The Baldwin Library
PLATE l
ee
PRIMARY COLORS.
Beacon Lith.Co. Bost)
INTRODUCTION
PHYSICAL SCIENCE.
BY
A. P. GAGE, Pa.D.,
Instructor IN Puysics, ENeLisH Hie Scuoox, Boston, AND
AUTHOR oF ‘‘ ELEMENTS oF PHysics.â€
BOSTON, U.S.A.:
GIN Al & COMPANY, PUBLISHERS.
1894. :
Entered according to Act of Congress, in the year 1887, by
A. P. GAGE,
in the Office of the Librarian of Congress, at Washington.
TYpocRarHy BY J. 8. CusHine & Co., Boston.
PRESSWORK BY GiINN & Co., Boston.
*
AUTHOR’S PREFACE.
— +2
An experience of about six years in requiring individual
laboratory work from my pupils has constantly tended to
strengthen my conviction that in this way alone can a pupil
become a master of the subjects taught. During this time
I have had the satisfaction of learning of the successful
adoption of laboratory practice in all parts of the United
States and the Canadas; likewise its adoption by some of
the leading universities as a requirement for admission. Mean-
time my views with reference to the trend which should be
_ given to laboratory work have undergone some modifications.
The tendency has been to some extent from qualitative to quan-
| titative work. With a text-book prepared on the inductive plan,
_ and with class-room instruction harmonizing with it, the pupil will
scarcely fail to catch the spirit and methods of the investiga-
- tor, while much of his limited time may profitably be expended
in applying the principles thus acquired in making physical
measurements.
A brief statement of my meted of conducting laboratory
exercises may be of service to some, until their own experience
has taught them better ways. As a rule, the principles and
laws are discussed in the class-room in preparation for subse-
quent work in the laboratory. ‘The pupil then enters the labo-
ratory without a text-book, receives his note-book from the
teacher, goes at once to any unoccupied (numbered) desk
containing apparatus, reads on a mural blackboard the ques-
tions to be answered, the directions for the work to be done
‘with the apparatus, measurements to be made, etc. Having
performed the necessary manipulations and made his observa-
iv AUTHOR’S PREFACE.
tions, he surrenders the apparatus to another who may be ready
to use it, and next occupies himself in writing up the results
of his experiments in his note-book. These note-books are
deposited in a receptacle near the door as he leaves the labo-
ratory. Nothing is ever written in them except at the times
of experimenting. These books are examined by the teacher ;
they contain the only written tests to which the pupil is sub-
jected, except the annual test given under the direction of the
Board of Supervisors. Pupils, in general, are permitted to com-
municate with their teacher only. ‘‘Order, Heaven’s first
law,†is absolutely indispensable to a proper concentration of
thought and to successful work in the laboratory.
Only in exceptional cases, such as work on specific gravity
and electrical measurements, has it been found necessary to
duplicate apparatus. The same apparatus may be kept on the
desks through several exercises, or until every pupil has. had
an opportunity of using it. Ordinarily two pupils do not per-
form the same kind of experiment at the same time. With
proper system, any teacher will find his labors lighter than
under the old elaborate lecture system; and he will never have
occasion to complain of a lack of interest on the part of his pupils,
I venture to hope, in view of the kind and generous reception
given to the Elements of Physics, that this attempt to make
the same methods available in a somewhat more elementary
work may prove welcome and helpful. It has been my aim
in the preparation of this book to adapt it to the requirements
and facilities of the average high school. With this view, I
have endeavored to bring the subjects taught within the easy
comprehension of the ordinary pupil of this grade, without.
attempting to ‘‘ popularize†them by the use of loose and |
unscientific language or fanciful and misleading illustrations |
and analogies, which might leave much to be untaught in after |
time. Especially has it been my purpose to carefully guard |
against the introduction of any teachings not in harmony with |
the most modern conceptions of Physical Science.
AUTHOR’S PREFACE. Vv
I would here acknowledge, in a very particular manner, my
obligations for invaluable assistance rendered by Dr. C. S.
Hastings, Professor of Physics in the Sheffield Scientific School,
New Haven, Conn., and Prof. S. W. Holman, of the Massa-
chusetts Institute of Technology, both of whom have care-
fully read all the proof-sheets. It would, however, be highly
improper to attribute to them in any measure responsibility
for whatever slips or inaccuracies may have crept into these
pages. lam also under obligations for valuable suggestions and
criticisms received from the veteran educator, Prof. B. F. Tweed,
of Cambridge, Mass.; George Weitbrecht, High School, St.
Paul, Minn.; John F. Woodhull, Normal School, New Paltz,
N.Y.; Robert Spice, Professor of Physics in the Technological
Institute, Brooklyn, N.Y. ; C. Fessenden, High School, Napance,
Ont.; A. H. McKay, High School, Pictou, N.S.; and F. W.
Gilley, High School, Chelsea, Mass.â€
CONTENTS.
CHAPTER I.
Matter, energy, motion, and force. — Attraction of gravitation.—
Molecular and molar forces
CHAPTER II.
Dynamics of fluids. —Pressure in fluids. —Barometers. — Com-
pressibility and elasticity of gases. — Buoyancy of fluids. —
Density and specific gravity . :
CHAPTER III.
General dynamics. — Momentum, and its relation to force. — Three
laws of motion. —Composition and resolution of forces. —
Center of gravity. — Falling bodies. — Curvilinear motion. —
EBhespendulumer we wean ee rs aie meer ay es
CHAPTER IV.
chines .
CHAPTER V.
Molecular energy, heat.—Sources of heat. — Temperature. —
Effects of heat. — Thermometry. — Convertibility of heat. —
' Thermo-dynamics.—Steam-engine .... .;
PAGE
1
29
67
Work and energy. — Absolute system of measurements. — Ma- |
98
121
vili CONTENTS.
CHAPTER VI.
Electricity and magnetism. — Potential and electro-motive force.
— Batteries. — Effects produced by electric current. — Elec-
trical measurements. — Resistance of conductors. —C.G.8.
magnetic and electro-magnetic units. — Galvanometers. —
Measuring resistances. — Divided circuits; methods of
combining voltaic cells.— Magnets and magnetism. — Cur-
rent and magnetic electric induction. —Dynamo-electric ma-
chines. — Electric light. — Electroplating and electrotyping.
— Telegraphy. — Telephony. — Thermo-electric currents. —
Static electricity. — Electrical machines .
CHAPTER VII.
Sound. — Study of vibrations and waves. — Sound-waves, veloc-
ity of; reflection of; intensity of; reénforcement of; inter-
ference of. — Pitch. — Vibration of strings. — Overtones and
harmonics. — Quality. — Composition of sonorous vibrations.
— Musical instruments. — Phonograph.— Ear. . . .
CHAPTER VIII.
PAGE
238
Radiant energy, ether-waves, light. — Photometry. — Reflection of -
light-waves. — Refraction. — Prisms and lenses. — Prismatic
analysis. — Color.— Thermal effects of radiation. — Micro-
scope and telescope. —Eye.—Stereopticon. . .....
APPENDIX: A, metric system; B, table of specific gravity; C,
table of natural tangents; D, table of specific resistances
NID EXE promi pe says pare «k= tera es aa eSATA Uno A a eee
281
341
349
_ INTRODUCTION TO PHYSICAL SCIENCE.
¢ Nature is the Art of God.†— Tuomas Browne.
CHAPTER If.
MATTER, ENERGY, MOTION, AND FORCE.
Section I.
MATTER AND ENERGY.
To tHE Tuacner:— That portion of this book which is printed tn the
larger type, including the experiments, is intended to constitute in itself a tolerably
full and complete working course in Physics, The portion in fine print may,
therefore, be wholly omitted without serious detriment; or parts of it may
be studied at discretion as time: may permit; or, perhaps still better, it
may be used by the student, in connection with works of other authors,
as subsidiary reading. It should be borne in mind that recitations from
“memory of mere descriptive Physics and Chemistry is of little educational
value. : ;
: To tz Purr: — “Read nature in the language of experimentâ€;
_that is, put your questions, when possible, to nature rather than to per-
“sons. “Teachers and books may guide you as to the best methods of
procedure, but your own hands, eyes, and intellect must acquire the
knowledge directly from nature, if you would really know.
_ 1. Matter. — Physics including Chemistry, may for the
present purposes at least be regarded as the science of mat-
ter and energy. The question, What is matter? is appar-
ently a very simple one, and easy to answer. One of the
first answers that will occur to many is, Anything that
can be seen is matter.
2. Is Matter ever Invisible ? — We are usually able to
Tecognize matter by seeing it. We wish to ascertain by
2 MATTER, ENERGY, MOTION, AND FORCE,
experiment, 7.2. by putting the question to nature, whether
matter is ever invisible. Now in experimenting there
must (1) be certain facts of which we are tolerably cer-
tain at the outset. These facts (2) lead us to place things
in certain situations (the operation is called manipulation)
in order to ascertain what results‘will follow. Then, in
the light of these results we (8) reason from the things
previously known to things unknown, i.e. to facts which we
_ wish to ascertain.
For example, we are certain that we cannot make our
two hands occupy the same space at the same time. All
Fig. 1. : Fig. 2. ,
experience has taught us that no two portions of matter can
occupy the same space at the same time. This property |
(called impenetrability) of occupying space, and not only.
occupying space, but excluding all other portions of matter!
from the space which any particular portion may chance |
to occupy, is peculiar to matter; nothing but matter,
possesses it. This known, we have a key to the solution
of the question in hand.
MATTER AND ENERGY. 3
There is something which we call air. It is invisible.
Ls air matter? Is a vessel full of it an “empty†vessel
as regards matter ?
Fig. 3.
Experiment 1. Thrust one end of a glass tube to the bottom of
a basin of waters blow air from the lungs through the tube, and
watch the ascending bubbles. Do you see the air of the bubbles, or
do you see certain spaces from which the air has excluded the water?
4 MATTER, ENERGY, MOTION, AND FORCE,
Is air matter? Is matter ever invisible? State clearly the argument
by which you arrive at the last two conclusions.
Experiment 2.— Float a cork on a surface of water, cover it with
a tumbler (Fig. 1) or a tall glass jar (Fig. 2), and thrust the glass
vessel, mouth downward, into the water. (In case a tall jar is used,
the experiment may be made more attractive by placing on the cork
a lighted candle.) State what evidence the experiment furnishes
that air is matter.
Relying upon the impenetrability of air, men descend in diving-bells
a (Fig. 3) to considerable depths
in the sea to explore its bot-
tom, or to recover lost prop-
erty.
Observe the cloud (Fig. 4)
formed in front of the noz-
zle of a boiling tea-kettle.
All the matter which forms
the large cloud escapes from
the orifice, yet it is invisible
at that point, and only be-
comes visible after mingling
with the cold outside air.
Place the flame of an alcohol
Fig. 4, lamp in the cloud; the matter
again becomes nearly or quite invisible in vicinity of the flame. True
steam is never visible. Here we see matter undergoing several changes from
the visible to the invisible state, and vice versa.
3. Matter, and only gt iter: has Weight.
Has air |
weight 2 |
Experiment 3.— Suspend from a scale-beam a hollow globe, a |
(Fig. 5), and place on the other end of the beam a weight, 6 (called a
counterpoise), which just balances the globe when filled with air in |
its usual condition. Then exhaust the air by means of an air-pump, |
or (if the scale-beam is very sensitive) by suction with the mouth. |
Having turned the stop-cock to prevent the entrance of air, replace |
the globe on the beam, and determine whether the removal of air —
has occasioned a loss of weight. If air has weight, what ought to k
MATTER AND ENERGY. 5
be the effect on'the scale-beam if you open the stop-cock and admit
air? Try it. Can matter exist in an invisible state? How does
nature answer, this question in the last experiment?
‘4, Energy.— Bodies of matter may possess the ability
to put other bodies of matter in motion; eg. the bended
bow can project an arrow, and the spring of a watch when
closely wound can putin motion the machinery of a watch.
Ability to produce motion is called energy. Nothing but
matter possesses energy. Does air ever possess energy ?
Fig. 5. Fig. 6.
Experiment 4:— Put about one quart of water into vessel A
(Fig. 6), called a condensing-chamber. Connect the condensing-
syringe B with it, and force a large quantity of air into the portion
of the chamber not occupied by water; in other words, fill this
portion with condensed air: Close the stop-cock C, and attach the
tube D as in the figure. Open the stop-cock, and a continuous stream
of water will be projected. to a great hight.
Experiment 5.— Remove any water which may remain, and again
condense air in the chamber. Connect the chamber by a rubber tube
with the nipple a of the glass flask (Fig. 7). Place a little water in
‘the neck of the flask, so as to cover the lower orifice of the rotating
6 MATTER, ENERGY, MOTION, AND FORCE.
bulb B. Slowly and carefully open the stop-cock. The escaping air
will cause the bulb B to rotate for a long time.
AB You will not attempt to say what
=— _ matter zs... This, no one knows. You
may, however, give a provisional
(answering the present needs) defini-
tion of matter, z.e. draw the limiting
line between what is matter and what
is not matter.
5. Minuteness of Particles of Mat-
ter. —If with a knife-blade you scrape
off from a piece of chalk (not from a_
3 blackboard crayon, for this is not chalk) |
ss a little fine dust, and place it under a.
Fig. 7. microscope, you will probably discover
is that what seen with the naked eye
appear to be extremely small, shapeless particles, are
really clusters or heaps of shells and corals more or less
broken. Figure 8
represents such a
cluster. Each of
these shells is sus-
ceptible of being
broken into thou-
sands of pieces.
Reflecting that Fig. 8.
one of these clus-
ters is so small as to be nearly canieables you will readily
conceive that if one of the shells composing a cluster
should be broken into many pieces, and the pieces sepa:
rated from one another, that they would be invisible to
the naked eye. Yet the smallest of the particles into
MATTER AND ENERGY. q
which one of these shells can be broken by pounding or: *
grinding is enormously large in comparison with bodies
called molecules, which, of course, have never been seen,
but in whose existence we have the utmost confidence.
(For definition and further discussion of the molecule, see
Chemistry, page 4.)
6. Theory of the Constitution of Matter. — For reasons.
which will appear as our knowledge of matter is extended,
physicists have generally adopted the following theory of
the constitution of matter: Hvery body of matter except the
molecule is composed of exceedingly small particles, called
molecules. No two molecules of matter in the universe
are in permanent contact with each other. Every molecule
is in quivering motion, moving back and forth between its
neighbors, hitting and rebounding from them. When we
heat a body we simply cause the molecules to move more
rapidly through their spaces; so they strike harder blows
on their neighbors, and usually push them away a very
little ; hence, the body expands.
7. Porosity.— If the molecules of a body are never
in contact except at the instants of collision, it follows
that there are spaces between them. These spaces are
called pores.
Water absorbs air and is itself absorbed by wood, paper, cloth, etc. It
enters the vacant spaces, or pores, between the molecules of these substances.
All matter is porous; thus water may be forced through the pores of cast
iron; and gold, one of the densest of substances, absorbs liquid mercury.
8. Volume, Mass, and Density.— The quantity of space
a body of matter occupies is its volwme, and is expressed
in cubic inches, cubic centimeters, etc. The quantity of
matter in a body is its mass, and is expressed in pounds,
1 References in this book are made to the Introduction to Chemical Science, by R. P.
Williams.
8 MATTER, ENERGY, MOTION, AND FORCE.
* ounces, kilograms, grams, etc. If you cut blocks of wood,
potato, cheese, lead, etc., of the same size and weigh them,
you will find their weights to be very different. From
this you infer that equal volumes of different substances
contain unequal quantities of matter. Those which con-
tain the greater quantity of matter in the same volume
Fig. 9. . Fig. 10.
are said to be denser than the others. By the density of
a body is meant its mass in a unit of volume; hence it can
be expressed only by giving both the units of mass and the
unit of volume. For example, the density of cast iron is
4.2 ounces per cubic inch, or 7.2 grams per cubic centi-
meter; the density of gold is 11 ounces per cubic inch, or
19.4 grams per cubic centimeter. Which of these two
metals is the denser?
MATTER AND ENERGY. 9
9. Three States of Matter.
Experiment 6.— Take a thin rubber foot-ball containing very lit-
tle air, close the orifice of the ball so that air cannot enter or escape,
place it under the receiver of an air-pump (Fig. 9), and exhaust the
air from the receiver. The air within the ball constantly expands
until the ball is completely inflated (Fig. 10).
We recognize three states or conditions of matter, viz.,
solid, liquid, and gaseous, fairly represented by earth,
water, and air. Every day observation teaches us that
solids tend to preserve a definite volume and shape; liquids
tend to preserve a definite volume only, their shape conforms
to that of the containing vessel; gases tend to preserve neither
a definite volume nor shape, but to expand indefinitely.
Liquids and gases in consequence of their manifest ten-
dency to flow are called fluids. Even solids possess the
property of fluidity to a greater or less extent when under
suitable stress. Bodies also exist in intermediate condi-
tions between the solid and liquid, and liquid and gase-
ous, so that there is no distinct limit between these states,
_and the distinctions given above are merely conventional
_ (e. growing out.of custom).
Which of the three states any portion of, matter assumes depends upon
_ its temperature and pressure. Just as at ordinary pressures of the atmos-
: phere water is a solid (i.e. ice), a liquid, or a gas (@.e. steam), according to
_ its temperature, so any substance may be made to assume any one of these
_ forms unless a change of temperature causes a chemical change, 7.¢. causes
_ it to break up into other substances. For example, wood cannot be melted,
because it breaks up into charcoal, steam, etc., before the melting-point is
reached. In order that matter may exist in a liquid (and sometimes in a
_ solid) state, a certain definite pressure is required. Ice vaporizes, but does
not melt (i.e. liquefy) in a space from which the air (and consequently
_ atmospheric pressure) has been removed. Iodine and camphor vaporize,
_ but do not melt unless the pressure is greater than the ordinary atmos-
_ pheric pressure. Charcoal has been vaporized, but has never been lique-
fied, undoubtedly because sufficient pressure has never been used.
As regards the temperature at which different substances assume the
10 MATTER, ENERGY, MOTION, AND FORCE.
different states, there is great diversity. Oxygen and nitrogen gases, or
air, — which is a mixture of the two,—liquefy and solidify only at
extremely low temperatures; and then, only under tremendous pressure.
On the other hand, certain substances, as quartz and lime, are liquefied
only by the most intense heat generated by an electric current.
Section II.
RELATIVE MOTION AND RELATIVE REST.
10. What constitutes Relative Motion and Relative
Rest ? — Two boys walk toward each other, or one boy
stands, and another boy walks either toward or from him;
in either case there is a relative motion between them,
because the length of a straight line (which may be imag-
ined to be stretched) between them constantly changes.
One boy stands, and another boy walks around him in a
circular path; there is a relative motion between them,
because the direction of a straight line between them
constantly changes. There is relative rest between two.
boys while standing, because a straight line between them
changes neither in length nor direction. Two boys while
running are in relative rest so long as neither the distance
nor the direction from each other changes.
QUESTIONS.
. What is wind? Give some evidence that it possesses energy.
. Give a provisional definition of matter.
. What is energy?
. What is an experiment? What is manipulation?
. What is an air-bubble? What important lesson does a mere.
bubble teach ?
OUR Cc be
FORCE. 11
6. What is impenetrability? State several properties that are
peculiar to matter.
7. Can water be rendered invisible? How?
8. Under what conditions would a flock of birds over your head be
at rest with reference to your body? Would the birds which com-
pose the flock be at rest with reference to one another? An apple
rests upon a table; are its molecules at rest?
9. Why do all moving bodies possess energy? Do all molecules
possess energy?
10. A span of horses harnessed abreast are drawing a street car on
a straight, level road. Is there any relative motion between the two
horses? Between the horses and the carriage? Between the team
and objects by the wayside? Suppose them to be travelling in a, cir-
cular path; is there relative motion between the horses?
11. A boat moves away from a wharf at the rate of five miles an
hour. A person on the boat’s deck walks from the prow toward the
stern, at the rate of four miles an hour; what is his rate of motion, i.e.
his velocity, with reference to the wharf? What is his velocity with
reference to the boat?
12. When is there relative motion between two bodies?
Section ILI.
FORCE.
11. Pushes and Pulls. — We are familiar with the
results of muscular force in producing motion. We are
also aware that there are forces, or causes of inotion, quite
independent of man; eg., the force exerted by wind,
running water, and steam. If we observe carefully, we
shall find that all motions are produced by pushes or pulls.
It is evident that there can be no push or pull except be-
tween at least two bodies or two parts of the same body.
12 MATTER, ENERGY, MOTION, AND FORCE.
Commonly, the bodies between which there is a push or
a pull are either in contact, as when we push or pulla
table, or the action is accomplished through an intermedi-
ate body, as when we draw some object toward us by
means of a string, or push an object away with a pole.
Can two bodies push or pull without contact and without
any tangible intermediate body; i.e. is there ever “action
at a distance†?
Experiment 7.— Fill a large bowl or pail with water to the brim.
Place on the surface of the water a half-dozen (or more) floating mag-
nets (pieces of magnetized sewing-needles thrust through thin slices
of cork). Hold a bar magnet vertically over the water with one end
near, but not touching, the floats; the floats either move toward or
away from the magnet. Invert the magnet, and the motions of the
floats will be reversed.
Notwithstanding there is no contact or visible connection between
the floats and the magnet, the motions furnish
conclusive evidence that there are pushes and
pulls. The motions are said to be due to mag-
netic force.
Experiment 8.— Suspend two pith balls by
silk threads. Rub a large stick of sealing-wax
with a dry flannel, and hold it near the balls.
The balls move to the wax as if pulled by it,
and remain in contact with it for atime. Soon
they move away from the wax as if pushed away.
Remove the wax; the balls do not hang side
Fig. 11. by side as at first, but push each other apart
(Fig. 11). These motions are said to be due to electric force. —
———
12. How Force is Measured. — Pulling and pushing
forces may be strong or weak, and are capable of being
measured. The common spring balance (Fig. 12) is a
very convenient instrument for measuring a pulling force.
As usually constructed, the spring balance contains a spiral
coil of wire, which is elongated by a pull; and the pulling
FORCE. 18
force is measured by the extent of the elongation.
may be so constructed that an elongated
coil may be compressed by a pushing force;
and when so constructed it serves to measure
a pushing force by the degree of compression.
All instruments that measure force, however
constructed, are called dynamometers (force-
measures). Observe that force is measured in
pounds; in other words, the unit by which force
is measured is called a pound.
183. Equilibrium of Forces.
Experiment 9.— Take a block of wood; insert two stout screw-
eyes in opposite extremities of the block. Attach a spring balance to
each eye. Let two persons pull on the spring balances at the same
time, and with equal force, as shown by their indexes, but in opposite
directions. The block does not move. One force just neutralizes the
_ other, and the result, so far as the movement of the block, i.e. the body
acted on, is concerned, is the same as if no force acted on it. When
one action, i.e. one push or pull, opposes in any degree another
action, each is spoken of as a resistance to the other. Let f represent
the number of pounds of any given force, and let a force acting in
any given direction be called positive, and indicated by the plus (+)
sign, and a force when acting in an opposite direction to a force
_ which we have denominated positive, be called negative, and indicated
_by the minus (—) sign. Then if two forces +fand —/ acting on a
_ body at the same point or along the same line are equal, the result is
_ that no change of motion is produced.
Viewed algebraically, +/f—/= 0; or, correctly interpreted, + f—f=
_ (is equivalent to) 0, i.e. no force. In all such cases there is said to
be an equilibrium of forces, and the body is said to be in a state of equi-
librium. If, however, one of the forces is greater than the other, the
excess is spoken of as an unbalanced force, and its direction is indi-
_ cated by one or the other sign, as the case may be. Thus, if a force
_ of + 8 pounds act on a body toward the east, and a force of — 10 pounds
act on the same body along the same line toward the. west, then the
unbalanced force is —2 pounds, i.e. the result is the same as if a
force of only 2 pounds acted on the body toward the west.
-14 MATTER, ENERGY, MOTION, AND FORCE.
14. Stress, Action, and Reaction; Force Defined. —
An unbalanced force always produces a change of motion.
As there are always two bodies or two parts of a body con-
cerned in every push or pull, there must be two bodies or
parts of a body affected by every push or pull. When the
effects on both parties to an action are considered with-
out special reference to either alone, the force is fre-
quently called a stress. But when we consider the effect
. on only one of two bodies, we find it convenient, and
almost a necessity, to speak of the effect as due to the
action of some other body, or, still more conveniently, to an
external force. The body which acts upon another, itself
experiences the effect of the reaction of the same force.
We may say, provisionally, that force is that which tends
to produce or change motion. Bringing a body to relative
rest is changing its rate of motion and requires force.
This definition of force conveys no idea of what force ts;
it merely distinguishes between what is force and what is
not force. :
QUESTIONS,
1. Give a provisional definition of force. In what two ways is it
exerted ?
2. How is motion produced? Destroyed? Changed in any way?
8. How many bodies or parts of a body must be concerned in the
action of any single force? How many are affected thereby?
4. What effect does an unbalanced force produce on a body?
5. How must the magnitude of two forces compare, and in what
directions must they act with reference to each other, that they may be
in equilibrium ?
6. When is a body in equilibrium ?
7. In what units is force estimated? In what units is mass esti-
mated? What force is required to support 10 pounds of sugar?
What is the common way of judging of the mass of a body?
ATTRACTION OF GRAVITATION, 15
8. Why will not a force of 10 pounds raise 10 pounds of sugar ?
If the force produces no change of motion, how can it consistently be
called a force?
9. A bullet is flying unimpeded through space; does it possess
energy? Is it (disregarding the force of gravity) exerting force?
Would it exert force if it should encounter some other body? Which
produces motion, energy or force? Which denotes ability to produce.
‘motion ?
—c0=0j00—
Section IV.
ATTRACTION OF GRAVITATION.
_ 15. Gravitation is Universal. — An unsupported body
falls to the earth. This is evidence of an action or stress
between the earth and the body. It has been ascertained
by careful observation that when a ball is suspended by
a long string by the side of a mountain, the string is
not quite vertical, but is deflected toward the mountain in
consequence of an attraction between the mountain and
he ball. That there is an attraction between the sun
and the earth, and the earth and the moon, is shown, as
we shall see. further on, by their curvilinear motions.
ides and tidal currents on the earth are due. to the
ttraction of the sun and the moon.
This attraction is called gravitation ; the force is called
gravity. When bodies under its influence tend to ap-
proach one another, they are said to gravitate. Since
this attraction ever exists between all bodies, at all dis-
ances, it is called universal gravitation.
16. Law of Universal Gravitation.— Methods too
fficult for us to comprehend at present have estab-
16 MATTER, ENERGY, MOTION, AND FORCE.
lished the fact that the strength of the attraction between
any two bodies depends upon two things; wz., their
masses, and the distance between certain points within
the bodies (to be explained hereafter), called their cen-
ters of gravity. The following law is found everywhere
to exist : —
The attraction between every two bodies of matter in the
universe varies directly as the product of their masses, and
inversely as the square of the distance between their centers
of gravity. Representing the masses of two bodies by
m and m’', the distance by d, and the attraction by g,
this relation is expressed mathematically, thus: g«
!
(varies as) ae For example, if the mass of either body.
is doubled, the product (mm!) of the masses is doubled,
and consequently the attraction is doubled. If the dis-
tance between their centers of gravity is doubled, then
2
ie = i) the attraction becomes one-fourth as great.
The mass of the moon is very much less than that of the earth; hence
the force of gravity at the surface of the former is much less than at the/
surface of the latter. A person who could leap a fence three feet high on.
the earth, could, by the exertion of the same muscular energy, leap a fence!
18 feet high on the moon. A boy might throw a stone a greater distance
on the moon than a rifle can project a bullet on the earth. The masses of]
Jupiter and Saturn, being so much greater than that of the earth, the!
corresponding greater attraction which they would exert would so impede
locomotion that a person would be able only to crawl along as though his,
feet were weighted with lead.
17. Weight.— We say that all matter has weight,
meaning that there is an attraction between the earth and
all kinds of matter. We say that the weight of a certain
body is ten pounds, meaning that this is the measure of.
the force of attraction between this body and the earth.
ATTRACTION OF GRAVITATION. 17
From the law of gravitation we infer that at equal dis-
tances from the earth’s center of gravity the weight of
bodies varies as their masses. Hence, when we weigh a body
we measure at the same time both the force with which
the earth attracts it and its mass; and both quantities
are commonly expressed in units of the same name. The
expression four pounds of tea conveys the twofold idea
that the quantity of tea is four pounds, and that the force
‘with which the earth attracts the tea is four pounds.
_ Again, we infer from the law of gravitation (1) that
a body weighs more at a given point on the surface of the
earth than at any point above this point.
(2) That inasmuch as some points on the earth’s sur-
face are nearer its center of gravity than others, the same
body will not have the same weight at all points on the earth's
surface. A given body stretches a spring balance less as
it is carried from either pole toward the equator. The
loss of weight due to the increase of distance from the
center of the earth is s4, of its weight at the poles.
18. Point of Maximum Weight. — There is no defi-
ite law which determines the change in the weight of a
ody when carried below the surface of the earth. Ob-
ervation has shown that at first a body increases in
eight slowly, in consequence of its approach to the
earth’s center of gravity. But at some undetermined
epth, in consequence of an increase of density of the
arth toward its center, the increase of weight must
ease; and at this point, consequently, a body has its
axzimum weight. From this point onward to the center
f gravity of the earth, a body will lose in weight as much as
would if it were being transferred to smaller and smaller
arths. '
18 MATTER, ENERGY, MOTION, AND FORCE.
QUESTIONS.
1. If the earth’s mass were doubled without any change of volume,
how would it affect your weight?
2. On what principle do you determine that the mass of one body
is ten times the mass of another body?
3. How many times must you increase the distance between the
centers of two bodies that their attraction may become one-fourth?
4. If a body on the surface of the earth is 4,000 miles from the
center of gravity of the earth, and weighs at this place 100 pounds,
what would the same body weigh if it were taken 4,000 miles above |
a earth’s surface? |
. The masses of the planets Mercury, Venus, Earth, and Mars are |
sy very nearly as 7, 79, 100, and 12; assuming that the dis-
tance between the centers of the first two is the same as the distance |
between the centers of the last two, how would the attraction between |
the first two compare with the attraction between the last two?
6. What would be the answer to the last question if the distance |
between the centers of the first two were four times the distance |
between the centers of the last two?
7. Would the weight of a soldier’s knapsack be sensibly less if it |
were carried on the top of his rifle? L
——0r9300—_
Section V.
MOLECULAR FORCES. L
19. Molecular Distinguished from Molar Forces},
Repellent Force.— Thus far we have considered only)
the effects of the action of bodies of sensible (perceived)
by the senses) size and at sensible distances. Have wel
any evidence that the molecules which compose these!
ee
bodies act upon one ‘another in a similar manner?
|
i
“MOLECULAR FORCES. 19
If you attempt to break a rod of wood or iron, or stretch
a piece of rubber, you realize that there is a force resisting
you. You reason that if the supposition be true, that the
grains or molecules that compose these bodies do not
touch one another, then there must be a powerful atérac-
tive force between the molecules, to prevent their separa-
tion. After stretching the rubber, let go one end; it
springs back to its original form. What is the cause?
The volume of most bodies is diminished by compression ;
when the pressure is removed, they recover to a greater
or less extent their previous volume. What is the cause?
Every body of matter, with the possible exception of the
molecule, whether solid, liquid, or gaseous, may be forced
| into a smaller volume by pressure; in other words,
matter is compressible. When pressure is removed, the
body expands into nearly or. quite its original volume.
This shows two things: first, that the matter of which a
body is formed does not really fill all the space which the
body appears to occupy; and, second, that in the body is a
force which resists outward pressure tending to compress tt,
and expands the body to its original volume when pressure is
removed. This is, of course, a repellent force, and is
exerted among molecules, tending to push them farther
apart.
For convenience, we call bodies of appreciable size
molar (massive) in distinction from molecules (bodies of
very small mass). Action between molar bodies, usually
at sensible distances, is called molar force; action between
molecules, always at insensible distances, is called molee-
ular force.
20. Cohesion, Tenacity. — That attraction which holds
the molecules of the same substance together, so as to form
20 MATTER, ENERGY, MOTION, AND FORCE.
larger bodies, is called cohesion. It is the attraction that
resists a force tending to break or crusha body. The tenacity
of solids and liquids, ¢.e. the resistance which they offer to
being pulled apart, is due to this attraction. It is greatest
in solids, usually less in liquids, and entirely wanting in
gases. It acts only at insensible distances, and is strictly
molecular. When cohesion is overcome, it is usually diffi-
cult to force the molecules near enough to one another for
this attraction to become effective again. Broken pieces
of glass and crockery cannot be so nicely readjusted that
they will hold together. Yet two polished surfaces of
glass or metal, placed in contact, will cohere quite strongly.
Or if the glass is heated till it is soft, or in a semi-fluid
condition, then, by pressure, the molecules at the two
surfaces will flow around one another, pack themselves
closely together, and the two bodies will become firmly
united. This process is called welding. In this manner
iron is welded,
Cohesive force varies greatly both in intensity and its behavior in differ-
ent substances, and even in the same substances under different circum-
stances. Modifications of this force give rise to certain conditions of matter
' designated as crystalline or amorphous, hard or soft, flexible or rigid, elastic,
viscous, malleable, ductile, tenacious, etc.
21. Crystallization.
Experiment 10.— Pulverize about three
ounces of alum. Take about a teacupful of
boiling hot water in a beaker, and sift into it
the powdered alum, stirring with a glass rod
as long as the. alum will dissolve readily.
Then suspend in the liquid to a little depth
one or more threads from a splinter of wood
laid across the top of a beaker (Fig. 18).
Place the whole where it will not be disturbed,
and allow it to cool slowly. It is well to allow it to stand for a day or
more.
Fig. 13:
MOLECULAR FORCES. 91
Beautiful transparent bodies of regular shape are formed
on the bottom and sides of the beaker and probably on
the thread. They are called crystals, and the process by
which they are formed is called crystallization.
Observe that the crystals formed on the thread in mid-
liquid are much more regular in shape than those formed
ou the surface of the glass. The latter are flattened, and
are said to be tabular.
Ina similar manner, obtain crystals of bichromate of potash, blue vitriol,
copperas, etc. Make up a cabinet of crystals, preserving them in small,
closely stoppered glass bottles.
Experiment 11.— Thoroughly clean a piece of window glass, by
breathing upon it, and then rubbing it with a piece of newspaper.
Warm the glass over an alcohol or Bunsen flame, and pour upon the
glass a strong solution of sal ammoniac, or saltpetre. Allow the
liquid to drain off, and hold the wet glass up to the sunlight, or view
it through a magnifying glass, and watch the growth of the crystals.
Experiment 12.— Examine with a magnifying glass the surface
fracture of a freshly broken piece of sugar loaf, and observe, if any,
small, smooth, glistening planes thus exposed.
These planes are surfaces of small, imperfectly formed
crystals closely packed together, similar to the imperfect
22 _ MATTER, ENERGY, MOTION, AND FORCE.
crystals of alum, etc., formed on the sides of the beaker.
Such bodies are said to have a crystalline fracture, and the
body itself is said to be crystalline in distinction from
amorphous matter like glass, glue, etc., which furnish no
evidence of crystalline structure.
Very interesting illustrations of crystallization are those delicate lace:
like figures which follow the touch of frost on the window-pane. Figure
14 represents a few of more than a thousand forms of snowflakes that have
been discovered, resulting from a variety of arrangement of the water
molecules.
Snow crystals are formed during free suspension of moisture in the air
and without interference from contact with any solid; hence their per-
fection of growth. If you gather snowflakes, as they fall, on cold, yellow
glass and examine them under a magnifying glass, you will find that all
erystals have a primary type of six rays, and hexagonal outline. Professor
Tyndall has succeeded in so unravelling lake ice as to show what he calls
“liquid flowers†in a block of ice, thus proving that ice is crystalline, or
composed of a compact mass of crystals. (Read Tyndall’s ‘Forms of
Water.â€â€™) :
Nature teems with crystals. Nearly every kind of matter, in passing
from the liquid state (whether molten or in solution) to the solid state,
tends to assume symmetrical forms. Crystallization 7s the rule; amorphism,
the exception. You can scarcely pick up a stone and break it without find-
ing the same crystalline fracture.
The massive pillars of basaltic rock found in certain localities, for ex-
ample, in Fingal’s Cave (Fig. 15), might in its broadest sense be regarded
as forms of crystallization, inasmuch as they are the result of natural |
causes. These hexagonal columns, however, probably resulted from great |
lateral pressure, exerted while cooling, upon molten matter thrown up
ages ago by submarine volcanoes. |
This tendency of the molecules of matter to arrange themselves in
definite ways during solidification is attended usually with a change of |
volume. The molecular force exerted at such a time is sometimes enor
mous, so as to burst the strongest vessels. .Hence our service pipes ar
burst when water is allowed to crystallize (freeze) in them.
22. Hardness.
Experiment 13.— Get specimens of the following substances: tale,|
chalk, glass, quartz, iron, silver, lead, copper, rock-salt, and marble. |
Ascertain which of them will scratch glass, and which are scratched)
|
|
!
MOLECULAR FORCES. 223
by giass. Which is the softest metal that you have tried? The hard- ,
est? Name some metal that you can scratch with a fingernail. See
if you can scratch a piece of copper with a piece of lead, and vice versa.
Which is softer, iron or lead? Which is the denser metal? Does
hardness depend upon density? What force must be overcome in
order to scratch a substance ?
:
|
To enable us to express degrees of hardness, the following table of
eference is generally adopted: —
MOHR’S SCALE OF HARDNESS.
1. Tale. 6. Orthoclase (Feldspar).
2. Gypsum (or Rock-Salt). 7. Quartz.
38. Calcite. 8. Topaz.
4, Fluor-Spar. 9. Corundum.
5. Apatite. 10. Diamond.
By comparing a given substance with the substances in the table, its
egree of hardness can be expressed approximately by one of the numbers
sed in the table. If the hardness of a substance is indicated by the num-
ber 4, what would you understand by it?
%
23. Hardening and Annealing; Flexibility.
_ Experiment 14.— Get pieces of wire, each ten inches long, of the
jfollowing metals: steel, iron, spring brass, hard copper, German silver,
24 MATTER, ENERGY, MOTION, AND FORCE.
platina, and phosphor-bronze. Place each in an alcohol or Bunsen
flame, and heat the wire near one end to a bright red glow, and then
thrust the heated part into cold water, and suddenly cool it. See
whether the part thus treated bends more or less readily than the
part which has not suffered the sudden change. When a body is
easily bent, ie. its cohesive force admits of a hinge-like movement
among its molecules without permanent separation, it is said to be
flexible. See whether the part treated has been hardened or softened
by the treatment. The process of rendering flexible and softening is
called annealing. ;
Next heat the opposite ends of the wires as before, and slowly (10
to 15 minutes) withdraw the wires from the flame by gradually
raising them above the flame, in order that the fall of ternperature may
be very gradual. Ascertain as before the effect of this treatment on
the flexibility and hardness of each. Classify the substances as an- |
nealed by sudden cooling, and annealed by slow cooling.
24. Elasticity.
Experiment 15.— Obtain thin strips of as many of the following
substances as practicable: rubber, different kinds of wood, ivory,
whalebone, steel, spring brass and soft brass, copper, iron, zinc, and
lead. ;
Bend each one of the above strips. Note which completely unbends
when the force is removed. Arrange the names of these substances in
the order of the rapidity and completeness with which they unbend.
The property which matter possesses of recovering its former shape
and volume, after having yielded to some force, is called elasticity.
25. Viscosity.
Experiment 16.— Support in a horizontal position, at one of its
extremities, a stick of sealing-wax, and suspend from its free extrem-
ity an ounce weight, and let it remain in this condition several days,
or perhaps weeks. At the end of the time the stick will be found per-
manently bent. Had an attempt been made to bend the stick quickly,
it would have been found quite brittle. A body which, subjected to
a stress for a considerable time, suffers a permanent change in form
is said to be viscous. Hardness is not opposed to viscosity. A lump
of pitch may be quite hard, and yet in the course of time it will flatten
itself out by its own weight, and flow down hill like a stream of syrup.
a maa
MOLECULAR FORCES. 25
Sealing-wax and pitch may be regarded as fluids whose flow is ex-
tremely slow; %.e. their viscosity or resistance to flow is very great.
Liquids like molasses and honey are said to be viscous, in distinc-
tion from limpid liquids like water and alcohol.
26. Malieability and Ductility.
Experiment 17.— Place a piece of lead on an anvil, or other flat
bar of surface, and hammer it. It spreads out under the hammer into
sheets, without being broken, though it is evident that the molecules
have moved about among one another, and assumed entirely different
relative positions. Heat a piece of soft glass tube in a gas-flame, and,
although the glass does not become a liquid, it behaves very much like
a liquid, and can be drawn out into very fine threads.
When a solid possesses sufficient fluidity to admit of being drawn
out into threads, it is said to be ductile. When it will admit of being
hammered or rolled into sheets, it is said to be malleable.
Platinum and gold are the most malleable and ductile metals. They
can be drawn into wire finer than a spider’s thread, or so as to require
very keen vision to see it. Gold can be hammered into leaves z 5555 of
an inch thick. Some metals, like iron, are more malleable and ductile at
ared heat; others, like copper, at an ordinary temperature.
It is remarkable that the tenacity of most metals is increased by being
drawn out into wires. It would seem that, in the new arrangement which
the molecules assume, the cohesive force is stronger than in the old.
Hence cables made of iron wire twisted together, so as to form an iron
rope, are stronger than iron chains of equal weight and length, and are
much used instead of chains where great strength is required.
27. Adhesion. — If you touch with your finger a piece
of gold-leaf, it will stick to your finger; if will not drop
off, it cannot be shaken off; and an attempt to pull it off
increases the difficulty. Dust and dirt stick to clothing.
Thrust your hand into water, and it comes out wet. We
could not pick up anything, or hold anything in our
hands, were it not that these things stick to the hands.
Every minute’s experience teaches us that not only is
there an attractive force between molecules of the same
26 MATTER, ENERGY, MOTION, AND FORCE.
kind of matter, but there is also an attractive force be-
tween molecules of unlike matter. That force which causes
unlike substances to cling together is called adhesion. Itis
probable that there is some adhesion between all substances
when brought in contact. Glass is wet by water, but is not
wet by mercury. Jf a liquid adheres to a solid more firmly
than the molecules of the liquid cohere, then will the solid be
wet by the liquid. If a solid isenot wet by a liquid, it is
not because adhesion is wanting, but because cohesion in
the liquid is stronger. |
28. Tension.— When a rubber band or cord is pulled or stretched,
it is said to be ina state of tension (i.e. of being stretched). The amount
of tension in a string supporting a stone is the weight of the stone. A
rubber balloon inflated with compressed air.is in a state of tension; the air
within is in a state of unusual compression. Gases are ever in a state of
compression, since they ever tend to expand without limit.
29. Surface Tension. —The molecular forces of cohesion and
adhesion give rise to a remarkable series of phenomena, especially obvious
in liquids, known as phenomena of surface tension. The general law gov-
erning all of this class of phenomena is that the surfaces of all bodies tend to
contract indefinitely. Since solids are those bodies which tend to resist any
force tending to alter their shape, and gases have no surfaces of their own,
it is obvious why liquids show the effects of such a force most readily.
The tendency of a surface of liquid to contract is illustrated in an imper-
fect manner by a stretched sheet of rubber; the latter, however, has a
constantly decreasing force of contraction as it approaches its original di-
mensions, and it may have a contractile force in only one direction, while
a surface sheet of liquid always tends to contract with the same force in-
dependently of its size, and it is exerted alike in all directions.
As a consequence of this, every body of liquid tends to assume the spherical
form, since the sphere has less surface than any other form having equal
volume. In large bodies the distorting forces due to gravity are generally
sufficient to disguise the effect; but in small bodies, as in drops of water or
mercury, it is apparent. Again, if the distorting effect of weight is elimi-
nated in any way, as by immersing a quantity of oil in a mixture of water and |
alcohol of its own density, or by replacing the central portion of the body |
MOLECULAR FORCES.
27
by a fluid much lighter than its own kind, as in the case of a soap-bubble,
the sphere is the resulting form.
Experiment 18.— Form a soap-bubble at the orifice of the bowl of a
tobacco pipe, and then, removing the mouth from the pipe, observe that
tension of the two surfaces (exterior and interior) of the bubble drives out
the air from the interior and finally the bubble contracts to a flat sheet.
30. Capillary Phenomena. — As a
result of molecular action it is found that the
surface of a given liquid will always meet a given
solid at a definite angle; thus the surface sep-
arating water and air always meets clean glass
ata very small angle (Fig. 15a); that separat-
ing mercury and air meets glass at an angle ff SS
about 135°. If clean silver is substituted for
glass, the first angle becomes large, not far from
90°, while the second would be reduced to zero;
in other words, the mercury creeps along the sur-
135°.
Se nto
Water, |
face of silver, its own air-exposed surface being parallel with that of the
silver.
From this it follows, that if a glass tube be dipped into water, the sur-
face tension will cause the liquid to rise in the bore of the tube above its level
outside ; while, on the contrary, if the tube be dipped into mercury, there
| will result a depression. These phenomena are known respectively as capil-
lary ascension and capillary depression.
ee
,
Os
CATE
If the bore of the tube is reduced one-half in diameter, the lifting force
i is reduced one-half, but the cross-section
will be reduced to one-fourth; hence in
order that the weight of the liquid lifted
may be one-half, it must rise twice as high
as before. Thus we have the law that the
ascension (or depression) of a liquid in a cap-
illary tube is inversely proportional to the
diameter of the bore.
Experiment 19.—Take a clean glass
tube of capillary (i.e. small, hair-like) bore,
and thrust one end to a depth of about a
Fig. 16. Fig. 17. quarter of an inch in water. Does the water
ascend or descend a little way in the tube?
the edge of the water next the tube on the cutside turned up-or down ?
Be is the shape of the surface of the water in the bore of the tube? Is
28 MATTER, ENERGY, MOTION, AND FORCE.
Repeat the experiment with tubes having bores of different size. Do you
notice any difference in the phenomena in the different tubes? It so, in
which are the phenomena most striking?
Repeat all the above experiments, and answer all the above questions,
using mercury instead of water.
Experiment 20. — Pour a little water into a U-shaped tube (Fig. 16),
one of whose arms has a capillary bore; how does the water behave in the
capillary tube? Pour a little mercury into another similar tube (Fig. 17) ;
how does the mercury behave? Describe the up-
per surfaces of both liquids.
Experiment 21.— Wipe the surface of a small
cambric needle with an oily cloth and place it
carefully on the surface of a cup of water. The
water surface will meet the oily surface at an an-
gle of about 135°, and the surface tension of the
liquid will act as a supporting force as represented
by the arrows in Figure 17a, and the needle will
float in a trough-shaped depression in the liquid surface.
Fig. 1%a.
QUESTIONS.
1. Why are pens made of steel? What moves the machinery of a
watch? What is the cause of the softness of a hair mattress or feather-
bed? On what does the entire virtue of a spring balance depend ? |
2. What name would you give to the attraction which causes your |
hands to be wet by a liquid? Is adhesion a molar or a molecular force ?
8. The tension of a violin string is 2 pounds; what is meant by this
statement ? |
4. Why are liquid drops round? Why are bubbles round ?
5. Why does surface tension cause capillary ascension in some cases
and depression in others? When does it cause ascension, and when depres-
sion ?
6. When an iron nail hangs from a magnet, there is stress between the |
nail and what bodies? One stress is magnotic; what is the other? Which |
is greater ?
CHAPTER It.
DYNAMICS} OF FLUIDS.
ees
Section I.
PRESSURE IN FLUIDS.
31. Cause of Pressure.— We live above a watery
ocean and at the bottom of an exceedingly rare and elas-
tic aerial ocean, called the atmosphere, extending with a
diminishing density to an undetermined distance into
space. Every molecule, in both the gaseous and liquid
oceans, is drawn toward the earth’s center by gravity.
This gives to both fluids a downward pressure upon
everything on which they rest.
The gravitating action of liquids is everywhere appar-
ent, as in the fall of drops of rain,
the descent of mountain streams,
and the weight of water in a
bucket. But to perceive that air
xerts a downward pressure re-
‘quires special manipulation. If
we lower a pail into a well, it
fills with water, but we do not
perceive that it becomes heavier
thereby; the weight of the water
in the pail is not felt. But when
‘We raise a pailful out of the water, it suddenly appears
Fig. 18.
1 Dynamies is the science which investigates the action of force.
80 DYNAMICS OF FLUIDS.
heavy. Ifwe could raise a pailful of air out of the ocean of
air, might not the weight of the air become perceptible?
If we dive to the bottom of a pond of water, we do not
feel the weight of the pond resting upon us. We do not
feel the weight of the atmospheric ocean resting upon us;
but we should remember that our situation with reference
to the air is like that of a diver with reference to water.
82. Gravity causes Pressure in All Directions. |
Experiment 22.— Fill two glass jars (Fig. 18) with water, A hav- |
ing a glass bottom, B a bottom provided |
by tying a piece of sheet-rubber tightly |
over the rim. Invert both in a larger |
vessel of water, C. The water in A does |
not feel the downward pressure of the |
air directly above it, the pressure being |
sustained by the rigid glass bottom. But
‘it indirectly feels the pressure of the air |
on the surface of the water in the open
vessel, ‘and it is this pressure that sus- |
tains the water in the jar. But the |
rubber bottom of the jar B yields some- |
what to the downward pressure of the
air, and is forced inward.
Experiment 23.— Fill a glass tube, D, with water, keeping one
end in the vessel of water, and a finger
tightly closing the upper end. Why
does not the water in the tube fall? —— “s
Remove your finger from the closed
end. Why does the water fall? =a
Experiment 24.— Fill (or partly
fill) a tumbler with water, cover the
top closely with a card or writing-paper, hold the paper in place
with the palm of the hand, and quickly invert the tumbler (Fig. 19).
Why does not the water fall out?
Experiment 25.— Force the piston A (Fig. 20) of the seven-in-one
apparatus (so called from the number of experiments that may be
performed with one piece of apparatus) quite to the closed end of the
ig
Fig. 19.
Fig. 20.
PRESSURE IN FLUIDS. ~ Bt
hollow cylinder, and close the stop-cock B. Try to pull the piston out
again. Why do you not succeed? Hold the apparatus in various
positions, so that the atmosphere may press down,
laterally, and up against the piston. Do you dis-
cover any difference in the pressure which it re-
ceives from different diréctions?
Experiment 26.— Force a tin pail (Fig. 21),
having a hole in its bottom, as far as possible into
water, without allowing water to enter at the top.
A stream of water spurts through the hole. Why?
g Why does it require so much effort to force the pail
Fig. 21. down into the water?
33. Comparison of Pressure at the Same Depth in
Different Directions. ;
Experiment 27.— Take a glass tube about 30 inches long and
one-fourth inch bore, and bend it into the shape of A (Fig. 22). Also
prepare tubes like B and C. Let the
bend a be about half full of water.
Slowly lower the end 7 into a tumbler
filled with water. . The water presses
up against the air in the tube, and
the air transmits the pressure to the
liquid in the bend. How is.the pres-
sure affected by depth? Does it
increase as the depth?
Experiment 28.— Connect c with
d by means of a rubber tube, and
lower the extremity m into the tum-
bler of water. As the tube is turned
up, the water must now press down
the tube against the air. Does the downward pressure increase as
the depth?
Experiment 29.— Connect e with c, and lower o into the water.
The water now presses laterally (sidewise) against the air. Does the
lateral pressure increase as the depth? me
Experiment 30.— Fill two tumblers with water, and lower n into one
and o into the other, keeping both extremities at the same depth
in the liquids. How is the liquid in the bend a affected? How do
32 DYNAMICS OF FLUIDS.
the upward and lateral pressures at
the same depth compare?
Experiment 31.— Once more con-
nect ¢ with d, and lower n and m to
the same depth into the water in the
two tumblers. How do the upward
and downward pressures at the sane
depth compare? At the same depth is
pressure equal in all directions ?
Experiment 32.— Connect the two
brass tubes at the extremities F and G
(Fig. 23). Fill the cup of the (eight-
in-one) apparatus with water, and re-
move the caps A, B,C, and D from
the branch tubes, so as to permit water
to escape from the orifices at their
ends. Does the water issuing from
these orifices show a lateral pressure?
What difference do you observe in the
flow of water from the different |
orifices? How do you account for |
it?
The results of experiments |
thus far show that at every |
point in a body of fluid gravity |
causes pressure to be exerted |
equally in all directions, and |
that in liquids the pressure in- |
creases as the depth increases. |
MEASUREMENT OF ATMOSPHERIC PRESSURE. 33
Section II.
MEASUREMENT OF ATMOSPHERIC PRESSURE, BAROMETERS.,
34. How Atmospheric Pressure is Measured.
Experiment 33 (preliminary).—Take a U-shaped glass tube
(Fig. 24), half fill it with
water, close one end with a
thumb, and tilt the tube so
that the water will run into
the closed arm and fill it;
then restore it to its original
vertical position.
not the water settle to the
Why does
Fig. 24.
same level in both arms?
Figure 25 represents a U-shaped glass tube closed at one end, 34
w----34 in:---------
Cyprenseneeeeeeee 80 iMpe-nnnewnennnennengh
inches in hight, and with a bore of 1 square inch
section. The closed arm having been filled with
mercury, the tube is placed with its open end up-
ward, as in the cut. The mercury in the closed arm
sinks about 2 inches to A, and rises 2 inches in the
open arm to C; but the surface A is 80 inches
higher than the surface C. This can be accounted
for only by the atmospheric pressure. The column
of mercury BA, containing 80 cubic inches, is an
exact counterpoise for a column of air of the same
diameter extending from C to the upper limit of
the atmospheric ocean, — an unknown hight.
The weight of the 80 cubic inches of mercury
in the column BA is about 15 pounds. Hence
the weight of a column of air of 1 square-inch sec-
tiop, extending from the surface of the sea to the
upper limit of the atmosphere, is about 15 pounds.
But in fluids gravity causes equal pressure in all
directions. Hence, at the level of the sea, all bodies
are pressed upon in all directions by the atmosphere, with a Sorce of aboui
15 Pounds per square inch, or about one ton per square foot.
:
:
Fig. 25.
:
. 84 DYNAMICS OF FLUIDS.
A pressure of 15 pounds per square inch is quite generally adopted
as a unit of gaseous pressure, and is called an atmosphere.
Fig. 26.
85. Barometer.— The hight of the
column of mercury supported by atmos-
pheric pressure is quite independent, how-
ever, of the area of the surface of the mer-
cury pressed upon; hence the apparatus
is more conveniently constructed in the
form represented in Figure 26.
A straight tube about 84 inches long
is closed at one end and filled with mer-
cury. A finger tightly closing the open
end, the tube is inverted, and this end is
inserted in a vessel of mercury and the
finger is withdrawn, when the mercury
sinks until there is equilibrium between
the downward pressure of the mercurial column AB an
BAROMETERS. 35
the pressure of the atmosphere. An apparatus designed
to measure atmospheric pressure is called a barometer
(pressure-measurer). A common form of barometer is
represented in Figure 27. Beside the tube and near its
top is a scale graduated in inches or centimeters, indi- -
cating the hight of the mercurial column. For ordinary
purposes this scale needs to have only a range of three or
four inches, so as to include the maximum fluctuations
of the column.
The hight of the barometric column is subject to fluc-
‘tuations; this shows that the atmospheric pressure is sub-
_ject to variations. The barometer is always a faithful
| monitor of all changes in atmospheric pressure. It is also
erviceable as a weather indicator. It does not indicate
‘weather that is present, but foretells coming weather.
Not that any particular point at which mercury may stand
‘foretells any particular kind of weather, but any sudden
| chang ge in the barometer indicates a change in the weather.
A rapid fall of mercury generally forebodes a storm,
_while a rising column indicates clearing weather.
86. Aneroid Barometer. — The aneroid (without moisture)
barometer employs no liquid. It contains’ a cylindrical box, D (Fig.
28), having a very flexible top. The air is partially exhausted from
within the box. The varying atmospheric pressure causes this top to
“rise and sink much like the chest of man in breathing. Slight move-
ments of this kind are communicated by means of multiplying-apparatus
(apparatus by means of which a small movement of one part is mag-
nified into a large movement of another part) to the index needle A.
The dial is graduated to correspond with a mercurial barometer. The
observer turns the button C and brings the brass needle B over the black
‘needle A, and at his next observation any departure of the latter from
the former will show precisely the change which has occurred between
the observations.
The aneroid can be made more sensitive (i.e. so as to show smaller
changes of atmospheric pressure) than the mercurial barometer. . If a
36 DYNAMICS OF FLUIDS.
barometer is carried up a mountain, it is found that the mercury constantly
falls as the ascent increases. Roughly speaking, the barometer falls one
inch for every 900 feet of ascent. Really, in consequence of the rapid
increase of the rarity of the air, the rate of fall diminishes as you ascenc.
It is obvious that the barometer will serve to measure approximately the
hights of mountains.
Fig. 28.
If a mercurial barometer stand at 760™™ on the floor, the same barom- |
eter on the top of a table 1â„¢ high should stand at a hight of 759.91â„¢, |
a change scarcely perceptible. The aneroid is, however, sometimes made |
so sensitive that the change of pressure experienced in this short distance
is rendered quite perceptible. :
The shading in Figure 29 is intended to indicate roughly the ravi
tion in the density of the air at different elevations above sea-level. ‘The|
figures in the left margin show the hight in miles; those in the first |
column on the right, the corresponding average hight of the mercurial |
BAROMETERS. 37
cclumn in inches; and those in the extreme right, the density of the air
compared with its density
curial column at sea-
level is about 380
inches (76eâ„¢),
- Ifanopeningcould
| be made in the earth,
| 85 miles in depth be-
low the sea-level, it
| is calculated that the
_ density of the air
, at the bottom would
' be 1,000 times that
/ at sea-level, so that
+ water would float in
‘it. Air has been com-
‘pressed to this den-
sity.
To what hight the
atmosphere extends
is unknown. It is
variously estimated
at from 50 to 200
miles. If the aerial
ocean were of uni-
form density, and of
the same density that
it is at the sea-level,
its depth would be a
little short of five
miles. Certain peaks
of the Himalayas
would rise above it.
at sea-level. The average hight of the mer-
|.
Ca LTS
3
“HIMALAYAS:
Fig. 29.
38 DYNAMICS OF FLUIDS.
Section ITI. —
COMPRESSIBILITY AND ELASTICITY OF GASES. — BOYLE’S
LAW.
37. Compressibility of Gases. — The increase of pres-
sure attending the increase in depth, in both liquids and
gases, is readily explained by the fact that the lower layers
of fluids sustain the weight of all the layers above. Con-
sequently, if the body of fluid is of uniform density, as is
very nearly the case in liquids, the pressure will increase
in nearly the same ratio as the depth increases. But the
aerial ocean is far from being of uniform density, in con-
sequence of the extreme compressibility of gaseous matter.
The contrast between water and air, in this respect, may
be seen in the fact that water subjected to a pressure of
one atmosphere is compressed 0.0000457 its volume; under
the same circumstances, air is compressed one-half. For
most practical purposes, we may regard the density of
water at all depths as uniform, while it is far otherwise in
large masses of gases. ;
38. Elasticity of Gases. — Closely allied to com-
pressibility is the elastieity of gases, or their power to
recover their former volume after compression. The elas-
ticity of all fluids is perfect. By this is meant, that the
force exerted in expansion is equal to the force used in
compression; and that, however much a fluid is com-
pressed, it will always completely regain its former bulk
when the pressure is removed. Hence the barometer
_ which measures the compressing force of the atmosphere
also measures at the same time the elastic force (¢.e. the
COMPRESSIBILITY AND ELASTICITY OF GASES. 39
tension or expansive force) of the air. Liquids are per-
fectly elastic; but, inasmuch as they are perceptibly com-
pressed only under tremendous pressure, they are regarded
as practically incompressible, and so it is rarely necessary
to consider their elasticity: It has already been stated
that matter in a gaseous state expands indefinitely unless
restrained by external force. The atmosphere is con-
fined to the earth by the force of gravity.
Experiment 34. — Force the piston of the seven-in-one apparatus
two-thirds the way into the cylinder, and close the aperture. Support
- the apparatus on blocks, with the piston upwards, remove the handle,
and place a weight on the piston, and place the
whole under the receiver of an air-pump. Exhaust
the air from the receiver; the outside pressure of
the air being partially removed, the unbalanced
force (i.e. the tension) of the air enclosed within
the cylinder willicause the piston to rise, and raise
the weight.
Experiment 35.— Arrange the same apparatus
as in Figure 30. Attach a small rubber tube to
the short tube, and suck as much air out of the
cylinder as possible. The air within, being rare-
fied, loses its tension, and the unbalanced outside
pressure forces the piston into
| the cylinder, raising the weight.
A very much heavier weight may be raised if the
i rubber tube connects the apparatus with an air-
pump.
Experiment 36.— Take a glass tube (Fig. 31)
having a bulb blown at one end. Nearly fill it
with water, so that when inverted there will be only
a bubble of air in the bulb. Insert the open end ,
in a glass of water, place under a receiver, and
exhaust. Nearly all the water will leave the bulb
and tube. Why? What will happen when air is admitted to the
receiver ? é
Fig. 30.
Fig. 31.
40 DYNAMICS OF FLUIDS.
39. Boyle’s or Mariotte’s Law.
Experiment 37.— Take a bent glass tube (Fig. 82), the short arm
being closed, and the long arm, which should be
at least 34 inches (85) long, being open at the
top. Pour mercury into the tube till the surfices
in the two arms stand at zero. Now the surface
in the long arm supports the weight of an atmos-
phere. Therefore the tension of the air enclosed
in the short arm, which exactly balances it, must
be about 15 pounds to the square inch. Next pour
mercury into the long arm till the surface in the
short arm reaches 5, or till the volume of air en-
closed is reduced one-half, when it will be found
that the hight of the column AC is just equal to
the hight of the barometric column at the time
the experiment is performed. It now appears
that the tension of the air in AB balances the
atmospheric pressure, plus a column of mercury
AC, which is equal to another atmosphere; .-. the
tension of the air in AB = two atmospheres. But
the air has been compressed into half the space it
formerly occupied, and is, consequently, twice as
dense. If the length and strength of the tube
would admit of a column of mercury above the
surface in the short arm equal to twice AC, the
air would be compressed into one-third its original
bulk; and, inasmuch as it would balance a pres-
= sure of three atmospheres, its tension would be
increased threefold. ;
From this experiment we learn that, at twice the pres-
sure there is half the volume, while the density and elas-
tic force are doubled. Hence the law: —
The volume of a body of gas at a constant temperature
varies inversely as the pressure, density, and elastic force.
For many years after the announcement of this law it
was believed to be rigorously correct for all gases, but
more recently, more precise experiments have shown that
RAREFYING AND CONDENSING INSTRUMENTS. 41
it is approximately but not rigidly true for any gas, that
the departure from the law differs with different gases,
and that each gas possesses a special law of compressibility.
Section IV.
INSTRUMENTS USED FOR RAREFYING AND CONDENSING
AIR.
