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UNIVERSITY OF CALIFORNIA 
 
 LIBRARY 
 
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 Accessions No . j..Pr..7.... Book No...*b. 
 
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INTRODUCTION 
 
 TO 
 
 PHYSICAL SCIENCE. 
 
 BY 
 
 A. P. GAGE, PH.D., 
 
 INSTRUCTOR IN PHYSICS, ENGLISH HIGH SCHOOL, BOSTON, AND 
 AUTHOR OF "PRINCIPLES OF PHYSICS." 
 
 BOSTON, ,l7.&A.j:.- -' . 
 GINN & COMPANY, PUBLISHEES. 
 
Entered according to Act of Congress, in the year 1887, by 
 
 A. P. GAGE, 
 in the Office of the Librarian of Congress, at Washington. 
 
 TYPOGRAPHY BY J. 8. GUSHING & Co., BOSTON. 
 
 PRESSWORK BY GINN & Co., BOSTON. 
 
AUTHOR'S PREFACE. 
 
 AN experience of about six years in requiring individual 
 laboratory work from my pupils has constantly tended to 
 strengthen my conviction that in this way alone can a pupil 
 become a master of the subjects taught. During this time 
 I have had the satisfaction of learning of the successful 
 adoption of laboratory practice in all parts of the United 
 States and the Canadas ; likewise its adoption by some of 
 the leading universities as a requirement for admission. Mean- 
 time my views with reference to the trend which should be 
 given to laboratory work have undergone some modifications. 
 The tendency has been to some extent from qualitative to quan- 
 titative work. With a text-book prepared on the inductive plan, 
 and with class-room instruction harmonizing with it, the pupil will 
 scarcely fail to catch the spirit and methods of the investiga- 
 tor, while much of his limited time may profitably be expended 
 in applying the principles thus acquired in making physical 
 measurements. 
 
 A brief statement of my method of cpnducting 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- 
 
 673277 
 
iv AUTHOR'S PREFACE. 
 
 tions, he surrenders the apparatus to another who may be ready 
 to use it, and next occupies himself in writing up the results 
 of his experiments in his note-book. These note-books are 
 deposited in a receptacle near the door as he leaves the labo- 
 ratory. Nothing is ever written in them except at the times 
 of experimenting. These books are examined by the teacher ; 
 they contain the only written tests to which the pupil is sub- 
 jected, except the annual test given under the direction of the 
 Board of Supervisors. Pupils, in general, are permitted to com- 
 municate with their teacher only. " Order, Heaven's first 
 law," is absolutely indispensable to a proper concentration of 
 thought and to successful work in the laboratory. 
 
 Only in exceptional cases, such as work on specific gravity 
 and electrical measurements, has it been found necessary to 
 duplicate apparatus. The same apparatus may be kept on the 
 desks through several exercises, or until every pupil has had 
 an opportunity of using it. Ordinarily two pupils do not per- 
 form the same kind of experiment at the same time. With 
 proper system, any teacher will find his labors lighter than 
 under the old elaborate lecture system ; and he will never have 
 occasion to complain of a lack of interest on the part of his pupils. 
 
 I venture tc 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. 
 
NOTE TO THE REVISED EDITION. 
 
 WHILE the general plan and arrangement of the original 
 edition of this work have been preserved in this revision, 
 numerous changes dictated by experience and improved 
 methods of presenting portions of this science have been 
 made here and there throughout the text. The subjects of 
 Electricity and Magnetism, however, have been entirely 
 rewritten and made to conform in plan and arrangement to 
 the treatment of the same subjects in my Principles of 
 Physics. 
 
 Although several new topics, for instance, Specific Heat, 
 have been introduced, yet the volume of the text proper has 
 been increased only sixteen pages. Aside from these changes 
 and additions, the matter of the text remains the same. 
 
 Several subjects treated in the text notably the Pendu- 
 lum, Expansion Coefficients, the Dynamo, and the Electric 
 Motor have been "continued" in the Appendix for the 
 benefit of those who may wish to pursue these subjects 
 further than a very elementary text-book will admit. 
 
 I may be permitted to suggest that copies of the Principles 
 of Physics, the style of which is naturally similar to the style 
 of this book, but the treatment much fuller, if made accessible 
 to both teacher and pupil, cannot fail to be very helpful to 
 both. 
 
 A. P. G. 
 
 1896. 
 
CONTENTS. 
 
 CHAPTER I. 
 
 Matter, energy, motion, and force. Attraction of gravitation. 
 Molecular and molar forces '. . 
 
 CHAPTER II. 
 
 Dynamics of fluids. Pressure in fluids. Barometers. Com- 
 pressibility and elasticity of gases. Buoyancy of fluids. 
 Density and specific gravity 29 
 
 CHAPTER III, 
 
 General dynamics. Momentum, and its relation to force. Three 
 laws of motion. Composition and resolution of forces. 
 Center of gravity. Falling bodies. Curvilinear motion. 
 The pendulum ; 67 
 
 CHAPTER IV. 
 Work and energy. Absolute system of measurements. Ma- 
 
 chines 
 
 CHAPTER V. 
 
 98 
 
 Molecular energy, heat. Sources of heat. Temperature. 
 Effects of heat. Thermometry. Convertibility of heat. 
 Thermo-dynamics. Steam-engine 121 
 
Vlll CONTENTS. 
 
 CHAPTER VI. 
 
 PAGE 
 
 Electro-statics. Induction. Potential. Electro-kinetics. 
 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 electro typing. 
 Telegraphy. Telephony. Thermo-electric currents . . 157 
 
 CHAPTER VII. 
 
 Sound. Study of vibrations and waves. Sound-waves, veloc- 
 ity of ; reflection of ; intensity of ; re enforcement of ; inter- 
 ference of. Pitch. Vibration of strings. Overtones and 
 harmonics. Quality. Composition of sonorous vibrations. 
 Musical instruments. Phonograph. Ear 248 
 
 CHAPTER VIII. 
 
 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 290 
 
 APPENDIX : A, metric system ; B, table of specific gravity ; C, 
 table of natural tangents; D, simple pendulum ; E, expansion 
 coefficients ; F, table of electrical resistance ; G, dynamos, 
 continued ; H, electric motors 357 
 
 INDEX . 371 
 
INTRODUCTION TO PHYSICAL SCIENCE. 
 
Nature is the Art of God." THOMAS BROWNE. 
 
 CHAPTER I. 
 MATTER, ENERGY, MOTION, AND FORCE. 
 
 Section, I.. 
 
 ^ ^ a* t 3 } 
 
 MATTER AND ENERGY.' " 
 
 To THE TEACHER : That portion of this book which is printed in the 
 larger type, including the experiments, is intended to constitute in itself a tolerably 
 full and complete working course in Physics. The portion in fine print may, 
 therefore, be wholly omitted without serious detriment ; or parts of it may 
 be studied at discretion as time may permit ; or, perhaps still better, it 
 may be used by the student, in connection with works of other authors, 
 as subsidiary reading. It should be borne in mind that recitations from 
 memory of mere descriptive Physics and Chemistry is of little educational 
 value. 
 
 To THE PUPIL : " Read nature in the language of experiment " ; 
 that is, put your questions, when possible, to nature rather than to per- 
 sons. Teachers and books may guide you as to the best methods of 
 procedure, but your own hands, eyes, and intellect must acquire the 
 knowledge directly from nature, if you would really know. 
 
 1. Matter. Physics is the science that treats of matter 
 and such changes in it as do not destroy its identity. Any. 
 observed change in matter is a phenomenon. To the 
 question, What is matter? one of the first answers that 
 will occur to many is, Anything that can be seen is 
 matter. 
 
 2. Is Matter ever Invisible ? We are usually able to 
 recognize matter by seeing it. We wish to ascertain by 
 
MATTER, ENERGY, MOTION, AND FORCE. 
 
 experiment, i.e. by putting the question to nature, whether 
 matter is ever invisible. Now in experimenting there 
 must (1) be certain facts of which we are tolerably certain 
 at the outset. These facts (2) lead us to place things in 
 certain situations (the operation is called manipulation) in 
 order to ascertain what phenomena will follow. Then, in 
 the light of these phenomena 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 
 occupy the same space at the same time. All 
 
 Fig. 1. 
 
 Fig. 
 
 experience has taught us that no two portions of matter can 
 occupy the same space at the same time. This property 
 (called impenetrability') of occupying space, and not only 
 occupying space, but excluding all other portions of matter 
 from the space which any particular portion may chance 
 to occupy, is peculiar to matter; nothing but matter 
 possesses it. This known, we have a key to the solution 
 of the question in hand. 
 
MATTER AND ENERGY. 
 
 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 ? 
 
 3. 
 
 Experiment 1. Thrust one end of a glass tube to the bottom of 
 a basin of water; blow air from the lungs through the tube, and 
 watch the ascending bubbles. Do you see the air of the bubbles, or 
 do you see certain spaces from which the air has excluded the water ? 
 
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- 
 erty. 
 
 Observe the cloud (Fig. 4) 
 formed in front of the noz- 
 zle of a boiling tea-kettle. 
 All the matter which forms 
 the large cloud escapes from 
 the orifice, yet it is invisible 
 at that point, and only be- 
 comes visible after mingling 
 with the cold outside air. 
 Place the flame of an alcohol 
 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 
 
 weight ? 
 
 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. into the neck of a flask (Fig. 7) partly filled 
 with water insert very tightly a cork through which passes a glass 
 tube nearly to the bottom of the flask. Blow forcibly into the flask. 
 On removing the mouth the condensed air will cause the water to 
 flow in a stream. 
 
MATTER, ENERGY, MOTION, AND FORCE. 
 
 You will not attempt to say what 
 matter is. This, no one knows. You 
 may, however, give a provisional (an- 
 swering the present needs) definition of 
 matter, ix. draw the limiting line be- 
 tween 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 black- 
 board crayon, for this is not 
 chalk) a little fine dust, and 
 place it under a microscope, 
 you will probably discover 
 Fig. 7. that what seen with the naked 
 
 eye appear to be extremely small, shapeless particles, are 
 really clusters or heaps of shells and corals more or less 
 broken. Figure 8 
 represents such a 
 cluster. Each of 
 these shells is sus- 
 ceptible of being 
 broken into thou- 
 sands of pieces. 
 Reflecting that 
 one of these clus- 
 ters is so small as to be nearly invisible, you will readily 
 conceive that if one of the shells composing a cluster 
 should be broken into many pieces, and the pieces 
 separated from one another, they would be invisible to 
 the naked eye. Yet the smallest of the particles into 
 
 Fig. 8. 
 
MATTER AND ENERGY. T 
 
 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 
 called pores. 
 
 Water absorbs air and is itself absorbed by wood, paper, cloth, etc. It 
 enters the vacant spaces, or pores, between the molecules of these substances. 
 All matter is porous ; thus water may be forced through the pores of cast 
 iron ; and gold, one of the densest of substances, absorbs liquid mercury. 
 
 8. Volume, Mass, and Density. The quantity of space 
 a body of matter occupies is its volume, and is expressed 
 in cubic inches, cubic centimeters, etc. By the mass of a 
 body is meant the quantity of matter in the body. 
 
 1 References in this book are made to the Introduction to Chemical Science, by 
 B. P. Williams. 
 
8 MATTER, ENERGY, MOTION, AND FORCE. 
 
 The unit of mass generally employed in science is the 
 gram or the pound. The gram is the one-thousandth part 
 of the standard kilogram. This standard is a piece of plati- 
 num 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 substance 
 which, placed on a scale pan, would just balance in a vacuum 
 the standard kilogram placed on the other pan. 
 
 Experiment 6. Place on one pan of a balance (Fig. 9) 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 empty vessel. Then place upon the same pan a kilogram mass, C. 
 
 Fig. 9. 
 
 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.? If the weight of the water in A should change (its 
 mass remaining the same), should we be able to detect the change by 
 the balance? 
 
 Mass is quite distinct from weight. The weight of a body is the 
 measure of the attraction between it and the earth, and is variable, 
 because the attraction of the earth varies with the distance of the body 
 from the earth, while its mass remains constant, 
 
MATTEK AND ENERGY. 9 
 
 The process of measuring the mass of a body must not be con- 
 founded with the process of finding how heavy a body is, 
 although both processes are, in common usage, called weigh- 
 ing. Weighing a body to ascertain its mass consists in 
 balancing it with a body or bodies of known mass, and is 
 performed with a scale balance and a set of masses (com- 
 monly called a set of weights). Weighing to ascertain 
 weight should be performed with an instrument adapted to 
 measuring force ( 11), e.g. a spring balance (Fig. 10). 
 For most practical purposes, however, these instruments \ 
 may be used interchangeably, inasmuch as at the same place " 
 mass is proportional to weight. 1 
 
 Equal volumes of different substances (e.g. cork, cheese, 
 lead) contain unequal quantities of matter. Of any 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 body is meant the mass of a unit of volume 
 of the body. 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. 
 
 9. Three States of Matter. We recognize three states 
 or conditions of matter, viz., solid, liquid and gaseous, fairly 
 represented by earth, water and air. Every-day observa- 
 tion 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 tendency to flow are called fluids. 
 
 Which of the three states any portion of matter assumes depends upon 
 its temperature and pressure. For example, at ordinary pressure of the 
 
 1 This is one of many instances in physics in which one quantity is indirectly 
 measured by measuring another proportional to it. 
 
10 MATTER, ENERGY, MOTION, AND FORCE. 
 
 atmosphere water is a solid (i.e. ice), a liquid, or a gas (i.e. steam), accord- 
 ing to its temperature. In order that matter may exist in a liquid (and 
 sometimes in a solid) state, a certain definite pressure is required. Ice 
 vaporizes, but does not melt (i.e. liquefy) in a space from which the air 
 (and consequently atmospheric pressure) has been removed. 
 
 Section II. 
 
 RELATIVE MOTION AND RELATIVE REST. 
 
 1O. What constitutes Relative Motion and Rela- 
 tive Rest ? Motion is a progressive change of position. 
 Two boys walk toward each other, or one boy stands, 
 and another boy walks either toward or from him ; 
 in either case there is a relative motion between them, 
 because the length of a straight line (which may be imag- 
 ined to be stretched) between them constantly changes. 
 One boy stands, and another boy walks around him in a 
 circular path; there is a relative motion between them, 
 because the direction of a straight line between them 
 constantly changes. There is relative rest between two 
 boys while standing, because a straight line between them 
 changes neither in length nor direction. Two boys while 
 running are in relative rest so long as neither the distance 
 nor the direction from each other changes. 
 
 QUESTIONS. 
 
 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 
 bubble teach? 
 
FORCE. 11 
 
 6. What is impenetrability? State several properties that are 
 peculiar to matter. 
 
 7. Can water be rendered invisible ? How ? 
 
 8. Under what conditions would a flock of birds over your head be 
 at rest with reference to your body? Would the birds which com- 
 pose the flock be at rest with reference to one another ? An apple 
 rests upon a table ; are its molecules at rest ? 
 
 9. Why do all moving bodies possess energy? Do all molecules 
 possess energy ? 
 
 10. A span of horses harnessed abreast are drawing a street car on 
 a straight, level road. Is there any relative motion between the two 
 horses? Between the horses and the carriage? Between the team 
 and objects by the wayside ? Suppose them to be travelling in a cir- 
 cular path ; is there relative motion between the horses ? 
 
 11. A boat moves away from a wharf at the rate of five miles an 
 hour. A person on the boat's deck walks from the prow toward the 
 stern, at the rate of four miles an hour; what is his rate of motion, i.e. 
 his velocity, with reference to the wharf? What is his velocity with 
 reference to the boat? 
 
 12. When is there relative motion between two bodies ? 
 
 Section III. 
 
 FORCE. 
 
