The elements of physics; a text-book for high schools and academies

Front matter

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Preface

Seventeen years ago, in the preface to the first edition of this work, the author urged the importance of experiments to be performed by the pupil, as an aid to his mastery of the science of Physics, in opposition to the then universal and exclusive text-book-memorizing or illustrated-lecture system. In these seventeen years he has seen the value of the " objective method of study " demonstrated in the case of more than two thousand pupils in his own classes, and has witnessed the spread of the " laboratory method " of teaching science through the larger portion of the high schools of the United States. But with this great improvement in educational method, he has observed the development of a tendency which threatens seriously to impair its usefulness.

This is the tendency to allow enthusiasm for experimentation, for mere manipulation of apparatus, to obscure the importance of an intellectual mastery of the facts and their underlying principles. In ^jheir zeal for " training the mental powers " of their pupils, teachers may easily reduce the study of physical science to a mere gymnastic^ forgetting that the object of training the mind is to render possible the greater acquisition of knowledge. If, then, the pupil has not at the end of his course a reasonably comprehensive and accurate grasp of the subject-matter of Physics, the instructor may be sure that he has failed to preserve a due proportion between study and experiment.

The author is convinced that both mental discipline and the acquisition of knowledge will be promoted if theory and

Q £^ Q n 4 Digitized by LjOOg IC

IV PREFACE.

experiment be somewhat sharply divided. If on the same page the pupil reads a statement of a scientific principle, the facts on which it is based, the reasoning by which it is deduced, together with elaborate detailed directions for preparing apparatus for exhibiting the facts in a series of experiments, and minute directions for the manipulation, he is almost certain to fail to discriminate in regard to the relative importance of each of these matters, and the relation which each sustains to the purposes of his study ; he is likely to bestow equal attention upon each — even (if not wholly emancipated from childish methods) to memorize all alike. To obviate the danger of this enormous misdirection of effort, the author has been led to construct a separate Manual of " Physical Experiments," by the use of which the attention of the pupil is concentrated upon apparatus, process, result, and inference, and to treat matter in the text-book principally as a body of systematized knowledge to be mastered — a science in the strictest application of that term.

In the laboratory, then, the pupil should rfo, should observe, should reflect, should infer, and should record the results of these processes in a suitable manner. In the class-room he should concentrate his attention upon the theory and principles of the science as laid down in the text-book, striving to bring these and the results recorded in his manual into their proper relations in his mind as a portion of a unified whole, the possession of which shall make him master of one department of human knowledge.

Certain topics that come under the head of molecular physics, e,g. absorption, osmosis, and crystallization, have been omitted in this revision, since their processes are deemed too obscure and imperfectly understood to be classified under the title of scientific knowledge. That department of ether dynamics known as double refraction and polarization of light has been omitted, as it is generally conceded to be too difficult of apprehension for the average high-school pupil.

PREFACE. V

The author wishes to make special acknowledgments for valuable suggestions and aid in correcting the proofs to his friend, I>r. Arthur W. Goodspeed, of the University of Pennsylvania, and to Mr. Albert P. Walker, his colleague in the English High School, Boston, who has read the work in manuscript and in proof sheets.

OOl^TENTS.

Introduction

PAGES

Domain of Pliysics. Some properties of matter. Physical measurements. Kinematics. Laws of accelerated motion. Composition of motions and velocities. Kinds of motion 1-24

CHAPTER n.

Molar Dynamics.

Force. Newton's Laws of Motion. Momentum. Measurement of force. Composition of forces. Moments of force. Center of mass. Curvilinear motion. The pendulum. Gravitation. Work, energy, and power. Machines. Properties of matter due to molecular forces 25-d7

CHAPTER m.

Dynamics of Fluids.

Law of transmission of pressure. Pascal's Principle. Atmospheric pressure. Boyle's Law. Barometer. Principle of Archimedes. Specific gravity 98-123

CHAPTER IV.

Molecular Dynamics. Heat.