40. The Air-Pump.— The air-pump, as its name im-
plies, is used to withdraw air from a closed vessel. Figure
33 will serve to 5 :
illustrate its op- §
eration. R is a
glass receiver from
which air is to be &f
exhausted. Bisa &
hollow cylinder of
brass, called the
pump-barrel. The
plug P, called a
piston, is fitted to
the interior of the
barrel, and can be Fig. 33.
moved up and down by the handle H; s and ¢ are valves.
A valve acts on the principle of a door intended to
open or close a passage. If you walk against a door
on one side, it opens and allows you to pass; but
if you walk against it on the other side, it closes the
passage, and stops your progress. Suppose the piston
to be in the act of descending; the compression of
42 DYNAMICS OF FLUIDS.
the air in B closes the valve t, and opens the valve s,
and the enclosed air escapes.. After the piston reaches
gy the bottom of the barrel, it begins its
ascent. This would cause a vacuum be-
tween the bottom of the barrel and the
ascending piston (since the unbalanced
pressure of the outside air immediately
closes the valve s), but the tension of
the air in the receiver R opens the
valve ¢ and fills this space. As the air
in R expands, it becomes rarefied and
loses some of its tension. The external
pressure of the air on R, being no longer ~
balanced by the tension of the air within,
presses the receiver firmly upon the plate
L. Each repetition of a double stroke
of the piston removes a portion of the
air remaining in R. The air is removed
from R by its own expansion. However
far the process of exhaustion may be
carried, the receiver will always be filled
with air, although it may be exceedingly
rarefied. The operation of exhaustion
is practically ended when the tension of
the air in R becomes too feeble to lift
the valve t.
Sometimes another receiver, D, is
used, opening into the tube T, that con-
nects the receiver with the barrel. In-
side the receiver is placed a barometer.
It is apparent that air is exhausted from
D as well as from R; and, as the pressure is removed
from the surface of the mercury in the cup, the bar-
RAREFYING AND CONDENSING INSTRUMENTS. 43
ometric column falls; so that the barometer serves as a
gauge to indicate the approximation to a vacuum. For
instance, when the mercury has fallen 3880" (15 inches),
one-half of the air has been removed. :
41. Sprengel Pump.
Experiment 38.— Remove the cap from j (Fig. 84), and connect
with a glass tube k, about 12 inches long. Let & dip into a tum-
bler of water, m.. Support the ap- é
paratus on a couple of blocks of
wood, so that when the stopper a
in the base is removed, the water
may fall freely out at the bottom.
Fill the cup g with water, and
allow it to escape at a. As the
water passes the branch tube j,
the expansive air in the tube gets
entangled in the water, and is con-
stantly removed by the falling
stream, and thus a partial vacuum
is formed in the tube & The pres-
sure of air on the surface of the
water in the open cup forces the
water up the tube &, and empties
the tumbler. If m were a closed
vessel filled with air, it is apparent
that a partial vacuum would be
created in it. An apparatus con-
structed like this, in which mercury
is employed instead of water, constitutes one of the most efficient
air-pumps in use. It is called the Sprengel pump.
Fig. 35.
Modifications of this pump have extensive use in the arts, such as
in obtaining high vacua in electrical lamps, radiometers, etc. By means
of a good Sprengel pump exhaustion to the hundred-millionth of an
atmosphere can be attained. In such a space it is calculated that a
molecule of air traverses an average distance of 33 feet before colliding
with another molecule of air. -
44
DYNAMICS OF FLUIDS.
42. Condenser.
Experiment 39. — Into the neck of a bottle par tly filled with water
(Fig. go) insert a cork very tightly, through which pass a glass tube
Fig. 36.
nearly to the bottom of the bottle. Blow forcibly
into the bottle. On removing the mouth water
will flow through the :
tube in a stream.
Explain.
Figure 6, page
5, represents in
perspective, and
Figure 36, in sec-
tion, an appara-
tus for condens-
ing air, called a
condenser. Its !
construction is Fig. 37.
like that of the barrel of an air-pump, except that the
direction in which the valves open is reversed.
Experiment 40.— Place a block having a wide platform at one
end on-the piston of the seven-in-one apparatus. On the platform let
a child stand. By means of a condensing syringe (Fig. 6), connected
by a rubber tube with the seven-in-one apparatus (Fig. 37), condense
the air in the cylinder and raise the child.
‘Section V.
APPARATUS FOR RAISING LIQUIDS.
43. Lifting or Suction Pump. — The common lifting-
pump is constructed like the barrel of an air-pump. Fig-
ure 38 represents the piston B in the act of rising. As
APPARATUS FOR RAISING LIQUIDS. 45
the air is rarefied below it, water rises in consequence
of atmospheric pressure on the water in the well, and
opens the lower valve D. Atmospneric pressure closes
‘Fig. 40.
the upper valve C in the piston. When
the piston is pressed down (Fig. 39), the
lower valve closes, the upper valve opens,
nd the water between the bottom of the
J barrel and the piston passes through the
Bie 335: upper valve above the piston. When
the piston is raised again (Fig. 40), the water above the
piston is raised and discharged from the spout.
The liquid is sometimes said to be raised
in a lifting-pump by the “force of suction.â€
Is there such a force?
Experiment 41.— Bend a glass tube into a U-shape,
with unequal arms, as in Figure 41. Fill the tube with
the liguid to the level cb. Close the end 6 with a finger, GiiNmmaed
and try to suck the liquid out of the tube. You find Fig. 41.
it impossible. Remove the finger from 6, and you can suck the liquid
out with ease. Why?
46 DYNAMICS OF FLUIDS.
44. Force-Pump.— The piston of a force-pump (Fig.
42) has no valve, but a branch pipe a leads from the lower
part of the barrel to an air-condensing chamber 8, at the
bottom of which is a valve ce, opening upward. As the
piston is raised, water is forced up through
the valve d, while water in 6 is pre-
vented from returning by the valve e.
When the piston is forced down, the
valve d closes, the valve ¢ opens, and the
water is forced into the chamber 38, con-
densing the air above the water. The
elasticity of the condensed air forces the
water out of the tube e in a continuous
stream.
QUESTIONS AND PROBLEMS.
1. What force is the cause of fluid pressure ?
2. Why does not a.person at the bottom of a
pond feel the weight of the water above him?
3. An aeronaut finds that on the earth his
oarometer stands at 30 inches. He ascends in a
balloon until the barometer stands at 20 inches.
About how high is he? What is the pressure of
the atmosphere at his elevation?
4, When a barometer stands at 30 inches, the
atmospheric pressure is 14.7 pounds. What is
the atmospheric pressure when the barometer stands at 29 inches?
5. Why is a barometer tube closed at the top? Why must air come
in contact with the mercury at the bottom? ee:
6. What would be the effect on an aneroid barometer if it were
placed under the receiver of an air-pump, and one or two strokes
of the pump were made?
7. Suppose a rubber foot-ball to be partially fnfiated with air at
the surface of the earth; what would happen if it were taken up in a
balloon ?
8. Mercury is 13.6 times denser than water. When a mercurial ba-
"Big. 42.
TRANSMISSION OF EXTERNAL PRESSURE. AT
rometer stands at 30 inches, how high would a water barometer stand?
How high, theoretically, could mercury be raised on such a day by
suction? How high could water be raised by the same means? How
many times higher can water be raised by a suction-pump than mer-
cury ?
9. What is that which is sometimes called the “force of suction �
10. The area of one side of the piston of the seven-in-one apparatus
is about 26 square inches. Suppose the piston to be forced into the
cylinder so as to drive out all the air, and then the orifice to be closed ;
what force would be required to draw the piston out, when the barom-
eter stands at 80 inches? What force would be required on the top of
a mountain where the barometer stands at 15 inches ?
11. Water is raised the larger part of the distance in our lifting-
pumps by atmospheric pressure; why, then, is not such a pump a
labor-saving instrument?
12. If water is to be raised from a well 50 feet deep, how high must
it be lifted, and how long must the barrel be?
Section VI.
TRANSMISSION OF EXTERNAL PRESSURE.
45. Pressure Transmitted Undiminished in All Direc-
tions.
Experiment 42.— Fill the glass globe and cylinder (Fig. 43) with
water, and thrust the piston into the cylinder. Jets of water will be
thrown not only from that aperture a in the globe toward which the
piston moves and the pressure is exerted, but from apertures on all
sides. Furthermore, the streams extend to equal distances in every
direction.
It thus appears that external pressure is exerted not
alone upon that portion of the liquid that lies in the
path of the force, but it is transmitted equally to all
parts and in all directions.
48 DYNAMICS OF FLUIDS.
Bxperiment 43.— Measure the diameter of the bore of each arm
ot the glass U-tube (Fig. 44). We will suppose, for illustration, that
the diameters are respectively 40™™ and
10™™; then the areas of the transverse
sections of the bores will be 402: 102= 16;
that is, when the tube contains a liquid,
the area of the free surface of the liquid
in the large arm will be 16 times as great
as that in the small arm. Pour mercury
into the tube until it stands about 1
above the bottom of the large arm. The
mercury stands at the same level in both
arms. Pour water upon the mercury in
the large arm until
this arm lacks only
about 1â„¢ of being
full. The pressure of
the water causes the
mercury to rise in the
small arm, and to be
depressed in the large
arm. Pour water very
slowly into the small
"arm from a beaker having a narrow lip, until the surfaces of the water
in the two arms are on the same level. It is evident that the quantity
of water in the large arm is 16 times as great as that in the small arm.
This phenomenon appears paradoxical (apparently contrary to the natu-
ral course of things), until we master the important hydrostatic princi-
ple involved. We must not regard the body of mercury as serving as
a balance beam between the two bodies of water, for this would lead
to the absurd conclusion that a given mass of matter may balance an-
other mass 16 times as great. We may best understand this phenom-
enon by imagining the body of liquid in the large arm to be divided
into cylindrical columns of liquid of the same size as that in the small
arm. There will evidently be 16 such columns. Then whatever
pressure is exerted on the mercury by the water in the small arm is
transmitted by the mercury to each of the 16 columns, so that each
column receives an upward pressure, or a supporting force equal to
the weight of the water in the small arm. This method of transmit-
Fig. 43. Fig. 44.
TRANSMISSION OF EXTERNAL PRESSURE. 49
ting pressure is peculiar to fluids. With solids it is quite different.
if the mercury in our experiment were a solid body, it would require
equal masses of water placed upon the two extremities to counter-
balance each other.
Experiment 44.— Support the seven-in-one apparatus with the
open end upward, force the piston in, and place on it a block of wood
4A. (Fig. 45), and on the block a heavy weight (or let a small child
stand on the block). Attach one end of the
rubber tube B (12 feet long) to the apparatus,
and insert a tunnel C in the other end of the
tube. Raise the latter end as high as practi-
cable, and pour water into the tube. Explain
how the few ounces of water standing in the
tube can exert a pressure of many pounds on
the piston, and cause it to rise together with
the burden that is on it.
Fig. 45. Fig. 46.
Experiment 45.— Remove the water from the apparatus, placé on
the piston a 16-pound weight, and blow (Fig. 46) from the lungs into
the apparatus. Notwithstanding that the actual pushing force ex-
erted through the tube by the lungs does not probably exceed an
ounce, the slight increase of tension caused thereby when exerted
upon the (about) 26 square inches of surface of the piston causes it to
rise together with its burden.
A pressure exerted on a given area of a fluid enclosed
in a vessel is transmitted to every equal area of the inte-
rior of the vessel; and the whole pressure that may be
exerted upon the vessel may be increased in proportion as
the area of the part subjected to external pressure ts de-
creased.
50 DYNAMICS OF FLUIDS.
46. Hydrostatic Press. — This principle has an im.
portant practical application in the hydrostatic press.
You see two pistons ¢ and s (Fig. 47). The area oi
the lower surface of ¢ is (say) one hundred times that of
the lower surface of
s. As the piston s is
raised and depressed,
water is pumped up
from the cistern A,
forced into the cylin-
der x, and exerts a
total upward pressure
against the piston ¢ one
hundred times greater
than the downward
pressure exerted upon -
s. Thus, if a pressure
of one hundred pounds
is applied at s, the cotton bales will be subjected to a
pressure of five tons.
Fig. 47
The pressure that may be exerted by these presses is enormous. The
hand of a child can break a strong iron bar. But observe that, although
the pressure exerted is very great, the upward movement of the piston ¢ is
very slow. In order that the piston ¢ may rise 1 inch, the piston s must de-
scend 100 inches. The disadvantage arising from slowness of operation is
little thought of, however, when we consider the great advantage accruing
from the fact that one man can produce as great a pressure with the press
as a hundred men can exert without it.
The press is used for compressing cotton, Hayne etc., into bales, and for
extracting oil from seeds. The modern engineer finds it a most efficient
machine, whenever great weights are to be moved through short distances,
as in launching ships.
PRESSURE EXERTED BY LIQUIDS. : 51
Section VII.
PRESSURE EXERTED BY LIQUIDS DUE TO THEIR OWN
W EIGHT.
47. Pressure Dependent on Depth, but Independ-
ent of the Quantity and Shape of a Body of Liquid. —
Having considered the transmission of external pressure ap-
plied to any portion of a liquid, we proceed to examine the
effects of pressure due to the weight of liquids themselves.
‘Fig. 49. Fig. 50. Fig. 51.
Experiment 46.— A and B (Fig. 48) are two bottomless vessels
which can be alternately screwed to a supporting ring C (Fig. 49). The
ring is itself fastened by means of a clamp to the rim of a wooden water-
pail. - A circular disk of metal, D, is supported by a rod connected with
one arm of the balance-beam E. When the weight F is applied to the
other arm of the beam, the disk D is drawn up against the ring so as
to supply a bottom for the vessel above. Take first the vessel A,
screw it to the ring, and apply the weight to the beam as in Figure 50.
Pour water slowly into the vessel, moving the index a@ up the rod so
62 : DYNAMICS OF FLUIDS. ‘
as to keep it just at the surface of the water, until the downward
pressure of the water upon the bottom tilts the beam, and pushes the
bottom down from the ring, and allows some of the water to fall into
the pail. Remove vessel A, and attach B to the ring as in Figure 51.
Pour water as before into vessel B; when the surface of the water
reaches the index a, the bottom is forced off as before. That is, at the
same depth, though the quantity of water and the shape of the vessel be dif-
ferent, the pressure upon the bottom of a vessel is the same, provided the
bottom ts of the same area.
48.. Rules for Calculating Liquid Pressure against
the Bottom and Sides of a Containing Vessel. — The
pressure due to gravity on any portion of the bottom of a ves-
sel containing a liquid is equal to the weight of a column of
the same liquid whose base ts the area of that portion of the
bottom pressed upon, and whose hight is the greatest depth
of the water in the vessel. Thus, suppose that we have
three vessels having bottoms of the same size: one of
them has flaring sides, like a wash-basin; another has —
cylindrical sides; and the third has conical sides, like a
coffee-pot. If the three vessels are filled with water to
the same depth, the pressure upon the bottom of each will
be equal to the weight of the water in the vessel of cylin-
drical shape. Suppose that the area of the bottom of
each is 108 square inches, and the depth of water is 16
inches; then the cubical contents of the water in the cylin-
drical vessel is 1,728 cubic inches, or 1 cubic foot. The
weight of 1 cubic foot of water is 624 pounds. Hence,
the pressure upon the bottom of each vessel is 624 pounds.
Evidently, the lateral pressure at any point of the side
of a vessel depends upon the depth of that point; and, as
depth at different points of a side varies, hence, to find the
pressure upon any portion of a side of a vessel, we find the
weight of a column of liquid whose base is the area of that
portion of the side, and whose hight is the average depth of
that portion.
PRESSURE EXERTED BY LIQUIDS. 53
49. The Surface of a Liquid at Rest is Level. — This
fact is commonly expressed thus: “ Water always seeks
its lowest level.†In accordance with this principle, water
flows down an inclined plane, and will not remain heaped
up. An illustration of the application of this principle, on
a large scale, is found in the method of supplying cities
with water. Figure 52 represents a modern aqueduct,
through which water is conveyed from an elevated pond
or river a, beneath a river 6, over a hill ¢, through a valley
Fig. 52.
d, to a reservoir e, in a city, from which water is distribu-
ted by service-pipes to the dwellings. The pipe is tapped
at different points,-and fountains at these points would
rise to the level of the water in the pond, but for the re-
sistance of the air, friction in the pipes, and the check
which the ascending steam receives from the falling drops.
Where sheuld the pipes be made stronger, on a hill
or in a valley? Where will water issue from faucets
with greater force, in a chamber or in a basement? How
high may water be drawn from the pipe in the house f?
54 ; DYNAMICS OF FLUIDS.
Section VIII.
THE SIPHON.
50. Construction and Operation of the Siphon. — A
siphon is an instrument used for transferring a liquid from
one vessel to another through the agency of atmospheric
pressure. It consists of a tube of any material (rubber is
often most convenient) bent into a shape somewhat like
the letter U. To set it in operation, fill the
tube with a liquid, stop each end with a
finger or cork, place it in the position rep-
_ resented in Figure 53, remove the stoppers
~ and the liquid will all flow out at the orifice
o. Why? The upward pressure of the at-
mosphere against the liquid in the tube is
the same at both ends; hence these two
forces are in equilibrium. But the weight
of the column of liquid ab is greater than
the weight of the column de; hence equilibrium is de-
stroyed and the movement is in the direction of the greater
(z.e. the unbalanced) force. The unbalanced force which
causes the flow is equal to the weight of the column eé,
If one end of the tube filled with liquid is immersed in
a liquid in some vessel, as in A, Figure 54, and the other
end is brought below the surface of the liquid in the vessel
and the stoppers are removed, the liquid in the vessel will
flow out through the tube until the distance ed becomes
Zero.
Fig. 53.
If one of the vessels is raised a little, as in C, the liquid will flow from
the raised vessel, till the surfaces in the two vessels are on the same level.
THE SIPHON. 55
The remaining diagrams in this cut represent some of the great variety of
uses to which the siphon may be put. D, E, and F are different forms of
siphon fountains. In D, the siphon tube is filled by blowing in the tube /.
Explain the remainder of the operation. A siphon of the form G is always
ready for use. It is only necessary to dip one end into the liquid to be
Fig. 54.
transferred. Why does the liquid not flow out of this tube in its present
condition? H illustrates the method by which a heavy liquid may be
removed from beneath a lighter liquid. By means of a siphon a liquid
may be removed from a vessel in a clear state, without disturbing sediment
56 DYNAMICS OF FLUIDS.
at the bottom. Iisa Tantalus Cup. A liquid will not flow from this cup
till the top of the bend of the tube is eovered. It will then continue to flow
as long as the end of the tube is in the liquid. The cup g (Fig. 34, page
42) is a Tantalus cup. The siphon J may be filled with a liquid that is
not safe or pleasant to handle, by placing the end j in the liquid, stopping
the end k&, and sucking the air out at the end / till the lower end is filled
with the liquid.
Gases heavier than air may be siphoned like liquids. Vessel o contains
carbonic-acid gas. As the gas is siphoned into the vessel p, it extinguishes
acandle-flame. Gases lighter than air are siphoned by inverting both the
vessels and the sipuon.
Section IX.
BUOYANT FORCE OF FLUIDS.
51. Origin of Buoyancy.
Experiment 47.— Gradually lower a large stone, by a string tied
to it, into a bucket of water, and notice that
its weight gradually becomes less till it is com-
pletely submerged. Slowly raise it out of the
water, and note the chance in weiglit as it emerges
from the water. Suspend the stone from a spring
balance, weigh it in air and then in water, and
ascertain its loss of weight in the latter.
It seems as if something in the fluid,
underneath the articles submerged, were
pressing up against them. A moment’s re-
flection will make the explanation of this
phenomenon apparent. We have learned (1) that pressure
at any given point in a body of fluid is equal in all direc-
tions. (2) That pressure in liquids increases as the
Fig. 55.
BUOYANT FORCE OF FLUIDS. 57
depth. Consequently, the downward pressure on the top
(i.e. the place of least depth) of a body immersed in a
fluid, as deba (Fig. 55), must be less than the upward
pressure against the bottom; hence, there is an unbal-
anced force acting upward, which tends to neutralize to
some extent the weight or gravity of the body. This
unbalanced force is called the buoyant force of fluids.
That there is equilibrium between the pressures on the
sides of a body immersed is shown by the fact that there
is no tendency to move laterally.
52. Magnitude of the Buoyant Force.
Experiment 48.— Suspend from one arm of a balance beam a
cylindrical bucket A (Fig. 56), and from the bucket a solid cylinder
whose volume is exactly equal to the
capacity of the bucket; in other words,
the latter would’ just fill the former.
Counterpoise the bucket and cylinder
with weights.
Place beneath the cylinder a tumbler of
water, and raise the tumbler until the cyl-
inder is completely submerged. The
buoyant force of the water destroys the
equilibrium. Pour water into the bucket;
when it becomes just even full, the equi-
librium is restored.
Now it is evident that the cylinder
immersed in the water displaces its own
volume of water, or just as much water
as fills the bucket. But the bucket full
of water is just sufficient to restore the weight lost by the subinersion
of the cylinder. Hence, a solid immersed in a liquid is buoyed up with a
force equal to (i.e. its apparent loss in weight is) the weight of the
liquid it displaces.
Experiment 49.— The last statement may be verified in another
way with apparatus like that shown in Figure 57. Fill the vessel A
till the liquid overflows at E. After the overflow ceases, place a ves-
58 DYNAMICS OF FLUIDS.
sel ¢ under the nozzle. Suspend a stone from the balance-beam B,
and weigh it in air, and then carefully lower it into the liquid,
when some of the liquid
will flow into the vessel e.
The vessel c having been
weighed when empty, weigh
it again with its liquid
contents, and it will be
found that its increase in
weight is just equal to the
loss of weight of the stone.
Experiment 50.— Next
suspend a block of wood
that will float in the liquid,
and weigh it in air: Then
float it upon the liquid, and
weigh'the liquid displaced as
before, and it will be found
that the weight of the liquid
displaced is just equal to the
weight of the block in air.
Henee, a floating body displaces its own weight. of liquid ;
in other words, a floating body will sink till it displaces an
equal weight of the liquid, or till it reaches a depth where
the buoyant force is equal to its own weight.
Experiment 51.— Place a baroscope (Fig. 58),
consisting of a scale-beam, a small weight, and a
. hollow brass sphere, under the receiver of an air-
\\, Pump, and exhaust the air. In the air the weight
and sphere balance each other; but when the
air is removed, the sphere sinks, showing that in
4 reality it is heavier than the weight. In the air
each is buoyed up by the weight of the air it dis-
places; but as the sphere displaces more air, it is
buoyed up more. Consequently, when the buoyant -
force is withdrawn from both, their equilibrium
is destroyed.
DENSITY AND SPECIFIC GRAVITY. 59
We see from this experiment that bodies weigh less in
aw than in a vacuum, and that we never ascertain the true
weight of a body, except when weighed in a vacuum.
The density of the atmosphere is greatest at the surface
of the earth. A body free to move cannot displace more
than its own weight of a fluid; therefore a balloon, which
is a large bag filled with a gas about fourteen times lighter
than air at the sea-level, will rise till the balloon, plus the
weight of the car and cargo, equals the weight of the air
displaced.
Figure 59 represents a water-tank in common use in our houses. Water
enters it from the main
P aS
until nearly full, when it
reaches the hollow metallic = ""°"™4'" \ ce
ball A, and raises it by its :
buoyant force and closes a
valve in the main pipe, and
thus prevents an overflow.
An overflow is still further
prevented by the waste
pipe and another “ball
tap,†B, which opens at
a suitable time © anothei
passage for the escape of
water.
Section X.
DENSITY AND SPECIFIC GRAVITY.
53. Meaning of the Terms and their Relation to
each Other. — The quantity of matter per unit of volume
represents the density of the matter filling that space.
60 DYNAMICS OF FLUIDS.
Thus, a gram of water at 4° C. (centigrade thermometer)
occupies a cubic centimeter; while the same space would
contain 11.5 grams of lead. Every kind of matter (ie.
* every substance) has a special or specific density of its
own. Pure water at 4° C. is taken as a standard; and its
density is said to be ( Hass aa =)1. In the same
volume i
way the density of lead is G- =) 11.5. A piece of lead
which occupies a given space not only contains 11.5 times
as much matter, but also weighs 11.5 times as much as the
quantity of water which would fill the same space. The
density of any liquid or solid compared ‘with that of water
is a ratio — called its specific density; this ratio ig numeri-
cally equal to the ratio, called its spectfie gravity, of its
weight compared with the weight of an equal volume of
water at the standard temperature.
54. Formulas for Specific Density and Specific Grav-
ity. —Let D represent the density of any given substance
(e.g- lead), and D’ the density of water, and let G and G’
represent respectively the weights of equal volumes of the
same substances; then
(1) Density of given substance _ D = Sp.D.
Density of water ~ Di
(2) Weight ofa given volume of thesubstance _ Cie Tc
Weight of equal volume of water Claas
The Sp. D. of lead =>, EEO Toe The Sp Gut
Gs :
lead = =——~=11.5. Hence Sp. D. and Sp. G. are
Cae
numerically equal. In the same way ratios may be found for
other substances and recorded in a table; such a table ex-
hibits both the specific densities and the specific gravities
of the substances. See Appendix B.
SPECIFIC GRAVITY AND SPECIFIC DENSITY. 61
Section XI.
EXPERIMENTAL METHODS OF FINDING THE SPECIFIC
DENSITY AND SPECIFIC GRAVITY OF BODIES.
55. Solids.
Experiment 52,.— From a hook beneath a scale-pan (Fig. 60)
suspend by a fine thread a small specimen of a substance whose
specific gravity is to be found, and weigh it, while dry, in the air. Then
immerse the body in a tumbler of water (do not allow it to touch the
tumbler, and see that it is completely submerged), and weigh it in
water. The loss of weight in water is evidently G', ie. the weight
of the water displaced by the body; or, in other words, the weight
of a body of water having the same volume as that of the specimen.
Apply the formula (2) for finding the specific gravity.
Big. 60. Fig. 61.
Experiment 53.— Take a piece of sheet lead one inch long and
one-half inch wide, weigh it in air and then in water, and find its loss
of weight in water. [It will not be necessary to repeat this part of
the operation in future experiments.] Weigh in air a piece of cork
or other substance that floats in water, then fold the lead-sinker, and
place it astride the string just above the specimen, completely immerse
both, and find their combined weight in water. Subtract their com-
bined weight in water from the sum of the weights of both in air;
this gives the weight of water displaced by both. Subtract from this
62 DYNAMICS OF FLUIDS.
the weight lost by the lead alone, and the remainder is G/; i.e. the
weight of water displaced by the cork. Apply formula (2), as before.
56. Liquids.
Experiment 54.— Take a specific-gravity bottle that holds when
filled a certain (round) number of grams of water, e.g. 1008, 2008, etc.
Fill the bottle with the liquid whose specific gravity is sought. Place
it on a scale-pan (Fig. 61), and on the other scale-pan place a piece of
metal a, which is an exact counterpoise for the bottle when empty.
On the same pan place weights 6, until there is equilibrium. The
weights placed in this pan represent the,weight G of the liquid in the
bottle. Apply formula (2). The G’ (ie. the 1008, 2008, etc.) is the
same in every experiment, and is usually etched on the bottle.
Experiment 55.— Take a pebble stone (e.g. quartz) about the
size of a large chestnut; find its loss of weight (i.e. G’) in water; find
its loss of weight (i.e. G) in the given liquid. Apply formula (2).
Prepare blanks, and tabulate the results of the experiments above
as follows : —
Name oF SUBSTANCE.
Lead
When the result obtained differs from that given in the table of
specific gravities (see Appendix B), the difference is recorded in the
column of errors (¢).- The results recorded in the column of errors
are not necessarily real errors; they may indicate the degree of im-
purity, or some peculiar physical condition, of the specimen tested.
57. Hydrometers. — If a wooden, an iron, and a lead
ball are placed in a vessel containing mercury (Fig. 62),
SPECIFIC GRAVITY AND SPECIFIC DENSITY. 63
they. will float on the mercury at different depths, accord-
ing to their relative densities. Ice floats, in water with
fey in mercury with ,$8,, of its bulk submerged. Hence
the Sp. D. of mercury is 918 + 68 =about 13.5.
We see, then, that the densities of liquids may be com-
pared by seeing to what depths bodies floating in them
will sink. An instrument (A, Fig. 63) called a hydrometer}
is constructed on this principle. It consists of a glass
tube with one or more bulbs blown in it, loaded at one
end with shot or mercury to keep it in a vertical position
when placed in a liquid. It has a scale of specific densities
on the stem, so that the experimenter has only to place it
in the liquid to be tested, and read its specific density or
specific gravity at that point, B, of the stem which is at
the surface of the liquid.
Fig. 62. Fig. 63.
58. Miscellaneous Experiments.
Experiment 56.— Find the cubical contents of an irregular shaped
body, e.g. astone. Find its loss of weight in water. Remember that
the loss of weight is precisely the weight of the water it, displaces, and
that the volume of one gram of water is one cubic centimeter.
1 Densimeter is 2 more suitable name for this instrument.
64 DYNAMICS OF FLUIDS.
Experiment 57.— Find the capacity of a test-tube, or an irregular
shaped cavity in any body. Weigh the body; then fill the cavity with
water, and weigh again. As many grams as its weight is increased, so
many cubic centimeters is the capacity of the cavity.
Experiment 58.— A fresh egg sinks in water. See if by dissoly-
ing table salt in the water it can be made to float. How does salt
affect the density of the water?
Experiment 59.— Float a sensitive hydrometer in water at about
60° F. (15° C.), and in other water at about 180° F. (82° C.). Which
water is denser?
EXERCISES.
1. In which does a liquid stand higher, in the snout of a coffee-pot
or in the main body? On which does this show that pressure depends,
on quantity or depth of liquid?
2. The areas of the bottoms of vessels A, B, and C (Fig. 64) are equal.
The vessels have the same depth, and are filled with water. Which
vessel contains the more water? On the bottom of which vessel is the
pressure equal to the weight of the water which it contains? How
does the pressure upon the bottom of vessel e compare with the
weight of the water in it?
Fig. 64.
3. A cubic foot of water weighs about 62.5 pounds or 1,000 ounces.
Suppose that the area of the bottom of each vessel is 50 square inches
and the depth is 10 inches; what is the pressure on the bottom of
each? ;
4. Suppose that the vessel A is a cubical vessel; what is the pres-
sure against one of its vertical sides?
5. Suppose that vessel A were tightly covered, and that a tube 10
feet long were passed through a perforation in the cover so that the end
just touches the upper surface of the water in the vessel; then sup-
pose the tube to be filled with water. If the area of the cross-section
SPECIFIC GRAVITY AND SPECIFIC DENSITY. 65
of the bore is 1 square inch, what additional pressure will each side of
the cube sustain ?
6. Suppose that the area of the end of the large piston of a hydro-
static press is 100 square inches; what should be the area of the end
of the small piston that a force of 100 pounds applied to it may produce
a pressure of 2 tons?
7. A solid body weighs 10 pounds in air and 6 pounds in water. (a)
What is the weight of an equal bulk of water? (6) What is its specific
gravity? (c) What is the volume of the body? (d) What would it
weigh if it were immersed in sulphuric acid? [See table of specific
gravities, Appendix B.]
8. A thousand-grain specific-gravity bottle filled with sea-water
requires in addition to the counterpoise of the bottle 1,026 grains to
balance it. (a) What is the specific gravity of sea-water? (b) What’
is the quantity of salt, etc., dissolved in 1,000 grains of sea-water ?
9. A piece of cork floating on water Gisplascs 2 pounds of water.
What is the weight of the cork?
10. In which would a hydrometer sink farther, in milk or water?
11. What metals will float in mercury ?
12. (a) Which has the greater specific gravity, water at 10° C. or
water at 20° C.? (6) If water at the bottom of a vessel could be
raised by application of heat to 20° C. while the water near the upper
surface has a temperature of 10° C., what would happen ?
18. A block of wood weighs 550 grams; when a certain irregular-
shaped cavity is filled with mercury the block weighs 570 grams.
What is the capacity or cubical contents of the cavity?
14. In which is it easier for a person to float, in fresh water or in
sea-water? Why?
15.. Figure 65 represents a beaker gr aduated &—
in cubic centimeters. Suppose that when water
stands in the graduate at 50°*, a pebble stone is
dropped into the water, and the water rises to
75e. (a) What is the volume of the stone?
(6) How much less does the stone weigh in water
than in air? (c) What is the weight of an equal
volume of water? :
16. If a piece of cork is floated on water in
a graduate, and displaces (i.e. causes the water :
to.rise) 7¢°, what is the weight of the cork? Fig. 65.
66 DYNAMICS OF FLUIDS.
17. If a piece of lead (sp. g. 11.85) is dropped into a graduate and
displaces 12¢¢ of water, what does the lead weigh? (a) How would
you measure out 50 grams of water in a graduate? (0) How would
you measure out the same weight of alcohol (sp. g. 0.8)? (¢c) How the
same weight of sulphuric acid (sp. g. 1.84)?
18. What is the density of gold? silver? milk? alcohol?
19. When the barometer stands at 80 inches, how high can alcohol
be raised by a perfect lifting-pump?
20. A measuring glass graduated in cubic centimeters contains
water. An empty bottle floats on the water, and the surface of the
water stands at 50¢. If 10€ of lead shot are placed in the bottle,
where will the surface of the water stand?
21. What evidence do we see daily that there is relative motion
between the sun and the earth ?
22. On what two things does the weight of a body depend?
-23. (a) Can you suck air out of a bottle? (b) Can you suck water
out of a bottle? Explain. .
24. (a) What bodies have neither volume nor shape? (b) What
have volume, but not shape? (c) What have both volume and shape?
_ 25. When the volume of a body of gas diminishes, is it due to con-
traction or compression, 7.e. to internal or external forces?
26. What is the hight of the barometer column when the atmos-
pheric pressure is 10 grams per square centimeter ?
27. A barometer in a diving-bell (page 3) stands at 96°" when a
barometer at the surface of the earth stands at 76°™; what is the
depth of the surface of water inside the bell below the surface
outside ?
28. (a) 40* of lead immersed in water will displace what volume
of water? (0) Will lose how much of its weight?
29. Find the sum in meters of 43m, 150em, 8dm, 65mm, 5,6em,
and 4mm,
30. The sp. g. of hydrogen gas is (page 345) 0.0693. What do
you understand by this statement ?
31. What is the mass of a liter of water at 4°C ?
CHAPTER IIL.
GENERAL DYNAMICS.
e
Section I.
MOMENTUM AND ITS RELATION TO FORCE.
59. Momentum.— An empty car in motion is much
more easily stopped than a loaded car moving with the
same speed. Evidently, if force is employed to destroy
motion, and it takes either a greater force to stop the
loaded car in a given time, or the same force a longer
time, it follows that there must be more motion to be
destroyed in the loaded car than in the empty car mov-
ing with the same velocity. Quantity of motion, more
briefly momentum, and velocity are not identical. Momen-
tum depends upon both mass and velocity; velocity is
independent of mass. Momentum = MV.
The momentum of a moving body is measured by the prod-
uct of tts mass multiplied by its velocity.
60. Relation of Momentum to Force.
Experiment 60.— Weights A and B of the Atwood machine
(Fig. 66), suspended by a thread passing over the wheel C, are in
equilibrium with reference to.the force of gravity; consequently neither
falls. Raise weight A, and let it rest on the platform D, as in Figure
67. The two weights are still in equilibrium. Place weight E, called
a “rider,†on A. There is now an unbalanced force, and if the plat-
form D is removed, there will be motion, 7.e. A and.E will fall, and
B willrise. Set the pendulum F to vibrating. At each vibration it
68
GENERAL DYNAMICS.
causes a stroke of the hammer on the bell G.
At the instant of the first stroke the pendulum
causes the platform D to drop so as to allow
the weights to move. When the weights reach
the ring H, the rider is caught off by the ring.
Raise and lower the ring on the graduated
pillar I, and ascertain by repeated trials the
average distance the weights descend in the in-
terval between the first two strokes of the bell.
Next substitute for E a weight L, double that
of E. Find by trial how far the weights now
descend in the same interval of time as before.
Tt will be found that in the latter case the
weights descend nearly twice as far as in the
first case.
Suppose that weights A and B are each 30
grams, and that weights E and L are respec-
tively 2 grams and 4 grams. Now the force of
gravity which acts on weight E is 2 grams.
Consequently the unbalanced force which put
in motion the three weights A, B, and E, whose
combined weight (disregarding the weight of
wheel C, which is also put in motion) is
(30 + 80 +2 =) 62 grams, was 2 grams. It
is now evident why the descent is slow, for in-
stead of a force of 1 gram acting upon each gram
of matter, as is usually the case with falling
bodies, we have a force of only 2 grams moving
62 grams of matter; consequently the descent
is about »; as fast as that of falling bodies
generally.
But when we employed weight L, we had a
force of 4 grams moving (30+380+4=) 64
grams of matter. Here the force is doubled,
and the distance traversed is nearly doubled;
consequently the average velocity and the mo-
mentum acquired are nearly doubled. Had the
masses moved in the two cases been exactly the
same, the velocity and the momentum would
have been exactly doubled.
FIRST LAW OF MOTION. 69
(1) In equal intervals of time change af momentum ts
proportional to the force employed. x
Experiment 61.— Once more place E on
A, and ascertain how far they will descend
between the first and third strokes of the
bell, 7c. in double the time employed before.
It will be found that they will descend in
the two units of time about four times as
far as during the first unit of time. Later
on it will be shown that, in order to accom-
plish this, the velocity at the end of the sec-
ond unit of time must be twice that at the end
of the first unit of time. If MV represent
the momentum generated during the first
unit of time, then the momentuin generated
during the second unit of time must be about
2MV.
(2) The momentum generated by a
given force is proportional to the time during which the force
acts.
Section II.
FIRST LAW OF MOTION.
The relations between matter and force are concisely
expressed in what are known as Zhe Three Laws of
Motion first enunciated by Sir Isaac Newton.
61. First Law of Motion. — A body at rest remains at
rest, and a body in motion moves with uniform velocity in a
straight line, unless acted upon by some external force.
That part of the law which pertains to motion is briefly
70 GENERAL DYNAMICS.
summarized in the familiar expression, “ perpetual motion.â€
“Is perpetual motion possible?†has been often asked.
The answer is simple, — Yes, more than possible, neces-
sary, uf no force interferes to prevent. What has a person
to do who would establish perpetual motion? Isolate a
moving body from interference of all external forces, such
as gravity, friction, and resistance of the air. Can the con-
dition be fulfilled ?
In consequence of its utter inability to put itself in motion or to stop
itself, every body of matter tends to remain in the state that it is in with
reference to motion or rest; this inability is called inertia. The First Law
of Motion is often appropriately called the Law of Inertia.
——soregoo— -
Section III.
SECOND LAW OF MOTION.
62. Graphical Representation of Motion and Force.
—TIf a person wishes to describe to you the motion of
a ball struck by a bat, he must tell you three things
(1) where it starts, (2) in what direction it moves, ana
(8) how far it goes. These three essential elements may
be represented graphically by
lines. Thus, suppose balls at A
and D (Fig. 68) to be struck
: by bats, and that they move re-
ee spectively to B and E in one
second. Then the points A and D are their starting-
points; the lines AB and DE represent the direction of
their motions, and the lengths of the lines represent the
SECOND LAW OF MOTION. | 71
distances traversed. In reading, the direction should be
indicated by the order of the letters, as AB and DE.
Likewise, the forces which produce the motion may be ~
represented graphically. For example, the points A and
D may represent the points where the forces begin to act,
the lines AB and DE represent the direction in which they
act, and the length of the lines represent their relative
intensities.
Let a force whose intensity may be represented numeri-
cally by 8 (e.g. 8 pounds), acting in the direction AB (Fig.
69), be applied continuously to :
a ball starting at A, and sup-
pose this force capable of mov-
ing it to B in one second; now,
at the end of the second let
a force of the intensity of 4,
directed at right angles to the
direction of the former force, S
act during a second — it would Fig. 69.
move the ball to C. If, however, when the ball is at A,
both of these forces should be applied at the same time, then
at the end of a second the ball will be found at C. Its
path will not be AB nor AD, but an intermediate one,
AC. Still each force produces its own peculiar result, for
neither alone would carry it to C, but both are required.
63. Second Law of Motion.— Change of momentum is
in the direction in which the force acts, and is proportional
to ats intensity and the time during which it acts.
This law implies that an unbalanced force of the same
imtensity, in the same time, always produces exactly the
same change of momentum, regardless of the mass of the
body on which tt acts, and regardless of whether the body is
im motion or at rest, and whether the force acts alone or with
others at the same time.
72 GENERAL DYNAMICS.
Section IV.
COMPOSITION AND RESOLUTION OF FORCES.
64. Composition of Forces. — It is evident that a sin-
gle force, applied in the direction AC (Fig. 69), might
produce the same result that is produced by the two
forces represented by AB and AD. Such a force is called
a resultant. A resultant is a single force that may be sub-
stituted for two or more forces,
and produce the same result
that the simultaneous action
of the combined forces produce.
The several forces that con-
tribute to produce the result-
ant are called its components.
When the components are
given, and the resultant re-
quired, the problem is called
composition of forces. The resultant of two forces acting
simultaneously at an angle to each other may always be
represented by a diagonal of a parallelogram, of which the
two adjacent sides represent the components. Thus, the
lines AD and AB represent respectively the direction and
relative intensity of each component, and AC represents
the direction and intensity of the resultant.
The numerical value of the resultant may be found by
comparing the length of the line AC with the length of
either AB or AD, whose numerical vaiues are known.
Thus, AC is 2.23 times AD; hence, the numerical value
of the resultant AC is (4 x 2.28 =) 8.92.
When more than two components are given, find the result-
Fig. 70.
COMPOSITION AND RESOLUTION OF FORCES. 73
ant of any two of them, then of this resultant and a third, and
so on until every component has been used. Thus in Fig. 70,
AC is the resultant of -AB and AD, and AF is the result-
ant of AC and AE, i.e. of the three forces represented by
the lines AB, AD, and AE. Generally speaking, a motion
may be the result of any number of forces. When we see a
body in motion, we cannot determine by its behavior how
many forces have concurred to produce its motion.
65. Resolution of Forces. — Assume that a ball moves
a certain distance in a cer-
tain direction, AC (Fig.
71), under the combined
influence of two forces,
and that one of the forces
that produces this motion
is represented in intensity
and direction by the line AB: what must be the intensity .
and direction of the other force? Since AC is the result-—
ant of two forces acting at an angle to each other, itis the
diagonal of a parallelogram of which AB is one of the sides.
From C draw CD parallel with and equal to BA, and com-
plete the parallelogram by connecting the points B and C,
and A and D. Then, according to the principle of compo-
sition of forces, AD represents the intensity and direction
of the force which, combined with the force AB, would move
the ball from A to C. The component AB being given,
no other single force than AD will satisfy the question.
Fig. 71.
Experiment 62. — Verify the preceding propositions in the follow-
ing manner: From pegs A and B (Fig. 72), in the frame of a black-
board, suspend a known weight W, of (say) 10 pounds, by means of
two strings connected at C. In each of these strings insert dyna-
mometers and y. Trace upon the blackboard short lines along the
strings from the point C, to indicate the direction of the two com-
74 GENERAL DYNAMICS.
ponent forces; also trace the line CD, in continuation of the line WC,
to indicate the direction and intensity of the resultant. Remove
the dynamometers, extend the
lines (as Ca and Cd), and on
these construct a parallelo-
gram, from the extremities of
the line CD regarded as a
diagonal. It will be found
that 10: number of pounds in-
dicated by the dynamometer
z::CD:Ca; also. that 10:
number of pounds indicated
by the dynamometer y::CD:
: Cb. Again, it is plain that a
single force of 10 pounds must act in the direction CD to produce the
same result that is produced by the two components. Hence, when
two sides of a parallelogram represent the intensity and direction of two
component forces, the diagonal represents the resultant. Vary-the problem
by suspending the strings from different points, as E and F, A and
F, ete.
Fig. 72.
An excellent verification of the Second Law of Motion
and the principle of composition of forces is found in the
fact that a ball, projected horizontally, will reach the
ground in precisely the same time that it would if dropped
from a state of rest from the same hight. That is, any
previous motion a body has in any direction does not
affect the action of gravity upon the body.
Experiment 63.— Draw back the rod d (Fig. 73) toward the left,
and place the detent-pin c in one of the slots. Place one of the brass
balls on the projecting rod, and in contact with the end of the instru-
ment, as at A. Place the other ball in the short tube B. Raise the
apparatus to as great an elevation as practicable, and place it in a
perfectly horizontal position. Release the detent, and the rod, pro-
pelled by the elastic force of the spring within, will strike the ball B
with great force, projecting it in a horizontal direction. At the same
instant that B leaves the tube and is free to fall, the ball A is re-
leased from the rod, and begins to fall. The sounds made on strik-
COMPOSITION AND RESOLUTION OF FORCES. 75
ing the floor reach the ears of the observer at the same instant;
this shows that both balls reach the floor in sensibly the same time,
and that the horizontal motion which one of the balls has does not
affect the time of its fall.
Fig. 73.
66. Composition of Parallel Forces, — If the strings
CA and CB (Fig. 72) are brought nearer to each other (as
when suspended from B and E) so that the angle formed
by them is diminished, the component forces, as indicated
by the dynamometers, will decrease, till the two forces
become parallel, when the sum of the components just
equals the weight W. Hence, (1) two or more forces
applied to a body act to the greatest advantage when they
are parallel, and in the same direction, in which case their
resultant equals their sum.
On the other hand, if the strings are separated from
each other, so as to increase the angle formed by them,
the forces necessary to support the weight increase until
they become exactly opposite each other, when the two
forces neutralize each other, and none is exerted in an
upward direction to support the weight. If the two strings
76 GENERAL DYNAMICS.
are attached to opposite sides of the weight (the weight
being supported by a third string), and pulled with equal
force, the weight does not move. But if one is pulled
with a force of 15 pounds, and the other with a force of
10 pounds, the weight moves-in the direction of the
greater force; and if a third dynamometer is attached to
the weight, on the side of the weaker force, it is found
that an additional force of five pounds must be applied
to prevent motion. Hence, (2) when two or more forces
are applied to a body, they act to greater disadvantage the
farther their directions are removed from one another ; and
the result of parallel forces acting in opposite directions is
a resultant force in the direction of the greater force, equal
to their difference.
~ When parallel forces are not applied at the same point,
the question arises, What will be the point of application
of their resultant? To the opposite extremities of a bar
AB (fig.74) apply two
sets of weights, which
shall be to each other
as 8 lbs.:1 lb. The
resultant is a single
force, applied at some
point between A and
B. To find this point it is only necessary to find a
point where a single force, applied in an opposite direc-
tion, will prevent motion resulting from the parallel
forces; in other words, to find a point where a support
may be applied so that the whole will be balanced. That
point is found by trial to be at the point C, which divides
the bar into two parts so that AC: CB::11b.:3 lbs.
Hence, (8) when two parallel forces act upon a body in
the same direction, the distances of their points of applica-
Fig. 74.
COMPOSITION AND RESOLUTION OF FORCES. 77
tion from the point of application of their resultant are
inversely as their intensities.
The dynamometer E indicates that a force equal to the
sum of the two sets of weights is necessary to balance the
two forces. A force whose effect is to balance the effects
of one or more forces is called an equilibrant. The result-
ant of the two components is a single force, equal to their
sum, applied at C in the direction CD.
67. Moment of a Force.— The tendency of a force
to produce rotation about a fixed point as C (Fig. 75)
is called its moment
about that point. The ; er a
perpendicular distance “|e 520) tae
(AC or BC) from the 5 : B
fixed point (C) to the eee:
line of direction in which the force acts (AD or BE) is
called the leverage or arm. The moment of a force is meas-
ured by the product of the number of units of force into the
number of units of leverage. For example, the moment of
the force applied at A is expressed numerically by the
number (80 x 2=) 60.
68. Equilibrium of Moments.— The moment of a
force is said to be positive when it tends to produce rota-
tion in the direction in which the hands of a clock move,
and negative when its tendency is in the reverse direction.
If two forces act at different points of a body which is
free to rotate about a fixed point, they will produce equi-
librium when their moments are opposite and their alge-
braic sum is zero. Thus the moment of the force applied
at A (Fig. 75) is (-80 X2)—60. The moment of the
force applied at B in an opposite direction is accordingly
(+20 x8=)+60. Their algebraic sum is zero, conse-
quently there is equilibrium between the forces.
78 GENERAL DYNAMICS.
When more than two forces act in this manner, there
will be equilibrium if the sum of all the positive mo-
i x ments is equal to the
sum of all the nega-
tive moments. Thus
the sum of the posi-
26 ig tive moments acting
pee: about point F (Fig.
76) is (f) 45+ (e) 25+ (a4) 80=100; the sum of the
negative moments acting about the same point is (¢) 80 +
(ad) 40+ (6) 80=100; the two sums being equal, the
forces are in equilibrium.
1g 8
69. Mechanical Couple. —
If two equal, parallel, and con-
trary forces are applied to op-
posite extremities of a stick
AB (fig. TT), no single force
can be applied so as to keep
ee the stick from moving; there
will be no motion of translation, but simply a rotation
around its middle point C. Such a pair of forces, equal,
parallel, and opposite, is called a mechanical couple.
Section V.
THE THIRD LAW OF MOTION.
70. Introductory Experiments.— We have learned
that motion cannot originate in a single body, but arises
from mutual action between two bodies or two parts of a
body. For example, a man can lift himself by pulling
THE THIRD LAW OF MOTION. 79
on a rope attached to some other object, but not by his
boot-straps, or a rope attached to his feet. In every change
in regard to motion there are always at least two bodies
oppositely affected.
Experiment 64,— Suspend the deep glass bucket A (Fig. 78) by
means of a strong thread two feet long, so that the long projecting
pointer may be directly over a dot made on a
piece of paper placed beneath ;. or place beneath
another pointer, B, so that the two points shall
just meet. Fill the bucket with water. Gravity
i causes the water to flow from the orifice C;
118A but the bucket moves in the opposite direction.
Fig. 78. Fig. 79.
_ Experiment 65.— Place the hollow glass globe and stand (Fig.
79) under the receiver of an air-pump, and exhaust the air. The air
within the globe expands, and escapes from the small orifices a and ¢
at the extremity of the two arms. But this motion of the air is
attended by an opposite motion of the arms and globe, and a rapid
rotation is caused.
A man in a boat weighing one ton pulls at one end of a
rope, the other end of which is held by another man, who
80 GENERAL DYNAMICS.
weighs twice as much as the first man, in a boat weighing
two tons: both boats will move towards each other, but
in opposite directions; if the resistances which the two
boats encounter were the same, the lighter boat would
move twice as fast as the heavier, but with the same
momentum.
If the boats are near each other, and ae men push each
other’s boats with oars, the boats will move in opposite
directions, though with different velocities, yet with equal
momenta.
The opposite impulses received by the bodies concerned
are usually distinguished by the terms action and reaction.
We measure these, when both are free to move, by the
momenta generated, which is always the same in both
bodies.
71. Third Law of Motion. — To every action there ts
an equal and opposite reaction.
The application of this law is not always obvious.
Thus, the apple falls to the ground in consequence of the
mutual attraction between the apple and the earth. The
earth does not appear to fall toward the apple. But,
as the mass of the earth is enormously greater than that
of the apple, its velocity, for an equal momentum, is
proportionately less.
EXERCISES.
1. (a) Why does not a given force, acting the same length of time,
give a loaded car as great a velocity as an empty car? (6) After
equal forces have acted for the same length of time upon both
cars, and given them unequal velocities, which will be the more
difficult to stop?
2. (a) The planets move unceasingly; is this evidence that here
are forces pushing or pulling them along? (6) None of their
motions are in straight lines; are they acted upon by external forces?
THE THIRD LAW OF MOTION. 81
8. A certain body is in motion; suppose that all hindrances to
motion and all external forces were withdrawn from it, how long
would it move? Why? In what direction? Why? With what
kind of motion, #.e. accelerated, retarded, or uniform? Why?
4, Copy upon paper and find the resultant of the components AB
and AC in each of the four diagrams in Figure 80. Also assign ap-
propriate numerical values to each component, and find the corre-
sponding numerical value of each resultant.
5. Explain how rotating lawn-sprinklers are kept in motion.
6. When you leap from the earth, which receives the greater mo-
mentum, your body or the earth ?
7. When you kick a door-rock, why does snow or mud on your
shoes fly off?
8. Why cannot a person propel a vessel during a calm by blowing
the sails with a big bellows placed on the deck of the same vessel?
9. In swimming, you put water in motion; what causes your body
to advance? What propels the bird in flying?
10. Could a rocket be projected in the usual way if there were no
atmosphere ?
11. If aman in a boat moves it by pulling on a rope at one end,
the other end being fastened to a post, how is the boat put in motion ?
Would it move either faster or slower if the other end were fastened
to another boat free to move, the man exerting the same force?
12. An ounce bullet leaves a gun weighing 8 pounds with a velocity
of 800 feet per second. What is the maximum velocity of the gun’s
recoil ?
82 GENERAL DYNAMICS.
Section VI.
APPLICATIONS OF THE THREE LAWS OF MOTION. — CENTER
OF GRAVITY.
72. Center of Gravity Defined. — Let Figure 81 repre-
sent any body of matter; for instance, a stone. Every
molecule of the body is acted upon by the force of gravity.
The forces of gravity of all the mole-
cules form a set of parallel forces act-
ing vertically downward, the resultant
of which equals their sum, and has the
same direction as its components. The
resultant passes through a definite
i point in whatever position the body
FY may be, and this point is called its cen-
Fig. 81. ter of gravity. The center of gravity
(eg.) of a body is, therefore, the point of application of the
resultant of all these forces ; and for practical purposes the
whole weight of the body may be supposed to be concentrated
at its center of gravity.
Let G in the figure represent this point. For practical
purposes, then, we may consider that gravity acts only
upon this point, and in the direction GF. If the stone
falls freely, this point cannot, in obedience to the first law
of motion, deviate from a vertical path, however much the
body may rotate about this point during its fall. Inas-
much, then, as the c.g. of a falling body always describes
a definite path, a line GF that represents this path, or the
path in which a body supported tends to move, is called
the line of direction.
It is evident that if a force is applied to a body equal to
APPLICATIONS OF THE THREE LAWS OF MOTION. 83
its own weight, and opposite in direction, and anywhere in
the line of direction (or its continuation), this force will
be the equelibrant of the forces of gravity; in other words,
the body subjected to such a force is in equilibrium,
and is said to be supported, and the equilibrant is called
its supporting force. To support any body, then, i is
only necessary to provide a support for tts center of grav-
ity. The supporting force must be applied somewhere in
the line of direction, otherwise the body will fall. The dit-
ficulty of poising a book, or any other object, on the
end of a finger, consists in keeping the Bupport under the
center of gravity.
Figure 82 represents a toy called a “ witch,†consisting of a cylinder of
pith terminating in a hemisphere of lead. |
The toy will not lie in a horizontal position,
as shown in the figure, because the support
is not applied immediately under its c.g. at
G; but when placed horizontally, it immedi-
ately assumes a vertical position. It appears
to the observer to rise; but, regarded in a mechanical sense, it really
falls, because its c.g., where all the weight is supposed to be concentrated,
takes a lower position.
Fig. 82.
73. How to Find the Center of Gravity of a Body. —
Imagine a string to be attached to
a potato by means of a tack, as in
Figure 88, and to be suspended
from the hand. When the potato
is at rest, there is an equilibrium
of forces, and the c.g. must be some-
where in the line of direction an;
hence, if a knitting-needle is thrust
vertically through the potato from
a, 80 as to represent a continuation ES EIEE SS.
of the vertical line oa, the c.g. must lie somewhere i in the
84 GENERAL DYNAMICS,
path an made by the needle. Suspend the potato from
some other point, as 6, and a needle thrust vertically
through the potato from 6 will also pass through the e.g.
Since the c.g. lies in both the lines an and 6s, it must be at
ce, their point of intersection. It will be found that, from
whatever point the potato is supported, the point e will
always be vertically under the point of support. On the
same principle the c.g. of any body is found. But the c.g.
of a body may not be coincident with any particle of the
body; for example, the c.g. of a ring, a hollow sphere, ete.
74. Equilibrium of Bodies. — That a body acted on
solely by its weight may be in equilibrium (7.e. supported),
it is sufficient that its line of direction shall pass through
the point or surface by which it is supported. For ex-
ample, when a body is to be supported at its base, the line
of direction must pass through the base. The base of a
body is not necessarily limited to that part of the under
surface of a body that touches its support. For example,
if a string is placed around the four legs of a table near
the floor, the rectangular figure bounded By the string is
the base of the table.
It is evident that the resultant weight of a body acting
at its c.g. tends to bring this point as low as possible; hence
a body tends to assume a position such that its cg. will be
as low as possible. .
In whatever manner a body is supported, ‘the equilib-
rium is stable if, on moving the body, the center of gravity
ascends; unstable, if it descends; and neutral, if it neither
ascends nor descends, as that of a sphere rolled on a
horizontal plane. ;
‘Experiment 66.— Try to support a ring on the end of a stick, as
at b (Fig. 84). If you can keep the support exactly under the c.g. of
APPLICATIONS OF THE THREE LAWS OF MOTION. 85
the ring, there will be an equilibrium of forces, and the ring will re-
main at rest. But if it is slightly disturbed, the equilibrium will be
destroyed, and the ring will fall. Support it at a; in this position its
c.g. is as low as possible, and any disturbance will raise its c.g.; but,
in consequence of the tendency of the c.g. to get as low as possible, it
will quickly fall back into its original position.
Fig. 84. Fig. 85.
Experiment 67.— Prepare a V-shaped frame like that shown in
Figure 85, the bar AC being about three feet long; place it so that
the end will overlap the table two or three inches, and hang a heavy
weight or a pail of water on the hook B, and the whole will be sup-
ported. Rock the weight back and forth by raising the end C and
allowing it to fall. What kind of equilibrium is this? Remove the
weight, and the bar falls to the floor. Why?
The stability of a body varies with its breadth of base, and
inversely with the hight of its e.g. above its base. Support
a book on a table so that it may have three different
‘legrees of stability, and account for the same.
QUESTIONS,
1. Why is a person’s position more stable when his
feet are separated a little, than when close together ?
2. How does ballast tend to keep a vessel from over-
turning ?
8. For what two reasons is a pyramid a very stable
structure ?
4. What point in a falling body descends in a straight
86 GENERAL DYNAMICS.
line? What is this line called? Disregarding the motions of the
earth, toward what point in the earth does this line tend?
5. It is difficult to balance a lead-pencil on the end of a finger;
but by attaching two knives to it, as in Figure 86, it may be rocked
to and fro without falling, Explain.
Section VII.
APPLICATIONS OF THE THREE LAWS OF MOTION CONTIN-
UED. — EFFECT OF A CONSTANT FORCE ACTING ON A
BODY PERFECTLY FREE TO MOVE.— FALLING BODIES.
75. Any Force, however Small, can move any Body
of however Great Mass. — For example, a child can move
a body having a mass equal to that of the earth, pro-
vided only that the motion of this body is not hindered
by a third body. Moreover, the amount of momentum
that the child can generate in this immense body in a
given time is precisely the same as that which it would
generate by the exertion of the same force for the same
length of time on a body having a mass of (say) 10 pounds.
Momentum is the product of mass into velocity; so, of
course, as the mass is large, the velocity acquired in a
given time will be correspondingly small. The instant the
child begins to act, the immense body begins to move.
Its velocity, infinitesimally small at the beginning, would
increase at almost an infinitesimally slow rate, so that it
might be months or years before its motion would become
perceptible. It is easy to see how persons may get the
impression that very large bodies are immovable except
by very great forces. The erroneous idea is acquired that
APPLICATIONS OF THE THREE LAWS OF MOTION. 87
bodies of matter have a power to resist the action of forces
in causing motion, and that the greater the mass, the
greater the resistance (“quality of not yielding to force,â€
Webster). The fact is, that no body of whatever mass has
any power to resist motion ; in other words, “a body free to
move cannot remain at rest under the slightest unbalanced
force tending to set it in motion.†Furthermore, a given
foree acting for the same length of time will generate the
same amount of momentum in all bodies free to move, trre-
spective of their masses.
_@6. Falling Bodies. -— A constant force is one that acts
continuously and with uniform intensity. Nature fur-
nishes no example of a body moved by a force so nearly
constant as that of a body falling through a moderate dis-
tance to the earth. Inasmuch as the velocity of falling
bodies is so great that there is not time for accurate obser-
vation during their fall, we must, in investigating the laws
of falling bodies, resort to some method of checking their
velocity, without otherwise changing the character of the
fall.
Experiment 68.— Ascertain, as in Experiment 60, how far the
weights, moved by a constant force (e.g. 2 grams), descend during
one swing of the pendulum. Inasmuch as all swings of the pendulum
are made in equal intervals of time, we may take the time of one
swing as our unit of time. We will, for convenience, take for our
unit of distance the distance the weights fall during the first unit of
time, call this unit a space, and represent the unit graphically by the
line ab (Fig. 87).
Next ascertain how far the weights fall from the starting-point
during two units of time (ie. two swings of the pendulum). The
distance will be found to be four spaces, or four times the distance
that they fell during the first unit of time. This distance is repre-
sented by the line ac. But we have learned that the weights descend
only one space (ab) during the first unit of time, hence they must
388 GENERAL DYNAMICS.
descend three spaces during the second unit of time. The weights,
under the action of the constant force, start from a state of rest, and
move through one space in a unit of time. This force, continuing to
act, accomplishes no more nor less during any subsequent
@ unit of time. But the weights move through three spaces
1UofT—p during the second unit of time; hence two of the spaces
must be due to the velocity they had acquired at the end
of the first unit. In other words, if the ring H is placed
at the point (corresponding to 0) reached by the weights
© at the end of the first unit of time, then weight E will be
caught off (i.e. the constant force will be withdrawn),
and the other weights will, in conformity with the first
law of motion, continue to move with uniform velocity
from this point (except as they are retarded by resist-
ance of the air and the friction of the wheel C), and will
descend two spaces during the second unit and reach
pointe. (Try it.)
The weights, therefore, have at the end of the first
unit of time a velocity (V) of two spaces. But they
sUofT—d started from a state of rest: hence the constant force
Fig. 87. causes, during the first unit of time, an acceleration of
velocity equal to two spaces.
Let the weights descend three units of time, and it will be found
that the weights will descend in this time nine spaces (ad), or five
spaces (cd) during the third unit of time. One of these five spaces
is due to the action of the force during the third unit of time; the
weights must then have had at point c (i.e. at the end of the second unit
of time) a velocity of four spaces. But at the end of the first unit
of time they had a velocity of two spaces; then they must have gained
during the second unit of time a velocity of two spaces. It seems,
then, that the effect of a constant force applied to a body is to produce
uniformly accelerated motion when there are no resistances.
The acceleration due to gravity is usually represented by g, and is
always twice the distance (4 g) traversed during the first unit of time.
When a body is acted upon by any other constant force, the accelera-
tion produced by the force is usually represented by the letter A.
2Uo0f Te
APPLICATIONS OF THE THREE LAWS OF MOTION. 89
Arrange the results of your observations in a tabulated form as
follows : —
: Distance passed
5 Total distance over in each
No. of units of passed over. unit; also av-
Velocity at the | Increase of ve-
end of each] locity in each
unit. unit, %.e. ac-
celeration.
time. (8) erage velocity.