 11. Pushes and Pulls. We are familiar with the 
 results of muscular force in producing motion. We are 
 also aware that there are forces, or causes of motion, 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 
 silk threads. Rub a large stick of sealing-wax 
 with a dry flannel, and hold it near the balls. 
 The balls move to the wax as if pulled by it, 
 and remain in contact with it for 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. 13 
 
 force is measured by the extent of the elongation. 
 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. 
 
 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 +/and /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, +/ /= ; or, correctly interpreted, +/ / 
 (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 Keaction ; 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. 1 But when we consider the effect 
 on only one of two bodies, we find it convenient, and 
 almost a necessity, to speak of the effect as due to the 
 action of some other body, or, still more conveniently, to an 
 external force. The body which acts upon another, itself 
 experiences the effect of the reaction of the same force. 
 
 To increase or decrease the speed of a moving body, 
 or to change the direction of its motion, requires an un- 
 balanced force. Force may be provisionally denned as the 
 immediate cause that produces, or tends to produce, a change 
 of motion either in magnitude or direction. This definition 
 conveys no idea of what force is ; it merely distinguishes 
 between what is force and what is not force. 
 
 QUESTIONS. 
 
 1. Give a provisional definition of force. In what two ways is it 
 exerted ? 
 
 2. How is motion produced ? Destroyed? Changed in any way ? 
 
 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 
 estimated? What force is required to support 10 pounds of sugar? 
 
 1 Tension in a stretched rubber band, and pressure between two bodies in contact 
 when compressed, are illustrations of stress. 
 
ATTRACTION OF GRAVITATION. 15 
 
 8. Why will not a force of 10 pounds raise 10 pounds of sugar ? 
 If the force produces no change of motion, how can it consistently be 
 called a force ? 
 
 9. A bullet is flying unimpeded through space; does it possess 
 energy? Is it (disregarding the force of gravity) exerting force? 
 Would it exert force if it should encounter some other body? Which 
 produces motion, energy or force ? Which denotes ability to produce 
 motion ? 
 
 Section IV. 
 
 ATTRACTION OF GRAVITATION. 
 
 15. Gravitation is Universal. An unsupported body 
 falls to the earth. This is evidence of an action or stress 
 between the earth and the body. It has been ascertained 
 by careful observation that when a ball is suspended by 
 a long string by the side of a mountain, the string is 
 not quite vertical, but is deflected toward the mountain in 
 consequence of an attraction between the mountain and 
 the ball. That there is an attraction between the sun 
 and the earth, and the earth and the moon, is shown, as 
 we shall see further on, by their curvilinear motions. 
 Tides and tidal currents on the earth are due to the 
 attraction of the sun and the moon. 
 
 This attraction is called gravitation. When bodies under 
 its influence tend to approach one another, they are said 
 to gravitate. Since this attraction ever exists between all 
 bodies, at all distances, it is called universal gravitation. 
 
 16. Law of Universal Gravitation. Methods too 
 difficult for us to comprehend at present have estab- 
 
16 MATTER, ENERGY, MOTION, AND FORCE. 
 
 lished the fact that the strength of the attraction between 
 any two bodies depends upon two things; 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 <x 
 
 (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 
 
 ( = -) the attraction becomes one-fourth as great. 
 
 The mass of the moon is very much less than that of the earth ; hence 
 the force of gravity at the surface of the former is much less than at the 
 surface of the latter. A person who could leap a fence three feet high on 
 the earth, could, by the exertion of the same muscular energy, leap a fence 
 18 feet high on the moon. A boy might throw a stone a greater distance 
 on the moon than a rifle can project a bullet on the earth. The masses of 
 Jupiter and Saturn, being so much greater than that of the earth, the 
 corresponding greater attraction which they would exert would so impede 
 locomotion that a person would be able ojily to crawl along as though his 
 feet were weighted with lead. 
 
 1 7. Weight. The weight of a body is the measure of 
 the attraction between it and the earth. It is applied only 
 to terrestrial bodies. We say that the weight of a certain 
 body is ten pounds, meaning that this is the measure of 
 the force of attraction between this body and the earth. 
 
ATTRACTION OF GRAVITATION. 17 
 
 From the law of gravitation we infer that at equal dis- 
 tances from the earth's center of gravity the weight of 
 bodies varies as their masses. Hence, when we weigh a body 
 we measure at the same time both the force with which 
 the earth attracts it and its mass ; and both quantities 
 are commonly expressed in units of the same name. The 
 expression four pounds of tea conveys the twofold idea 
 that the quantity of tea is four pounds, and that the force 
 with which the earth attracts the tea is four pounds. 
 
 Again, we infer from the law of gravitation (1) that 
 a body iveighs more at a given point on the surface of the 
 earth than at any point above this point. 
 
 (2) That inasmuch as some points on the earth's sur- 
 face are nearer its center of gravity than others, the same 
 body will not have the same weight at all points on the earths 
 surface. A given body stretches a spring balance less as 
 it is carried from either pole toward the equator. The 
 loss of weight due to the increase of distance from the 
 center of the earth is -g-^g- of its weight at the poles. 
 
 18. Gravitation Units of Force. The weight of a 
 body is found by determining the elongation of the spring 
 in the spring-balance ( 12). The units employed are the 
 pound and the kilogram, and are called the gravitation 
 units 1 of force. All forces may be measured in the same 
 units. To say that a man pulls a boat with a force of one 
 hundred pounds is equivalent to saying that he pulls with 
 a force equal to the force which, at that locality, acts 
 between the earth and a body having a mass of one 
 
 1 There are two sytems of units in use, the Gravitation System and the Absolute 
 System. In the former the pound or kilogram denotes force or mass, in the latter 
 they denote only mass. 
 
18 MATTER, ENERGY, MOTION, AND FORCE. 
 
 hundred pounds. A force of one pound, then, is an 
 abbreviated expression for a force equal to the weight 
 (at the locality in question) of one pound of matter. 
 
 QUESTIONS. 
 
 1. If the earth's mass were doubled without any change of 
 volume, how would it affect your weight? 
 
 2. On what principle do you determine that the mass of one body 
 is ten times the mass of another body? 
 
 3. How many times must you increase the distance between the 
 centers of two bodies that their attraction may become one-fourth ? 
 
 4. If a body on the surface of the earth is 4,000 miles from the 
 center of gravity of the earth, and weighs at this place 100 pounds, 
 what would the same body weigh if it were taken 4,000 miles above 
 the earth's surface ? 
 
 Section V. 
 
 MOLECULAR FORCES. 
 
 19. Molecular Attractive Forces ; Molecular Dis- 
 tinguished from Molar Forces. Thus far we have 
 considered only the effects of the action of bodies of 
 sensible (perceived by the senses) size and at sensible 
 distances. Have we any evidence that the molecules 
 which compose these bodies act upon one another in a 
 similar manner? 
 
 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 
 
MOLECULAR FORCES. 19 
 
 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 ? 
 
 Every body of matter, whether solid, liquid, or gaseous, 
 may be forced into a smaller volume by pressure ; in 
 other words, matter is compressible. When pressure is 
 removed, the body expands into nearly or quite its 
 original volume. What is the cause ? According to the 
 theory of the constitution of matter ( 6) the molecules 
 of every mass are in ceaseless motion, hitting and re- 
 bounding from one another. This tends to drive the 
 molecules apart. In gaseous masses the molecules move 
 without restraint ; hence gaseous bodies always tend to 
 expand. In solids and liquids the molecules are held 
 under the action of a very powerful attractive force which 
 prevents their separation beyond certain limited distances 
 except under the action of considerable external force. 
 If, however, the molecular motions in solid and liquid 
 masses become great enough (i.e. the masses be sufficiently 
 heated) the molecules will become separated beyond the 
 limits of this attractive force, and the solids and liquids 
 will be converted into gases. 
 
 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- 
 ular force. 
 
 2O. Cohesion, Tenacity. That attraction which holds 
 the molecules of solids and liquids together, so as to form 
 
20 MATTER, ENERGY, MOTION, AND FORCE. 
 
 masses, 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 one another, pack themselves 
 closely together, and the two bodies will become firmly 
 united. This process is called welding. In this manner 
 iron is welded. 
 
 Cohesive force varies greatly both in intensity and its behavior in differ- 
 ent substances, and even in the same substances under different circum- 
 stances. Modifications of this force give rise to certain conditions of matter 
 designated as crystalline or amorphous, hard or soft, flexible or rigid, elastic, 
 viscous, malleable, ductile, tenacious, etc. 
 
 21. Crystallization. 
 
 Experiment 10. Pulverize about three 
 ounces of alum. Take about a teacupful of 
 boiling hot water in a beaker, and sift into it 
 the powdered alum, stirring with a glass rod 
 as long as the alum will dissolve readily. 
 Then suspend in the liquid to a little depth 
 one or more threads from a splinter of wood 
 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 
 
 more. 
 
MOLECULAR FORCES. 
 
 21 
 
 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. 
 
 Fig. 14. 
 
 Warm the glass over an alcohol or Bunsen flame, and pour upon the 
 glass a strong solution of sal ammoniac, or saltpetre. Allow the 
 liquid to drain off, and hold the wet glass up to the sunlight, or view 
 it through a magnifying glass, and watch the growth of the crystals. 
 
 Experiment 12. Examine with a magnifying glass the surface 
 'fracture of a freshly broken piece of sugar loaf, and observe, if any, 
 small, smooth, glistening planes thus exposed. 
 
 These planes are surfaces of small, imperfectly formed 
 crystals closely packed together, similar to the imperfect 
 
22 MATTER, ENERGY, MOTION, AND FORCE. 
 
 crystals of alum, etc., formed on the sides of the beaker. 
 Such bodies are said to have a crystalline fracture ', and the 
 body itself is said to be crystalline in distinction from 
 amorphous matter like glass, glue, etc., which furnish no 
 evidence of crystalline structure. 
 
 Very interesting illustrations of crystallization are those delicate lace- 
 like figures which follow the touch of frost on the window-pane. Figure 
 14 represents a few of more than a thousand forms of snowflakes that have 
 been discovered, resulting from a variety of arrangement of the water 
 molecules. 
 
 Snow crystals are formed during free suspension of moisture in the air 
 and without interference from contact with any solid; hence their per- 
 fection of growth. If you gather snowflakes, as they fall, on cold, yellow 
 glass and examine them under a magnifying glass, you will find that all 
 crystals have a primary type of six rays, and hexagonal outline. Professor 
 Tyndall has succeeded in so unravelling lake ice as to show what he calls 
 " liquid flowers " in a block of ice, thus proving that ice is crystalline, or 
 composed of a compact mass of crystals. (Read Tyndall's "Forms of 
 Water.") 
 
 Nature teems with crystals. Nearly every kind of matter, in passing 
 from the liquid state (whether molten or in solution) to the solid state, 
 tends to assume symmetrical forms. Crystallization 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. 
 
 22. Hardness. 
 
 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 ? 
 
 ITig. 15. 
 
 To enable us to express degrees of hardness, the following table of 
 reference is generally adopted : 
 
 MOHR S SCALE OF HARDNESS. 
 
 6. Orthoclase (Feldspar). 
 
 7. Quartz. 
 
 8. Topaz. 
 
 9. Corundum. 
 10. Diamond. 
 
 1. Talc. 
 
 2. Gypsum (or Rock-Salt). 
 
 3. Calcite. 
 
 4. Fluor-Spar. 
 
 5. Apatite. 
 
 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 
 called annealing. 
 
 Next heat the opposite ends of the wires as before, and slowly (10 
 to 15 minutes) withdraw the wires from the flame by gradually 
 raising them above the flame, in order that the fall of 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. 
 
 24. Elasticity. 
 
 Experiment 15. Obtain thin strips of as many of the following 
 substances as practicable : rubber, different kinds of wood, ivory, 
 whalebone, steel, spring brass and soft brass, copper, iron, zinc, and 
 lead. 
 
 Bend each one of the above strips. Note which completely unbends 
 when the force is removed. Arrange the names of these substances in 
 the order of the rapidity and completeness with which they unbend. 
 
 The property which matter possesses of recovering its former form 
 or volume, 1 after having yielded to some force, is called elasticity. 
 
 25. Viscosity. 
 
 Experiment 16. Support in a horizontal position, at one of its 
 extremities, a stick of sealing-wax, and suspend from its free extrem- 
 ity an ounce weight, and let it remain in this condition several days, 
 or perhaps weeks. At the end of the time the stick will be found 
 permanently 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. 
 
 1 It is called elasticity of form when the form is restored after removing the 
 distorting force, and elasticity of volume when the original volume is restored. 
 Fluids possess only elasticity of volume. 
 
MOLECULAR FORCES. 25 
 
 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 around 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 sWozrtf ^ 
 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 
 between molecules of unlike matter. That force which 
 causes unlike substances to cling together is called ad- 
 hesion.^ 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 is stretched, it is said to be 
 in a state of tension, and there exists between its molecules a contractile 
 or resilient stress which tends to restore the body to its normal condition. 
 A rubber balloon inflated with compressed air is in a state of tension in 
 every direction. 
 
 29. Surface Tension and Surface Viscosity. Every 
 liquid behaves as if a thin film forming its external layer were ever in a 
 state of tension, or were exerting a constant effort to contract. This 
 superficial film is tough or hard to break as compared with the interior 
 mass. This property is called surface viscosity. It is not within the scope 
 of this book to explain how the molecular forces produce this result ; it 
 must suffice to call attention to the peculiar condition, with reference to 
 mutual attractions, of those molecules which compose the surface film. 
 In the interior of a liquid body each molecule is surrounded by other 
 similar molecules, and is acted upon equally in all directions. At a free 
 surface the molecules can be acted upon only by others lying internal to 
 them ; the outcome of this is that it tends to reduce the free surface to 
 the least possible area. This tendency of a liquid surface to contraction 
 means that it acts like an elastic membrane, equally stretched in all 
 directions, and by a constant tension. 
 
 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 
 
 1 This distinction is merely a matter of convenience. It must not be supposed 
 that the forces of cohesion and adhesion themselves differ. 
 
MOLECULAK FORCES. 
 
 27 
 
 Fig. 15a. 
 
 contracts to a flat sheet. The viscosity of a free surface of a solution 
 of soap in water is greater than that of pure water ; hence its greater 
 adaptability to the formation of bubbles. 
 
 As a consequence of surface tension, every body of liquid tends to 
 assume a spherical form, since the sphere has less surface than any 
 other form having equal volume. In large bodies of liquids the 
 superior force of gravitation generally disguises this effect ; but in 
 small bodies, as in drops of water or mercury, it is quite apparent. 
 
 3O. 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 
 
 separating water and air always meets clean 
 
 glass at a very small angle (Fig. 15a) ; that 
 
 separating mercury and air meets glass at an 
 
 angle of about 135. If clean silver is substi- 
 tuted for glass, the first angle becomes large, 
 
 not far from 90, while the second would be 
 
 reduced to zero; in other words, the mercury 
 
 creeps along the surface of silver, its own air-exposed surface being 
 
 parallel with that of the silver. 
 
 From this it follows, that it a glass tube be dipped into water, the free 
 
 surface of the water within the bore will be concave, and the surface 
 
 tension will cause an upward pull upon the liquid, and the liquid will 
 
 rise in the bore above its level outside ; while, if the tube be dipped into 
 mercury, the free surface of the mercury 
 within the bore will be convex, and the 
 surface tension will cause a pressure upon 
 the liquid, and the mercury will be de- 
 pressed below the level outside. 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 is reduced 
 one-half, but the cross-section will be re- 
 duced 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 
 
 capillary tube is inversely proportional to the diameter of the bore. 
 
 fig. 16. 
 
 Fig. 17. 
 
28 MATTER, ENERGY, MOTION, AND FORCE. 
 
 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 ? What 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 ? 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 upper surfaces of both 
 ^ 4 liquids. 
 
