand, how and
where will each of them feel the shock? By what
means can the shock be made to pass in different
directions ?
[$ 298.] Has the velocity with which electri-
city moves through a conductor, been, as yet,
ascertained ? How is the electric shock felt in a
circuit of 4 miles ?

EXERCISES IN CHAPTER VIII.
261
[S 299.] How is the velocity of the electric
fluid affected, when it meets with an impediment
to its passage, either in a bad conductor, or in the
inadequate size of it? What is the electric fluid,
in this case, frequently observed to do?
[S 300.] What is observed when the metallic
passage, offered to a stream of electricity, is inter-
rupted by small pieces of glass or other non-
conducting substances ?
What phenomena does this peculiarity in the motion
of accumulated electricity explain?
F. Effect of Electricity on Bodies.
[$ 301.] Does the simple accumulation of
electricity in bodies, produce the least perceptible
change in their properties?
Is a person, standing on an insulating stool, and in
this state charged with any quantity of electricity from
a machine, in any manner affected by it, before a spark
is drawn from him ? Does the electric fluid spread
through the whole substance of a body, or does it
merely accumulate upon its surface ?
[S 302.] Does the uninterrupted passage of
electricity through a conductor of sufficient size,
produce any perceptible change in its properties?
But what takes place when a charge of electricity
is sent through a non-conductor, or through a
conductor of insufficient magnitude !
[$ 303.] What are the mechanical effects of
electricity on non-conductors, which are in the
line of its course, similar to ? To what other
agent are many of the effects of electricity at
tributed ?

262
EXERCISES IN CHAPTER VIII.
G. Of the Electricity of the Atmosphere.
[$ 304.] With what is our atmosphere almost
continually charged ? Is the quantity in which
electricity exists in the atmosphere, always the
same ?
Is it always of the same (positive or
negative) kind? Is it stronger in daytime, or
during the night? During what hours of the day
is it strongest? When is it weakest ?
[$ 305.] With what kind of electricity is
the air generally charged in clear weather ?
When does it change from the positive to the
negative state ? On what occasions do these al-
ternate states of electricity follow each other with
surprising rapidity ?
By what means may the electricity with which the
air is charged, be discovered ? By what means may
the electricity of higher strata of air be investigated?
[$ 306.] Who first proved by actual experi-
ment the identity of the electric fluid with that of
lightning?
(The teacher might here ask for the occasion which
led Dr Franklin to this discovery.)
[$ 307.] In what manner may buildings be
secured from the effect of lightning ? What
ought to be the thickness of the rods, which are
to be placed upon the highest parts of the build-
ings they are to protect? How far ought they to
be continued ?
What metal is preferable to iron for the construction
of lightning-rods? Why? Why ought the points of
the lightning-rods to be gilt, or be made of platina ?
Why do large buildings require several rods to protect
them against the effects of lightning ?

EXERCISES IN CHAPTER IX.
263
EXERCISES IN CHAPTER IX.
OF GALVANISM.
[308.] Are there, besides friction, any other
means of producing electricity? What are they?
Do different degrees of temperature affect the con-
ducting power of water?. At what degree of tempe-
rature does ice cease to be a conductor, and become
an electric ? Are there any other substances upon
which changes of temperature produce similar effects ?
Give instances of this kind. What kind of stone is
the Tourmaline? What property does this stone ac-
quire by heat ?
[$ 309.] What is that science called, which
treats of the electric phenomena produced by
contact ? Who is the author of Galvanism ?
[$ 310.] What are the two principal facts on
which the whole theory of Galvanism is estab-
lished ?
[$ 311.] What are the effects produced by
Galvanism on the human body?
Is the sensation of light, produced by the contact of
different metals, felt also by other individuals, or
merely by him who performs the experiment? What
phenomena are explained by the effects of Galvanic
electricity on the body ?
[S 312.] How does the influence of Galvanic
electricity, on the bare nerves and muscles of dead
animals, become manifest ? Are cold blooded an-
imals, or quadrupeds and birds most affected by
Galvanic electricity ?
Describe Galvani's experiment with the bare leg of
a frog ? What takes place when, in this experiment,

