l U D
A. P. GAGE, PH.D.,
I4&TRPCrIOR i PHYSIOs, ENGLISH HIGH SCHOOL, BOSTON, AND
AUTHOR OF "ELEMENTS OF PHYsICS."
GINN & COMPANY, PUBLISHERS.
Entered according to Act of Congress, in the year 1887, by
A. P. GAGE,
in the Office of the Librarian of Congress, at Washington.
TYPoRAPrHY BY J. S. CusHING & Co., BOSTON.
PRESSWORK BY GINN & CO., BOSTON.
AN experience of about six years in requiring individual
laboratory work frgm 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
A brief statement of my method 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-
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. V
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. I am 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.
SMatter, energy, motion, and force.- Attraction of gravitation.-
Molecular and molar forces . . ... 1
SDynamics of fluids. -Pressure in fluids. --Barometers. -Com-
pressibility and elasticity of gases. -Buoyancy of fluids.-
Density and specific gravity . . ... 29
SGeneral dynamics. Momentum, and its relation to force. Three
3 laws of motion. -Composition and resolution of forces.-
Center of gravity. Falling bodies. Curvilinear motion. -
S The pendulum .... . . . 67
J Work and energy. Absolute system of measurements. Ma-
: chines. .. .. ............ 98
Molecular energy, heat. -Sources of heat. -Temperature. -
Effects of heat. Thermometry. Convertibility of heat. -
Thermo-dynamics. Steam-engine ... .. . 121
Electricity and magnetism. -Potential and electro-motive force.
-Batteries. -Effects produced by electric current. -Elec-
trical measurements. -Resistance of conductors. C.G.S.
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 . ... 154
Sound. Study of vibrations and waves. Sound-waves, veloc-
ity of; reflection of; intensity of; reinforcement of; inter-
ference of. -Pitch. Vibration of strings. Overtones and
harmonics. Quality. Composition of sonorous vibrations.
Musical instruments. -Phonograph. -Ear. . 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. . ... 281
APPENDIX: A, metric system; B, table of specific gravity; C,
table of natural tangents; D, table of specific resistances 341
INDEX . . . . 349
INTRODUCTION TO PHYSICAL SCIENCE.
-' Nature is the Art of God." THoMAs BROWNE.
MATTER, ENERGY, MOTION, AND FORCE.
MATTER AND ENERGY.
10. ItHE TEACHER:--That portion of this book which is printed in the
lr,'q.,' Iyf. 1, including the experiments, is intended to constitute in itself a tolerably
t1;'/ 1,ri *'..rplete working course in Physics. The portion in fine print may,
tireflore. lie wholly omitted without serious detriment; or parts of it may
ibe tiudicd at discretion as time may permit; or, perhaps still better, it
mady he u.ed by the student, in connection with works of other authors,
-,b.l-i.ary reading. It should be borne in mind that recitations from
iui ii,.ry o:f mere descriptive Physics and Chemistry is of little educational
To iHF PUPI,:- "Read nature in the language of experiment";
tht is, p lt your questions, when possible, to nature rather than to per-
;a:,i.-. Teachers and books may guide you as to the best methods of
'pr;ocrdure. but your own hands, eyes, and intellect must acquire the
klrno l.: d ge directly from nature, if you would really know.
S1. Matter.-Physics including Chemistry, may for the
,present purposes at least be regarded as the science of mat-
-thr anild energy. The question, What is matter? is appar-
Iently a very simple one, and easy to answer. One of the
first answers that will occur to many is, Anything that
Scan ibe seen is matter.
2. Is Matter ever Invisible? -We are usually able to
Iretogriize matter by seeing it. We wish to ascertain by
2 MATTER, ENERGY, MOTION, AND FORCE.
experiment, i.e. by lpittiin 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 (3) 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 lat tei
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.
There is something which we call air. It is invisible.
Is air matter? Is a vessel full of it an "empty" vessel
as regards matter?
Experiment 1.- Thi u l t. one end of a glass tube to the bottom of
a basin of :att-r; blov air from the lungs through the tube, and
watch the asce-ilingr huil1i. Do you see the air of the bubbles, or
do you see certain ispa' 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
(Fig. 3) to considerable depths
in the sea to explore its bot-
tom, or to recover lost prop-
Observe the cloud (Fig. 4)
formed in front of the noz-
zle of a boiling tea-kettle.