(s) (vy)
2G9)
4 “
6 7
8 6c
77. Formulas for Uniformly Accelerated Motion. —
If we substitute A for g, and represent the distance
traversed during a given unit of time by s, and the total
distance the body has accomplished from the outset to
the end of a given unit of time (T) by S, we derive from
our tabulated results the following formulas for solving
problems of uniformly accelerated motion : —
@) V=(Ax2T)=AT.
(2) s=fsA(2T—1).
(83) S=3ZAT2
Hence, (1) the velocity acquired varies as the time; (2) the
spaces passed over in successive equal intervals of time vary
as the odd numbers 1, 8, 5, T, etc.; and (8) the entire space
traversed varies as the square of the time.
Strictly speaking, a falling body is not under the influence of a constant
force, inasmuch as gravity varies inversely as the square of the distance
from the center of the earth. But for small distances the variation may
be, for all practical purposes, disregarded, as at a hight of a kilometer
(about 2 of a mile) it is only about z7,, of the weight at the surface. It
can be shown mathematically that the velocity that would be acquired by
a body falling freely to the earth’s surface from an infinite distance would
be about 35,000 feet per second.
90 GENERAL DYNAMICS.
78. Velocity of a Falling Body Independent of its
Mass and Kind of Matter. — If we grasp a coin and a bit
of paper between the thumb and finger, and release both
at the same instant, the coin will reach the floor first. It
would seem as though a heavy body falls faster than a
light body. Galileo was the first to show the falsity of
this assumption. He let drop from an eminence iron balls
of different weights: they all reached the ground at the
same instant. Hence he concluded that the velocity of a
falling body is independent of its mass.
He also dropped balls of wax with the iron balls. The
iron balls reached the ground first. Are some kinds of
matter affected more strongly by gravitation than
others? If a coin and several bits of paper are
placed in a long glass tube (Fig. 88), the air ex-
hausted, and the tube turned end for end, it will
be found that the coin and the paper will fall with
equal velocities. Hence, the earth attracts all matter
alike. A wax ball of the same size as an iron ball
meets with the same resistance from the air that
the iron ball does; but since the mass of the former
is less than that of the latter, the force acting on
the former is less, and a less force cannot over-
Fig. come the same resistance as quickly, consequently
88. in the air the wax ball falls a little more slowly.
We conclude, therefore, that in a vacuum all bodies fall
with equal velocities.
Experiments show that in the latitude of the Northern
States the acceleration, 7.e. the value of g, is, near sea-level
and in a vacuum, 324 feet (9.8") per second; that is, the
velocity gained by a falling body, disregarding the resist-
ance of the air, is 325 feet per second, and the body falls
in the first second 167, feet (4.9â„¢).
APPLICATIONS OF THE THREE LAWS OF MOTION. 91
EXERCISES.
1. What is a constant force? What effect does it produce on every
body waoen there are no resistances?
2. (a) How far will ap B Cc D
a body fallina vacuum _{_ H
in one second? (6) What
is its velocity at theend
of the first second? (e)
What is its acceleration
per second?
3. (a) How far will a G M
body fall in ten seconds?
(6) How far will it fall
in the tenth second? P
(c) What is its velocity
at the end of the tenth second? (d) What is its average velocity
during the tenth second?
4. (a) How far will a body fall in one-fourth of a second? What
is the velocity of a falling body at the
end of the first quarter of a second of
its fall?
5. A body is projected from point
A (Fig. 89) in the horizontal direction
AII. (a) If there were no resistance
of the air, and gravity did not act on
it, it would go a distance during the
first unit of time represented by AB;
how far would it go during the second
and third units of time? (In every
answer quote the law of motion in
conformity with which your answer is
given.) (6) If the body were dropped
from A, it would, reach successively
points E, F, and G at the ends of the
first, second, and third units of time.
If the body were projected horizontally
in the direction AH, and gravity acts
during its flight, what points will the Fig. 90.
body successively reach at the end of the same units of time?
Fig. 89.
92 GENERAL DYNAMICS.
6. (a) Suppose that a body is projected obliquely upward in the
direction AH (Fig. 90), (gravity meantime acting on the body); what
points will the body reach successively at the end of the first, second,
and third units of time? (6) How far will the ascending body vir-
tually fall- during the first unit of time? (c) How far during the
second unit? (d) How far during the third unit? (e) Show that your
answers are consistent with the Second Law of Motion.
7. (a) Under the action of a constant force, a body meeting with no
resistances moves from a state of rest 20 feet during the first minute:
how far will it goin an hour? (4) Suppose at the end of the first
minute the force should cease to act, how far would the body go in an
hour from that instant?
—-059400——
Section VIII.
APPLICATIONS OF THE THREE LAWS OF MOTION CONTIN-
UED. — CURVILINEAR MOTION.
79. How Curvilinear Motion is Produced. — Motion
is curvilinear when its direction changes at every point.
But according to the first law of motion, every moving
body proceeds in a straight line, unless compelled to
depart from it by some external force. Hence curvilinear
motion can be produced only by an external force acting
continuously upon the body at an angle to the straight
path in which the body tends to move, so as constantly
to change its direction. In case the body moves in a>
circle, this force acts at right angles to the path of the
body or towards the center of motion ; hence this deflecting
force has received the name of centripetal force. —
80. Centrifugal Force.
Experiment 69.— Cause a ball to rotate around your hand by
means of a string attached to it and held in the hand. Observe
APPLICATIONS OF THE THREE LAWS OF MOTION. 938
closely every phase of the operation. First, you make a movement as
if to project the ball in a straight line. Immediately you begin to
pull on the string to prevent its going in a straight line. By a con-
tinuous exertion of these two forces in a short time the ball acquires
great speed. You may now cease to exert any projecting force, and
simply keep the hand still; but as the ball has acquired a motion, and
all motion tends to be in a straight line, you are still obliged to exert a
pulling force to deflect it from this path. Observe that as the velocity
of the ball is retarded by the resistance of the air, the pulling or
deflecting force which you are obliged-to employ rapidly diminishes. .
To satisfy yourself that the ball tends to move in a straight line, let
go the string or cut it, and the ball immediately moves off in a straight
line, or simply perseveres in the direction it had at the instant the
string was cut. Observe that the ball appears while rotating to be
pulling your hand; but you know that all the force concerned originates
in yourself, and that this apparent pull on the part of the ball is only
the effect of the reaction of the force which you exert on the ball.
This apparent reactionary force is called centrifugal force.
Centrifugal force is the reaction of a revolving body on
the body that guides it, and is equal and opposite to the cen-
tripetal force (see Third Law of Motion).
When you swing the ball about your hand you ae
that the force of the pull increases with the velocity, and
more rapidly than the velocity. Careful observations have
determined that for bodies revolving in circular orbits the
centripetal (and, of course, centrifugal) force varies as the
mass of the body and the square of its velocity.
The farther a point is from the axis! of motion of a rigid body, the
farther it has to move during a rotation; consequently the greater its
velocity. Hence, bodies situated at the earth’s equator have the greatest
velocity, due to the earth’s rotation, and consequently the greatest tendency
to fly off from the surface, the effect of which is to neutralize, in some
measure, the force of gravity. It is calculated that a body weighs about
yg less at the equator than at either pole, in consequence of the greater -
centrifugal force at the former place. But 289 is the square of 17; hence,
£
1 dais; an imaginary straight line passing through a body about which it rotates.
94 GENERAL DYNAMICS.
if the earth’s velocity were increased seventeen-fold, objects at the equator
would weigh nothing.
We have also learned (page 17) that a body weighs more at the poles,
in consequence of the oblateness of the earth. This is estimated to make
a difference of about ;4;. Hence a body will weigh at the equator sit
gig= (about) 74, less than at the poles.
The attraction between the sun and the earth causes these bodies to
move in curvilinear paths,
performing what is called
1, annual revolutions. The
HE motion of both these bodies, ~
were it not for this mutual
attraction (and the attraction
of other celestial bodies),
would be eternally in straight lines, but in consequence of their mutual
attraction both rotate about a point C (Fig. 91), which is the center of
gravity of the two bodies considered as one body (as if connected by a
rigid rod). If both bodies had equal masses, the center of gravity and
center of motion would be half-way between the two bodies; but as the
mass of the earth is less than that of the sun, so its velocity and distance
traversed are proportionally greater.
Fig. 91.
i
Fig. 93.
Experiment 70.— Arrange some kind of rotating apparatus, e.g.
R (Fig. 92). Suspend a skein of thread a (Fig. 93) by a string, and
rotate; it assumes the shape of the oblate spheroid a’. Suspend a
glass globe G (Fig. 92) about one-tenth full of colored water, and
rotate. The liquid gradually leaves the bottom, rises, and forms an
equatorial ring within the glass. This illustrates the probable method
by which the earth, on the supposition that it was ence in a fluid
APPLICATIONS OF THE THREE LAWS OF MOTION. 95
state, assumed its present spheroidal state. (Explain.) Pass a string
through the longest diameter of an onion c¢, and rotate; the onion
gradually changes its position so as to rotate on its shortest axis.
It may be demonstrated mathematically, as well as experi-
mentally, that a freely rotating body is in stable equilib-
rium only when rotating about its shortest diameter; hence
the tendency of a rotating body to take this position.
QUESTIONS.
1. (@) What is the cause of the stretching force exerted on the
rubber cord when you swing a return-ball about your hand?
(6) Suppose that you double the velocity of the ball; how many times
will you increase this stretching force?
2. Why do wheels and grindstones, when rapidly rotating, tend to
break, and the pieces fly off? :
3. On what does the magnitude of the pull between a rotating body
and its center of motion depend?
4. (a) Explain the danger of a carriage being overturned in turning
a corner. (0) How many fold is the tendency to overturn increased
by doubling the velocity of the carriage?
——-0£9g00——
Section IX.
APPLICATION OF THE THREE LAWS OF MOTION CONTIN-
UED. — THE PENDULUM.
81. Laws of the Pendulum.
Experiment 71.— Suspend iron balls by strings, as in Figure 94.
Make A and B the same length. Draw A and B one side, and to dif-
ferent hights, so that one may swing through a longer are than the
other, and let both drop at the same instant. One moves much
faster than the other, and completes a longer journey at each swing,
but both complete their swing or vibration at the same time.
Hence (1) the time of vibration of a pendulum is (strictly speaking,
approximately) independent of the iength of the arc.
96 GENERAL DYNAMICS.
Experiment 72.— Set all the balls swinging; only A and B swing
together, i.e. in the same time. The shorter the pendulum, the faster
it swings. Make B about 89 inches long from the point of sus-
pension to the center of the ball, regulating
this length, as necessity may require, so that
the number of vibrations made by the pen-
dulum in one minute shall be exactly 60; in
other words, so that it shall “beat seconds.â€
(Accurately, a pendulum that beats seconds
is 39.09 inches long.) Make C one-fourth
as long as B. Count the vibrations made
by C in one minute; it makes 120 vibrations
in the same time that B makes 60 vibrations.
Make D one-ninth the length of B; the
former makes three vibrations while the
latter makes one. Consequently the time of
vibration of the former is one-third that of
the latter.
Hence (2) the time of vibration of a pendu-
lum varies as the square root of its length.
By experiments too difficult for ordinary
school work, it has been ascertained that
(8) the time of vibration of a pendulum varies
inversely as the square root of the force of
gravity (apon which the value of g depends).
Hence it is apparent that by determining
the time of vibration of a pendulum of the
Fig. 94. same length, at different distances from the
center of gravity of the earth (e.g. at the top and bottom of a
mountain, or at- sea-level at different latitudes), the relative value
of g at these places may be ascertained.
Experiment 73.— Loosen the binding-screw in the bob of the pen-
dulum of the Atwood machine (Fig. 66), and place the bob at differ-
ent elevations on the pendulum-rod. Count the number of vibrations
made by the pendulum in a minute, when the bob is placed at these
different elevations. The greater the elevation of the bob, — in other
words, the shorter the pendulum, —the greater the number of vibra-
tions made. We learn by this experiment that the time of vibration
of a pendulum may be regulated by raising or lowering its bob.
APPLICATIONS OF THE THREE LAWS OF MOTION. 97
EXERCISES.
1. One pendulum is 20 inches long, and vibrates four times as fast
as another. How long is the other?
2. (a4) What effect on the rate of vibration has the weight of its
bob? (6) What effect has the length of the arc? (c) What affects
the rate of vibration of a pendulum?
3. How can you quicken the vibration of a pendulum threefold?
4, A clock loses time. (a2) What change in the pendulum ought to
be made? (6) How would you make the correction ?
5. Two pendulums are four and nine feet long respectively. While
the short one makes one vibration, how many will the long one
make ?
6. How long is a pendulum that makes two vibrations in a second ?
7. What is the time of vibration of a pendulum (39.09 + 4=) 9.75 in.
long?
8. The number of vibrations made by a given pendulum in a given
time varies as the square root of the force of gravity. Force of grav-
ity at any place is expressed by the value of g (i.e. by the acceleration
which it produces). (a) If at a certain place a pendulum 89.09 in.
long make 8600 vibrations in an hour, and the value of g is 32.16 ft.,
what is the acceleration at a place where the same pendulum makes
3590 vibrations in the same time? (6) Which of the two places is
nearer the center of gravity of the earth?
9. Suggest some way by which the force of gravity at different
latitudes and altitudes may be determined.
10. (a) A certain body weighs 12 lbs. where the value of g is 32.16 ft.;
what will the same body weigh at a place where g= 82 ft.? (6) Sup-
pose that the former place is at the surface of the earth and 4000 miles
from the earth’s center of gravity; how far above it is the latter place?
(See page 16.)
11. A pebble is suspended by a thread 2 ft. long; required the
number of vibrations it will make in a minute.
12. Why do not heavy bodies fall faster than light ones in a vacuum?
13. Take equal masses of wood and lead; which weighs more?
14. A stone falls from the top of a railway carriage which is mov-
ing at the rate of one-half of a mile a minute. Find what horizontal
distance and what vertical distance the stone will have passed through
in one-tenth of a second, disregarding the resistance of the air.
Ans. 4.4 ft.; .16 ft.
CHAPTER IV.
WORK AND ENERGY.
Section I.
METHODS OF ESTIMATING WORK AND ENERGY.
$2. Work.— Whenever a force causes motion, it does
work. A force may act for an indefinite time without
doing work; for example, a person may support a stone
for a time and become weary from the continuous appli-
cation of force to prevent its falling, but he does no work
upon the stone because he effects no change. When a
force acts through space, work is done. Let.the person
holding the weight exert just a little more force; the
weight will rise, and work will be done.
A body that is moved is said to have work done upon tt;
and a body that moves another body is said to do work
upon the latter. When the heavy weight of a pile-driver
is raised, work is done upon it; when it descends and
drives the pile into the earth, work is done upon the pile,
and the pile in turn does work upon the matter in its
path. ;
The act of doing work may consist in a mere transfer of
energy from the body doing work to the body on which work
is done, or tt may consist in a transformation of energy from
_ one kind to some other kind, as when the pile-driver strikes
METHODS OF ESTIMATING WORK AND ENERGY. 99
the pile and the pile is forced into the earth, a part of the
energy concerned in each case is transformed into heat,
which we shall learn farther on is molecular energy.
In future chapters we shall discuss the subject of transformations of
energy; for the present our discussions relate chiefly to transferences of
energy.
83. Formulas for Estimating Work. — Force and space
(or distance) are the essential elements of work, and neces-
sarily are the quantities employed in estimating work. A
given force acting through a space of one foot, in raising
a weight, does a certain amount of work; it is evident
that the same force acting through a space of two feet
would do twice as much work. Hence the general formula
FS=W, - (1)
in which F represents the force employed, S the space
through which the force acts, and W the work done.
In case a force encounters resistance, the magnitude of
the force necessary to produce motion varies as the resist-
ance. Often the work done upon a body is more con-
veniently determined by multiplying the resistance by the
space through which tt is overcome, and our formula becomes
by substitution of R (resistance) for F (the force which
overcomes it)
RS = W. (2)
For example, a ball is shot vertically upward from a rifle
in a vacuum; the work done upon the ball (by the explo-
sive force of the gunpowder) may be estimated by multi-
plying the average force (difficult to ascertain) exerted
upon it, by the space through which the force acts (a little
greater than the length of the barrel); or by multiplying
the resistance to motion offered by gravity, z.e. its weight
(easily ascertained) by the distance the ball ascends.
* 100 WORK AND ENERGY.
84. Energy, Kinetic and Potential. — Every moving
body can impart motion; hence it can do work upon an-
other body, and is therefore said to possess energy. The
energy of a body ts tts “capacity to do work.†The energy
which a body possesses in consequence of its motion is
called kinetic energy.
A stone lying on the ground is devoid of energy. Raise
it and place it on a shelf; in so doing you perform work
upon it. As you look atit lying motionless upon the shelf,
it appears as devoid of energy as when lying on the earth.
Attach one end of a cord to it and pass it over a pulley
and wind a portion of the cord around the shafé connected
with a sewing-machine, coffee-mill, lathe, or other con-
venient machine. Suddenly withdraw the shelf from be-
neath the stone. The stone moves; it communicates motion
to the machinery, and you may sew, grind coffee, turn
wood, etc., with the energy given to the machine by the
stone.
The work done on the stone in raising it was not lost;
the stone pays it back while descending. ‘There is a very
important difference between the stone lying on the floor,
and the stone lying on the shelf: the former is powerless
to do work; the latter can do work. Both are alike
“motionless, and you can see no difference, except an
advantage that the latter has over the former in having
a position such that it can move. What gave it this
advantage? Work. A body, then, may possess energy
due merely to ADVANTAGE OF POSITION, derived always
From work bestowed upon it. Energy due to advantage of
position is called potential energy. We see, then, that
energy may exist in either of two widely different states.
It may exist as actual motion, or it may exist in a stored-up
condition, as in the stone lying on the shelf,
METHODS OF ESTIMATING WORK AND ENERGY. 101
Possibly some will object that the work done is performed by gravity,
and not by the stone; that if this force should cease to exist, the stone
would not move when the shelf is removed, and consequently no work
would be done. All this is very true, and it is likewise true that when
the stone is on the ground, the same force of gravity is acting, but can do
no work simply because the position of things is such that the stone cannot
move. The energy which the stone on the shelf possesses is due to the fact
that its position is such that it can move, and that there is a stress between
it and the earth which will cause it to move. Both advantage of position
and stress are necessary, but the former is attained only by work per-
formed. The force of gravity is employed to do work, as when mills are
driven by falling water; but the water must first be raised from the ocean-
bed to the hillside by the work of the sun’s heat. The elastic force of
springs is employed as a motive power; but this power is due to an advan-
tage of position which the molecules of the springs have first acquired by
work done upon them.
We are as much accustomed to store up energy for future use as pro-
visions for the winter’s consumption. We store it when we wind up the
spring or weight of a clock, to be doled out gradually in the movements
of the machinery. We store it when we bend the bow, raise the hammer,
condense air, and raise any body above the earth’s surface.
A body possesses potential energy when, in virtue of work
done upon it, it occupies a position of advantage, or tts mole-
cules occupy positions of advantage, so that the energy ea
pended can be at any time recovered by the return of the body
to its original position, or by the return of its molecules to
their original positions.
85. Unit of Work and Energy. — Inasmuch as a
body’s capacity to do work is dependent wholly upon
the work which has been done upon it, it is evident that
both work and energy may be measured by the same unit.
The unit adopted is the work done or energy imparted in
raising one pound through a vertical hight of one foot. It
is called a foot-pound. (The French unit is the work done
or energy imparted in raising 1* to a vertical hight of
* 102 WORK AND ENERGY.
1, and is called a kilogrammeter.) Since the work done
in raising 1 pound 1 foot high is 1 foot-pound, the work of
raising it 10 feet high is 10 foot-pounds, which is the same
as the work done in raising 10 pounds 1 foot high; and
the same, again, as raising 2 pounds 5 feet high.
In this unit, and by means of formulas (1) and (2), page —
99, we are able to estimate any species of work, and thereby
compare work of any kind with that of any other kind.
For instance, let us compare the work done by a man in
sawing through a stick of wood, whose saw must move 100
feet (S) against an average resistance (R) of 20 pounds,
with that done by a bullet in penetrating a plank to the
depth of 2 inches (4 foot) against an average resistance of
500 pounds. Moving a saw 100 feet against a resistance
of 20 pounds is equivalent to raising 20 pounds 100 feet
high, or doing (RS = 20 x 100 =) 2,000 foot-pounds of work
(W); a bullet moving ¢ foot against 500 pounds’ resistance
does the same amount of work as is required to raise 500
pounds 4 foot high, or (500 x $=) 83.3 + foot-pounds of |
work. Hence (2,000+ 83.3=) about 24 times as much
work is done by the sawyer as by the bullet.
Let us estimate the energy stored in a bow, by an archer whose hand
in pulling on the string, while bending the bow moves 6 inches (3 foot)
against an average resistance of 20 pounds. Here RS = 20 x 4= 10
foot-pounds of work done upon the bow, or 10 foot-pounds of energy
stored in the bow.
86. Distinction between Force and Energy. — Force
may be measured by an instrument called a dynamometer.
Energy which is the product of force into space cannot
be measured directly by any instrument. Force can be in-
creased indefinitely by means of machines, as a lever,
hydrostatic press, etc.; energy cannot be imereased by any
instrument or means whatsoever,
METHODS OF ESTIMATING WORK AND ENERGY. 103
87. Formula for Calculating Kinetic Energy. — The
kinetic energy of a moving body is calculated by means of
the following formula : —
wv
2g
in which W represents the weight. of the body, V its ve-
locity, and g the acceleration (in this latitude 32} feet, or
9.8" per second) due to gravity. [For the derivation of this
formula, see the Author’s Elements of Physics, pages 123
and 124.] For example, the energy of a cannon-ball weighing
50 pounds and moving with a velocity of 1,000 feet per sec-
= ao (about) 779,301 foot-pounds.
Certain deductions from this formula should be strongly
impressed upon the mind; viz., (1) with the same velocity
the kinetic energy of a body varies as its weight; (2) with
the same weight its kinetic energy varies as the square of tts
velocity. Doubling the velocity multiplies the energy four-
fold; trebling the velocity multiplies it ninefold. A bullet
moving with a velocity of 600 feet per second will pene-
trate, not twice, but four times, as far into a plank as one
having a velocity of 300 feet per second.
A railway train having a velocity of 20 miles an hour
will, if the steam is shut off, continue to run four times as
far as it would if its velocity were 10 miles an hour. The
reason is apparent why light substances, even so light as
air, exhibit great energy when their velocity is great.
= energy,
ond =
88. Wasted Work. — As a, stone is raised higher and
higher, the work acewmulates in the form of potential en-
ergy. As a body free to move (i.e. meeting with no re-
sistance) acquires, under the influence of a constant force,
uniformly accelerated motion, so does work, in the form
' 104 WORK AND ENERGY.
of kinetic energy, accumulate. But accumulated work or
energy does not’ always vary as the work performed. In
practice, more or less of the work done, especially that
done in overcoming friction, resistance of fluids, etc., is
wasted. The work done by the sawyer and bullet, page
102, so far as imparting energy to the bodies on which they
do work, is all lost. Of the vast amount of work done in
propelling a steamer across the ocean none accumulates;
all is wasted, distributed along the watery path, and can-
not be recovered or made available for doing more work.
Evidently the accumulated work or available energy that a
body possesses is the work done upon the body less the
wasted work. We may then calculate in foot-pounds (or
kilogrammeters) according to formulas (1) or (2), page 99,
the work performed on a body, and from this deduct the
number of foot-pounds wasted; the remainder is the num-
ber of foot-pounds of available energy that is imparted
to the body.
89. Power of an Agent to do Work, or Rate at
which an Agent can do Work. —In estimating the total
amount of work done, the time consumed is not taken
into consideration. The work done by a hod-carrier, in
carrying 1,000 bricks to the top of a building, is the same
whether he does it in a day or a week. But in estimating
the power of any agent to do work, as of a man, a horse,
or a steam-engine, in other words, the rate at which it is
capable of doing work, it is evident that time is an impor-
tant element. The work done by a horse, in raising a
barrel of flour 20 feet high, is about 4,000 foot-pounds;
but even a mouse could do the same amount of work in
time.
The unit in which power or rate of doing work is esti-
METHODS OF ESTIMATING WORK AND ENERGY. 105
mated is called Gnappropriately) a horse-power. A horse-
power represents the power to perform 33,000 foot-pounds of
work in @ minute (or 550 foot-pounds in a second).
EXERCISES.
1. Can a person lift himself, or put himself in motion, without
exerting force upon some other body ?
2. Can a body do work upon itself? Can a body generate energy
in itself, Ze. increase its own energy?
3. (a) Suppose that an average: force of 25 pounds is exerted
through a space of 10 inches in bending a bow; what amount of
energy will it give the bow? (6) What kind of energy will the bow,
when bended, possess ?
4. (a) What amount of kinetic energy does a body weighing 20
pounds, and moving with a velocity of 300 feet per second, possess ?
(6) What amount of work can the body do?
5. (@) What amount of work is required to raise 50 tons of coal
from a mine 200 feet deep? (6) An engine of how many horse-power
would be required to do it in two hours ?
6. How many fold is the kinetic energy of a body increased by
doubling its velocity ?
7. Twelve hundred foot-pounds of energy will raise 100 pounds
how high, if none is wasted ?
8. A force of 500 pounds acts upon a body through a space of 20
feet. One-fourth of the work is wasted in consequence of resistances.
How much available energy is imparted to the body?
9. How much energy is stored in a body weighing 1,000 pounds, at
a hight of 200 feet above the earth ?
10. How much work can a 2 horse-powér engine do in an hour?
ll. A horse draws a carriage on a level road at the uniform rate
of 5 miles an hour. (a) Does work accumulate? (b) What kind of
energy does the carriage possess? (c) Suppose that the carriage were
drawn up a hill; would energy accumulate? (d) What kind of energy
would it possess when at rest on the top of the hill? (e¢) How would
you calculate the quantity of energy it possesses when at rest on top
of the hill? (/) Suppose that the carriage is in motion on top of the
hill; what two formulas would you employ in calculating the total
energy which it possesses ?
106 WORK AND ENERGY.
Section II.
THE ABSOLUTE OR C.G.S. SYSTEM OF MEASUREMENTS.
90. Fundamental Units. — For many scientific purposes, espe-
cially in establishing a complete set of electrical units, a different system
for measuring physical quantities than that in common use and called
the gravitation system, is indispensable. In the new system, all physical
quantities may be expressed in terms of three units, which are called funda-
mental units. All others are deduced from these by definition, and are called
derived units. The fundamental units and their symbols are as follows: —
Unit of length, L: the centimeter, or the hundredth part of a meter.
Unit of mass, M: the gram, or the mass of one cubic centimeter of
distilled water at 4° C.
Unit of time, T: a second.
The system of units based on these three fundamental units is called
the Absolute System, or the Centimeter-Gram-Second System, or, by
abbreviation, C.G.S. System.
91. Derived Units. — There are a great number of derived units.
We give a few of those in most common use.
Unit of velocity, V: one centimeter per second; in uniform motion,
v-8.
T
Unit of acceleration, A: an increase of velocity of one centimeter per
second. :
Unit of force, FE: a dyne; it is that force which, acting for a second,
will give to a mass of one gram an acceleration of one centimeter per
second, 7.c. one unit of acceleration. It is the i part of the weight of the
g
unit of mass.
ML
F=MA= 12’ or MLT~?.
Unit of work, W; or of energy, E: an erg; it is the work done or
energy imparted by a force of one dyne working through a length or
distance of one centimeter.
WorE=FS= Mas = ML’
2 Tp?
92. Relation of the Dyne to the Gram or Gravitation
Unit of Weight. — When a body falls in a vacuum, gravity imparts to
or ML?T — 2,
THE ABSOLUTE OR C.G.S. SYSTEM OF MEASUREMENTS. -107
it an acceleration of g (in the latitude of the Northern States, 980) centi-
meters per second. The force of gravity, therefore, acting on a unit of
mass is, according to definition, g (980) dynes. The weight of a mass of
one gram is in the gravitation system one gram. Hence the gram (gravi-
tation unit of weight) must be equal to g dynes, or, in the Northern United
States, to 980 dynes. The weight of a mass of one gram varies with the
latitude and hight above the earth’s surface, while the mass of a gram and
the dyne are constant quantities; their value does not change with place.
93. Another Formula for Computing Kinetic Energy.
—It is evident that the weight of a body is dependent upon its mass and
the force of gravity; in other words, (W = Mg) the weight of a body is
measured by the product of the acceleration which the force of gravity
produces into its units of mass. Hence the mass of a body is numerically
£ its weight. Substituting the value of W given above in the formula
wv? Mv?
. 108), E——_, we have E= When the latter formula is used,
: 2,
it is evident that the mass of the moving body must be found by dividing
its weight in grams by 980, or its weight in pounds by 32.1+. ,
The absolute system is used in all refined physical measurements,
but the gravitation system is more convenient and is universally used in
the ordinary affairs of life.
QUESTIONS.
[Designed for only those who may take up the absolute system.]
1. (a) Name some unit of force which is based upon the weight of
some definite mass. (6) Name some unit of force which is based upon the
amount of acceleration which a force can impart to a body of a given
mass ina given time. (c) Have both of these units absolute (unchange-
able) values? (d) What names do you employ in distinguishing these
two classes of units ? :
2. (a) What are the fundamental units of the absolute system?
(6) Why are they called fundamental units ?
3. A force of 208 is equivalent to how many dynes?
4, (a) A force of 20 dynes would perform how many ergs of work in
acting through a distance of 10°? (6) How many ergs of work would a
force of 20 grams perform in acting through the same distance? (c) How
many kilogrammeters of work would a force of 20 grams perform in acting
through the same distance ?
5. What is the weight of a mass of 1é in dynes?
108:
94. Uses of Machines.
WORK AND ENERGY.
Section III.
MACHINES.
Experiment 74.— Suspend, as in Figure 95, a fixed pulley, A, and
a movable pulley, B. The scale-pan C counterbalances the pulley B,
so that there will be equilibrium. Suspend from B two balls, LL, of
equal weight, and suspend on the side where the pan is, a single ball,
Fig. 95.
K, equal to one of the former. The
single ball supports the two balls;
4 i.e. by the use of the machine, a force
of 1 is enabled to balance a force of
2. So far no work is done. (Why?)
Place a very small weight in the pan,
and the balls LL begin to rise, and
work is done.
As the weight K plus a very small
weight causes the motion,-we shall
regard this as the force (F); and as
the weights LL-are the bodies moved
(the pulleys and pan being parts of
the machine may be disregarded),
they may be regarded as the re-
sistance (R) overcome, or the body
on which work is done. Measure
- the respective distances through
which F acts and R moves during
the same time. R moves only one-
half as great a distance as that through which F acts; ie. if R rises
2 feet, F must act through 4 feet.
Suppose that R is 2 pounds, then
F is 1+ pounds. Now 2 (pounds) x2 feet =4 foot-pounds of work
done on R. Again, 1+ (pounds) x 4 feet =a little more than 4 foot-
pounds of work (or energy) expended.
It thus seems that, although a machine will enable a
small force to balance a large force, when work is per-
MACHINES. 109
formed, the work applied to the machine is greater, rather
than less, than the work which the machine transmits to
the resistance. The work applied is greater than the
work transmitted by the amount of work wasted in conse-
quence of friction and other extra resistances. So that
by the employment of a machine nothing is gained in work
which the force is required to do, but always something lost.
What, then, is the advantage gained in using this
machine? Suppose that R is 400 pounds, and that the
utmost force that a man can exert is a little more than
200 pounds. Then, without the machine, the services of
two men would be required to move the resistance;
whereas one man can move it with a machine, only that
he will be obliged to move twice as far as the resistance
moves, a matter of little consequence in comparison with
the advantage of being able to do the work alone. The
advantage gained in this instance seems to be one of con-
venience. Men, however, are accustomed to speak of it as
“a gain of foree,†(or more commonly and inaccurately,
“of powerâ€), inasmuch as a small force overcomes a
large resistance.
Hzperiment 75.—If instead of applying the small additional
weight to the pan, it be suspended from one of the balls LL, the weight
of these balls, together with the additional weight, becomes the cause
of motion, and K is the resistance. In this case there is a loss of
force, because the force employed is more than twice as great as the
force overcome. Measure the distances traversed respectively by F and
R in the same time. R moves twice as far as F, and of course with
twice the velocity. There is a gain of velocity at the expense of force.
It thus appears that, if it should be desirable to move a
resistance with greater velocity than it is possible or con-
venient for the force to act, it may be accomplished
through the mediation of a machine, by applying to it a
110 WORK AND ENERGY.
force proportionately greater than the resistance. This
apparatus is one of many contrivances called machines,
through the mediation of which force can be applied to re-
sistance more advantageously than when it 1s applied directly
to the resistance. Some of the many advantages derived
from the use of machines are : —
~ (1) They may enable us to exchange intensity of force
for velocity, or velocity for intensity of force. A gain of in-
tensity of force or a gain of velocity is called a mechani-
cal advantage.
(2) They may enable us to employ a force in a direction
that ts more convenient than the direction in which the resist-
ance ts to be moved.
—! (8) They may enable us to employ other
forces than our own in doing work; e.g.
the strength of animals; the forces of wind,
water, steam, etc.
How are the last two uses illustrated in
Figure 96? The pulleys employed are
called fixed pulleys, ¢.e. they have no motion
except that of rotation. Is any mechani-
cal advantage gained by fixed pulleys?
What is the use of a fixed pulley? Pulley
B (fig. 94) is a movable pulley. What
kind of advantage is gained by
means of a movable pulley?
95. General Law of Machines.
— From the experiments and dis-
cussion above we derive the following formula for ma-
chines : —
FS = RS’ + 4,
MACHINES. 111
in which F represents the force applied, and S the distance
through which F acts; R represents the resistance over-
come, and 8’ the distance through which its point of ap-
plication is moved; w represents the wasted work. A
machine in which there is no wasted work is a perfect
machine. Such a machine is purely ideal, as none exists.
If in our calculations we regard a machine as perfect
(though subsequently suitable allowance must be made
for the wasted work), then our formula becomes
FS = RS’.
Whence R:F::8:8'; ie. the force and resistance vary
inversely as the distances which their respective points of ap-
plication move. In other words, the ratio of the resistance
to the force is the reciprocal of the ratio of the distances
which these points move. ;
R:F=4, then §’/:S =4,
This law applies to every machine of whatever descrip-
tion; hence it is called the General or Universal Law of
Machines. When R is greater than F, there is a gain of
force, and # the ratio of gain of force. When S! is
/
greater than §, there is a gain of velocity, and los the
ratio of gain of velocity.
Experiment 76.— Support a lever, as in Figure 97, so that there
shall be unequal arms. Move w until the lever is balanced in a hori-
zontal position. Suspend (say)
seven balls from the short arm
(say) one space from the ful-
crum. Then from the other
arm suspend a single ball from
such a place (in this case seven
equal spaces from the fulcrum)
that it will balance the seven
balls. There is now equilibrium between the two forces. Suppose
Fig. 97.
112 WORK AND ENERGY.
the smaller force to be increased a little and to produce motion; what
mechanical advantage (i.e. intensity of force or velocity) would be
gained by the use of the machine? What is the ratio of gain neg-
lecting the small additional force? How does this ratio compare with
the ratio between the length of the two arms? For convenience we
call the distance of the point of application of the force from the
fulcrum the jorce-arm, and the distance of the resistance from the
fulcrum the resistance-arm.
Suppose the small additional force is applied to the short arm;
what mechanical advantage would be gained? What would be the
ratio of gain?
While the general law of machines is always applica-
ble, a special law, one in
which the relation be-
tween the ratio of gain
and the ratio between
certain dimensions of
the machine is stated, is
often more convenient in
practice. For example,
in our experiment with
the lever we discover
that R: F:: force-arm :
resistance-arm, te. the
force and resistance vary
inversely as the lengths
af their respective arms.
Compare this special law
with the general law.
Place the fulcrum at other points in the lever, and thereby
vary the length of the arms, and. verify by numerous
experiments the special law of levers.
Fig. 98.
Experiment 77.— By means of a pulley, D, so arrange (Fig. 98)
that both F and R may be on the same side of the fulcrum. First,
MACHINES. 113
place in the pan weights sufficient to produce equilibrium in the
machine (for example, in this case, one ball). Then suspend weights
at some point, as A, and place other weights in the pan to counter-
balance these. Verify the law of levers. If A is the resistance, what
mechanical advantage is gained? What is the ratio of gain? If B
is the resistance, what mechanical advantage will be gained?
Experiment 78.— Obtain ;
a toy carriage, place it on an
inclined plane, pass the cord
over a pulley, B (Fig. 99),
so adjusted that the cord
between the carriage and
pulley shall be parallel with
the plane. Suspend a small
bucket, P, and place sand in
it to balance the carriage. ;
Place in the carriage a weight W, and place weights in the bucket to
balance W. The weights placed in the bucket represent the force
Fig. 99.
‘ig. 100. Fig. 101.
applied; then what advantage is gained in the use of an inclined plane
as a machine? W, in traversing the inclined plane AB, only rises
- through the vertical hight CB, while P must move through a distance
equal to AB. Measure the distances AB and CB. How does the ratio
114 - WORK AND ENERGY.
between these distances compare with the ratio of gain? Construct a
special law of the inclined plane.
Experiment 79.— Place a ‘‘wheel and axle†(Fig. 100) on the
support A. Wind a cord around the wheel B, and another in the re-
verse direction around the axle C. Suspend a weight, D, from the
axle, and another, E, from the wheel, to balance it. If E be the
force applied, what advantage is gained? What, if D is the force
applied? What is the ratio of advantage in either case? How does
the ratio of advantage compare with the ratio between the radius of
the wheel AC (Fig. 101) and the radius of the axle BC? Construct a
special law of the wheel and axle.
Fig. 102.
, EXERCISES.
1. (a) When is a machine said to gain intensity of force? (6) When
is it said to gain velocity?
MACHINES. 115
2. (a) Can any machine do work? (6) Can we by the use of any
machine accomplish more work than the work performed upon the
machine? What is the proof?
8. How is intensity of force
gained by the use of a machine?
4. What machine is used only
to change the direction of motion?
5. (2) What is a mechanical
advantage? (b) Give a rule by which the mechanical advantage
that may be gained by any machine may be calculated. » e
6. Figure 102 repre-
sents a pile-driver. (a)
How can the energy or
the work which the weight
W can do when it is raised
a given distance be com-
puted? (6) What benefit is derived from the use of the machine in
raising the weight? .(c) Suggest some simple attachment to the
machine which would enable one man to raise the weight. (d) Sug-
gest some attachment by means of which a horse could be made to do
the work. (¢) What
difference will it make
whether the weight is
raised 5 feet or 10 §
feet? (/f) Tllustrate,
by means of this ma-
chine, what you un-
derstand by force and
energy. (g) Which,
while the weight rises,
is constantly accumu-
lating, and which re-
mains nearly constant? E
(k) Which can be meas- ee
ured with an instrument, and what is the name of the instrument?
7. (a) What advantage is gained by a lever when its force-arm is
longer than its resistance-arm? (6) What, when its resistance-arm is
longer ?
8. (a) What advantage is gained by a nutcracker (Fig. 103)?
(©) What is the ratio of gain?
Fig. 103.
Fig. 104.
116 WORK AND ENERGY.
9. (a) What advantage is gained by cutting far back on the blades
of shears near the fulerum? Why? (6) Should shears for cutting
metals be made with short handles and long blades, or the reverse ?
(c) What is the advantage of long blades ?
10. Is work done when the
moment of the force applied
to a lever is equal to the mo-
ment of the resistance? Why?
ll. (a) If P (Fig. 105),
weighing 1 pound, is suspend-
ed 15 spaces from the fulerum
of the steelyard, what weight
(W), suspended 38. similar
spaces the other side of the
fulcrum, will balance it? (6)
Where would you place the one-pound weight in order to weigh out
6 pounds of tea?
12. (a) If the circumference of the axle (Fig. 106) is 15 inches,
and: the force applied to the crank acts through 15 feet during each rev-
olution, what force will be necessary
to raise the bucket of coal weighing
(say) 36 pounds? (6) Through how
many feet must the force act to raise
the bucket from a cavity 48 feet
deep?
18. The arm is raised by the con-
traction (shortening by muscular
force) of the muscle A (Fig. 107),
which is attached at one extremity
to the shoulder and at the other ex-
‘tremity B to.the fore-arm, near the
elbow. (a) When the arm is used, as represented in the figure, to
raise a weight, what kind of a machine is it? (6) What mechanical
advantage is gained by it? (¢) How can the ratio of gain be com-
puted? (d) For which purpose is the arm adapted, to gain intensity
of force or velocity?
The lengths of the two arms of a balance, such as is used in finding
specific gravity (Fig. 60, page 61), should be exactly equal. The arms
may be of unequal length, and yet the beam may be in equilibrium
Fig. 106.
Fig. 107.
MACHINES. 117
(i.e. take a horizontal position when no weights are applied), in conse-
quence of having more matter in the shorter arm, as in Figure 97, page
111. Such a balance is called a false balance.
14. (a) How would you test a balance to ascertain whether it is
true or false? (6) If you were buying diamonds, and the seller should
sell them to you by weight as obtained by placing them on the shorter
arm of a false balance, would you be the loser or gainer?
The true weight of a body may be found with a false balance by a
process called double weighing. The article to be weighed is placed in one
pan, and a counterpoise of sand in the other pan. The article is then
removed, and known weights placed in the pan until equilibrium is again
produced. These weights represent the correct weight of the article. In
this way the balances used in the school laboratory should be tested by
the pupil.
i im I 5 I Hr i
SA
Fig. 108. ' Fig. 109.
15. During one revolution a screw. advances a distance equal to
the distance between two threads, measured in the direction of the
axis of the screw. Suppose the screw in the letter-press (Fig. 108) to
advance 1 inch at each revolution, and a force of 25 pounds to be
applied to the circumference of the wheel B, whose diameter is 14
inches. What pressure would be exerted on articles placed beneath
the screw? (The circumference of a circle is 8.1416 times its diame-
ter.)
16. The toggle-joint (Fig. 109) is a machine employed where great
pressure has to be exerted through a small space, as in punching and
118 WORK AND ENERGY.
shearing iron, and in printing-presses, in pressing the types forcibly
against the paper. An illustration
may be found in the joints used to
raise carriage-tops. Force applied
to the joint C will cause the two
links AC and BC to be straight-
ened, or carried forward to e. If
point C moves 5 inches while G
moves 3 inch, then what pressure
will a force of 50 pounds applied
at C exert on the book below?
17. Show that the hydrostatic
. press (page 50) conforms in its
operation to the general law of machines.
18. A wedge may be regarded as two inclined
planes placed base to base, as de (Fig. 110).
(a) What mechanical advantage is gained by it?
(6) Suppose that the thickness ab is 4 inches,
and the length de is 8 inches, and that the aver-
age pressure exerted upon it by the blow of a
sledge is 100 pounds; what will be the average
pressure exerted by the wedge tending to separate
Fig. 110.
the fibers of wood?
a
Pre
ES
AS
Fig. 112.
consisting of three movable pulleys?
Fig. 111.
' A compound machine is one consisting of two or more machines
combined in one; eg. com-
pound pulleys (Fig. 111) and
compound wheels and axles
(Fig. 112). The mechanical
advantage that may be gained
by a compound machine may
be calculated by multiplying
continuously together the ra-
B tios of the several machines.
19..(a) How great is the
advantage gained by one mov-
able pulley? (6) How great is
@ the advantage gained by the
compound pulley (Fig. 111)
MACHINES. 119
20. Suppose that the radii of the wheels a, d, and f (Fig. 112) are,
respectively, 20 inches, 16 inches, and 24 inches, and the radii of their
axles are, respectively, 2 inches, 4 inches, and 6 inches; how great
advantage may be gained by the compound machine?
A |
Wi
rt i
INNO Wy maui Pe MDH INULIN aL
Fig. 113,
21. How would you calculate the mechanical advantage gained by
a machine like that of Figure 113? (On the axle A is an endless screw,
by means of which motion is communicated from the axle to the
wheel W.)
22. (a) What kind of a machine is a claw-hammer (Fig. 114)?
(6) What mechanical advantage is gained by it?
23. In its technical meaning, a “perpetual motion machine†is not
a machine that will run indefinitely, but a machine which can do work
without the expenditure of energy. Is such a machine possible?
24, A plank 12 feet long and weighing 24 pounds is supported by
two props, one 8 feet from one end, and the other 1 foot from the
other end. What is the pressure on each prop?
25. With a movable pulley what force will support a weight of
100 pounds?
26. The gradient of a certain road on a hillside is one foot in ten
feet. What force must a horse exert on a carriage which weighs to-
gether with its load one ton, to prevent its descent?
27. What must be the diameter of a wheel in order that a force of
20 pounds applied at its circumference may be in equilibrium with a
resistance of 600 pounds applied to its axle, which is 8 inches in diam-
eter?
120 WORK AND ENERGY.
28. Draw a straight line to represent a lever; locate the fulerum,
and locate the points of application of the force and resistance un-
equally distant from the fulcrum. Draw lines from the points of
application of the force and resistance so that they will make some
angle with each other (ze. not parallel with each other) to represent
the directions in which the two forces respectively act. Ascertain the
ratio between the two forces when their moments are equal, i.e. when
the two forces are in equilibrium.
CHAPTER V.
MOLECULAR ENERGY.— HEAT.
Section I.
WHAT HEAT IS.—SOME SOURCES OF HEAT.
96. Theory of Heat.— A body loses motion in com-
municating it. The hammer descends and strikes the
anvil; its motion ceases, but the anvil is not sensibly
moved; the only observable effect produced is heat. In-
stead of a motion of the hammer and anvil, there is now,
according to the modern view, an increased vibratory mo-
tion of the molecules that compose the hammer and anvil,
—simply a change from molar to molecular motion. Of
course, this latter motion is invisible. According to this
view, heat is but a name for the energy of vibration of the
molecules of a body. A body is heated by having the
motion of its molecules quickened, and cooled by parting
with some of its molecular motion. One body is hotter
than another when the average kinetic energy of each mole-
cule in it is greater than in the other.
As late as the beginning of the present century heat was generally
regarded as “a sensation which the presence of fire†(an “igneous fluid,â€
“matter of heat,†called sometimes “caldricâ€) “occasions in animate and
inanimate bodies.†A text-book of that period makes this significant
statement: “There is fire in the wood, and there is air in the field, though
we do not perceive either while at rest. Rubbing two pieces of wood does
not create fire any more than the blowing of the wind creates air. Motion
renders both perceptible.†The former and the more modern views are in
122 MOLECULAR ENERGY. — HEAT,
harmony in attributing the immediate cause of the sensation to motion.
According to the former view, the sensation is produced by putting an
emaginary fluid in motion ; according to the modern view it is produced by
quickening the motion of the molecules of a body.
97. Artificial Sources of Heat.— As heat is energy,
so all heat must originate in some form of energy, i.e. by
the transformation of some other form of energy into heat.
Experiment 80.— Place a ten-penny nail on a stone or a flat
piece of iron and hammer it briskly for a few minutes. It soon be-
comes too hot to be handled with comfort. Rub a desk with your fist;
your coat-sleeve with a metallic button; both the rubbers and the
things rubbed become heated.
(1) Heat is generated at the expense of molar motion,
te. molar motion checked becomes molecular motion, or heat.
Experiment 81.— Take a glass tést-tube half full of cold water
and pour into it one-fourth its volume of strong sulphuric acid. The
liquid almost instantly becomes so hot that the tube cannot be held in
the hand.
When water is poured upon quicklime, heat is rapidly
developed. The invisible oxygen of the air combines with
the constituents of the various fuels, such as wood, coal,
oils, and illuminating-gas, and gives rise to what we call
burning, or combustion, by which a large amount of heat is
generated. In all such cases the heat is generated by the
combination or clashing together of molecules of sub-
stances that have an affinity (ec. an attraction) for one
another. Before union the energy of the molecules is of
the same kind as that of a stone on a shelf. When the
shelf is withdrawn, gravity converts the potential energy
of the stone into kinetic energy; so affinity converts the
potential energy of the molecules into kinetic energy
of vibration; 7.e. into heat.
WHAT HEAT IS. > ales
(2) Molecular (or atomic) potential energy is transformed
in the act of chemical combination into heat.
98. The Sun as a Source of Heat and Energy. — The
sun is the source of very nearly all the energy employed by
man in doing work. Our coal-beds, the results of the de-
posit of vegetable matter, are vast storehouses of the sun’s
energy, rendered potential during the growth of the plants
many ages ago. The animal finds its food in the plant,
appropriates the energy stored in the plant, and converts
it into energy of motion in the form of animal heat and
muscular motion. Every rain-drop that rolls its way to the
sea, contributing its mite to the immense water-power of
the earth, derives its energy from the sun.
QUESTIONS.
1. On every hand we see what appears to be at least an almost
universal tendency to destruction of motion. Is the destruction
usually an annihilation of motion?
2. What name is usually given to molecular energy?
3. How does it appear that heat is energy?
4. What do you mean when you say that one body is hotter than
another ?
5. How must all heat originate ?
6. State all the sources of heat with which you are now acquainted.
7. (a) Give an illustration of mechanical or visible motion trans-
formed into molecular motion. (6) Give an illustration of molecular
motion transformed into mechanical motion.
8. What kind of energy does coal and other fuel possess ?
9. A lump of coal is raised and placed upon a shelf. (@) How can
the potential energy of the lump be transformed into kinetic energy?
(6) Will the kinetic energy resulting from the transformation be
mechanical or molecular? (c) When the lump strikes the earth, what
transformation of energy occurs?
10. Every lump of coal possesses molecular potential energy. (a)
How can its energy be transformed into kinetic energy? (0) What
124 MOLECULAR ENERGY. — HEAT.
two varieties of potential energy does a lump of coal on the shelf
possess ?
11. (a) How do bodies acquire energy? (6) From what source did
coal obtain its molecular potential energy? (c) What does the entire
value of coal consist in?
12. How does animal energy originate?
Section II.
TEMPERATURE. — METHODS OF EQUALIZATION.
99. Temperature Defined. —If body A is brought
in contact with body B, and A tends to impart heat
to B, then A is said to have a higher temperature than
B. Temperature is the state of a body with reference to
tts tendency to communicate heat to, or receive heat from,
other bodies. The direction of the flow of heat deter-
mines which of two bodies has the higher temperature.
If the temperature of neither body rises at the expense
of the other, then both have the same temperature.
100. Temperature distinguished from Quantity of
Heat.— The term temperature does not signify quantity
of heat. If we dip from a gallon of boiling water a cupful,
the cup of water is just as hot, z.e. has the same tempera-
ture, as the larger quantity, although of course there is a
great difference in the quantities of heat the two bodies of
water contain. Temperature depends upon the average ki-
netie energy of the individual molecule, while quantity of
heat depends upon the average kinetic energy of the indi-
vidual molecule multiplied by the number of molecules.
TEMPERATURE. — METHODS OF EQUALIZATION. 125
There is always a tendency to equalization of tempera-
ture; that is, heat has a tendency to pass from a warmer
body to a colder, or from a warmer to a colder part of the
same body, until there is an equality of temperature.
101. Conduction.
Experiment 82.— Place one end of a wire about 10 inches long
in a lamp-flame, and hold the other end in the hand. Heat gradually
travels from the end in the flame toward the hand. Apply your fin-
gers successively at different points nearer and nearer the flame; you
find that the nearer you approach the flame, the hotter the wire is.
The flow of heat through an unequally heated body,
from places of higher to places of lower temperature, is
called conduction ; the body through which it travels is
called a conductor. The molecules.of the wire in the flame
have their motion quickened; they strike their neighbors
and quicken their motion; the latter in turn quicken the
motion of the next; and so on, until some of the motion
is finally communicated to the hand, and creates in it the
sensation of heat.
Experiment 83.— Figure 115 represents a board on which are
fastened, by means of staples, four wires: (1)
iron, (2) copper, (8) brass, and (4) German
silver. Place a lamp-flame where the wires meet.
In about a minute run your fingers along the
wires from the remote ends toward the flame, 5
and see how near you can approach the flame on ¢
each without suffering from the heat. Make a
list of these metals, arranging coe in the order Fig. 115.
of their conductibility.
You learn that some substances conduct heat much more
rapidly than others. The former are called good conduc-
tors, the latter poor conductors. Metals are the best con-
ductors, though they differ widely among themselves.
126 MOLECULAR ENERGY. — HEAT.
Experiment 84.— Fill a test-tube full of water, and hold it some-
what inclined (Fig. 116), so that a flame may heat the part of the
tube near the surface of the water. Do
& not allow the flame to touch the part of
: the tube that does not contain water.
The water may be made to boil near its
surface for several minutes before any
change of the temperature at the bottom
will be perceived.
Liquids, as a class, are poorer
= conductors than solids. Gases are
Pig. 116. much poorer conductors than liquids.
It is difficult to discover that pure, dry air possesses any
conducting power. The poor conducting power of our
clothing is due partly to the poor conducting power of
the fibers of the cloth, but chiefly to the air which is
confined by it. »
Loose garments, and garments of loosely woven cloth, inasmuch as
they hold a large amount of confined air, furnish a good protection from
heat and cold. Bodies are surrounded with bad conductors, to retain heat
when their temperature is above that of surrounding objects, and to
exclude it when their temperature is below that of surrounding objects.
In-the same manner double windows and doors protect from cold.
102. Convection in Gases.
Experiment 85.— Hold your hand a little way
from a flame, beneath, on the side of, and above the
flame. At which place is the heat most intense?
Experiment 86.— Draw on thin glazed paper
an unfolding line, so that the windings shall be
about $ inch apart. Cut along the line; give the
central portion a conical form; place the cone on
a pointed end of a vertical wire, and allow the
remainder of the paper to fall spirally around the
A wire asin Figure 117. Place the spiral over a flame
Fig, 117. or hot stove. A continuous current of air, a mini-
ature wind, moving upward from the flame or stove causes the spiral
TEMPERATURE. — METHODS OF EQUALIZATION. 127
to rotate. This current tends only upward. ‘The air having become
heated by contact with the surfaces of the flame or stove conveys, in
its ascent, heat to objects above. Heat is thus diffused by a process
called convection (conveying).
Experiment 87.— Cover a candle-flame with a glass chimney (Fig.
118), blocking the latter up a little way so that there may be a circu-
lation of air beneath. Hold the spiral over the chimney; the rotation
is much quicker than before. Hold smoking touch-paper near the
bottom of the chimney; the smoke seems to be drawn with great
rapidity into the chimney at the bottom; in other words, the office of
the chimney is to create what is called a draft of air. Notice whether
the combustion takes place any more rapidly with than without the
chimney.
Fig. 118. Fig. 119.
Experiment 88.— Place a candle within a circle of holes cut in the
cover of a vessel, and cover it with a chimney, A (Fig. 119). Over
an orifice in the cover place another chimney, B. Hold a roll of
smoking touch-paper over B. The smoke descends this chimney,
passes through the vessel and out at A. This illustrates the method
often adopted to produce a ventilating draft through mines. Let the
interior of a tin vessel represent a mine deep in the earth, and the
chimneys two shafts sunk to opposite extremities of the mine. A fire
kept burning at the bottom of one shaft will cause a current of air
128 MOLECULAR ENERGY. — HEAT.
to sweep down the other shaft, and through the mine, and thus keep
up a circulation of pure air through the mine.
The cause of the ascending currents is evident. Air, on becoming
heated, expands rapidly and becomes much rarer than the surround-
ing colder air; hence it rises much like a cork in water, while cold
air pours in laterally to take its place. In this manner winds are
created.
The so-called trade-winds originate in the torrid or heated zone of the
earth. The air over the heated surface of the earth rises, and the colder
air from the polar regions flows in on both sides, giving rise to a constant
southward wind in the northern hemisphere, and northward wind in the
southern hemisphere.
Chemistry teaches us the vital
importance of thorough ventilation.
Figure 120 represents a scheme for
heating a room by steam, and venti-
lating it by convection. Steam is
conveyed by a pipe from the boiler
to a radiator box just beneath the
floor of the room. The air in the
box becomes heated by contact with
and radiation from the coil of pipe
in the box, and rises through a pas-
sage opening by means of a register
into the room near the ficor at C, a
supply of pure air being kept up by
means of a tubular passage opening
into the box from the outside of
the building. Thus the room is fur-
nished with pure warm air, which,
mingling with the impurities aris-
ing from the respiration of its occu-
pants, serves to dilute them, and
render them less injurious. At the
same time, the warm and partially
vitiated air of the room passes
through the open ventilator, A, into the ventilating-flue, and escapes, so
that in a moderate length of time a nearly complete change of air is
effected. It is evident that on the coldest days of winter the convection
is most. rapid; indeed, it may be so rapid that the air cannot be heated
sufficiently to render the room neayv the floor comfortable. At such times
SSS SSeS
=
3S
YA
My
34
Fig. 120.
TEMPERATURE. — METHODS OF EQUALIZATION. 129
the ventilator A may be closed, while the ventilator B is always open.
The heated air rises to top of the room and, not being able to escape,
crowds the colder air beneath out at the ventilator B. No system of
ventilation dependent wholly on convection is adequate to ventilate
properly crowded halls; air is too viscous and sluggish in its movements.
in such cases ventilation should be assisted by some mechanical means,
such as a blower or fan, worked by steam or water power.
108. Convection in Liquids.
Experiment 89.— Fill a small (6 ounce), thin glass flask with
boiling hot water, color it with a teaspoonful of ink, stopper the flask,
and lower it deep in a tub, pail, or other large vessel filled with cold
water. Withdraw the stopper, and the hot, rarer, colored water will
rise from the flask, and the cold water will descend into the flask.
The two currents passing in and out of the neck of the flask are easily
distinguished. The colored liquid marks distinctly the path of the
heated convection currents through the colored liquid and makes clear
the method by which heat, when applied at the bottom of a body of
liquid, becomes rapidly diffused through the entire mass notwithstand-
ing that liquids are poor conductors.
Experiment 90.— Fill again the flask with hot colored water,
stopper, invert, and introduce the mouth of the flask just beneath the
surface of a fresh pail of cold water. Withdraw the stopper with as
little agitation of the-water as possible. What happens? Explain.
104, Radiation.—In some way the sun is the cause
of a large amount of the heat which the surface of the
earth possesses. On the other hand, the earth in some
way parts with a large amount of heat. It is quite
apparent that the earth does not receive heat from the
sun by conduction or convection, and that by neither
of these processes does it part with heat. It is also
apparent that there is another and a much more rapid
and effectual method by which bodies of higher tempera-
ttire on the earth part with their heat, and other bodies of
lower temperature acquire heat at the expense of distant
bodies, than by either of the two comparatively slow pro-
cesses of diffusion so far described. This process is called
130 MOLECULAR ENERGY. — HEAT.
radiation. The process is a very peculiar one, and must
be reserved for discussion in its proper place in the chapter
on Radiant Energy.
QUESTIONS.
1. Why does more heat reach your hand above than at an equal
distance beside a flame?
2. Why is loose clothing warmer than tight-fitting clothing?
8. (a) Which contains more heat, the Atlantic Ocean or a tea-kettle
fuli of boiling water? (6) Which is capable of giving heat to the
other? (c) Can a body have less heat than another and yet be hotter
than the other?
4. Why should heat be applied to the bottom of a body of water?
5. (a) How is equalization of temperature effected in solids? (6) In
liquids and gases?
Section III.
EFFECTS OF HEAT. — EXPANSION.
105. Expansion of Solids, Liquids, and Gases.
Experiment 91.— The brass ring and ball (Fig. 121) are so
constructed that the latter will just pass through
the former when both have the same, or nearly the
same, temperature. Heat the ball quite hot in a
flame, and ascertain by trying to pass it through the
ring whether it has increased in size. Devise some
method of passing it through the ring without cooling
the ball.
Experiment 92.— Figure 122 represents a thin
Hig. 121. brass plate and an iron plate of the same dimensions
riveted together so far as to form what is called a compound bar.
Place the bar edgewise in a flame, dividing the flame in halves (one-
EFFECTS OF HEAT. — EXPANSION. 1381
half on each side of the bar) so that both metals may be equally
heated. The bar, which was at first straight, is now bent, owing to
the unequal expansion of the two metals on receiving equal
increments of heat. Which metal expands more rapidly?
Thrust the hot bar into cold water. What happens? Cover
the bar with chips of ice. What happens?
Experiment 93.— Fit stoppers (perforated rubber stop-
pers are best) tightly in the necks of two similar thin
glass flasks (or test-tubes), and through each stopper pass
a glass tube about 18 inches long. The flasks should be
nearly of the same size. Fill one flask with water and the
other with alcohol, and crowd in the stoppers so as to force
the liquids up the tubes a little way above the stoppers.
Set both flasks at the same time into a large basin of hot
water in order that both may have the same opportunity to
acquire heat. Soon the liquids begin to expand and rise in the
tubes. Which liquid is more expansible?-
Experiment 94.— Take a dry flask like that used in Experiment
94, insert the end of the tube in a bottle of
colored water (Fig. 123), and apply heat to the
flask; the enclosed air expands and comes out
through the liquid in bubbles. After a few
minutes, withdraw the heat, keeping the end
of the.tube in the liquid; as the air left in the
flask cools, it loses some of its tension, and
the water is forced by atmospheric pressure up
the tube into the flask, and partially fills it.
Experiment 95. — Partly fill a foot-ball (see
Fig. 9, page 8) with cold air, close the orifice,
md -place it near a fire. The air will expand
and distend the ball.
Different substances, both in the solid
and liquid states, expand unequally on Mies Ane:
experiencing equal changes of temperature. Except at
very low temperatures, all gases expand alike for equal
changes of temperature. Under uniform pressure (as is
very nearly the case in the experiment with the balloon)
132 MOLECULAR ENERGY. — HEAT.
the volume of any body of gas varies z+, its volume at
the freezing-point of water for every degree Centigrade,
or zt; for every degree Fahrenheit, its temperature is
changed. But if the gas is confined in a vessel of rigid
sides, so that its volume is necessarily constant, then
its tension varies in the same ratio for every degree its
temperature is changed.
The force exerted by bodies in expanding or contracting is very great,
as shown by the following rough calculation: If an iron bar, 1 square inch
in section, is raised from 0° C. (freezing-point of water) to 500° C. (a dull,
red heat), its length, if allowed to expand freely, will be increased from
1 to 1.006. Now, a force capable of stretching a bar of iron of 1 square
inch section this amount is about 90 tons, which represents very nearly the
force that would be necessary to prevent the expansion caused by heat.
It would require an equal force to prevent the same amount of contraction
if the bar is cooled from 500° to 0° C.
Boiler plates are riveted with red-hot rivets, which, on cooling, draw the
plates together so as to form very tight joints. Tires are fitted on carriage-
wheels when red hot, and, on cooling, grip them with very great force.
‘106. Abnormal Expansion and Contraction of Water.