264
EXERCISES IN CHAPTER IX.
What care
the zinc and silver are connected by a conductor, say
a piece of wire ? Is the same phenomenon produced,
when a piece of glass is substituted for the wire ?
[$ 313.] By what apparatus can the electricity
produced by contact be much increased, and ren-
dered visible ? Who is the inventor of this appa-
ratus ? Of what does it consist ?
must be taken in its construction ? What are the
ends of the Voltaic pile called?
What metal may be substituted for silver in the
construction of a Galvanic pile? If the pile is to pro-
duce the desired effect, of how many plates ought it,
at least, to consist? By what means can the conduct-
ing power of the cloth or card be increased ?
[$ 314.] When several Voltaic piles are con-
nected with each other, what are they said to
form? By what means is this connexion effect-
ed? What are the two extremities of the battery
called ?
[$ 315.] What are the most remarkable ex-
periments that can be made with the Voltaic pile
or battery?
[$ 316.] What is the most remarkable modern
discovery on the subject of Galvanic electricity ?
If instead of separating each pair of plates of a
Voltaic pile by a piece of wet card or cloth, a liquid
(a saline solution) is employed, what is the apparatus
so constructed, called ? Describe such an apparatus.
Is the chemical operation of the Trough-Battery greater
or less than that of a simple Galvanic pile? Have
any attempts been made to construct Voltaic piles
without the assistance of liquids ? Of what do such
piles then consist? How long does the effect of such
piles continue ? What do you know about their
chemical operation? Can you describe the perpetuum
mobile which is constructed by means of two such
piles? How does it operate ?

EXERCISES IN CHAPTER IX.
265
Theory of Galvanic Electricity and the Voltaic
Pile.
[$ 317.] How many different kinds of con-
ductors of electricity are there? What are they?
What bodies are the principal exciters of electri-
city? Do you recollect a series of metals, in
which each receives + E when combined with
one that precedes it, but — E, when combined
with one which comes after it ?
What kind of conductors did Prof. Erman of Berlin
lately discover? Which kind of electricity does dry
soap conduct ? Which does it insulate ? What kind
of electricity does the flame of phosphorus conduct?
Which does it insulate? Can a Galvanic pile be dis-
charged with a uni-polar conductor of electricity ?
What then can such a conductor be used for ?
[§ 318.] How do the different properties of
exciters and mere conductors of electricity enable
you to explain the operation of the Voltaic pile ?
(3.)* Is the electricity of the pile increased or
diminished, when the lowest copper plate commu-
nicates with the floor? What takes place when
the pile is insulated ? (4.) What takes place
when both poles of the pile communicate with the
earth? (5.) What is formed, when the two poles
of the pile communicate with each other by some
conducting substance, for instance a piece of
wire ?
How do those philosophers, who believe in the ex-
istence of two distinct electric fluids, account for the
* The questions marked (3), (4), (5), refer to page 184,
3, 4, 5.
23

266
EXERCISES IN CHAPTER X.
phenomena of the Voltaic pile ? How is the conduct-
ing liquid affected by the agency of the pile? How
are the plates themselves affected? Do the effects of
the Voltaic pile become weaker or more energetic, as
the process of oxidation is going on more rapidly?
Organic-Electric Phenomena.
[$ 319.] What property is possessed by a
certain kind of fish ? What are the shocks,
which are felt when they are touched at two dif-
ferent parts of their bodies, similar to ? Do these
fishes affect an electrometer, or has it been pos-
sible, as yet, to draw any sparks from them?
Can you tell the names of the fishes which belong
to the kind you have just described ?
[$ 320.]' When do these fishes lose the power
of producing shocks ? What is the reason of it ?
EXERCISES IN CHAPTER X.
OF MAGNETISM.
[S 321.] What peculiar property is possessed
by certain pieces of black iron-oxid? What are
these pieces called? Can the power of attracting
iron be communicated to other iron or steel?
What is a piece of iron or steel which has thus
received the power of a magnet, called ?