S All the matter which forms
I 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 Matter, has Weight.- Has air
Experiment 3.- Suspend from a scale-beam a hollow globe, a
(Fig. 5), and place on the other end of the beam a weight, b (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
MATTER AND ENERGY.
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; e.g. the bended
bow can project an arrow, and the spring of a watch when
closely wound can put in 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
wilh the nipple a of the glass flask (Fig. 7). Place a little water in
th.d neck of the flasks 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.
B You will not attempt to say what
Smatter is.... This, no one knows. You
may, however, give a provisional
(answering the present needs) defini-
tion of matter, i.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
a blackboard crayon, for this is not chalk)
a little fine dust, and place it under a
Fig. 7. microscope, you will probably discover
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- '
ters is so small as to be nearly invisible, you will leadil
conceive that if one of the shells composing a clust.:I
should be broken into many pieces, and the pieces sel[ .-
rated from one another, that they would be invisible t,:
the naked eye. Yet the smallest of the particles iunt
MATTER AND ENERGY.
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.)1
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: Every 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
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 volume, 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.
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
.. .. .. I. .. .: _a
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. 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
I [:,o:'erty of fluidity to a greater or less extent when under
i; 'it:.ble stress. Bodies also exist in intermediate condi-
tio:n- between the solid and liquid, and liquid and gase-
,:'us. so that there is no distinct limit between these states,
.1nl the distinctions given above are merely conventional
S(i.,. growing out of custom).
SWhich of the three states any portion of, matter assumes depends upon
'. i :. ,iperature and pressure. Just as at ordinary pressures of the atmos-
r'l r, water is a solid (i.e. ice), a liquid, or a gas (i.e. steam), according to
ri i: tr: perature, so any substance may be made to assume any one of these
Si. tlni, unless a change of temperature causes a chemical change, i.e. causes
i t... I.reak up into other substances. For example, wood cannot be melted,
6:.. auj se it breaks up into charcoal, steam, etc., before the melting-point is
i: led. In order that matter may exist in a liquid (and sometimes in a
*1;. 1; state, a certain definite pressure is required. Ice vaporizes, but does
Si...t u.elt (i.e. liquefy) in a space from which the air (and consequently
:3 iLa.'.pheric pressure) has been removed. Iodine and camphor vaporize,
u, i J.)o not melt unless the pressure is greater than the ordinary atmos-
p!i.:r;. pressure. Charcoal has been vaporized, but has never been lique-
Si.. undoubtedly y because sufficient pressure has never been used.
: A 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.
-----oo o ----
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.
1. What is wind? Give some evidence that it possesses energy.
2. Give a provisional definition of matter.
3. What is energy?
4. What is an experiment? What is manipulation?
5. What is an air-bubble? What important lesson does a mere
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
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
liour. 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?
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 notion, quite
independent of man; e.g., 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 pull a
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
Ssilk 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 a time. 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 is measured by the extent of the elongation. -It
may be so constructed that an elongated A
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. Fig. 1s.
13. 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 -f 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--f= 0; or, correctly interpreted, +f-fu
(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
externalforce. 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 is;
it merely distinguishes between what is force and what is
1. Give a provisional definition of force. In what two ways is it
2. How is motion produced? Destroyed? Changed in any way?
3. 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.
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
i, ,.,l t i,:,I ?
ATTRACTION OF GRAVITATION.
15. Gralvitation is Universal. An unsupported body
'4f.I th, I- arth. This is evidence of an action or stress
bo-t,~,e.-ii tlh earth and the body. It has been ascertained
b i: r. Il observation that when a ball is suspended by
1th h111n *iliiig by the side of a mountain, the string is
.ii.rt ii.ite vertical, but is deflected toward the mountain in
c-iii'. -li ,ir:e of an attraction between the mountain and
tle .i1il. That there is an attraction between the sun
anl,, tlhe ea-th, and the earth and the moon, is shown, as
W-e !'.alil ee- further on, by their curvilinear motions.