— Water presents a partial exception to the general rule
that matter expands on receiving heat and contracts on
losing it. If a quantity of water at 0°C., or 32° F., is
heated, it contracts as its temperature rises, until it reaches
4° C., or about 39° F., when its volume is least, and there-
fore it has its mavimum density. If heated beyond this
temperature, it expands, and at about 8° C. its volume is
the same as at 0°. On cooling, water reaches its maximum
density at 4° C., and expands as the temperature falls be-
low that point.
THERMOMETRY. 1838
Section IV.
THERMOMETRY.
A thermometer primarily indicates changes in volume;
but as changes of volume are caused by changes of tem-
perature, it is commonly used for the more important pur-
pose of indicating temperature.
107. Construction of a Thermometer. — A. thermom-
eter generally consists of a glass tube of capillary bore,
terminating at one end in a bulb. The bulb and part of
the tube are filled with mercury, and the space in the tube
above the mercury is usually a vacuum. On the tube, or
on a plate behind the tube, is a scale to show the hight of
the mercurial column.
108. Standard Temperatures. — That a thermometer
may indicate any definite temperature, it is necessary that
its scale should relate to some definite and unchangeable
points of temperature. Fortunately nature furnishes us
with two convenient standards. It is found that under
ordinary atmospheric pressure ice always melts at the
same temperature, called the melting-point, or, more com-
monly, the freezing-point (water freezes and ice melts at
the same temperature). Again, the temperature of steam
rising from boiling water under the same pressure is always
the same.
109. Graduation of Thermometers. — The bulb of a
thermometer is first placed in melting ice (Fig. 124), and
allowed to stand until the surface of the mercury becomes
184 MOLECULAR ENERGY. — HEAT.
stationary, and a mark is made upon the stem at that
point, and indicates the freezing-point. Then the instru-
ment is suspended in steam rising from boiling water (Fig.
125), so that all but the very top of the column is in the
steam. The mercury rises in the stem until its tempera-
ture becomes the same as that of the steam, when it again
becomes stationary, and another mark is placed upon the
stem to indicate the botling-point. Then the space be-
Fig. 124. Fig. 125.
tween the two points found is divided into a convenient
number of equal parts called degrees, and the scale is ex-
tended above and below these points as far as desirable.
- Two methods of division are adopted in this country:
by one, this space is divided into 180 equal parts, and the
result is called the Fahrenheit scale, from the name of its
author; by the other, the space is divided into 100 equal
parts, and the resulting scale is called centigrade, which
means one hundred steps. In the Fahrenheit scale, which
is generally employed in English-speaking countries for
ordinary household purposes, the freezing and boiling
THERMOMETRY. 135
points are marked respectively 82° and 212°.
The 0 of this scale (82° below freezing- a
point), which is about the lowest tempera-
ture that can be obtained by a mixture of
snow and salt, was incorrectly supposed to
be the lowest temperature attainable. The 10 yet
centigrade scale, which is generally em-
ployed by scientists, has its freezing and
boiling points more conveniently marked,
respectively 0° and 100°. A temperature be-
low 0° in either scale is indicated by a minus
sign before the number. Thus, — 12° F. in-
dicates 12° below 0° (or 44° below freezing-
point), according to the Fahrenheit scale.
FAHRENHEIT
CENTIGRADE
To reduce a Fahrenheit reading to a 4
centigrade reading, first subtract 32 from J 32°
the given number, and then multiply by 3. |
Thus, ; a f
5 (F—82)=C. -17.8 0
To change a centigrade reading to a Fah-
renheit reading, first multiply the given
number by 2, and then add 32. Thus,
2C+82=F.
EXERCISES,
1. Express the following temperatures of the centigrade scale in the
Fahrenheit scale: 100°; 40°; 56°; 60°; 0°; —20°; —40°; 80°; 150.
Norz.—In adding or subtracting 32°, it should be done algebraically.
Thus, to change — 14° C. to its equivalent on the Fahrenheit scale: 2x
(— 14) = — 25.2°; —25.2° + 32° = 6.8°, the. required temperature on the
Fahrenheit scale. Again, to find the equivalent of 24° F. in the centi-
grade scale: 24—32=—8; —8x%=—4é4; hence, 24°F. is equivalent
to—4.4°4 C.
2. Express the following temperatures of the Fahrenheit scale in the
centigrade scale: 212°; 82°; 90°; 77°; 20°; 10°; —10°; —20°; —40°;
40°; 59°; 829°.
186 MOLECULAR ENERGY. — HEAT.
Section V.
EFFECTS OF HEAT CONTINUED. — LIQUEFACTION AND
VAPORIZATION.
110. Liquefaction.— As previously stated (page 9),
whether a body exist in a solid, liquid, or gaseous state
depends upon its temperature and the pressure which it is
under.
Bzxperiment 96.— Take a lump of ice as large as your two fists,
put it into boiling water; when reduced to about } its original size
skim it out. Wipe the Tap: and place one hand on it and the other
on a lump to which heat has not been applied. Do you perceive any
difference in their temperatures? Ice reduces the temperature of
victuals in our refrigerators; do the victuals raise the temperature of
the ice? How does the heat which the victuals impart to the ice
affect it?
Experiments and experience teach that (1) the melting
or solidifying point (they are always the same for the same
substance) may vary widely for different substances, but
for the same substance it is invariable when under the same
pressure.
(2) The temperature of a solid or liquid remains con-
stant at the melting-point from the moment that melting or
solidification begins.
111. Vaporization.
Experiment 97.— Place a test-tube (Fig. 127),
half filled with ether, in a beaker containing water at
a temperature of 60°C. Although the temperature of
the water is 40° below its boiling-point, it very quickly
raises the temperature of the ether sufficiently to cause
Fig. 127. it to boil violently. Introduce a chemical thermometer!
into the test-tube, and ascertain the boiling-point of ether.
1 A chemical thermometer has its scale on the glass stem, instead of a plate, and is
otherwise adapted to experimental use.
LIQUEFACTION AND VAPORIZATION. 137
Experiment 98.— Take two beakers half full of water. Raise
both to the boiling-point. Dissolve pulverized saltpetre in one as
long as it readily dissolves. Suspend in both liquids chemical ther-
mometers, so that the bulb of each shall be within one inch of the
bottom. Does the boiling water, as you continue to apply heat, get
hotter? Is the boiling solution any hotter than the boiling water ?
Does the solution get hotter as it becomes concentrated by loss of
water by vaporization ?
After a liquid begins to boil, the temperature remains con-
stant until the whole is vaporized, if the density of the liquid
and the pressure remain constant.
Experiment 99.—Place a beaker, half full of water at 80° C.,
under the receiver of an air-pump, and exhaust the air. The water,
though far below its usual boiling-point, boils violently. Readmit the
air, and test the temperature of the water which has just been boiling.
Fig. 129.
Experiment 100.— Half fill a thin glass flask with water. Boil
the water over a Bunsen burner; the steam will drive the air from
the flask. Withdraw the burner, quickly cork the flask very tightly,
invert the flask, and pour cold water upon the part containing steam,
as in Figure 128; the water in the flask, though cooled several degrees
188 MOLECULAR ENERGY. — HEAT.
below the usual boiling-point, boils again violently. The application
of cold water to the flask condenses some of the steam, and diminishes
the tension of the rest, so that the pressure upon the water is dimin-
ished, and the water boils at a reduced temperature.
If hot water is poured upon the flask, the water ceases to boil.
Why? F
Experiment 101.— Provide a tumbler of cold water, a test-tube
nearly filled with water, tightly stoppered, and having glass tubes ex-
tending through the stopper, as represented in Figure 129. Place the
exposed end of the bent tube in the tumbler of water, and apply heat to
the bottom of the test-tube, and boil the water for about five minutes.
Then remove the heat, leave the end of the tube in the tumbler of
water, and allow the water of the test-tube to cool for some time; or,
better, to hasten the
cooling, place the test-
tube in another tum-
bler of cold water. Ob-
serve carefully, and
explain all phenomena
which occur from the
beginning to the end
of the operation.
112. Distillation.
Experiment 102, —
Vessel A (Fig. 180)
(called a condenser)
contains a coil (called
a worm) of copper
tube, terminating at
one extremity at a. The other end of the tube, }, projects through
the side of the vessel near its bottom. Near the top of the vessel
projects another tube, ¢ (called the overflow), with which is con-
nected a rubber tube, e. This tube conveys the warm water which
rises from the surface of the heated worm away to a sink or other
convenient receptacle.
Take a glass flask of a quart capacity, fill it three-fourths full of pond
or bog water. Connect the flask by means of a glass delivery-tube with
the extremity a of the worm. Heat the water in the flask; as soon as
Fig. 130.
LIQUEFACTION AND VAPORIZATION. 1389
it begins to boil, commence siphoning cold water through a small tube,
d, from an elevated vessel E into the condenser. Inasmuch as the worm
is constantly surrounded with cold water, the steam on passing through
it becomes condensed into a liquid, and the liquid (called the distillate)
trickles from the extremity } into a receiving vessel. The distillate
is clear, but the water in the flask acquires a yellowish brown tinge
as the boiling progresses, due to the concentration of impurities
(largely of vegetable matter) which are held in suspension and solu-
tion in ordinary pond water. The apparatus used is called a still, and
the operation distillation.
When a volatile liquid is to be separated from water, for example,
when alcohol is separated from the vinous mash after fermentation (see
Chemistry, page 184), the mixed liquid is heated to its boiling-point, which
is lower than that of water. Much more of the volatile liquid will be con-
verted into vapor than of the water, because its boiling point is lower.
Thus a partial separation is effected. By repeated distillations of the
distillate, a 95 per cent alcohol is obtained. .
113. Evaporation. —In boiling, the heat, applied at
the bottom, rapidly converts the liquid into vapor, which,
rising in bubbles and breaking at or near the surface, pro-
duces a violent agitation in the liquid, called boiling or
ebullition. Boiling takes place only at a definite tempera-
ture, which depends on the kind of liquid and the pressure
that is on it. Hvaporation is that form of vaporization
which takes place quietly and slowly at the surface. Al-
though hastened by heat, the evaporation of water occurs
at any temperature, however low; even ice and snow
evaporate.
The rapidity of evaporation increases with the tempera-
ture, amount of surface exposed, dryness of the atmosphere,
and diminution of pressure. This vapor of water mixes
freely with the air, and diffuses rapidly through it, acting
like another gas. A given space, —for example, a cubic
foot (it matters little whether there is air in the space or
whether it is a vacuum), can hold only a limited amount
140 MOLECULAR ENERGY. — HEAT. |
of water vapor. This quantity depends on the tempera-
ture of the vapor. The capacity of a space for water
vapor increases rapidly with the temperature, being nearly
doubled by a rise of 10° C. When a space contains such
an amount of water vapor that its temperature cannot be
lowered without some of the water being precipitated in
the form of a liquid, the vapor is said to be saturated,
and the temperature at which this happens is called the .
dew-potnt.
Experiment 103.— Take a bright nickel-plated cup, such, for ex-
ample, as are used for lemonade-shakers; pour into it a small quantity
of tepid water. Place in the water the bulb of a chemical thermome-
ter. Gradually reduce the temperature of the water by stirring into
it ice water until you discover a slight dimness of the luster of that
portion of the outside of the cup next the water. If the ice water
does not reduce the temperature sufficiently, add ice, keeping the mix-
ture briskly stirring. If the ice does not answer, pour out some of
the water and sprinkle salt on the ice, keeping the bulb of the ther-
mometer in the remaining water. Note the temperature of the water
at the instant that the first mist or dimness appears on the cup.
Wait until the dimness or mist disappears, and note the temperature
of the water when the last disappears. Take the mean of the two
temperatures for the dew-point.
The form in which the condensed vapor appears is, according to its
location, dew, fog, or cloud.) The atmosphere is said to be dry or humid,
not according to the quantity of water vapor which it at any time contains,
but according as it can contain much or little more than it has. The air
in summer months usually contains a large amount of water vapor, yet it
is usually very dry. The heat of a stove dries the air of a room without
destroying any of its water vapor. In such a room, the lips, tongue,
throat, and skin experience a disagreeable sensation of dryness, owing to
the rapid evaporation which takes place from their surfaces. This should
be taken as nature’s admonition to keep water in the stove urns, and
tanks connected with furnaces,
1 A cloud is simply a fog in an elevated region of the atmosphere. It is composed of
minute spheres of water from 7245 to yyy Of an inch in diameter.
HEAT CONVERTIBLE INTO POTENTIAL ENERGY. 141
Section VI.
HEAT CONVERTIBLE INTO POTENTIAL ENERGY, AND VICE
VERSA. :
_ 114, Heat Units. — It is frequently necessary to meas- °
ure quantity of heat, and for this purpose a standard unit
of measurement is required. The heat unit generally
adopted is the amount of heat required to raise the tempera-
ture of one kilogram of water from 0° to1° C. This unit is
called a calorie, or kilogram-centigrade.
Let it be required to find approximately the amount of
heat that disappears during the melting of one kilogram
of ice.
Experiment 104.— Weigh out 2008 of dry (dry it with a towel)
ice chips whose temperature in a room of ordinary temperature may
be safely assumed to be 0°C. Weigh out 2008 of boiling water, whose
temperature we assume to be 100°C. Pour the hot water upon the
ice, and stir until the ice is all melted. Test the temperature of the
resulting liquid.
Suppose its temperature is found to be 10°C. It is evident that
the temperature of the hot water in falling from 100° to 90° would
yield sufficient heat to raise an equal weight of water from 0° to 10°
C. Hence it is clear that the heat which the water at 90° yields in
falling from 90° to 10°—a fall of 80°— in some manner disappears.
At this rate had you used 1* of ice and 1* of hot water, the amount of
heat lost would be 80 calories. Careful experiments, in which suit-
able allowances are made for loss or gain of heat by radiation and
conduction, have determined that 80 calories of heat are consumed in
melting 1 kilogram of ice. How near to this do the results of your ex-
periments approach ?
Next let it be required to find the amount of heat that disappears
during the conversion of 1 kilogram of water into steam.
Experiment 105.— Take in a porcelain evaporating-dish 508 of
142 MOLECULAR ENERGY. — HEAT.
ice water at (say) 5° C. Place it over a flame, and, watch in hand,
note the time in seconds which elapses before it boils. Then note
the time which elapses before it is all converted into steam. Suppose
that it required 100 seconds to raise the water from 5° to its boiling-
point, which we assume is 100°—a rise of 95°; and that it requires
530 seconds to convert the water, after it commences to boil, into
steam. Then the latter operation consumes (530+100=) about 5.3
times as much time as the former. But the heat applied to the water
while boiling does not raise its temperature (see Exp. 98, page 187);
then all the heat given to the water during the interval of time dis-
appears. Had you taken 1* of water, it would have required 95 calo-
ries ‘to raise the water from 5° to 100°C. Hence, in converting the
1* of water into steam, 95%5.3= (about) 503 calories disappear.
Accurate methods have determined that 537 calories disappear during
the conversion of 1* of water into steam.
The heat which disappears in melting and boiling is
generally, but with our present knowledge of the subject,
rather objectionably, called latent (hidden) heat. The
error consists in calling that heat which has ceased to be
heat. The heat, ze. kinetic energy, that disappears in
melting is consumed in doing interior (i.e. molecular) work.
The molecules that in the solid are held firmly in their
places by molecular forces, are moved from their places
during melting, and so work is done against these forces,
much as work is done against gravity when a stone is
raised. In both cases kinetic energy is consumed — disap-
pears; but this means simply that it is transformed into
potential energy. The so-called latent heat is simply a
misnomer for molecular potential energy.
When water is converted into steam, the larger portion of the heat,
which is rendered latent, is consumed in separating the molecules so far
that molecular attraction is no longer sensible; a small portion — about
7s —is consumed in overcoming atmospheric pressure. The amount of
work done in melting and boiling — especially the latter —is very great,
as shown by the amount of heat consumed. Hence it requires a long time
to acquire ‘the requisite amount of heat. This is a protection against
HEAT CONVERTIBLE INTO POTENTIAL ENERGY. 143
sudden changes. For example, if snow and ice melted immediately on
reaching the melting-point, all the snow and ice would melt in a single
warm day in winter, creating most destructive freshets.
115. Potential Energy converted into Heat by the
Solidification of Liquids and the Liquefaction of
Vapors. —If our theory be true that heat is converted
into potential energy during vaporization and melting,
then ought the energy to be restored to the kinetic state
(i.e. the heat which disappears during these operations
ought to be restored) when the molecules return to their
original positions, 7.e. when vapor becomes liquid, or when
liquids solidify.
Experiment 106.— Take in a beaker C (Fig. 131) 1 of water at
(say) 12°C. Take about
5008 of water in a flask A,
and raise it to the boiling-
point. As soon as it be-
gins to boil, connect the
flask with the beaker by
a delivery-tube B, carry-
ing the end of the tube
nearly to the bottom of the
beaker. When about one-
fifth of the water has boiled
away, remove the delivery
tube from C, and immedi-
ately test the temperature of the water in the beaker, and weigh it.
Assume that the temperature of the steam is 100° C., and we will
suppose, for illustration, that there are 1,100% of water now in the
beaker; then 1008 of water have been converted into steam which
has passed into the beaker and been condensed or liquefied by the
cold water. Suppose, again, that the temperature of the water
in the beaker was raised thereby to 70° C. Now 1008 of water at
100° C. (resulting from the condensation of the steam) in falling to
70° C. could yield (80+10=) only 3 calories; hence it could raise the
1¥ of water only 8°; i.e. from 12° to 15° C. Then it is evident that
it must have acquired the balance of (70—15 =) 55 calories, by the
Fig. 131.
144 MOLECULAR ENERGY. — HEAT.
restoration of the latent heat to real heat when the steam is liquefied.
If the liquefaction of 100% of steam yields 55 calories, then the lique-
faction of 1* of steam would yield 550 calories. Accurate methods
give 587 calories.
Various phenomena show that heat is developed during the solidifica-
tion of liquids, but as the development is slow, and the loss by radiation
rapid, it is difficult to make measurements. There are good reasons for
assuming, however, that there are 80 calories of heat generated for every
kilogram of water that is frozen. Farmers sometimes turn to practical
use this well-known phenomenon. Anticipating a cold night, they carry
tubs of water into cellars to be frozen. The heat generated thereby,
although of a low temperature, is sufficient to protect vegetables which
freeze at a lower temperature than water.
Steam is a most convenient vehicle for the conveyance of latent heat.
For example, every kilogram of steam that is condensed in the radiator
box (Fig. 120, p. 128) contributes to the air which passes through the box
587 calories, or heat sufficient to raise 5.37* of ice water to the boiling-
point. 4
116. Methods of Producing Artificial Cold. — The
fact that heat must be consumed because work is done, in
the conversion of solids into liquids and liquids into
vapors, is turned to practical use in many ways for the
purpose of producing artificial cold. The following ex-
periments will illustrate.
117. Cold by Dissolving. —— Freezing Mixtures.
Experiment 107.— Prepare a mixture of 2 parts, by weight, of
pulverized ammonium nitrate and 1 part of ammonium chloride.
Take about 75° of water (not warmer than 8° C.), and into it pour
a large quantity of the mixture, stirring the same, while dissolving,
with a test-tube containing a little cold water. The water in the
test-tube will be quickly frozen. A finger placed in the solution will
feel a painful sensation of cold, and a thermometer will indicate a
temperature of about —10°C.
One of the most common freezing mixtures consists of
3 parts of snow or broken ice and 1 part of common salt.
The affinity of salt for water causes a liquefaction of the
HEAT CONVERTIBLE INTO POTENTIAL ENERGY. 145
ice, and the resulting liquid dissolves the salt, both opera-
tions requiring heat.
118. Cold by Evaporation.
Experiment 108.— Fill the palm of the hand with ether; the
ether quickly evaporates, and produces a painful sensation of cold.
Experiment 109.— Place water at about 30°C. in a thin porous
cup, such as is used in the Grove’s battery, and the same amount of
water, at the same temperature, in a glass beaker of as nearly as pos-
sible the same size as the porous cup. Introduce into each a chemi-
cal thermometer. The comparatively large amount of surface exposed
by means of the porous vessel will so hasten the evaporation in this
vessel, that, in the course of 10 to 15
minutes, quite a sensible difference of
temperature will be indicated by the
thermometers in the two vessels.
Experiment 110.— Cover closely the
bulb of an air thermometer (Fig. 132)
with thin muslin, and partly fill the stem
with water. Let one person slowly drop
ether on the bulb, while another briskly
blows the air charged with vapor away
from the bulb with a bellows; or, place
the bulb in a window whose sash is raised
a little way, so as to be in a draft. As
the air changes rapidly, it does not become saturated with vapor so
as to impede evaporation, and in 10 to 15 minutes the water in the
stem freezes, even in a warm room.
Fig. 132.
The evaporation of perspiration conduces to our health and comfort by
relieving us of surplus heat. We cool.the fevered forehead by bathing it
with a volatile liquid, such as a solution of alcohol in water. Windy days
seem colder to us than still days, although the temperature of both is the
same, because evaporation of perspiration takes place more rapidly in a
changing air. Fanning in a similar way changes the air next our persons,
thereby quickening the evaporation of the perspiration, and cooling the
surface of the body. Ice is now manufactured in large quantities during
the summer season in warm climates by the evaporation of liquid ammo-
nia. Evaporation is the most efficient means of producing extremely
low temperatures.
146 MOLECULAR ENERGY. — HEAT.
QUESTIONS.
1. How can water be made to boil at a low temperature ?
2. Upon what does the tension of steam depend ?
2. Why can you not make ice warm ?
4. Does ice always have the same temperature; i.e. can: it be made
colder than 82° F.?
5. What is the lowest temperature any body can have?
6. (a) Where does the “sweat†on ice-pitchers come from? (6) Where
does dew on grass come from? (c) How are clouds formed ?
7. (a) When the sweat on ice-pitchers is very abundant, what
does it indicate about dew-point? (6) Does it forebode fair or rainy
weather ?
8. How will you easily show that ether boils at a lower tempera-
ture than water ?
9. In which will vegetables cook quicker, — in fresh or salt water?
10. How could you separate the alcohol of rum or brandy from
the watery part?
11. (a) On what kind of days do clothes dry fastest? (6) Will
frozen clothes dry ?
12. (a) How does heat dry the air? (0) How does heat dry Retest 2
18. Suppose that 10* of steam, at 100° C., is condensed in the
steam-pipe in the radiator box, Figure 120, per hour; how much heat
will it furnish to the surrounding air? :
14. How much heat will be produced by freezing one cubic foot
(about 29* or 62.5 pounds) of water?
15. (a) When the barometric column stands at 760mm, what
quantity of heat must be applied to 5* of ice at 0°C to convert it
into steam in an open vessel? (6) What will be the temperature of
the steam at the instant of generation? (¢) How much of the heat
applied is rendered latent during the conversion from ice to steam?
16. Is there any reason why the boiling point.of water in an open
vessel should be different on the top of a mountain from what it is
at its base?
17. Why does ice melt slowly even in warm places ?
18. 10* of water at 100°C will melt how much ice at 0°?
19. The freezing of the water of lakes and other bodies of water
tends to produce what change in the temperature of the air?
20. Why does not all the water in a tea-kettle flash into steam at
the instant it reaches its boiling point?
THERMO-DYNAMICS. 147
Section VII.
THERMO-DYNAMICS.
119. Thermo-dynamics Defined. — Thermo-dynamics 1s
that branch of science that treats of the relation between heat
and mechanical work. One of the most important discov-
eries in science is that of the equivalence of heat and work ;
that is, that a definite quantity of mechanical work, when
transformed without waste, will yield a definite quantity of
heat; and conversely, this heat, if there were no waste, could
perform the original quantity of mechanical work.
120. Transformation, Correlation, and Conservation
of Energy. — The proof of the facts just stated was one of
the most important steps in the establishment of the grand
twin conceptions of modern science: (1) That all kinds of
energy are so related to one another that energy of any kind
can be transformed into energy of any other kind, — known
as the doctrine of CORRELATION OF ENERGY; (2) That
when one form of energy disappears, an exact equivalent of
another form always takes its place, so that the sum total of
energy is unchanged, —known as the doctrine of CONSER-
VATION OF ENERGY. These two principles constitute the
corner-stone of physical science. Chemistry teaches that
there is a conservation of matter.
121. Joule’s Experiment. — The experiment to ascer-
tain the “mechanical value of heat,†as performed by Dr.
Joule of England, was conducted about as follows. He
caused a paddle-wheel to revolve in water, by means of a
falling weight attached to a cord wound around the axle
148 MOLECULAR ENERGY. — HEAT.
of a wheel. The resistance offered by the water to the
motion of the paddles was the means by which the mechan-
ical energy of the weight was converted into heat, which
raised the temperature of the water. Taking a body of a
known weight, e.g. 80", he raised it a measured distance,
e.g. 58" high; by so doing 4,240" of work were performed
upon it, and consequently an equivalent amount of energy
was stored up in it ready to be converted, first into me-
chanical motion, then into heat. He took a definite
weight of water to be agitated, e.g. 2*, at a temperature of
0°C. After the descent of the weight, the water was
found to have a temperature of 5°C.; consequently the
2 of water must have received 10 units of heat (careful
allowance being made for all losses of heat), which is the
amount of heat-energy that is equivalent to 4,240â„¢ of
work, or one unit of heat is equivalent to 424" of work.
122. Mechanical Equivalent of Heat.— As a con-
verse of the above it may be demonstrated by actual ex-
periment that the quantity of heat required to raise 1* of
water from 0° to 1°C. will, if converted into work, raise a
424* weight 1â„¢ high, or 1* weight 424" high, According
to the English system, the same fact is stated as follows:
The quantity of heat that will raise 1 pound of water 1° F.
will raise 772.55 pounds 1 foot high. The quantity, 424",
is called the mechanical equivalent of one calorie, or Joule’s
equivalent (abbreviated simply J.). Or, we may say that
one calorie is the thermal equivalent of 424**â„¢ of work.
STEAM-ENGINE. : 149
Section VIII.
STEAM-ENGINE.
123. Description of a Steam-Engine. — A steam-en-
gine is a machine in which the elastic force of steam is the
motive power. Inasmuch as the elastic force of steam is
entirely due to heat, the steam-engine is properly a heat en-
gine; that is, it is a machine by means of which heat is
continuously transformed into work or mechanical motion.
The modern steam-engine consists essentially of an ar-
rangement by which steam from a boiler is conducted to
both sides of a piston alternately ; and then, having done
its work in driving the piston to and fro, is discharged
from both sides alternately, either into the air or into a
‘condenser. The diagram in Figure 183 will serve to illus-
trate the general features and the operation of a steam-en-
gine. The details of the various mechanical contrivances
are purposely omitted,so as to present the engine as nearly
as possible in its simplicity.
In the diagram, B represents the boiler, F the furnace,
S the steam-pipe through which steam’ passes from the
boiler to a small chamber VC, called the valve-chest. In
this chamber is a sizde-valve V, which, as it is moved to
and fro, opens and closes alternately the passages M and
N leading from the valve-chest to the cylinder C, and thus
admits the steam alternately each side of the piston P.
When one of these passages is open, the other is always
closed. Though the passage between the valve-chest and
the space in the cylinder on one side of the piston is
closed, thereby preventing the entrance of steam into this
space, the passage leading from the same space is open
150 MOLECULAR ENERGY. — HEAT.
through the interior of the valve, so that steam can escape
from this space through the exhaust-pipe E. Thus, in the
position of the valve represented in the diagram, the pas-
sage N is open, and steam entering the cylinder at the top
drives the piston in the direction indicated by the arrow.
At the same time the steam on the other side of the piston
escapes through the passage M and the exhaust-pipe E.
While the piston moves to the left, the valve moves to the
Ia
Hit
LO
G
NUTT
lk
COT
ap
Ty
nn
OS
Si
| TG
TA
i i
WE
ld
I
A
Fig. 133.
right, and eventually closes the passage N leading from
the valve-chest, opens the passage M into the same, and
thus the order of things is reversed.
Motion is communicated by the piston through the
piston-rod R to the crank G, and by this means the shaft
‘A is rotated. Connected with the shaft by means of the
STEAM-ENGINE. 151
crank H is a rod R’ which connects with the valve V, so
that, as the shaft rotates, the valve is made to slide to and
fro, and always in the opposite direction to that of the
motion of the piston.
The shaft carries a fly-wheel W. This is a large, heavy
wheel, having the larger portion of its weight located near
its circumference; it serves as a reservoir of energy which
is needed to make the rotation of the shaft and all other
machinery connected with it uniform, so that sudden
changes of velocity resulting from sudden changes of the
driving power or resistances are avoided. By means of a
belt passing over the wheel W’ motion may be communi-
cated from the shaft to any machinery desirable.
124.- Condensing and Non-Condensing Engines.! —
Sometimes steam, after it has done- its work in the cylin-
der, is conducted through the exhaust-pipe to a chamber
Q, called a condenser, where, by means of a spray of cold
water introduced through a pipe T, it is suddenly con-
densed. This water must be pumped out of the condenser
by a special pump, called technically the atr-pump ; thus
a partial vacuum is maintained. Such an engine is called
a condensing engine. The advantage of such an engine is
obvious, for if the exhaust-pipe, instead of opening into a
condenser, communicates with the outside air, as in the
non-condensing engine, the steam is obliged to move the
piston constantly against a resistance arising from atmos-
pheric pressure of 15 pounds for every square inch of the
surface of the piston. But in the condensing engine no
resistance arises from atmospheric pressure, and so with a
given steam pressure in the boiler the effective pressure
on the piston is considerably increased; hence, condensing
engines are usually more economical in their working.
1 The terms, low-pressure and high-pressure engines, are not distinctive as applied to
engines of the present day.
152 MOLECULAR ENERGY. — HEAT.
125. Compound Condensing Engine. — This engine has
two cylinders, each like that of a simple engine. One, A (Fig. 184),
called the high-pressure cylinder, receives steam of very high pressure
directly from the boiler. The steam, after it has done work in this cylinder,
passes through the steam-port into cylinder B, called the low-pressure
cylinder. Cylinder B is larger than cylinder A. The steam which enters
cylinder B possesses considerable tension, and is therefore capable of
doing considerable work under suitable conditions. It should be borne in
mind that in order that steam may do work in any cylinder, it is necessary
Fig. 134.
that an inequality in the tension of the steam each side of the piston
should be maintained; just as an inequality of level, i.e. a head, is essen-
tial to water-power. The steam, after it has done its work in cylinder B,
passes through a port into a condenser (not represented in the figure),
where it is suddenly condensed or let down to a very low tension. If a
vertical glass tube were led from the condenser to a vessel of mercury
below, the mercury would ordinarily stand about 25 inches high in the
tube, which would show that the tension of the steam against which the
steam when it enters cylinder B does work, is only about one-sixth of an
atmosphere. Much energy is economized by the compound engine.
126. The Locomotive. — The distinctive feature of the loco-
motive engine is its great steam-generating capacity, considering its size
and weight, which are necessarily limited. To do the work ordinarily
required of it, from three to six tons of water must be converted into
cat ict aan Rca a
STEAM-ENGINE. 153
steam per hour. This is accomplished in two ways: viz., first, by a rapid
combustion of fuel (from a quarter of a ton to a ton of coal per hour);
second, by bringing the water in contact with a large extent (about 800
square feet) of heated surface. The fire in the “fire-box†A (Fig. 185,
Plate II.) is made to burn briskly by means of a powerful draft
which is created in the following manner: The exhaust steam, after it
has done its work in the cylinders B, is conducted by the exhaust-pipe C
to the smoke-box D, just beneath the smoke-stack E. The steam, as it
escapes from the blast-pipe F, pushes the air above it, and drags by fric-
tion the air around it, and thus produces a partial vacuum in the smoke-
box. The external pressure of the atmosphere then forces the air through
the furnace grate and hot-air tubes G, and thus causes a constant draft.
The large extent of heated surface is secured as follows: The water of
the boiler is brought not only in contact with the heated surface of the
fire-box, but it surrounds the pipes G (a boiler usually contains about
150). These pipes are kept hot by the heated gases and smoke, all of
which must pass through them to the smoke-box and smoke-stack.
The steam-engine, with all its merits and with all the
improvements which modern mechanical art has devised,
is an exceedingly wasteful machine. The best engine that
has been constructed utilizes only about twenty per cent of
the heat-power generated by the combustion of the fuel.
QUESTIONS.
1. What kind of engine (i.e. condensing or non-condensing) is that
which produces loud puffs? What is the cause of the puffs?
2. Why ‘does the temperature of steam suddenly fall as it moves
the piston?
3. What do you understand by a ten horse-power steam- eee
4, Upon what does the power of a steam-engine depend?
5. Is the compound engine a condensing or a non- condensing. en-
gine? Which is the locomotive engine?
6. The area of a piston is 500 square inches, and the average unbal-
anced steam pressure is 30 pounds per square inch; what is the total
effective pressure? Suppose that the piston travels 30 inches at each
stroke, and makes 100 strokes per minute, allowing 40 per cent for
wasted energy, what power does the engine furnish, estimated in
horse-powers ?
CHAPTER VI.
ELECTRICITY AND MAGNETISM.
Section I.
INTRODUCTORY EXPERIMENTS.
No other department of Physics presents so many favorable oppor-
tunities for individual work as that of Electricity. There is none in
connection with which apparatus sufficient to equip a laboratory can be
provided so cheaply, when the amount of work which can be done with
it is considered; certainly there is no other department in connection
with which laboratory work is so indispensable in order to acquire a working
knowledge of the subject.
127. Apparatus Required. — A tumbler 2 full of water into
which has-been poured two or three tablespoonfuls of strong sulphu-
ric acid; a strip of sheet-copper, and two pieces of zinc,
each about 5 inches long and 14 inches wide. The pieces
of zinc should be 8; of an inch thick. A piece of No. 16
copper wire, 12 inches long, should be soldered to one end
of each piece of metal. The soldering should be covered
with asphaltum paint. Also, a rod of Norway iron, 6 inches
long and 4 of an inch in diameter; 4 yards of No. 23. in-
sulated copper wire; a magnetic needle, 6 inches long, nicely
poised on a fine needle-point; some fine iron turnings; and
two double connectors. These connectors (Fig. 136) serve
to connect two wires, without the inconvenience of twisting
them together. Wind the wire closely, with the exception
of about 10 inches at each extremity, around the iron-rod,
nearly from end to end, in two or three layers, as the case
may require. Amalgamate one of the zincs as follows: first dip the
zinc, with the exception of about 4 an inch at the soldered end, into
the acidulated water; then pour mercury over the surface, and finally
rub the surface wet with mercury with a cloth.
Fig. 136.
INTRODUCTORY EXPERIMENTS. 155
Experiment 111.— Put the unamalgamated (dark colored) zine
into the liquid. Bubbles of gas arise from the zinc. These bubbles,
Chemistry (page 24) teaches, are hydrogen gas. Put the copper strip
into the liquid, but do not allow the two metals or their wires to
touch. Do bubbles rise from the copper?
Experiment 112.— Remove the metals, and allow the liquid to
become clear. Connect their wires with a double connector, and in-
troduce both metals into the liquid, about 1 inch apart. Hold them
perfectly still for a minute, and observe whether any bubbles escape
from the copper.
Bubbles escaping from both metals make it appear as ‘if chemical
action were taking place between both metals and the liquid. But
experience will teach you that the BEpoarance is deceptive, as you will
‘find that only the zinc is consumed.
Experiment 113.— Put the amalgamated (bright) zinc into the
liquid. If the zinc is properly amalgamated, no bubbles will rise
from it. Do you discover any? If so, report it to your teacher.
Experiment 114.— Put the copper strip into the liquid. Do not
allow the metals or their wires to touch. Do bubbles rise from
either metal? Connect their wires. Do bubbles now rise from either
metal?
Lesson learned: — An amalgamated zinc is not acted
on by the liquid unless a copper strip is also in the
liquid, and not then unless the metals are connected.
It then we would at any
time stop the action, we
have only to disconnect
the metals.
It seems that the wire
connector serves a very
important purpose. Does
it, meantime, possess any
unusual properties ?
Fig. 137.
Experiment 115.— Place a magnetic needle (Fig. 187) near your
tumbler. When the needle comes to rest, it points north and south. .
156 ELECTRICITY AND MAGNETISM.
Place the connecting wire. over and near the needle, so that that por-
tion of the wire which is over the needle shall have a northerly and
southerly direction. Does the needle move? Does the end of the
needle pointing to the north (called the north-seeking pole of the
needle) move toward the east or the west? Imagine that your wire
is a tube through which there is flowing a liquid. Turn the tumbler
half way around, so that the current in that portion of the wire
which is over the needle shall be reversed. Do you observe any
change in the deflection of the needle? Next, lower that portion of
the wire which is over the needle, and place it nearly under the
needle. Do you observe any change in the deflection of the needle?
Lesson learned: — (1) The wire connector does pos-
sess an unusual property. It is capable of exercising an
unusual form of force. This new form of force is called
electro-magnetic force. (2) Although we have no positive
evidence that anything of the nature of a fluid flows
through the wire, yet in discussing certain phenomena,
such, for example, as the deflection of the needle, it is
extremely convenient, at least, to wmagime that a current
passes through the wire. Something does pass through the
wire. What this something is, physicists have not deter-
mined. They have merely given it a name — electricity.
128. Some Technical Terms. — Experiments, not
easily performed by the pupil, show that the current
traverses the liquid between the metals at the same time
that it traverses the connecting wire, so that the current
makes a complete circuit. The term circuit is applied to
the entire path along which electricity flows, and the wire
through which it flows is called the conductor. Bringing
the two extremities of the wires, or other parts of the
circuit, in contact. (so as to complete the circuit) and
separating them, are called, respectively, closing and open-
ing, or making and breaking, the circuit. Opening a circuit
INTRODUCTORY EXPERIMENTS. 157
at any point, and filling the gap with an instrument of any
kind, so that the current is obliged to pass through it, is
called introducing an instrument into the cirewit. Our ar-
rangement of acidulated water and two metals is called a
voltate cell, and the two metals are called its elements.
A series of cells properly connected is called a battery,
though this term is frequently applied to a single cell.
The free extremities of the wires are called poles or elec-
trodes, and the same terms may be applied to any two
points of contact in any part of the circuit.
129. Conductors and Non-Conductors.
Experiment 116.— Will every substance answer for a conductor ?
Introduce into the circuit between the electrodes, pieces of wood,
paper, cloth, glass, iron, brass, zinc, lead; also, a drop of mercury on a
glass plate. Place the connecting wire over the magnetic needle, and
determine, by the deflection of the needle, through which of these
substances electricity will pass. Those substances through which
electricity passes readily are called good conductors. Substances
through which electricity passes with great difficulty are called bad
conductors, non-conductors, or insulators. Are metals conductors or
non-conductors ?
130. Direction of the Current, etc. —It is evidently
necessary in describing a current to assign it a direction.
Electricians have universally agreed, for the purpose of
uniformity and convenience, to assume that in such a cell
as described, electricity flows from the zinc, where the
chemical action takes place, through the liquid to the
copper element, thence through the wire to the starting-
point, #.e. the zinc element. If we take any two points in
a circuit, of course the current will be from one toward
the other. The former point is said to be positive (+)
with reference to the latter point which is said to be
negative (—). Which is the positive element of a battery,
the zinc or the copper plate? Which electrode, ¢.e. the
158 ELECTRICITY AND MAGNETISM.
free end of the wire connected with the zinc plate, or the
end of the wire connected with the copper plate, is posi-
tive ?
Experiment 117.— Place the connecting-wire over the magnetic
needle, in such a manner that the current will flow northward through
that section of the wire that is above the needle. Then reverse the
direction of the current. Finally, place the wire under the needle.
In each different position verify the following rule for determining
the direction of the deflection when the direction of the current is
known.
131. Ampére’s Rule. — Imagine yourself to be swim-
ming in the current, and with (ie.
a your head in the same direction as)
cerece, the current, and facing (i.e. look-
= ing up or down according as the
needle is above or below you) the
needle; in such a position the
north pole of the needle is always
deflected toward your left.
Fig. 158.
132. Galvanoscope.— The magnetic needle serves the
purpose of determining the presence of a current in a wire.
A needle used for this purpose is called a galvanoscope.
Electricity set in motion by a voltaic battery is called
galvanic or voltaic and sometimes current or dynamic
electricity.
POTENTIAL AND ELECTRO-MOTIVE FORCE. 159
Section II.
POTENTIAL AND ELECTRO-MOTIVE FORCE.
133. Potential.— In order that water may flow from
- one vessel A to another B through a connecting pipe,
there must be a difference of level in the two vessels; t.e.
in ordinary language there must be a head of water in A.
The head of water in A causes a greater pressure at the
end of the pipe next this vessel than at the end next B,
and this unbalanced force causes a flow of water from
A to B until there is the same level in both vessels. So,
in order that there may be a flow of electricity from a
body A to a body B, or from a given point A in a body
to another given point B in the same body, there must
be a difference of electrical condition between A and B.
This difference of condition may be imagined as a differ-
ence of electrical pressure and is called a difference of
electrical potential.
In any case we may say that difference of potential with
reference to electricity is analogous to difference of pres-
sure in fluids, and that electricity always tends to flow
from places of high to places of low potential.
184. Electro-Motive Force.— When two conductors
are connected by a wire it is found that the rate at which
electricity passes from one to the other is proportional to
the difference of potential of the two conductors, and that
this is proportional to the work that would be expended
in carrying a unit quantity of electricity backwards
through the wire. So, too, in any circuit it is found that
the quantity of electricity flowing in any time is strictly
proportional to the amount of work necessary to carry a
:
160 ELECTRICITY AND MAGNETISM.
unit quantity of electricity backwards through the circuit.
This important magnitude receives the name electro-motive
force (E.M.F.), although it is apparent that it is not a
force. The E.M.F., or work done, ts the cause of difference
of potential.
We might agree to call any point in a liquid stream
positive with reference to all points below it or of lower
level, and negative with reference to all points above it,
or points of higher level. So any point in an electrical
conductor is said to be positive with reference to all points of
lower potential, and negative with reference to all points of
higher potential.
Is there such a thing as a difference of electrical condition?
(| I | i p
(, Ae
(i _
| hi
A)
ae
j i mm D
AAT
vl
mi
Fig. 139.
Experiment 118. — Separate a little way the two conductors C and
D (Fig. 189), of a Holtz machine. Hold two pith balls suspended
by white silk threads against one of the conductors and turn the
plate a few times. Remove the pith balls and hold them near each
other. They repel each other. Next place one of the pith balls in
contact with one of the conductors and the other pith ball in contact
with the other conductor. Turn the plate as before, remove the pith
balls, and hold them near each other. Now, in the first case, the two
POTENTIAL AND ELECTRO-MOTIVE FORCE. 161
pith balls were placed in contact with the same conductor, and hence
acquired the same electrical condition (i.e. potential) as that con-
ductor. In this condition they repel each other. But after being
in contact with different conductors, as in the second case, they at-
tract each other (Fig. 140).
Hence, we conclude that the
two conductors are in a dif-
ferent electrical condition.
It is in consequence of
this difference of elec-
trical condition, which
always exists between
such bodies, that the = ==
electricity. passes from ~* ee
one conductor through - ‘Fig. 140.
the air to the other, rendering the air in its path tem-
porarily luminous. The most convenient test of the
electro-motive force of an electrical machine is the length
of spark it gives.
135. Electro-Chemical Series.
Experiment 119.— Take two plates of zinc, either both amalga-
mated or both unamalgamated, connect them, put them into acidu-
lated water, and place the connecting wire over a magnetic needle.
Does the galvanoscope show that there is a current in the wire? Is
there, then, a difference of potential between the two plates?
It is important that only one of the two elements of a vol-
tate cell should be acted upon by the liquid. The. greater
the disparity between the two solid elements, with reference
to the action of the liquid on them, the greater the difference
in potential ; hence, the greater the current. In the follow-
ing electro-chemical series the substances are so arranged
that the electro-positive, or those most affected by dilute
sulphuric acid, are at the beginning; while the electro-
162 ELECTRICITY AND MAGNETISM.
negative, or those least affected by the acid, are at the
end. The arrow indicates the direction of the current
through the liquid.
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It will be seen that zinc and carbon are the two sub-
stances best adapted to give a strong current.
The essential parts of a galvanic cell are a liquid and two
different conductors, one of which is more readily acted
upon chemically by the liquid than the other.
136. Importance of Amalgamating the Zine. — All
commercial zinc contains impurities, such as carbon, iron,
etc. Figure 141 represents a zinc element having on its
surface a particle of carbon a, purposely magnified. If
such a plate is immersed in dilute sulphuric
acid, the particles of carbon will form with the
zine numerous voltaic circuits, and a transfer
of electricity along the surface will take place.
This coasting trade, as it were, between the
zinc and the impurities on its surface, diverts
so much from the regular battery current, and
thereby weakens it. In addition to this, it
Fig.141. o¢casions a great waste of chemicals, because,
when the regular circuit is broken, this local action,
as it is called, still continues. If pure zine were used
(formerly it was used), no local action would occur at
any time, and there would be no consumption of chemi-
cals, except when the circuit is closed. If mercury is
rubbed over the surface of the zinc, after the latter has
been dipped into acid to clean its surface, the mercury
POTENTIAL AND ELECTRO-MOTIVE FORCE. 163
dissolves a portion of the zinc, forming with it a semi-
liquid amalgam which covers up its impurities, and the
amalgamated zinc then comports itself like pure zinc.
137. How Electric Energy Originates. — According
to the doctrine of the conservation of energy, whenever
any new form of energy is generated it is always at the ex-
pense of some other form of energy; in other words, some
other form of energy is transformed into the new form.
When, as in Experiment 118, you turn the plate of a
Holtz machine, you feel a peculiar resistance that is not
wholly due to the friction of the parts. The mechanical
energy which you expend in overcoming friction is con-
verted into heat energy. The mechanical energy which
you expend in overcoming the peculiar resistance is trans-
formed into electric energy.
We are already familiar with the fact that the chemical
potential energy in a lump of coal is converted during the
process of combustion into heat energy. When zinc is
placed in acidulated water, a similar combustion occurs,
and if a thermometer is placed in the liquid, it will show
a rise of temperature as the burning progresses. If, how-
ever, the zinc is connected with the copper, or some other
suitable element, there is less heat generated by the com-
bustion, because a portion of the chemical potential energy
is converted into electric energy. Electric energy origi-
nates in a voltaic cell from the conversion of chemical
potential energy into this form of energy.
164 ELECTRICITY AND MAGNETISM.
Section III.
BATTERIES.
138. Polarization of Elements. — If you connect any
voltaic cell with a sensitive galvanoscope, such as will be
described hereafter, you will find that in a few minutes
after making the connection, the deflection diminishes
somewhat. This is due to the collection of hydrogen at
the electro-negative plate. The effect of the hydrogen is
to raise the potential of this element and thereby diminish
the difference of potential between the two plates. What-
ever tends to diminish the difference of potential between
the two elements, tends to diminish the current of electric-
ity, and to that extent to diminish the value of a voltaic
cell. This action is called, technically, polarization of the
elements. Among the different methods that have been
devised for remedying this evil, the most efficient is that
in which the pydregeny is disposed of by surrounding the
electro-negative element with a
liquid with which the hydrogen
will readily enter into combina-
tion. A good illustration of this
method may be found in the ac-
tion of the Bunsen battery.
139. Bunsen Battery. — The
metal employed for the electro-positive
plate in this, as in nearly all batteries, is
zinc. The zinc is immersed in sulphuric
! acid diluted with about ten times its volume
Fig. 142. of water. Inside of the hollow cylindrical
zinc plate (Fig. 142) is a cup of porous unglazed earthenware. This cup con-
tains a liquid composed of a saturated solution of potassium bichromate,
BATTERIES. 165
or (better) sodium bichromate, mixed with one-sixth its volume of sulphu-
ric acid. This cup serves to keep the two liquids separate, but does not
prevent electrical action. In this cup is placed a bar of carbon, which is
the electro-negative plate. The larger portion of the hydrogen generated
by the action between the zine and the acidulated water enters into com-
bination with some of the constituents of the bichromate of potash, and
thereby prevents in a large measure the polarization of the electro-
negative element. Such a battery is called a two-fluid battery.
140. Grenet Battery. — In this battery a small flat plate of zine,
2 (Fig. 143) is suspended between two carbon plates, CC. The carbons re-
main in the liquid all the time. The zinc should be drawn up out of the
liquid by means of a slide rod a when the battery is not in use, as a
broken circuit does not prevent the consumption of the zinc when it is in
the liquid, even though the zinc is well amalgamated.
Fig. 143. Fig. 144,
This battery gives a more energetic current fora short time than the
Bunsen battery, but the carbon in this battery becomes sooner polarized,
and the liquid sooner exhausted than in the Bunsen battery. It is an
extremely convenient and popular battery for brief schoolroom use, as it
is very energetic in its action and requires little care.
141. Daniell Battery. — One of the chief virtues of this battery
(Fig. 144) is, that it polarizes less than most other kinds of batteries, and
therefore gives a more constant current. The zinc is suspended. in a
166 ELECTRICITY AND MAGNETISM.
porous cup, either in pure water, or in water to which has been added a
little zinc sulphate to hasten the action when the battery is first set up.
The zinc is not amalgamated. Outside the cup is a thin sheet of copper
in the form of a hollow cylinder immersed in a saturated solution of
copper sulphate. Ina pocket near the top of the copper sheet are kept
lumps of copper sulphate, which are gradually dissolved to take the place
of that which is consumed by the action of the battery. This battery
requires very little attention, and is largely used in England for tele-
graphing,
Section IV.
SOME EFFECTS PRODUCED BY AN ELECTRIC CURRENT.
142. Heating and Luminous Effects.
Experiment 120. — Connect six or eight Bunsen (or Grenet cells)
abreast (see page 186). Attach connectors to the electrodes, and intro-
duce between the connectors a piece of No. 80 platinum wire, less than
half an inch long. The platinum wire is heated to a luminous state.
Place the platinum wire over a gas burner, turn on the gas, and
light it by the heat of the wire. This illustrates one of the practical
uses to which the electric current is put in lighting numerous gas
burners in halls and theatres. Remove the platinum wire, and intro-
duce into the circuit an incandescent lamp of from four to six
candle-power. Does this arrangement of battery render the carbon
filament luminous?
Experiment 121.— Connect the eight cells in series (see page 187),
and introduce the same lamp into the circuit. Does the filament
become luminous? Remove the lamp from the circuit, and insert the
platinum wire as before. Does the platinum wire become as hot as
in the former arrangement of cells? Which arrangement gives the
greater heating effect with the platinum wire? Which with the
lamp? :
143. Chemical Effects.
Experiment 122.— Take in a test-tube a quantity of an infusion of
purple cabbage (the cabbage may be found at a suitable time of the
EFFECTS PRODUCED BY AN ELECTRIC CURRENY. 167
year in any market) prepared by steeping its leaves until well cooked.
Pour into this infusion a few drops of any alkali, such as a solution
of caustic soda. The infusion is changed thereby from a purple to a
green color. In another test-tube take another portion of the purple
infusion. Into this pour a few drops of any acid, such as dilute sul-
phuric acid. The purple is changed toared. Only acids will turn
this infusion to a red and only alkalies will turn it toa green. Into a
rather strong solution of sodium sulphate pour enough of the purple
infusion to give it a decided color.
Pour some of this colored solution into a V-shaped glass tube
(Fig. 145). Take two short pieces of copper wire covered with rubber
and having strips of platinum soldered upon one
of their ends for electrodes, and introduce one of
these electrodes into each arm of the tube until
it nearly reaches the bottom or angle of the V.
By means of connectors connect the battery (of
three cells in series) wires with the free extremities
of these wires. The liquid between the two plati-
num electrodes forms a part of the circuit, so that
the current of electricity passes through this por-
tion of the liquid. Soon the liquid around the
— electrode is turned green, while that around the :
+ electrode is turned red. Evidently, decomposition of the sodium sul-
phate has taken place. An acid and an alkali are the results.
A substance that may be decomposed by electricity is
called an electrolyte, aud the process electrolysis. An elec-
trolyte must be a compound substance, and in a liquid state.
When a salt (see Chemistry, page 54) is electrolyzed, the
base appears at the — pole, and the acid at the + pole.
Experiment 123.— Wet a piece of writing paper with a liquid
prepared in the following manner. Dissolve by heating about three
grains of pulverized potassium iodide in about a tablespoonful of
water. Make a paste by boiling pulverized starch in water. Take a
portion of this paste about the size of a pea, stir it into the solution.
Spread the wet paper smoothly on a piece of tin, e.g. on the bottom
of a tin basin. Press the — pole of your battery against an uncov-
ered part of the tin. Draw the + pole over the paper. A mark is
168 ELECTRICITY AND MAGNETISM.
produced upon the paper as if the pole were wet with a purple ink.
In this case the potassium iodide is decomposed, and the iodine com-
bining with the starch forms a purplish blue compound.
In the experiment with the cabbage infusion you proba-
bly discovered bubbles of gas arising from this liquid, caus-
ingafoam. This is evidence that there was another de-
composition going on besides that of the sodium sulphate
—a sort of double decomposition. We will now take
measures to collect these gases for examination.
' Experiment 124.— Take a dilute solution of sulphuric acid (1
part by bulk to 20), pour some of it into
the funnel (Fig. 146), so as to fill the
U-shaped tube when the stoppers are re-
moved. Place the stoppers which support
the platinum electrodes tightly in the
tubes. Connect with these electrodes the
battery wires. Instantly bubbles of gas
arise from both electrodes, accumulating
in the upper part of the tube and forcing
the liquid back into the tunnel. Twice
as much gas arises from the — electrode
as from the + electrode. Close the pas-
sage in the rubber tube by turning down
the screw of the pinch-cock a. Light a
splinter of fine wood, blow out the flame,
leaving it glowing; remove the stopper
holding the + electrode and introduce the
glowing splinter into the gas in this arm
of the tube. It relights and burns vigor-
a ously, showing that the gas is oxygen.
Fig. 146. (See Chemistry, page 19.) Platinum elec-
trodes are used, otherwise a portion of the oxygen carried to the
+ electrode would not be set free, but would oxydize the metal (e.g.
copper), instead of appearing as a gas in this arm of the tube. Fill
this arm of the tube with water and stopper it. Invert the U-tube;
the gas in the other arm of the U-tube collects in the bend of the
tube and in the small branch tube. Light a match, remove the
EFFECTS PRODUCED BY AN ELECTRIC CURRENT. 169
rubber tube, and quickly hold the match at the orifice of the branch
tube. The gas burns. (See Chemistry, page 25.) It is hydrogen.
This operation is commonly called “decomposing water by electric-
ity.†See if you can “decompose water†with your battery of three
cells connected abreast.
Experiment 125.— This delightful experiment may be performed
by the teacher, or an experienced pupil, before the class. Take about
one-fourth of a teacupful of water, guyz zs
dissolve in. it about two grams of &
silver nitrate. Do not wet the hands
with the solution, as it will stain
them black. Nearly fill the electrol-
ysis tank (Fig. 147) which accom-
panies the porte-lumiere (page 310).
Arrange a battery
of two cells in
series. Place the
tank in position
in the porte-lu-
mitre to project
it on a screen
in a dark room.
Connect the. bat-
tery wires with
the electrodes in § : :
exit: the tank. A beau- LESS
tiful deposit of silver will be made on the —electrode, spreading
therefrom toward the + electrode, and bearing a strong resemblance to
vegetable growth; hence it is called the “silver tree.†In Figure 148,
A represents a silver tree deposited from a weak solution and B
from an extremely weak solution.
144. Physiological Effects.
Experiment 126.— Take a single Bunsen cell and place its elec-
trodes each side of the tip of the tongue. A slight stinging (not
painful) sensation is felt, followed by a peculiar acrid taste.
When a battery is known not to be very powerful, the
tongue serves as a convenient galvanoscope to determine
whether the battery is in working condition. '
170 ELECTRICITY AND MAGNETISM.
145. Magnetic Effects.
Experiment 127.— Take the iron rod having an insulated wire
wound around it, and connect the extremities of the wire with the
battery wires; in other words, introduce this wire
into the circuit. Bring a nail (Fig. 149) or other
piece of iron near one end of the rod. The rod at-
tracts the nail with considerable force, and this
nail will attract other nails. The rod has all the
properties of a magnet, as will be seen hereafter.
Break the circuit. The iron rod instantly loses
its magnetic force, and the nails drop.
The iron rod is called a core, the coil of wire a
helix, and both together an electro-magnet. In order
to take advantage of the attraction of both ends
or poles of the magnet, the rod is most frequently
bent into a U-shape (A, Fig. 150), and then it is
called a horse-shoe magnet. More frequently two
iron rods are used, connected by a rectangular
piece of iron, as a in B of Figure 150. The method
of winding is such that if the iron core of the horse-shoe were
straightened, or the two spools were placed together end to end,
, one would appear as a contin-
uation of the other. A piece of
soft iron, 6, placed across the
ends and attracted by them, is
called an armature. The piece
Fig. 150. of iron, a, is called a yoke.
Experiment 128. Be dutange a battery of four cells in series. In-
troduce into the circuit an electromagnet wound with a long, fine
wire (having a resistance of not less than 25 ohms.! Ascertain
approximately the force required to pull’an armature (e.g. a large
nail) off the poles.
Next remove this electro-magnet, and introduce into the circuit in
its place an electro-magnet wound with coarse wire (which has a
resistance not exceeding 1 ohm). See, by pulling, with what force it
holds a nail on one of its poles.
Experiment 129.— Arrange a battery of four cells abreast. In-
troduce into the circuit the fine wire magnet. See with what force it
Fig. 149.
1 See page 178.
ELECTRICAL MEASUREMENTS. 171
holds its armature. Which arrangement of cells produces the greater
magnetic power with this electro-magnet?
Next introduce in its place the low-resistance electro-magnet and
find with what force it holds the nail. Which arrangement of cells
produces the greater magnetic power in this magnet?
Important Lesson: The results of our experiments
thus far teach, that the arrangement of a battery of several
cells and the apparatus used should be adapted to each other.
It is apparent that, if there are rules or laws which will enable a person
who would use an electric current for experimental or industrial purposes,
to determine by calculation just what is the best method of arrangement
in any given case, it is of the utmost importance that these laws should
be understood.
Section V.
ELECTRICAL MEASUREMENTS.
The wonderful developments which have been made in recent years
in electrical science, and which have led to the employment of electric
energy in connection with a great diversity of industrial arts, are almost
wholly due to a better understanding of what electrical measurements can
be made, and how to make them. Indeed, little of a practical nature can
be done without some acquaintance with the methods of making these
measurements.
146. Some Technical Terms.— A quantity of water
may be measured either in quarts or pounds; te. by its
volume or weight. Although electricity has neither vol-
ume nor weight, yet it has that which answers strictly to
the term quantity, and the quantity can be measured by
suitable means. The unit employed for the measurement
of a quantity of electricity is called a coulomb. A stream of
water flowing through a pipe might be described by stating
the number of quarts which flow through the pipe, or past
172 ELECTRICITY AND MAGNETISM.
any point in the pipe, in a minute. In a similar manner,
we describe an electric current by stating the number of
coulombs that pass through a conductor, or that pass a
given point of a conductor, in a second.
The quantity of electricity passing through a conductor
in a given time, in other words the rate of flow, determines
the strength of the current. When the quantity passing
is one coulomb! per second, the strength of the current is
said to be one ampére. A current of 10 coulombs per
second has a strength of 10 ampéres. The ampére is the
unit for measuring current strength. There is no unit
analogous to this for measuring liquid currents. It should
be observed that the term strength refers only to the
quantity of electricity passing, and not to the energy of the
current.
As we might calculate the energy of a current of water
by multiplying the weight of water falling by the distance
it falls, so if we represent by C the strength of current in
ampéres, and by V the electro-motive force or difference of
potential in volts (see next paragraph), then
. CV = power of current,
which is expressed in a unit called an ampére-volt (or
watt?), much as we express mechanical energy in foot-
pounds. This is equivalent to about 74, horse-power.
From this formula we infer that when the electro-motive
force remains the same, the power of a current varies as
its strength; and when the current strength does not
change, the power varies as the electro-motive force. As
indicated above, difference of potential and electro-motive
force are measured in a unit called a volt. For our pur-
1 A coulomb is the quantity of electricity delivered by a one-ampére current in one second.
2 A watt is the power of a current of one ampére when maintained by one volt.
C.G.8. MAGNETIC AND ELECTRO-MAGNETIC UNITS. 173
pose it will answer to consider a volt as ‘the electro-motive
force of a Daniell’s cell; ¢.e. it is about the difference of
potential between the zinc and the copper of this cell.
——c-0sa400—
Section VI.
C.G.8. MAGNETIC AND ELECTRO-MAGNETIC UNITS.
[This section is intended to assist the student who is ambitious to read
technical works on electricity, but, like other matter in fine print, it is not
included in the course of study prescribed in this book.]
147. Magnetic Units.—These units are based on the forces
exerted between two magnetic poles. They form the basis for the electri-
cal units adopted by the Congress of Electricians, held at Paris in 1871.
Unit Magnetic Pole. — A unit magnetic pole is one which repels a similar
pole placed at a distance of 1°™ with a force of 1 dyne. It has no special
name; its dimensions are MGL?T-1,
Unit of Intensity of a Magnetic Field. —The intensity of a magnetic
field is one C.G.S. unit when the force which acts on a unit magnetic pole
in this field is 1 dyne. Its dimensions are M-2L2T-1,
148. Electro-Magnetic Units and Practical Units. —
Unit of Current Strength: — A current has the strength of one C.G.S. unit,
if, in passing through a circuit 1â„¢ long, bent into the form of an arc of a
circle of 1°™ radius (so as to be always 1° away from the magnet- pole),
it exerts a force of 1 dyne on a unit magnet-pole placed at the center.
Unit of Quantity: —The quantity of electricity which passes through a
circuit in one second when the strength of the current is one C.G.S. unit.
Unit of Electro-motive Force : —The E.M.F. necessary in order that a unit
of quantity may do the work of an erg. [W=QE.]
Unit of Resistance: — A conductor has a resistance of one C.G.S. unit
when a unit difference of potential between its two ends causes a unit of
current to pass through it.
Inasmuch as in practice the employment of these units leads to thera use
of very large numbers, units have been adopted which are decimal multi-
ples of the C.G.S. units. They have received special names and are
known as the practical units.
174 ELECTRICITY AND MAGNETISM.
TABLE OF ELECTRO-MAGNETIC UNITS.
NO. OFC.G.S.
NAME OF |" UNITS IN
QUANTITIES. SYMBOL. rarer ONE PRAC- DIMENSIONS OF UNIT.
TICAL UNIT,
Resistance. . . . Ohm 109 LT“
Electro-motive force Volt | 108 MLig-2
Current Strength . Ampere | LOS M3L3T-1
Quantity . . . . Coulomb 10 1 MELE
Section Vil.
GALVANOMETERS.
149. Introductory Experiments.
Experiment 130.— Wind a battery wire lengthwise once around
a book, and place the book either above or below and near to a
magnetic needle, and hold the book in such a position that that por-
tion of the current which circulates around the book will have a
northetly and southerly direction. Notice the extent of the deflection
of the needle. Then wind the wire closely 20 or 80 times around
the book, and hold it in the same position, and at the same distance
from the needle as before. The needle, now that the current is carried
several times past it, makes a larger deflection; consequently the
effect of several windings is to render the needle more sensitive to
weak currents.