Theory of heat. Sources of heat. Thermometry. Calorimetry. Specific heat. Laws of gaseous bodies. Fusion.- Latent heat. Artificial cold. Hygrometry. Diffusion of heat. Thermo-dynamics. Steam engine ,.,.., ^. . .,124-165

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Vm CONTENTS.

CHAPTER V.

Energry of Maes Vibration.

PAGES

Simple harmonic motion. Wave-motion. Sound-waves. Beenforcement of sound-waves. Pitch. Composition of wave-forms. Discord and harmony. Musical instruments. Vocal organs. The ear 166-205

CHAPTER VI.

Etber Dynamics. Radiant Energry.

The ether. Radiation. Light. Intensity of illumination. Mirrors. Refraction. ' Prisms and lenses. Prismatic analysis of light. Spectroscopy. Color. Optical instruments. The eye. Thermal effects of radiation . 206-267

CHAPTER VII.

Ether Dynamics. Electrostatics.

Electrification. Conduction. Induction. Potential. Atmospheric

electricity 268-278

CHAPTER VIII.

Mectrokinetics.

Voltaic cells. Effects producible by electric current. Electrical quantities. Ohm's law. Instruments for measurement of electric current. Resistance and its measurement. Divided circuits. Methods of combining cells. Magnets and magnetism. Magnetic relations of the current. Mutual action of currents. Electromagnetic induction. Dynamos. Electric motors. Storage batteries. Thermo-electric currents. Electric light. Electroplating and electrotyping. Telegraph. Telephone and microphone. Electro-magnetic theory of light. Radiography. Tesla's investigations 279-366

Appendix 367-375

LIST OF PLATES AND PORTRAITS.

Spectbums, Plate I . . . . Frontispiece.

Sir Isaac Newton 28

Galileo 38

Archimedes 118

Benjamin Franklin 278

Lord Kelvin 306

Michael Faraday 330

Telboraph, Plate II 355

Radiooraph, Plate III 362

Bead Nature ^Nk^Ag if Experiment,

ELEMENTS OF PHYSICS.

oJOio

CHAPTER I.

INTRODUCTION.

Section I. Domain Of Physics

1. The perception of changes constantly taking place in the external world is a universal human experience. The manifestations of these changes to the senses are called phenomena; that which undergoes change is called matter. Since most of the changes which come within the scope of our present studyare due to the motions ^ of portions of matter, we may adopt the following provisional definition : ^

Physics is the science which treats of the phenomena of Tnatter and motion.

2. Some Properties of Matter or of Material Bodies:

(1) Extension. Every portion of matter, however small, ^ occupies space, i.e. it has length, breadth, and thickness. The property thus manifested is called extension,

^ Sound, heat, and light, considered as distinct from the sensations to which they giye rise, are nothing but motions.

"1 do not belieye that there exists in external bodies anything for exciting tastes, smells, and' sounds, but motion, swift or slow ; and if tongues, noses, and ears were removed, I am of the opinion that motion would remain, but there would be an end of tastes, smells, and sounds." — Galtleo.

> A proyieional definition is one that answers present needs.

INTRODUCTION.

Fig. 1.

(2) ImpenetrahUity, While matter occupies any portion of space it excludes all other matter from that portion. It is an axiom, exemplified in everyday experience, that no two bodies (e.g. our two hands) can occupy the same space at the same time} The property in virtue of which a body occupies space to the exclusion of all other bodies is called impenetrability.

Air and other gases are invisible, and hence are not readily recognized ajs matter. If, however, we show that air possesses impenetrability, we have reason to believe that air is matter, since it possesses one of the characteristic properties of matter.

Ezperiment 1. — Float a cork on a surface of water, cover it with a tumbler as in Fig. 1, and force the tumbler, mouth downward, deep into the water. State what evidence the experiment furnishes that air is matter.