Ti,.le- :~il i.idal currents on the earth are due to the
'tr-,,i:ti...r ._.t the sun and the moon.
Thlii ittiaction is called gravitation; the force is called
.greI'. .. When bodies under its influence tend to ap-
ilr.:-i.- .:.lie another, they are said to gravitate. Since
t-i4 a.ttr.:-tion ever exists between all bodies, at all dis-
S.i..-,~i it i called universal gravitation.
16. La w of Universal Gravitation. --Methods too
iffi.:ilrt 1', 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; viz., 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 c
(varies as) m 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
12 1 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 :, 1
surface of the latter. A person who could leap a fence three feet high nni
the earth, could, by the exertion of the same muscular energy, leap a f,- r. .
18 feet high on the moon. A boy might throw a stone a greater d;_t.ii,.
on the moon than a rifle can project a bullet on the earth. The r.u-:,-S-
Jupiter and Saturn, being so much greater than that of the earth. ti..
corresponding greater attraction which they would exert would so iii..p-.i
locomotion that a person would be able only to crawl along as thi'ughl IiI
feet were weighted with lead.
17. Weight.-We say that all matter has wei-l'i
meaning that there is an attraction between the earth 'l,
all kinds of matter. We say that the'weight of a :-ert.liIl
body is ten pounds, meaning that this is the measure IiI
the force of attraction between this body and the c.I tI1
ATTRACTION OF GRAVITATION.
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 thatn 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
t is carried from either pole toward the equator. The
oss of weight due to the increase of distance from the
enter of the earth is 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
arth'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
maximum weight. From this point onward to the center
gravity of the earth, a body will lose in weight as much as
would if it were being transferred to smaller and smaller
MATTER, ENERGY, MOTION, AND FORCE.
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
the earth's surface ?
5. The masses of the planets Mercury, Venus, Earth, and Mars are
respectively 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 ?
19. Molecular Distinguished from Molar Force :'
Repellent Force.--Thus far we have consideil e ... i
the effects of the action of bodies of sensible (pert:-iv.n,'
by the senses) size and at sensible distances. Illv- '
any evidence that the molecules which compo.- tIli,-
bodies act upon one another in a similar mann.-r '
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 attrac-
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 orn 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 it,
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
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 molec-
20. Cohesion, Tenacity.-That attraction which holds
the molecules of the same substance together, so as to form
MATTER, ENERGY, MOTION, AND FORCE.
larger bodies, is called cohesion. It is the attraction that
resists a force tending to break or crush a body. The tenacity
of solids and liquids, i.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 .pne 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.
i. [-- Experiment 10. -Pulverize about three
"ounces of alum. Take about a teacupful of
S-- 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
L one or more threads from a splinter of wood
Fig. 13. laid across the top of a beaker (Fig. 13).
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
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
on the surface of the glass. The latter are flattened, and
are said to be tabular.
In a 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
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
crystals have a primary type of six rays, and hexagonal outline. Professor
Tyndail 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
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. Crystallzation is 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 are
burst when water is allowed to crystallize (freeze) in them.
Experiment 13.-Get specimens of the following substances: talc,
chalk, glass, quartz, iron, silver, lead, copper, rock-salt, and marble.
Ascertain which of them will scratch glass, and which are scratched
MOLECULAR FORCES. 23
by glass. Which is the softest metal that you have tried? The hard-
est ? Name some metal that you can scratch with a finger-nail. 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
reference is generally adopted: -
following table of
MOHR'S SCALE OF HARDNESS.
1. Talc. 6. Orthoclase (Feldspar).
2. Gypsum (or Rock-Salt). 7. Quartz.
3. Calcite. 8. Topaz.
4. Fluor-Spar. 9. Corundum.
5. Apatite. 10. Diamond.
By comparing a given substance with the substances in the table, its
degree of hardness can be expressed approximately by one of the numbers
used 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
following 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, i.e. 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
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 temperature 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.
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
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.
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 tltis 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.