 V / Experiment 21. Wipe the surface of a 
 
 \ JL / small cambric needle with an oily cloth and 
 
 "^(BB^^^^rKf^^^BHIMi^ 
 
 place it carefully on the surface of a cup of 
 
 water. The water surface will meet the oily 
 
 Tp|<r 1 "73, ^ 
 
 surface at an angle of about 135, and the 
 
 surface tension of the liquid will act as a supporting force as repre- 
 sented by the arrows in Figure 17a, and the needle will float in a 
 trough-shaped depression in the liquid surface. 
 
 QUESTIONS, 
 
 1. Why are pens made of steel ? What moves the machinery of 
 a watch ? What is the cause of the softness of a hair mattress or 
 feather-bed? On what does the entire virtue of a spring balance 
 depend ? 
 
 2. What name would you give to the attraction which causes your 
 hands to be wet by a liquid ? Is it a molar or a molecular force ? 
 
 3. The tension of a violin string is 2 pounds ; what is meant by 
 this statement ? 
 
 4. Why are bubbles and liquid drops round ? 
 
CHAPTER II. 
 
 DYNAMICS* OF FLUIDS. 
 
 Section I. 
 
 PRESSURE IN FLUIDS. 
 
 31. Cause of Pressure. We live above a watery 
 ocean and at the bottom of an exceedingly rare and elas- 
 tic aerial ocean, called the atmosphere, extending with a 
 diminishing density to an undetermined distance into 
 space. Every molecule, in both the gaseous and liquid 
 oceans, is drawn toward the earth's center by gravity. 
 This gives to both fluids a downward pressure upon 
 everything on which they rest. 
 
 The gravitating action of liquids is everywhere appar- 
 ent, as in the fall of drops of rain, 
 the descent of mountain streams, 
 and the weight of water in a 
 bucket. But to perceive that air 
 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 
 we raise a pailful out of the water, it suddenly appears 
 
 1 Dynamics is the science which investigates the action of force. 
 
30 
 
 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 
 riot feel the downward pressure of the 
 air directly above it, the pressure being 
 sustained by the rigid glass bottom. But 
 it indirectly feels the pressure of the air 
 on the surface of the water in the open 
 vessel, and it is this pressure that sus- 
 tains the water in the jar. But the 
 rubber bottom of the jar B yields some- 
 what to the downward pressure of the 
 air, and is forced inward. 
 Experiment 23. Fill a glass tube, D, with water, keeping one 
 
 end in the vessel of water, and a finger 
 
 tightly closing the upper end. Why 
 
 does not the water in the tube fall? 
 
 Remove your finger from the closed 
 
 end. Why does the water fall ? 
 
 Experiment 24. Fill (or partly 
 
 fill) a tumbler with water, cover the 
 
 top closely with a card or writing-paper, hold the paper in place 
 
 with the palm of the hand, and quickly invert the tumbler (Fig. 19). 
 
 Why does not the water fall out? 
 Experiment 25. Force the piston A (Fig. 20) of the seven-in-one 
 
 apparatus (so called from the number of experiments that may be 
 
 performed with one piece of apparatus) quite to the closed end of the 
 
 Fig. 19. 
 
 Fig. 30. 
 
PRESSURE IN FLUIDS. 
 
 31 
 
 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 
 Different Directions. 
 
 Experiment 27. Take a glass tube about 30 inches long and 
 one-fourth inch bore, and bend it into the shape of A (Fig. 22). Also 
 prepare tubes like B and C. Let the 
 bend a be about half full of water. 
 Slowly lower the end n into a tumbler 
 filled with water. The water presses 
 up against the air in the tube, and 
 the air transmits the pressure to the 
 liquid in the bend. How is the pres- 
 sure affected by depth? Does it 
 increase as the depth ? 
 
 Experiment 28. Connect c with 
 d by means of a rubber tube, and 
 lower the extremity m into the tum- 
 bler of water. As the tube is turned 
 up, the water must now press down 
 the tube against the air. Does the downward pressure increase as 
 the depth? 
 
 Experiment 29. Connect e with c, and lower o into the water. 
 The water now presses laterally (sidewise) against the air. Does the 
 lateral pressure increase as the depth? 
 
 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 
 
 Fig. 22. 
 
32 
 
 DYNAMICS OF FLUIDS. 
 
 tig. 3. 
 
 the 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 
 pressure equal in all directions ? 
 
 Experiment 32. Connect the two 
 brass tubes at the extremities F and G 
 (Fig. 23). Fill the cup of the (eight- 
 in-one) apparatus with water, and re- 
 move the caps A, B, C, and D from 
 the branch tubes, so as to permit water 
 to escape from the orifices at their 
 ends. Does the water issuing from 
 these orifices show a lateral pressure ? 
 What difference do you observe in the 
 flow of water from the different 
 orifices? How do you account for 
 it? 
 
 The results of experiments 
 thus far show that at every 
 point in a body of fluid gravity 
 causes pressure to be exerted 
 equally in all directions, and 
 that in liquids the pressure in' 
 creases as the depth increases. 
 
MEASUREMENT OF ATMOSPHEEIC PRESSURE. 
 
 33 
 
 Section II. 
 
 Fig. 24. 
 
 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 go 
 
 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 the 
 
 same level in both arms ? 
 
 Figure 25 represents a U-shaped glass tube closed at one end, 34 
 inches in hight, and with a bore of 1 square inch 
 section. The closed arm having been filled with 
 mercury, the tube is placed with its open end up- 
 ward, as in the cut. The mercury in the closed arm 
 sinks about 2 inches to A, and rises 2 inches in the 
 open arm to C ; but the surface A is 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 
 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 
 the weight of a column of air of 1 square-inch sec- 
 tion, extending from the surface of the sea to the 
 upper limit of the atmosphere, is about 15 pounds. 
 But in fluids gravity causes equal pressure in all 
 directions. Hence, at the level of the sea, all bodies 
 
 are pressed upon in all directions by the atmosphere, with a force of about 
 
 15 pounds per square inch, or about one ton per square foot. 
 
 Fig. 35. 
 
34 
 
 DYNAMICS OF FLUIDS. 
 
 A pressure of 15 pounds per square inch is quite generally adopted 
 as a unit of gaseous pressure, and is called an atmosphere. 
 
 Fig. 6. 
 
 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 inches long 
 is closed at one end and filled with mer- 
 cury. A finger tightly closing the open 
 end, the tube is inverted, and this end is 
 inserted in a vessel of mercury and the 
 finger is withdrawn, when the mercury 
 sinks until there is equilibrium between 
 the downward pressure of the mercurial column AB and 
 
BAROMETERS. 35 
 
 the pressure of the atmosphere. An apparatus designed 
 to measure atmospheric pressure is called a barometer 
 (pressure-measurer). A common form of barometer is 
 represented in Figure 27. Beside the tube and near its 
 top is a scale graduated in inches or centimeters, indi- 
 cating the hight of the mercurial column. For ordinary 
 purposes this scale needs to have only a range of three or 
 four inches, so as to include the maximum fluctuations 
 of the column. 
 
 The hight of the barometric column is subject to fluc- 
 tuations ; this shows that the atmospheric pressure is sub- 
 ject to variations. The barometer is always a faithful 
 monitor of all changes in atmospheric pressure. It is also 
 serviceable as a weather indicator. It does not indicate 
 weather that is present, but foretells coining 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 observations. 
 
 The aneroid can be made more sensitive (i.e. so as to show smaller 
 changes of atmospheric pressure) than the mercurial barometer. If a 
 
36 DYNAMICS OF FLUIDS. 
 
 barometer is carried up a mountain, it is found that the mercury con- 
 stantly 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 approxi- 
 mately the hights of mountains by ascertaining the barometric readings 
 on the summit and at sea-level. 
 
 If a mercurial barometer stand at 760 mm on the floor, the same barom- 
 eter on the top of a table l m high should stand at a hight of 759.91 mm , 
 
 a change scarcely perceptible. The an- 
 eroid is, however, sometimes made so 
 sensitive that the change of pressure ex- 
 perienced in this short distance is ren- 
 dered quite perceptible. 
 
 The barometer is sometimes called a 
 " weather-glass," chiefly because its scale 
 frequently bears the words /air, rainy, 
 storm, etc. These words are very objec- 
 tionable, since they are totally wrong 
 from a meteorological point of view. To 
 form a forecast of the weather of much 
 Fi 88 value, a barometer, a thermometer, and 
 
 a hygrometer must be consulted, and one 
 
 must be familiar with the laws which govern the relations between 
 atmospheric pressure, temperature, moisture, etc. 
 
 Many physical operations require a standard pressure for reference. 
 The standard generally adopted is the pressure exerted by a column of 
 pure mercury at C. and 76 cm (29.922 inches) high, which is about the 
 average hight of the barometric column at sea-level in latitude 45. The 
 pressure corresponding to this hight is 1033.3 grams per square centi- 
 meter, or 14.69 pounds per square inch. 
 
 The shading in Figure 29 is intended to indicate roughly the variation 
 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. 
 
 If an opening could be made in the earth 35 miles in depth below the 
 sea-level, it is caleulated 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 compressed to this density. 
 
BAROMETERS. 
 
 37 
 
 To what hight the atmosphere extends is unknown. It is variously 
 estimated at from 50 to 200 miles. If the aerial ocean were of uniform 
 
 -nfoa 
 
 Fig. 29. 
 
 density, and of the same density that it is at sea-level, its depth would be 
 a little short of five miles. Certain peaks of the Himalayas would rise 
 above it. 
 
 QUESTIONS. 
 
 1. What is the pressure per square centimeter when the barometric 
 reading is 770 mm ? 
 
 2. At a certain point on a mountain the average barometric hight 
 is 24.5 inches ; what is the average atmospheric pressure at this 
 point ? 
 
 3. What is the approximate elevation of the point mentioned in 
 the last question above the sea-level? 
 
 4. Consult Figure 29, and determine what portion of the matter of 
 the atmospheric ocean must be below the summit of Mt. Blanc. 
 
38 DYNAMICS OF FLUIDS. 
 
 Section III. 
 
 COMPRESSIBILITY AND ELASTICITY OF GASES. BOYLE'S 
 
 LAW. 
 
 37. Compressibility of Gases. The increase of pres- 
 sure attending the increase in depth, in both liquids and 
 gases, is readily explained by the fact that the lower layers 
 of fluids sustain the weight of all the layers above. Con- 
 sequently, if the body of fluid is of uniform density, as is 
 very nearly the case in liquids, the pressure will increase 
 in nearly the same ratio as the depth increases. But the 
 aerial ocean is far from being of uniform density, in con- 
 sequence of the extreme compressibility of gaseous matter. 
 The contrast between water and air, in this respect, may 
 be seen in the fact that water subjected to a pressure of 
 one atmosphere is compressed 0.0000457 its volume ; under 
 the same circumstances, air is compressed one-half. For 
 most practical purposes, we may regard the density of 
 water at all depths as uniform, while it is far otherwise in 
 large masses of gases. 
 
 38. Elasticity of Gases. Closely allied to com- 
 pressibility is the 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 will cause the piston to rise, and raise 
 
 the weight. 
 
 Experiment 35. Arrange the same apparatus 
 
 as in Figure 30. Attach a small rubber tube to 
 
 the short tube, and suck as much air out of the 
 
 cylinder as possible. The air within, being rarefied, 
 
 exerts less pressure, 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- 
 pump. 
 
 Experiment 36. Take a glass tube (Fig. 31) 
 having a bulb blown at one end. Nearly fill it 
 with water, so that when inverted there will be only 
 a bubble of air in the bulb. Insert the open end 
 in a glass of water, place under a receiver, and 
 exhaust. Nearly all the water will leave the bulb 
 
 and tube. Why? What will happen when air is admitted to the 
 
 receiver ? 
 
 Fig. 30. 
 
 Fig. 31. 
 
40 
 
 DYNAMICS OF FLUIDS. 
 
 -Bi 
 
 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 
 (85 cm ) long, being open at the top. Pour mercury 
 into the tube till the surfaces in the two arms are at 
 the same level AB. The body of air to be experi- 
 mented with is in the short arm between A and C. 
 The dimensions of this body can vary only in 
 hight ; hence its hight, H, may represent its volume. 
 Measure H (i.e. the distance between A and C) and 
 regard the number of inches (or centimeters) as 
 representing the volume, V. Its pressure, P, evi- 
 dently is the same as that of the atmosphere at the 
 time. Consult a barometer, and ascertain the hight 
 of the barometric column ; represent this hight by 
 P. Pour a little mercury into the tube ; the mer- 
 cury rises (say) to A l and Bj . Measure the verti- 
 cal distance between A 1 and C ; this number repre- 
 sents the volume, V x , of the body of air now. 
 Measure the vertical distance between A 1 and B x ; 
 this number represents the increase in pressure, 
 which, added to P, gives its present pressure, P 1 . 
 Now pour more mercury into the tube, so that it will rise to (say) 
 A 2 and B 2 . Determine as before the new volume, V 2 , and the new 
 pressure, P 2 . So continue to add mercury a third and a fourth time, 
 and get new values for the volume, V 3 and V 4 , and for the pressure, 
 P 3 and P 4 . Arrange the results as follows : 
 
 V = P = v X P = 
 
 Va ='.'.'.'.'. P! = V 2 X P 2 = 
 
 etc. etc. 
 
 It will be found that the series of products in the last column are 
 approximately equal (due allowance being made for errors in meas- 
 urement, etc.) ; consequently the product of the volume of a body of 
 gas multiplied by its pressure is constant, and the volume varies 
 inversely as its pressure. Hence the (Boyle's) law : 
 
 The volume of a body of gas at a constant temperature varies inversely 
 as its pressure, density, and elasticity. 
 
 B 
 
 Fig. 32. 
 
RAREFYING AND CONDENSING INSTRUMENTS. 41 
 
 For many years after the announcement of this law it was believed to be rigor- 
 ously correct for all gases ; but more recently more precise experiments have shown 
 that it is approximately but not rigidly true for any gas. There is a limit beyond 
 which this law does not hold. This limit is soonest reached with those gases, like 
 carbon-dioxide, chlorine, etc., that are most readily liquefied. A gas conforms more 
 nearly to Boyle's law, in proportion as it is farther, as regards both pressure and 
 temperature, from its liquefying point. As a gas approaches this point its density 
 increases more rapidly than its elasticity. 
 
 Section IV. 
 
 INSTRUMENTS USED FOR RAREFYING AND CONDENSING 
 
 AIR. 
 
 4O. 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 
 pump-barrel. The 
 plug P, called a 
 piston, is fitted to 
 the interior of the 
 barrel, and can be m s- 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 
 
42 DYNAMICS OF FLUIDS. 
 
 the air in B closes the valve , and opens the valve s, and 
 the enclosed air escapes. After the piston reaches the 
 bottom of the barrel, it begins its ascent. This would 
 cause a vacuum between the bottom of the barrel and the 
 ascending piston (since the unbalanced pressure of the 
 outside air immediately closes the valve *), but the pressure 
 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 
 exerts less pressure. The external pressure of the air on 
 R, being no longer balanced by the pressure of the air 
 within, presses the receiver firmly upon the plate L. Each 
 repetition of a double stroke of the piston removes a por- 
 tion of the air remaining in R. The air is removed from 
 R by its own expansion. However far the process cf 
 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 
 pressure of the air in R becomes too feeble to lift the valve t. 
 Sometimes another receiver, D, is used, opening into the 
 tube T, that connects the receiver with the barrel. Inside 
 the receiver is placed a barometer. It is apparent that air 
 is exhausted from D as well as from R ; and, as the pres- 
 sure is removed from the surface of the mercury in the 
 cup, the barometric column falls ; so that the barometer 
 serves as a gauge to indicate the approximation to a 
 vacuum. For instance, when the mercury has fallen 
 380 mm (15 inches), one-half of the air has been removed. 
 