(3) Divisibility. Bodies of matter with which we are acquainted are divisible beyond any appreciable limits, but scientists assume that there are ultimate portions which cannot undergo further division. It is certain that every kind of material substance known has a minimum limit of division which is never exceeded in that substance. A molecule of any stthstance is one of the ultimate homogeneous portions of which the substance is composed,

A grain of musk will scent a room for years by constantly discharging into the air particles of musk. These particles are so small that the original grain does not perceptibly diminish in weight. Yet the smallest particle of musk dust, or the smallest particle of any substance that can be obtained by mechanical division, is very large in comparison with the molecules of which the particle is composed. 2

1 This is quite as axiomatic as the fact that "a body cannot be in two places at the same time."

* " In a cubic inch of any gas at atmospheric pressure and at ordinary temperatures there are about 3 x 10^ detached particle^ absolutely similar and equal to one Wiother." — Tajt, r^^^^T^

PROPBBTIES OF MATTER. 3

(4) Compressibility and expansibility. All bodies of matter are compressible and expansible, though in very different degrees. A proof of the existence of molecules and the molecular constitution of bodies (though by no means the most conclusive proof) may be found in this fact. Matter {e.g. gold or water) is either continuous as it appears to the eye, or it is discontinuous, granular, composed of distinct particles (molecules) somewhat as represented in Fig. 2. Bvt bodies are compressible and expansible, ''-'-' :\: /,'.',

On the supposition that matter is continu- "'*"«d: '.:•*. •*.:>*.• ous, these phenomena are unexplainable ; but .*/ 1 •. *.; : : '.;.

on the supposition that matter is granular *':;.'.:..../"

or molecular they are easily explainable. ~*^;;?;"/5::/(^i: According to the latter supposition, a change i>.-::-.y.-:i

of volume by contraction or expansion means ^'^ ^*

simply a coming together or a separation of the molecules composing the body, as represented in Fig. 2.

3. Theory of the Constitution of Matter. Porosity. — 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 disconnected particles, called molecules. No two molecules of matter in the universe are in permanent contact vnth each other. Every molecule is in rapid motion, moving back and forth among 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 ustcally push them away a very little ; hence the body expands. If the molecules of a body are never in contact except at the instants of collision, it follows that there are spaces between them. These spaces are called pores.

It is estimated that even in dense solids the average distance between molecules Is many times the diameter of a molecule, Oooalp

^ 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.

Impenetrability may be affirmed of molecules, but not necessarily of masses. The term pores, in physics, is restricted to the invisible spaces that separate molecules, and does not include such cavities as may be seen with the naked eye^in sponges, and with a microscope in wood, etc.

4. Physical Measurements. — Physics is essentially a science of measurements. Measuring consists in finding how many times a definite quantity, called a unit, is contained in the quantity to be measured. For example, should we wish to measure the length of a table, we may choose arbitrarily for a unit of measurement the length of a certain pencil and proceed to find how many times this pencil may be laid along the length of the table. If ten times, we say the table is ten pencil-lengths long.

The unit of measurement must be a definite quantity of the same kind as the thing to be measured. Thus a unit for measuring length must be a certain length, a unit for measuring surface must be a certain quantity of surface, and a unit for measuring volume must be a definite volume. A unit which has become legalized either by statute or by common usage is called a standard unit. The expression of a physical quantity consists of a statement of the concrete unit employed, e.g. pound, foot, quart, etc., with the numher of those units prefixed. The numerical part, called the numeric^ is obtained by measurement.

5. Metric System of Measures. — [In this connection the Tables of Metric Measures, in the Appendix, should be studied.] The term metric is derived from the word mster, which is the name of the fundamental unit employed in this system for measuring length. The international standard meter is defined by law to be the shortest distance between two lines engraved on a given platinum bar (carefully preserved by the French government) at the temperature of

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VOLUME, MASS, DENSITY. 5

0° C. (32** F.).^ The metric system is now generally employed in scientific work.*

6. 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. By the 7nass of a body is meant the qtiantity of matter in the body.