Sealing-wax and pitch may be regarded as fluids whose flow is ex-
tremely slow; i.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. Malleability 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-yzz of
an inch thick. Some metals, like iron, are more malleable and ductile at
a red 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; it 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. It is
probable that there is some adhesion between all substances
when brought in contact. Glass is wet by water, but is not
wet by mercury. If 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 is not 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 in a 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
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
at a very small angle (Fig. 15a); that separat- 135.
ing mercury and air meets glass at an angle of
about 1350. If clean silver is substituted for Water. l ercury/
glass, the first angle becomes large, not far from -
900, while the second would be reduced to zero; Fig. 15a.
in other words, the mercury creeps along the sur-
face of silver, its own air-exposed surface being parallel with that of the
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.
If the bore of the tube is reduced one-half in diameter, the lifting force
Fg 16 Fi 17
Fig. 16. Fig. 17.
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
quarter of an inch in water. Does the water
ascend or descend a little way in the tube ?
v nat is the shape of the surface of the water in the bore of the tube ? Is
the edge of the water next the tube on the outside turned up-or down?
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 ? If 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
r"z- i. water surface will meet the oily surface at an an-
gle of about 1350, and the surface tension of the
Fig. 17a. 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.
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 ?
3. The tension of a violin string is 2 pounds; what is meant by this
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-
6. When an iron nail hangs from a magnet, there is stress between the
nail and what bodies ? One stress is magnetic; what is the other ? Wlich
is greater ?
DYNAMICS' OF FLUIDS.
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
exerts 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 Fig. 1s.
we raise a pailful out of the water, it suddenly appears
1 Dynamics is the science which investigates the action of force.
DYNAMICS OF FLUIDS.
heavy. If we 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.
32. 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
S air directly above it, the pressure being
SI 1 sustained by the rigid glass bottom. But
Sit indirectly feels the pressure of the air
1! f'' on the surface of the water in the open
S\ vessel, 'and it is this pressure that sus-
S tains the water in the jar. But the
rubber bottom of the jar B yields some-
Fg. 19. 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?
Remove your finger from the closed
end. Why does the water fall?
Experiment 24.-Fill (or partly
fill) a tumbler with water, cover the Fig. 0o.
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
PRESSURE IN FLUIDS. 81
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 directions?
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?
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
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 n into a tumbler
filled with water.. The water presses
up against the air in the tube, and d
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 ? B
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 n Fig. 22.
up, the water must now press down
the tube against the air. Does the downward pressure increase as
Experiment 29.- Connect e with c, and lower o into the water.
The water now presses laterally sidewisee) against the air. Does the
lateral pressure increase as the depth?
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
DYNAMICS OF FLUIDS.
Sthe upward and lateral pressures at
the same depth compare?
Experiment 31.- Once more con-
nect c 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 same
depth compare? At the same depth is
E pressure equal in all directions?
Experiment 32.-Connect the two
brass tubes at the extremities F and G
c (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
The results of experiments
thus far show that at every
Ha 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
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. Why does -
not the water settle to theig. 24.
same level in both arms?
Figure 25 represents a U-shaped glass tube close at one end, 34
inches in hight, and with a bore of 1 square inch
section. The closed arm having been filled with
S 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 30 inches
higher than the surface C. This can be accounted
for only by the atmospheric pressure. The column
of mercury BA, containing 30 cubic inches, is an
I 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 30 cubic inches of mercury
in the column BA is about 15 pounds. Hence
C-- --- -- B 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.
Fig. 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 force of about
15 pounds per square inch, or about one ton per square foot.
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.
35. 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 34 inclies 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 2
sinks until there is equilibrium between
the downward pressure of the mercurial column AB and
tipe 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
serviceable 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
change 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.
36. 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 aneroid can be made more sensitive (i.e. so as to show smaller
changes of atmospheric pressure) than the mercurial barometer. If a
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 ascend.
It is obvious that the barometer will serve to measure approximately the
heights of mountains.
If a mercurial barometer stand at 760mm" on the floor, the same barom-
eter on the top of a table 1m high should stand at a hight of 759.91"m,
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 varia-
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
column in inches; and those in the extreme right, the density of the air
compared with its density at sea-level. The average hight of the mer-
curial column at sea-
level is about 30
If an openingcould
be made in the earth,
35 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-
To what hight the
is unknown. It is
at from 50 to 200
miles. If the aerial
ocean were of uni-
form density, and of
the same density that
t is at the sea-level,
ts depth would be a
little short of five
f the Himalayas
would rise above it.