 41. The Mercury Air-Pump. In recent years the 
 so-called mercury air-pump has largely displaced the pump 
 described above, since it is capable of producing a much 
 greater rarefaction. In brief, it makes use of the Torri- 
 cellian vacuum, such as is formed in the top of a barometer 
 tube. On account of its simplicity, the Geissler pump, 
 
RAREFYING AND CONDENSING INSTRUMENTS. 43 
 
 Fig. 34 
 
 the first of the kind invented, is chosen for illustration. 
 A (Fig. 34) is a glass tube more than thirty-four inches 
 long, having a globe-like enlargement B of about a liter 
 capacity. Above this globe 
 leads a tube containing a 
 three-way stop-cock and a 
 branch tube D. By means 
 of this stop-cock B may be 
 placed in communication 
 either through D with the 
 atmosphere, as shown in M 
 (Fig. 35), or through E 
 with the receiver to be ex- 
 hausted, as shown in N. 
 Connected with the lower 
 end of A by means of a thick rubber tube is a vessel G 
 containing mercury. The pump is operated as follows : 
 C is turned as in M, G is raised so that the mercury will 
 flow from it into B and fill it, the air escaping through D. 
 Then the stop-cock is placed as in N, and G is lowered so 
 as to allow the mercury to flow back into it. A Torricel- 
 lian vacuum would be formed in B were it not in commu- 
 nication through E with the receiver. AS it is, the air in 
 this space expands and fills B, and is thus to this extent 
 rarefied. By a sufficient number of repetitions of this 
 process, a very high vacuum is obtainable. There are many 
 modifications of this pump, in some of which the stop-cock 
 is dispensed with, and consequently the trouble of operat- 
 ing it is avoided. With the common pump a vacuum of 
 a millimeter of mercury is considered exceedingly good ; 
 but with a mercury pump it is easy to obtain a vacuum of 
 .00076 of a millimeter, which represents about one mil- 
 lionth the normal pressure of the atmosphere. 
 
44 
 
 DYNAMICS OF FLUIDS. 
 
 42. Condenser. 
 
 Experiment 39. Blow into a U-shaped glass tube open at both 
 ends and partly filled with mercury. Measure the vertical distance 
 between the two surfaces of mercury and calcu- 
 late the excess of the pressure of the condensed 
 air above that of 
 the atmospheric 
 pressure. 
 
 Figure 6, page 
 5, represents in 
 perspective, and 
 Figure 36, in sec- 
 tion, an appara- 
 tus for condens- 
 ing air, called a 
 condenser. Its 
 Fig. 36. construction is 
 
 like that of the barrel of an air-pump, except that the 
 direction in which the valves open is reversed. 
 
 Experiment 40. Place a block having a wide platform at one 
 end on the piston of the seven-in-one apparatus. On the platform let 
 a child stand. By means of a condensing syringe (Fig. 6), connected 
 by a rubber tube with the seven-in-one apparatus (Fig. 37), condense 
 the air in the cylinder and raise the child. 
 
 Section V. 
 
 APPARATUS FOR RAISING LIQUIDS. 
 
 43. Lifting or Suction Pump. The common lifting- 
 pump is constructed like the barrel of an air-pump. Fig- 
 ure 38 represents the piston B in the act of rising. As 
 
UNIVERSITY OF CALIFORNIA 
 
 DEPARTMENT OF PHYSICS 
 APPARATUS FOE RAISING LIQUIDS. 
 
 45 
 
 the air is rarefied below it, water rises in consequence 
 of atmospheric pressure on the water in the well, and 
 opens the lower valve D. Atmospheric pressure closes 
 
 Fig. 39. 
 
 Fig. 40. 
 
 the upper valve C in the piston. When 
 the piston is pressed down (Fig. 39), the 
 lower valve closes, the upper valve opens, 
 and the water between the bottom of the 
 barrel and the piston passes through the 
 Fig. ss. 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 Vi s *! 
 it impossible. Remove the finger from b, and you can suck the liquid 
 out with ease. Why? 
 
46 
 
 DYNAMICS OF FLUIDS. 
 
 44. Force-Pump. The piston of a force-pump (Fig. 
 42) has no valve, but a branch pipe a leads from the lower 
 part of the barrel to an air-condensing chamber >, 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. 
 When the piston is forced down, the 
 valve d closes, the valve c opens, and the 
 water is forced into the chamber 6, con- 
 densing the air above the water. The 
 elasticity of the condensed air forces the 
 water out of the tube e in a continuous 
 stream. 
 
 QUESTIONS AND PROBLEMS. 
 
 1. What force is the cause of fluid pressure ? 
 
 2. Why does not a person at the bottom of a 
 pond feel the weight of the water above him ? 
 
 3. An aeronaut finds that on the earth his 
 barometer stands at 30 inches. He ascends in a 
 balloon until the barometer stands at 20 inches. 
 About how high is he ? What is the pressure of 
 the atmosphere at his elevation ? 
 
 4. When a barometer stands at 30 inches, the 
 atmospheric pressure is 14.7 pounds. What is 
 
 the atmospheric pressure when the barometer stands at 29 inches ? 
 
 5. Why is a barometer tube closed at the top ? Why must air come 
 in contact with the mercury at the bottom ? 
 
 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 
 balloon ? 
 
 8. Mercury is 13.6 times denser than water. When a mercurial ba- 
 
 Fig. 43. 
 
TRANSMISSION OF EXTERNAL PRESSURE. 47 
 
 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 coukl water be raised by the same means? How 
 many times higher can water be raised by a suction-pump than mer- 
 cury? 
 
 9. What is that which is sometimes called the "force of suction "? 
 
 10. The area of one side of the piston of the seven-in-one apparatus 
 is about 26 square inches. Suppose the piston to be forced into the 
 cylinder so as to drive out all the air, and then the orifice to be closed ; 
 what force would be required to draw the piston out, when the barom- 
 eter stands at 30 inches ? What force would be required on the top of 
 a mountain where the barometer stands r,,t 15 inches ? 
 
 11. Water is raised the larger part of the distance in our lifting- 
 pumps by atmospheric pressure ; why, then, is not such a pump a 
 labor-saving instrument? 
 
 12. If water is to be raised from a well 50 feet deep, how high must 
 it be lifted, and how long must the barrel be? 
 
 Section VI. 
 
 TRANSMISSION OF EXTERNAL PRESSURE. 
 
 45. Pressure Transmitted TJndiminished in All Direc- 
 tions. 
 
 Experiment 42. Fill the glass globe and cylinder (Fig. 43) with 
 water, and thrust the piston into the cylinder. Jets of water will be 
 thrown not only from that aperture a in the globe toward which the 
 piston moves and the pressure is exerted, but from apertures on all 
 sides. Furthermore, the streams extend to equal distances in every 
 direction. 
 
 It thus appears that external pressure is exerted not 
 alone upon that portion of the liquid that lies in the 
 path of the force, but it is transmitted equally to all 
 parts and in all directions. 
 
48 
 
 DYNAMICS OF FLUIDS. 
 
 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 40 mm and 
 10 mm ; then the areas of the transverse 
 sections of the bores will be 40 2 : 10 2 = 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 l cm 
 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 l cm of being 
 full. The pressure of 
 the water causes the 
 mercury to rise in the 
 small arm, and to be 
 depressed in the large 
 arm. Pour water very 
 slowly into, the small 
 arm from a beaker having a narrow lip, until the surfaces of the water 
 in the two arms are on the same level. It is evident that the quantity 
 of water in the large arm is 16 times as great as that in the small arm. 
 This phenomenon appears paradoxical (apparently contrary to the natu- 
 ral course of things), until we master the important hydrostatic princi- 
 ple involved. We must not regard the body of mercury as serving as 
 a balance beam between the two bodies of water, for this would lead 
 to the absurd conclusion that a given mass of matter may balance an- 
 other mass 16 times as great. We may best understand this phenom- 
 enon by imagining the body of liquid in the large arm to be divided 
 into cylindrical columns of liquid of the same size as that in the small 
 arrn. There will evidently be 16 such columns. Then whatever 
 pressure is exerted on the mercury by the water in the small arm is 
 transmitted by the mercury to each of the 16 columns, so that each 
 column receives an upward pressure, or a supporting force equal to 
 the weight of the water in the small arm. This method of transmit- 
 
 Fig. 43. 
 
 Fig. 44. 
 
TRANSMISSION OF EXTERNAL PRESSURE. 
 
 49 
 
 ting pressure is peculiar to fluids. With solids it is quite different. 
 If the mercury in our experiment were a solid body, it would require 
 equal masses of water placed upon the two extremities to counter- 
 balance each other. 
 
 Experiment 44. Support the seven-in-one apparatus with the 
 open end upward, force the piston in, and place on it a block of wood 
 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 
 tube. Raise the latter end as high as practi- 
 cable, and pour water into the tube. Explain 
 how the few ounces of water standing in the 
 tube can exert a pressure of many pounds on 
 the piston, and cause it to rise together with 
 the burden that is on it. 
 
 Fig. 45. 
 
 Fig. 46. 
 
 Experiment 45. Remove the water from the apparatus, place on 
 the piston a 16-pound weight, and blow (Fig. 48) 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 pressure 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- 
 creased. 
 
50 
 
 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 a?, 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 
 Flg * 47 ' of one hundred pounds 
 
 is applied at 8, 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. 
 
 51 
 
 Section VII. 
 
 PRESSURE EXERTED BY LIQUIDS DUE TO THEIR OWN 
 WEIGHT. 
 
 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 
 
52 
 
 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 
 different, the pressure upon the bottom of a vessel is the same, provided the 
 bottom is of the same area. 
 
 48. Methods of Calculating Liquid Pressure. Conceive 
 of a square prism of water (Fig. 51a) in the midst of a body of water, its 
 
 upper surface coinciding with 
 the free surface of the liquid. 
 Let the prism be 4 cm deep and 
 l cm square at the end ; then 
 the area of one of its ends is 
 licm ? anc i the volume of the 
 prism is 4 cc . Now the weight 
 - of 4 CC of water is 4s, hence this 
 prism must exert a downward 
 pressure of 4e upon an area of 
 1 <i cin . But at the same depth 
 the pressure in all directions 
 is the same, hence, generally, 
 the pressure at any depth in 
 water may be taken approxi- 
 mately as one gram per square 
 centimeter for each centimeter 
 of depth (=0= l,000 k per qm 
 for each meter of depth; or, 
 Fig. 5la. since the weight of water is 
 
 about 62.3 Ibs. per cu. ft., the 
 
 pressure is 62.3 Ibs. per square foot for each foot of depth). In any other 
 liquid, to determine the pressure at any depth the water pressure at the 
 given depth must be multiplied by the specific gravity of the liquid. 
 
 The conclusions arrived at may be summarized as follows : The 
 pressure due to gravitation on any portion of the bottom of a vessel contain- 
 ing 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. 
 
PRESSURE EXERTED BY LIQUIDS. 53 
 
 Evidently the lateral pressure at any point of the side of a vessel 
 depends upon the depth of that point ; and, as depth at different points 
 of a side varies, hence, to find the pressure upon any portion of a side of a 
 vessel, we find the weight of a column of liquid whose base is the area of 
 that portion of the side, and whose hight is the average depth of that portion. 
 
 49. The Surface of a Liquid at Best is Level. This 
 fact is commonly expressed thus: "Water always seeks 
 its lowest level." In accordance with this principle, water 
 flows down an inclined plane, and will not remain heaped 
 up. An illustration of the application of this principle, on 
 a large scale, is found in the method of supplying cities 
 with water. Figure 52 represents a modern aqueduct, 
 through which water is conveyed from an elevated pond 
 or river a, beneath a river 6, over a hill <?, through a valley 
 
 Fig. 52. 
 
 d, to a reservoir 0, 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? 
 
54 
 
 DYNAMICS OF FLUIDS. 
 
 Section VIII. 
 
 THE SIPHON. 
 
 5O. Construction and Operation of the Siphon. A 
 
 siphon is an instrument used for transferring a liquid from 
 one vessel to another through the agency of atmospheric 
 pressure. It consists of a tube of any material (rubber is 
 often most convenient) bent into a shape somewhat like 
 the letter U. To set it in operation, fill the 
 tube with a liquid, stop each end with a 
 finger or cork, place it in the position rep- 
 resented in Figure 53, remove the stoppers 
 and the liquid will all flow out at the orifice 
 o. Why? The upward pressure of the at- 
 mosphere against the liquid in the tube is 
 the same at both ends ; hence these two 
 forces are in equilibrium. But the weight 
 of the column of liquid db is greater than 
 the weight of the column dc\ 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 
 zero. 
 
 Fig. 53. 
 
 If one .of the vessels is raised a little, as in C, the liquid will flow from 
 the raised vessel, till the surfaces in the two vessels are on the same level 
 
THE SIPHON. 
 
 55 
 
 The remaining diagrams in this cut represent some of the great variety of 
 uses to which the siphon may be put. D, E, and F are different forms of 
 siphon fountains. In D, the siphon tube is filled by blowing in the tube /. 
 Explain the remainder of the operation. A siphon of the form G is always 
 ready for use. It is only necessary to dip one end into the liquid to be 
 
 54. 
 
 transferred. Why does the liquid not flow out of this tube in its present 
 condition"? H illustrates the method by which a heavy liquid may be 
 removed from beneath a lighter liquid.. By means of a siphon a liquid 
 may be removed from a vessel in a clear state, without disturbing sediment 
 
56 
 
 DYNAMICS OF FLUIDS. 
 
 at the bottom. I is a Tantalus Cup. 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 end j in the liquid, stopping 
 the end k, and sucking the air out at the end / till the lower end is filled 
 with the liquid. 
 
 Gases heavier than air may be siphoned like liquids. Vessel o contains 
 carbonic-acid gas. As the gas is siphoned into the vessel p, it extinguishes 
 a candle-flame. Gases lighter than air are siphoned by inverting both the 
 vessels and the siphon. 
 
 Section IX. 
 
 BUOYANT FORCE OF FLUIDS. 
 
 51. Origin of Buoyancy. 
 
 Experiment 47. Gradually lower a large stone, by a string tied 
 to it, into a bucket of water, and notice that 
 its weight gradually becomes less till it is com- 
 pletely submerged. Slowly raise it out of the 
 water, and note the 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. 
 
 It seems as if something in the fluid, 
 underneath the articles submerged, were 
 pressing up against them. A moment's re- 
 flection will make the explanation of this 
 phenomenon apparent. We have learned (1) that pressure 
 at any given point in a body of fluid is equal in all direc- 
 tions. (2) That pressure in liquids increases as the 
 
 Fig. 55. 
 
BUOYANT FORCE OF FLUIDS. 
 
 57 
 
 depth. Consequently, the downward pressure on the top 
 (i.e. the place of least depth) of a body immersed in a 
 fluid, as dcba (Fig. 55), must be less than the upward 
 pressure against the bottom; hence, there is an unbal- 
 anced force acting upward, which tends to neutralize to 
 some extent the weight or gravity of the body. This 
 unbalanced force is called the buoyant force of fluids. 
 That there is equilibrium between the pressures on the 
 sides of a body immersed is shown by the fact that there 
 is no tendency to move laterally. 
 
 52. Magnitude of the Buoyant Force. 
 
 Experiment 48. Suspend from one arm of a balance beam a 
 cylindrical bucket A (Fig. 56), and from the bucket a solid cylinder 
 whose volume is exactly equal to the 
 capacity of the bucket; in other words, 
 the latter would just fill the former. 
 Counterpoise the bucket and cylinder 
 with weights. 
 