The unit of mass generally employed in science is the gram, or, in the British system, the pound. The gram is the onethousandth part of the standard kilogram. This standard is a piece of platinum carefully preserved by the French government at Paris. Originally it was intended to represent the mass of a cubic decimeter of pure water at the temperature of 4° C. A kilogram of any substance is that quantity of the svhstance which, placed on a scale pan, would just balance in a vacuum the standard kilogram placed on the other pan.

PlO. 3.

Rsperiment 2. — Place on one pan of a balance (Fig. 3) a vessel, A, whose capacity is one liter, i.e. one cubic decimeter (see Appendix). Place upon the other pan some body, B, which will just counterbalance

» The United States Government carefully preserveB in Washington copies of the international meter. These are declared by Congress to be the standard units of length for this country.

« ** The British measurements are infinitely inconvenient and wasteful of brain energy." — Tait. " I look upon our English system as a wickedly brain-destroying piece of bondage under which we suffer." — Lord Kelvin. ^<-^ I the empty vessel. Then place upon the same pan a kilogram mass, C. Now pour water slowly into the vessel until the water and kilogram mass counterbalance each other. What mass of water does the vessel contain ? How does the mass of water in A compare with the mass of the body C ? How does the volume of water compare with the volume of the body C ?

Mass is quite distinct from weight. The weight of a body is the measure of the attraction between it and the earth, and may vary with change of position, because the earth's attraction varies with the distance of the body from the earth, while the mass of the body remains constant. Mass does not depend upon weight, but weight depends upon mass. .

When we open a heavy iron gate, it is its mass with which we have to deal ; if it were lying on the ground and we should try to raise it, we should have to deal simultaneously with both its mass and its weight.

The process of measuring the mass of a body must not be

Q confounded with the process of finding how heavy a body is, although both processes are, in common usage, called weighing. Weighing a body to ascertain its rridss consists in balancing it with a body or bodies of known mass, and is performed with a scale balance (Fig. 3) and a set of masses (commonly called a set of

T weights). Weighing to ascertain weight should be performed with an instrument adapted to measuring force, e.g. a spring balance (Fig. 4). For most prac- ^^' *• tical purposes, however, the latter instrument may be used to measure mass, inasmuch as at the same place mass is proportional to weight}

JSqital volumes of different substances (e.g, cork, cheese, lead) contain unequal quantities of matter. Of two substances, that which contains the greater quantity of matter in the same volume is said to be the denser. By the density of a substance

» This is one of many instances in pliysics in which one quantity is indirectly measured by measuring another proportional to it.

THREE STATES OP MATTER. 7

is meant the mass in a unit of volume of that substance. The density of water (at 4° C.) is one gram per cubic centimeter, and the density of cast iron is about 7.12 grams per cubic centimeter.

The mean (or average) density of a body is found by dividing its mass by its volume. Thus, if the mass of a body be 32 g. and its volume be 5 cc, its mean density is (32 -^ 5 =) 6.4 g. per cc.

7. Three States of Matter. Fluidity. We recognize three states or conditions of matter, viz, solids liquid, and gaseous, distinctively represented by earth, water, and air. Everyday observation teaches us that solids tend to preserve a definite volume and shape; liquids tend to preserve a definite volume only, while their shape conforms to that of the containing vessel; gases tend to preserve neither definite volume nor shape, hut to expand indefinitely.

In consequence of their manifest tendency to flow, liquids and gases are called fluids.

Susceptibility of motion of the molecules of a body around and among one another is called fluidity. All bodies of matter, including solids, possess this property, but in very different degrees. It is due to this property that solids can be bent, stretched, and compressed, and that most metals can be drawn into wires and rolled or hammered into sheets.

EXERCISES.

1. (a) Give names of at least three substances. (6) Give a name of a body of each substance named.

2. What additional idea does the term * impenetrability" imply besides extension ?

3. How may it be shown that air is matter ?

4. (a) What is an air bubble (e.g, in water)? (6) What property does it show that air possesses ?