Experiment 131, — Connect two cells abreast, and once more hold
the book with its many turns of wire near the needle, ag in the last
experiment. The deflection is larger than before, which is due to
the fact that the two cells give a stronger current, than one cell.
It thus seems that a galvanoscope, in addition to its other
uses, may indicate the strength of a current, and when
properly constructed to measure the relative strength of
currents it is called a galvanometer.
GALVANOMETERS. 175
150. Tangent Galvanometer.— The galvanometer G,
represented in Figure 151, has a magnetic needle about
4 inch long and an indicator of light aluminum wire about
3.5 inches long, resting upon and parallel with the needle.
The whole is suspended from a brass frame by a very fine,
untwisted, silk fiber, just over a coil of wire such as was
formed by winding a wire about the book. Between the
needle and coil is a card containing a circle divided into
halves by a diameter parallel with the wires of the coil
below. Each extremity of this diameter is numbered zero.
Each semicircle is divided into halves, and each quarter
circle is divided into ninety degrees and numbered each way
from zero to the ninetieth degree. The whole is covered
with a glass case to prevent disturbance by currents of air.
When the needle of a galvanometer is short in compari-
son with the length of its coil the strength of currents varies
as the tangents of the angles of deflection. Such a galvan-
ometer is called a tangent galvanometer. For example,
suppose that the deflections produced in the same tangent
galvanometer by two currents are 80° and 70°. Consult-
ing the Table of Tangents in Appendix, C, we find the
tangents of these angles are respectively 5.67 and 2.75;
hence the former current is (5.67 + 2.75 = ) 2 + times as
strong as the latter.
The student should understand that the galvanometer described above,
is not, strictly speaking, a standard tangent galvanometer. The manifold
uses to which galvyanometers are put in a physical laboratory, properly
require a variety of instruments, which would make an equipment very
expensive. The galvanometer here described answers very well all the
purposes of this book. The results obtained by its use are approximately
those which would be obtained by a standard tangent galvanometer of the
usual form, in which the needle is suspended at the center of a large cir-
cular coil of wire.
151. Galvanometer with an Astatic Needle. — This needle
is much more sensitive to weak currents than the needle described above.
176 ELECTRICITY AND MAGNETISM.
It consists of two magnetic needles fastened to a common axis, but having
their poles reversed, so that, for example, the + pole of one is over the
—pole of the other. It is suspended by a silk fiber, so that one of the
needles may rotate within the coil while the other rotates above the coil.
The current acts upon both needles to turn them in the same direction.
Moreover the current both above and below acts in the same direction on
the needle which is suspended within the coil, hence the astatic needle is
much more sensitive than a single needle. The needle does not point
north and south like the ordinary needle, but more nearly east and west.
——oobgyo0—
Section VIII.
RESISTANCE OF CONDUCTORS.
152. External Resistance.
Experiment 132.— Introduce into a circuit a galvanometer, and
note the number of degrees the needle is deflected. Then introduce
into the same circuit the wire on the spool numbered 4 on the plat-
form, § (Fig. 151). (The wire on any one of the five spools on this
platform can at any time be introduced into a cireuit, by connecting
the battery wires with the binding screws on each side of the spool
to be introduced.)
Fig. 151.
The deflection is now less than before. The copper wire on this
spool is 16 yards in length; its size is No. 80 of the Brown and
Sharpe wire gauge. When this spool is in circuit, the circuit is 16
yards longer than when the spool is out. The effect of lengthening
RESISTANCE OF CONDUCTORS. 177
the circuit is to weaken the current, as shown by the diminished
deflection. .
Experiment 133.— Next, substitute Spool 2 for Spool 4. This
contains 32 yards of the same kind of wire as that on Spool 4. The
deflection is still smaller.
The weakening of the current by introducing these wires is caused
by the resistance which the wires offer to the current, much as the
friction between water and the interior of a pipe impedes, to some
extent, the flow of water through it. The longer the pipe the greater
is the resistance to the flow.
Tf the wire on the spools had been the only resistance in the cir-
cuit, then, when Spool 2 was in the circuit, the resistance of the circuit
would have been double the resistance that it was when Spool 4 was
in the circuit, and the current, with double the resistance, would have
been half as strong.
@) Other things being equal, the resistance of a conductor
varies as its length.
Experiment 134.— Next substitute Spool 1 for Spool 2. This
spool contains 82 yards of No. 28 copper wire, —a thicker wire than
that on Spool 2, but the length of the wire is the same. The deflec-
tion is now greater than it was when Spool 2 was in circuit. This
indicates that the larger wire offers less resistance.
Careful experiments show that (2) the resistance of
all conductors varies inversely as the areas of their cross
sections. If the conductors are cylindrical it varies inversely
as the square of their diameters.
Experiment 135.— Substitute Spool 5 for Spool 1, and compare
the deflection with that obtained when Spool 4 was in the circuit.
The deflection is smaller than when Spool 4 was in circuit. The wire
on these two spools is of the same length and size, but the wire of
Spool 5 is German silver. It thus appears that German silver offers
more resistance than copper.
(8) Inestimating the resistance of a conductor, the specific
resistance of the substance must enter into the calculation.
(See Table of Specific Resistances, Appendix, D.)
178 ELECTRICITY AND MAGNETISM.
The resistance of metal conductors increases slowly with
the temperature of the conductor. The resistance of Ger-
man silver is affected less by changes of temperature than
that of most metals; hence its general use in standards of
resistance.
153. Internal Resistance.
Experiment 136.— Connect the copper and zine strips used in
Experiment 114 with the galvanometer, and introduce the strips into
a tumbler nearly full of acidulated water. Note the deflection. Then
raise the strips, keeping them the same distance apart, so that less and
less of the strips will be submerged. As the strips are raised, the
deflection becomes smaller. This is caused by the increase of resistance
in the liquid part of the circuit, as the body of liquid lying between
the two strips becomes smaller. The resistance of the liquid: part of
the battery is called internal resistance, in distinction from that of the
rest of the circuit, which may be regarded as external resistance.
(4) The internal resistance of a circuit varies inversely
as the area of the cross section of the liquid between the two
elements.
In a large cell the area of the cross section of the liquid
between the elements is larger than in a small cell, con-
sequently the internal resistance is less. This is the only
way in which the size of a cell affects the current.
154. Measurement of Resistance; The Ohm. — Re-
sistance is measured by a unit called an ohm. An ohm
is the resistance of about 9 inches of No. 30 (B. & S. G.)
German silver wire, or about 9.3 feet of No. 30 copper
wire at ordinary temperature.
155. Description of the Rheostat. — Figure 152 represents a
wooden box containing what is equivalent to a series of coils of German
silver wire, whose resistance ranges from 0.1 ohm to 100 ohms. Each of
these coils is connected with a brass stud on the top of the box.
_ Three switches, A, B, and C, so connect the coils with the binding screws
a and d that a current can be sent through any three coils at the same time
by moving the switches on to the proper studs. The resistance in ohms
RESISTANCE OF CONDUCTORS. 179
of each coil is marked on the box near its stud. When the three switches
rest upon studs marked 0, the current meets with no appreciable resist-
ance in passing through
the box, but any desired
resistance within the
range of the instrument
can be introduced by
moving the switches on
to the studs, the sum of
whose resistances is the
resistance required. This
instrument is called a
rheostat.
Fig. 152.
Experiment 137.— Measure in ohms the resistance of the wire on
each one of the spools used above, as follows :— Introduce into circuit
(as in Figure 151) a galvanometer and the spool whose resistance is
sought. Note the deflection in degrees. ° Then remove the spool, and
introduce the rheostat in its place. Place all the switches on the zero
studs. The deflection of the galvanometer needle is now evidently
greater than when the spool was in circuit. Move the switches, throw-
ing in or taking out resistance (much as you use weights in weighing),
until the deflection becomes the same as the deflection was when the
spool was in circuit. It is evident that the sum of the resistances, as
indicated by the three switches, must be the same as the required
resistance of the wire on the spool.
In the same manner, measure the resistance of the electro-magnets
of telegraph sounders, relays, incandescent lamps, etc.
The method of measuring resistance given above is
called the method by substitution or balancing. ‘The results
obtained by this method are accurate only on condition
that the electro-motive force and internal resistance of the
battery remain sensibly constant throughout the operation.
This rarely happens, so that the results obtained can be
regarded as only approximately correct. When great
accuracy is required, it is necessary that some means of
measuring should be adopted in which the fluctuations of
180 ELECTRICITY AND MAGNETISM.
the battery will not affect the results. -This difficulty is
obviated by the use of the invaluable instrument called
(from the name of its inventor) the Wheatstone bridge.
156. Wheatstone Bridge. — Figure 153 represents a perspective
view of the bridge (as modified
by the Author), and Figure 154
represents a diagram of the es-
sential electrical connections.
The battery wires are connected
with the bridge at the binding
B S screws, BB!. A galvanometer g
Fig. 153. is connected at GG/, a rheostat
r at RR, and the object x, whose resistance is sought, at XX.
On closing the circuit by pressing on the knob T the current, we will sup-
pose, enters at B; on reaching the point A it ‘divides, one part flowing via
- the branch AGB’, and the other
via the branch ADB’. If points D
and G in the two branches have
different potentials and a con-
nection is made between them
through the galvanometer, g,
by pressing on the knob §S, there
will be a current through this
bridge wire and through the
galvanometer, and a deflection
of the needle will be produced.
But if the points D and G have
the same potential, there will
be no cross current through the
bridge wire and no deflection.
Now it can be demonstrated
that points D and G will have
the same potential when R (the
resistance) of AD: R of DB/:: R of AG: R (the unknown resistance)
of. GB’. Between A and Dand A and G there are three coils of wire
having resistances respectively of 1,10, and 100 ohms. One or more of
these coils are introduced into the circuit by removing the corresponding
plugs a,b,c, d,e, and f. As the other connections between A and D, and
A and G, have no appreciable resistance, being for the most part short
brass bars, the only practical resistance between these points is that intro-
! !
RESISTANCE OF CONDUCTORS. 181
duced at will through the coils. Similarly between points D and B’, the
only practical resistance is that introduced at will through the rheostat,
and between points G and B’ the resistance is the resistance (x) sought.
It is apparent, then, that in using the bridge after the connections are
properly made through the several instruments and certain known resist-
ances are introduced between A and D, and A and G, we have simply to
regulate the resistance through the rheostat so that there will be no deflec-
tion in the galvanometer; then we are sure that the above proportion is
true. The first three terms of the proportion being known, the fourth
term, which is the resistance sought, is computable.
In using the instrument, observe the following directions. (1) Always
close the circuit at T before closing the bridge connections at 8. (2)
Introduce between A and D, and A and G, resistance as nearly equal to
the resistance (x) sought as practicable, as the galvanometer is then most
sensitive. If you have no conception what the unknown resistance is, it is
best to begin by using high resistances. (8) The sensitiveness of the gal-
vanometer may be greatly increased by placing on the table a bar magnet
in the magnetic meridian with its north-seeking pole turned toward the
north-seeking pole of the needle.
Experiment 138.— Measure the resistances of the several spools
of wire used above, —electro-magnets, electric lamps, etc.,— using
the bridge. Place the switches of the rheostat on the zero studs.
Make connections as in the description above. Then close the circuit
at T, and afterward the bridge at S. There will probably be a deflec-
tion in the galvanometer. Regulate the resistance through the rhe-
ostat, throwing in or taking out resistance according as one or the
other tends to reduce the deflection (the process is much as in weigh-
ing), until there is no deflection. Then compute the resistance sought
according to the above proportion. Compare the results with those
obtained by the process of substitution.
‘Experiment 139.— Measure the resistance of the human body.
Let some person grasp in his dry hands two metallic handles, such as
are used in giving shocks; connect the handles by wires at X X.
Introduce 100 ohms between A and G, and 1 or 10 ohms between
A and D, and proceed as hitherto.
The cuticle, or dry outer skin of the body, offers great resistance.
Let the same person wet his hands, and measure the resistance again,
and ascertain how much the wetting of the cuticle reduces the resist-
ance. Then let the person wet his hands with BLO, salt brine, and
once more measure the resistance.
182 ELECTRICITY AND MAGNETISM.
Section IX.
ELECTRO-MOTIVE FORCE OF DIFFERENT BATTERIES;
OHM’S LAW.
157%. Electro-Motive Force of Different Batteries.
—If a galvanometer is introduced into a circuit with
different battery cells, e.g. Bunsen, Grenet, Daniell, etc.,
very different deflections will be obtained, showing that the
different cells yield currents of different strength. This
may be due in some measure to a difference in their inter-
nal resistance, but it is chiefly due to the difference in their
electro-motive force. We learned (page 161) that difter-
ence of electro-motive force is due to the difference of the
chemical action on the two plates used, and this depends
largely upon the nature of the substances used. It is wholly
independent of the size of the plates; hence the electro-
motive force of a large battery cell is no greater than that
of a small one of the same kind. Consequently any dif-
ference in strength of current yielded by battery cells of
the same kind, but of different sizes, is due wholly to a
difference in their internal resistance.
The electro-motive force of the Bunsen, Grenet, and
Daniell cells are respectively about 1.8, 2, and 1 volts.
In consequence of polarization of the plates, the electro-motive force of
most batteries diminishes more or less rapidly after beginning to work.
For example, the current of the Leclanché battery weakens so rapidly that-
it can be used only in cases in which the battery is required to work only
for a few minutes at a time, such as for ringing annunciator bells,
telephony, etc.
158. Ohm’s Law. — The strength of current in any vol-
taic circuit varies directly as the electro-motive force and in-
ELECTRO-MOTIVE FORCE.—OHM’S LAW. 183
versely as the total resistance of the cireut. Likewise, the
current between any two points varies as the difference of
potential between those points, and inversely as the resist-
ance to be overcome. This law is usually expressed in
the form of the mathematical formula
E E
C= R: whence E = RC, and R=@
in which C represents the strength of current, E the elec-
pees force, and R the entire resistance. The above
fr nehon R’ when the external resistance is considered sepa-
rately from the internal, must be converted thus; calling
the former R, and the latter 7, the expression becomes
igen
R+r-
If acell has E =1 volt, and ry =1 ohm, and the connecting
wire is short and stout, so that R may be disregarded, then
the current has a value of one ampére. In other words, an
ampére might be defined as the strength of current which
an electro-motive force of one volt will maintain bhrongh
a resistance of one ohm.
C=
EXERCISES.
1. What E.M.F. is required to maintain a current of one ampere
through a resistance of one ohm?
2. An E.M.F. of 10 volts will maintain a current of 5 ampéres
through what resistance ?
3. What current ought an E.M.F. of 20 volts to maintain through
a resistance of fi ohms?
4, A volt-meter applied each side of an electric lamp shows a dif-
ference of potential of 40 volts; what current flows through the lamp,
if it has a resistance of 10 ohms?
5. The resistance between two points in a circuit is 10 ohms. An
184 ELECTRICITY AND MAGNETISM.
ammeter (an instrument which measures the strength of a current in
amperes) shows that there is a current strength in the circuit of 0.5
ampere ; what is the difference in potential between the points?
6. What current will a Bunsen cell furnish when r= 0.9 ohm (about
the resistance of a quart cell), E=1.8 volts, and R=0.01 ohm (about
the resistance of 3 ft. of No. 16 wire)?
Section X.
DIVIDED CIRCUITS: METHODS OF COMBINING VOLTAICG
CELLS.
159. Divided Circuits; Shunts.
Experiment 140.— Make a divided circuit as in Figure 155 (using
double connectors a and 6). Insert a galvanometer, G, in one branch
and a rheostat, R, in the other. The current, wher:
it reaches a, divides, a portion traversing one branch
through the galvanometer, and the remainder passes
through the other branch and the rheostat. Either
branch may be called a shunt to the other. Increase
gradually the resistance in the rheostat. The result is
that it throws more of the current through the gal-
vanometer, as shown.by the increase of deflection.
Fig. 155.
In a divided circuit the current divides between the paths
inversely as their resistances. For example, if the resistance
of the rheostat above is 4 ohms and the resistance in the
galvanometer is 1 ohm, then four-fifths of the current will
traverse the latter and one-fifth the former.
Suppose that the rheostat and galvanometer are removed
from the shunts, and that the shunts are of the same length,
size, and kind of wire, and consequently have equal resist-
ances. Using: the two wires instead of one to connect a
METHODS OF COMBINING VOLTAIC CELLS. 185
and 0 is equivalent to doubling the size of this portion of
the conductor; consequently the resistance of this portion
is reduced one-half.
Generally, the joint resistance of two branches of a circuit
is the product of their respective resistances divided by their
sum. (For demonstration of this law, see Gray’s Absolute
Measurements in Electricity, page 84.)
160. Methods of Combining Cells.
Experiment 141.— Take two Bunsen cells, and connect the two
zine plates by a wire. Then connect each of the carbon plates with
a galvanometer. The current from the two cells, if there were any,
would flow in opposite directions. But you find that there is either
no deflection in the galvanometer, or at most a very small one, and
this shows either that there is no current or that the current is very
weak. The reason is evident. You have connected two carbons,
which have theoretically the same potential, through the galvanome-
ter; consequently there should be no current between them. The
cells are said to be connected in opposition.
A very simple way of showing that a large cell has no
greater electro-motive force than a small one is to connect
two such cells in opposition through a galvanometer, or,
what answers the same purpose, raise the zinc of one of
two cells of the same size, connected in opposition, nearly
out of the liquid. The absence of a current shows that
the two carbons have the same potential, and conse-
quently their electro-motive force is the same.:
A number of cells connected in such a manner that the
currents generated by all have the same direction consti-
tutes a voltaic battery.
The object of combining cells is to get a stronger cur-
rent than one cell will afford. We learn from Ohm’s law
that there are two, and only two, ways of increasing the
strength of a current. It must be done either by increasing
186 ELECTRICITY AND MAGNETISM.
the E.M.F. or by decreasing the resistance. So we com-
bine cells into batteries, either to secure
greater E.M.F., or to diminish the internal
resistance. Unfortunately, both purposes can-
not be accomplished by the same method.
161. Batteries of Low Internal Resist-
ance.— Figure 156 represents three cells
having all the carbon (¢) plates electrically
connected with one another, and all the
zinc (2) plates connected with one another,
and the triplet carbons are connected by the
leading-out wires through a galvanometer
with the triplet zincs.
It is easy to see that through the battery
the circuit is divided into three parts, and
consequently the conductivity in this part of
Fig. 156. the circuit, according to the principle stated
in § 159, must be increased threefold; in other words, the
internal resistance of the three cells is one-third of that of
a single cell. This is called connecting cells “abreast,â€
or “in multiple are,†and
the battery is called a
“battery of low internal
resistance.†The resistance
of the battery is decreased
as many times as there are
cells connected in “arc,â€
but the E.M.F. is that of
one cell. only.
Fig. 157.
162. Batteries of High Internal Resistance and
Great E.M.F.—— Figure 157 represents four cells having
the carbon or +plate of one connected with the zine or
METHODS OF COMBINING VOLTAIC CELLS. 187
-- plate of the next, and the + plate at one end of the
series connected by leading-out wires through a galva-
nometer with the —plate at the other end of the series.
It is evident that the current in this series traverses the
liquid four times, which is equivalent to lengthening
the liquid conductor four times, and, of course, increasing
the internal resistance fourfold. But, while the internal
resistance is increased, the E.M.F. of the battery is in-
creased as many times as there are cells in series. The
gain by increasing the E.M.F. more than offsets, in many
cases (always when the internal resistance is a small
part of the whole resistance of the circuit), the loss
occasioned by increased resistance.
1638. Best Arrangement of Cells.
Experiment 142.— Introduce into circuit with a single Bunsen
cell a rheostat and a galvanometer. Throw a resistance of (say) 50
ohms into the circuit by means of the rheostat. Note the deflection.
Then add another cell, in series, to the cell already in use. The de-
flection is considerably increased. Other cells may be added with
similar results.
Experiment 143.— Connect the two cells abreast, keeping the
same resistance in the rheostat. The deflection is only a very little
greater than that caused by a single cell.
Experiment 144.— Connect a single cell with a galvanometer? of
low resistance, so that the whole external resistance may be less than
the resistance of the’single cell. Note the deflection. Then introduce
another cell abreast. ‘The deflection is considerably increased.
Experiment 145.— Connect the same cells in series. The deflec-
tion differs but little from that produced by a single cell.
Hence (1) when the external resistance is large, connect
cells in series ; (2) when the external is less than the internal
resistance, connect cells in are.
1 The galvanometers furnished. by the author have a resistance of about one ohm.
The internal resistance of a Bunsen cell can easily be made greater than this if the cell
is filled not more than one-fifth full with liquid.
188 ELECTRICITY AND MAGNETISM.
The maximum current with a given number of cells
through a given external resistance ts attained when the
external and internal resistances are most nearly equal.
Caution: — Never increase the external resistance for
the purpose of making the two resistances equal.
EXERCISES.
In the following exercises, whenever a Bunsen cell is mentioned it
may be understood to be a quart cell, having a resistance of about 0.9
ohm. Its E.M.F. is about 1.8 volts.
1. (@) When is a large cell considerably better than a small one?
(b) When does the size of the cell make little difference in the current?
2. If you have a dozen quart cells, how can you make them equiva-
lent to one 3 gallon cell?
3. If a battery of 10 cells has an E.M.F. ten times greater than
that of a single cell, why will not the battery yield a current ten
times as strong?
4. (a) The internal resistance of ten cells, connected in are, is what
part of that of a single cell? (6) If the cells were connected, in series,
how would the resistance of the battery compare with that of one of
its cells? (c) How would the E.M.F. of the latter battery compare
with that of a single cell?
' 5, What current will a single Bunsen cell furnish through an
external resistance of 10 ohms?
6. What current will 8 Bunsen cells, in series, furnish through the
same resistance ?
Dee lsaas
R+r 10+ (0.98)
7. What current will 8 Bunsen cells, in arc, furnish through the
same external resistance?
Ea ees
R+r 10+ (0.9 +8)
8. What current will a Bunsen cell furnish through an external
resistance of 0.4 ohm?
9. What current will a battery of two Bunsen cells, in series, fur-
nish through the same resistance as the last?
10. What current will two cells, in arc, furnish through the same
resistance ?
SoLurTion:
= 0,83 + ampére.
SoLurtion: = 0.17 + ampere.
TRANSFORMATION OF ELECTRIC ENERGY. 189
Section XI.
TRANSFORMATION OF ELECTRIC ENERGY INTO HEAT.
164. Transformation Inside and Outside a Battery.
Experiment 146.— Arrange two batteries, each consisting of two
(Bunsen) cells connected in arc. Use thick copper wire for leading-
out wires. Attach, by means of a connector, a piece of platinum wire
about 1 inch long to one of the electrodes of one of the batteries.
Place a thermometer in the dilute acid of one cell of each of the
batteries. Close the circuits of both batteries (one through the plati-
num wire) at the same moment. Watch for changes of temperature
in the liquids. The temperature of the battery which is not in circuit
with the platinum wire rises faster than the other.
That portion of the energy of an electric current which
is not transformed into heat, or other kind of work, in other
parts of the circuit, is transformed into heat in the battery.
The transformation is greatest where the resistance is
greatest. The platinum wire being small, and having a
relatively large specific resistance, offers much more resist-
ance to the current than the copper wire, consequently it
becomes much hotter. Much of the electric energy being
transformed into heat in the platinum wire, there is less
to be transformed in the battery; consequently the battery
remains comparatively cool.
——_-950300-—_
Section XIL.
MAGNETS AND MAGNETISM.
165. Law of Magnets. — Suspend by fine threads in a
horizontal position two stout darning-needles which have
190 ELECTRICITY AND MAGNETISM.
been drawn in the same direction (e.g. from eye to point)
several times over the same pole (better the — pole) of a
powerful electro-magnet. These needles, separated a few
feet from each other, take positions parallel with each
other, and both lie in a northerly and southerly direction
with the points of each turned in the same direction.
That point in the Arctic zone of the earth toward which
magnetic needles point is called the north magnetic pole
of the earth. That end of a needle which points toward
the north magnetic pole of the earth is called the north-
seeking, marked, or + pole (inasmuch as this is the end
that is always marked for the purpose of distinguishing
one from the other). That end of the needle which
points southward is called the south-seeking, unmarked,
or — pole.
Experiment 147.— Bring both points near each other; they repel
each other. Bring both eyes near each other; they likewise repel
each other. Bring a point and an eye near each other; they attract
each other.
Like poles of magnets repel, unlike poles attract one
another.
166. Magnetic Transparency and Induction.
Experiment 148.— Interpose a piece of glass, paper, or wood-
shaving between the two magnets. These substances are not them-
selves perceptibly affected by the magnets, nor do they in the least
affect the attraction or repulsion between the two magnets.
Substances that are not susceptible to. magnetism are
said to be magnetically transparent. When a magnet
causes another body, in contact with it or in its neighbor-
hood, to become a magnet, it is said to induce magnetism
in that body; t.e. it influences it to be like itself. As attrac-
tion, and never repulsion, occurs between a magnet and
MAGNETS AND MAGNETISM. 191
an unmagnetized piece of iron or steel, it must be that the
magnetism induced in the latter is such that opposite poles
are adjacent; that is, a N or + pole induces a S or — pole
next itself, as shown in Figure 158.
Ss XN Ss NX Ss aN
\e +\ \- +\ \E aN
Fig. 158.
167. Polarity.
Experiment 149.— Strew iron filings on a flat surface, and lay
a bar-magnet on them. On raising the magnet, it is found that
large tufts of filings cling to the poles, as in Figure 159,
especially to the edges; but the tufts diminish regularly in
size from either pole towards the centre, where none are
found.
Magnetic attraction is greatest at the poles, and
diminishes towards the center, where it is nothing,
or the center of the bar is neutral. The dual char-
acter of the magnet, as exhibited in its opposite
extremities, is called polarity, and magnetism is
styled a polar force. If a magnet is broken, each
piece becomes a magnet with two poles and a
neutral line of its own. _ Fig. 159.
168.. Coercive Force. — It is more difficult to magnet-
ize steel than iron; on the other hand, it is difficult to
demagnetize steel, while soft iron loses nearly all its mag-
netism as soon as it is removed from the influence of the
inducing body. The quality of steel by which it at first
resists the power of magnets, and resists the escape of
magnetism which it has once acquired, is called coercive
force. The harder steel is, the greater is ts coercive force.
Hence, highly tempered steel is used for permanent mag-
nets. Hardened iron possesses considerable coercive force ;
192 ELECTRICITY AND MAGNETISM.
hence, the cores of electro-magnets should be made of the
softest iron, that they may acquire and part with magnet-
ism instantaneously.
169. Forms of Artificial Magnets. — Artificial mag-
nets, including permanent magnets and electro-magnets,
are usually made in the shape either of a straight bar, or of
the letter U, called the horseshoe, according to the use made
of them. If we wish, as in the experiments already de-
scribed, to use but a single pole, it is desirable to have the
other as far away as possible; then, obviously, the bar
magnet is most convenient. But if the magnet is to be
used for lifting or holding weights, the horseshoe form is
far better, because the attraction of both poles is conven-
iently available, and because their combined power is more
than twice that of a single pole. Magnets, when not in
use, ought always to be protected by armatures (A, Fig.
160) of soft iron; for, notwithstanding the coercive power
of steel, they slowly part with their magnetism. But
when an armature is used, the opposite poles of the mag-
net and armature being in contact with one
another, z.e. N with S, they serve to bind one
another’s magnetism. Thin bars of steel can
be more thoroughly magnetized than thick
ones. Hence, if several thin bars (Fig. 160)
are laid side by side, with their corresponding
poles turned in the same direction and then
screwed together, a very powerful magnet is
the result. This is called a compound magnet.
Fig. 160.
170. Attraction and Repulsion between Currents:
Laws of Currents.
Experiment 150.— Figure 161 represents a portion of a divided
circuit. The lower ends of the wires dip at the lower extremities one-
MAGNETS AND MAGNETISM. 193
sixteenth of an inch into mercury, and they are so suspended that
they are free to move toward or from each other. Send a current of
a battery of two or three Bunsen cells, in arc, through this divided
circuit. The two portions of the current travel in the same direction
and parallel with each other, and the two wires at the lower extremi-
ties move toward each other, showing an attraction.
Experiment 151.— Make the connections (Fig. 162) so that the
current will go down one wire and up the other. They repel each
other.
i
K
Experiment 152.— Send a current through the spiral wire repre-
sented in Figure 163. Here the current flows nearly parallel with
itself, and the attraction causes the coil to contract and to be lifted
out of the cup of mercury below. But the instant it leaves the mer-
cury the circuit is broken, the current and attraction cease, and the
wire dips into the mercury again. Thus rapid vibratory motion of
the coil is produced. :
First Law of Currents. — Parallel currents in the same
direction attract one another ; parallel currents in opposite
directions repel one another.
Experiment 153.— Figure 164 represents a small battery floating
on water. The wire of the battery is wound into a horizontal coil. In
a few minutes after the battery is floated it will take a position so
that its coil will point north and south, like a magnetic needle.
194 ELECTRICITY AND MAGNETISM.
Place the wire of another battery over and parallel with the coil, so
that the two currents will flow in planes at right angles with each
other. The coil is deflected like a magnetic needle. A careful exami-
nation will disclose
the fact that not only
have the planes in
which the two cur-
rents flow become
parallel, but that the
current in the half
of the coil (where
. the influence due to
proximity is greatest) flows in the same direction that the current above
wt flows.
Reverse the direction of the current above and the deflection is
reversed.
Fig. 164.
Second Law of Currents.— Angular currents tend to
become parallel and flow in the same direction.
‘Experiment 154.— Remove the primary coil from the secondary
coil (Fig. 169), send a current through the former, and hold one of its
ends near to one end of the coil of
the floating battery, as in Figure
165, in such a manner that the cur-
rent will flow in the same direction
in the ends presented to each other.
The coils attract one another like
two magnets in accordance with the
First Law of Currents. Present the
same end of the coil to the other
end of the floating battery coil. Now the currents in the two ends
flow in opposite directions, and the coils repel each other.
Experiment 155.— Observe that at one end of the floating battery
coil the current revolves in the direction that the hands of a watch
move, and at the opposite end it revolves in a direction contrary to
the movement of the hands of a watch. Bring the north pole of a
bar-magnet near that end of the coil where the motion of the current
corresponds to the movement of the hands of a watch. They attract
one another; but if the same end of the coil is approached by the
south pole of the magnet, repulsion follows,
Fig. 165.
MAGNETS AND MAGNETISM. © 195
Hence, that is the south pole of a helix where the current corre-
o™é~
sponds to the motion of the hands of a watch, S, and that is the north
pole where the current is in the reverse direction, N.. But the impor-
tant lesson derived from these latter experiments is, that coils through
which currents are flowing behave toward one another, or toward a mag-
net, in many respects as if they were magnets.
171. Ampére’s Theory of the Magnet.— Facts like
those which we have just studied led Ampére to devise a
theory for the explanation of magnetism. Little credence
is given to this theory by electricians ; nevertheless a slight
acquaintance with it is of great service to the beginner in
aiding him to picture to himself how certain phenomena
occur. Ampére was led to suppose that something like an
infinite number of currents invests at all times every piece
of steel, iron, and other magnetizable substance. That in
a magnetized bar of steel or iron these currents are all
parallel with one another, and we have the combined
effects (¢.e. of attraction or repulsion) of all the currents.
When a magnet, having all its currents parallel, is brought
near to an unmagnetized piece of iron or steel in which
the currents have no common direction, the former in-
duces magnetism in the latter, ¢.e. it causes the currents
of the latter to become parallel with its own, in accord-
ance with the Second Law of Currents. For convenience
we may call the hypothetical currents Ampérian currents.
Fig. 166.
This ingenious theory will enable us to understand how
the core of the electro-magnet is magnetized. The real
currents circulating in the wire outside cause the Ampér-
196 ELECTRICITY AND MAGNETISM.
jan currents to become parallel with them, and as both flow
in the same direction as represented in Figure 166, we
have, in the electro-magnet, the combined effect of both
sets of currents.
172. Lines of Magnetic Force; Magnetic Field.
Experiment 156.— Sup-
port asmall pane of window
glass on a table, by placing
under the glass near its
angles four slices of cork
about one-eighth of an
inch thick. Beneath the
center of the glass on the
table place a circular disk
of magnetized steel. Sift
iron turnings upon the
upper face of the glass
through a fine wire sieve.
Gently tap the glass at
convenient points with the
end of a lead-pencil. The
filings arrange themselves
in lines radiating from
either pole, and form grace-
ful curves from pole to pole,
as represented in Figure
166a. These represent what are called lines of magnetic force. They
represent the results of the combined action of the two poles.
A magnet seems to be surrounded by an atmosphere of magnetic
influence called the magnetic field. A body brought within the limit
of its influence is said to be within the field of the magnet.
173. The Earth is a Magnet. —A dipping-needle is so
supported that it can revolve in a vertical plane. Indiffer-
ent equilibrium is first established in the steel needle, so
that if placed in a horizontal (or any other) position it will
rest in that position. Then it is strongly magnetized.
MAGNETS AND MAGNETISM. 197
Afterward it will take the horizontal position only at the
magnetic equator of the earth.
Experiment 157.— Place a dipping-needle over the + pole of a
bar-magnet (Fig. 167). The needle takes a vertical position with
its —pole down. Slide the supporting stand along the bar; the
—pole gradually rises
until it reaches the
middle of the bar,
where it becomes hori-
zontal. Continue mov-
ing the stand toward ,
the — pole of the bar ; Ie Eke
after passing the middle of the bar the + pole begins to dip, and the
dip increases until the needle reaches the end of the bar, when the
needle is again vertical with its + pole down.
If the same needle is carried northward or southward along the
earth’s surface, it will dip in the same way as it approaches the polar
regions, and be horizontal only at or near the equator.
Experiment 158.— Suspend a small magnetized cambric needle by
a fine thread at its center and carry it around the disk (Fig. 166a). The
needle passes through all the phases stated above, so that we may
fancy the disk to be the earth, and study therefrom, in a general way,
the changes that the needle undergoes, as it is carried around the
earth in a northerly or southerly direction.
174. Magnetic Poles of the Earth. — Those points on
the earth’s surface where the dipping-needle stands vertical
are the magnetic poles of the earth. A point was found a
little northwest of Hudson’s Bay, in latitude 70° 5’ N., and
longitude 96° 45’ W., by Sir James Ross, in the year 1882,
where the dipping-needle lacked only one-sixtieth of a de-
gree of being vertical. The same voyager subsequently
reached a point in Victoria Land where the needle with its
poles reversed lacked only 1° 20' of being vertical.
The magnetic poles are not, however, fixed objects that
can be located like an island or cape, but are constantly
198 ELECTRICITY AND MAGNETISM.
changing. They appear to swing, somewhat like a pen-
dulum, in an easterly and westerly direction, each swing
requiring centuries to complete it. The north magnetic
pole is now on its westerly swing.
175. Variation of the Needle. — Inasmuch as’ the
magnetic poles of the earth do not coincide with the
geographical poles, it follows that in most places the
needle does not point due north and south. The angle
which the needle makes with the geographical meridian
is known as the angle of declination. This angle differs
at different places.
176. Inclination or Dip of the Needle. — The angle
that a dipping-needle makes with a horizontal line is
called its inclination or dip. A line drawn around the
earth connecting those places where there is no dip
would represent the magnetic equator.
Experiment 159.— Place the dipping-needle on a horizontal surface,
apart from any iron (such as nails, etc.), and so that the plane of rota-
tion of the needle will be in the magnetic meridian, and ascertain
from the divided arc (approximately, at least) the dip at the place
where you live,
EXERCISES.
1. Stretch a string between two pins stuck in a table, so that it will
lie in the geographical meridian, i.c. in the direction of the North Star.
On this string set the stand holding a magnetic needle about 6 inches
long. Determine whether there is any magnetic declination at the
place where you are, and, if so, in what direction it is.
2. What is the declination and dip at your place of residence?
Let A (Fig. 168) represent a magnetic pole and B the North Star.
Jt will be seen that there is a position in which the needle will point
due north, A line passing around the earth through the two magnetic
CURRENT AND MAGNETIC ELECTRIC INDUCTION. 199
- poles, connecting those places where the needle cas due north, is
called a line of no variation.
3. Take a map of the United Biates
and draw on it a pencil line, starting at a f
point on the Atlantic coast where the two
Carolinas meet; continue it a little west of
Pittsburg, Pa., and through lakes Erie and
Huron, and this line will represent very
nearly the line of no variation at the present time. It is slowly
moving westward. At places in the United States east of this line
the + pole of the needle points west of north, e.g. the New England
States and New York; but most of the States lie west of this line, so
in them the needle points east of north. At Harvard University, in
Cambridge, Mass., in 1887, the declination was 11.87° W. of N.; in
1872 it was 0.7°. In 1880 the declination at Halifax, N.S., was 20.3°
W. of N.; at San Francisco it was 16.52° E, of N.
Fig. 168,
Section XIII.
CURRENT AND MAGNETIC ELECTRIC INDUCTION.
177. Description of Apparatus. — A (Fig. 169) is a short coil
of coarse wire (i.e. the wire which .
it contains is comparatively short),
and has, of course, little resistance.
B is a long coil of fine wire having
high resistance. Coil A is in circuit
with two Bunsen cells in arc. This
circuit we call the primary circuit,
the current in this circuit the pri-
mary or inducing current, and the
coil the primary coil. Another cir-
cuit, having in it no battery or
other means of generating a current,
contains coil B and a galvanoscope
with an astatic needle. This circuit
is called the secondary circuit, the .
200 ELECTRICITY AND MAGNETISM.
coil the secondary coil, and the currents which circulate through this cir-
cuit are called secondary or induced currents.
’ Experiment 160.— After all the connections are made, and a
current is established in the primary circuit, and the galvanoscope
needle is brought to zero, lower the primary coil quickly into the
secondary coil, watching at the same time the needle of the galvano-
scope to see whether it moves, and, if so, in what direction. Simul-
taneously with this movement is a movement of the needle, showing
that a current must have passed through the secondary circuit. Let
the primary coil rest within the secondary, until the needle comes to
rest. After a few vibrations the needle settles at zero, showing that
the secondary current was a temporary one. Now, watching the
needle, quickly pull the primary coil out; another deflection in an
opposite direction occurs, showing that a current in an opposite direc-
tion is caused by withdrawing the coil. Just how the necessary con-
dition (i.e. E.M.F.) for an electric current is brought about we do not
know; but we do know that it is done under the influence of the
primary current (hence the process is called induction) and at the ex-
pense of mechanical energy. ,
Fig. 170.
Experiment 161.— Place the primary coil within the secondary.
Open the primary wire at some point and then close the circuit
(Fig. 170) by bringing in contact the extremities of the wires. A
deflection is produced. As soon as the needle becomes quiet, break
the circuit by separating the wires; a deflection in the opposite direc-
tion occurs.
On introducing the primary coil into the secondary, and on closing
CURRENT AND MAGNETIC ELECTRIC INDUCTION. 201
the primary circuit, currents are induced in the reverse direction in
the secondary circuit that the primary current has; on the withdrawal
of the primary coil, or on breaking the primary circuit, the induced
current generated is in the same direction as of that of the primary
current.
Experiment 162.— Introduce the bundle, D (Fig. 169), of soft
iron wires, called the core, into the primary coil, and make and break
the primary circuit as before. The deflections are now very much
increased.
Experiment 163.— Substitute a person for the galvanometer in the
secondary circuit, the person grasping some metallic handles made for
the purpose and used as electrodes. The person experiences at the
instant of making and breaking a peculiar sensation in his wrists and
arms, called a shock.
Experiment 164.— Introduce into the primary circuit the auto-
matic make-and-break piece C (Fig. 169). Remove the core from the
primary coil. Let a person grasp
the electrodes of the secondary
circuit. This person experiences
a series of shocks which seem to
him almost, if not quite, contin-
uous. These shocks can be in-’
tensified to suit the pleasure o!
the person who is receiving them,
by gradually lowering the core
into the primary coil. But no
temptation to fun should lead
the experimenter to be so cruel
as to drop the core into the coil
suddenly. ,
Experiment 165.— Reflecting that you have found hitherto a coil
of wire having a current passing through it acting as a magnet, you
have now an opportunity to try the converse, i.e. to see whether a
magnet may not take the place of a current-bearing coil. Introduce
suddenly a bar-magnet (Fig. 171) into the secondary coil, as in Ex-
periment 160. A deflection is produced; withdraw it and an opposite
deflection occurs.
Fig. 171.
202 ELECTRICITY AND MAGNETISM.
Laws of Induced Currents: The general laws of in-
duced currents are summed up in the following table : —
eaned | INVERSE INDUCED DIRECT INDUCED
ND p | CURRENT. CURRENT.
1
A magnet sh | Approaching. Receding.
Approaching. Receding.
A current Beginning. Stopping.
Increasinginstrength.| | Diminishing in strength.
178. Extra Currents.— Pupils, while handling the
naked electrodes of a battery having an electro-magnet or
other coil in the circuit, at the instant of dropping or tak-
ing hold of the electrodes frequently experience slight
shocks. This is due to what are called extra currents in-
duced in the battery circuit itself at the instants of making
and breaking. As the battery current advances or retires
through the wire, each convolution of wire acts inductively
upon the neighboring convolutions, in a manner similar to
that of the primary coil upon the secondary. The sparks
invariably attending the touching and separating of elec-
trodes, e.g. those seen at the make-and-break piece C
(Fig. 169), are produced by extra currents.
179. Ruhmkorff’s Induction Coil. — Figure 172 represents, in
diagram, an ideal induction coil. A A is the core around which is wound
the primary wire. Outside of the whole is the secondary coil. The
directions of the several currents are indicated by arrows at the instant the
primary circuit is closed at bin the automatic piece cd. The condenser
BB was the important addition made by Ruhmkorff. —
It consists of two sets of layers of tin-foil separated by paraffine paper ;
the layers are connected alternately with one and the other pole of the
battery, as the figure shows, so that they serve as a sort of expansion of
the primary wire. When the circuit is broken, the extra current would
CURRENT AND MAGNETIC ELECTRIC INDUCTION. 208
jump across at b, and would vaporize the points of contact, and form a
bridge with the vapor of metal that would prolong the time of breaking.
But, when the condenser is attached, the extra current finds an escape into
Saat
B
Fig. 172.
it easier than to jump across at b, so the vaporizing of the contact is
avoided, and the time of breaking being much shortened, the secondary
current is much more intense.
Experiment 166. — Connect
a battery of two Bunsen cells,
in are, with a Ruhmkorff coil
(Fig. 173). Bring the electrodes
of the secondary coil within
one-fourth of an inch to. one
inch of each other, according to
the capacity of the instrument.
A series of sparks in rapid suc-
cession pass from pole to pole.
Experiment 167. — Intro-
duce a Geissler tube, A, into the
secondary circuit. These tubes
Fig. 173.
contain highly rarefied gases of different kinds. Platinum wires
are sealed into the glass at each end to conduct the electric cur-
204 ELECTRICITY AND MAGNETISM.
rent through the glass. The sparks become diffused in these tubes
so as to illuminate the entire tubes with an almost continuous glow.
Observe that the electrodes are separated from each other much
more widely than would be admissible in air of ordinary density,
showing that rarefied gases offer less resistance than dense gases.
Gases have been so highly rarefied, however, that an electric cur-
rent would not pass. This shows that a material conductor and
one of sufficient density is absolutely necessary for the massaee of
a current.
180. Electric Motor.
Experiment 168.— This experiment will require two separate bat-
teries. Join one battery to a small Ruhmkorff coil, and connect its
secondary coil with the apparatus represented in Figure 174, intro-
ducing the wires at the binding screws,
cand d. Join the wires of the other
battery with the same instrument; in-
serting the wires at the binding screws,
aand 6. The first battery in conjunc-
tion with the coil causes induced cur-
rents to enter this instrument and pass
through the Geissler tube, A. The
other battery causes the tube to rotate.
In a darkened room the appearance is
that of a luminous wheel of great
beauty having many spokes. Various
optical illusions attend the experi-
ment, which make it very attractive.
The instrument used is one form of an electric motor. An electric
motor is a device for transforming the energy of. an electric current
into mechanical energy, i.e. into motive power. It is usually accom-
plished through the use of electro-magnets, and hence a motor is
frequently called an electro-magnetic engine. Electric motors of great
power have been constructed, and are successfully used for propelling
railway cars, etc.
Fig. 174.
181. Characteristics of Induced Currents.—The student
cannot have failed to observe that induced electricity has a power for
penetrating a non-conductor far superior to that of primary currents.
DYNAMO-ELECTRIC MACHINES. 205
The former can penetrate the air passing through it from electrode
to electrode, at distances varying from one-hundredth of an inch to
three feet in the largest induction coils. They can perforate cardboard,
panes of glass, and produce various other mechanical effects. They may
be so intense as to produce instantaneous death. On the other hand, it
would require the E.M.F. of several thousand voltaic cells connected, in
series, to furnish sufficient power to penetrate the air so as to maintain
a current when the electrodes are separated only one-hundredth of an
inch,
Section XIV.
DYNAMO-ELECTRIC MACHINES.
182. A Simple Dynamo and the Gramme Dynamo.
Experiment 169.— Take the secondary coil of the induction coil
apparatus (Fig. 169), place within it the core of iron wires. Introduce
into circuit with this coil a galvanoscope with an astatic needle. Take
a powerful compound horseshoe; suspend it in a vertical position
with the poles downward. Move the coil back and forth under and
near to the magnet, so that the core will come alternately under each
pole. Deflections alternating in direction show the production of
induced currents.
The student should look thoughtfully at this contrivance, be-
cause he has before him a dynamo-electric machine in its simplicity.
It consists, like all the more complicated machines, of these two
essential parts, viz. (usually) a long coil containing an iron core,
constituting an armature, and a powerful magnet (either a perma-
nent steel magnet, or, more frequently, because more powerful,
an electro-magnet) called the field magnet. The method by which
currents are generated in this contrivance and in all dynamos is the
same, viz. by the movement of an armature within the field of an electro-
magnet and across the lines of magnetic force.
206 ELECTRICITY AND MAGNETISM.
Much more than the above it is not important that the general student
should know. Matters of detail differ widely in different machines, and
the student is not supposed to be especially interested in any particular
machine. To give a full and intelligible description of any machine in a
single page is not an easy matter. For the bonefit of the more ambitious
students, we submit the following condensed description of the Gramme
dynamo. Its armature, ns (Fig. 175), con-
sists of a ring composed of a bundle of.
soft iron wires (better shown in Figure
Fig. 175.
177, Plate III.) surrounded by what is virtually an endless coil of wire.
The wire, however, is wound in sections separated by suitable partitions,
and the wire of each section carried to and connected electrically with a
copper plate on the axle mm. The several copper plates (as many as
there are sections) are insulated from one another. (To enable the
pupil better to understand the method of winding, making connections,
etc., the author has prepared a model (Fig. 176) of this machine, which
will furnish at a glance information respecting the method of winding,
making connections, etc., which no book can do.) A horseshoe magnet
NS (only a portion of which is shown in the cut) is so placed that one-
half of the ring is under the influence of the N-pole, and the other half
under that of the S-pole. Suppose the ring to rotate in the direction of
the arrow; then every point of the iron core, as it comes opposite a
given point of the magnet, will successively become a pole of opposite
name, while the points ¢ and 7! are the neutral points,
Plate [f.
Fig. 179.
NS =
DYNAMO-ELECTRIC MACHINES. 207
If we imagine the core to be divided at the points n and s, we have
two semicircular magnéts whose north poles and whose south poles re-
spectively face one another. In the two mutually facing poles on either
side, the Ampérian currents must be in opposite directions... Now an
attentive study of this ideal diagram, in the light of what you have
previously learned respecting the generation of induced currents, will
enable you to see that as the ring armature rotates, the corresponding
advance of the induced poles of the ring will induce currents.in the wire
in such a manner that all the coils which at any given moment are in the
semicircle next one of the magnet poles (say the North) are traversed
by a current in one direction. Similarly, the semicircle formed by the
coils immediately approaching, or immediately receding from the South
pole are at the same time traversed by a current in the opposite direction. -
The result is that currents in the lower half tend toward the point m on
the axis, and in the upper half from point m’. So long as the leading-out
wires from these points are open, these currents have no outlet, and conse-
quently oppose and neutralize one another. But if the points m and m!
are connected by a wire L, we shall have a constant and non-alternating cur-
rent flowing through the wire from m to m!.. The contact at these points
is made by means of brushes of thick wire. These press on the contact
pieces, and make practically a constant connection with the two halves of
the circuit. :
Inasmuch as an electro-magnet may be made a much more powerful
magnet than a permanent magnet, it is now extensively used as the induc-
ing or the so-called field magnet. Such a machine is called a dynamo-elec-
trical machine, or often more briefly a dynamo. Figure 178, Plate III.,
represents such a machine. EE is the stationary field magnet, A, the
moving armature, and N and S large pole-pieces brought as near as prac-
ticable to the armature and partially encircling it. When the machine
is at rest, there are no currents; but when the armature is in motion, the
residual magnetism (a small portion of which is always retained by soft iron
after it has been magnetized) induces at first a weak current in the wire
of the armature; but as a portion of this current is carried. by means
of a shunt wire J through the coil of the field magnet, and magnetizes
the core more strongly, the current in both the shunt / and the main -
wire L quickly reaches its maximum.
By permission of the United States Electric Lighting Company we in-
troduce a cut (Fig. 179, Plate III.), of the American dynamo called the
Weston. It will be seen that in this machine a powerful field magnet
is placed on each side of the revolving armature. A steam-engine com-
municates motion to the dynamo by means of a belt passing over the
208 ELECTRICITY AND MAGNETISM.
circumference of the wheel W, and causes the armature, which is on the
axle of this wheel, to revolve.
1838. The Dynamo as an Electric-motor. — If, instead of
expending mechanical energy, such as that of a steam-engine, etc., in
rotating the armature of a dynamo, a current from another dynamo (or
other source) is sent through the coil of its armature, the armature will
rotate under the action of the electric energy, and the dynamo thus
becomes an electric-motor. In the generating dynamo mechanical energy
is transformed into electric energy; in the receiving dynamo (used as
a motor) the electric energy is transformed again into mechanical energy.
A series of dynamos (only limited in number by the loss of energy by
waste) might be so connected that transformation in each is the reverse
of that in the preceding.
184. Uses of Dynamos.— We live at the interesting epoch
when dynamos are being rapidly introduced for purposes of electric light-
ing, electroplating, motive power, telegraphy, charging storage batteries,
etc., supplanting to a large extent other instrumentalities and branches of
industry, much as sixty years ago the locomotive commenced its dis-
placement of the stage coach.
185. Transmission of Electric Energy. — One of the most
important projects which is enlisting the attention of electricians at the
present time is to devise some efficient means of economically transform-
ing, by means of dynamos, some of the wasting energies of nature, such,
for example, as that of waterfalls, into electric energy, and in this con-
venient form transferring the energy through wires to distant and availa-
ble places, such as large cities, where it may be transformed by lamps into
heat and light, or by electric-motors into mechanical energy for doing
almost any kind of work. The project is theoretically possible. One of
the principal practical difficulties is that of safely, and without great waste,
transmitting currents of great magnitude long distances through conduc-
tors such as are now in use. In many ways electric energy is one of the
* most convenient forms of energy; hence its desirability for propelling
street cars, for operating light machinery, etc. It is apparent that if this
form of energy could somehow be, as it were, bottled up or stored in large
quantities in a small space, so that it could be transported easily to places
where it is needed, it would be a valuable achievement. This is in a
measure practicable through the agency of the so-called “ storage bat-
teries.â€
ELECTRIC LIGHT. 209
186. Storage Batteries. — The storage battery is virtually an
electrolysis apparatus, having instead of two platinum electrodes two
lead plates coated with red lead (Pb,O,) with a layer of paper or cloth
between, the whole suspended in dilute sulphuric acid. (See directions
for making storage batteries in the author’s Physical Technics, page
122.) When these electrodes are connected with a powerful voltaic bat-
tery, or, better, with a dynamo, the + electrode becomes peroxydized
(PbO,) by the oxygen liberated by electrolysis, while the — electrode is
deoxydized by the hydrogen liberated. In other words, the energy of
the current is transformed into the potential energy of chemical affinity.
Note that it is an electrical storage of energy, not a storage of electricity, —
two very different things. When these chemical changes have progressed
as far as possible the battery is said to be charged. These plates may
remain for many days in this condition, if the circuit is left open, and
may be transported long distances and used in the same way and for the
same purposes that any powerful voltaic battery can be used. Storage
cells may be combined the same as voltaic cells (which in fact they are
after charging), and with similar results. Some idea of the capacity of
these cells may be formed from the following estimate. In a cell whose
interior dimensions are eight inches square and four inches deep, there
can be stored up energy sufficient to furnish one-half of a horse-power
working for an hour.
— 0.0503 00 —_——.
Section Xv.
USEFUL APPLICATIONS OF ELECTRIC ENERGY.— ELECTRIC
LIGHT.
The applications of electric energy to industrial uses are so numerous
and varied that the limits of an ordinary text-book on general Physics
can do little justice to the subject, and, indeed, a description of the
various appliances in use is of a too technical character to come properly
within the scope of a general high-school course. Public libraries are
now well provided with popular works relating to every industrial appli-
cation. Students may consult with profit such books as Prescott’s The
210° ELECTRICITY AND MAGNETISM.
Telegraph and Telephone, Dolbear’s The Telephone, Urquhart’s Electro-
plating, S. P. Thompson’s Dynamo-Electric Machinery, and Sawyer’s
Electric Lighting.
187%. Electric Light: Voltaic Arc.—If the terminals
of wires from a powerful dynamo or galvanic battery are
brought together, and then separated 1 or 2™™, the cur-
rent does not cease to flow, but volatilizes a portion of
the terminals. The vapor formed becomes a conductor
of high resistance, and remaining at a very high temper-
ature produces intense light. The light rivals that of the
sun both in intensity and whiteness. The heat is so great
that it fuses the most refractory substances, including even
the diamond. Metal terminals quickly melt and drop off
like tallow, and thereby become so far separated that the
electro-motive force is no longer sufficient for the increased
resistance, and the light is extinguished. Hence, pencils
A 8 of carbon (prepared
or ma XX from the coke de-
posited in the dis-
tillation of coal in-
| side of gas retorts),
see being less fusible,
are used for terminals. For simple experiments, these
pencils may be held in forceps (Fig. 180) at the ends of
two brass rods, to which the battery wires are attached.
These rods slide in brass heads, A and B, supported by in-
sulating pillars, so that the distance between the carbon
points may be regulated.
The light is too intense to admit of examination with
the naked eye; but if an image of the terminals is thrown
on a screen by means of a lens, or a pin-hole in a card, an
arch-shaped light is seen extending from pole to pole, as
shown in Figure 181. This light has received the name
ELECTRIC LIGHT. 211
of the voltate arc. The larger portion of the light, how-
ever, emanates from the tips of the two car-
bon terminals, which are heated to an intense
whiteness, but some emanates from the arc. The
+ pole is hotter than the —pole, as is shown by
its glowing longer after the current is stopped.
The carbon of the + pole becomes volatilized,
and the light-giving particles are transported
from the + pole to the —pole, forming a bridge
of luminous vapor between the poles. What we see is
not electricity, but luminous matter.
The light of the ordinary
street arc-lamp has an inten-
sity varying from one to
two thousand candle-power,
or the combined intensity of ==
from fifty to a hundred ordi- &
nary gas-lights. To sustain
such a light, about one horse-
power per lamp must be ap-
plied at the dynamo.
188. Electric Lamp. — It
is apparent that the + pole is
subject to a wasting away;
so also the — pole wastes
away, but not so fast. At the
point of the former a coni-
cal-shaped. cavity is formed,
while around the point of
the latter warty protuber-
ances appear. When, in con-
sequence of the wearing away of the + pole, the distance
Fig. 182.
. 212 ELECTRICITY AND MAGNETISM.
between the two pencils becomes too great for the elec-
tric current to span, the light goes out. Numerous self-
acting regulators for maintaining a uniform distance
between the poles have been devised. Such an arrange-
ment (Fig. 182) is called an electric lamp. The move-
ments of the carbons are accomplished automatically by
the action of the current itself.
The difference between the arc-lamps of the various in-
ventors is a difference in the mode of adjusting or “feed
ing†the carbons. We give below the plan of the
Fig. 185.
189. Brush Lamp. — The current, entering at A (Fig. 183), divides
at B into two branches which pass around the bobbin C in opposite direc-
tions, one branch being a coarse wire of low resistance and in the same
circuit as the carbons, and the other branch SS being a shunt of high
Tesistance, connecting the terminals B and G. Inside the bobbin is a soft
iron core,.F, which is attached to the upper carbon. When a current
passes through the two branch circuits on the bobbin C, they tend to mag-
netize the core in opposite directions, but the resistances and number of
turns in the two circuits are so proportioned that the magnetic field due to
the low resistance branch is the stronger, and the core F is therefore
ELECTRIC LIGHT, 213
drawn up into the bobbin, lifting the upper carbon and establishing the
arc. Should the carbons become too widely separated the resistance of
the arc, and consequently of the coarse wire circuit on C, increases, dimin-
ishing the current in © and increasing that in the shunt 8. The field due
to the shunt is therefore strengthened, and that due to the coarse wire
diminished, allowing the core F to fall slightly, bringing the carbons
nearer together. By the device of the two opposing fields, due to the
coils on C being wound in.opposite directions, the feeding of the lamp is
done automatically, and the actual distance of the two carbons varies but
little. ¢ a:
190. Incandescent Electri¢é Lamps.— The incandes-
cent (or “glowâ€) light is produced by the heating of
some refractory body to a state of incandescence by the
passage of an electric current, as, for example, the light
given off by heated platinum in Experiment 120. Plati-
num is little used for this purpose on account of its lia-
bility to melt. Carbon filaments are. now exclusively
used in incandescent lamps. In the Swan lamp (Fig. 184)
a filament of carbonized cotton, twisted into a sort of
curl, is attached at its ends to two little platinum wires,
aand 6, which have previously been sealed into the neck
of the glass bulb. The filament of the Edison lamp
(Fig. 185) is carbonized bamboo. It is essential that the
oxygen of the:
air be removed
from these bulbs,
otherwise the car-
bons would be
quickly burned
out; hence very
high vacua are Weo\cgutve
produced in the — Fig. 186.
bulbs with a mercury pump.
An Edison 16 candle-power lamp has a resistance (when hot) of
about 140 ohms, the difference of potential at its terminals is about 100
214 ELECTRICITY AND MAGNETISM.
volts, and it requires a current of 0.75 ampére. Each lamp consumes
about one-tenth of a horse-power.
Incandescent lamps are usually introduced into the circuit in multiple
arc (Fig. 186), the current being equally divided by properly. regulating
the resistance between all the lamps in the circuit.
—\-0 505 0 ——_.
Section XVI.
USEFUL APPLICATIONS OF ELECTRICITY CONTINUED. —
ELECTROTYPING AND ELECTROPLATING.
191. Electrotyping.—This book is printed from electrotype
plates. A molding-case of brass, in the shape of a shallow pan, is filled to
the depth of about one-quarter of an inch with melted wax. A few pages
are set up in common type, and an impression or mold is made by press-
ing these into the wax. The type is then distributed, and again used to
set up other pages. Powdered plumbago is applied by brushes to the sur-
face of the wax mold to render it a conductor. The case is then sus-
pended in a bath of copper sulphate dissolved in dilute sulphuric acid.
The — pole of a galvanic battery or dynamo machine is applied to it; and
from the + pole is suspended in the bath a copper plate opposite and near
to the wax face. The salt of copper is decomposed by the electric cur-
rent, and the copper is deposited on the surface of the mold. The sul-
phuric acid.appears at the + pole, and, combining with the copper of this
ELECTROTYPING AND ELECTROPLATING. 215
pole, forms new molecules of copper sulphate. When the copper film
has acquired about the thickness of an ordinary visiting card, it is removed
from the mold. This shell shows distinctly every line of the types or
engraving. It is then backed, or filled in, with melted type-metal, to give
firmness to the plate. The plate is next fastened on a block of wood,
and thus built up type-high, and is now ready for the printer. (or full
directions which will enable a pupil to electrotype in a small way, see the
author’s Physical Technics.)
192. Electroplating. —The distinction between electroplating
and electrotyping is, that with the former the metallic coat remains per-
manently on the object on which it is deposited, while with the latter it is
intended to be removed. The processes are, in the main, the same. The
articles to be plated are first thoroughly cleaned and suspended on the
Fig. 18%.
—pole of a battery, and then a plate of the same kind of metal that is to
be deposited on the given articles is suspended from the + pole (Fig. 187).
The bath used is a solution of a salt of the metal to be deposited. The
cyanides of gold and silver are generally used for gilding and silvering.
Many of the base metals require to be electro-coppered first, in order to
secure the adhesion of the gold or silver. The magneto-electric machine
has almost completely replaced the voltaic battery for electrotyping and
electroplating purposes.
216 ELECTRICITY AND MAGNETISM,
Section XVII.
USEFUL APPLICATIONS OF ELECTRIC ENERGY CON-
TINUED. ——- TELEGRAPHY.
193. The Telegraph. — The word telegraph, literally, signifies to
write far away. In its broadest sense it embraces all methods of commu-
nicating thought with great speed to a distance, by means of intelligible
characters, sounds, or signs; but usually it is applied only to electrical
methods.
†First, it should be understood that, instead of two lines of wire, one
to convey the electric current far away from the battery, and another
to return it to the battery, if the distant pole is connected with
a large metallic plate buried in moist earth, or, still better, with a
gas or water pipe that leads to the earth, and the other pole near
the battery is connected in like manner with the earth, so that the earth
forms about one-half of the circuit, there will be needed only one wire
to connect telegraphically two places that are distant from each other,
Furthermore, the resistance offered by the earth to the electric current is prac-
tically nothing ; so that, disregarding the resistance of the ground connec-
tions, there is a saving of one-half the wire and one-half the resistance,
and consequently of one-half the battery power.
Let B, Figure 188, Plate IV., represent the message sender, or operator’s
key; Y, the message receiver. It may be seen that the circuit is broken
ai, B. Let the operator press his finger on the knob of the key. He closes
the circuit, and the electric current instantly fills the wire from Boston to
New York. It magnetizes a; a draws down the lever 6, and presses the
point of a style on a strip of paper, c, that is drawn over aroller. The
operator ceases to press upon the key, the circuit is broken, and instantly
bis raised from the paper by a spiral spring, d. Let the operator press
upon the key only for an instant, or long enough to count one: a simple
dot or indentation will be made in the paper. But if he presses upon the
key long enough to count three, the point of the style will remain in contact
with the paper the same length of time; and, as the paper is drawn along
beneath the point, a short straight line is produced. This short line is
called a dash. These dots and dashes constitute the alphabet of telegraphy.
For instance, a part of a message, “man is in,†is represented as printed
in telegraphic characters on the strip of paper. The Roman letters above
interpret their meaning.
BosTon
LOCAL
VAN aa
BAT. BAT. es
Fig. 188.
SSS
Wiener
SSS
MAIN
SY
LOCAL
BAT.