 Place beneath the cylinder a tumbler of 
 water, and raise the tumbler until the cyl- 
 inder is completely submerged. The 
 buoyant force of the water destroys the 
 equilibrium. Pour water into the bucket ; 
 when it becomes just even full, the equi- 
 librium is restored. 
 
 Now it is evident that the cylinder 
 immersed in the water displaces its own 
 volume of water, or just as much water 
 as fills the bucket. But the bucket full 
 of water is just sufficient to restore the weight lost by the 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. 
 
 Experiment 49. The last statement may be verified in another 
 way with apparatus like that shown in Figure 57. Fill the vessel A 
 till the liquid overflows at E. After the overflow ceases, place a ves- 
 
 Fig. 56. 
 
58 
 
 DYNAMICS OF FLUIDS. 
 
 Bel 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, ^nd it will be 
 found that its increase in 
 weight is just equal to the 
 loss of weight of the stone. 
 Experiment 50. Next 
 suspend a block of wood 
 that will float in the liquid, 
 and weigh it in air. Then 
 float it upon the liquid, and 
 weigh the liquid displaced as 
 before, and it will be found 
 that the weight of the liquid 
 Fig. 67. 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 
 is destroyed. 
 
 Fig. 68. 
 
DENSITY AND SPECIFIC GRAVITY. 
 
 59 
 
 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 
 displaced. 
 
 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 
 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 another 
 passage for the escape of 
 water. 
 
 Pig. 39. 
 
 Section X. 
 
 DENSITY, SPECIFIC DENSITY, AND SPECIFIC GRAVITY. 
 
 53. Terms Defined. The density of a substance at 
 any temperature is the mass per unit of volume of the 
 substance at that temperature. Thus, the density of water 
 
60 DYNAMICS OF FLUIDS. 
 
 at 4 C. is one gram per cubic centimeter, and the density 
 of cast iron at the same temperature is about 7.12 grams 
 per cubic centimeter. The mean density of a body is 
 found by dividing its mass by its volume. 
 
 The specific density of a substance is the number which 
 expresses how many times denser the substance is than some 
 standard substance. The specific gravity of a substance is 
 the ratio of the weight of a body of that substance to the 
 weight of an equal volume of some standard. The standard 
 adopted for solids and liquids is distilled water at some 
 definite temperature (in scientific work at 4 C.). Evi- 
 dently the number which expresses the specific density of 
 a substance and the number which expresses the specific 
 gravity of the same substance are identical, and both are 
 abstract numbers. 
 
 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 f 
 represent respectively the weights of equal volumes of the 
 same substances; then 
 
 Density of given substance _ D ^ -^ 
 
 Density of water " D' " 
 
 Weight of a given volume of the substance _ G_ _ o ^ 
 Weight of equal volume of water ~ G ; ~ 
 
 The Sp. D. of lead = f = = 11.5. The Sp. G. of 
 lead =~=-iM = 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. 
 
 61 
 
 Section XI. 
 
 EXPERIMENTAL METHODS OF FINDING THE SPECIFIC 
 DENSITY AND SPECIFIC GRAVITY OF BODIES. 
 
 55. Solids. 
 
 Experiment 52. From a hook beneath a scale-pan (Fig. 60) 
 suspend by a fine thread a small specimen of a substance whose 
 specific gravity is to be found, and weigh it, while dry, in the air. Then 
 immerse the body in a tumbler of water (do not allow it to touch the 
 tumbler, and see that it is completely submerged), and weigh it in 
 water. The loss of weight in water is evidently G ', 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 
 
62 
 
 DYNAMICS OF FLUIDS. 
 
 the weight lost by the lead alone, and the remainder is G' ; i.e. the 
 weight of water displaced by the cork. Apply formula (2), as before. 
 
 56. Liquids. 
 
 Experiment 54. Take a specific-gravity bottle that holds when 
 filled a certain (round) number of grams of water, e.g. 100s, 200&, 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 100s, 200s, 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. 
 
 G in 
 
 Grams. 
 
 G' in 
 Grams. 
 
 Sp. G. 
 or 
 Sp. D. 
 
 E. 
 
 Lead .... 
 
 7.2 
 
 .66 
 
 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. 
 
 63 
 
 they will float on the mercury at different depths, accord- 
 ing to their relative densities. Ice floats, in water with 
 T VA> in mercury with yf-j^, of its bulk submerged. Hence 
 the Sp. D. of mercury is 918 -f- 68 = about 13.5. 
 
 We see, then, that the densities of liquids may be com- 
 pared by seeing to what depths bodies floating in them 
 will sink. An instrument (A, Fig. 63) called a hydrometer 1 
 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. 
 
 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. 
 
64 DYNAMICS OF FLUIDS. 
 
 Experiment 57. Find the capacity of a test-tube, or an irregular 
 shaped cavity in any body. Weigh the body ; then fill the cavity with 
 water, and weigh again. As many grains 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 F. (15 C.), and in other water at about 180 F. (82 C.). Which 
 water is denser ? 
 
 EXERCISES. 
 
 1. In which does a liquid stand higher, in the snout of a coffee-pot 
 or in the main body? On which does this show that pressure depends, 
 on quantity or depth of liquid ? 
 
 2. The areas of the bottoms of vessels A, B, and C (Fig. 64) are equal. 
 The vessels have the same depth, and are filled with water. Which 
 vessel contains the more water ? On the bottom of which vessel is the 
 pressure equal to the weight of the water which it contains ? How 
 does the pressure upon the bottom of vessel B compare with the 
 weight of the water in it? 
 
 Fig. 64. 
 
 3. A cubic foot of water weighs about 62. 5 pounds or 1,000 ounces. 
 Suppose that the area of the bottom of each vessel is 50 square inches 
 and the depth is 10 inches ; what is the pressure on the bottom of 
 each? 
 
 4. Suppose that the vessel A is a cubical vessel of 10 in. side ; 
 what is the pressure 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 
 
SPECIFIC GRAVITY AND SPECIFIC DENSITY. 
 
 65 
 
 suppose the tube to be filled with water. 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 ? (5) What is its specific 
 gravity ? (c) What is the volume of the body ? (d) What is its 
 density ? 
 
 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 ? (&) 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 C. or 
 water at 20 C.? (5) If water at the bottom of a vessel could be 
 raised by application of heat to 20 C. while the water near the upper 
 surface has a temperature of 10 C., what would happen? 
 
 13. A block of wood weighs 550 grams ; when a certain irregular- 
 shaped cavity is fi)led with mercury the block weighs 570 grams. 
 What is the capacity or cubical contents of the cavity? 
 
 14. In which is it easier for a person to float, in fresh water or in 
 sea-water? Why? 
 
 15. Figure 65 represents a beaker graduated 
 in cubic centimeters. Suppose that when water 
 stands in the graduate at 50 CC , a pebble stone is 
 dropped into the water, and the water rises to 
 75. (a) What is the volume of the stone? 
 (&) How much less does the stone weigh in water 
 than in air? (c) What is the weight of an equal 
 volume of water ? 
 
 16. If a piece of cork is floated on water in 
 a, graduate, and displaces (i.e. causes the water 
 to rise) 7 CC , what is the weight of the cork ? 
 
66 DYNAMICS OF FLUIDS. 
 
 17. If a piece of lead (sp. g. 11.35) is dropped into a graduate and 
 displaces 12 CC of water, what does the lead weigh? (a) How would 
 you measure out 50 grams of water in a graduate ? (6) 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 50 CC . If 10s of lead shot are placed in the bottle, 
 where will the surface of the water stand? 
 
 21. What mass of alcohol can be put into a vessel whose capacity is 
 1 liter ? 
 
 22. On what two things does the weight of a body depend ? 
 
 23. (a) Can you suck air out of a bottle V (6) Can you suck water 
 out of a bottle ? Explain. 
 
 24. (a) What bodies have neither volume nor shape ? (6) 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 96 cm when a 
 barometer at the surface of the earth stands at 76 cra ; what is the 
 depth of the surface of water- inside the bell below the surface 
 outside ? 
 
 28. (a) 40 k of lead immersed in water will displace what volume 
 of water ? (6) Will lose how much of its weight ? 
 
 29. Find the sum in meters of 4^ m , 150 cm , 8 dm , 65 im , 5.6 m , 
 and 4 mm . 
 
 30. The sp. g. of hydrogen gas is (page 359) 0.0693. What do 
 you understand by this statement ? 
 
 31. What is the mass of a liter* of water at 4C ? 
 
CHAPTER IIL 
 
 GENERAL DYNAMICS. 
 
 Section I. 
 
 MOMENTUM AND ITS RELATION TO FORCE. 
 
 59. Momentum. Everyone knows that the effort to 
 stop a moving body in a given time must depend both 
 upon the mass of the body and its velocity. An empty car 
 in motion is much more easily stopped than a loaded car, 
 and a ball tossed is a different affair from a ball thrown. 
 We have an instinctive dread of the approach of large 
 masses and of swiftly moving masses. Thus we are led 
 to the consideration of a quantity called momentum, which 
 is t he product of the mass of a body multiplied by its velocity. 
 A unit of momentum is the momentum of a unit mass 
 moving with unit speed, and has no special name. Mo- 
 mentum depends upon both mass and, velocity ; velocity 
 is independent of mass. Momentum = MV. 
 
 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 equi- 
 librium 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. 
 
 Fig. 66. 
 
 causes a stroke of the hammer on the bell G. 
 At the instant of the first stroke the pendulum 
 causes the platform D to drop so as to allow 
 the weights to move. When the weights reach 
 the ring H, the rider is caught off by the ring. 
 
 Raise and lower the ring on the graduated 
 pillar I, and ascertain by repeated trials the 
 average distance the weights descend in the in- 
 terval between the first two strokes of the bell. 
 
 Next substitute for E a weight L, double that 
 of E. Find by trial how far the weights now 
 descend in the same interval of time as before. 
 It will be found that in the latter case the 
 weights descend nearly twice as far as in the 
 first case. 
 
 Suppose that weights A and B are each 30 
 grams, and that weights E and L are respec- 
 tively 2 grams and 4 grams. Now the force of 
 gravity which acts on weight E is 2 grams. 
 Consequently the unbalanced force which put 
 in motion the three weights A, B, and E, whose 
 combined weight (disregarding the weight of 
 wheel C, which is also put in motion) is 
 (30 + 30 + 2 = ) 62 grams, was 2 grams. It 
 is now evident why the descent is slow, for in- 
 stead of a force of 1 gram acting upon each gram 
 of matter, as is usually the case with falling 
 bodies, we have a force of only 2 grams moving 
 62 grams of matter; consequently 'the descent 
 is about -fa as fast as that of falling bodies 
 generally. 
 
 But when we employed weight L, we had a 
 force of 4 grams moving (30 + 30 + 4 =) 64 
 grams of matter. Here the force is doubled, 
 and the distance traversed is nearly doubled; 
 consequently the average velocity and the mo- 
 mentum acquired are nearly doubled. Had the 
 masses moved in the two cases been exactly the 
 same, the velocity and the momentum would 
 have been exactly doubled. 
 
FIRST LAW OF MOTION. 69 
 
 (1) In equal intervals of time change 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 
 on it will be shown that, in order to accom- 
 plish this, the velocity at the end of the sec- 
 ond unit of time must be twice that at the end 
 of the first unit of time. If MV represent 
 the momentum generated during the first 
 unit of time, then the momentum generated 
 during the second unit of time must be about 
 2MV. 
 
 (2) The momentum generated "by a 
 
 given force is proportional to the time during which the force 
 acts. 
 
 Conclusions (1) and (2) are summarized in the formula 
 MV= Ft, and in the Second Law of Motion, 63. 
 
 Section II. 
 
 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 external force. 
 
70 GENERAL DYNAMICS. 
 
 A body is said to be acted upon by an "external force " 
 when the action is between that body and some other body 
 (in contradistinction from an action between parts of the 
 same body). 
 
 The tendency of matter to remain in the state that it is 
 in, whether it be rest or motion, is called inertia; hence 
 the First Law of Motion is often called the Law of Inertia. 
 
 The backward motion of passengers when a car is suddenly started, 
 and their forward motion when the car is suddenly stopped, the difficulty 
 in starting a vehicle and the comparative ease of keeping it in motion 
 after it is put in motion, and the ceaseless motion of the planets, are 
 illustrations of inertia. By virtue of inertia the swiftly flying bullet 
 pierces a plank. 
 
 Section III. 
 
 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, es. spectively to B and E in one 
 second. Then the points A and D are their starting- 
 points ; the lines AB and DE represent the direction of 
 their motions, and the lengths of the lines represent the 
 
SECOND LAW OF MOTION. 71 
 
 distances traversed. In reading, the direction should be 
 indicated by the order of the letters, as AB and DE. 
 
 Likewise, the forces which produce the motion may be 
 represented graphically. For example, the points A and 
 D may represent the points of application of two forces, 
 the lines AB and DE represent the direction in which they 
 act, and the length of the lines represent their relative 
 intensities. 
 
 Let a force whose intensity may be represented numeri- 
 cally by 8 (e.g. 8 pounds), acting in the direction AB (Fig. 
 69), be applied continuously to 
 a ball starting at A, and sup- 
 pose this force capable of mov- 
 ing it to B in one second ; now, 
 at the end of the second let 
 a force of the intensity of 4, 
 directed at right angles to the 
 direction of the former force, 
 act during a second it would rig. 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, bat 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 L.aw 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 (see Sec. I). 
 
 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. 
 
72 GENERAL DYNAMICS. 
 
 Section IV. 
 
 COMPOSITION AND RESOLUTION OF FORCES. 
 
 64. Composition of Forces. It is evident that a sin- 
 gle force, applied in the direction AC (Fig. 69), might 
 produce the same result that is produced by the two 
 forces represented by AB and AD. Such a force is called 
 a resultant. A resultant is a single force that may be sub- 
 stituted for two or more forces, 
 and produce the same result 
 that the simultaneous action 
 of the combined forces produce. 
 The several forces that con- 
 tribute to produce the result- 
 ant are called its components. 
 When the components are 
 given, and the resultant re- 
 quired, the problem is called 
 
 composition of forces. The resultant of two forces acting 
 simultaneously at an angle to each other may always be 
 represented ly 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 (Fig. 69) with the 
 length of either AB or AD, whose numerical values are 
 known. Thus, AC is 2.23 times AD ; hence, the numer- 
 ical value of the resultant AC is (4 X 2.23 = ) 9.92. 
 When more than two components are given, find the result- 
 
COMPOSITION AND RESOLUTION OF FORCES. 73 
 
 ant of any two of them, then of this resultant and a third, and 
 so on until every component has been used. Thus in Fig. 70, 
 AC is the resultant of AB and AD, and AF is the result- 
 ant of AC and AE, i.e. of the three forces represented by 
 the lines AB, AD, and AE. Generally speaking, a motion 
 may be the result of any number of forces. When we see a 
 body in motion, we cannot determine by its behavior how 
 many forces have concurred to produce its motion. 
 
 65. Resolution of Forces. Assume that a ball moves 
 a certain distance in a cer- 
 tain direction, AC (Fig. 
 71), under the combined 
 influence of two forces, 
 and that one of the forces 
 that produces this motion 
 is represented in intensity 
 
 and direction by the line AB : what must be the intensity 
 and direction of the other force ? Since AC is the result- 
 ant of two forces acting at an angle to each other, 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 com- 
 
74 GENERAL DYNAMICS. 
 
 ponent forces ; also trace the line CD, in continuation of the line WC, 
 to indicate the direction and intensity of the resultant. Remove 
 
 the dynamometers, extend the 
 lines (as Ca and C6), and on 
 these construct a parallelo- 
 gram, from the extremities of 
 the line CD regarded as a 
 diagonal. It will be found 
 that 10 : number of pounds in- 
 dicated by the dynamometer 
 o:::CD:Ca; also that 10: 
 number of pounds indicated 
 by the dynamometer y : : CD : 
 C6. Again, it is plain that a 
 
 single force of 10 pounds must act in the direction CD to produce the 
 same result that is produced by the two components. Hence, when 
 two sides of a parallelogram represent the intensity and direction of two 
 component forces, the diagonal represents the resultant. Vary the problem 
 by suspending the strings from different points, as E and F, A and 
 F, etc. 
 