DYNAMICS OF FLUIDS.
COMPRESSIBILITY AND ELASTICITY OF GASES. BOYLE'S
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 elasticity 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 (i.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 willabause the piston to rise, and raise
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
rubber tube connects the apparatus with an air-
ll Experiment 36.-Take a glass tube (Fig. 31)
having a bulb blown at one end. Nearly fill it
i 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
DYNAMICS OF FLUIDS.
39. Boyle's or Mariotte's Law.
Experiment 37. Take a bent glass tube (Fig. 32), the short arm
being closed, and the long arm, which should be
at least 34 inches (85cm) long, being open at the
top. Pour mercury into the tube till the surfaces
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
Sbulk; and, inasmuch as it would balance a pres-
sure of three atmospheres, its tension would be
Fig. 32. 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.
INSTRUMENTS USED FOR RAREFYING AND CONDENSING
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
illustrate its op-
eration. R is a
glass receiver from
which air is to be
exhausted. B is a
hollow cylinder of
brass, called 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 t 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
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
Sthe bottom of the barrel, it begins its
ascent. This would cause a vacuum be-
l tween the bottom of the barrel and the
A ascending piston (since the unbalanced
pressure of the outside air immediately
f H closes the valve s), but the tension of
the air in the receiver R opens the
valve t 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,
S | presses the receiver firmly upon the plate
L. 'Each repetition of a double stroke
of the.piston removes a portion of the
m 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.
e Sometimes another receiver, D, is
-IR used, opening into the tube T, that con-
nects the receiver with the barrel. In-
side the receiver is placed a barometer.
ig. 34. 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.
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 380mm (15 inches),
one-half of the air has been removed.
41. Sprengel Pump.
Experiment 38.- Remove the cap from j (Fig. 34), and connect
with a glass tube'k, about 12 inches long. Let k dip into a tum-
bler of water, m. Support the ap-
paratus on a couple of blocks of
wood, so that when the stopper a I
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 k. The pres-
sure of air on the surface of the
water in the open cup forces the
water up the tube k, 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 Fig. 35.
is employed instead of water, constitutes one of the most efficient
air-pumps in use. It is called the Sprengel pump.
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.
DYNAMICS OF FLUIDS.
Experiment 39. Into the neck of a bottle partly filled with water
(Fig. 35) insert a cork very tightly, through which pass a glass tube
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. .
Figure 6, page .
5, represents in
perspective, and i
Figure 36, in sec- -
tion, an appara-
tus for condens-
ing air, called a
condenser. Its ,I i;_
Fig. 36. 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.
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.
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. Atmospheric pressure closes
Fig. 39. Fig. 40.
the upper valve C in the piston. When
the piston is pressed down (Fig. 39), the
Slower valve closes, the upper valve opens,
and the water between the bottom of the
Barrel and the piston passes through the
Fig. 38. 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."
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 liquid to the level cb. Close the end b with a finger,
and try to suck the liquid out of the tube. You find Fig. 41.
it impossible. Remove the finger from b, and you can suck the liquid
out with ease. Why?
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 chainber b, at the
bottom of which is a valve c, opening upward. As the
piston is raised, water is forced up through
the valve d, while water in b is pre-
vented from returning by the valve c.
e When the piston is forced down, the
valve d closes, the valve c opens, and the
water is forced into the chamber b, con-
densing the air above the water. The
elasticity of the condensed air forces the
b water out of the tube e in a continuous
QUESTIONS AND PROBLEMS.
C 1. What force is the cause of fluid pressure?
a 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
S 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?
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 inflated with air at
the surface of the earth; what would happen if it were taken up in a
8. Mercury is 13.6 times denser than water. When a mercurial ba-
TRANSMISSION OF EXTERNAL PRESSURE.
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-
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 30 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
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?
TRANSMISSION OF EXTERNAL PRESSURE.
45. Pressure Transmitted Undiminished in All Direc-
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
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.
DYNAMICS OF FLUIDS.