EXERCISES IN CHAPTER X.
267
[S 322.] Are there, besides iron, any other
metals which participate in the magnetic proper-
ties? What are all bodies, according to modern
discoveries, susceptible of ?
In what parts of the world are native magnets
found?
A. Relation of native Magnets to unmagnetic Iron.
[$ 323.] What metals adhere to native magnet
with considerable force ?
How can this power be measured ? Does this power
depend on the size of, and is it always the same in one
and the same magnet ?
[$ 324.] Does the magnetic power operate in
all points of the surface of a magnet with equal
intensity? How many places are there, in which
its attractive powers are greatest ?
What are
these places called ?
How can they be made visible? What position
will a thin piece of iron have, at the poles of the mag-
net? What position will it have in the middle ?
What, in any other place of its surface ?
[$ 325.] Is the magnetic attraction increased
or diminished, when both poles are made to ope-
rate at the same time?
What shape is, on this account, generally given to
artificial inagnets?
[$ 326.] Is the attractive power of magnet
manifest only in contact, or does it operate, also,
at considerable distances ? What general law
does, in this repect, apply also to the magnet?

268
EXERCISES IN CHAPTER X.
[$ 327.] What takes place, when a native
magnet is placed under a plate of glass, wood,
paste-board, or even metal, which is thinly covered
with iron-filings?
What does this experiment prove ?
[$ 328.] How may the power of a magnet be
preserved, or even increased ?
Does oxidation increase or diminish the attractive
power of magnet? What effect has heat upon it?
B. Relation of a Magnet to itself, and to another
Magnet.
[$ 329.] When a magnet is so situated that it
can freely move in an horizontal position, in what
determined direction does it always place itself?
What is this wonderful property of the magnet
called ?
What all-important instrument is constructed upon
this property of the magnet? Was this property
known to the ancients ?
[$ 330.] Does the attraction which exists be-
tween a magnet and unmagnetic iron, exist also
between two magnets? What law is there with
regard to the respective poles of two magnets ?
How can this law be exhibited? What are the two
poles which mutually attract each other, called ?
What are those poles called, which seem to repel each
other?

EXERCISES IN CHAPTER X.
269
Imparting of Magnetism.
[S 331.] How many different methods are
there of making artificial magnets? What are
they?
[§ 332.] Explain the method of single touch :
(1.) With one magnet only. (2.) Explain the
same operation, when two magnets are employed.
(3.) What is the most effectual way of communi-
cating magnetism by the single touch?
[S 333.] Explain the method by double touch.
[$ 334.] Explain the method by percussion.
Why is it best (in the method by percussion) to
hammer the steel-bars upon soft iron or steel, in pre-
ference to wood, or any other substance ?
[$ 335.) What is the general law observed in
making artificial magnets, by any method what-
ever?
Which is easier magnetised —-soft iron, or steel?
In which is the magnetic power more permanent?
[$ 336.] Does the magnet, which is employed
in magnetising a steel bar, lose much of its own
power? Can one and the same magnet be em-
ployed for magnetising several bars? What is
the name of an apparatus, formed by the combina-
tion of a number of such bars?
[$ 337.] In what state is a piece of iron, as
long as it is attached to a magnet? What is it, in
this state, said to be? Does the magnetic power
* The signs (1), (2), (3), refer to 190, 1st, and 191, 20
and 3d.
23
来
​
270
EXERCISES IN CHAPTER X.
thus acquired, continue after the magnet is re-
moved from it?
[$ 338.] What is the law of magnetic attrac-
tion similar to ? What pole does the south pole
of a magnet excite in the end of an iron bar,
which is in its immediate neighborhood? What,
in that end which is most remote from it? What
state of magnetism, therefore, does each pole
communicate to the neighboring iron ?
[$ 339.] What inference have some philoso-
phers drawn from the similarity between the laws
of electricity and magnetism ?
What did Aepinus suppose all magnetic phenomena
to proceed from? How, then, did he account for the
magnetic phenomena ? How do Wilke and Brugman
explain the magnetic phenomena ?
Of the Variation and Dip of the Magnetic Needle.
IS 340.] When an unmagnetic iron needle
is poised in its centre, upon a sharp point, so that
its position is perfectly horizontal, and it is after-
wards magnetised, what position will it then, in
most places, assume ? What is the deviation from
due north called? What, the inclination to the
horizon ?
TE
[$ 341.] How many degrees westward of due
north does the north pole of the compass deviate
in England, and throughout Europe? Do these
deviations remain always the same? What is
the line in which the compass points exactly