 An excellent verification of the Second Law of Motion 
 and the principle of composition of forces is found in the 
 fact that a ball, projected horizontally, will reach the 
 ground in precisely the same time that it would if dropped 
 from a state of rest from the same hight. That is, any 
 previous motion a body has in any direction does not 
 affect the action of gravity upon the body. 
 
 Experiment 63. Draw back the rod d (Fig. 73) toward the left, 
 and place the detent-pin c in one of the slots. Place one of the brass 
 balls on the projecting rod, and in contact with the end of the instru- 
 ment, as at A. Place the other ball in the short tube B. Raise the 
 apparatus to as great an elevation as practicable, and place it in a 
 perfectly horizontal position. Release the detent, and the rod, pro- 
 pelled by the elastic force of the spring within, will strike the ball B 
 with great force, projecting it in a horizontal direction. At the same 
 instant that B leaves the tube and is free to fall, the ball A is re- 
 leased from the rod, and begins to fall. The sounds made on strik- 
 
COMPOSITION AND RESOLUTION OF FORCES. 
 
 75 
 
 ing the floor reach the ears of the observer at the same instant; 
 this shows that both balls reach the floor in sensibly the same time, 
 and that the horizontal motion which one of the balls has does not 
 affect the time of its fall. 
 
 Fig. 73. 
 
 66. Composition of Parallel Forces, If the strings 
 CA and CB (Fig. 72) are brought nearer to each other (as 
 when suspended from B and E) so that the angle formed 
 by them is diminished, the component forces, as indicated 
 by the dynamometers, will decrease, till the two forces 
 become parallel, when the sum of the 'components just 
 equals the weight W. Hence, (1) two or more forces 
 applied to a body act to the greatest advantage when they 
 are parallel, and in the same direction, in which case their 
 resultant equals their sum. 
 
 On the other hand, if the strings are separated from 
 each other, so as to increase the angle formed by them, 
 the forces necessary to support the weight increase until 
 they become exactly opposite each other, when the two 
 forces neutralize each other, and none is exerted in an 
 upward direction to support the weight. If the two strings 
 
76 GENERAL DYNAMICS. 
 
 are attached to opposite sides of the weight (the weight 
 being supported by a third string), and pulled with equal 
 force, the weight does not move. But if one is pulled 
 with a force of 15 pounds, and the other with a force of 
 10 pounds, the weight moves in the direction of the 
 greater force ; and if a third dynamometer is attached to 
 the weight, on the side of the weaker force, it is found 
 that an additional force of five pounds must be applied 
 to prevent motion. Hence, (2) when two or more forces 
 are applied to a body, they act to greater disadvantage the 
 farther their directions are removed from one another ; and 
 the result of parallel forces acting in opposite directions is 
 a resultant force in the direction of the greater force, equal 
 to their difference. 
 
 When parallel forces are not applied at the same point, 
 the question arises, What will be the point of application 
 of their resultant? To the opposite extremities of a bar 
 
 AB(Fig.74) apply two 
 sets of weights, which 
 shall be to each other 
 as 3 Ibs. : 1 Ib. 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 Ib. : 3 Ibs. 
 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. 77 
 
 tion from the point of application of their resultant are 
 inversely as their intensities. 
 
 The dynamometer E indicates that a force equal to the 
 sum of the two sets of weights is necessary to balance the 
 two forces. A force whose effect is to balance the effects 
 of one or more forces is called an equilibrant. The result- 
 ant of the two components is a single force, equal to their 
 sum, applied at C in the direction CD. 
 
 67. Moment of a Force. The value of a force 
 to produce rotation about a given axis as C (Fig. 75) 
 is called its moment 
 
 A fcjt C 3ft B 
 
 about that axis. The 
 
 a 
 
 Ibs. ,a) UB, 
 
 \ \ 
 
 n M 
 
 perpendicular distance * 
 (AC or BC) from the 
 fixed point (C) to the M* re- 
 
 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 
 (+ 20 X 3 =) -f 60. Their algebraic sum is zero, conse- 
 quently there is equilibrium between the forces. 
 
78 GENERAL DYNAMICS. 
 
 When more than two forces act in this manner, there 
 will be equilibrium if the sum of all the positive mo- 
 ll * ments is equal to the 
 a\ b\ sum of all the nega- 
 
 soi ^ T j ^ |3o tive moments. Thus 
 
 c \ d \ c \ f\ the sum of the posi- 
 
 ijg s 2% vt tive moments acting 
 
 Fig * 76 * about point F (Fig. 
 
 76) is (/) 45 + (e)25 + (a) 30 =100; the sum of the 
 
 negative moments acting about the same point is (c) 30 + 
 
 (<f) 40 + (6) 30 = 100 ; the two sums being equal, the 
 
 forces are in equilibrium. 
 
 69. Mechanical Couple. 
 Two equal forces applied to the 
 same body (e.g. AB, Fig. 77) in 
 parallel and opposite directions 
 not in the same line constitute 
 what is called a mechanical 
 77 - couple. The effect of a couple 
 
 is to produce rotation, but no motion of translation. The 
 moment of a couple is the sum of the moments of its two 
 components around the axis of rotation. 
 
 Section V. 
 
 THE THIRD LAW OF MOTION. 
 
 7O. Introductory Experiments. We have learned 
 that motion cannot originate in a single body, but arises 
 from mutual action between two bodies or two parts of a 
 body. For example, a man can lift himself by pulling 
 
THE THIRD LAW OF MOTION. 
 
 79 
 
 on a rope attached to some other object, but not by his 
 boot-straps, or a rope attached to his feet. In every change 
 in regard to motion there are always at least two bodies 
 
 oppositely affected. 
 
 Experiment 64. Suspend the deep glass bucket A (Fig. 78) by 
 means of a strong thread two feet long, so that the long projecting 
 pointer may be directly over a dot made on a 
 piece of paper placed beneath ; or place beneath 
 another pointer, B, so that the two points shall 
 just meet. Fill the bucket with water. Gravity 
 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 
 
80 GENBBAL DYNAMICS. 
 
 weighs twice as much as the first man, in a boat weighing 
 two tons : both boats will move towards each other, but 
 in opposite directions ; if the resistances which the two 
 boats encounter were the same, the lighter boat would 
 move twice as fast as the heavier, but with the same 
 momentum. 
 
 If the boats are near each other, and the men push each 
 other's boats with oars, the boats will move in opposite 
 directions, though with different velocities, yet with equal 
 momenta. 
 
 The opposite impulses received by the bodies concerned 
 are usually distinguished by the terms action and reaction. 
 We measure these, when both are free to move, by the 
 momenta generated, which is always the same in both 
 bodies. 
 
 71. Third Law of Motion. To every action there 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 
 proportionately less. 
 
 EXERCISES. 
 
 1. (a) Why does not a given force, acting the same length of time, 
 give a loaded car as great a velocity as an empty car? (6) After 
 equal forces have acted for the same length of time upon both 
 cars, and given them unequal velocities, which will be the more 
 dimcult to stop? 
 
 2. (a) The planets move unceasingly ; is this evidence that there 
 are forces pushing or pulling them along? (&) None of their 
 motions are in straight lines; are they acted upon by external forces? 
 
THE THIRD LAW OF MOTION. 81 
 
 
 
 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. 
 
 Tig. 80. 
 
 5. Explain how rotating lawn-sprinklers are kept in motion. 
 
 6. When you leap from the earth, which receives the greater mo- 
 mentum, your body or the earth ? 
 
 7. When you kick a door-rock, why does snow or mud on your 
 shoes fly off? 
 
 8. Why cannot a person propel a vessel during a calm by blowing 
 the sails with a big bellows placed on the deck of the same vessel ? 
 
 9. In swimming, you put water in motion ; what causes your body 
 to advance? What propels the bird in flying? 
 
 10. Could a rocket be projected in the usual way if there were no 
 atmosphere ? 
 
 11. If 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. W'hat is the maximum velocity of the gun's 
 recoil? 
 
 13. A boat of mass 5 tons moves at the rate of 4 miles an hour ; 
 another boat of 3 tons moves at the rate of 10 miles an hour. 
 Compare their momenta. 
 
 14. Two balls whose masses are respectively 10 k and 4 k have 
 equal momenta. If the velocity of the first be 40 m per sec., what is 
 the velocity of the other ? 
 
82 GENERAL DYNAMICS. 
 
 Section VI. 
 
 APPLICATIONS OF THE THREE LAWS OF MOTION. CENTER 
 OF GRAVITY. 
 
 72. Ceuter of Gravity Defined. Let Figure 81 repre- 
 sent any body of matter; for instance, a stone. Every 
 molecule of the body is acted upon by the force of gravity. 
 The forces of gravity of- all the mole- 
 cules form a set of parallel forces act- 
 ing vertically downward, the resultant 
 of which equals their sum, and has the 
 same direction as its components. The 
 resultant passes through a definite 
 point in whatever position the body 
 may be, and this point is called its cen- 
 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 
 is not applied immediately under its e.g. at 
 G; but when placed horizontally, it immedi- 
 ately assumes a vertical position. It appears Flg * 82 * 
 to the observer to rise; but, regarded in a mechanical sense, it really 
 falls, because its e.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 e.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 lice oa, the e.g. must lie somewhere in the 
 
84 GENERAL DYNAMICS. 
 
 path an made by the needle. Suspend the potato from 
 some other point, as 5, and a needle thrust vertically 
 through the potato from b will also pass through the e.g. 
 Since the e.g. lies in both the lines an and 6s, it must be at 
 , 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 e.g. of any body is found. But the 
 e.g. of a body may not be coincident with any particle of 
 the body ; for example, the e.g. of a ring, a hollow 
 sphere, etc. 
 
 74. Equilibrium of Bodies. A body will rest in 
 equilibrium when its line of direction passes through its 
 point of support. A body will be supported at its base 
 when its line of direction falls within its base or lowest 
 side. [The base of any body, e.g. a chair, is the polygon 
 formed by joining by straight lines the points of support.] 
 There are three kinds of equilibrium : 
 
 (1) A body so supported that when slightly disturbed it tends to return 
 to its original position, is said to be in stable equilibrium. This will be 
 the case whenever such a disturbance raises its e.g., for the weight of the 
 body acting at its e.g. tends to bring this point as low as possible and 
 thus causes it to return to its former position. A supported body is in 
 stable equilibrium if its e.g. be as low as possible. Evidently a body is 
 in stable equilibrium when the supporting force is applied in the line of 
 direction above its e.g. 
 
 (2) A body so supported that a slight disturbance tends to cause it to 
 take a new position with its e.g. lower than before is in unstable equi- 
 librium. 
 
 (3) A supported body whose e.g. is neither raised nor lowered by a 
 disturbance (e.g. a sphere on a horizontal plane) is in neutral equilibrium. 
 
 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 e.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 
 e.g. is as low as possible, and any disturbance will raise its e.g. ; but, 
 in consequence of the tendency of the e.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. 
 
 QUESTIONS. 
 
 1. Why is a person's position more stable when his 
 feet are separated a little, than when close together ? 
 
 2. How does ballast tend to keep a vessel from over- 
 turning ? 
 
 3. For what two reasons is a pyramid a very stable 
 structure ? 
 
 4. What point in a falling body descends in a straight Fig. 86. 
 
86 GENERAL DYNAMICS. 
 
 line? What is this line called? Disregarding the motions of the 
 earth, toward what point in the earth does this line tend ? 
 
 5. It is difficult to balance a lead-pencil on the end of a finger ; 
 but by attaching two knives to it, as in Figure 86, it may be rocked 
 to and fro without falling, Explain. 
 
 Section VII. 
 
 APPLICATIONS OF THE THREE LAWS OF MOTION CONTIN- 
 UED. EFFECT OF A CONSTANT FORCE ACTING ON A 
 BODY PERFECTLY FREE TO MOVE. FALLING BODIES. 
 
 75. Any Force, however Small, can move any Body 
 of however Great Mass. For example, a child can move 
 a body having a mass equal to that of the earth, pro- 
 vided only that the motion of this body is not hindered 
 by a third body. Moreover, the amount of momentum 
 that the child can generate in this immense body in a 
 given time is precisely the same as that which it would 
 generate by the exertion of the same force for the same 
 length of time on a body having a mass of (say) 10 pounds. 
 Momentum is the product of mass into velocity; so, of 
 course, as the mass is large, the velocity acquired in a 
 given time will be correspondingly small. The instant the 
 child begins to act, the immense body begins to move. 
 Its velocity, infinitesimally small at the beginning, would 
 increase at almost an iniinitesimally 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 mass has 
 any power to resist motion ; in other words, " a body free to 
 move cannot remain at rest under the slightest unbalanced 
 force tending to set it in motion." Furthermore, a given 
 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 
 fall. 
 
 Experiment 68. Ascertain, as in Experiment 60, how far the 
 weights, moved by a constant force (e.g. 2 grams), descend during 
 one swing of the pendulum. Inasmuch as all swings of the pendulum 
 are made in equal intervals of time, we may take the time of one 
 swing as our unit of time. We will, for convenience, take for our 
 unit of distance the distance the weights fall during the first unit of 
 time, call this unit a space, and represent the unit graphically by the 
 line db (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 (aft) during the first unit of time, hence they must 
 
GENERAL DYNAMICS. 
 
 1 Uof T 
 
 S Uof T 
 
 descend three spaces during the second unit of time. The weights, 
 under the action of the constant force, start from a state of rest, and 
 move through one space in a unit of time. This force, continuing to 
 act, accomplishes no more nor less during any subsequent 
 unit of time. But the weights move through three spaces 
 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 
 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 
 started from a state of rest: hence the constant force 
 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 (ac?), 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 velocity of a body at any instant is the distance which it would 
 traverse in a unit of time if its motion should continue unchanged 
 during that time. Acceleration is the change of velocity in a unit of 
 time. The acceleration due to gravity is usually represented by g, 
 and is always twice the distance (^ g) traversed during the first unit 
 of time. When a body is acted upon by any other constant force, 
 the acceleration produced by the force is usually represented by the 
 letter A. 
 
 s Uof T 
 Fig. 87. 
 
APPLICATIONS OF THE THREE LAWS OF MOTION. 89 
 
 Arrange the results of your observations in a tabulated form as 
 follows : 
 
 No. of units of 
 time. 
 
 Total distance 
 passed over. 
 (S) 
 
 Distance passed 
 over in each 
 unit; also av- 
 erage velocity. 
 (s) 
 
 Velocity at the 
 end of each 
 unit. 
 (V) 
 
 Increase of ve- 
 locity in each 
 unit, i.e. ac- 
 celeration. 
 
 1 
 
 1(M) 
 
 10 9) 
 
 2 ) 
 
 2 Q </) 
 
 2 
 
 4 " 
 
 3 
 
 4 
 
 2 
 
 3 
 
 9 " 
 
 5 " 
 
 6 " 
 
 2 " 
 
 4 
 
 16 " 
 
 7 
 
 8 " 
 
 2 
 
 etc. 
 
 etc. 
 
 etc. 
 
 etc. 
 
 etc. 
 