Experiment 43.--Measure the diameter of the bore of each arm
of the glass U-tube (Fig. 44). We will suppose, for illustration, that
the diameters are respectively 40mm and
10mm; 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 1Cm
I 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 1cm of being
full. The pressure of -
the water causes the
mercury to rise in the d
a small arm, and to be
depressed in the large
F. 4. arm. Pour water very Fig. 44.
Fig. 43. Fig. 44.
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-
TRANSMISSION OF EXTERNAL PRESSURE.
Using 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
A (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
S 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
B 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, place 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 is de-
DYNAMICS OF FLUIDS.
46. Hydrostatic Press. -This principle has an im,
portant practical application in the hydrostatic press.
You see two pistons t and s (Fig. 47). The area of
the lower surface of t 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 t one
hundred times greater
than the downward
pressure exerted upon
s. Thus, if a pressure
Fig. 47 of one hundred pounds
is applied at s, the cotton bales will be subjected to a
pressure of five tons.
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 t is
very slow. In order that the piston t 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, hay, 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.
PRESSURE EXERTED BY LIQUIDS DUE TO THEIR OWN
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
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 is 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 is 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 62y pounds. Hence,
the pressure upon the bottom of each vessel is 621 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
PRESSURE EXERTED BY LIQUIDS.
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 b, over a hill c, through a valley
1 .. *. *l
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 should 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?
DYNAMICS OF FLUIDS.
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
d C. 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-
L=_--[J- resented in Figure 53, remove the stoppers
c 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
Sthe same at both ends; hence these two
0 b forces are in equilibrium. But the weight
Fig. 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
(i.e. the unbalanced) force. The unbalanced force which
causes the flow is equal to the weight of the column eb.
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 eb becomes
If one Df 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 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 f.
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
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
DYNAMICS OF FLUIDS.
at the bottom. I is a Tantalus Gup. A liquid will not flow from this cup
till the top of the bend of the tube is covered. 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 endj in the liquid, stopping
the end k, and sucking the air out at the end I 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
a candle-flame. Gases lighter than air are siphoned by inverting both tile
vessels and the sipuon.
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 change in weight 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.
-_ _i It seems as if something in the fluid,
underneath the articles submerged, were
pressing up against them. A moment's re-
Fig. 5s. election 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
BUOYANT FORCE OF FLUIDS.
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
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; 4 ,
when it becomes just even full, the equi-
librium is restored. ,i'
Now it is evident that the cylinder ''' l
immersed in the water displaces its own ii
volume of water, or just as much water Fig. 56.
as fills the bucket. But the bucket full
of water is just sufficient to restore the weight lost by the submersion
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.
SExperiment 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-
DYNAMICS OF FLUIDS.
sel c 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 c.
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
S weigh the liquid displaced as
before, and it will be found
that the weight of the liquid
Fig. 57. displaced is just equal to the
weight of the block in air.
Hence, 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
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
Fig. 58 is destroyed.
DENSITY AND SPECIFIC GRAVITY.
We see from this experiment that bodies weigh less in
air 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
Figure 59 represents a water-tank in common use in our houses. Water
enters it from the main
until nearly full, when it
reaches the hollow metallic R M'" M L A
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 anotheion oR S
passage for the escape of
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.
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 (i.e.
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 _tm = 1 = 1. In the same
(volume I 1CO
way the density of lead is (11 = ) 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 is numeri-
cally equal to the ratio, called its specific 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 Dr
) Weightof a given volume of the substance G .
Weight of equal volume of water G'
The Sp. D. of lead = D = 1 11.5. The Sp. G. of
lead = G' 1 5=11.5. Hence Sp. D. and Sp. G. are
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.
EXPERIMENTAL METHODS OF FINDING THE SPECIFIC
DENSITY AND SPECIFIC GRAVITY OF BODIES.
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', i.e. 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.
Fig. 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
DYNAMICS OF FLUIDS.
the weight lost by the lead alone, and the remainder is G'; ie. the
weight of water displaced by the cork. Apply formula (2), as before.
Experiment 54. Take a specific-gravity bottle that holds when
filled a certain (round) number of grams of water, e.g. 100s, 200s, 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 b, 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' (i.e. the 1009, 2009, 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. in G in S. G.
Grams. Grams. o E.