ST
AL 2°
TELEGRAPHY. 217
194, The Sounder. — If the strip of paper is removed, and the style
is allowed to strike the metallic roller, a sharp click is heard. Again, when
the lever is drawn up by the spiral spring, it strikes a screw point above
(not represented in the figure), and another click, differing slightly in
sound from the first, is heard. A listener is able to distinguish dots from
dashes by the length of the intervals of time that elapse between these two
sounds. Operators generally read by ear, giving heed to the clicking
sounds produced by the strokes of a little hammer. A receiver so used is
called a sounder, a common form of which is represented in the lower cen-
tral part of Plate IV.
195. The Relay and the Repeater. — The strength of the cur-
rent is diminished, of course, as the line is extended and the number of in-
struments in the circuit is increased. Hence, a current that would move
the parts of a single sounder audibly, on a short line, would not move the
same parts of many sounders on a long line with sufficient force to render
the message audible. Resort is had to relays and repeaters.
In Figure 189, Plate IV., the letter R represents a relay and S a sounder.
Suppose a weak current arrives at New York from Boston, and has suffici-
ent strength to attract the armature of the relay at that station. This, as
may be seen by examination of the diagram, will close another short circuit,
called the local circuit, and send a current from a, local battery located in the
same office through the sounder at that station. The sounder, being op-
erated by a battery in a circuit of only a few feet in length, delivers the
message audibly. If it is desired that the message should go beyond New
York, —for instance, to Philadelphia, — then we have only to suppose the
local line at New York to be lengthened so as to extend to Philadelphia,
and a powerful.line battery to be substituted for the small local; then the
message that.leaves Boston will be shifted from one circuit to the other at
New York, and be delivered in Philadelphia without the intervention of
any operator on the route. In this case a relay is called a repeater. The
electro-magnets in relays are wound with long, thin wire, while those
of sounders are wound with short, large wire. The main battery consists
of many cells in series. It may be located at either terminus, but it is
generally split in halves, and one half placed at each terminus.
In the diagram, the circuit is represented as open at both keys. When
the line is not in use, the circuit ought always to be left closed, by means
of switches connected with the keys (not represented in the diagram), so
that when the line is not “at work†an electric current is constantly tray-
ersing the wire. Sending a message, consequently, consists in interrupting
this current by means of a key. Suppose that Boston wishes to communi-
218 ELECTRICITY AND MAGNETISM.
cate with New York. He first removes the switch on his key, which breaks
the circuit and enables him to control the circuit with his key. He then
manipulates his key so as to produce an understood signal, which will at-
tract New York’s attention. Every time that Boston presses on his key,
every armature in his own office, and in the New York office, and at way
stations, falls. Of course the message may be read at every station on the
route.
TELEGRAPHIC ALPHABET.
A B -C D E F
G H I J K L
M N oO P Q R
8 T U Vv WwW x
Y Z & 5 2
TELEGRAPHIC FIGURES.
1 2 3 4 5 6
7 8 9 0
——0£¢40-0-——_.
Section XVIII.
USEFUL APPLICATIONS OF ELECTRIC ENERGY CON-
TINUED. —_ TELEPHONY.
196. Bell Telephone. — Figure 190 represents a sectional and a
perspective view of this instrument. It consists of a steel magnet A,
encircled at one extremity by a spool B of very fine insulated wire, the
ends of which are connected with the binding-screws DD. Immediately
in front of the magnet is a thin circular iron disk EE. The whole is en-
closed in a wooden or rubber case F. The conical-shaped cavity G serves
the purpose of either a mouth-piece or an ear-trumpet. There is no dif-
ference between the transmitting and receiving telephone; consequently
TELEPHONY. 219
either instrument may be employed as a transmitter, while the other serves
asareceiver. Two magneto telephones in a circuit are virtually in the
relation of a dynamo and a motor. The. transmitter being in itself a
diminutive dynamo, of course no battery is required in the circuit. Con-
nect in circuit two such telephones, and the apparatus is ready for use.
When a person talks near the disk of. the transmitter, he throws it into
rapid vibration. The disk, being quite close to the magnet, is magnetized
by induction; and as it vibrates, its magnetic power is constantly chang-
Fig. 190.
ing, being strengthened as it approaches the magnet, and enfeebled as it
recedes. This fluctuating magnetic force will of course induce currents
in alternate directions in the neighboring coil of wire. These currents
traverse the whole length of the wire, and so pass through the coil of the
distant instrument. When the direction of the arriving current is such as
to re-enforce the power of the magnet of the receiver, the magnet attracts
the iron disk in front of it more strongly than before. If the current is in
the opposite direction, the disk is less attracted, and flies back. Hence,
whatever movement is imparted to the disk of the transmitting telephone,
the disk of the receiving telephone is forced to repeat. The vibrations of
the latter disk become sound in the same manner as the vibrations of a
tuning-fork or the head of a drum.
The above is a description of the original and simplest form of the
Bell telephone. It is apparent that the original energy, ie. that of the
Voice, applied at the transmitter must, during its successive transforma-
220 ELECTRICITY AND MAGNETISM.
tions and especially during its transmission in the form of electric energy
through large resistances, become very much enfeebled, so that when it
reappears as sound, the sound is quite feeble and frequently inaudible.
The first grand improvement on the original consists in introducing a bat-
tery into the circuit, and so arranging that the. voice, instead of being
obliged to generate currents, should be required to act only as a controlling
force of. a current already generated by the battery. It is evident that
only a fluctuating or undulating current can produce: the necessary vibra-
tions in the disk of the receiver. The fluctuations are caused by a vary-
Fig. 191.
Fig. 192.
ing resistance in the circuit. The pupil must have learned by experience
ere this that the effect of a loose contact between any two parts of a cir-
cuit is to increase the resistance and thereby weaken the current; but the
effect of a slight variation in pressure is especially noticeable when either
or both of the parts are carbon. Figure 191 illustrates a simple telephonic
circuit in which are included a variable resistance transmitter T, a mag-
neto receiver R, and a battery B. One of the electrodes, a platinum
point, touches the center of the transmitter disk; the other electrode, a
carbon button a, is pressed by a spring gently against the platinum point.
Every vibration of the disk, however minute, causes a variation in the
pressure between the two electrodes and a corresponding variation in the
circuit resistance. As changes the resistance, so changes the current
TELEPHONY.
221
strength, and so consequently changes the force with which the magnet
in the receiver R pulls its disk. The vary-
ing tension between magnet and disk causes
the latter to vibrate and reproduce sounds.
The next improvement of considerable
importance consists in the adoption of an
induction coil, which, we have learned, pro-
duces a current of much greater electro-
motive force than is possessed by the original
battery current. By its adoption we are able
to converse over much longer distances, and
since the battery current traverses only a
local circuit, as may be seen by reference to
Figure 192, a single Leclanché cell is gener-
ally sufficient to operate it. The currents
induced by the fluctuating primary current
traverse the line wire and generate sonorous
vibrations in the disk of the receiver in the
same manner as in the original telephone.
Figure 198 represents the entire’ tele-
phonic apparatus required at any single
station. The box A contains a small hand-
dynamo, such as is represented in Figure
194. A person turning the crank F gener-
ates a current which rings a pair of elec-
tric bells G, both at his own and at a dis-
tant station, and thus attracts attention. He
next takes the receiver B off the supporting
hook and places it to his ear. When the
weight is removed from the hook, the
hook rises a little and throws the dynamo
and bells out of the circuit, and at the
same time introduces the receiver B, the
transmitter C, and the battery D, so that the
circuit stands as represented in Figure 192.
The box C contains the induction coil. E
is a “lightning arrester.â€
197. Microphone. — In Figure 195,
A and B are buttons of carbon; the former
is attached to a sounding-board of thin
Sround
Bil
|
ne
re, LineWire
Fig. 194.
999 ELECTRICITY AND MAGNETISM.
pine wood, the latter to a steel spring C, and both are connected in
circuit with a battery and a telephone used as a receiver. The spring
presses B against A, and any slight jar will cause a variation in the
pressure and corresponding variations in the current strength.
Fig. 195.
By means of this instrument, called the microphone, any little sounds, as
its name indicates, such as the ticking of a watch or the footfall of an
insect, may be reproduced at a considerable distance, and be as audible as
though the original sounds were made close to the ear.
Section XIX.
THERMO-ELECTRIC CURRENTS.
198. Heat Energy transformed directly into Electric
Energy.
Experiment 170. — Insert in one screw-cup of an astatic galvan-
ometer an iron wire, and in the other cup a copper, or better, a Ger-
THERMO-ELECTRIC CURRENTS. 223
man silver wire. Twist the other ends of the wire together, and heat
them at their junction in a flame; a deflection of the needle shows
that a current of electricity is traversing the wire. Place a piece of
ice at their junction; a deflection in the opposite direction shows
that a current now traverses the wire in the opposite direction.
Experiment 171.— Take a strip of sheet copper about 15 inches
long and three-fourths of an inch wide, and a strip of zine of the same
dimensions. Lay them one upon the other, and fold over each end
upon itself for about half an inch, and hammer the joints flat, so that
they shall hold together quite
firmly. Then separate the two
strips into a somewhat elliptical
or rectangular shape, as shown in
Figure 196. Cut a hole through
the center of one of the strips,
and pass the wire support of
a magnetic needle through it. .
Place the band in the magnetic meridian parallel with the needle.
Direct a flame against one of the junctions, and note the deflection,
and determine the direction in which the current traverses the band,
ie. whether the current passes from the heated junction through the
copper or the zine strip.
These currents are named, from their origin, thermo-
electric. The apparatus required for the generation of
these currents is very simple, consisting merely of bars of
two different metals joined at one extremity, and some
means of raising or lowering their temperature at their
junction, or of raising the temperature at one extremity
of the pair and lowering it at the other; for the electro-
motive force, and consequently the strength of the cur-
rent, is nearly: proportional to the difference in tempera-
ture of the two extremities of the pair. The strength of
the current is also dependent, as in the voltaic pair, on
the thermo-electromotive force of the metals employed.
The following thermo-electric sertes is so arranged that if
the temperatures of both junctions are near the ordinary
224 ELECTRICITY AND MAGNETISM.
temperatures of the air, those metais farthest removed
from each other give the strongest current when com-
bined; and the current passes, when heated at their junc-
tion, from the one first named to that succeeding it. The
arrows indicate the direction of.the current at the heated
and the cold ends respectively. At high temperatures the
current may be reversed.
B Cold.
z <
ee é e
& a. tel 3 aS 9
Bees ees Sea vee ie es
TP RUcees)
a : S elas eee
FAN SOm rn aS OMAN Eon nah reli at
>
Feat.
199. Thermo-electric Batteries and Thermo-pile. —
The electro-motive force of the thermo-electric pair is very
small in comparison with that. of the voltaic pair; hence
the greater necessity of combining a large number of pairs
with one another in series. This is done on the same
principle, and in the same manner, that voltaic pairs are
united; viz., by joining the +metal of one pair to the
— metal of another. Figure 197 represents
such an arrangement. The light bars are
bismuth, and the dark ones antimony. If
the source of heat is strong and near, one
face may be heated much hotter than the
other, and a current equal to that from an
ordinary galvanic cell is often obtained.
-Such contrivances for generating electric
currents are called thermo-electric batteries. They are
seldom used, inasmuch as the best of them transform less
than one per cent of the heat energy given out by the
source of heat.
STATIC ELECTRICITY. 225
If the source of heat is feeble or distant, the feeble cur-
rent may serve to measure the difference of temperature
between the ends of the bars turned toward the heat and the
other ends, which are at the temperature of the air. The
apparatus, when used for this purpose,
is called a thermo-pile, or a thermo- |
multiplier. A combination (Fig. 198)
of as many as thirty-six pairs of anti-
mony and bismuth bars, connected with
a very sensitive galvanometer, consti-
tutes an exceedingly delicate thermoscope
and thermometer. Changes of tempera- l
ture that would not produce a percep- Fig. 198.
tible change in an ordinary thermometer, can, by the
use of a thermo-electric pile, be made to produce large
deflections of the galvanometer needle. Heat radiated
from the body of an insect several inches from the pile
may cause a sensible deflection.
Section XX.
STATIC ELECTRICITY.
200. Mechanical Energy transformed into Electric
Potential Energy or Electrification.
Experiment 172. — Prepare an insulated stool (Fig. 199) by plac-
ing a square board on four dry and clean glass tumblers, used as legs.
Let a person, whom we will call John, stand on this stool, and let a
seccnd person, James, strike John a few times with a cat’s fur. Then
let James bring the knuckle of a finger near to some part of John’s
226 ELECTRICITY AND MAGNETISM.
person, for instance his hand, chin, or nose; an electric spark will
pass between the two, and both will experience a slight shock. ‘The
length of the spark shows that the electricity is urged by a high
E.M.F., like the induced currents of the magneto-machine and in-
duction coil.
‘As mechanical energy is transformed into potential
energy in the act of bending a bow or stretching a rub-
ber band, in other
words, a peculiar
molecular stress is
developed thereby,
<< so by the expendi-
ture of mechanical
energy in separating
- the fur from the boy
at the end of each
.. stroke there is de-
' veloped a phase of
potential energy; the
ae Eo bodies in which it is
developed are said to be in a state of electrification, in
other words, there exists between them a form of electric
stress. The electrified bodies are sometimes said to be
“charged†with electricity.
201. Electroscope.
Experiment 173.— Suspend in a loop, tied in a white silk thread,
a strip of “Dutch metal,†so that the two vertical por-
{ tions may be near each other. After John has been
{j struck a few times with the fur, let him bring a finger
~ gradually near the upper extremity of the foil; the two
portions of the foil gradually diverge, as in Figure |
200, indicating the action of an unusual force between |
Fig. 200. them.
STATIC ELECTRICITY. 22%
Any arrangement, like that of the foil just described,
intended to detect the presence of electrification, is called
an electroscope. One of the most common and useful:
electroscopes consists of one or two pith-balls, made from
the pith of elder or sunflower, suspended by silk thread.
If an electroscope is brought near to either pole of a sec-
ondary wire of an induction coil, a. similar electrification
is manifested by the poles. Likewise, by means of very
delicate electroscopes, the poles of a galvanic battery, or
of a thermo-battery, are found to be feebly electrified.
202. Attractions and Repulsions.
Experiment 174. — Poise a flat wooden ruler on an inverted bottle
or flask, having a round bottom, asin .
Figure 201. Draw a rubber comb two
or three times through your hair, or
rub it with a woollen cloth, and place
it near one end of the ruler; instantly
the ruler moves toward the comb.
Experiment 175.— Hold the comb
over a handful of bits of tissue paper;
the papers quickly jump to the comb,
stick to it for an instant, and then leap
energetically from the comb. The
papers are first attracted to the comb,
but in a short time acquire some of its
electrification, and then are repelled.
Experiment 176.— Support a plate
of window glass (Fig. 202) about two
inches from a table. Rub its upper
surface with a silk handkerchief, and
place pith-balls or bits of tissue paper on the table beneath the glass.
They will dance up and down between the plate and table in a lively
manner.
Fig. 202.
203. Two States of Electricity. — It is quite apparent
that we are now dealing with a very different class of
228 ELECTRICITY AND MAGNETISM.
electrical phenomena from any that we have previously
observed. It is also quite as obvious that we are dealing
with electricity in a very different state or condition from
that in which we have before studied it. Hitherto we
have studied only those phenomena produced by electric-
ity when in motion; and, inasmuch as when in that state
its energy is expended in work, or transformed into some
other form of energy as rapidly as it is generated, there
was no such thing as an accumulation of electricity. In
our late experiments there is wanting anything like a cur-
rent; but, on the other hand, we find that electricity in
this new state may accumulate, be stored up, and remain
in a quiescent state for an indefinite time. In the latter
state it is incapable of affecting a magnetic needle, mag-
netizing, generating heat, illuminating, producing decom-
position, or giving shocks. But in this state of apparent
repose it may attract and afterwards repel light bodies. in
the vicinity of the body in which it resides. These attrac-
tions and repulsions are quite distinct from the attractions
and repulsions which occur between parallel currents.
This state of electricity is called statze, in distinction
from the current state, which is often called dynamic.
We have seen that, under certain conditions, electricity
may change from one state to the other, as when the elec-
tricity which had accumulated in the boy on the insulated
stool passed to the other boy, producing, in its current
state, both illuminating and physiological effects; and
again, when a circuit is broken, the current ceases, but
electricity accumulates in the wire. We have also learned
that electricity of high E.M.F., such as is most readily
developed by friction, exhibits the static phenomena, 1.e.
attractions and repulsions, most strikingly.
STATIC ELECTRICITY. 229
204. Two Kinds of Electrification.
Experiment 177.— Bend a small glass tube into the form repre-
sented by A (Fig. 203), insert one end in a block of wood B fora
base; and suspend from the tube a pith-ball C by a silk thread. Rub
a glass rod D with a silk handkerchief, and present it to the ball;
attraction at first occurs, followed by repulsion after contact. Now
rub a stick of sealing-wax, or a hard-rubber ruler, with flannel, and
present it to the ball, which is in a condition such that it is repelled
by the electrified glass; it is attracted by the electrified sealing-wax.
We are led to suspect that the sealing-wax possesses a different kind
of electrification from that
of the glass. Let us fur-
ther test the matter.
Fig. 203. Fig. 204.
Experiment 178.— Suspend two glass rods that have each been
rubbed with silk in two wire stirrups (Fig. 204), and present them to
each other; they repel one another. Suspend two sticks of sealing-
wax that have been rubbed with flannel in the same manner; the
same result follows. Now, in a like manner, present one of the glass
rods and one of the sticks of sealing-wax to each other; they attract
one another. : :
It is evident (1) that there are two kinds or conditions of
electrification, or, for convenience, we sometimes say two
hinds of electricity ; (2) that they are so related to each
other that like kinds repel, and unlike kinds attract each
other. The two kinds are usually distinguished from
each other by the names positive and negative, or, more
briefly, as +E and —E. The former is, by definition,
230 ELECTRICITY AND MAGNETISM.
such as is developed on glass when rubbed with silk, and
the latter is the kind developed on sealing-wax when
rubbed with flannel. There is no reason, except custom,
for calling the one positive rather than the other.
Experiment 179.— Once more electrify a stick of sealing-wax with
a flannel, and present it to a pith-ball, and after the ball is repelled,
bring the surface of the flannel which had electrified the rod near
the ball; the ball is attracted by it, showing that the rubber is also
electrified and with the opposite kind to that which the sealing-wax
possesses. :
One kind of electrification is never developed alone ;
when two bodies are rubbed together they become equally but
oppositely electrified.
B
Fig. 205.
205. Induction.
Experiment 180.— Suspend by silk threads from a glass tube
two egg-shells covered with tin foil, so as to touch each other, as in
Figure 205. Bring near to one end of the shells, but not to touch, a
sealing-wax rod excited with flannel, and therefore having —E. While
the rod is in this position, carry a thin strip of tissue paper, or a pith-
ball suspended by a silk thread, along the eggs. The paper is attracted
most strongly at the ends; but in the middle, where the shells are in
contact, there is very little electrification. Separate B from A about —
STATIC ELECTRICITY. 281
10, while the rod D is still in position. Then place D midway be-
tween A and B; the rod repels B and attracts A. It appears that
when the two shells touched each other, thereby constituting practi-
cally one body, that the shells were oppositely electrified, as repre-
sented by the signs + and — in the diagram; and when the two bodies
were separated, they retained their opposite charges.
We learn from this experiment that by induction we
may charge at the same time two bodies, one with +H
and the other with — E.
206. Discharge.
Experiment 181.— Bring the two shells oppositely charged near
each other; when near enough they exhibit mutual attraction for
each other. On bringing them still nearer, a spark passes between
them, their mutual attraction suddenly ceases, and on testing them
with an electroscope, it is found that both have lost their electrifica-
tion, i.e. both have become discharged.-
When two bodies equally and oppositely electrified are brought together, both
become discharged. During the process of discharge, the electricity which
was previously in a condition of rest, or a static state, assumes a condition
of motion, or a dynamic state, as is shown by a spark passing between
the two bodies when brought near each other. One -of the bodies (that
positively charged) is at a potential higher than that of the earth, the other
is at a lower potential. When they are brought sufficiently near, the ten-
dency of the electricity to pass from the region of higher potential becomes
strong enough to penetrate the insulating air and establish a condition of
equilibrium. In this particular case the result is zero potential or no elec-
trification; but in general both bodies would be left at a like condition of
electrification, its sign depending upon the sign of that electricity which
was in excess. ;
We may now understand how it is that an electrified body attracts to
itself. light bodies in its vicinity. For example, a stick of sealing-wax,
excited with —E, brought near a pith-ball, induces +E next itself, and
repels — E to its farthest side; then, of course, attraction follows. There
is the same attraction between heavy bodies, but usually not sufficient to
produce motion.
232 ELECTRICITY AND MAGNETISM.
207. Insulation.— A body that is to receive a perma-
nent charge of electricity must be insulated, 7.2. have no
connection with the earth through a conducting sub-
stance. Some of the best insulating substances are dry
air, ebonite, shellac, resins, glass, silks, and furs. Moisture
injures the insulation of bodies; hence experiments suc-
ceed best on dry, cold days of winter, when moisture of
the air is least liable to be condensed on the surfaces of
apparatus, especially if they are kept warm.
Section XXI.
ELECTRICAL MACHINES. — CONDENSERS, ETC. —
208. Plate Machine. — An electrical machine is an
instrument intended for transforming mechanical energy
into ‘the energy of electrification. The plate machine
(Fig. 206) consists of a conductor A, a glass plate B, a
rubber C made of two cushions covered with a prepara-
tion which facilitates the excitation, and a brass chain
-E used to connect the cushions with the earth. An
extension of the conductor consists of a comb D whose
pointed teeth are turned towards the plate. When the
plate is turned in the direction indicated by the arrow,
it passes between the rubbers, and the friction causes
“+E to collect on the plate and —E on the rubber.
The electrified portion of the plate then comes opposite
the comb, when it polarizes the conductor, attracting
—E and repelling +E. But the —E escapes from the
ELECTRICAL MACHINES. 283
points of the comb to the plate, neutralizes the +E of the
plate, and thereby leaves the conductor charged with + E.
Sonal
Ee a Lu
OM i rR
i l
ou
Fig. 206.
209. Electrophorus. — This apparatus is
used to incite electrification by induction. It con-
sists of a shallow iron dish A (Fig. 207) filled
with sealing-wax. At the center of the dish is
a protuberance B which extends just through
the wax.
lating handle.
Experiment 182. — Strike the surface of the
wax a few times with a cat’s fur, or rub it with
a dry flannel. The wax becomes electrified with
—E. Place the disk C upon it. The + E of the
disk is bound (i.e. held by the attraction of) the
—E of the wax, but the —E of the disk is re-
pelled by the — E of the wax and passes through
the protuberance B to the dish below, and Fig. 207.
thence to the earth. Consequently when the disk C is raised by
234 ELECTRICITY AND MAGNETISM.
the insulating handle from the wax, it is charged with +E, and the
charge can be transferred to any body (e.g. a Leyden jar), and then
the disk can be recharged by replacing it on the wax. This may
be repeated many times without sensibly reducing the inductive
power of the wax.
The Holtz machine (Fig. 139) is a sort of a continuous electroph-
orus which is capable of developing electrification by induction so
rapidly and continuously as to give an almost incessant flow of sparks
between the two conductors.
210. Condenser.— A very important adjunct to an
electrical machine is a condenser of some kind, by means
of which a large quantity of electricity can be collected
on a small surface.
Experiment 183.— Let a person stand on an insulated stool
(page 226), and place one hand on the conductor of a machine. Let
the other open hand press against a plate of glass or a disk of vul-
canite, held on the open hand of a second person standing on the
floor. After afew turns of the machine, let the hand that has been
on the prime conductor grasp the free hand of the second person.
Quite a shock will be felt by both.
It is evident that by this process an unusual quantity
of electricity had collected previous to the discharge.
The explanation is simple. The hand of the first person,
charged with +E, acts by induction through the glass
upon the second person, attracting —E to the surface of
the glass with which his hand is in contact, and repelling
+E to the earth. Thus, through their mutual attraction, |
the two kinds of electricity become, as it were, heaped up
opposite each other, and yet are prevented, by the insu-
lating glass, from uniting.
211. Leyden Jar.
condenser is the Leyden jar (Fig. 208). It is a wide-
The most convenient form of
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ELECTRICAL MACHINES. 235
mouthed glass jar lined on the inside and outside for
about two-thirds its height with tin foil. Through the
stopper passes a brass rod terminating at its upper ex-
tremity in a brass ball a, and at the other extremity in
a brass chain which touches the inner coating of tin foil.
The jar may be charged
by connecting one of its
coatings with the conductor
of an electrical machine, and
the other with the earth.
Or it may be charged by
connecting the outside coat-
ing with one of the poles of the Holtz machine, and
bringing the other pole near to the ball leading from the
inner coating. To discharge the jar, connect the outer
coating with the knob of the jar. To avoid a shock in so
doing a discharger is used (Fig. 209), which consists of a
bent wire terminating at each end with metal balls. The
wire is held by a glass insulating handle.
Fig. 208. Fig. 209.
212. Electrification confined to the External Surface.
Hxperiment 184. — Place a tin fruit-can on a clean, dry glass
tumbler (Fig. 210). Fasten a circular disk a of tin 15™™ in diameter
to one end of a rod of sealing-wax. Charge the can heavily
with electricity from an electrical machine. Through an
orifice c in the can introduce the disk, and touch the in-
terior surface of the can. Withdraw the disk, and present
it to an electroscope. Jt shows no electrification. Now
touch the exterior surface of the can with the disk and
present it tc the electroscope; it is found to be electrified.
This experiment shows that no electricity can be found
inside of a hollow charged conductor; or, roughly stated,
a static charge of electricity resides on the exterior surface
of a conductor.
236 ELECTRICITY AND MAGNETISM.
213. Effect of Points. — An electrical flyer, F Fig. 206),
consists of a cap of metal resting upon a pointed wire,
which serves as a pivot. The cap has pointed wires
branching out from it like the spokes of a wheel, bent
near the ends and turned in the same direction. “If this
is placed on an insulating stand and connected with the
conductor of an electrical machine when in operation, the
air particles around the electrifying points become excited
like so many pith-balls, and are rapidly repelled, produc-
ing a continuous current of air issuing from the points.
The reaction of these air-particles causes the wheel to
revolve in the opposite direction. As we might reason-
ably expect, currents of excited air-particles issuing from
the points on an excited conductor serve to carry away
with them portions of the charge, so that the effect of
points on an electrified insulated body ts greatly to facilitate
its discharge.
214. Lightning. — Certain clouds which have formed very rapidly
are highly charged with electricity, usually positively charged. The sur-
face.of the earth and objects thereon immediately beneath the cloud are
charged inductively with the opposite kind of electricity. The cloud and
the-earth correspond to the coatings, and the intervening air to the glass
of a huge Leyden jar. The charge in the earth and that in the cloud hold
each other prisoner by their mutual attraction, until, as the charges accu-
mulate, the attraction becomes great enough to disrupt the insulating
medium, i.e. the intervening air, when a discharge takes place. It is the
accumulation of induced electricity on elevated: objects, such as buildings
and trees, that offers an attraction for the opposite electricity of the
cloud, and renders them especially liable to be struck by lightning.
215. Lightning-Rods.— The flash will pass along the line of
least resistance. A good lightning conductor offers a peaceful means
of communication between the earth and a cloud; it leads the electricity of
the earth gently up toward the cloud, and allows it to combine with its
opposite without disturbance, thereby so far discharging the cloud as to
prevent a lightning stroke; or, if the tension is too great to be thus quietly
ELECTRICAL MACHINES. 2387
disposed of, the flash strikes downward, and is led harmlessly to the earth
by the conductor. An ill-constructed lightning-rod may be worse than none.
A rod should be made of good conducting material, so large that it will
not be melted, and free from loose joints. The lower end should be
buried in earth that is always moist, and the upper end should terminate
in several sharp points,
CHAPTER VIL
~ SOUND.
- Oo.
Section I.
STUDY OF VIBRATIONS AND WAVES.
The subjects of Sound-waves and Light-waves, which we are about to
study, have two important characteristics in common that distinguish them
from the subjects already studied. First, each of them affects its peculiar
organ of sense, the ear or the eye. Secondly, both originate in vibrating
bodies, and reach us only by the intervention of some medium capable
of being set in vibration.
216. Period of Vibration.
Experiment 185.— Suspend an iron ball by a string, as in Experi-
* ment 71, cause it to vibrate, and, watch in hand, ascertain the num-
ber of vibrations made in a given number of seconds; e.g. 60 seconds.
Then, remembering that all the vibrations are made in equal intervals
of time, ascertain the period of vibration of this pendulum; ize. the
time it takes to make each vibration, using the formula
ae
n
in which t= the period, and n=the number of vibrations made in s
seconds.
217. Direction of Vibration.
Experiment 186.— Grasp one end of a small rod or yardstick in
a vice, pull the free end one side, and set it in vibration. Pluck a
string of a piano or violin. Note that the motions of all the bodies
which thus far we have caused to vibrate are at right angles to their
length. These are called transverse vibrations.
Experiment 187.— Hang up a spiral spring or elastic cord with a
small weight attached at the lower end; lift the weight, and, drop-
STUDY OF VIBRATIONS AND WAVES. 239
ping it, notice that the cord vibrates lengthwise. This is a case of
longitudinal vibration. ‘There may also be torsional vibrations, for ex-
ample children often amuse themselves by producing these by twist-
ing a window cord and tassel.
218. Propagation of Vibration; Waves.
Experiment 188.— Take a rubber cord about the size of an ordi-
nary lead-pencil and 12 feet long. Attach at intervals a few glass
beads and fasten one end of the cord to the wall of the room. Hold
the free end in the hand and draw the cord’ out so as to be nearly
horizontal. By quick movements of the hand in a horizontal or a
vertical direction set this end in vibration. Notice that these vibra-
tions are communicated from point to point along the cord, and that
each point in the cord successively goes through a vibration precisely
similar to that held in the hand. Fix the eyes upon any one of the
beads; it simply vibrates transversely. Observe the cord as a whole;
waves traverse it from end to end, but it is easy to see that it is only
a form that traverses it; the beads and all other points of the cord
move transversely. These successive transverse movements give rise
to the wave-line into which the cord is thrown.
219. Wave-Length and Amplitude.— Imagine an in-
stantaneous photograph taken of the cord along which con-
tinuous waves are passing. It
would appear much like the
curved line CD (Fig. 211).
This curved line represents
what is known as a simple Fig. 211.
wave-line. The distance from any vibrating point to the
nearest point which is in exactly the same stage of its
vibration is called a wave-length, as wx, uv, or en.
The distance between the extreme positions of a vibrat-
ing point or the length of its journey is called the ampli-
tude of the wave or the amplitude of vibration.
220. Reflection of Waves; Interference.
Experiment 189,— Stretch the cord horizontally between two
240 SOUND.
elevated points, and pluck it with the hand or strike it with a stick
near one end, and send along it a: single pulse, forming a crest on the
rope (A, Fig. 212). This
travels to the other end,
and there we see it re-
flected and inverted (B).
Experiment 190. —
Just at the instant of re-
flection, start a second
crest; these two, the crest
and thereturning inverted
Fig. 212. crest or trough (C), are
- now travelling along the rope in opposite directions, and must meet
at some point. This point will be urged upward by the crest and
downward by the trough, and so its motion will be due to the differ-
ence of the two forces.
Experiment 191.—Send along the rope, first a trough, then a
crest; now two crests (D)-will meet near the middle of the rope, and
the motion here will be due to two forces acting in the same direc-
tion, so that the resulting crest will be greater than either of the origi-
nal ones. :
This action on a single point of two pulses, or two trains
of waves, no matter if from different sources, is termed
interference. The resulting motion may be greater or less
than that due to either pulse alone, or it may be zero.
221. Stationary Vibrations, Nodes, ete.
Experiment 192.— Hold one end of the cord while the other is
fixed, and send along it a regular succession of equal pulses from the
Fig. 213.
vibrating hand; it will be easy, by varying the tension and rate a
little, to obtain a succession of hazy spindles (Fig. 218), separated by
points that are nearly or quite at rest, Unlike the earlier experiments,
STUDY OF VIBRATIONS AND WAVES. 241
the waves here do not appear to travel along the tube; yet in reality
they do traverse it. The deception is caused by stationary points being
produced by the interference of the advancing and retreating waves.
This interference of direct and reflected waves gives
rise to the important class of so-called stationary vibrations.
The points of least motion, as @ and 0, are called nodes ;
the points of greatest motion, ¢ and d, are called antinodes ;
and the portion of the rope between two nodes, as ab, is
a ventral segment.
222. Longitudinal Waves. -
Experiment 193.— Figure 214 represents a brass wire wound in
the form of a spiral spring, about 12 feet long. Attach one end toa
cigar-box, and fasten the box to a table. Hold the other end H of
the spiral firmly in one hand, and with the other hand insert a knife-
blade between the turns of the wire, and quickly rake it for a short
distance along the spiral toward the box, thereby crowding closer
together for a little distance (B) the turns of wire in front of the
_ hand, and leaving
the turns behind egeze7eero~,
pulled wider apart coe 1 (| |
(A) for about an Se SOSAARKS
equal distance. The
crowded part of the spiral may be called a condensation, and the
stretched part a rarefaction. The condensation, followed by the rare-
faction, runs with great velocity through the spiral, strikes the
box, producing a sharp thump; is reflected from the box to the
hand, and fromthe hand again to the box, producing ‘a second
thump; and by skilful manipulation three or four thumps will be
produced in rapid succession. If a piece of twine be tied to some
turn of. the wire, it will be seen, as each wave passes it, to receive a
slight jerking movement forward and backward in the direction of
the length of the spiral.
Fig. 214.
How is energy transmitted through the spring so as to
deliver the blow.on the box? Certainly not by a bodily
movement of the spiral as a whole, as might be the case if
it were a rigid rod. The movement of the twine shows
242 SOUND.
that the only motion which the coil undergoes is a vibra-
tory movement of its turns. Here, as in the case of
water-waves, energy is transmitted through a medium by
the transmission of vibrations.
There are two important distinctions between these
waves and those which we have previously studied: the
former consist of condensations and rarefactions; the
latter, of elevations and depressions. In the former, the
vibration of the parts is in the same line with the path
of the wave, and hence these are called longitudinal waves ;
- in the latter, the vibration is across its path; they are
therefore called transverse waves.
A wave cannot be transmitted through an inelastic soft
iron spiral. Hlasticity is essential in a medium, that it may
transmit waves composed of condensations and rarefactions ;
and the greater the elasticity, the greater the facility and
rapidity with which a medium transmits waves.
223. Air as a Medium of Wave-Motion. — May not
air and other gases, which are elastic, serve as media. for
waves?
EW ie ai ai
: Fig. 215.
Experiment 194.— Place a candle flame at the orifice a of the
tube (Fig. 215), and strike the table a sharp blow with a book near
the orifice &. Instantly the candle flame is quenched. The body of
air in the tube serves as a medium for transmission of motion to the
candle.
Was it the motion of a current of air through the tube, a minia-
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STUDY OF VIBRATIONS AND WAVES. 243
ture wind, or was it the transfer of a vibratory motion? Burn touch-
paper? at the orifice b, so as to fill this end of the tube with smoke,
and repeat the last experiment.
Evidently, if the body of the air is moved along through the tube,
the smoke will be carried along with it. The candle is blown out as
before, but no smoke issues from the orificea. It isclear that there is no
translation of material particles from one end to the other, — nothing
like the flight of a rifle bullet. The candle flame was struck by some-
thing like a pulse of air, not by a wind.
224. Howa Wave is propagated through a Medium.
—The effect of applying force with the hand to the spiral
spring is to produce in a certain section (B, Fig. 214) of
the spiral a crowding togéther of the turns of wire, and
at A a separation; but the elasticity of the spiral instantly
causes B to expand, the effect of which is to produce a
crowding together of the turns of wire in front of it, in
the section C, and thus a forward movement of the con-
densation is made. At the same time, the expansion of B
causes a filling up of the rarefaction at A, so that this
section is restored to its normal state. This is not all:
the folds in the section B do not stop in their swing when
they have recovered their original position, but, like a
pendulum, swing beyond the position of rest, thus produc-
ing a rarefaction at B, where immediately before there
was a condensation. Thus a forward movement of the
rarefaction is made, and thus a pulse or wave is trans-
mitted with uniform velocity through a spiral spring, air,
or any elastic medium.
225. Graphical Method of Studying Vibrations.
Experiment 195.— Attach, by means of sealing-wax, a bristle or
a fine wire to the end of one of the prongs of a large steel fork (like
1 To prepare touch-paper, dissolve about a teaspoonful of saltpetre in a half-teacupful
of hot water, dip unsized paper. in the solution, and then allow it to dry, The paper
produces much smoke in burning, but no flame,
244 SOUND.
a tuning-fork, but larger) called a diapason. Set the fork in vibra-
tion, and quickly draw the point of the bristle lightly over a smoked
glass (A, Fig. 216). A
= beautiful wavy line will be
traced on the glass, each
wave corresponding to a
vibration of the prong when vibrating as a whole.
Next, tap the fork, near its stem, on the edge of a table, and trace
its vibrations on a smoked glass as before. You will generate a
similar set of waves, but, running over these, is another set, of much
shorter period, like No. 3 of Figure 230, showing that. the prong
vibrates, not only as a whole, but in parts: The serrated wavy line
_ produced represents the resultant of the combined vibrations, and
may be called a complex wave-line.
QUESTIONS.
1. In what kind of motion does all wave-motion originate? .
2. Watch the waves of the ocean moving landward; what is it
that advances? af
- 8. Throw a cord into wavy motion by the movement of your
hand; upon what do the number and the length of the waves which
traverse the cord at any given time depend?
4, How is a node produced ?
5. How do the vibrations in longitudinal waves differ from the
vibrations in transverse waves? —
6. Are the vibrations in air-waves longitudinal or transverse?
Section IT.
SOUND-WAVES.
226. How Sound-waves Originate. — Listen to a
sounding church-bell. It produces a sensation; it is
heard. The ear is the organ through which the sensation
SOUND-W AVES. » 245
of hearing is produced. The bell is at such a distance
that it cannot act directly on the ear; yet something
must act on the ear, and it must be the bell which causes
that something to act.
Commencing at the origin of sound, let the Ase in-
quiry be, How does a sounding body differ from a silent
body ?
Experiment 196.— Strike a bell or a glass bell-jar, and touch the
edge with a small cork ball suspended by a thread; you not only hear
the sound, but, at the same time, you see a tremulous motion of the
ball, caused by a motion of the bell. Touch the bell gently with a
finger, and you feel a tremulous motion. Press the hand against the
bell; you stop its vibratory motion, and at that instant the sound
ceases. Strike the prongs of a tuning-fork, press the stem against a
table: you hear a sound. Thrust the ends of the prongs just beneath
the surface of water; the water is thrown off in a fine spray on either
side of the vibrating fork. Watch the strings of a piano, guitar, or
violin, or the tongue of a JEWe Darp, when sounding. You can see that
they are in motion.
Sound-waves originate in a vibrating body.
227. How Sound-waves Travel. — How can a bell,
sounding at a distance, affect the ear? If the bell while
sounding possesses no peculiar property except motion,
then it has nothing to communicate to the ear but motion.
But motion can be communicated by one body to another
at a distance only through some medium.
Do sound-waves require a medium for their communi-
cation ?
Experiment 197.— Lay a thick tuft of cotton-wool on the plate
of an air-pump, and on this, face downward, place a loud-ticking
watch, and cover with the receiver. Notice that the receiver, inter-
posed between the watch and your ear, greatly diminishes the sound,
or interferes with the passage of something to the ear. Take a few
strokes of the pump and listen; the sound is more feeble, and con-
246 SOUND.
tinues to grow less and less distinct as the exhaustion progresses,
until either no sound can be heard when the ear is placed close to the
receiver, or an extremely faint one, as if coming from a great dis-
tance. The removal of air from a portion of the space between the
watch and your ear destroys the sound. Let in the air again, and the
sound is restored.
Sound-waves cannot travel through a vacuum, t.e. with-
out a medium.
Boys often amuse themselves by inflating paper bags,
and with a quick blow bursting them, producing with
each a single loud report. First the air is suddenly and
greatly condensed by the blow, and the bag is burst; the
air now, as suddenly and with equal force, expands, and
by its expansion condenses the air for a certain distance
all around it, leaving a rarefaction where just before had
been a condensation. If many bags were burst at the
same spot in rapid succession, the result would be that
alternating shells of condensation and rarefaction would
be thrown off, all having a common center, enlarging. as
they advance, like the waves formed by stones dropped
into water; except that, in this case, the waves are not
like rings, but hollow globes; not circular, but spherical.
In this manner sound-waves produced by the vibration
of a sounding body travel through the air.
As a wave advances, each individual air-particle con-
cerned in its transmission performs a short excursion to
and fro in the direction of a straight line radiating from
the center of the shells or hollow globes. A sound-wave
travels its own length in the time that a particle occupies
in going through one complete vibration so as to be ready
to start again.
Experiment 198.— Take a strip of black cardboard 4.5 inches x
linch. Cut a slit about one-sixteenth of an inch wide lengthwise
and centrally through the strip nearly, from end toend. Place the
SOUND-WAVES. 947
slit over the dotted line at the bottom of Figure 217, and draw the
book along underneath in the direction of the arrow. Imagine that
the short white dashes seen through the slit represent a series of air-
particles, and the slit itself represents the direction in which a series
of sound-waves are travelling. It will be seen that each air-particle
moves a little to and fro in the direction in which the sound travels
and comes back to its starting-point; but the condensations and rare-
factions, represented by a group (half a wave-length) of dots being
alternately closer together or farther apart, are transmitted through
the whole series of air-particles.
Fig. 217.
228. What Sound Is.— Sound is a sensation caused
usually by waves of air beating upon the organ of hearing.
229. Solids and Liquids as Media for transmitting
Sound-waves.
Experiment 199.—Lay a watch, with its back downward, on a
248 SOUND.
long board (or table), near to one of its ends, and cover the watch
with loose folds of cloth till its ticking cannot be heard through the
_ air in any direction at a distance equal to the length of the board.
Now place the ear in contact with the farther end of the board, and
you will hear the ticking of the watch very distinctly.
Experiment 200.— Place one end of a long pole on a cigar box,
and apply the stem of a vibrating diapason to the other end; the
sound-vibrations will be transmitted through the pole to the box, and
a loud sound will be given out by the box, as though that, and not the
tuning-fork, were the origin of the sound.
Experiment 201.— Place the ear to the earth, and listen to the
rumbling of a distant carriage; or put the ear to one end of a long
stick of timber, and let some one gently scratch the other end with a
pin.
Solids and liquids, as well as gases, transmit sound-
vibrations.
Section III.
VELOCITY OF SOUND-WAVES.
230. The Velocity of Sound-waves depends on the
Elasticity and Density of the Medium. — The relation
of velocity to the density and elasticity of gases, as ascer-
tained by careful experiment, is as follows: theevelocity
of sound-waves in gases is directly proportional to the square
root of their elasticity, and inversely proportional to the
square root of their respective densities.
The velocity of sound-waves in air at 0°C. is (888")
1098 feet per second. The velocity increases nearly two
feet for each degree centigrade. At the temperature of
16°C. (60° F.) we may reckon the velocity of sound-waves
at about (842â„¢) 1125 feet per second.-
REFLECTION OF SOUND-WAVES. — ECHOES. 249
The greater density of solids and liquids, as compared
with gases, tends, of course, to diminish the velocity of
sound-waves; but their greater incompressibility more
than compensates for the decrease of velocity occasioned
by the increase of density. As a general rule, solids are
more incompressible than liquids; hence, sound-waves
generally travel faster in the former than in the latter.
For example, sound-waves travel in water about 4 times
as fast as in air, and in iron and glass 16 times as fast. .
Section IV.
REFLECTION OF SOUND-WAVES. — ECHOES.
231. Reflection.—In the experiment with the spiral
spring, waves were reflected from the box to the hand, and
from the hand to the box. When a sound-wave meets an
obstacle in its course, it is reflected; and the sound re-
sulting from the reflected waves is often called an echo,
or, when they are many times reflected so that the sound
becomes, nearly contin-
nous, a reverberation.
232. Sound-waves
reflected by Concave
Mirrors.
Experiment 202.—Place
a watch at the focus A (Fig.
218) of a concave mirror G. At the focus B of another concave
mirror H, place the large opening of a small tunnel, and with a
tubber connector attach the bent glass tube C to the nose of the
Fig. 218.
250 SOUND.
tunnel. The extremity D being placed in the ear, the ticking of the
watch can be heard very distinctly, as though it were somewhere near
the mirror H. Though the mirrors be 12 feet apart, the sound will
be louder at B than at an intermediate point E.
How is this explained? Every air-particle in a certain
radial line, as Ac, receives and transmits motion in the
direction of this line; the last particle strikes the mirror
at c, and being perfectly elastic, bounds off in the direc-
tion ce’, communicating its motion to the particles in this
line. At ce’ a similar reflection gives motion to the air
particles in the line c'B. In consequence of these two re-
flections, all divergent lines of motion as Ad, Ae, etc., that
meet the mirror G, are there rendered parallel, and after-
wards rendered convergent at the mirror H. The prac-
tical result of the concentration of this scattering energy
is, that a sound of great intensity is heard at B. The
points A and B are called the foct of the mirrors. The
front of the wave as it leaves A is convex, in passing
from G to H it is plane, and from H to B concave. If
you fill a large circular tin basin with water, and strike
one edge with a knuckle, circular waves with concave
fronts will close in on the centre, heaping up the water
at that point.
Long “ whispering-galleries†have been constructed on this principle.
Persons stationed at the foci of the concave ends of the long gallery can
carry on a conversation in a whisper which persons between cannot hear.
The external ear is a wave-condenser. The hand held concave behind
the ear, by its increased surface, adds to its efficiency. An ear-trumpet,
by successive reflections, serves to concentrate, at the small orifice open-
ing into the ear, the sound-waves that enter at the large end.
INTENSITY OF SOUND. 251
Section V.
INTENSITY OF SOUND.
233. Intensity depends on the Amplitude of Vibra-
tion.— Gently tap the prongs of a tuning-fork and dip
them into water, —the water is scarcely moved by them;
increase the force of the blow,—the vibrations become
wider, and the water spray is thrown with greater force
and to a greater distance. The same thing occurs when the
fork vibrates in the air; though we do not see the air-par-
ticles as they are batted by the moving fork, yet we feel the
effects as a sound sensation, and we judge of their energy
by the intensity of the sensation which they produce.
Loudness of sound refers to the intensity of a sensation.
We have no standard of measurement for a sensation, so
we are compelled to measure the intensity of the sound-
wave, knowing at the same time that loudness zs not pro-
portional to this intensity. Unfortunately, the expressions
loudness and intensity of sound-wave are often inter-
changed. The intensity of a vibration is measured by
the energy of the vibrating particle. It is clear that if
the amplitude of vibration of a particle is.doubled while
its period remains constant, its velocity is doubled, and
its energy is increased fourfold. Hence, (1) measured
mechanically, the intensity of a sound-wave is proportional
to the square of the amplitude of the vibrations of the
vibrating body.
234. Intensity depends upon the Density of the Me-
dium.—JIn the experiment with the watch under the
receiver of the air-pump (page 245), the sound grew
252 SOUND.
feebler as the air became rarer. Aéronauts are obliged to
exert themselves more to make their conversation heard
when they reach great hights than when in the denser
lower air. (2) The intensity of sownd-waves increases with
the density of the medium in which they are produced.
235. Intensity depends on Distance. —It is a mat-
ter of every-day observation that the loudness of a sound
diminishes very rapidly as the distance from the source
of the waves to the ear increases. As a sound-wave ad-
vances in an ever-widening sphere, a given amount of
energy becomes distributed over an ever-increasing sur-
face ;.and as a greater number of particles partake of the
motion, the individual particles receive proportionately
less energy; hence it follows,—as a consequence of the
geometrical truth, that “the surface of a sphere varies
as the square of its radius,’ —that (8) the intensity of
a sound-wave varies inversely as the square of the distance
from its source. For example, if two persons, A and B,
are respectively 500 and 1000 rods from a gun when it
is discharged, the waves that reach A will be four times
as intense as the same when they reach B.
236. Speaking-Tubes.
Experiment 203. — Place a watch at one end of the long tin tube
(Fig. 215), and the ear at the other end. The ticking sounds very
loud, as though the watch were close to the ear.
Long tin tubes, called speaking-tubes, passing through many apartments
in a building, enable persons at the distant extremities to carry on conver-
sation in a low tone of voice, while persons in the various rooms through
which the tube passes hear nothing. The reason is that the sound-waves
which enter the tube are prevented from expanding, consequently the
intensity of sound is not affected by distance, except as its energy is wasted
by friction of the air against the sides of the tube.
REENFORCEMENT OF SOUND-WAVES. 253
Section VI.
REENFORCEMENT OF SOUND-WAVES AND INTERFERENCE
OF SOUND-WAVES.
237. Reénforcement of Sound-waves.
Experiment 204.— Set a diapason in vibration; you can scarcely
hear the sound unless it is held near the ear. Press the stem against
a table; the sound rings out loud, but the waves seem to proceed
from the table.
When only the fork vibrates, the prongs presenting
little surface cut their way through the air, producing very
slight condensations, and consequently waves of little in-
tensity. When the fork rests upon the table, the vibrations
are communicated to the table; the table with its larger
surface throws a larger mass of air into vibration, and
thus greatly intensifies the sound-waves. The strings of
the piano, guitar, and violin
owe as much of their loud- *
ness of sound to their elas-
tic sounding-boards, as the
fork does to the table.
238.. Reénforcement by
Bodies of Air; Resona-
tors.
Experiment 205.— Take a
glass tube A (Fig. 219), 16 inches
long and 2 inches in diameter;
thrust one end into a vessel of
water C, and hold over the other
end a vibrating diapason B that makes (say) 256 vibrations in a
second. Gradually lower the tube into the water, and when it reaches
a
Fig. 219.
954 SOUND.
. acertain depth, i.e. when the column of air oc attains a certain length,
the sound of the fork becomes very loud; continuing to lower the
tube, the sound rapidly dies away.
Columns of air are thus found to serve, as well as sound-
ing-boards, to reénforee sound-waves. The instruments
which enclose the columns of air are called resonators.
Unlike sounding-boards, they can respond loudly to only
one tone, or to a few tones of widely different pitch.
How is this reénforcement effected? When the prong
a moves from one extremity of its arc a’ to the other a’,
it sends a condensation down the tube; this condensation
striking the surface of the water, is reflected by it up the
tube. Now suppose that the front of this reflected con-
densation should just reach the prone, at the instant it is
starting on its retreat from a’! to a’; then the reflected
condensation will conspire with the peeaten formed by
the prong in its retreat to make a greater condensation in
the air outside the tube. Again, the retreat of the prong
from a! to a! produces in its rear a rarefaction, which also
runs down the tube, is reflected, and will reach the prong
at the instant it is about to return from a! to a’’, and to
cause a rarefaction in its rear; these two rarefactions
moving in the same direction conspire to produce an in-
tensified rarefaction. The original sound-waves thus com-
bine with the reflected, to produce resonance ; but this can
only happen when the like parts of each wave coincide
each with each; for if the tube were somewhat longer or
shorter than it is, it is plain that condensations would
meet rarefactions in the tube, cup tend to destroy one
another.
The loudness of sound of all wind instruments is due to the resonance
of the air contained within them. A simple vibratory movement at the
mouth or orifice of the instrument, scarcely audible in itself, such as the
REENFORCEMENT OF SOUND-WAVES. 255°
vibration of a reed in reed pipes, or a pulsatory movement of the air pro-
duced by the passage of a thin sheet of air over a sharp wooden or metallic
edge, as in organ pipes, flutes, and flageolets, or more simply still by the
friction of a gentle stream of breath from the lips sent obliquely across
the open end of a closed tube, bottle, or pen-case, is sufficient to set the
large body of enclosed air in the instrument into vibration, and thus re-
enforced, the sound becomes audible at long distances.
Experiment 206.— Attach a rose gas-burner A (Fig. 220) to a
metal gas-tube about 1â„¢ in length, and connect this by a rubber tube
with a gas-burner. Light the gas at the rose burner, 7
and you will hear a low, rustling noise. Remove the
conical cap from the long tin tube (Fig. 215), support
the tube in a vertical position, and gradually raise the
burner into the tube; when it reaches a certain point
not far up, the body of air in the tube will catch up
the vibrations, and give out deafening sound-waves
that will shake the walls and furniture in the room.
239. Measuring Wave-Lengths and the
Velocity of Sound-waves. — Experiments
like that described on page 253 enable us read-
ily to measure the wave-length produced by a
fork that makes a given number of vibrations
in a second, and also to measure the velocity _4
of sound-waves. It is evident that if a con- Fig. 220.
densation generated by the prong of the fork in which its
forward movement from a! to a’! (Fig. 220) met with no
obstacle, its front, meantime, would traverse the distance
od, or twice the distance oc; hence the length of the
condensation is the distance od. But a condensation is
only one-half of a wave, and the passage of the prong
from a! to a!’ is only one-half of a vibration; conse-
quently the distance od is one-half of a wave-length, and
the distance oc is one-fourth of a wave-length. The
measured distance of oc in this case is about 13.13 inches ;
hence the length of wave produced by a C’-fork making
256 SOUND.
256 vibrations in a second is (13.13 inches x 4=) 52.5
inches = 4.88 feet. And since a wave from this fork
travels 4.38 feet in 51, of a second, it will travel in an
entire second (4.88 feet x 256 =) 1121 feet. The dis-
tance oc varies with the temperature of the air.
It is evident that the three quantities expressed in the
formula
velocity
wave-length = number of vibrations
bear such a relation to one another that if any two are
known, the remaining quantity can be computed. It
will further be observed that with a given velocity the wave-
length varies inversely as the number of vibrations ; t.e. the
greater the number of vibrations per second, the shorter
the wave-length.
240. Interference of Sound-Waves.
Experiment 207.— Hold a vibrating diapason over a resonance-
<<. jar as in Figure 221. Roll the
\ diapason over slowly in the fin-
gers. At certain points, a quarter
W of a revolution apart, when the
diapason is in an oblique posi-
tion with reference to the edge
of the jar as represented in the
figure, the reénforcement from
the tube almost entirely dis-
appears, but reappears at the
intermediate points. Return to
the position where there is no
resonance, and enclose in a loose
roll of paper, the prong farthest
from the tube, without touching the diapason, so as to prevent the
sound-waves produced by that prong from passing into the tube; the
resonance resulting from the vibrations of the other prong immediately
appears,
REENFORCEMENT OF SOUND-WAVES. 257
Experiment 208.—Select two of the tubes (Fig. 235) of nearly
he same length, blow through them, and notice the peculiar throbbing
ound produced by the interference of the two sounds. me
Experiment 209.—Stop one of the orifices of a
vicyclist’s whistle (Fig. 222), and sound one whistle ata
ime. The sound of each is clear and smooth. Sound 4
both whistles at the same time, and you obtain the usual
rough and discordant sound.
The two whistles of unequal length give out waves of
slightly different length, so that at certain short inter-
vals the same phases of both sets will coincide (i.e. con-
Jensation with condensation) and produce intensified
sounds which are heard at long distances, while at other
intervals opposite phases coincide (i.e. condensation with
rarefaction), and the result of their mutual destruction
is to cause the otherwise smooth sound to become broken
or rattling.
Two sound-waves may unite to-produce a sound louder or
weaker than either alone would produce, or even cause silence.
241. Forced and Sympathetic Vibrations.
Experiment 210.— Suspend from a frame several pendulums, A,
B, C, etc. (Fig. 223). A and D are each 3 feet long, C a little longer,
and B and E are shorter. Set A in vibration, and slight impulses
will be communicated through the frame to
D and cause it to vibrate. The vibration-
period of D being the same as that of A,
all the impulses tend to accumulate motion
in D, ‘so that it soon vibrates through arcs
as large as those of A. On the other hand,
C, B, and E, having different rates of vibra-
tion from that of A, will at first acquire a
slight motion, but soon their vibrations will
be in opposition to those of A, and then the
impulses received from A will tend to destroy
the slight motion they had previously acquired.
Experiment 211.— Press down gently one of the keys of a piano
so as to raise the damper without making any sound, and then sing
Fig. 223.
258 SOUND.
loudly into the instrument the corresponding note. The string cot.
responding to this note will be thrown into vibrations that can be
heard for several seconds after the voice ceases. If another note be
sung, this string will respond only feebly.
Raise the dampers from all the strings of the piano by pressing the
foot on the right-hand pedal, and sing strongly some note into the
piano. Although all the strings are free to vibrate, only those will
respond loudly that correspond to the note you sing, i.e. those that are
capable of making the same number of vibrations per second as are
produced by your voice. —
These experiments show that a vibrating body tends to
make other bodies near it vibrate even if their periods of
vibrations are different. Vibrations of this kind, such, for
example, as those of B, C, and E in Experiment 210 and
those generated in the sounding-boards of pianos, violins,
etc., are called forced vibrations. But if the period of the
incident waves of air is the same as that of the body which
they cause to vibrate, the amplitude and intensity of the
‘vibrations become very great, like that of the pendulum D,
and those of the piano strings which gave forth the loud
sounds. Such are called sympathetic vibrations.
QUESTIONS.
1. Why do not sound-waves travel with the same velocity through
all bodies?
2. How are echoes produced ?
3. On a day when sound-waves travel through the air at the rate of
1120 feet per second, what is the length of the sound-waves that pro-
ceed from a church bell which makes 192 vibrations in a second?
4, With what velocity do sound-waves travel when a jar whose
depth is 10 inches gives the maximum reénforcement for a diapason
which makes 256 vibrations in a second?
5. Great danger often arises from vibrations of the walls of a
building caused by certain vibratory movements of machinery within.
The danger in such cases can frequently be greatly diminished by
changing the rate of motion in the machinery. Explain.
PITCH OF MUSICAL SOUNDS. 259
Section VII.
PITCH OF MUSICAL SOUNDS.
242. On What Pitch Depends.
Experiment 212.— Draw the finger-nail or a card slowly, and
then rapidly, across the teeth of acomb. The two sounds produced
are commonly described as low or grave, and high or acute. The hight
of a musical sound is its pitch.
Experiment 213.— Cause the circular sheet-iron disk A (Fig. 224)
to rotate, and hold a corner of a visiting-card so that at each hole an
audible tap shall be made. Notice that when
the separate taps or noises cease to be distin-
guishable, the sound becomes musical; also,
that the pitch of the musical sound depends
upon the rapidity of the rotation, i.e. upon the
frequency of the taps.
Experiment 214.— Hold the orifice of a
glass tube B so as to blow through the holes as
they pass. When rotating slowly, separate puffs
are heard, from which it hardly seems possible
to construct a musical sound. When, however,
the ear is no longer able to detect the separate putts, the sound be-
comes quite musical, and the pitch rises and falls with the speed.
Fig. 224.
Pitch depends upon frequency of vibration, or wave-
length ; i.e. the greater the number of vibrations per second,
or the shorter the wave-length, the higher the pitch.
243. Musical Scale.— The pitch of a sound produced
by twice as many vibrations as that of another sound is
called the octave of the latter. Between two such sounds
the voice rises or falls in a manner very pleasing to the
ear by a definite number of steps. This gives rise to the
260 SOUND.
so-called musical scale, or gamut. The number of vibra-
tions which shall constitute a given note
is purely arbitrary, and differs slightly
in different countries; but the ratios
between the vibration numbers of the
several notes of the gamut and the
vibration number of the first or funda-
mental note of the gamut, are the same
among all enlightened nations. The
vibration numbers given in Figure 225
correspond to those of German instru-
ments. For example, the string corre-
sponding to the middle C (the key at
the left of the two black keys near the
Fig. 225. middle of the key-board) of a German
piano makes 264 vibrations in a second.
numbers.
Vibration
Vibration
ratios.
&
°
Zi
Cc
D
E
F
G
A
B
olen nsleacaliainence|e ea
Cdeeloorsiemaleo NDonl
1
voles
f
iN
Section VIII.
VIBRATION OF STRINGS.
244. Sonometer.
Experiment 215.—Stretch an elastic wire @ over the bridges
of the sonometer (Fig. 226), so that the portion between will be free
Fig. 226.
to vibrate. Pluck the string at.its middle with the thumb and finger,
causing’ it to vibrate, and observe the pitch. Next place a movable
bridge d half-way between the two fixed bridges and cause the portion
VIBRATION OF STRINGS. 261
between either fixed bridge and the movable bridge to vibrate, and
observe the change in pitch. How is the vibration period changed?
Experiment 216.— Stretch another wire 0, either thicker or thin-
ner than the last, employing the same length and tension as before,
and notice the change in pitch due to the difference of weight of
the wire. How is the vibration period changed?
Experiment 217.— Increase the tension of either wire by turning
the pin, to which one end of the wire is attached, with a wrench C,
and observe the change in pitch caused by change of tension. How
does an increase of tension affect the vibration period?
Careful experiments show that the vibration numbers of
strings of the same material vary inversely as their lengths
and the square roots of their weights, and directly as the
square roots of their tension.
245, Beats.
Experiment 218.—Sirike simultaneously the lowest note of a
piano and its sharp (black key next above), and listen to the result-
ing sound.
You hear a peculiar wavy -or throbbing sound, caused
by an alternate rising and sinking in loudness. These
alternations in loudness are called beats.
Fig. 227.
' Let the continuous curve line AC (Fig. 227) represent a
series of waves caused by striking the lower key, and the.
dotted line a series of waves proceeding from the upper
key. Now the waves from both keys may start together
at A; but as the waves from the lower key are given less
262 SOUND.
frequently, so are they correspondingly longer; and at
certain intervals, as at B, condensations will correspond
with rarefactions, producing by their interference momen-
tary silence, too short, however, to be perceived; but the
sound as perceived by the ear is correctly represented in
its varying loudness by the curved line in the lower pari
of the figure.
The number of beats per second due to two simple tones ts
equal to the difference of their respective vibration numbers.
The sensation produced on the ear by such a throbbing
sound, when the beats are sufficiently frequent, is un-
pleasant, much as the sensation produced by flashes of
light that enter the eye, when you walk on the shady
side of a picket fence, is unpleasant. The unpleasant
sensation, called by musicians discord, is due to beats.
Section IX.
OVERTONES AND HARMONICS.
246. Vibration in Parts.
Experiment 219.— Hang up a rubber cord AC (Fig. 228) 4 feet
long, and fasten both ends. Pluck it near the middle, and it will
swing to and fro as a whole (2), at a rate dependent on its length,
tension, etc. Hold it fast at B (8), and pluck it at a point half-way
between A and B. Both halves are thrown into independent vibra-
tions, and continue so to vibrate for a brief time after the hand is
withdrawn from B. Again hold it fast at B, one-third its length
above A (4), and pluck it half-way between A and B; the length BC
instantly divides itself at B’ into two equal parts, and on withdraw-
ing the hand from B, the whole cord is seen to vibrate in three dis-
tinct and equal sections. In a similar manner it may be made to
vibrate in four, five, etc., sections.
OVERTONES AND HARMONICS. 263
Sounds coming from a string or other body that vibrates
in parts are called overtones. If, as is the case with a
string, the vibration num-
ber of the overtone is
just two, three, four, etc.,
times that of the funda-
mental or lowest tone,
the sound is called a har-
monic. Many overtones
can be produced from a
steel bar or a metallic
plate, but no harmonics.