EXERCISES IN CHAPTER X.
271
north, called ? What are the deviations beyond
this line ?
What does the line of no deviation seem to form ?
Through what countries does it pass? Into what is
the whole earth by this line divided ? Which way
does the compass deviate, in the first hemisphere?
Which, in the second ?
[$ 342.] What is the most remarkable phenom-
enon accompanying the variation of the compass ?
How far do the western deviations increase ?
When do they begin to diminish? Which way
do they increase after becoming zero ?
Through what part of the world did the line of no
deviation go in the 17th century ? What are the suc-
cessive, but slow deviations of the compass to the west-
ward and eastward, similar to ?
[$ 343.] What other remarkable phenomenon
deserves to be noticed? What is the diurnal mo-
tion of the magnetic needle?
By whom was this gradual motion of the compass
first discovered? What agent has a powerful influ-
ence on this motion? What kind of needles must be
used for this experiment?
[$ 344.] Is the dip of the magnetic needle the
same in all parts of the globe ? What general
rule can you give respecting the dip of the mag-
netic needle ? In what line are those places at
which there is no dip, situated? What is this line
called ?
[$ 345.] Does the magnetic equator coincide
with the equator of the earth ? How then is it
inclined to the earth's equator? In how many
points does it cut the terrestrial equator ?

272
EXERCISES IN CHAPTER X.
Magnetism of the Earth.
[$ 346.] What did many philosophers of emi-
nence consider our whole globe to be? Why?
How can you illustrate the operation of terrestrial
magnetism?
[$ 347.] Is it probable that a fixed, limited
magnet exists in the centre of the earth ? How
then do you account for the magnetism of the
earth?
If there are large masses of magnet scattered in
the interior of our globe, by what will their combined
effect be more or less influenced? What does this
explain ?
[$ 348.] If our earth contains large magnetic
masses in its centre, what must become of all the
iron in its vicinity? What phenomena would,
by this supposition, be explained ?
[$ 349.] What important fact must be ascribed
to the operation of terrestrial magnetism? Is the
magnetic power, acquired through the influence
of terrestrial magnetism, permanent ?
By what other means can iron instruments become
magnetic ? What phenomena does this explain?
Intensity of Magnetism.
[$ 350.] In what manner does a magnetic
needle move, when it is brought out of its natural
position, and then let free again? What are we
able to estimate, by the velocity of these vibra-
tions ?

EXERCISES IN CHAPTER X.
273
What important law did La Place discover, respect-
ing the intensities of the magnetic power in two
different places?
[$ 351.] What other remarkable fact, strongly
corroborating the hypothesis of terrestrial mag-
netism, results from the observations of Alexander
von Humbolt ?
Is the intensity of magnetism subjected to the same
local disturbances as the magnetic needle ?
Modern Discoveries in Magnetism.
[$ 352.] What intimate connexion is, by mod-
ern discoveries, proved to exist between electricity
and magnetism? What facts can you adduce, to
establish the truth of this assertion ?
Does the magnetism, imparted to a needle by elec-
tric sparks, increase with the number of sparks? On
what, then, does its maximum depend ?
[$ 353.] What remarkable experiment was
first made by Prof. Seebeck, on the subject of the
influence of heat upon magnetism? If, in the
experiment you have just described, antimonium
be substituted for bismuth, what results will then
be obtained ?
Are bismuth and antimonium the only metals which,
combined with copper and then heated, produce de-
viations of the magnetic needle ?
[$ 354.] What influence of light on magnetism
did Marochini, in Rome, first discover ? Were
similar results obtained by any other person? By
whom?