Lead 7.2 6.6 10.9 0.45
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 (e). 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.
they will float on the mercury at different depths, accord-
ing to their relative densities. Ice floats, in water with
98, in mercury with -4 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 hydrometer1
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. a stone. 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 a more suitable name for this instrument.
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 dissolv-
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 o F. (15 C.), and in other water at about 180 F. (82 C.). Which
water is denser?
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 B compare with the
weight of the water in it?
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
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.
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 ? (b) 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 displaces 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 0 C. or
water at 200 C.? (b) If water at the bottom of a vessel could be
raised by application of heat to 20 o C. while the water near the upper
surface has a temperature of 10 0 C., what would happen?
13. 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
15. Figure 65 represents a beaker graduated 47 -
in cubic centimeters. Suppose that when water
stands in the graduate at 501e, a pebble stone is 100
dropped into the water, and the water rises to 5-
75ce. (a) What is the volume of the stone?
(b) How much less does the stone weigh in water
than in air? (c) What is the weight of an equal ---s
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) 7cc, what is the weight of the cork? Fig. 65.
DYNAMICS OF FLUIDS.
17. If a piece of lead (sp. g. 11.35) is dropped into a graduate and
displaces 12ce of water, what does the lead weigh? (a) How would
you measure out 50 grams of water in a graduate? (b) 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 30 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 50eC. If 10g 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, i.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 96cm when a
barometer at the surface of the earth stands at 76cm; what is the
depth of the surface of water inside the bell below the surface
28. (a) 40k of lead immersed in water will displace what volume
of water? (b) Will lose how much of its weight?
29. Find the sum in meters of 4m11, 150cm, 8dm, 65mm, 5.6cm,
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 4C ?
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 its 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, i.e. A and,E will fall, and
B will rise. Set the pendulum F to vibrating. At each vibration it
68 GENERAL DYNAMICS.
C 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.
D aise 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.
It will be found that in the latter case the
weights descend nearly twice as far as in the
Suppose that weights A and B are each 30
Grams, and that weights E and L are respec-
1 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
I A combined weight (disregarding the weight of
wheel C, which is also put in motion) is
(30 + 30 + 2 =) 62 grams, was 2 grams. It
is now evident why the descent is slow, for in-
S 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 ~i- as fast as that of falling bodies
But when we employed weight L, we had a
force of 4 grams moving (30+30+4=) 64
I I 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
Fig. 66. have been exactly doubled.
FIRST LAW OF MOTION.
(1) In equal intervals of time change of momentum is
proportional to the force employed.
Experiment 61. Once more place E on
A, and ascertain how far they will descend
between the first and third strokes of the
bell, i.e. 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 D'
on it will be shown that, in order to accom-
plish this, the velocity at the end of the sec- v
ond unit of time must be twice that at the end
of the first unit of time. If V represent ;,, ,
the momentum generated during the first
unit of time, then the momentum generated
during the second unit of time must be about
(2) The momentum generated by a .
given force is proportional to the time during which the force
FIRST LAW OF MOTION.
The relations between matter and force are concisely
expressed in what are known as The 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 externalforce.
That part of the law which pertains to motion is briefly
summarized in the familiar expression, perpetual motion."
"Is perpetual motion possible?" has been often asked.
The answer is simple, -Yes, more than possible, neces-
sary, if 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.
SECOND LAW OF MOTION.
62. Graphical Representation of Motion and Force.
--If 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, and
(3) 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-
Fig. 68. 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.
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
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,
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 its intensity and the time during which it acts.
This law implies that an unbalanced force of the same
intensity, in the same time, always produces exactly the
same change of momentum, regardless of the mass of the
body on which it acts, and regardless of whether the body is
in motion or at rest, and whether the force acts alone or with
others at the same time.
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
g. o 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 values are known.
Thus, AC is 2.23 times AD; hence, the numerical value
of the resultant AC is (4 x 2.23 =) 8.92.
When more than two components are given, find the result-
COMPOSITION AND RESOLUTION OF FORCES.
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, it is 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.