This distinction is of
great importance, for,
practically, no musical
instruments are of much
use unless their vibrat-
ing parts furnish harmon-
1s. Fig. 228.
Experiment 220.— Press down the C’-key (middle C) of a piano
gently, so that it will not sound; and while holding it down, strike
the C-wire strongly. In a few seconds release the key, so that its
damper will stop the vibrations of the string that was struck, and
you will hear a sound which you will recognize by its pitch as com-
ing from the C!-wire. Place your finger lightly on the C’-wire, and
you will find that it is indeed vibrating. Press down the right pedal
. with the foot, so as to lift the dampers from all the wires, strike the
C-key, and touch with the finger the C’-wire; it vibrates. Touch the
keys next to C’, viz. Band D’; they have only a slight forced vibra-
tion. Touch G!; it vibrates.
Now it is evident that the vibrations of the C’ and G’-
wires are sympathetic. A C-wire vibrating as a whole
cannot cause sympathetic vibrations in a C’-wire; but if
it vibrates in halves, it may. Hence we conclude that
264 SOUND.
when the O-wire was struck, it vibrated, not only as a
whole, giving a sound of its own pitch, but also in halves;
and the result of this latter set of vibrations was, that an
additional sound was produced by this wire, just an octave
higher than the first-mentioned sound.
Again, the G/-wire makes three times as many vibra-
tions as are made by the C-wire; hence the latter wire,
in addition to its vibrations as a whole and in halves, must
have vibrated in thirds, inasmuch as it caused the G’-wire
to vibrate. It thus appears that a string may vibrate at
the same time as a whole, in halves, thirds, etc., and the
result is that a sound is produced that is compounded of
several sounds of different pitch.
Not only do stringed instruments produce compound
tones, but no ordinary.musical instrument is capable of
producing a simple tone, z.e. a sound generated by vibra-
tions of a single period. In other words, when any note of
any musical instrument is sounded, there.is produced, in
addition to the primary tone, a number of other tones in a
progressive series, each tone of the series being usually of
less intensity than the preceding. The primary or lowest
tone of a note is usually sufficiently intense to be the most
prominent, and hence is called the fundamental tone.
That two notes sounded together may harmonize, it ts
essential not only that the pitch of their fundamental tones
be so widely different that they cannot produce audible beats,
but that no beat shall be formed by their overtones, or by an
overtone and a fundamental. Not only is there perfect
agreement among the overtones of two notes an octave
apart when sounded together, as when male and female
voices unite in singing the same part of a melody, but
the richness and vivacity of the sound is much increased
thereby.
QUALITY OF SOUND. 265
Section X.
QUALITY OF SOUND.
247. How Sounds from Different Sources are Distin-
guished. — We easily learn to distinguish by certain pecu-
liarities the voices of our acquaintances. So we readily
distinguish sounds emanating from various musical instru-
ments, e.g. a piano, violin, harp, and cornet. It is not
necessarily by the loudness or pitch of the sounds that we
recognize them. It is by another property of sound called
quality. Two sounds can differ from each other in only
three particulars, viz. intensity, pitch, and quality.
Pitch depends on frequency of vibrations, loudness on
their amplitude; on what does quality depend ?
248. Analysis of Sounds. — The unaided ear is unable,
except to a very limited
extent, to distinguish the
individual tones that com-
pose a note. Helmholtz ar-
ranged a series of resona-
tors consisting of hollow
‘spheres of brass, each hay-
ing two openings: one (A,
Fig. 229) large, for the re-
ception of the sound-waves,
and the other (B) small and funnel-shaped, and adapted
for insertion into the ear. Each resonator of the series
was adapted by its size to resound powerfully to only a
single tone of a definite pitch. When any musical sound
is produced in front of these resonators, the ear, placed at
the orifice of any one, is able to single out from a collec-
tion that overtone, if present, to which alone this resonator
266 SOUND.
is capable of responding. In this manner a complete
analysis of any musical sound may be made, and the pitch
and intensity of each of its components determined.
It is found that when a note is produced on a given instrument, not
only is there a great variety of intensity represented by the overtones, but
all the possible overtones of the series are by no means present. Which
are wanting depends very much, in stringed instruments, upon the point of
the string struck. For example, if a string is struck in its middle, no node
can be formed at that point; consequently, the two important overtones
produced by 2 and 4 times the number of vibrations of the fundamental
will be wanting. Strings of pianos, violins, etc., are generally struck near
one of their ends, and thus they are deprived of only some of their higher
and feebler overtones.
249. Synthesis of Sounds. — The sound of a tuning-
fork, when its fundamental is reénforced by a suitable
resonance-cavity, is very nearly a simple tone. By sound-
ing simultaneously several forks of different but appropri-
ate pitch, and with the requisite relative intensities, Helm-
holtz succeeded in producing sounds peculiar to various
musical instruments, and even in imitating most of the
vowel sounds of the human voice.
Thus it appears that he has been able to determine,
both analytically and synthetically, that the quality of a
given sound depends upon what overtones combine with its
Fundamental tone, and on their relative intensities; or, we |
may say more briefly, upon the form of vibration, since the
form must be determined by the character of its components.
COMPOSITION OF SONOROUS VIBRATIONS. 267
Section XI.
COMPOSITION OF SONOROUS VIBRATIONS, AND THE
RESULTANT WAVE-FORMS.
250. . Method of Representing Sound-Vibrations
Graphically. —It is evident that there must be a particular aérial
wave-form corresponding to each compound vibration, otherwise the ear
would not be able to appreciate a difference in the quality of sounds to
which these combination forms give rise. Every particle of air engaged in
, iN
A) HE i
(ca
fl
(hi
= NINH
= ANN | :
ITT CEI |!
UTE i TE
Fig. 232.
transmitting a compound sound-wave is simultaneously acted upon by
several sets of vibratory movements, and it remains to investigate what
its motion will be under their joint influence.
The light wave-lines AB (Fig. 230) represent typically two series of
268 SOUND.
aerial sound-waves, corresponding respectively to a fundamental tone and its
first overtone. The heavy line represents the form of the joint wave which
results from the combination of the two constituents. If we suppose lines
perpendicular to the axis, that is, to the dotted line, or line of repose, to
be drawn to each point in this line, as ad, cd, eF, etc., they will represent
by their varying lengths the displacement of any particle in a vibrating
body, or any particle of air traversed by sound-waves, from its normal
position.
a = The rectangular dia-
gram CD is intended
to represent a portion
of a transverse section
of a body of air trav-
ersed by the joint wave
represented by the
heavy wave-line above.
The depth of shading
in different. parts in-
dicates the degree of
condensation at. those
parts.
Figure 231 repre-
sents wave-lines drawn
by an instrument call-
ed a vibrograph (Fig.
232). The second line
represents a sound two
octaves above that
which the first line rep-
resents, and the third
line shows the result of
the combination of the
Fig..288- two sets of vibrations.
251. Manometric Flames. — Apparatus like that shown in
Figure 233 will serve to illustrate in a pleasing manner many facts per-
taining to sound vibrations.
The cylindrical box A is divided by a membrane a into two compart-
ments.c and d. Jlluminating-gas is introduced into the compartment ¢,
through. the rubber tube x, and burned at the orifice d. CDis a frame
holding two mirrors, M, placed back to back, so that whichever side is
turned toward the flame there is a reflection of the flame.
if
i
i
|
H
I
}
|
COMPOSITION OF SONOROUS VIBRATIONS. 269
When the mirror is at rest, an image of the flame will appear in the
mirror as represented by A (Fig. 234). If the mirror is rotated, the
flame appears drawn out in a band of light, as shown in B of the same
figure.
de
Fig. 234.
Sing into the cone B (Fig. 234) the sound of oo in tool, and waves of
air will run down the tube, beat against the membrane a, causing it to
vibrate, and the membrane in turn acts upon the gas in the compartment c,
throwing it into vibration. The result is, that instead of a flame appear-
ing in the rotating mirror as a continuous band of light, as B, Figure 234,
270 SOUND.
it is divided up into a series of tongues of light, as shown in C, each con-
densation being represented by a tongue, and each rarefaction by a dark
interval between the tongues.. If a note an octave higher than the last is
sung, we obtain, as we should expect, twice as many tongues in the same
space, as shown in D. E represents the result when the two tones are
produced simultaneously, and illustrates in a striking manner the effect of
interference. F represents the result when the vowel e is sung on the key
of C’; and G, when the vowel ois sung on the same key. These are called
manometric flames.
Section XII.
MUSICAL INSTRUMENTS.
, 252. Classification of Musical Instruments. — Musi-
cal instruments may be grouped into three classes: (1)
stringed instruments; (2) wind instruments, in which
the sound is due to the vibration of columns of air con-
fined in tubes; (8) instruments in which the vibrator
is a membrane or plate. The first class has received its
share of attention; the other two merit a little further
consideration.
253. Wind Instruments.
Experiment 221.—Figure 235 represents a set of Quinke’s
whistles. The tubes are of the same size, but of varying length.
Blow through the small tube across the lips of the large tube of each
whistle in the order of their lengths, commencing with the longest.
Repeat the experiment, closing the end of the whistle farthest
from you with a finger, so as to make what is called a “closed pipe.â€
The pitch of vibrating air-columns, as well as of strings,
varies with the length, and in both stopped and open pipes
MUSICAL INSTRUMENTS. Q71
the number of vibrations is inversely proportional to the
length of the pipe. An open pipe gives a note an octave
higher than a closed pipe of the same length.
Fig. 235.
Experiment 222.—Take some of the longer whistles, blow as
before, gradually increasing the force of the current. It will be found
that only the gentle current will give the full musical fundamental
tone of the tube, —a little stronger current produces a mere rustling
sound; but when the force of the current reaches a certain limit, an
overtone will break forth; and, on imereasing still further the power
of the current, a still higher overtone may be reached.
Figure 236 represents an open organ-pipe provided with a glass
window A in one of its sides. A wire hoop B has stretched over it a
membrane, and the whole is suspended by a thread within the pipe. If
the membrane is placed near the upper end, @ buzzing sound proceeds
272 SOUND.
from the membrane when the fundamental tone of the pipe is sounded;
and sand placed on the membrane will dance up and down in a, lively
manner. On lowering the membrane, the buzzing sound becomes
fainter, till, at the middle of the tube, it ceases entirely, and the sand
becomes quiet. Lowering the membrane still further, the sound and
dancing recommence, and increase as the lower end is approached.
When the fundamental tone of an open pipe ts produced,
its air-column divides itself into two equal vibrating sections,
with the anti-node at the extremities of the
tube, and a node in the center.
Fig. 236. ; Fie. 237.
If the pipe is stopped, there is a node at the stopped
ond: if it is open, there is an anti-node at the open
end; and in both cases there is an anti-node at the end
where the wind enters, which’ is always to a certain
extent open.
A, B, and C of Figure 237 show respectively the posi-
tions of the nodes and anti-nodes for the-fundamental tone
MUSICAL INSTRUMENTS, 273
and first and second overtones of a closed pipe; and
A', B’, and C’ show the positions of the same in an
open pipe of the same length. The distance between the
dotted lines shows the relative amplitudes of the vibra-
tions of the air-particles at various points along the tube.
Now the distance between a node and the nearest anti-
node is a quarter of a wave-length. Comparing, then,
A and A’, it will be seen that the wave-length of the
fundamental of the closed pipe must be twice the wave-
length of the fundamental of the open pipe; hence the
vibration period of the latter is half that of the former;
consequently the fundamental of the open pipe must be
an octave higher than that of the closed pipe.
x
Fig. 238.
254. Sounding Plates, ete.
Experiment 223. — Fasten with a screw the elastic brass plate A
(Fig. 238) on the upright support. Strew writing-sand over the plate,
and draw a rosined bass bow steadily and firmly over one of its
edges néar a corner; and. at the same time touch the middle of one
274 SOUND.
of its edges with the tip of the finger; a musical sound will be
produced, and the sand will dance up and down, and quickly collect
in two rows, extending across the plate at right angles to one an-
other. Draw the bow across the middle of an edge, and touch with a
finger one of its corners; the sand will arrange itself in two diagonal
rows (2) across the plate, and the pitch of the note will be a fifth
higher. Touch, with the nails of the thumb and forefinger, two
points a and 6 (8) on one edge, and draw the bow across the middie
c of the opposite edge, and you will obtain additional-rows and a
shriller note.
Fig. 239.° ME
By varying the position of the point touched and bowed,
a great variety of patterns can be obtained, some of which
are represented in Figure 239. It will be seen that the
effect of touching the plate with a finger is to prevent
vibration at that point, and consequently a node is there
produced. The whole plate then divides itself up into
segments with nodal division lines in conformity with the
MUSICAL INSTRUMENTS. 275
node just formed. The sand rolls away from those parts
which are alternately thrown into crests and troughs, to
the parts that are at rest.
255. Interference.
Hxperiment 224. —C (Fig. 238) is a tin tube made in two parts to
telescope one within the other. The extremity of one of the parts ter-
minates in two slightly smaller branches. Bow the plate, as in the first
experiment (1), place the two orifices of the branches over the segments
marked with the + signs, and regulate the length of the tube so as to
reénforce the note given by the plate, and set the plate in vibration.
Now turn the tube around, so that one orifice may be over a + seg-
ment, and the other over a —segment; the sound due to resonance
entirely ceases. It thus appears that the two segments marked +
pass through the same phases together; likewise the phases of — seg-
ments correspond with one another; ie. when one + segment is
bent upward, the other is bent upward, and at the same time the two
—segments are bent downward; for, when the two orifices of the
tube are placed over two + segments or two — segments, two condensa-
tions followed by two rarefactions pass up these branches and unite
at their junction to produce a loud sound; but when one of the
orifices is over a + segment, and the other over a — segment, a con-
densation passes up one branch at the same time that a rarefaction
passes up the other, and the two destroy one another when they come
together; i.e. the two sound-waves combine to produce silence.
256. Bells.— A bell or goblet is sub-
ject to the same laws of vibration as a: |
plate. ,
Experiment 225.— Nearly fill a large goblet
with water, strew upon the surface lycopodium
powder, and draw a rosined bow gently across the
edge of the glass. The surface of the water will
become rippled with wavelets (Fig. 240) radiating
from four points 90° apart, corresponding to the
centers of four ventral segments into which the
goblet is divided, and the powder will collect in lines proceeding from
the nodal points of the bell. By touching the proper points of a
Fig. 240.
276 SOUND.
bell or glass with a finger-nail, it may be made to divide itself, like 4
plate, into 6, 8, 10, etc. (always an even number), vibrating parts..
Experiment 226.— Remove the brass plate (Fig. 239) from iis
support, and fasten the bell B (Fig. 241) on the support. Bow the
edge of the bell at some point, and
hold the open tube C in a horizon-
tal position with the center of one
of its walls near that point of the
edge of the bell which is opposite
the point bowed. The tube loudly
_ reénforces the sound of the bell.
Move the tube around the edge of
Fig. 241. the bell and find its nodes.
Thrust the plunger D into the open end E of the tube, and find
what part of the length of an open tube a closed tube should be to
reénforce a sound of a given pitch. —
257. Vocal Organs. —It is difficult to say which is
more to be admired,—the wonderful capabilities of the
human voice or the extreme sim-
plicity of the means by which it is
produced. The organ of the voice
is a reed instrument situated at the
top of the windpipe, or trachea. A
pair of elastic bands aa (Fig. 242),
called the vocal chords, is stretched
across the top of the windpipe. The
air-passage 6, between these chords,
is open while a person is breathing;
Fig. 242. but when he speaks or sings, they
are brought together so as to form a narrow, slit-like
opening, thus making a sort of double reed, which vibrates
when air is forced from the lungs through the narrow
passage, somewhat like the little tongue of a toy trum-
pet. The sounds are grave or high according to the
tension of the chords, which is regulated by muscular
SOME SOUND-WAVE RECEIVERS. 277
action. The cavities of the mouth and the nasal passages
form a compound resonance-tube. This tube adapts it-
self, by its varying width and length, to the pitch of the
note produced by the vocal chords. Place a finger on
the protuberance of the throat called “Adam’s apple,â€
and sing a low note; then sing a high note, and you will
observe that the protuberance rises in the latter case, thus
shortening the distance between the vocal chords and the
lips. Set a tuning-fork in vibration, open the mouth as if
about to sing the corresponding note, place the fork in
front of it, and the cavity of the mouth will resound to
the note of the fork, but will cease to do so when the
mouth adapts itself-to the production of some other note.
The different ‘qualities of the different vowel sounds are
produced by the varying forms of the resonating mouth-
cavity, the pitch of the fundamental tones given by the
vocal chords remaining the same. This constitutes artécu-
lation. .
Section XIII.
SOME SOUND-WAVE RECEIVERS.
258. The Phonograph.— Figure 243 represents the Edison
phonograph. A metallic cylinder A is rotated by means of a crank. On
the surface of the cylinder is cut a shallow helical groove running around
the cylinder from end to end, like the thread of a screw. A small metallic
point, or style, projecting from the under side of a thin metallic disk D
(Fig. 244), which closes one orifice of the mouth-piece B, stands directly
over the thread. By a simple device the cylinder, when the crank is
turned, is made to advance just rapidly enough to allow the groove to
keep constantly under the style. The cylinder is covered with tinfoil.
The cone F is usually applied to the mouth-piece to concentrate the sound-
waves upon the disk D,
278 SOUND.
Now, when a person directs his voice toward the mouth-piece, the aérial
waves cause the disk D to participate in every motion made by the parii-
cles of air as they beat against it, and the motion of the disk is communi-
ae
Ta
Ha
Fig. 243.
cated by the style to the tinfoil, producing thereon impressions or indenta-
tions as it passes on the rotating cylinder. The result is that there is left
upon the foil an exact representation in relief of every movement made by
the style. Some of the indentations are quite perceptible to the naked
eye, while others are visible only with
the aid of a microscope of high power.
Figure 245 represents a piece of the foil
as it would appear inverted after the in-
dentations (here greatly exaggerated)
have been imprinted upon it.
The words addressed to the phonograph having been thus impresscil
upon the foil, the mouth-piece and style are temporarily removed, while
the cylinder is brought back to the position it had
eee when the talking began, and. then the mouth-piece
is replaced. Now, evidently, if the crank is turned
Fig. 245. in the same direction as before, the style, resting
upon the foil beneath, will be made to -play up and down as it passes
over ridges and sinks into depressions; this will cause the disk D to
SOME SOUND-WAVE RECEIVERS. 279
reproduce the same vibratory movements that caused the ridges and
depressions in the foil. The vibrations of the disk are communicated
to the air, and through the air to the ear; thus the words spoken to the
apparatus may be, as it were, shaken out into the air again at any subse-
quent time, even centuries after, accompanied by the exact accents, into-
nations, and quality of sound of the original.
259. The Ear. — In Figure 246, A represents the external ear-passage;
ais a membrane, called the tympanum, stretched across the bottom of the
passage, and thus closing the orifice of a cavity b, called the drum, cisa
Fig. 246.
chain of small bones stretching across the drum, and connecting the
tympanum with the thin membranous wall of the vestibule e; ff are a
series of semicircular canals opening into the vestibule; g is the open-
ing into another canal in the form of a snail-shell g’, hence called the
cochlea (this is drawn on a reduced scale); d is a tube (the Eustachian
tube) connecting the drum with the throat; and A is the auditory nerve.
The vestibule and all the canals opening into it are filled with a trans-
parent liguid. The drum of the ear contains air, and the Eustachian tube
forms a means of ingress and egress for air through the throat.
Now how does the ear hear? and how is it able to distinguish between
the infinite variety of form, rapidity, and intensity of aérial sound-waves
280 SOUND.
so as to interpret correctly the corresponding quality, pitch, and loudness
‘of sound? Sound-waves enter the external ear-passage A as ocean-waves
enter the bays of the seacoast, are reflected inward, and strike the tym-
panum. The air-particles, beating against this drum-head, impress upon
it the precise wave-form that is transmitted to it through the air from the
sounding body. The motion received by the drum-head is transmitted
by the chain of bones to the membranous wall of the vestibule. From
the walls of the spiral passage of the cochlea project into its liquid con-
tents thousands of fine elastic threads or fibres, called “rods of Corti.â€
As the passage becomes smaller and smaller, these vibratile rods become
of gradually diminishing length and size (such as the wires of a piano
may roughly represent), and are therefore suited to respond sympatheti-
cally to a great variety of vibration-periods. This arrangement is some-
times likened to a “harp of three thousand strings†(this being about
the number of rods). The auditory nerve at this extremity is divided
into a large number of filaments, like a cord unravelled at its end, and
one of these filaments is attached to each rod. Now, as the sound-
waves reach the membranous wall of the vestibule, they set it, and by
means of it the liquid contents, into forced vibration, and so through the
liquid all the fibres receive an impulse. Those rods whose vibration
periods correspond with the periods of the constituents forming the com-
‘pound wave are thrown into sympathetic vibration. The rods stir the
“nerve filaments, and the nerve transmits to the brain the impressions re-
ceived. Just as a piano when its dampers are raised and a person sings
into it, may be said to analyze each sound-wave, and show by the vibrat-
ing strings of how many tones it is composed, as well as their respective
pitch, and by the amplitude of their vibrations their respective intensi-
ties ; so, it is thought, this wonderful harp of the ear analyzes every com-
plex sound-wave into a series of simple vibrations. Tidings of the dis-
turbances are communicated to the brain, and there, in some mysterious
manner, these disturbances are interpreted as sound of definite quality,
pitch, and intensity.
CHAPTER VIII.
RADIANT ENERGY, ETHER-WAVES,— LIGHT.
Section I.
INTRODUCTION.
260. Energy Received from the Sun. — Exposed to
the sun, the skin is warmed,—the sense of touch is
affected; it is illuminated, thereby the
sense of sight is affected; it is tanned, —
its chemical condition is changed. It is
evident that we receive something which
must come to us from the sun. To the
sense of touch it appears to be heat; in
the eye it produces the sensation of light;
in certain: substances it has the power to
produce chemical changes. What is it that
we receive from the sun?
Figure 247 represents an instrument
called a radiometer. The moving part is
a small vane resting on the point of a
needle. It is so nicely poised on this pivot —=
that it rotates with the greatest freedom. PAB Re 4:
To the extremities of each of the four arms of the vane
are attached disks of aluminum, which are white on one
side and black on the other. The whole is enclosed in a
glass bulb, and the air within is reduced to less than one-
millionth its usual density. If the instrument is exposed
=
282 RADIANT ENERGY.
to the sun the wheel will rotate with the white faces in
advance.
In just what manner it is caused to rotate does not con-
cern us at present; but the fact that it rotates, and that
it is caused to rotate directly or indirectly by something
that comes from the sun, is pertinent to the question be-
fore us. Whenever a body is caused to move or increase
its rate of motion, energy must be imparted to it; hence
energy must be imparted to the radiometer-vane by the sun.
That which we receive from the sun, whether it affects
the sense of touch or of sight, or produces chemical changes,
is in reality some form of energy and is one and the same
form whatever the effect.
261. Ether the Medium of Motion. —If we receive
the energy of motion, what moves? Our atmosphere is
but a thin mantle covering the earth, while the great space
that separates us from the sun contains no air or other
known substance. But empty space cannot communicate
motion. It is assumed —7t ts necessary to asswme — that
there is some medium filling the interplanetary space,
in fact, filling all space otherwise unoccupied, a medium
by which motion can be communicated from one point to
another. This medium has received the name of ether.
We cannot see, hear, feel, taste, smell, weigh, nor meas-
ure it. What evidence, then, have we that it exists?
This: phenomena occur just as they would occur 7 all
space were filled with an ethereal mecium capable of
transmitting motion; we have been able to account for
these phenomena on no other hypothesis, hence our belief
in the existence of the medium.
The transmission of energy through the medium of
ether is called radiation; energy so transmitted is called
UNDUL&TORY THEORY. 288
radiant energy, and the body emitting energy in this
manner is called a radiator.
262. Undulatory Theory; the Sensation of Light.
— All evidence points to one conclusion: that we receive
energy from the sun in the form of vibrations or waves ;
that a portion of these waves having suitable wave-length
are capable of causing through the eye the sensation of
light. Such as affect the sense of sight are called light-
waves. This is known as the undulatory theory. Accord-
ing to this theory light! is a sensation caused, usually, by
the action of ether-waves on the organ of sight. The term
light is commonly applied to the agent which produces the
sensation, but it is thought that in a scientific treatise
much may be gained in many ways by restricting the term
to the sensation, and applying to the agent the appropriate
term light-waves.
All ether-waves are Capable of generating heat and,
consequently, of causing the sensation of warmth. A
large portion of the ether-waves are also capable of pro-
moting chemical action in certain substances.
263. Sources of Light-waves, Incandescence and
Phosphorescence.— Every form of matter when suff-
ciently heated emits light-waves; in other words, when
the vibration period of its molecules becomes such as to
create ethereal waves that are capable of affecting the
sense of sight, the body is said to be luminous. This con-
dition is termed incandescence. ‘The sun and fixed stars
are in a condition of intense incandescence. Nearly all
the artificial sources of light-waves, such as lamp and gas
flames and electric lamps, depend upon the development
of light-waves mainly through the incandescence of carbon.
1 The optical sensations are Light, Color, and Lustre.’’ — Bain’s Mental Science.
/
284 RADIANT ENERGY.
There is a class of substances, such as the sulphides of
calcium, strontium, etc., which, after several hours’ expos-
ure to light-waves, absorb their
energy (de. their molecules ac-
quire sympathetic vibrations)
without becoming hot, and in
turn emit light-waves, which are
quite perceptible in a dark room
for several hours after the ex-
posure. This property of shining
in the dark after having been
exposed to light-waves is termed
phosphorescence. A so-called lumi-
nous paint is prepared and ap-
Fig. 248, plied to certain parts of bodies
that are exposed to sunshine during the day; at night
those parts to which the paint is applied are alone lumi-
nous. This paint may be used for a variety of purposes,
such as rendering luminous danger signals, door numbers
and plates (Fig. 248), etc.
264. Light-waves travel in Straight Lines. — The
path of light-waves admitted into a darkened room through
a small aperture, as indicated by the illuminated dust, is
perfectly straight. An object is seen by means of light-
waves which it sends to the eye. A small object placed in
a straight line between the eye and a luminous point
may intercept the light-waves in that path, and the point
become invisible. Hence we cannot see around a corner,
or through a bent tube.
265. Ray, Beam, Pencil. — Any line RR, Figure 249,
which pierces the surface of an ether-wave ab perpen-
RAY, BEAM, PENCIL. 285
dicularly is called a ray. The term “ray†is but an
eapression for the direction in which motion is propagated,
and along which the successive effects of ether-waves occur. *
If the wave-surface a/b’ is a plane,
the rays R/R’ are parallel, and a
collection of such rays is called a
beam. If the wave-surface a!’b!!
is spherical or concave, the rays
RR†have a common point at
the center of curvature; and a
collection of such rays is called
a pencil.
266. Transparent, Translu-
cent, and Opaque Bodies. —
Bodies are transparent, translu-
cent, or opaque, according’ to
’ the manner in which they act
upon the light-waves which pass
through them. Generally speak-
ing, those objects are transparent that allow other objects
to be seen through them distinctly, e.g. air, glass, and
water. Those objects are translucent that allow light-
waves to pass, but in such a scattered condition that
objects are not seen distinctly through them, e.g. fog,
ground glass, and oiled paper. Those objects are opaque
that apparently cut off all the light-waves and prevent
objects from being seen through them.
Fig. 249.
267. Luminous and Illuminated Objects. — Some
bodies are seen by means of light-waves which they emit,
eg. the sun, a candle flame, and a “live†coal; they are
called luminous bodies. Other bodies are seen only by
ts
286 RADIANT ENERGY.
means of light-waves which they receive from luminous
ones; and when thus rendered visible are said to be
illuminated, e.g. the moon, a
man, a cloud, and a “deadâ€
coal.
_Hvery point of a luminous
= body is an independent source of
light-waves, and emits light-waves
in every direction. Such a point
is called a luminous point. In
Figure 250 there are represented
a few of the infinite number of
pencils emitted by three lumi-
nous points of a candle flame. Every point of an illumi-
nated object, ab, receives light-waves from every luminous
point.
Fig. 250.
268. Images formed through Small Apertures.
’ Experiment 227.— Cut a hole about 4 inches square in one side of
a box; cover the hole with tin-foil, and prick a hole in the foil with a
pin. Place the box in a darkened room, and a candle flame in the box
near to the pin-hole. Hold an oiled-paper screen before the hole in
the foil; an inverted image of the candle flame will appear upon the
translucent paper.
An image is a kind of picture of an object. If light-
waves from objects illuminated by the sun, e.g. trees,
houses, clouds, or even an entire landscape, are allowed
to pass through a small aperture in a window shutter
and strike a white wall in a dark room, inverted im-
ages of the objects in their true colors will appear upon
it. The cause of these phenomena is easily understood.
When no screen intervenes between the candle and the
screen A, Figure 251, every point of the screen receives
SHADOWS. 287
light-waves from every point of the candle; consequently,
on every point on A, im-
ages of the infinite num-
ber of points of the candle
are formed. The result
of the confusion of images fF
is equivalent to no image.
But let the screen B, |
containing a small hole,
be interposed ; then, since ; Fig. 251.
light-waves travel only in straight lines, the point Y’
can only receive an image of the point Y, the point Z’
only of the point Z, and so for intermediate points;
hence a distinct image of the object must be formed on
the screen A.
That an image may be distinct, the rays from different
points of the object must not mix on the image, but all rays
from each point on the object must be carried to its own
point on the image.
269. Shadows.
Experiment 228. — Procure two pieces of tin or cardboard, one
18" square, the other 8° square. Place the first between a white
wall and a candle flame in a darkened room. The opaque tin inter-
cepts the light-waves that strike it, and thereby excludes light-waves
from a space behind it.
This space is called a shadow. That portion of the sur-
face of the wall that is darkened is a section of the shadow,
and represents the form of a section of the body that
intercepts the light-waves. A section of a shadow is fre-
quently for convenience called a shadow. Notice that the
shadow is made up of two distinct parts, —a dark center
bordered on all sides by a much lighter fringe. The
288 RADIANT ENERGY.
dark center is called the wmbra, and the lighter envelope
is called the penumbra.
Experiment 229.— Carry the tin nearer the wall, and notice that
the penumbra gradually disappears and the outline of the umbra be-
comes more distinct. Employ two candle flames, a little distance apart,
and notice that two shadows are produced. Move the tin toward the
wall, and the two shadows approach one another, then touch, and
finally overlap. Notice that where they overlap the shadow is deepest.
This part gets no light-waves from either flame, and is a section of
the umbra; while the remaining portion gets light-waves from one
or the other, and is a section of the penumbra. Or move the eye
across the shadow from side to side and see parts of the flame in the
penumbra, but none in the umbra.
Just so the umbra of every shadow is the part that gets no
light-waves from a luminous body, while the penumbra is
the part that gets light-waves from some portion of the body,
but not from the whole.
Experiment 230.— Repeat the above experiments, employing the
smaller piece of tin, and note all differences in phenomena that occur.
Hold a hair in the path of the sun’s waves, about a quarter of an inch
in front of a fly-leaf of this book, and observe the shadow cast by
the hair. Then gradually increase the distance between the hair
and the leaf, and note the change of phenomena.
If the source of light-waves were a single luminous point, as A (Fig.
252), the shadow of an opaque body B
would be of infinite length, and would
consist only of an umbra. But if the
source of light-waves has a sensible size,
Vig. 252. the opaque body will intercept just as
many separate pencils as there are luminous points, and consequently will
cast an equal number of independent shadows.
Let AB (Fig. 253) represent a luminous body, and CD an opaque body.
The pencil from the luminous point A will be intercepted between the
lines CF and DG, and the pencil from B will be intercepted between the
PHOTOMETRY, VISUAL ANGLE, ETC. 289
wave-lines CH and DF. Hence the light-waves will be wholly excluded only
from the space between the lines CF and DF, which enclose the umbra.
Fig. 253.
The enveloping penumbra, a section of which is included between the lines
CE and CF, and between DF and DG, receives light-waves from certain
points of the luminous body, but not from all.
- Section II.
PHOTOMETRY, VISUAL ANGLE, ETC.
270. Law of Inverse Squares.
Experiment 231. — Arrange apparatus as follows: Draw a straight
chalk-line across a table, and place at right angles to this line a row
of four lighted candles, and on the same line, at a distance, a single
lighted candle. Half-way between this candle and the row of candles
place a paper disk having a circular translucent spot in the center, as in
Figure 254. It is evident that one side of the paper receives four times
the radiant energy that the other does. Move the row of candles
290 RADIANT ENERGY.
slowly away from the paper, or move the single candle toward the
paper, until a point is found where the spot nearly disappears. The
paper now receives the same amount of energy from the single flame
as from the four flames, but
it will be found that the
row of flames is twice as
far from the paper as the
single flame.
Thus, by doubling
| Fig. 254. the distance,’ the in-
tensity of illumination is diminished fourfold. In a similar
manner it may be shown that at three times the distance
it takes nine flames to be equivalent to one flame. Hence,
the intensity of illumination diminishes as the square of the
distance increases. This is called the law of inverse squares.
Experiment 232. — Introduce the paper disk, as above, between
a candle flame and a kerosene or a gas flame, and so regulate the dis-
tance that the central spot will disappear; then calculate the relative
intensities of the flames in accordance with the law of inverse squares.
This is the method usually employed by gas inspectors
for testing the intensity of light-waves. Apparatus ar-
ranged for this purpose is called a photometer. “The
candle power, which is the unit of intensity generally em-
ployed in photometry, is the intensity of the flame of a
sperm candle weighing one-sixth of a pound, and burning
one hundred and twenty grains an hour.â€
The relative brightness of the common sources of light-
waves are approximately as follows: !—
Sun atitssurface. . . . . . { . . 190,000 candle power.
Most powerful electric are... . . 55,900 “ os
Incandescent calcium . ...'.. . 1,300 “ 3
Ordinary gas-burner. . .. .. . . 12t0o16 “ ss
Standard candle . ........ ces se
1C, A. Young.
PHOTOMETRY, VISUAL ANGLE, ETC. , 291
271. Visual Angle. ;
Experiment 233. — Prick a pin-hole in a card, place an eye near
the hole, and look at a piri about 20 distant. Then bring the pin
slowly toward the eye, and the dimensions of the pin will appear to
increase as the distance diminishes.
Why is this? We see an object by means of its image
formed on the retina of the eye; and its apparent magni-
tude is determined by the extent of the retina covered by
its image. Rays proceeding from opposite extremities of
an object, as AB (Fig. 255), meet and cross one another
Fig. 255.
in the window of the eye, called the pupil. Now, as the
distance between the points of the blades of a pair of
scissors depends upon the angle that the handles form
with one another, so the size of the image formed on the
retina depends upon the size of the angle, called the wswal
angle, formed by these rays as they enter the eye. But
the size of the visual angle diminishes as the distance of
the object from the eye increases, as shown in the dia-
gram; e.g. at twice the distance the angle is one-half as
great; at three times the distance the angle is one-third
as great; and so on. Hence, distance affects the apparent
size of an object. Our judgment of size is, however, influ-
enced by other things besides the visual angle which they
subtend,
292 RADIANT ENERGY.
272. Velocity of Light-Waves. — By several ingenious
methods it has been ascertained that light-waves travel at
the rate of about 186,000 miles in a second, a velocity
which would enable them to go around the earth about
seven times in a second. Sound-waves travel in air at the
rate of only about one-fifth of a mile per second. This
great difference can be accounted for only on the suppo-
sition that the rarity and elasticity of ether are enormously
greater than that of air.
Section ITI.
REFLECTION OF LIGHT-WAVES.
273. Law of Reflection.
Experiment 234.— Look through the hole in the metal band (Fig.
256), marked zero, at the mirror. You see in the mirror an image of
the hole through which you
are looking, but you do not
see the image of any of
the other holes. Rays that
pass through this hole strike
the mirror perpendicularly,
and are called incident rays.
The reflected rays are thrown back in the same line and through the
same hole that the incident rays travel to the eye.
Hold a candle flame at one of the other holes (or stop it with a fin-
ger), e.g. at the hole marked 10. You can see the reflected rays of the
candle flame only through the hole of the same number on the other
side, i.e. for example, incident rays making an angle of 10° (called the
angle of incidence) with the perpendicular to the surface of the mirror
is reflected at an angle of 10° (called the angle of reflection) with the
perpendicular. The angle of reflection is always equal to the angle of
incidence.
Fig. 256.
REFLECTION OF LIGHT-WAVES. 293
274. Reflection from Plane Mirrors; Virtual Im-
ages. —MM (Fig. 257) represents :
a plane mirror, and AB a pencil of
divergent rays proceeding from the
point A of an object AH. Erect-
ing perpendiculars at the points of
incidence, or the points where these
rays strike the mirror, and mak-
ing the angles of reflection equal
to the angles of incidence, the
paths BC and EC of the reflected
rays are found. Big. 25%.
It appears that divergent incident rays remain divergent
after reflection from a plane mirror. (In like manner con-
struct a diagram, and show that parallel incident rays are
parallel after reflection.) Construct another diagram, and
show that convergent incident rays are convergent after re-
flection, i.e. reflection from a plane surface does not alter
the angle between rays. To an eye placed at C, the points
from which the rays appear to come are of course in the
direction of the rays as they enter the eye. These points
may be found by continuing the rays CB and CE behind
the mirror, till they meet at the points D and N. Every
point of the object AH sends out its pencil of rays; and
those that strike the mirror at a suitable angle to be
reflected to the eye, produce on the retina of the eye an
image of that point, and the point from which the light-
waves appear to emanate is found, as previously described.
Thus, the pencils EC and BC appear to emanate from the
points N and D; and the whole body of light-waves re-
ceived by the eye seems to come from an apparent object
‘ND behind the mirror. This apparent object is called an
image; but as, of course, there can be no real image
294 RADIANT ENERGY.
formed there, it is called a virtual or an imaginary image.
It will be seen, by construction, that an image in a plane
mirror appears as far behind the mirror as the object is in
Sront of it, and is of the same size and shape as the object.
275. Reflection from Concave Mirrors. — Let MM!
(Fig. 258), represent a section of a concave mirror, which
may be regarded as a small part of a hollow -spherical
shell having a polished interior surface. The distance
MM’ is called the diameter of the mirror. C is the center
of the sphere, and is
called the center of
i curvature. G is the
vertex of the mirror.
A straight line DG
drawn through the
center of curvature
and the vertex is
MAGES: called the principal
avis of the mirror. A concave mirror may be considered
as made up of an infinite number of small plane surfaces.
All radii of the mirror, as CA, CG, and CB, are perpen-
dicular to the small planes which they strike. If C bea
luminous point, itis evident that all light-waves emanating
from this point, and striking the mirror, will be reflected
to its source at C.
Let E be any luminous point in front of a concave
mirror. To find the direction that rays emanating from
this point take after reflection, draw any two lines from
this point, as EA and EB, representing two of the infi-
nite number of rays composing the divergent pencil that
strikes the mirror. Next, draw radii to the points of inci-
dence A and B, and draw the lines AF and BF, making
REFLECTION OF LIGHT-WAVES. 295
the angles of reflection equal to the angles of incidence.
Place arrow-heads on the lines representing rays to indi-
cate the direction of the motion. The lines AF and BF
represent the direction of the rays after reflection.
It will be seen that the rays after reflection are con-
vergent, and meet at the point F, called the focus. This
point is the focus of all reflected rays that emanate from
the point E. It is obvious that if F were the luminous
point, the lines AE and BE would represent the reflected
rays, and E would be the focus of these rays. Since the
relation between the two points is such that light-waves
emanating from either one are brought by reflection to a
focus at the other, these points are called conjugate foci. Con-
jugate foct are two points so related that the image of either is
formed at the other. The rays EA and EB emanating from
E are less divergent than rays FA and FB, emanating from
a point F less distant from the mirror, and striking the
same points. Rays emanating from D, and striking the
same points A and B, will be still less divergent; and if
the point D were removed to a distance of many miles,
the rays incident.at these points would be very nearly
parallel. Hence rays may be regarded
as practically parallel when their source
is at a very great distance, e.g. the sun’s
rays. If a sunbeam, consisting of a
bundle of parallel rays, as EA, DG,
and HB (Fig. 259), strike a concave Fig. 259.
mirror parallel with its principal axis, these rays become
convergent by reflection, and meet at a point (F) in the
principal axis. This point, called the principal focus, is
just half-way between the center of curvature and the
vertex: of the mirror.
On the other hand, it is obvious that divergent rays
296 RADIANT ENERGY.
emanating from the principal focus of a concave mirror
become parallel by reflection.
If a small piece of paper is placed at the principal focus
of a concave mirror, and the mirror is exposed to the par-
allel rays of the sun, the paper will quickly burn.
Construct a diagram, and show that rays proceeding
from a point between the principal focus and the mirror
are divergent after reflection, but less divergent than the
incident rays. Reversing the direction of the rays the
same diagram will show that convergent rays are rendered
more convergent by reflection from concave mirrors.
The general effect of a concave mirror is to increase the
convergence or te
decrease the diver-
gence of inetdent
rays.
The statement, that
parallel rays after re-
flection from a concave
mirror meet at the prin-
cipal focus, is only ap-
proximately true. The
smaller the diameter of
the mirror, the more nearly true is the statement. It is strictly true only
of parabolic mirrors. Such are used in the head-lights of locomotives.
Fig. 260.
276. Formation of Images. ;
» Experiment 235.— Hold some object, e.g. a rose, as ab (Fig. 260),
a few feet in front of a concave mirror. Looking in the direction of
the axis of the mirror you see a small inverted image AB of the object
between the center of curvature, C, of the mirror and its principal
focus F. ,
Evidently if AB represent an object placed between the principal
focus and center of curvature, then ad will represent the image of the
object. ‘The image in this case may be projected upon a screen, but
it will not be so bright as in the former case, because the light-waves
are spread over a larger surface. “a a
REFLECTION OF LIGHT-WAVES. 297
Bxperiment 236.— Place a candle in an otherwise dark room 20
feet from the mirror, catch the focused light-waves upon a paper
screen, and show that the focus is half-way between the vertex and
the center of curvature of the mirror.
Bxzperiment 237.— Advance the distant candle flame toward the
mirror, moving it up and down. (1) Show that the focus advances to
meet the flame, and that when the flame is raised, the focus is depressed,
and the converse. (2) Show that when the flame is at the center of
curvature, there also is the focus. (3) Show that when the flame is be-
tween the center of curvature and the principal focus, the focus of the
flame is farther away than the center of curvature. (4) Show that
when the flame is at the principal focus, the reflected rays are parallel,
or the focus is at an infinite distance. (5) Show that when the flame is
still nearer, the reflected rays diverge and appear to come from a point
behind the mirror. (6) Notice that in all ogses except the ‘last: the im-
ages are real and inverted, and that in all cases where a real image is
formed, the flame and the image may change places.
Experiment 238.— Form a real image of the flame between your-
self and the mirror; view the :
image through a convex lens
(Fig. 280); show that the im-
age can be magnified by a
convex lens, and thereby illus-
trate the principle of an astro-
nomical reflecting telescope.
Construct the image of
an object placed. between Fig. 261.
the principal focus and the mirror, as in Figure 261. It
will be seen in this case that a pencil of rays proceeding
from any point of an object, e.g. D, has no actual focus,
but appears to proceed from a virtual focus D', back of the
mirror; and so with other points, as E. The image of an
object placed between the principal focus and the mirror is
virtual, erect, larger than the object, and ts back of the mirror.
277. Convex Mirrors. — The general effect of convex
mirrors is to separate incident rays. In them all images
are virtual, erect, and smaller than the objects. i
298 RADIANT ENERGY.
Section IV.
REFRACTION.
278. Introductory Experiments.
Experiment 239.— Into a darkened room admit a sunbeam so
that its rays may fall obliquely on the bottom of the basin (Fig. 262),
and note the place on the bottcm
where the edge of the shadow DE
cast by the side of the basin DC
meets the bottom at E. Then,
without moving the basin, fill it
even full with water slightly clouded
with milk or with a few drops of a
solution of mastic in alcohol. It
will be found that the edge of the
shadow has moved from DE to DÂ¥,
and meets the bottom at F. Beat
a blackboard rubber, and create a
loud of dust in the path of the beam in the air, and you will dis-
cover that the rays GD that graze the edge of the basin at D be-
come. bent at the point where they enter the water, and now move
in the bent line GDF, instead of, as formerly, in the straight line GE.
The path of the line in the water is now nearer to the vertical side DC;
in other words, this part of the beam is more nearly vertical than before.
Experiment 240.— Place a coin (A, Fig. 263) on the bottom of
an empty basin, so that, as you look firouen a small hole in a card
BC over the edge of the vessel, the coin is
just out of sight. Then, without moving the
card or basin, fill the latter with water. Now,
on looking through the aperture in the card,
the coin is visible. The beam AE, which
formerly moved in the straight line AD, is
now bent at E, where it leaves the water,
and, passing through the aperture in the card,
enters the eye. Observe that, as the beam Fig. 263.
passes from the water into the air, it is turned farther from a verti-
Fig. 262.
REFRACTION. 299
cal line EF; in other words, the beam is farther from the vertical than
before.
Experiment 241.— From the same position as in the last experi-
ment, direct the eye to the point G in the basin filled with water.
Reach your hand around the basin, and place your finger where that
point appears to. be. On examination, it will be found that your
finger is considerably above the bottom. Hence, the effect of the bend-
ing of rays, as they pass obliquely out of water, is to cause the botiom to
appear more elevated than it really is ; in other words, to cause the water
to appear swallower than it is.
Experiment 242.— Thrust a pencil obliquely into water; it will
appear shortened, bent at the surface of the water, and the immersed
portion elevated.
Experiment 243.—Place a piece of wire (Fig. 264) vertically in
front of the-eye, and hold a narrow strip of thick plate glass horizon-
tally across the wire, so that the light-waves from the wire
may pass obliquely through the glass to the eye. -The wire
will appear to be broken at the two edges of the glass, and
the intervening section will appear to the right or left accord-
ing to the inclination of the glass; but if the glass is not
inclined to the one side or the other, the wire does not
appear broken.
Experiment 244.— Partly fill the cell (Fig. 147) with carbon
bisulphide, then add water. Place the cell in the path of a beam re-
flected from a porte lumiére. Place vertically in front of the cell a
wire, and project with a lens a shadow of the wire on a screen. Turn
the cell obliquely, as in the last experiment, and notice the difference
‘in the refracting power of the two liquids.
Experiment 245.— Partly fill the same cell with water. Focus
it on the screen so that the surface.of the water will be visible. Add
a lump of ice on the water. Observe the streakiness caused by differ-
ence in the density of water at different temperatures.
Experiment 246.— Project with a lens a luminous Grete on a
‘screen. Hold, a few feet in front of the screen, a candle flame in the
path of the light-waves. Observe the wavy streakiness arising from
the eieneing density of the air and convection currents.
Fig. 264.
“When a light-beam passes from one medium into another
of different density, it is bent or refracted at the boundary
300 RADIANT ENERGY.
plane between the two media, unless it falls exactly per.
pendicularly on this plane. Jf i pass into a denser
medium, tt ts refracted toward a perpendicular to this plane ;
of into a rarer medium, it is refracted from the perpendicu-
lar. The — GDO (Fig. 262) is called the angle of in-
eidence; EDN, the angle of
refraction ; and EDF, the an-
gle of deviation.
279. Cause of Refraction.
— Careful experiments have proved that
the velocity of light-waves is less in a
dense than in a rare medium. Let the
series of parallel lines AB (Fig. 265)
represent a series of wave-fronts leav-
ing an object C, and passing through
a rectangular piece of glass DE, and
constituting a beam. Every point
in a wave-front moves with equal
Fig. 265. velocity as long as it traverses the
same medium; but the point a of a given wave ab enters the glass first,
and its velocity is impeded, while the point 6 retains its original velocity ;
so that, while the point a moves to a’, b moves to 3’, and the result is
that the wave-front assumes a new direction (very much in the same
manner as a line of soldiers execute a wheel), and a ray or a line drawn
perpendicularly through the series of waves is turned out of its original
direction on entering the glass. Again, the extremity ce of a given wave-
front cd first emerges from the glass, when its velocity is immediately
quickened; so that, while d advances to d!, c advances to c’!, and the
direction of the ray is again changed. The direction of the ray, after
emerging from the glass, is parallel to its direction before entering it, but
it has suffered a lateral displacement. Let C represent a section of the
wire used in Experiment 262, and the cause of the phenomenon observed
will be apparent. If the beam strike the glass perpendicularly, all points
of the wave will be checked at the same instant on entering the glass ;
consequently it will suffer no refraction. :
280. Index of Refraction. — The deviation of light-
waves, in passing from one medium to another, varies
with the medium and with. the angle of incidence. It
REFRACTION. 301
diminishes as the angle of incidence diminishes, and is
zero when the incident ray is normal (i.e. perpendicular
to the surface of the medi-
um). It is highly impor-
tant, knowing the angle
of incidence, to be able to
determine the direction
which a ray will take on
entering a new medium.
Describe a circle around
the point of incidence A
(Fig. 266) as a center;
through the same point
draw IH perpendicular to ae 208:
the surfaces of the two media, and to this line drop per-
pendiculars BD and CE from the points where the circle
cuts the ray in the two media. Then suppose that the
perpen BD is £, of the radius AB; now this frac-
tion 38 is called (cn trigonometry ) the sine of the angle
DAB. Hence, 8 is the sine. of the angle of incidence.
Again, if we suppose that the perpendicular CE is ~ of
the radius, then the fraction 5% is the sine of. the angle of
refhactacs The sines of the two angles are to on another
as 38: 38, or as 4:3. The quotient (in this case 4 =1.88-++)
obtained by dividing the sine of the angle of Se ised by
the sine of the angle of refraction is called the index of
refraction. It can be proved to be the ratio of the velocity
of the incident to that of the refracted light-waves. It is
found that for the same media the index of refraction is
a constant quantity ; i.e. the incident ray might be more
or less oblique, still the quotient would be the same.
281. Indices of Refraction. — The index of refraction for light-
waves in passing from air into water is approximately $, and from air into
302 RADIANT: ENERGY.
glass $; of course, if the order is reversed, the reciprocal of these frac-
tions must be taken as. the indices; eg. from water into air, the index is 3;
from glass into air, 2. When a ray passes from a vacuum into a medium,
the refractive index'is greater than unity, and is called the absolute index
of refraction. The relative index of refraction, from any medium A into another
B, is found by dividing the absolute index of B by the absolute index of A.
The refractive index varies with wave-length. The following: table is
intended to represent mean indices : —
TABLE OF ABSOLUTE INDICES. . ;
Air at 0° C., and ee apteasure - 1.000294 | Carbon bisulphide . .... . 1.641
1
- Purewater. .. . . 1.33 Crown glass (about). . . . . . 1.58
Alcohol . . . aes : my LST Flint glass (about) .. . . . . . 1é6i
Spirits of turpentine. . >. « 1.48 Diamond (about). . . .... 25
Humors of the eye (about) oe . 1,85 Lead chromate. ... . . .-. . 297
282. Critical Angle; Total Reflection. — Let SS’
(Fig. 267) represent the boundary surface between two
media, and AO and BO incident rays in the more refractive
medium (e.g. glass); then OD and OE may represent the
same rays. respectively after they enter the less refractive
=i = == = =
= |
= ==
= 4
a = A
= = =e = = == =
Fig. 267.
medium (e.g. air). It will be seen that, as the angle of
incidence is increased, the refracted ray rapidly approaches
the surface OS. Now, there must be an angle of incidence
(e.g. COM) such that the angle of refraction will be 90°;
REFRACTION. 3038
in this case the incident ray CO, after refraction, will just
graze the surface OS. This is called the eritical or limiting
angle. Any incident ray, as LO, making a larger angle
with the normal than the critical angle, cannot emerge from
the medium, and consequently is not refracted. Experi-
ment shows that all such rays undergo internal reflection ;
e.g. the ray LO is reflected in the direction ON. Reflec-
tion in this case is perfect, and hence is called total reflec-
tion. Total reflection occurs when rays in the more refractive
medium are incident at an angle greater than the critical angle.
Surfaces of transparent media, under these circumstances, constitute the
best mirrors possible. The critical angle diminishes as the refractive index
increases. For water it is about 483°; for flint glass, 38° 41’; and for the
diamond, 28° 41’. Light-waves cannot, therefore, pass out of water into
air with a greater angle of incidence than 483°. The brilliancy of gems,
particularly the.diamond, is due in part to their extraordinary power of
internal reflection, arising from their large indices of refraction.
283. Illustrations of Refraction and Total Reflection.
Experiment 247.— Observe the image of a candle flame reflected
by the surface of water in a glass beaker, as in Figure 268.
Bxperiment 248.— Thrust the closed end of a glass test-tube
(Fig. 269) into water, and incline the tube. Look down upon the
immersed part of the tube, and its upper surface will look like bur-
: d,
a
Sa
Fig. 268. Fig. 269.
nished silver, or as if the tube contained mercury. Fill the test-tube
with water, and immerse as before; the total reflection which before
occurred at the surface of the air in the submerged tube now disap-
pears. Explain.
804 RADIANT ENERGY.
Section V.
DOUBLE REFRACTION.
284. Double Refraction.
Experiment 249.— Through a card make a pin-hole, and hold
the card so that you may see the sky through
the hole. Now bring a crystal of Iceland spar
(Fig. 270) between the eye and the card, and
look at the hole through two parallel surfaces
of the crystal. There will appear to be two
holes, with light-waves passing through each.
‘ Cause the crystal to rotate in a plane parallel
with the card, and one of the holes will appear
to remain nearly at rest, while the other rotates
Fig. 270. - around the first. A ray na immediately on
entering the crystal is divided into two parts, one of which obeys the
regular law of refraction; the other does not. The former is called
the ordinary ray; the latter, the extr aordinary ray. The ray$i issue from
the crystal parallel with each other.
In every direction in which one looks through the crystal,
except that parallel to AB, objects seen through it appear
double. (See Figure 271.) The line AB is called the optic
Fig. 271.
axis of the crystal, and is a line around which the mole-
cules of the crystal appear to be arranged symmetrically.
A crystal is called wniaxial when it has only one optic axis,
PRISMS AND LENSES. 805
and biawial when it has two such axes. By far the larger
number of crystals of other substances possess the prop-
erty of causing objects seen through them to appear
double. This phenomenon is called double refraction.
Section VI.
PRISMS AND LENSES.
285. Optical Prisms. — An optical prism is a trans-
parent, wedge-shaped body. Figure 272 represents a
transverse section of such a prism. Let AB be a ray
incident upon one of its surfaces. On entering the prism
it is refracted toward the normal, and takes the direc-
tion BC. On emerging from the prism it is again re-
fracted, but now from the normal in the direction CD.
The object that emits the
ray will appear to be at F.
Observe that the ray AB,
at both refractions, is bent
toward the thicker part, or
base, of the prism.
Fig. 272.
286. Lenses. — Any fe!
parent medium bounded by two spherical cunldcce or by
one plane and the other curved, is a lens.
Experiment 250. — Procure a couple of lenses thicker in the mid-
dle than at the edge: strong spectacle glasses, or the large lenses in
an opera glass, will answer. Hold one of the lenses in the sun’s rays,
and notice the path of the beam in dusty air (made so by striking
together two blackboard rubbers), after it passes through the lens;
306 RADIANT ENERGY.
also, that on a paper screen all the rays may be brought to a small
cirele, or even to a point, not far from the lens. This point is called
the focus, and its distance from the lens, the focal length of the
lens.
Find the focal length of this lens, then of the second, and then of
the two together. You find the focal length of the two combined is
less than of either alone, and learn that the more powerful a lens or
combination of them is, the shorter the focal length; that is, the more
quickly are the parallel rays that enter different parts of the lens
brought to cross one another.
Experiment 251.— Procure a lens thinner in the middle than at
its edge. One of the small lenses or eye-glasses of an opera glass will
answer. Repeat the above experiment with this lens, and notice that
the rays emerging from the lens, instead of coming to a point, become
spread out.
Lenses are of two classes, converging and diverging,
according as they collect rays or cause them to diverge.
Hach class comprises three kinds (Fig. 273) : —
Cuass I. Cuass II.
( Diverging, or con-
2. Plano-convex lenses thicker in 4. Double-concave cave lenses thin-
38..Concavo-convex. the middle than at
(or meniscus) J the edges. _
5. Plano-concave
6. Convexo-concave ner in the middle
1. Double-convex (ene or convex
than at the edges.
A straight line, as AB, normal to both surfaces of a
lens, and jens through its center of curvature, is called
: =, its principal axis.
In every thin lens
there is a point in
the principal axis
called the optical
Fig. 273. center. Every ray
that passes through it has parallel directions at incidence
and emergence, #.¢. can suffer at most only a slight lateral
displacement. In lenses 1 and 4 it is half-way between
their respective curved surfaces. A ray, drawn through
PRISMS AND LENSES. 807
the optical’ center from any point of an object, as Aa
(Fig. 282), is called the secondary axis of this point.
287. Effect of Lenses. — We may, for convenience of
illustration, regard a convex lens as composed, approxi-
mately; of two prisms placed base to base, as A (Fig.
274), and a concave lens as composed of two prisms with
their edges in contact, as B. Inasmuch as a beam rat
natily strikes a lens in such a manner
that it is bent toward the thicker parts
or bases of these approximate prisms,
it is obvious that the lens A tends to
bend the transmitted rays toward one
another, while the lens B tends to
separate them. The general effect of all Fig. 274. -
convex lenses is to converge transmitted rays; that of con-
cave lenses,'to cause them to diverge. Incident rays parallel
with the principal axis of a convex lens are brought to
a focus F (Fig. 275)
at a point in the prin-
fe cipal axis. This point
Hj is called the: principal
_ focus, i.e. it is the focus
of incident - rays. par-
allel with the principal
: axis. It may be found
by holding the lens so that the rays of the sun may fall
pesnendreulan ly upon it, and then moving a sheet of paper
back and forth behind it until the image of the sun
formed on the paper is brightest and smallest. Or, in a
room, it may be found approximately, by holding a lens at
a considerable distance from a window, regulating. the.
distance so that a distinct image of the window will be
Fig. 2B
808 RADIANT ENERGY.
projected upon the opposite wall, as in Figure 276. Tho
focal length is the distance of the optical center of the lens
im y
‘ i
i
"
i
ull
re
|
to the center of the image on the paper. The shorter
this distance the greater is the power of the lens.
If the paper is kept at the principal focus for a short time,
it will take fire. The reason is apparent why convex lens-
es are sometimes
| called “burning
glasses.†A pencil
g of rays emitted
from the princi-
pal focus F (Fig.
275), as a lumi-
nous point, be-
Big. 277. comes parallel on
emerging from a convex lens. If the rays emanate from
a point nearer the lens, they diverge after egress, but the
divergence is less than before; if from a point beyond
the principal focus, the rays are rendered convergent. A
Fig. 276.
PRISMS AND LENSES. 309
concave lens causes parallel incident rays to diverge as
if they came from a point, as F (Fig. 277). This point is
therefore its pm Pale focus. It is, of course, a virtual
focus.
288. Conjugate Foci.— When a luminous point 8 (Fig.
278) sends
rays to a con-
vex lens, the
emergentrays
converge to
another point
S/; rays sent Fig. 278.
from 8! to the lens would converge to S. Two points
thus related are called conjugate foci. The fact that rays
which emanate from one point are caused by convex
lenses to collect at one point, gives rise v0 real images, as
in the case of concave mirrors.
Fig. 279.
289. Images Formed.— Fairly distinct images of objects
may be formed through very small apertures (page 287) ;
but owing to the small amount of radiant energy that passes
through the aperture, the images are very deficient in bril-
liancy. If the aperture is enlarged, brilliancy is increased
310- RADIANT ENERGY.
at the expense of distinctness. A convew lens enables us to
obtain both brilliancy and distinctness at the same time.
Experiment 252.—By means of a porte lumiére A (Fig. 279) in-
troduce a horizontal beam into a darkened room. In its path place
some object, as B, painted in transparent colors or
photographed on glass. (Transparent pictures are
cheaply prepared by photographers for sun-light and
lime-light projections.) Beyond the object place.a
convex lens L (such as represented in Figure 279), and
- beyond the lens a screen §. The object being illu-
minated by the beam, all the rays diverging from
any point a@ are bent by the lens so as to come to-
gether at the point a’. In like manner, all the rays
proceeding from c are brought to the same point c’;
and so also for all intermediate points. Thus; out of
the innumerable rays emanating from each of the in-
numerable points on the object, those that reach the lens are guided
by it, each to its own appropriate point in the image. It is evident
that there must result an image, both bright and distinct, provided the
screen is suitably placed, 7.c. at the place where the rays meet. But if
the screen is. placed at S’ or 8â€, it is evident that a blurred image
will be formed. Instead of moving the screen back and forth, in order
to “focus†the rays properly, it is customary to move the lens.
Fig. 280.
: Experiment 253.— Make a series of experiments similar to those
(Experiment 237). with the concave mirror. -Ascertain the focal length
of the convex lens. Place the lens a distance from a white wall about
equal to its-focal length. Place a candle flame (better the flame of
a fish-tail burner) at such a distance the other side of the lens that it
will produce a distinct and well-defined image on the wall (Fig. 281).
(1) Observe and note on paper the size and kind of image. Advance
the flame toward the lens, regulating at the same time the distance
between the lens and wall, so as to preserve a distinctness of image.
(2) Note the changes which the image undergoes. (8) When the
image and flame become of the same size, measure and note the dis-
tances of each from the lens. (4) Advance the flame still nearer,
and note the changes in the image, until it is impossible. to obtain an
image on the wall. Measure the distance of the flame from the lens,
and compare this distance with the focal length of the lens. (5) Move
PRISMS AND LENSES. 811
the flame still nearer. Note whether the rays, after emerging from
the lens, are divergent or convergent. (6) See whether an image and
: 0 na
Fig. 281.
an object may change places. (7) Form images of the flame on the
wall at different distances from the lens; measure the distances, also
the linear dimensions (e.g. the width, or the vertical hight) of the
images, and determine whether the linear dimensions of’ images are pro-
portional to their distances from the lens.
290. To Construct the Image Formed by a Convex
Lens, — Given : : a —_
the lens L (Fig.
282), whose prin-
cipal focus is at
F (or F’, for rays
coming from the
other direction), §
and object AB in
front of it; any
two of the many
rays from A will
determine where ,
its image a is formed. The two that can be traced easily are, the one
along the secondary axis AOa, and the one parallel to the principal
axis AA': the latter will be deviated so as to. pass through the principal
Fig. 282.
812 RADIANT ENERGY.
focus F, and will afterward intersect the principal axis at some point a;
so this is the conjugate focus of A; similarly for B, and all intermediate
points along the arrow. Thus, a zeal inverted image is formed at ab.
Fig. 283.
291. Virtual Images; Simple Microscope. — Since
rays that emanate from a point nearer the lens than the
principal focus diverge after egress, it is evident that their
focus must be virtual and on the same side of the lens as
the object. Hence, the image of an object placed nearer
the lens than the
principal focus
is virtual, mag-
nified, and erect,
as shown in
Figure 283. A
p convex lens
ss Fig, 284. Z used in this
manner is called a simple microscope.