 77. Formulas for Uniformly Accelerated Motion. 
 
 If we substitute A for #, and represent the distance 
 traversed during a given unit of time by s, and the total 
 distance the body has accomplished from the outset to 
 the end of a given unit of time (T) by S, we derive from 
 our tabulated results the following formulas for solving 
 problems of uniformly accelerated motion: 
 
 (1) V= 
 
 (2) , = 
 
 (3) S = 
 
 Hence, (1) the velocity acquired varies as the time; (2) the 
 spaces passed over in successive equal intervals of time vary 
 as the odd numbers 1, 3, 5, 7, etc. ; and (3) the entire space 
 traversed varies as the square of the time. 
 
 Strictly speaking, a falling body is not under the influence of a constant 
 force, inasmuch as gravity varies inversely as the square of the distance 
 from the center of the earth. But for small distances the variation may 
 be, for all practical purposes, disregarded, as at a hight of a kilometer 
 (about f of a mile) it is only about yfa-g of the weight at the surface. It 
 can be shown mathematically that the velocity that would be acquired by 
 a body falling freely to the earth's surface from an infinite distance would 
 be about 35 000 feet per second. 
 
90 GENERAL DYNAMICS. 
 
 78. Velocity of a Falling Body Independent of its 
 Mass and Kind of Matter. If we grasp a coin and a bit 
 of paper between the thumb and finger, and release both 
 at the same instant, the coin will reach the floor first. It 
 would seem as though a heavy body falls faster than a 
 light body. Galileo was the first to show the falsity of 
 this assumption. He let drop from an eminence iron balls 
 of different weights : they all reached the ground at the 
 same instant. Hence he concluded that the velocity of a 
 falling body is independent of its mass. 
 
 He also dropped balls of wax with the iron balls. The 
 iron balls reached the ground first. Are some kinds of 
 matter affected more strongly by gravitation than 
 others? If a coin and several bits of paper are 
 placed in a long glass tube (Fig. 88), the air ex- 
 hausted, and the tube turned end for end, it will 
 be found that the coin and the paper will fall with 
 equal velocities. Hence, the earth attracts all matter 
 alike. A wax ball of the same size as an iron ball 
 meets with the same resistance from the air that 
 the iron ball does ; but since the mass of the former 
 is less than that of the latter, the force acting on 
 the former is less, and a less force cannot over- 
 come the same resistance as quickly, consequently 
 88 * in the air the wax ball falls a little more slowly. 
 We conclude, therefore, that in a vacuum all bodies fall 
 with equal velocities. 
 
 Experiments show that in the latitude of the Northern 
 States the acceleration, i.e. the value of #, is, near sea-level 
 and in a vacuum, 32|- feet (9.8 m ) per second; that is, the 
 velocity gained by a falling body, disregarding the resist- 
 ance of the air, is 32J feet per second, and the body falls 
 in the first second 16^ feet (4.9 m ). 
 
APPLICATIONS OF THE THREE LAWS OF MOTION. 91 
 
 M 
 
 Fig. 89. 
 
 What is its average velocity 
 
 EXERCISES. 
 
 1. What is a constant force? What effect does it produce on every 
 body wnen there are no resistances? 
 
 2. (a) How far will A B C D 
 
 a body fall in a vacuum E ^ ---JK 
 
 in one second? (6) What 
 is its velocity at the end F 
 of the first second? (c) 
 What is its acceleration 
 per second? 
 
 3. (a) How far will a G 
 body fall in ten seconds? 
 
 (b) How far will it fall 
 
 in the tenth second? p 
 
 (c) What is its velocity 
 
 at the end of the tenth second? 
 during the tenth second ? 
 
 4. (a) How far will a body fall in one-fourth of a second ? 
 is the velocity of a falling body at the 
 
 end of the first quarter of a second of 
 its fall? 
 
 5. A body is projected from point 
 A (Fig. 89) in the horizontal direction 
 AH. (a) If there were no resistance 
 of the air, and gravity did not act on 
 it, it would go a distance during the 
 first unit of time represented by AB ; 
 how far would it go during the second 
 and third units of time? (In every 
 answer quote the law of motion in 
 conformity with which your answer is 
 given.) (6) If the body were dropped 
 from A, it would reach successively 
 points E, F, and G at the ends of the 
 first, second, and third units of time. 
 If the body were projected horizontally 
 in the direction AH, and gravity acts 
 
 during its flight, what points will the Fig. 90. 
 
 body successively reach at the end of the same units of time ? 
 
92 GENERAL DYNAMICS. 
 
 6. (a) Suppose that a body is projected obliquely upward m the 
 direction AH (Fig. 90), (gravity meantime acting on the body) ; what 
 points will the body reach successively at the end of the first,, second, 
 and third units of time? (6) How far will the ascending body vir- 
 tually fall during the first unit of time? (c) How far during the 
 second unit? (d) How far during the third unit? (e) Show that your 
 answers are consistent with the Second Law of Motion. 
 
 7. (a) Under the action of a constant force, a body meeting with no 
 resistances moves from a state of rest 20 feet during the first minute : 
 how far will it go in an hour? (&) Suppose at the end of the first 
 minute the force should cease to act, how far would the body go in an 
 hour from that instant ? 
 
 Section VIII. 
 
 APPLICATIONS OF THE THREE LAWS OF MOTION CONTIN- 
 UED. CURVILINEAR MOTION. 
 
 79. How Curvilinear Motion is Produced. Motion 
 is curvilinear when its direction changes at every point. 
 But according to the first law of motion, every moving 
 body proceeds in a straight line, unless compelled to 
 depart from it by some external force. Hence curvilinear 
 motion can be produced only by an external force acting 
 continuously upon the body at an angle to the straight 
 path in which the body tends to move, so as constantly 
 to change its direction. In case the body moves in a 
 circle, this force acts at right angles to the path of the 
 body or towards the center of motion ; hence this deflecting 
 force has received the name of centripetal force. 
 
 80. Centrifugal Tendency. 
 
 Experiment 69. Cause a ball to revolve around your hand by 
 means of a string attached to it and held in the hand. Observe 
 
APPLICATIONS OF THE THREE LAWS OF MOTION. 93 
 
 closely every phase of the operation. First, you make a movement as 
 if to project the ball in a straight line. Immediately you begin to 
 pull on the string to prevent its going in a straight line. By a con- 
 tinuous exertion of these two forces in a short time the ball acquires 
 great speed. You may now cease to exert any projecting force, and 
 simply keep the hand still ; but as the ball has acquired a motion, 
 and all motion tends to be in a straight line, you are still obliged to 
 exert a pulling force to deflect it from this path. Observe that as the 
 velocity of the ball is retarded by the resistance of the air, the pulling 
 or deflecting force which you are obliged to employ rapidly diminishes. 
 To satisfy yourself that the ball tends to move in a straight line, 
 let go the string or cut it, and the ball immediately moves off in a 
 straight line, or simply perseveres in the direction it had at the 
 instant the string was cut. 
 
 The direction which a revolving body tends to move at 
 every point is a tangent to that point of its curvilinear 
 path. The tendency of a revolving body to " fly off " tan- 
 gentially is called the centrifugal tendency. Illustrations 
 of this tendency may be found in a vehicle turning a 
 corner, a stone leaving a sling, water escaping from a 
 rotating grindstone, pieces broken from fly-wheels, etc. 
 
 In order that a body may move in a circular path the 
 centripetal force must have a definite magnitude which 
 depends upon the mass of the body and its velocity. Careful 
 observations have determined that for bodies revolving in 
 circular orbits the centripetal force (and centrifugal tendency) 
 varies as the mass of the body and the square of its velocity. 
 
 The farther a point is from the axis of motion of a rotating body, the 
 farther it has to move during a rotation ; consequently the greater its 
 velocity. Hence, bodies situated at the earth's equator have the greatest 
 velocity, due to the earth's rotation, and consequently the greatest tendency 
 to fly off from the surface, the effect of which is to neutralize, in some 
 measure, the force of gravity. It is calculated that a body weighs about ^\^ 
 less at the equator than at either pole, in consequence of the greater cen- 
 trifugal tendency at the former place. But 289 is the square of 17 ; hence, 
 
94 
 
 GENERAL DYNAMICS. 
 
 if the earth's velocity were increased seventeen-fold, objects at the equator 
 
 would weigh nothing. 
 
 We have also learned (page 17) that a body weighs more at the poles, 
 
 in consequence of the oblateness of the earth. This is estimated to make 
 
 a difference of about ^-g. Hence a body will weigh at the equator -^g-4- 
 
 j|^ = (about) T ^ less than at the poles. 
 
 The attraction between the sun and the earth causes these bodies to 
 
 move in curvilinear paths, 
 
 ^- ^s. i performing what is called 
 
 annual revolutions. The 
 motion of both these bodies, 
 were it not for this mutual 
 attraction (and the attraction 
 of other celestial bodies), 
 
 Fig. 91. 
 
 would be eternally in straight lines, but in consequence of their mutual 
 attraction both revolve about a point C (Fig. 91), which is the center of 
 gravity of the two bodies considered as one body (as if connected by a 
 rigid rod). If both bodies had equal masses, the center of gravity and 
 center of motion would be half-way between the two bodies ; but as the 
 mass of the earth is less than that of the sun, so its velocity and distance 
 traversed are proportionally greater. 
 
 Fig. 92. Fig. 93. 
 
 Experiment 70. Arrange some kind of rotating apparatus, e.g. 
 R (Fig. 92). Suspend a skein of thread a (Fig. 93) by a string, and 
 rotate; it assumes the shape of the oblate spheroid a'. Suspend a 
 glass globe G (Fig. 92) about one-tenth full of colored water, and 
 rotate. The liquid gradually leaves the bottom, rises, and forms an 
 equatorial ring within the glass. This illustrates the probable method 
 by which the earth, on the supposition that it was once in a fluid 
 
APPLICATIONS OF THE THREE LAWS OF MOTION. 95 
 
 state, assumed its present spheroidal state. (Explain.) Pass a string 
 through the longest diameter of an onion c, and rotate; the onion 
 gradually changes its position so as to rotate on its shortest axis. 
 
 It may be demonstrated mathematically, as well as experi- 
 mentally, that a freely rotating body is in stable equilib- 
 rium only when rotating about its shortest diameter ; hence 
 the tendency of a rotating body to take this position. 
 
 QUESTIONS. 
 
 1. (a) What is the cause of the stretching force exerted on the 
 rubber cord when you swing a return-ball about your hand? 
 (6) Suppose that you double the velocity of the ball ; how many times 
 will you increase this stretching force ? 
 
 2. Why do wheels and grindstones, when rapidly rotating, tend to 
 break, and the pieces fly off? 
 
 3. On what does the magnitude of the pull between a rotating body 
 and its center of motion depend ? 
 
 4. (a) Explain the danger of a carriage being overturned in turning 
 a corner, (b) How many fold is the tendency to overturn increased 
 by doubling the velocity of the carriage? 
 
 Section IX. 
 
 APPLICATION OF THE THREE LAWS OF MOTION CONTIN- 
 UED. THE PENDULUM. 
 
 81. Laws of the Pendulum. 
 
 Experiment 71. Suspend iron balls by strings, as in Figure 94. 
 Make A and B the same length. Draw A and B one side, and to dif- 
 ferent hights, so that one may swing through a longer arc than the 
 other, and let both drop at the same instant. One moves much 
 faster than the other, and completes a longer journey at each swing, 
 but both complete their swing or vibration at the same time. 
 
 Hence (1) the time of vibration of a pendulum is (strictly speaking, 
 approximately) independent of the length of the arc. 
 
96 
 
 GENERAL DYNAMICS. 
 
 Experiment 72. Set all the balls swinging ; only A and B swing 
 together, i.e. in the same time. The shorter the pendulum, the faster 
 it swings. Make B about 39 inches long from the point of sus- 
 pension to the center of the ball, regulating 
 this length, as necessity may require, so that 
 the number of vibrations made by the pen- 
 dulum in one minute shall be exactly 60 ; in 
 other words, so that it shall "beat seconds." 
 (Accurately, a pendulum that beats seconds 
 is 39.09 inches long.) Make C one-fourth 
 as long as B. Count the vibrations made 
 by C in one minute ; it makes 120 vibrations 
 in the same time that B makes 60 vibrations. 
 Make D one-ninth the length of B; the 
 former makes three vibrations while the 
 latter makes one. Consequently the time of 
 vibration of the former is one-third that of 
 the latter. 
 
 Hence (2) the time of vibration of a pendu- 
 lum varies as the square root of its length. 
 
 By experiments too difficult for ordinary 
 school work, it has been ascertained that 
 (3) the time of vibration of a pendulum varies 
 inversely as the square root of the force of 
 gravity (upon which the value of g depends). 
 Hence it is apparent that by determining 
 the time of vibration of a pendulum of the 
 same length, at different distances from the 
 center of gravity of the earth (e.g. at the top and bottom of a 
 mountain, or at sea-level at different latitudes), the relative value 
 of g at these places may be ascertained. 
 
 Experiment 73. Loosen the binding-screw in the bob of the pen- 
 dulum of the Atwood machine (Fig. 66), and place the bob at differ- 
 ent elevations on the pendulum-rod. Count the number of vibrations 
 made by the pendulum in a minute, when the bob is placed at these 
 different elevations. The greater the elevation of the bob, in other 
 words, the shorter the pendulum, the greater the number of vibra- 
 tions made. We learn by this experiment that the time of vibration 
 of a pendulum may be regulated by raising or lowering its bob. For 
 further development of the pendulum see Appendix, Section D. 
 
 Fig. 94. 
 
APPLICATIONS OF THE THREE LAWS OF MOTION. 97 
 
 EXERCISES. 
 
 1. One pendulum is 20 inches long, and vibrates four times as fast 
 as another. How long is the other ? 
 
 2. (a) What effect on the rate of vibration has the weight of its 
 bob? (5) What effect has the length of the arc? (c) What affects 
 the rate of vibration of a pendulum ? 
 
 3. How can you quicken the vibration of a pendulum threefold? 
 
 4. A clock loses time, (a) What change in the pendulum ought to 
 be made? (6) How would you make the correction? 
 
 5. Two pendulums are four and nine feet long respectively. While 
 the short one makes one vibration, how many will the long one 
 make ? 
 
 6. How long is a pendulum that makes two vibrations in a second ? 
 
 7. What is the time of vibration of a pendulum (39.09 -r- 4 =) 9.75 in. 
 long? 
 
 8. The number of vibrations made by a given pendulum in a given 
 time varies as the square root of the force of gravity. Force of grav- 
 ity at any place is expressed by the value of g (i.e. by the acceleration 
 which it produces), (a) If at a certain place a pendulum 39.09 in. 
 long make 3600 vibrations in an hour, and the value of g is 32.16 ft., 
 what is the acceleration at a place where the same pendulum makes 
 3590 vibrations in the same time? (6) Which of the two places is 
 nearer the center of gravity of the earth ? 
 
 9. Suggest some way by which the force of gravity at different 
 latitudes and altitudes may be determined. 
 
 10. (a) A certain body weighs 12 Ibs. where the value of g is 32.16 ft. ; 
 what will the same body weigh at a place wher,e g 32 ft. ? (b) Sup- 
 pose that the former place is at the surface of the earth and 4000 miles 
 from the earth's center of gravity; how far above it is the latter place? 
 (See page 16.) 
 
 11. A pebble is suspended by a thread 2 ft. long; required the 
 number of vibrations it will make in a minute. 
 
 12. Why do not heavy bodies fall faster than light ones in a vacuum? 
 
 13. Take equal masses of wood and lead ; which weighs more ? 
 
 14. A stone falls from the top of a railway carriage which is mov- 
 ing at the rate of one-half of a mile a minute. Find what horizontal 
 distance and what vertical distance the stone will have passed through 
 in one-tenth of a second, disregarding the resistance of the air. 
 
 Ans. 4.4ft.; .16ft. 
 
CHAPTER IV. 
 WORK AND ENERGY. 
 
 Section I. 
 
 METHODS OF ESTIMATING WORK AND ENERGY. 
 