5. Why is matter compressible ?

6. How may bodies of matter be expanded ?

7. Heating a body is attended with what molecular changes ?

8. (a) Distinguish between the mass and the weight of a body. (6) Which may change, and why, while the other remains constant ?

9. Wliich instrument represented in Figs. 3 and 4 will not show a change of weight of a body occasioned by a change of distance from the earth?

10. (a) Which is more difficult, to roll a cannon ball along a smooth floor or to raise the same from the floor ? (b) In rolling the ball, with which do we deal, its mass or its weight? (c) In raising the ball, with what do we deal ?

11. In weighing articles of groceries, such as tea, sugar, etc., is the purpose to measure their mass or the force of gravity ?

12. If the mafls of 45 cc. of cork be 10.8 g., what is the density of cork?

SECTION XL

KINEMATICS.

8. Kinematics. Kinematics treats of motions without reference to their causes. Nearly all physical phenomena are attributable to motions (§ 1), hence the great importance of this subject. Motions of bodies of sensible size are called molar or mechanical motions in distinction from molecular motions. The motions of the molecules of a body constitute its heat, and will therefore be treated under that head.

9. Motion. Motion is a continuotts change of position. That which moves is known as matter. The position of a particle of matter is determined by its direction and distance from another particle, or from some point of reference. A particle moves relatively to a given point while an imaginary straight line connecting it with the point changes either in direction or in length. A particle is at rest relative to a given point while a straight line joining them changes neither in direction rurr in length.

MOTION.

When you open or shut the legs of a pair of dividers (A, Fig. 5), a straight line, a^ b^, connecting the points at the ends of the legs changes in length; hence there is relative motion between. these points. If (B, Fig. 6) you open the legs a little way, and, fixing the end of one of the legs upon a plane surface, trace a circle with the end of the other leg around the former as a center, there will be relative motion between the two points, since a line joining them, a b, a b', etc., changes in direction.

If (C, Fig. 5) you trace with the points of the open dividers two straight parallel lines on a plane surface, the two points will be relatively at rest, just as surely as if the dividers were lying upon the table, since in both cases a straight line connecting the points a b, a^b', etc., changes neither in length nor in direction.

Fig. 5.

A point may be at the same instant at rest with reference to certain points and in motion with reference to certain other points. For example, while the points of the dividers are tracing straight lines on the plane surface (C, Fig. 5), and are relatively at rest, they are in motion with reference to every point in the plane surface. A passenger in a railway car may be at rest relative to the car and the other passengers, but in rapid motion relative to objects by the roadside.

In ordinary language the phrase "a body at rest", means a body that does not change its position with reference to that on which it stands, as, for instance, the surface of the earth or the deck of a ship. It can mean nothing else, for both the body said to be ** at rest " and all points on the earth's surface are in rapid motion with reference to the sun and other heavenly bodies, and also with reference to the earth's axis.

10. Velocity. Velocity is rate of change of position. It involves units of distance (or length) and units of time, and is commonly expressed in units of distance per unit of time, e.g. feet per second, miles per hour, etc.

If a particle move through equal distances in equal periods of time, the velocity is said to be uniform. If the distances traversed in equal intervals of time continually increase or continually decrease, the velocity is said to be accelerated.

Velocity is determined by dividing the distance traversed

by the time consumed. If a body move s feet in t seconds, its

s s

velocity, v, is -■ feet per second, or v = - . In case the velocity

v t

be accelerated, this result is to be regarded as the average velocity for that distance; and in the case of uniform motion the average velocity is the same as the actuxil velocity at every instant. It is evident that the actual velocity of a body whose rate of motion changes can be given only at some definite instant or point in its journey. It denotes the space which would be traversed in a unit of time, if at the given instant the velocity should become uniform.

When a particle experiences equal changes of velocity in equal units of time, its motion is said to be uniformly accelerated, and its change of velocity per unit of time is called its rate of acceleration, or simply its acceleration^ and is represented by a. When the velocity increases, as in the case of a falling stone, its acceleration is said to be positive (+ a); when the velocity decreases, as in the case of a stone thrown upward, its acceleration is said to be negative (— a).