Since the effect of concave lenses is to scatter transmitted
rays, pencils of rays emitted from A and B (Fig. 284),
after refraction, diverge as if they came from Aland B',
and the image will appear to be at A B’. Hence, images
formed by concave lenses are virtual, erect, and smaller than
the object,
PRISMS AND LENSES. 313
292. Spherical Aberration. —In all ordinary convex
lenses the curved surfaces are spherical, and the angles
which incident rays make with the little plane surfaces, of
which we may imagine the spherical surface to be made
Fig. 285.
up, increase rapidly toward the edge of the lens. Thus,
while those rays from a given point of an object, as A
(Fig. 285), which pass through the central portion, meet
approximately at the same point F, those which pass
through the marginal portion are deviated so much that
they cross the axis at nearer points, e.g. at F’; so a blurred
image results. This wandering of the rays from a single
focus is called spherical aberration. The evil may be
largely corrected by interposing a diaphragm DD’, pro-
vided with a central aperture, smaller than the lens, so
as to obstruct those rays that pass Ce the cet
part of the lens.
Experiment 254.— (Illustrating spherical aberration.) Cut a
cardboard disk as large as the convex lens (Fig. 280). Cut a ring of
holes near the circumference, and also a ring near the center. Sup-
port the disk close to the lens, so as to cover one of its surfaces.
Place: the whole in a beam from a porte lumiére. Catch refracted
beams on a screen. Move the screen away from the lens. The beams
through the outer ring of spots are the first to cross one another and
form animage. Further away, the inner beams coincide, forming an
image. The outer ones having crossed, form a ring of spots.
$14 RADIANT ENERGY.
Section VII.
PRISMATIC ANALYSIS OF LIGHT-WAVES. — SPECTRA.
293. Analysis of Light-Waves which Produce the
Sensation of White.
Experiment 255.— Place the disk with adjustable slit in the aper-
ture of a porte lumiére, so as to exclude all light-waves from a darkened
room except those which pass through the slit. Near the slit inter-
pose a double-convex lens of (say) 10-inch focus. A narrow sheet of
light will traverse the room and produce an image AB (Fig. 286) of
the slit on a white screen placed in its path. Now place a glass prism
C in the path of the narrow sheet of light-waves and near to the lens
with its edge vertical. (1) The light-waves now are not only turned
|
i
A
from their former path, but that which before was a narrow sheet, is,
after emerging trom the prism, spread out fan-like into a wedge-shaped
body, with its thickest part resting on the screen. (2) The image,
' before only a narrow, vertical band, is now drawn out into a long
PRISMATIC ANALYSIS OF LIGHT-WAVES. 815
horizontal ribbon, DE. (8) The image, before white, now presents all
the colors of the rainbow, from red at one end to violet at the other ;
it passes gradually through all the gradations of red, orange, yellow,
green, blue, and violet. (The difference in deviation between the red
and the violet is purposely much exaggerated in the figure.)
From this experiment we learn (1) that white waves (i.e.
those waves which are capable of producing the sensation
of white) are not simple in their composition, but the result
of a minature. (2) The color waves of which white waves are
composed may be separated by refraction. (8) The cause of
the separation is due to the different degrees of deviation
which they undergo by refraction. Red waves, which are
always least turned aside from a straight path, are the
least refrangible. Then follow orange, yellow, green, blue,
and violet in the order of their refrangibility. The many-
colored ribbon DE is called the solar spectrum. This
separation of white waves into their constituents is called
dispersion. The variety of color waves of which white
waves are composed is really infinite; but we name the
seven principal ones as follows: red, orange (or citron),
yellow, green, cyan-blue, ultramarine-blue, and violet; these
are called the prismatic colors. The names of the blues
are derived from the names of the plement which most
closely resemble them.
294. The Rainbow. — The rainbow is an illustration of a solar
spectrum on a grand scale. It is the result of refraction, reflection, and dis-
persion of sunlight by falling raindrops. Let spheres 1 and 2 (Fig. 287)
represent drops at the extreme opposite edges of the bow. The eye is ina
position to receive after the dispersion and internal reflection of the light-
waves within this drop, only the red waves; consequently this part of the
bow appears red. So, likewise, from drop 2, the eye receives only violet;
consequently this edge appears violet. In like manner, the intermediate
colors of the bow are sifted out.
Outside the primary bow a secondary bow (Fig. 288) is sometimes seen.
Drops 8 and 4 (Fig. 287) are supposed to be at the opposite edges of the
316 RADIANT ENERGY.
Fig. 287.
secondary bow. It will be seen that the light-waves undergo two internal
reflections within the drops which produce this bow. The colors of this
bow are in reverse order of those of the primary bow, and less brilliant.
Fig. 288.
295. Synthesis of White Waves.—The composition
of white waves has been ascertained by the process of anal-
ysis; can it be verified by synthesis? —7.e. can the colors
PRISMATIC ANALYSIS OF LIGHT-WAVES. 317
after dispersion be reunited? and, if so, will white be re-
stored ?
Experiment 256.— Place a second prism (2) in such a position
(AX7) that light-waves which have passed through one prism (1), and
been refracted and decomposed, may be refracted back, and the colors
will be reblended, and a white image of the slit will be restored on
the screen.
Experiment 257.— Place a large convex lens, or a concave mirror,
so as to receive the colors after dispersion by a prism, and bring the rays
to a focus on a’screen. The image produced will be white.
' 296. Cause of Color Revealed by Dispersion. — Color
is determined solely by the number of waves emitted by a
luminous body in a second of time, or by the corresponding
wave-length. In a dense medium, the short waves are more
retarded than the longer ones; hence they are more re-
Jracted. This is the cause of dispersion. The ether waves
diminish in length from the red to the violet. As pitch
depends on the number of aérial waves which strike the
ear in a second, so color depends on the number of ethereal
waves which strike the eye in a second.
- From-well-established data, determined by a variety of methods (see
larger works), physicists have calculated the number of waves that suc-
ceed one another for each of the several prismatic colors, and the corre-
sponding wave-lengths; the following table contains the results. The let-
ters A, C, D, etc., refer to Fraunhofer’s lines (see Plate I.).
Length of waves Number of waves
in millimeters. per second.
Dark red ......A........ .000760.......... 895,000,000,000,000
Orange........ Orsi shear .000656.......... 458,000,000,000,000
Yellow........ ID arncesreicte .000589.......... 510,000,000,000,000
_Green......... heey: 000527........4. 570,000,000,000,000
C@uBluess.<.0 7h eee 000486.......... 618,000,000,000,000
We Blues. 2: Gove. o 000481.......... 697,000,000,000,000
Violet......... yee hise ays .000897.......... 760,000,000,000,000
There is a limit to the sensibility of the eye as well as of the ear. The
limit in the number of vibrations appreciable by the eye lies approximately
318 _ RADIANT ENERGY.
within the range of numbers given in the above table; ic. if the succes.
sion of waves is much more or less rapid than indicated by these numbers,
they do not produce the sensation of sight.
297. Continuous Spectra. — All luminous solids and
liquids give continuous spectra. If the spectrum is not
. complete, as when the temperature is too low, it will begin
with red, and be continuous as far as it goes.
298. Spectroscope.— A small instrument called a pocket spectro-
scope + will answer for all experiments given in this book. More elaborate
experiments ‘require more elaborate apparatus, a description of which
must be sought for in larger works on this subject. This instrument con-
tains three or more prisms, A, B, and C (Fig. 289). The prisms are en-
closed in a brass tube D, and this tube’ in another tube E. F is a convex
lens, and G is an adjustable slit. By moving the inner tube back and
forth, the instrument may be so focused that parallel rays will fall upon
prism A. By varying the kind of glass used in the different prisms,? as
well as their structure, the deviation of light-waves from a straight path,
in passing through them, is overcome, while the dispersion is preserved.
On account of the directness of the path of light-waves through it, this
instrument is called a direct-vision spectroscope.
299. Bright Line, Absorption, or Reversed Spectra.
Experiment 258.— Open the slit about one-sixteenth of an inch
wide, by turning the milled ring M (Fig.
290), and look through the spectroscope at
the sky (not at the sun, for its light-waves
are too intense for the eye), and you will see
a continuous spectrum.
Fig. 290.
1It is expected that the pupil will be provided with a pocket spectroscope, the cost of
which need not exceed ten dollars.
2 A and C are crown-glass, and B is flint-glass,
PRISMATIC ANALYSIS OF LIGHT-WAVES. 819
Experiment 259.— Repeat the last experiment with a candle,
kerosene, or ordinary gas flame, and you will obtain similar results.
Experiment 260.— Take a piece of platinum wire 16 inches long.
Seal one end by fusion to a short glass tube for a handle. Bend the
wire at a right angle. Dip a portion of the wire into a strong solution
of common salt, and support it by a clamp in the midst of the almost
invisible and colorless flame of a Bunsen burner or
alcohol lamp (Fig. 291). Instantly the flame becomes
luminous and colored a deep yellow. Examine it with
a spectroscope, and you will find, instead of a continuous
spectrum beginning with red, only a bright, narrow
line of yellow, in the yellow part of the spectrum, next
the orange. Your spectrum consists essentially of a 4g
single bright yellow line on a comparatively dark
ground (see Sodium, Plate I., frontispiece).
Experiment 261.— Heat the platinum wire until it ceases to color
the flame, then dip it into a solution of chloride of lithium, and repeat
the last experiment. You obtain a carmine-tinted flame, and see
through the spectroscope a bright red line and a faint orange line
(see Lithium, Plate I.). : :
Experiment 262.— Use potassium hydrate, and you obtain a
violet-colored flame, and a spectrum consisting of a red line and a
violet line (the latter is very difficult to see even with the best instru-
ments). Use strontium nitrate, and obtain a crimson flame, and a
spectrum consisting of several lines in the red and the orange, and a
blue line (see Potassium and Strontium, Plate L.).
Experiment 263.— Use a mixture of several of the above chemi-
cals, and you will obtain a spectrum containing all the lines that char-
acterize the several substances.
Fig. 291.
Every chemical compound used in the above experiments
contains a different metal,,e.g. common salt contains the
metal sodium ; the other substances used successively con-
tain respectively the metals lithium, potassium, and stron-
tium. These metals, when introduced into the flame, are
vaporized, and we get their spectra when in a gaseous
state. All incandescent gases, unless under great pressure,
give discontinuous, or bright line, spectra, and no two gases
give the same spectra.
320 : RADIANT ENERGY.
300. Dark-line Spectra.
Experiment 264. — Close the slit of the spectroscope so that the
aperture will be very narrow; direct it once more to the sky, and
slowly move the inner tube back and forth, and you will find, with a
certain suitable adjustment which may be obtained by patient trial,
that the solar spectrum is not in reality continuous, but is crossed by
several dark lines (see Solar Spectrum, Plate I.).
Remark. — In general it is best to focus either the D line in the orange,
or the E line in the green. The inner sliding tube ought to be drawn out
a little when examining the blue end of the spectrum, and pushed in for
focusing the lines in the red.
Experiment 265.— Put a few copper turnings in a test-tube, add
a little nitric acid. Hold the tube causing the colored vapor before
the slit, and notice the black bands.
Experiment 266.— The electric light is now in so common use
that it may be possible to perform this experiment. Between the
electric light and the spectroscope introduce the flame of a Bunsen
burner, and color it yellow with salt. Examine the spectrum formed
through this yellow flame.
In the last experiment you would naturally expect to
find the yellow part of the spectrum uncommonly bright,
for there would apparently be added to the yellow waves
of the electric light the yellow waves of the salted flame.
But precisely where you would look for the brightest
yellow, there you discover that the spectrum is crossed
by a dark line. If you use salts of lithium, potassium,
and strontium in a similar manner, you will find in every
case your spectrum crossed by dark lines where you would
expect to find bright lines. Remove the Bunsen flame,
and the dark lines disappear. It thus appears that the
vapors of different substances absorb or quench the very
same waves that they are capable of emitting; very much,
it would seem, as a given tuning-fork selects from various
sound-waves only-those of a definite length corresponding
PRISMATIC ANALYSIS OF LIGHT-WAVES. 821
to its own vibration-period. The dark places of the spec-
trum are illuminated by the salted flame; but these places
are so feebly illuminated in comparison with those places
illuminated by the electric light, that the former appear
dark by contrast. Light-waves transmitted through cer-
tain liquids (as sulphate of quinine and blood) and certain
solids (as some colored glasses) produce dark-line spectra.
These spectra are obtained only when light-waves pass
through media capable of absorbing waves of certain
length; hence they are commonly called absorption spec-
- tra, Since a given vapor causes dark lines precisely where, ~
if it were itself the only radiator of light-waves, it would
cause bright lines, dark-line spectra are frequently called
reversed spectra. There are then three kinds of spectra:
continuous spectra, produced by luminous solids, liquids,
or, as has been found in a few instances, gases under great
pressure; bright-line spectra, produced by luminous vapors;
and absorption spectra, produced by light-waves that have
been sifted by certain media.
301. Spectrum Analysis. — More elaborate spectroscopes contain
many prisms, by which the purity of the spectrum is greatly increased.
(By purity is meant a freedom from the overlapping of images of the slit,
by which many lines of the spectrum are obscured.) They also contain an
illuminated scale which may be seen adjacent to the spectrum, by which the
exact position of the lines and their relative distances from one another
can be accurately determined, and a telescope by which the spectrum and
scale may be magnified. The positions of some of the prominent lines of
the solar spectrum were first determined, mapped, and distinguished from
one another by certain letters of the alphabet, by Fraunhofer; hence the
dark lines of the solar spectrum are commonly called Fraunhofer’s lines.
So far as discovered, no two substances have a spectrum consisting of the
same combination of lines; and, in general, different substances but very
rarely possess lines appearing to be common to both. Hence, when we have
once observed and mapped the spectrum of any substance, we may ever
after be able to recognize the presence of that substance when emitting
light-waves, whether it is in our laboratory or in a distant heavenly body.
322 RADIANT ENERGY.
The spectroscope, therefore, furnishes us a most efficient means of detect.
ing the presence (or absence) of any elementary substance, even when
it is combined or mixed with other substances. It is not necessary that
the given substance should exist in large quantities; for example, a
fourteen-millionth of a milligram of sodium can be detected by the spec-
troscope. .
302. Celestial Chemistry and Physics. — The spectrum of
iron has been mapped to the extent of 460 bright lines. The solar spec-
‘trum furnishes dark lines corresponding to nearly all these bright lines.
Can there be any doubt of the existence of iron in the sun? By exami-
nation of the reversed spectrum of the sun, we are able to determine
with certainty the existence there of sodium, calcium, copper, zinc,
magnesium, hydrogen, and many other known substances. The moon *
and other heavenly bodies that are visible only by reflected sunlight give
the same spectra as the sun, while those that are self-luminous give spectra
which differ from the solar spectrum.
303. Relative Heating and Chemical Effects of
Ether-Waves of Different Lengths. —If a sensitive thermome-
ter is placed in different parts of the solar spectrum, it will indicate heat in
all parts; but the heat generally increases from the violet toward the red.
It does not cease, however, with the limit of the visible spectrum; indeed,
if the prism is made of flint glass, the greatest heat is just beyond the red.
A strip of paper wet with a solution of chloride of silver suffers no change in
the dark; in the light-waves it quickly turns black; exposed to the light-
waves of the solar spectrum, it turns dark, but quite unevenly. The change
is slowest in the red, and constantly increases, till about the region indicated
by G (see Solar Spectrum, Plate I.), where it attains its maximum ; from
this point it falls off, and ceases at a point considerably beyond the limit of
the violet. It thus appears that the solar spectrum is not limited to the
visible spectrum, but extends beyond at each extremity. Those waves
that are beyond the red are usually called the infra-red waves, while those
that are beyond the violet are called the ultra-violet waves. The infra-red
waves are of longer vibration-period, and the ultra-violet of shorter period,
than the light-waves.
804. Only one Kind of Radiation. — It has been shown that
radiant energy may produce three distinct effects, according to the means
by which it is absorbed or the sense which it affects. But the radiant
energy producing these three and other effects is but one and the same
thing. The only difference in radiant energy is that which is common to
PRISMATIC ANALYSIS OF LIGHT-WAVES. 3238
ali wave-motion, viz. difference in wave-length and difference in amplitude,
the latter causing the wave to possess more energy as the amplitude is
greater. By a lamp-blacked surface nearly all the radiant energy of waves
of whatever length is absorbed and transformed into heat. By exposing
such a surface to spectra we learn that the longer waves possess more
energy than the shorter. On the other hand, most chemical mixtures which
are affected by sunlight are more sensitive to the shorter waves, 7.e. this
rate of vibration stimulates chemical action to a greater extent. But the
sense of sight is affected only by waves within the range already stated,
§ 297.
While waves traverse the ether there is neither heat nor light (7.e.
sensation) ; hence the propriety of applying either of these terms to a
. train of waves traversing the ether may well be called in question. Yet
this is all that traverses the space between the sun and the earth.
305. Chromatic Aberration. — There is a serious de-
fect in ordinary convex lenses, to which we have not before
alluded, called chromatic aberration, which has required
the highest skill to correct. The convex lens both re-
fracts and disperses the light-waves that pass through it.
The tendency, of course, is to bring the more refrangible
rays, as the violet, to a focus much sooner than the less
refrangible rays, such as the red. The result is a disagree-
able coloration of the images that are formed by the lens,
especially by that portion of the light-waves that passes
through the lens near its edges. This evil has been
overcome very effectually by combining with the
convex lens a plano-concave lens. Now, if a crown-
glass convex lens is taken, a flint-glass concave
lens may be prepared that will correct the disper-
sion of the former without neutralizing all its Fis-292.
refraction.! A compound lens, composed of these two
lenses (Fig. 292) cemented together, constitutes what is
called an achromatic lens.
1 The refractive and dispersive powers of the two lenses are not proportional.
824 RADIANT ENERGY.
Section VIII.
COLOR.
306. Color Preduced by Absorption. — “Color is a
sensation†[Alfred Daniell]. ‘All objects are black in °
the darkâ€; this is equivalent to saying that without light
waves there is no color. Is color due to some quality of an
object, or is it due to a quality of the light-waves which
illuminate the object?
Experiment 267.— We have found that common salt introduced
into a Bunsen flame renders it luminous, and that the light-waves, when
analyzed with a prism, is found to contain only yellow. Expose papers
or fabrics of various colors to these light-waves in a darkened room.
No one of them exhibits its natural color, except yellow.
Experiment 268.— Hold a narrow strip of red paper or ribbon in
the red portion of the solar spectrum; it appears red. Slowly move
it toward the other end of the spectrum; on leaving the red it be-
comes darker, and when it reaches the green it is quite black, or
colorless, and remains so as it passes the other colors of the spectrum.
Repeat the experiment, using other colors, and notice that only in
light-waves of its own color does each strip of paper appear of its
color; while in all other colors it is dark.
These experiments show that (1) color is due to a quality
of the light-waves which illuminate, and not of the object
illuminated, though by a conventionality of language we
ascribe colors to objects; (2) in order that an object may
appear of a certain color, it must receive light-waves of that
color; and of course if it receives other color waves at the
same time, it must be capable of absorbing or transmitting
them. The energy of the waves absorbed is converted into
heat; and warms the object. When white waves (7c. those
capable of producing the sensation of white) strike an
COLOR. 825
object, it appears white if it reflects all the color waves. If
red waves fall upon the same object, it appears red, for it
is capable of reflecting red waves; or it appears green, if
green waves alone fall on it. If white waves fall upon
an object, and all the color waves are absorbed except the
blue, the object appears blue. When we paint our houses
we do not apply color to them. We apply substances,
called pigments, that have a property of absorbing all the
color waves except those which we would have our houses
appear.
Experiment 269.— By means of a porte lumiére introduce a beam
into a dark room. Cover the orifice with a deep red (copper) glass.
The white waves, in passing through the glass, appear to be colored
red. Does the glass color the waves red?
Experiment 270.— With the slit, lens, and prism form a solar
spectrum,.and between the prism and screen interpose the red glass.
Very few light-waves, except the red, are transmitted; the rest are
absorbed by the glass.
It thus appears that a red transparent body is red because
it transmits few light-waves except the red, not because the
body colors the waves.
307. Sky Colors.
‘Experiment 271.— Dissolve a little white castile soap in a tum-
bler of water; or, better, stir into the water a few drops of an alcoholic
solution of mastic, enough to render the water slightly turbid. Place
a black screen behind the tumbler, and examine the liquid by reflected
sunlight, —the liquid appears to be blue. Examine the liquid by
transmitted sunlight, — it now appears yellowish red.
Sky-light is the result of reflected light-waves. The particles of atmos-
pheric dust (of water, probably) that pervade the atmosphere, like the fine
particles of mastic suspended in the water, reflect blue light-waves; while
beyond the atmosphere is a black background of darkness. But we must
not, from this, conclude that the atmosphere is blue; for, unlike blue
glass, but like the turbid liquid, it transmits yellow and red rays freely,
326 RADIANT ENERGY.
so that, seen by reflected light-waves, it is blue, but seen by transmitted
light-waves it is yellowish red.
Experiment 272.— Pour some of the turbid liquid into a small
test-tube, and examine it and the tumbler of liquid by transmitted
light-waves; the former appears almost colorless, while the latter is
quite deeply colored.
When the sun is near the horizon, its rays travel a greater distance in
the air to reach the earth than when it is in the zenith; consequently, there
isa greater loss by absorption and reflection in the former case than in the
latter. But the yellow and red rays suffer less destruction, proportionally,
than the other colors; consequently, these colors predominate in the morn-
ing and evening.
The remarkable “yellow days†of the summer of 1882 are explained in
this way. The atmosphere on this continent was remarkably turbid dur-
ing those days.
308. Mixing Colors. — A mixture of all the prismatic
colors, in the proportion found in sunlight, produces white.
Can white be produced in any other way?
Experiment 273.—On a black surface A (Fig. 293), about 2
inches apart, lay two small rectangular pieces of paper, one yellow
and the other blue. In a vertical position between,
and from 2 inches to 6 inches above, these papers,
hold a slip of plate glass C. Looking obliquely
down through the glass you may see the blue paper
by transmitted light-waves and the yellow paper
by reflection. That is, you see the object itself
in the former case, and the image of the object
in the latter case. By a little manipulation, the
image and the object may be made to overlap
one another, when both colors will apparently
a disappear, and in their place the color which is
Fig. 293. the result of the mixture will appear. In this
case it will be white, or, rather, gray, which is white of a low degree
of luminosity. If the color is yellowish, lower the glass; if bluish,
raise it.
Experiment .274.— With the rotating apparatus, rotate the disk
(Fig. 294) which contains only yellow and blue. The colors so blend
|
|
COLOR. 327
(i. the sensations) in the eye as to produce the sensation of Bray, ie.
white of low luminosity.
Fig. 294. Fig. 295. Fig. 296.
Figure 295 represents “ Newton’s disk,†which contains
the seven prismatic colors arranged in a proper proportion
to produce gray when rotated.
In like manner, you may produce white by mixing pur-
ple and green; or, if any color on the circumference of
the circle (see Complementary Colors, Plate I.) is mixed
with the color exactly opposite, the resulting color will be
white. Again, the three colors, red, green, and violet,
arranged as in Figure 296, with rather less surface of the
green’exposed than of the other colors, will give gray.
Green mixed with red, in varying proportions, will produce
any of the colors in a straight line between these two
colors in the diagram (Plate I.); green mixed with violet
will produce any of the colors between them; and violet
mixed with red gives purple.
All colors are represented in the spectrum, except the purple hues. The
latter form the connecting link between the two ends of the spectrum.
Our color chart (Plate I.) is intended to represent the sum total of all the
sensations of color. By means of this chart we may determine the result
of the (optical) mixture of any two colors as follows : Find the places
occupied upon the chart by the two colors which are to be mixed, and
unite the two points by a straight line. The color produced by the mix-
ture will invariably be found at the center of this line.
328 RADIANT ENERGY.
309. Mixing Pigments.
Experiment 275.— Mix a little of the two pigments, chrome
yellow and ultramarine blue, and you obtain a green pigment.
The last three experiments show that mixing certain
colors, and mixing pigments of the same name, may pro-
duce very different results. In the first experiments you
mixed colors; in the last experiment you did not mix
colors, and we must seek an explanation of the result ob-
tained. If a glass vessel with parallel sides containing
a blue solution of sulphate of copper is interposed in the
path of the light-waves which form a solar spectrum, it will
be found that the red, orange, and yellow waves are cut
out of the spectrum, 7.e. the liquid absorbs these waves.
And if a yellow solution of dichromate of potash is inter-
posed, the blue and violet waves will be absorbed. It
is evident that, if both solutions are interposed, all the
colors will be destroyed, except the green, which alone
will be transmitted; thus : —
Cancelled by the blue solution, K@YGBV.
Cancelled by the yellow solution, ROY G 3% M.
Cancelled by both solutions, KROYGRY.
In a similar manner, when white waves strike a mixture
of yellow and blue pigments on the palette, they penetrate
to some depth into the mixture; and, during its passage in
and out, all the colors are destroyed, except the green; so
the mixed pigments necessarily appear green. But when
a mixture of yellow and blue waves enters the eye, we get,
as the result of the combined sensations produced. by the
two colors, the sensation of white; hence a mixture of
yellow and blue gives white. .
The color square 3 (Plate I.) represents the result of the mixture of
pigments 1 and 2; while 4 represents the result of the optical mixture of
the same colors. :
COLOR. 829
310. Complementary Colors.
Experiment 276.— On a piece of white, or better, gray, paper, lay
a circular piece of blue paper 15™™ in diameter. Attach one end of a
piece of thread to the colored paper, and hold the other end in the
hand. Place the eyes within about 15â„¢ of the colored paper, and
look steadily at the center of the paper for about fifteen seconds;
then, without moving the eyes, suddenly pull the colored paper away,
and instantly there will appear on the gray paper an image of the
colored paper, but the image will appear to be yellow. This is
usually called an after-image. If yellow paper is used, the color of the
after-image will be blue; and if any other color given in the diagram
(Plate I.), the color of its after-image will be the color that stands
opposite to it.
This phenomenon is explained as follows: When we
look steadily at blue for a time, the eyes become fatigued
by this color, and less susceptible to its influence, while
they are fully susceptible to the influence of other colors;
so that when they are suddenly brought to look at white,
which is a compound of yellow and blue, they receive a
vivid impression from the former, and a feeble impression
from the latter; hence the predominant sensation is yellow.
Any two colors which together produce white are said to
be complementary to each other. The opposite colors in
the diagram (Plate I.) are complementary to one another.
311. Effect of Constrast. — When any two colors given in the
circle (Plate I.) are brought in contrast, as when they are placed next one
another, the effect is to move them farther apart. For example, if red
and orange are brought in contrast, the orange assumes more of a yellowish
hue, and the red more of a purplish hue. Colors that are already as far
apart as possible, e.g. yellow and blue, do not change their hue, but merely
cause one another to appear more brilliant.
312. Color Produced by Interference.
Experiment 277.—In a vise or other convenient instrument,
press two clean pieces of thick plate glass firmly together. A number
of colors will be seen arranged in a certain order, and forming curves
more or less regular around the point of pressure.
3380 RADIANT ENERGY.
This, together with many other kindred color phenomena, is caused
by the mutual destruction by interference of certain of the colors which
compose white, the resulting colors being the product of the combination
of those which are not so extinguished. Much as certain over-tones might
destroy one another, and the quality of the resulting sound would be deter-
mined by the composition of the surviving tones.
Thin, transparent films of varying thickness, such as the film of a soap
bubble, are well suited to show the effects of interference of light-waves.
Some of the light-waves which strike the anterior surface of the film are
reflected; another portion enters the film, and is reflected from the pos-
terior surface; but, by travelling twice through the film, the waves lose
ground, so that, on emergence, their phases may-or may not correspond
with the phases of the former portion: this will depend evidently upon the
thickness of the film at a given point, and the length of the waves striking
that point. In this manner the phenomena obtained in the experiment are
explained; the film in this case is the layer of air between the two surfaces
of glass.
Colors are produced by reflection from the surfaces of thin transparent
films of all kinds; for example, the colors of the soap bubble, of oil on
water, of the thin coating of metallic oxide formed in tempering steel,
Section IX.
THERMAL EFFECTS OF RADIATION.
$183. Diathermancy and Athermancy.
Experiment 278.— Prepare a differential
thermometer with two glass flasks and a glass
tube, as represented in Figure 297. Cover one
of the flasks with lamp-black by holding it
above a smoking kerosene flame. Place colored
liquid in the bend A. Stopper both vessels
tightly and expose the apparatus to the direct
rays of the sun. . The rays pass through the
clean glass and through the air within, affecting
the temperature of either but little. But the
lamp-black absorbs the radiations, the flask be-
THERMAL EFFECTS OF RADIATION. 331
comes heated, the enclosed air becomes heated by contact with the
heated flask, the heated air expands and pushes the liquid in the
tube toward the cooler flask.
What becomes of radiations that strike a body depends
largely upon the character of the body. If the nature of
the body is such that its molecules can accept the motion of
the ether, the undulations of ether are said to be absorbed
by the body, and the body is thereby heated; that is, the
radiant energy is transformed into heat energy. A good
illustration of this is the experiment with blackened glass.
On the other hand, the unblackened glass allows the radi-
ations to pass freely through it, and very little is trans-
formed into heat. Notice how cold window-glass may
remain, while radiations pour through it and heat objects
within the room. It must be constantly borne in mind
that only those radiations that a body absorbs heat tt ; those
that pass through it do not affect its temperature. Bodies
that transmit radiant energy freely are said to be diather-
manous, while those that absorb it largely are called ather-
manous. The most diathermanous solid is rock salt.
Among the most athermanous solids are lamp-black and
alum. Carbon bisulphide, among liquids, is exceptionally
transparent to all forms of radiation ; while water, trans-
parent to short waves, absorbs the longer waves, and is
thus quite athermanous.
Dry air is almost perfectly diathermanous. All of the sun’s radiations
that reach the earth pass through a layer of air from fifty to two hundred
miles in depth, which contains a vast amount of aqueous vapor. This
vapor, like water, is comparatively opaque to long waves; hence it modi-
fies very much the character of the radiations which reach the earth. This
fact enables us to understand the method by which our atmosphere becomes
heated. First, a very considerable portion of the radiant energy which
_ comes to us from the sun, in the form of relatively long waves, is stopped
by the watery vapor in the air, which is, in consequence, heated. Most of
8382 RADIANT ENERGY.
that which escapes this absorption heats the earth by falling upon it. The
warmed earth loses its heat, — partly by conduction to the air, still more
largely by radiation outward. The form of radiation, however, has been
greatly changed; for now, coming from a body at a low temperature, it is
chiefly in long waves that the energy is transmitted; while, as we have
seen, it was largely in the form of short waves that the earth received its
heat. But it is exactly these long waves which are most readily stopped
by the atmosphere; hence the atmosphere, or rather the aqueous vapor of
the atmosphere, acts as a sort of trap for the energy which comes to us
from the sun. Remove the watery vapor (which serves as a ‘‘ blanketâ€
to the earth) from our atmosphere, and the chill resulting from the rapid
escape of heat by radiation would put an end to all animal and vegetable
life. Glass does not screen us from the sun’s radiations, but it can very
effectually screen us from the radiations from a stove or any other terres-
trial object. Glass is diathermanous to the sun’s radiations (simply because
they have already lost most of the very long waves by atmospheric absorp-
tion), but quite athermanous to other radiations. This is well illustrated
in the case of hot-beds and green-houses. The sun’s radiations pass through
the glass of these enclosures, almost unobstructed, and heats the earth ;
but the radiations given out in turn by the earth are such as cannot pass
out through the glass; hence the heat is retained within the enclosures.
314. All Bodies Radiate Heat. — Hot bodies usually
part with their heat much more rapidly by radiation than
by all other processes combined. But cold bodies, like
ice, radiate heat even when surrounded by warm bodies.
This must be so from the nature of the case, for the mole-
cules of the coldest bodies possess some motion, and, being
surrounded by ether, they cannot move without imparting
some of their motion to the ether, and to that extent be-
come themselves colder.
815. Theory of Exchanges. — Let us suppose that we
have two bodies, A and B, at different temperatures, A
warmer than B. Radiation takes place not only from A
to B, but from B to A; but, in consequence of A’s excess
of temperature, more radiant energy passes from A to
B than from B to A, and this continues until both bodies
SOME OPTICAL INSTRUMENTS. 333
acquire the same temperature. At this point radiation by
no means.ceases, but each now gives as much as it receives,
and thus equilibrium is kept up. This is known as the
“Theory of Exchanges.â€
816. Good Absorbers, Good Radiators.
Experiment 279.— Select two small tin boxes of equal capacity ;
one should be bright outside, while the other should be’covered thinly —
with soot from acandle-flame. Cuta hole in the cover of each box
large enough to admit the bulb of a thermometer. Fill both boxes
with hot water, and introduce into each a thermometer. They will
register the same temperature at first. Set both in a cool place, and
in half an hour you will find that the thermometer in the blackened
box registers several degrees lower than the other. Then fill both
with cold water, and set them in front of a fire or in the sunshine, and
it will be found that the temperature in the blackened box rises faster.
As bodies differ widely in their absorbing power, so they
do in their radiating power, and it is found to be univer-
sally true that good absorbers are good radiators, and bad ©
absorbers are bad radiators. Much, in both cases, depends
upon the character of the surface as well as the substance.
Bright, polished surfaces are poor absorbers and poor
radiators; while tarnished, dark, and roughened ‘surfaces
absorb and radiate heat rapidly. Dark clothing absorbs
radiations and radiates more rapidly than light clothing.
Section X.
SOME OPTICAL INSTRUMENTS.
$17. Compound Microscope. — The stmple microscope
was described on page 312. When it is desired to magnify
an: object more than can be done conveniently and with
334 RADIANT ENERGY.
distinctness by a single lens, two convex lenses are used,
— one (O, Fig. 298) called the object-glass, to form a mag-
nified real image A’B! of the object AB; and the other
(E) called the eye-glass, to magnify this image so that the
image A’B’ appears of the size A//Bâ€â€™.
Fig. 298.
Hence the compound microscope is virtually a simple
microscope applied not to the object, but to its image
already magnified by the object lens. Both lenses should be
Or achromatic and aplanatic (free from
spherical aberration).
The eye-piece is made of two or more
lenses, because it is found that if the
_ refractions are thus distributed, the ex-
E rp’ tent of the useful field may be greatly
increased. Ordinarily two lenses are
a 3 sufficient.
The article to be examined is placed
on a glass stage, ab (Fig. 299), and, if
the object is transparent, it is strongly
TENT im@ illuminated by focusing light upon it by
Fig. 299. means of a concave mirror, P. [If the
ol
SOME OPTICAL INSTRUMENTS. 335
object is opaque, it is illuminated by light-waves converged
upon it obliquely from above by a convex lens not shown
in the figure.
Fig. 300.
318. Astronomical Telescope. — The astronomical re-
fracting telescope consists essentially, like the compound
microscope, of two lenses. The object-glass (O, Fig. 800)
forms a real diminished image ab of the object AB; this
image, seen through the eye-glass E, appears magnified and
of the size cd. The object-glass is of large diameter, in
order to concentrate as much as possible the radiations from
a distant object for a better illumination of the image.
Fig. 301.
319. Photographer’s Camera.— The photographer's
camera or camera obscura, of which AB (Fig. 301) repre-
sents a vertical section, consists of a dark box painted
black on the interior. A screen of ground glass S forms
a partition in the box. A sliding tube T contains a con-
836 RADIANT ENERGY.
vex lens L. If an object D is placed some distance in
front, and the distance of the lens from the screen is suit-
ably adjusted, a distinct, real, and inverted image can be
seen upon the screen by looking through the aperture C.
When the image is properly focused, the photographer re-
places the ground-glass plate by a sensitized plate, and the
chemical power of the sun’s rays imprints a true picture
of the object on this plate.
320. The Human Eye. — Figure 302 represents a horizontal
section of this wonderful organ. Covering the front of the eye, like a
watch-crystal, is a transparent coat
1, called the cornea. A tough mem-
brane 2, of which the cornea is a con-
tinuation, forms the outer wall of the
eye, and is called the sclerotic coat, or
‘cwhite of the eye.†This coat is
lined on the interior with a delicate
membrane 8, called the choroid coat;
the latter contains a black pigment,
which prevents internal reflection.
The inmost coat 4, called the retina,
is formed by expansion of the optic
nerve O. The muscular tissue 7 is
Fig. 302. called the tris; its color determines
the so-called ‘color of the eye.†In the center of the iris is a circular
opening 5, called the pupil, whose function is to regulate, by involuntary
enlargement and contraction, the quantity of light-waves admitted to
the anterior chamber of the eye. Just back of the iris is a tough, elastic,
and transparent body 6, called the crystalline lens. This lens divides the eye
into two chambers; the anterior chamber 7 is filled with a limpid liquid,
called the aqueous humor ; the posterior chamber 8 is filled with a jelly-like
substance, called the vitreous humor.
Experiment 280.— Make a model of an eye. Fill an 8-ounce
flask with clear water (eye-ball). Cover one side with black paper
having a round hole in it (iris and pupil). Place a slightly convex
lens in front of the hole (cornea and crystalline lens combined; the
latter outside the eye-ball instead of inside). Place a candle flame
in front of the hole (object); catch (inverted) image of the flame
SOME OPTICAL INSTRUMENTS. 3837
on a paper screen (retina) behind the flask. Move the candle a little
way from the flask; the image becomes indistinct. Restore it by in-
terposing another convex lens (cure of long sight). Bring the candle
near to the flask till the image is indistinct. Interpose concave lens
to restore the clearness (cure of short sight).
Experiment 281.— Make two dots on paper two inches apart.
Close the left eye, and bring the right one over the left spot. Ata
distance of about six inches the right spot becomes invisible. As you
bring the paper nearer, the eye turns to regard the left spot, the image
of the right spot meantime travels noseward over the retina, until it
reaches a spot, called the blind spot, on the retina, which is not sensitive
to the action of light-waves. This spot is where the optic nerve enters
the eye.
The eye is a camera obscura, in which the retina serves
as a screen. Images of outside objects are projected by
means of the crystalline lens, assisted by the refractive
_ powers of the humors, upon this screen, and the impres-
sions thereby made on this delicate network of nerve fila-
ments are conveyed by the optic nerve to the brain. If
the two outer coatings are removed from the back part of
the eye of an ox recently killed, so as to render it some-
what transparent, true images of whole landscapes may be
seen formed upon the retina of the eye, when it is held in
front of your eye. With the ordinary camera, the distance
of the lens from the screen must be regulated to adapt
itself to the varying distances of outside objects, in order
that the images may be properly focused on the screen. In
the eye this is accomplished by changing the convexity of
the lens. We can almost instantly and involuntarily
change the lens of the eye, so as to form on the retina a
distinct image of an object miles away or only a few inches
distant. The nearest limit at which an object can be
placed, and form a distinct image on the retina, is about
five inches. On the other hand, the normal eye in a pas-
sive state is adjusted for objects at an infinite distance.
838 RADIANT ENERGY.
Curiously enough, the retina, on careful examination, is
found to be composed in part of little elements in its back
portion, which have received, from their appearance, the
names of vods and cones. It is thought that these rods
and cones receive and respond to the vibrations of ether;
in other words, that they co-vibrate with the undulations
of the ether, and thereby we get our sensation of light.
321. Stereopticon.— This instrument is extensively
employed in the lecture-room for producing on a screen
magnified images of small, transparent pictures on glass.
Fig. 303.
called slides; also for rendering a certain class of experi-
ments visible to a large audience by projecting them on a
screen. The lime light is most commonly used, though
the electric light is preferred for a certain class of pro-
jections. The flame of an oxyhydrogen blow-pipe A
(Fig. 803) is directed against a stick of lime B, and raises
it to a white heat. The radiations from the lime are
condensed, by means of a convex lens ¢, called the con-
densing lens (usually two plano-convex lenses are used),
so that a larger quantity of radiations will pass through the
convex lens E, called the projecting lens. The latter lens
produces (or projects) a real, inverted, and magnified
image of the picture on the screen S. The mounted lens
SOME OPTICAL INSTRUMENTS. 339
KE may be slid back and forth on the bar F, so as properly
to focus the image. (For useful information relating to
the operation of projection, see Dolbear’s Art of Projec-
tion.)
EXERCISES,
1. What is light ?
2. State points of resemblance and points of diftarenes between
light-waves and sound-waves. Which can traverse a vacuum (as re-
gards matter) ?
8. Two books are held, respectively, 2 feet and 7 feet from the same
gas-flame. Compare the intensities of the illumination of their respec-
tive pages.
4, What is the general effect of a concave mirror on light-waves ?
What kind of lens produces a similar effect ?
: How can a beam be bent?
. State different ways by which he colors which compose white
= may be revealed.
7. How do you account for the color of flowers? -How do you
account for the colors seen on a soap-bubble ?
8. Why do white surfaces appear gray at twilight?
9. How are objects heated by the sun?
10. What evidences can you give that the earth receives energy
from the sun?
APPENDIX:
Millimeters. Centimeters.
A cube of water, one of whose sides is this area,
is a cubic decimeter or a liter of water, and at the
temperature of 4° C. weighs a kilogram. The
same volume of air at 0° C., and under a pressure
of one atmosphere, weighs 1.293 grams. The
The area of this figure is a square decimeter. |
gram is the weight of lee of pure water at 4° C. |
Square Inch.
Square i i
Centimeter} i
342
APPENDIX.
SHCTION A.
Metric system of measures. — The term metric is derived from
the word meter, which is the name of the fundamental unit employed
in this system for measuring length, and from which ‘all other units
of the system are derived. The meter is, approximately, the ten-
millionth part of the distance from the Equator to the North Pole.
Defined by law, it is the distance at 0° C. between two lines engraved
on a platinum bar kept in the Paris Observatory. The gram is theo-
retically the mass of lee of distilled water at 4°C. By law itis ayy
of the mass of a piece of platinum preserved in the same observatory.
At Washington are kept exact copies of the meter and other metric
measures.
The following tables contain all the requirements of this book. The
pupil will find more complete tables in any good arithmetic.
TABLE OF LENGTHS.
10 millimeters (™™) = 1 centimeter (°™).
10 centimeters = 1 decimeter (4).
10 decimeters = 1 meter (â„¢).
1000 meters = 1 kilometer (*â„¢).
TABLE OF AREAS.
100 square millimeters (#â„¢) = 1 square centimeter (@â„¢).
100 square centimeters = 1 square decimeter (9%).
100 square decimeters = 1 square meter (4â„¢).
1,000,000 square meters = 1 square kilometer (9*â„¢),
844 . APPENDIX.
TABLE OF VOLUMES.
1000 cubic millimeters (™™) = 1 cubic centimeter (C™or°).
1000 cubic centimeters = 1 cubic decimeter (¢4™),
1000 cubic decimeters = 1 cubic meter (©).
The volumes of liquids and gases are either expressed in the units
of the above table or in liters. The:liter is 1¢¢, or 1000¢.
TABLE OF MASSES OR WEIGHTS.
10 milligrams (™8) = 1 centigram (¢).
10 centigrams =.1 decigram (48).
10 decigrams = 1 gram (8). :
1000 grams = 1 kilogram or kilo (*).
TABLE OF EQUIVALENTS.
1 inch = 0.0254 meter, or about 21 centimeters.
1 foot = 0.3048 meter, or about 30 centimeters.
lyard= 0.9144 meter, or about 12 meter.
1 mile = 1609.0000 meters, or about 1,8, kilometers.
0.946 liter, alittle less
ae liquid = 2
1U.S.4 4 ry quart = or teers: more tian 1 liter.
1U.S. gallon = 3.785 liters, or about 3,8, liters.
2835 kilo, less
14 They and , ounce =4 993110 kilo, OP Pather{ ore
Troy and apdthecaries
than 30 grams.
1 avoirdupois pound = 0.45359 kilo, or about 3; kilo.
When great accuracy is not required, it will be found convenient to
remember that
centimeters x # = inches (nearly) ;
inches X $ =centimeters (nearly);
5 meters =1rod (nearly);
also, kilos x 44 = pounds (nearly) ;
pounds X= kilos (nearly).
APPENDIX. 345
SECTION B.
TABLES OF SPECIFIC GRAVITIES OF BODIES.
[The standard employed in the tables of solids and liquids is distilled water at 4° C.]
I. Solids.
Antimony......0.+.--+: 6.712 | Diamond .............. 3.530
Bismuth .....-+..ee- ... 9.822 | Glass, flint............ 3.400
Brass .....cccccccssccee 8.380 | Human body........... ~ 0.890
Copper, cast ........... SEED: | aitcrooogsgnaopadossane 0.920
Tridium.........0..0005 23.000 | Quartz ........:..ceee ee 2.650
Tron, cast........+--+6- 7.210 |- Rock salt .............. 2.257
Iron, bar ......0..-e00. 7.780 | Saltpetre............--- 1.900.
Gol deiisaractowriersterecisis 19.360 | Sulphur, native ........ 2.033
» Tuead, cast.........2000 11.850 | Tallow........-..-ee0e, 0.942
Platinum ...........265 QO O69: Wak a2
Silver, cast ............ 10-4705 |S COorki cece coe cece so cies 0.240
Tin, cast ...0...---00... 7-290 | Pime..........ee-eeeeee 0.650
AN CMCASt a ciejeclsicreicis/alers 65860 > Oak sencccecsiccesecees 0.845
Anthracite coal........ 1,800 | Beech ......-.eeeeeeees 0.852
Bituminous coal........ 1.250 | Ebony...cccccseseeeees 1.187
Ik. Liquids.
Alcohol, absolute...... 0.800 | Nitric acid............. 1.420
Bisulphide of carbon.... 1.293 | Oil of turpentine ....... 0.870
Mithetacsareesseces cee 0.723 | Olive oil........... cee 0.915
Hydrochloric acid...... 1.240 | Sea water...... Melero rst eietst 1.026
Mercury ... ....-..-.- . 18.598 | Sulphuric acid.......... 1.841
Ndi Pespaccaanondansonees 1.032 | Water, 4°C., distilled... 1.000
Naphtha ............... 0.847 | Water, 0°C., distilled... 0.999
III. Gases.
[Standard : air at 0°C.; barometer, 76°™.]
PANT rareeearets sist locusts 1.0000 | Hydrogen........e.eees 0.0693
AMMONIA ...- seer eee eee 0.5867 | Nitrogen ...........+..- 0.9714
Carbonic acid .......... 1.5290 | Oxygen........ceeeeee 1.1057
Chlorine ............... 3.4400 |. Sulphuretted hydrogen.. 1.1912
Hydrochloric acid ...... 1.2540 | Sulphurous acid..... ore 2.2474
APPENDIX.
‘SECTION C.
TABLE OF NATURAL TANGENTS.
—______.,
Deg. |\Tangent.|| Deg. | Tangent. | Deg. Tangent. || Deg. Tangent. |
od 017 24 . 445 47 1.07 70 2.75
2) 0385 ¢ 25 466: 48 1.11 71 2.90
38 -052 26 488 49 1.15 72 38.08
4- -070 27 -510 50 1.19 73 3.27
B:| .087 28 532 51 1.238 74 38.49
6° -105 29 554 52 1.28 15 3.78
7 123 30 577 53 1.33 76 4.01
8° 141 31 -601 54 1.38 17 4.33
9° -158 82 -625 55 1.48 78 4.70
10° -176 33 -649 56 1.48 79 5.14
Il 194 84 -675 57 1.54 80 5.67
12 -213 85 -700 58 1.60 81 6.31
13 -2381 36 727 | 59 1.66 82 7.12
14 249 37 «154 60 1.73 83 8.14
“15 -268 388 - -781 61 1.80 84 9.51
16 -287 39 -810 62 1.88 85 | 11.48
17: 806 40 +839 63 1.96 86 14.30
18 825 41 -869 64 2.05 87. 19.08
19. B44 42 -900 65 2.14 88 28.64
20 864 43 933 66 2.25 89 57.29
‘21 884 | 44 -966 67 2.36 90 |. Infinite. |
22 404 45 1.000 68 2.48
424 69 2.61
APPENDIX, 347
SECTION D.
REFERENCE TABLE OF RELATIVE RESISTANCES, ETC.
Rel. Resist. K,
Silverss:sscch eset ee @W2Ohcasscogascsacdens TOO RFs <5 9.15
Copper ......2. cece eeee Oe oe oRoiis crore ares TOG wereioiss 9.72
Ali cose cosoeaoe OOD UOO SBME bavareletei sieisesiare relevent © 8.74 2.00. 34.2
Pe LaGinuU Mee erste icles es ccruitstolersieloreveyevarstherieis ets 6.02 55.1
MP OM eer eee eis ers . We poue Ob Do OBO DDOUS 6.46) seer 59.1
German silver......... Ce alah etna ey tore hae te UGeO lees 127.3
Mercury .......65 eee ace ee elevoicresiodsiefsiccesers (oi ore 63.24 ..... 578.6
Rel. Resist.
Nitric Acid — commercial....@ 15° to 28° C..........06 ,. 1,100,000
Sulphuric Acid, 1 to 12 parts water ‘6 oo... cee cece eee eee 2,000,000
Common salt — saturated sol. eta Rosier tists exe espucveloetor ais 8,200,000
Sulphate Copper og : la orate Pareteyaslateisiar 18,000,000
Distilled waters 5.0 cere ce cee sec cece sc not less than 10,000,000,000
(GUnehicauucs paces aunceaacn (@22002. Ce eee ee 15,000,000,000,000
Gutta percha, ........---+---- @ 0° C...5,000,000,000,000,000,000,000
INDEX.
(NUMBERS REFER TO PaGEs.]
A.
Aberration, Chromatic, 323.
Spherical, 313.
Action and reaction, 14.
Adhesion, 25.
Air-pump, 41.
Sprengel, 43.
Amalgamating battery zincs, 162.
Ampere, The, 172.
Ampéere’s rule, 158.
Ampere-volt, The, 172.
Atmosphere, 29.
- Atmospheric pressure, measurement
of, 38.
B.
Barometer, mercurial, 34.
Aneroid, 35.
Batteries of different kinds, 164.
of high resistance, 186.
of low resistance, 186.
Batteries, Storage, 209.
Battery, what constitutes a voltaic, 185.
Beats in music, 261.
Boyle’s or Mariotte’s law, 40.
Buoyant force of fluids, 56.
Cc.
Calorie, The, 141.
Camera, Photographer's, 335.
Capillary phenomena, 27.
Celestial chemistry and physics, 322.
Center of gravity defined, 82.
of gravity, how found, 83.
Centrifugal and centripetal forces, 92.
Cohesion, 20.
Cold, Methods of producing, artificially,
144. :
Color, Cause of, revealed by dispersion,
317.
produced by absorption, 324,
produced by interference, 329.
Colors, Complementary, 329.
Effect of contrast, 329.
Effect of mixing, 326.
Sky, 325.
Component forces, 72.
Composition of parallel forces, 75.
Compressibility of gases, 38.
Condenser, Air, 44. .
Conduction of heat, 125.
Convection in gases, 126.
in liquids, 129.
Coulomb, The, 171, 172.
Couple, Mechanical, 78.
Critical angle, 302.
Crystallization, 20.
Crystals, 21.
Curvilinear motion, 92.
Currents, Attraction and repulsion be-
tween, 192.
Extra, 202.
Induced, 200, 202.
Laws of, 198, 194.
Laws of induced, 202.
Thermo-electric, 222.
D.
Density, 8, 59.
Specific, 60.
‘Dew-point, 140.
Diathermancy and athermancy, 330.
Discord in music, 262.
Distillation, 188.
Divided circuits, 184.
Dynamo as an electric motor, 208.
Uses of, 208.
350 INDEX.
Dynamo-electric machine, 205, Equilibrium, 13.
Dynamometers, 13.
Dyne, The, 106.
Ductility, 25,
Ear, The, 279.
Elasticity, 24.
of gases, 38.
Electrical measurements, 171.
Electric battery defined, 157.
Electrification, 226.
confined to the external surface, 235.
Two kinds of, 229.
Electric condenser, 234.
current, chemical effects of, 166.
current, heating and luminous effects |
of, 166.
current, magnetic effects of, 170.
current, physiological effects of, 169.
current, direction of, 157.
discharge, 231.
energy, how it originates, 137.
induction, 230.
insulation, 232,
machine, 282.
motor, 204.
Electricity, Conductors and non-con-
ductors of, 157,
Static, 225.
Two states of, 227,
Electro-chemical series, 161,
Electrolysis, 167.
Electro-motive force, 159.
force of different batteries, 182.
Electrophorus, 233.,
Electroplating and _ electrotyping,
214, 215. :
Electroscope, 226.
Energy, 5.
Distinction between force and, 102.
Formulas for calculating kinetic, 103,
107.
Kinetic and potential, 100.
received from the sun, 281.
Transformation, correlation, and con-
servation of, 147.
Unit of, 101.
Equilibrant, 77.
of moments, 77.
Three states of, 84.
Erg, The, 106.
Ether, a medium of motion, 282.
Ether-waves, Heating and chemical
effects of, 322.
Evaporation, 189.
Expansion, Abnormal, 132.
of solids, liquids, and gases, 130.
Eye, The human, 336.
E.
Falling bodies, laws of, 89.
bodies, velocity of, independent of
mass, 90.
Flexibility, 24.
Foot-pound, 101.
Fluids, 9.
Force, 11, 14.
Centripetal and centrifugal, 92.
Effect of a constant, 86.
graphically represented, 70.
how measured, 12.
Moment of, 77.
Forces, Composition of, 72.
Equilibrant of, 77.
Resolution of, 78.
Resultant of, 72.
G,
Galvanometer, 174.
Tangent, 175.
with astatic needle, 175.
Galvanoscope, 158.
Geissler tube, 203.
Gramme-dynamo, 205.
Gravitation and gravity, 15.
Law of universal, 16.
H.
Hardening and annealing, 23,
Hardness, 22.
Heat, Artificial sources of, 122.
generated by solidification and lique
faction, 148.
Latent, 142.
Mechanical equivalent of, 148,
Theory of, 121.
INDEX.
Heat, The sun as a source of, 123.
unit, 141.
Holtz machine, 160.
Horse-power, 105.
Hydrometers, 62.
I.
Images, 286.
formed by lenses, 309.
formed through apertures, 286.
Virtual, 293.
Impenetrability, 2.
Incandescence, 283.
Induction coil, Ruhmkorff’s, 202.
Induced currents, characteristics of,
204,
Inertia, 70.
J.
Joule’s equivalent, 148.
experiment, 147.
K.
Kinetic energy, 100.
L.
Lamp, Brush, 212.
Electric, 211.
Incandescent electric, 213,
Latent heat, 142.
Lenses, 305.
Achromatic, 323.
Effects of, 307."
Leyden jar, 234.
Light defined, 288.
Electric, 210.
Lightning, 236.
rods, 236.
Light-waves, Reflection of, 292.
Sources of, 283.
Velocity of, 292.
Liquefaction, 186.
Locomotive, The, 152.
Luminous and illuminated objects, 285.
M.
Machines, General law of, 111.
Uses of, 108, 110.
Magnet, Ampére’s theory of, 195.
351
Magnets, Coercive force of, 191.
Forms of artificial, 192.
Law of, 190. :
Polarity of, 191.
Magnetic equator, 198,
field, 196.
force, lines of, 196.
needle, dip of, 198.
needle, variation of, 198.
poles of the earth, 197.
transparency and induction, 190.
Malleability, 25.
Manipulation, 2.
Manometric flames, 268.
Mass, defined, 7.
Matter, Theory of its constitution, 7%
What is it, 1.
Microphone, The, 221.
Microscope, Compound, 333.
Simple, 312.
Minuteness of particles of matter, 6.
Mirrors, concave, 294.
convex, 297.
plane, 293.
Mixing colors, effects of, 326.
“pigments, effects of, 328.
Molar forces, 19.
Molecular forces, 18, 19.
Moment of a force, 77.
Momentum, 67.
its relation to force, 67.
Motion, First Law of, 69.
Graphical representation of, 70.
Relative, 10.
Second Law of, 71.
Third Law of, 80.
Musical instruments, 270.
scale, 259.
Nodes, 240.
Ohm, 174, 178.
Chim’s law, 182.
Overtones and harmonics, 262.
P.
Pendulum, Laws of, 95.
Phonograph, The, 277.
352
Phosphorescence, 283.
Photometry, 289.
Physies defined, 1.
Pitch, Musical, 259.
Polarization of electric elements, 164,
Pores and porosity, 7.
Potential, Electric, 159.
Press, Hydrostatic, 50.
Pressure, Atmospheric, 29.
in fluids, 29, 51.
transmitted by fluids, 47.
Prisms, Optical, 305.
Pump, Air, 41.
Force, 46.
Lifting or suction, 44.
Pump, Sprengel, 43.
Q.
Quality of sound, 265.
R.
Radiant energy, 281.
Radiation, 129.
Only one kind of, 322.
Thermal effects of, 330.
Radiometer, 281.
Rainbow, The, 315. :
Ray, beam, and pencil defined, 284.
Reflection, Total, 302.
Refraction, 298.
Cause of, 300,
Double, 304.
Index of, 300, 301.
Relay and repeater, 217.
’ Resistance measured by substitution,
179.
of battery, 178,
of electric conductors, 176,
Resonators, 253.
Rheostat, Description of, 178.
8.
Shadows, 287.
Shunts, 184.
Siphon, 54.
Sonometer, 260.
Sound, Analysis of, 265,
defined, 247,
INDEX.
Sound, Intensity of, 251.
Quality of, 265.
Synthesis of, 266.
Sounding-plates and bells, 273-275.
Sound-vibrations, Method of repre.
senting graphically, 267.
Sound-waves, How they originate, 244.
How they travel, 245,
Measuring length and velocity of, 255-
Media for transmitting, 247.
Reénforcement and interference of,
258, 256,
Reflection of, 249.
Velocity of, 248.
Speaking-tubes, 252.
Specific gravity and specific density, 59.
Formulas for, 60.
Spectra, 314,
Bright-line, 318.
Dark-line, 320.
Continuous, 318.
Spectrum analysis, 321.
Stability of a body, on what it depends,
85.
Steam-engine, Compound, 152.
Condensing and non-condensing, 151.
Description of simple, 149.
Stereopticon, 338.
Storage batteries, 209.
Surface of a liquid at rest is level, 53.
Synthesis of white waves, 316.
T.
Telescope, Astronomical, 335,
Telegraph, The, 216.
Telephone, The Bell, 218.
Temperature, defined, 124.
distinguished from quantity of heat,
124.
Temperatures, Standard, 133.
Tenacity, 20.
Tension, 26.
Theory of exchanges, 332.
Thermo-dynamics defined, 147.
Thermo-electric batteries and ther.
mopiles, 224,
currents, 222.
series, 224,
Thermometer, Construction of, 183.
Graduation of, 183. :
INDEX. 353
Thermometry, 133. Viscosity, 24.
Three states of matter, 9. Visual angle, 291.
Transformation of electric energy,
208.
of electric energy into heat, 189.
of heat energy into electric energy,
222.
of mechanical energy into electric po-
tential energy, 225,
Transparency, translucency, and
opacity, 285.
U.
Undulatory theory of radiation, 283.
Unit of heat, 141,
of intensity of a magnetic field, 173.
of magnetic pole, 173.
Units, Absolute, 106.
C.G.8. magnetic and electro-magnetic,
173.
Fundamental and derived, 106.
Vv.
Vaporization, 186.
Ventilation, 128.
Vibration of strings, 260.
Period of, 238.
Vibrations forced and sympathetic,
257.
Graphical method of studying, 243.
Propagation of, 289,
Stationary, 240,
Vocal organs, 276.
Volt, The, 172.
Voltaic are, 210.
cells, best arrangement of, 187.
cells connected in opposition, 185,
cells, methods of combining, 185.
Volume, 7.
Waitt, 172.
Waves, 239.
Amplitude of, 289.
how propagated, 243,
Interference of, 239.
Length of, 239.
Longitudinal and transverse, 241, 242.
Reflection of, 239.
Wave-motion, Air as a medium of,
242,
Weight, 16.
Point of maximum, 17.
Welding, 20.
Wheatstone bridge, 180.
Work, 98.
Formula for estimating, 99.
Rate of doing, 104.
Unit of, 101.
wasted, 103.
100 NATURAL SCIENCE.
Introduction to Physical Science.
By A. P. Gace, Instructor in Physics in the English High School, Bos-
ton, Mass., and author of Elements of Physics, etc. 12mo. Cloth.
viii+ 353 pages. With a color chart of spectra, etc. Mailing price,
$1.10; for introduction, $1.00.
HE constantly increasing popularity of Gage’s Elements of
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Recent advances in physics have been faithfully recorded, and
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NATURAL SCIENCE.
101
ing and coating; and, while teaching the facts, to impart the spirit
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Physics, University of Texas: Icon-
sider that the principal features of
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Physical Laboratory Manual and Note Book.
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a
102 NATURAL SCIENCE.
4 .
A Students’ Manual of a Laboratory Course in
i eo ete ae
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S. P. Langley, Sec. Smithsonian Institution, Wash., D.C., and Pres. National
Academy of Sctences : “1 know no better book (not to say as good a one) for its pur-
pose on the subject.â€
YOUNG’S ELEMENTS OF ASTRONOMY. A Text-book for Use in High Schools and
Academies, with a Uranography. By Cuartes A. Youne, author of ‘ Young's
General Astronomy,†“ The Sun,†etc. $1.40. Uranography. From “ Young’s
Elements of Astronomy.†-30 cents.
S. H. Brackett, Teacher of Mathematics, St. Fohusbury Acadenty, Vie: “Tt
is just what I expected it would be, the very best which I have ever seen.â€
YOUNG’S LESSONS IN ASTRONOMY. Including Uranography. By Cuaries A.
Younc, author of “ A General Astronomy,†“Elements of Astronomy,†etc.
Prepared for schools that desire a brief course free from mathematics. $ x.20.
AN INTRODUCTION TO SPHERICAL AND PRACTICAL ASTRONOMY. By
Dascom GREENE, Prof. of Mathematics and Astronomy in the Rensselaer Poly~
technic Institute, Troy, N.Y $1.50. :
Davis Garber, Prof of Astronomy, Muhlenberg College: “Students pursuing
astronomy on a practical line will find it a very excellent and useful book.â€
ELEMENTS OF STRUCTURAL AND SYSTEMATIC BOTANY. For High
Schools and Elementary College Courses. By Doucras HoucuTon CAMPBELL,
Ph.D., Prof. of Botany in the Indiana University. $1.12.
Charles W. Dodge, Teacher of Botany, High School, Detrott, Mich.: “It is the
only English work at all satisfactory for high-school students.â€
BLAISDELL’S PHYSIOLOGIES: Our Bodies and How We Live, 65 cents; How
to Keep Well, 45 cents; Child’s Book of Health, 30 cents.
True, scientific, interesting, teachable. ‘
ELEMENTARY METEOROLOGY. By Witt1am M. Davis, Prof. of Physical Geogra-
phy in Harvard University. With maps, charts, and exercises. $2.50.
Copies will be sent, post paid, to teachers for examination on receipt of the introduc
tion prices given above.
GINN & COMPANY, Publishers.
Boston. New York. Cuicaco. Lonpon.
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