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 x and y. Trace upon the blackboard short lines along the
strings from the point C, to indicate the direction of the two con-
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 Cb), and on
these construct a parallelo-
gram, from the extremities of
the line CD regarded as a
c diagonal. It will be found
that 10: number of pounds in-
dicated by the dynamometer
x::CD:Ca; also that 10:
number of pounds indicated
Fig. t2. 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
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.
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.
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
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.
SWhen 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 3 lbs.:1 lb. The
resultant is a single
force, applied at some
Fig. 74. 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 ::1 lb.: 3 lbs.
Hence, (3) when two parallel forces act upon a body in
the same direction, the distances of their points of applica-
COMPOSITION AND RESOLUTION OF FORCES.
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
A A C. sft
about that point. The a
perpendicular distance 80 *1b. I.
(AC or BC) from the ,
fixed point (C) to the Fig. 75.
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 (30 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 (-30 X 2) -60. The moment of the
force applied at B in an opposite direction is accordingly
(+20x3=)+60. Their algebraic sum is zero, conse-
quently there is equilibrium between the forces.
When more than two forces act in this manner, there
will be equilibrium if the sum of all the positive mo-
2 1 ments is equal to the
a b sum of all the nega-
1o 5 -- 10 o-so tive moments. Thus
c e / the sum of the posi-
8 2s tive moments acting
Fig. ,6. about point F (Fig.
76) is (f) 45 + (e) 25 + (a) 30 =100; the sum of the
negative moments acting about the same point is (c) 30 +
(d) 40 + (b) 30 = 100; the two sums being equal, the
forces are in equilibrium.
69. Mechanical Couple. -
If two equal, parallel, and con-
trary forces are applied to op-
posite extremities of a stick
AB (Fig. 77), no single force
can be applied so as to keep
Fig. 77. 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.
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.
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
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
causes the water to flow from the orifice C;
A 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 c
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
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
If the boats are near each other, and the men push each
other's boats with oars, the boats will move in opposite
directions, though with different velocities, yet with equal
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
moment generated, which is always the same in both
71. Third Law of Motion.- To every action there is
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
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? (b) 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 there
are forces pushing or pulling them along? (b) None of their
motions are in straight lines; are they acted upon by external forces?
THE THIRD LAW OF MOTION.
3. 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, i.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
11. If a man 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
APPLICATIONS OF THE THREE LAWS OF MOTION.- CENTER
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-
S.,. ing vertically downward, the resultant
of which equals their sum, and has the
same direction as its components. The
resultant passes through a definite
point in whatever position the body
F may be, and this point is called its cen-
Fig. 8s. ter of gravity. The center of gravity
(e.g.) 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 e.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 equilibrant 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, it is
only necessary to provide a support for its center of grav-
ity. The supporting force must be applied somewhere in
the line of direction, otherwise the body will fall. The dif-
ficulty of poising a book, or any other object, on the
end of a finger, consists in keeping the support 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 G ..,
is not applied immediately under its c.g. at
G; but when placed horizontally, it immedi-
ately assumes a vertical position. It appears Fig. 82.
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.
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 83, 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, so as to represent a continuation Fig 83.
of the vertical line oa, the c.g. must lie somewhere in the
path an made by the needle. Suspend the potato from
some other point, as b, and a needle thrust vertically
through the potato from b will also pass through the c.g.
Since the c.g. lies in both the lines an and bs, it must be at
c, their point of intersection. It will be found that, from
whatever point the potato is supported, the point c 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, etc.
74. Equilibrium of Bodies.- That a body acted on
solely by its weight may be in equilibrium (i.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 c.g. 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
'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
degrees of stability, and account for the same.
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-
3. For what two reasons is a pyramid a very stable
4. What point in a falling body descends in a straight Fig. 86.
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.
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,"
Webster). The fact is, that no body of whatever /ns, 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
force acting for the same length of time will generate the
same amount of momentum in all bodies free to move, irre-
spective of their masses.
76. 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
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 (i.e. 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
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
a unit of time. But the weights move through three spaces
1 Uof T- b 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 b) reached by the weights
at the end of the first unit of time, then weight E will be
subfrT- c 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
point e. (Try it.)
The weights, therefore, have at the end of the first
unit of time a velocity (V) of two spaces. But they
S Iof T- 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 (I 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.