The acceleration of a body falling in a vacuum and of a body projected vertically upward in a vacuum is practically uniform; in the former case it is about 32.2 feet (or 9.8 m.) per second; in the latter case it is a negative acceleration of about 32.2 feet per second. C^ooalp

ACCELERATED MOTION. 11

The rate of acceleration of a particle in traversing a certain

distance in a given time is found by dividing the entire change

in velocity, v, by the units of time, ty consumed in making the

V i

change ; i,e. a = -, whence v== at. , '

Thus, if the velocity of a railroad train at a certain instant be 26 miles per hour, and half an hour hence it be 16 miles per hour, then the entire change of velocity, », is — 10 miles per hour; hence the average acceleration, i,e. the acceleration if it were uniformly distributed throughout the

30 minutes, is = ( — ^ j of a mile per minute. Again, if a stone

falling with a uniformly accelerated velocity acquire in 4 seconds a

128 8 velocity of 128.8 feet per second, its acceleration is ' = $2.2 feet per

second.

SECTION m.

LAWS OP UNIFORMLY ACCELERATED MOTION.

11. First Law. If a particle starting from a state of rest move with uniform acceleration, a, its velocity, v, at the end of any given unit of time, t, is found by the equation (1). V = at, as given in § 10. From this equation we derive the following law:^

Change of velocity due to uniform a^cceleration is equal to the product of the acceleration multiplied' by the units of time; or, the change of velocity is proportional to the rate of acceleration and to the time occupied.

But if a particle be in motion, and at a qertain instant have a velocity, F", and its acceleration be a, then its velocity at any subsequent instant is expressed as follows:

After a lapse of one unit of time, v = V^ (a x 1). u u u u two units " " V =,rv± (a X 2).

1 A physical law is an expression of the relation which has been discoyered to exist between certain physical quantities. ' . r^ ^

INTRODUCTION.

12. Second Law. Since the velocity of a particle starting from a state of rest increases from zero to a t, the average velocity must be

+ at

= i at At this rate in the

M ;

Fia. 6.

same time, t, it would traverse a distance, S, equal to i atxt = i at* units; hence, (3) S=iat*, From this we derive the law:

The distance traversed in a given time by a particle starting from a state of rest and having uniformly accelerated velocity is one half the product of the a^cceleration and the square of the units of time; or, th^ entire distance traversed is proportional to the rate of acceleration and to the square of the time occupied.

If a particle, instead of starting from a state of rest, have an initial velocity, F, it would move in t units of time without acceleration a distance Vxt) to this distance must be added the distance it moves in consequence of acceleration, in order to obtain the entire distance traversed in t units, and our formula becomes (4)

S = Vt + }iat\

If it be required to find the distance passed over during any specified unit of time we may subtract the distance traversed in ^ — 1 units from the distance traversed in t units. Thus, representing the required distance traversed during a specified unit of time t by s, we have (6)

AGGBLEBATED MOTION.

13. Verification. The laws given above are verified approximately and conveniently by the use of the venerable Atwood's machine, i The equal weights A and B (Fig. 6) are suspended by a thread passing over the wheel C. Inasmuch as the weights are equal, they counterbalance each other and remain at rest. Raise the weight A and place it on the platform D as shown in Fig. 7. Place on this weight a small additional one, E, called a ''rider," the weight of which sets the system in motion. Set the pendulum F swinging. At each swing it 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 they reach the ring H, the rider, not being able to pass through, is caught oft by the ring. Raise and lower the ring on the graduated pillar I, and ascertain by repeated trials the average distance the weights move between the first two strokes of the bell, i.e. 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 a unit of time. We will also, for convenience, take for a unit of distance the distance the weights move during the first unit of time, call this unit a space, and represent the unit graphically by the Une a b (Fig. 8).