274
EXERCISES IN CHAPTER X.
What rays are without magnetic effect ?
What
rays produce magnetic polarity? Which rays produce
the least, and which the greatest polarity? In what
manner must the needles be prepared, and how long
must they remain exposed to the influence of the rays,
before they exhibit magnetic polarity? In how many
minutes is the same result obtained in the focus of a
burning-glass? What part of the needle becomes
the north pole? Does the light of the moon or of a
lamp produce similar effects ?

TABLES.
275
TABLE I.
Specific Gravities of Bodies, compared to Distilled
Water.
.
66
66
.
a
Ivory
Alcohol, highly rec- Mercury, at 60°
tified
0.809 Fahrenheit . 13.58
Blood
1.053 Nickel, cast 8.279
Camphor
0.988 Platinum
21.47
Chalk
2.657 Silver
10.47
Diamond (Oriental) 3.521 hammered. 10.51
(Brazilian) 3.444 Steel, soft
7.833
Ether
0.866 66 hardened 7.840
Flint
2.582 Tellurium, from
Crown-Glass
2.5201
5.700 to 6.115
Flint-Glass, from Tin
7.291
2.760 to 3.000 Zinc, from 6.900 to 7.191
Gunpowder, loose 0.836
solid 1.745
Wood.
Indigo
1.009
Apple-tree
0.793
Isinglass
1.111
Beech
0.852
1.825
Brazilian, Red 1.031
Limestone, from
Cedar, American 0.561
2.386 to 3.000
Cherry-tree
0.715
Marble
2.716
Cork
0.240
Ebony, American 1.331
Metals.
Elm
0.671
Antimony
6.702 Lignum Vitae 1.333
Arsenic
: 5.763 Mahogany . 1.063
Bismuth
9.880 Maple
0.750
Brass, from 7.824 to 8.396 Oak
1.170
Cobalt
: 8.600 Olive-tree
0.927
Copper.
8.900 Orange-tree
0.705
Gold, cast
19.25 Pear-tree
0.166
Gold, hammered
19.35 Poplar
0.383
Iron, cast
7.248 Vine
1.327
Iron, bar-hammered 7.778 Walnut
0.681
Lead
11.35 Willow
0.585
Manganese
8.000 Wood-stone, from
2.045 to 2.675

276
TABLES.
TABLE II,
Exhibiting the Specific Caloric contained in some Sub-
stances, compared to the quantity of Caloric contained
in an equal Weight of Water.
Gases and Liquids.
Metals.
.
.
Oxygen
Azote
Water
Air
Hydrogen Gas
Carbonic Acid
Aqueous Vapor
.
0.2361 Bismuth
0.2754 Lead
1.0000 Gold
0.2669 Platinum
3.2936| Tin
0.2210 Silver
0.8470 Zinc
Tellurium
Copper
Nickel
Iron
Cobalt
Sulphur
0.0288
0.0298
0.0298
0.0314
0.0514
-0.0557
0.0927
0.0912
0.0949
0.1005
0.1100
0.1498
0.1880
TABLE III.
Boiling Points.
Ether
Alcohol
Nitric Acid
Water
Sea Salt solution)
Muriate of Lime
Muriatic Acid
Nitric Acid
Oil of Turpentine
Linseed Oil
Mercury
100° Fahr.
1731
210
212
2243
230
232
240
316
640
656

TABLES.
277
TABLE IV,
Exhibiting the Degree of Temperature at which various
Liquids congeal, or freeze.
.
Sulphuric Ether
Nitric Acid
Sulphuric Acid
Mercury
Brandy
Pure Prussic Acid
Strong Wines
Oil of Turpentine
Blood
Vinegar
Milk
Water
460
45.5
45
39
7
+ 4
20
14
25
+ 28
+ 30
+30
TABLE V,
Showing the Refractive Power of several Substances ;
that of atmospheric Air being taken for Unity.
.
•
Diamond
2.755 Horn
1.565
Melted Sulphur 2.148 Resin
1.559
Sulphate of Lead
1.925 Turpentine
1.557
Sapphire, blue
1.794 Amber
1.547
white 1.768 Oil of Tobacco 1.547
Glass
1.732 Plate Glass
1.514
Topaz, Brazil. 1.640 Colophony
1.543
Mother of Pearl . 1.653 Beeswax
1.542
Oil of Cassia 1.641 Gum of Tragacanth 1.520
Castor
1.626 Gum Arabic . 1.502
Tortoise-Shell 1.591 | Oil of Caraway-seed 1.491
.
.
.
24

278
TABLE OF REFRACTIVE POWERS.
.
.
66
.
Castor Oil
1.490 Ice.
Camphor
1.487 | Atmospheric Air
Oil of Turpentine 1.475 Oxygen
Oil of Lavender. 1.462 Hydrogen
Camomile 1.457 Azote
Fluor Spar
1.434 Chlorine
Alcohol
1.372 Nitrous Gas .
White of Eggs. 1.361 Oxid of Carbon
Ether
1.358 Carbonic Acid
Crystalline Lens of Muriatic Ether
the human Eye 1.384 Sulphurous Acid
1.308
1.000
0.924
0.470
1.020
2.623
1.030
1.157
1.526
3.720
2.260
.
THE END

THE FOLLOWING WORKS, BY THE AUTHOR OF THIS
VOLUME, ARE PUBLISHED BY
CARTER AND HENDEE,
BOSTON.
ARITHMETICAL AND ALGEBRAIC PROBLEMS AND FOR-
MULÆ Translated from the last German Edition of MEIER
HIRSCH, and adapted to the Use of American Students. By F. J.
GRUND, Author of "A Treatise on Plane and Solid Geometry.'
In 1 vol. 12mo.
AN ELEMENTARY TREATISE ON GEOMETRY. Simplified
for Beginners not versed in Algebra. Part I. Containing PLANE
GEOMETRY, with its Application to the Solution of Problems. By
FRANCIS J. GRUND. Second Edition.
[Popular education, and the increased study of Mathematics, as the
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" The book under consideration has, we think, effected its object.
The lessons are well graduated and explained. The threshold of every
science has usually presented a stumbling block to the feet of youth,
and before they have felt the high gratification, which accompanies
the more advanced researches in mathematics, they have fallen into
the common error, and pronounced the science a dull and uninteresting
We think these · First Lessons' have removed the stumbling
bleck. The definitions are simple and accurate, and the questions
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trated afterwards; the sectional division of the work is judicious, and
the recapitulation of the truths established in each section is original
and exceedingly useful. The problems are unusually numerous, and
well calculated to call forth a practical application of all the principles
that have previously been inculcated. The author has confined him-
self to Plane Geometry, as the title of his book indicates, but we think
the public will not let him stop here. Simplicity, freedom from mys-
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“Mr Grund’s Geometry unites, in an unusual degree, strictness of
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suited to form habits of exact reasoning in young beginners, and to
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text-book in my own school.” — George B. Emerson, Principal of
the English Classical School, Boston.
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young scholars.” — F. P. Leverett, Principal of the Public Latin
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AN ELEMENTARY TREATISE ON GEOMETRY. Simplified
for Beginners not versed in Algebra. Part II. Containing SOLID
GEOMETRY, with its Application to the Solution of Problems. By
FRANCIS J. GRUND.
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be well adapted to the wants of academies and schools. Jacob Abbott.
[At a meeting of the School Committee of the city of Boston, Mr
Grund's Geometry was recommended as a suitable book to be used in
the Public Schools. Similar testimonies to the merits and usefulness
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66





Coll & ok 17885
6-8-73
CZ
1832
Gri
Grund, Francis T.
= (Francis Joseph)
WILLIAM L. CLEMENTS
LIBRARY OF
AMERICAN HISTORY
UNIVERSITYOF MICHIGAN