 82. Work. Whenever a force causes motion, it does 
 work. A force may act for an indefinite time without 
 doing work ; for example, a person may support a stone 
 for a time and become weary from the continuous appli- 
 cation of force to prevent its falling, but he does no work 
 apon the stone because he effects no change. When a 
 force acts through space, work is done. Let the person 
 holding the weight exert just a little more force ; the 
 weight will rise, and work will be done. 
 
 A body that is moved is said to have work done upon it ; 
 and a body that moves another body is said to do work 
 upon the latter. When the heavy weight of a pile-driver 
 is raised, work is done upon it; when it descends and 
 drives the pile into the earth, work is done upon the pile, 
 and the pile in turn does work upon the matter in its 
 path. 
 
 The act of doing work may consist in a mere transfer of 
 energy from the body doing work to the body on which work 
 is done, or it may consist in a transformation of energy from 
 one kind to some other kind, as when the pile-driver strikes 
 
METHODS OF ESTIMATING WORK AND ENERGY. 99 
 
 the pile and the pile is forced into the earth, a part of the 
 energy concerned in each case is transformed into heat, 
 which we shall learn farther on is molecular energy. 
 
 In future chapters we shall discuss the subject of transformations of 
 energy ; for the present our discussions relate chiefly to transferences of 
 energy. 
 
 83. Formulas for Estimating Work. Force and space 
 (or distance) are the essential elements of work, and neces- 
 sarily are the quantities employed in estimating work. A 
 given force acting through a space of one foot, in raising 
 a weight, does a certain amount of work; it is evident 
 that the same force acting through a space of two feet 
 would do twice as much work. Hence the general formula 
 
 FS = W, (1) 
 
 in which F represents the force employed, S the space 
 through which the force acts, and W the work done. 
 
 In case a force encounters resistance, the magnitude of 
 the force necessary to produce motion varies as the resist- 
 ance. Often the work done upon a body is more con- 
 veniently determined by multiplying the resistance by the 
 space through which it is overcome, and our formula becomes 
 by substitution of R (resistance) for F (the force which 
 overcomes it) 
 
 RS = W. (2) 
 
 For example, a ball is shot vertically upward from a rifle 
 in a vacuum ; the work done upon the ball (by the explo- 
 sive force of the gunpowder) may be estimated by multi- 
 plying the average force (difficult to ascertain) exerted 
 upon it, by the space through which the force acts (a little 
 greater than the length of the barrel) ; or by multiplying 
 the resistance to motion offered by gravity, i.e. its weight 
 (easily ascertained) by the distance the ball ascends. 
 
100 WORK AND ENERGY. 
 
 84. Energy, Kinetic and Potential. Every moving 
 body can impart motion ; hence it can do work upon an- 
 other body, and is therefore said to possess energy. The 
 energy of a body is its " capacity to do work." The energy 
 which a body possesses in consequence of its motion is 
 called kinetic energy. 
 
 A stone lying on the ground is devoid of energy. Raise 
 it and place it on a shelf; in so doing you perform work 
 upon it. As you look at it lying motionless upon the shelf, 
 it appears as devoid of energy as when lying on the earth. 
 Attach one end of a cord to it and pass it over a pulley 
 and wind a portion of the cord around the shaft connected 
 with a sewing-machine, coffee-mill, lathe, or other con- 
 venient machine. Suddenly withdraw the shelf from be- 
 neath the stone. The stone moves; it communicates motion 
 to the machinery, and you may sew, grind coffee, turn 
 wood, etc., with the energy given to the machine by the 
 stone. 
 
 The work done on the stone in raising it was not lost ; 
 the stone pays it back while descending. There is a very 
 important difference between the stone lying on the floor, 
 and the stone lying on the shelf: the former is powerless 
 to do work; the latter can do work. Both are alike 
 motionless, and you can see no difference, except an 
 advantage that the latter has over the former in having 
 a position such that it can move. What gave it this 
 advantage? Work. A body, then, may possess energy 
 due merely to ADVANTAGE OF POSITION, derived always 
 from work bestowed upon it. Energy due to advantage of 
 position is called potential energy. We see, then, that 
 energy may exist in either of two widely different states. 
 It may exist as actual motion, or it may exist in a stored-up 
 condition, as in the stone lying on the shelf. 
 
METHODS OF ESTIMATING WORK AND ENERGY. 101 
 
 Possibly some will object that the work done is performed by gravity, 
 and not by the stone ; that if this force should cease to exist, the stone 
 would not move when the shelf is removed, and consequently no work 
 would be done. All this is very true, and it is likewise true that when 
 the stone is on the ground, the same force of gravity is acting, but can do 
 no work simply because the position of things is such that the stone cannot 
 move. The energy which the stone on the shelf possesses is due to the fact 
 that its position is such that it can move, and that there is a stress between 
 it and the earth which will cause it to move. Both advantage of position 
 and stress are necessary, but the former is attained only by work per- 
 formed. The force of gravity is employed to do work, as when mills are 
 driven by falling water ; but the water must first be raised from the ocean- 
 bed to the hillside by the work of the sun's heat. The elastic force of 
 springs is employed as a motive power; but this power is due to an advan- 
 tage of position which the molecules of the springs have first acquired by 
 work done upon them. 
 
 We are as much accustomed to store up energy for future use as pro- 
 visions for the winter's consumption. We store it when we wind up the 
 spring or weight of a clock, to be doled out gradually in the movements 
 of the machinery. We store it when we bend the bow, raise the hammer, 
 condense air, and raise any body above the earth's s.urfpjce. ; ';,' 
 
 A body possesses potential energy ivKen^ in mrfye\b* \work 
 done upon it, it occupies a position of advantage, or its mole- 
 cules occupy positions of advantage, so that the energy ex- 
 pended can be at any time recovered by the return of the body 
 to its original position, or by the return .of its molecules to 
 their original positions. 
 
 85. Unit of Work and Energy. Inasmuch as a 
 body's capacity to do work is dependent wholly upon 
 the work which has been done upon it, it is evident that 
 both work and energy may be measured by the same unit. 
 The unit adopted is the work done or energy imparted in 
 raising one pound through a vertical hight of one foot. It 
 is called a foot-pound. (The metric unit is the work done 
 or energy imparted in raising l k to a vertical hight of 
 
102 WORK AND ENERGY. 
 
 l ra , and is called a kilogram meter.) Since the work done 
 in raising 1 pound 1 foot high is 1 foot-pound, the work of 
 raising it 10 feet high is 10 foot-pounds, which is the same 
 as the work done in raising 10 pounds 1 foot high ; and 
 the same, again, as raising 2 pounds 5 feet high. 
 
 In this unit, and by means of formulas (1) and (2), page 
 99, we are able to estimate any species of work, and thereby 
 compare work of any kind with that of any other kind. 
 For instance, let us compare the work done by a man in 
 sawing through a stick of wood, whose saw must move 100 
 feet (S) against an average resistance (R) of 20 pounds, 
 with that done by a bullet in penetrating a plank to the 
 depth of 2 inches Q- foot) against an average resistance of 
 500 pounds. Moving a saw 100 feet against a resistance 
 of 20 pounds is equivalent to raising 20 pounds 100 feet 
 high, or doing (RS = 20 X 100 =) 2,000 foot-pounds of work 
 (W) ;*a bullet -moving^- -foot against 500 pounds' resistance 
 does the same amount of work as is required to raise 500 
 po-iinds^- foot faigh, or- (500 X =) 83.3 + foot-pounds of 
 work. Hence (2,000 * 83.3 ) about 24 times as much 
 work is done by the sawyer as by the bullet. 
 
 Let us estimate the energy stored in a bow, by an archer whose hand 
 in pulling on the string, while bending the bow moves 6 inches Q foot) 
 against an average resistance of 20 pounds. Here RS = 20 X f = 10 
 foot-pounds of work done upon the bow, or 10 foot-pounds of energy 
 stored in the bow. 
 
 86. Distinction between Energy and Force. 
 
 W (i.e. energy transmitted) = FS (p. 99) ; hence force is 
 only a factor of energy. A body must be set in motion or 
 have some form of energy conferred upon it before it can 
 exert force, so that force is merely a manifestation of 
 energy. Force can be increased indefinitely by means of 
 machines, as a lever, hydrostatic press, etc. ; energy cannot 
 be increased by any instrument or means whatsoever. 
 
METHODS OF ESTIMATING WORK AND ENEEGY. 103 
 
 87. Formula for Calculating Kinetic Energy. The 
 
 kinetic energy of a moving body is calculated by means of 
 the following formula : 
 
 WV 2 
 
 = energy, 
 
 in which W represents the weight of the body, V its ve- 
 locity, and g the acceleration (in this latitude 32^ feet, or 
 9.8 m per second) due to gravity. [For the derivation of this 
 formula, see the Author's Principles of Physics, pages 91 
 and 92.] For example, the energy of a cannon-ball weighing 
 50 pounds and moving with a velocity of 1,000 feet per sec- 
 
 ond = - = p X - (about) 779,301 foot-pounds. 
 
 2 X 
 
 Certain deductions from this formula should be strongly 
 impressed upon the mind ; viz., (1) with the same velocity 
 the kinetic energy of a body varies as its weight ; (2) with 
 the same weight its kinetic energy varies as the square of its 
 velocity. Doubling the velocity multiplies the energy four- 
 fold ; trebling the velocity multiplies it ninefold. A bullet 
 moving with a velocity of 600 feet per second will pene- 
 trate, not twice, but four times, as far into a plank as one 
 having a velocity of 300 feet per second. 
 
 A railway train having a velocity of 20 miles an hour 
 will, if the steam is shut off, continue to run four times as 
 far as it would if its velocity were 10 miles an hour. The 
 reason is apparent why light substances, even so light as 
 air, exhibit great energy when their velocity is great. 
 
 88. Wasted Work. As a stone is raised higher and 
 higher, the work accumulates in the form of potential en- 
 ergy. As a body free to move (i.e. meeting with no re- 
 sistance) acquires, under the influence of a constant force, 
 uniformly accelerated motion, so does work, in the form 
 
104 WORK AND ENERGY. 
 
 of kinetic energy, accumulate. But accumulated work or 
 energy does not always vary as the work performed. In 
 practice, more or less of the work done, especially that 
 done in overcoming friction, resistance of fluids, etc., is 
 wasted. The work done by the sawyer and bullet, page 
 102, so far as imparting energy to the bodies on which they 
 do work, is all lost. Of the vast amount of work done in 
 propelling a steamer across the ocean none accumulates ; 
 all is wasted, distributed along the watery path, and can- 
 not be recovered or made available for doing more work. 
 Evidently the accumulated work or available energy that a 
 body possesses is the work done upon the body less the 
 wasted work. We may then calculate in foot-pounds (or 
 kilogram meters) according to formulas (1) or (2), page 99, 
 the work performed on a body, and from this deduct the 
 number of foot-pounds wasted ; the remainder is the num- 
 ber of foot-pounds of available energy that is imparted 
 to the body. 
 
 89. Power of an Agent to do Work, or Rate at 
 which an Agent can do Work. -In estimating the total 
 amount of work done, the time consumed is not taken 
 into consideration. The work done by a hod-carrier, in 
 carrying 1,000 bricks to the top of a building, is the same 
 whether he does it in a day or a week. But in estimating 
 the power of any agent to do work, as of a man, a horse, 
 or a steam-engine, in other words, the rate at which it is 
 capable of doing work, it is evident that time is an impor- 
 tant element. The work done by a horse, in raising a 
 barrel of flour 20 feet high, is about 4,000 foot-pounds ; 
 but even a mouse could do the same amount of work in 
 time. 
 
 The unit in which power or rate of doing work is esti- 
 
METHODS OF ESTIMATING WORK AND ENERGY. 105 
 
 mated is called (inappropriately) a horse-power. A horse- 
 power represents the power to perform 33,000 foot-pounds of 
 work in a minute (or 550 foot-pounds in a second). 
 
 EXERCISES. 
 
 1. Can a person lift himself, or put himself in motion, without 
 exerting force upon some other body ? 
 
 2. Can a body do work upon itself? Can a body generate energy 
 in itself, i.e. increase its own energy ? 
 
 3. (a) Suppose that an average force of 25 pounds is exerted 
 through a space of 10 inches in bending a bow; what amount of 
 energy will it give the bow ? (6) What kind of energy will the bow, 
 when bended, possess ? 
 
 4. (a) What amount of kinetic energy does a body weighing 20 
 pounds, and moving with a velocity of 300 feet per second, possess ? 
 (&) What amount of work can the body do ? 
 
 5. (a) What amount of work is required to raise 50 tons of coal 
 from a mine 200 feet deep ? (6) An engine of how many horse-power 
 would be required to do it in two hours ? 
 
 6. How many fold is the kinetic energy of a body increased by 
 doubling its velocity? 
 
 7. Twelve hundred foot-pounds of energy will raise 100 pounds 
 how high, if none is wasted? 
 
 8. A force of 500 pounds acts upon a body through a space of 20 
 feet. One-fourth of the work is wasted in consequence of resistances. 
 How much available energy is imparted to the body ? 
 
 9. How much energy is stored in a body weighing 1,000 pounds, at 
 a hight of 200 feet above the earth ? 
 
 10. How much work can a 2 horse-power engine do in an hour ? 
 
 11. A horse draws a carriage on a level road at the uniform rate 
 of 5 miles an hour, (a) Does work accumulate ? (b) What kind of 
 energy does the carriage possess ? (c) Suppose that the carriage were 
 drawn up a hill ; would energy accumulate ? (W) What kind of energy 
 would it possess when at rest on the top of the hill ? (e) How would 
 you calculate the quantity of energy it possesses when at rest on top 
 of the hill ? (/") Suppose that the carriage is in motion on top of the 
 hill ; what two formulas would you employ in calculating the total 
 energy which it possesses ? 
 
106 WORK AND ENERGY. 
 
 Section II. 
 
 THE ABSOLUTE OR C.G.S. SYSTEM OF MEASUREMENTS. 
 
 90. Fundamental Units. For many scientific purposes, espe- 
 cially in establishing a complete set of electrical units, a different system 
 for measuring physical quantities than that in common use and called 
 the gravitation system, is indispensable. In the new system, all physical 
 quantities may be expressed in terms of three units, which are called funda- 
 mental units. All others are deduced from these by definition, and are called 
 derived units. The fundamental units and their symbols are as follows : 
 
 Unit of length, L : the centimeter, or the hundredth part of a meter. 
 
 Unit of mass, M : the gram, or the mass of one cubic centimeter of 
 distilled water at 4 C. 
 
 Unit of time, T: a second. 
 
 The system of units based on these three fundamental units is called 
 the Absolute System, or the Centimeter-Gram-Second System, or, by 
 abbreviation, C.G.S. System. 
 
 91. Derived Units. There are a great number of derived units. 
 We give a few of those in most common use. 
 
 Unit of velocity, V: one centimeter per second; in uniform motion, 
 
 v=. 
 
 T 
 
 Unit of acceleration, A : an increase of velocity of one centimeter per 
 second. 
 
 Unit of force, F: a dyne,- it is that force which, acting for a second, 
 will give to a mass of one gram an acceleration of one centimeter per 
 second, i.e. one unit of acceleration. It is the - part of the weight of the 
 unit of mass. ^ 
 
 F = MA = , or MLT- 2 . 
 
 T 2 
 
 Unit of work, W ; or of energy, E : an erg ; it is the work done or 
 energy imparted by a force of one dyne working through a length or 
 distance of one centimeter. 
 
 W or E = FS = MAS = M -^, or ML 2 T~ 2 . 
 
 92. Relation of the Dyne to the Gram or Gravitation 
 Unit of Weight. When a body falls in a vacuum, gravity imparts to 
 
THE ABSOLUTE OR C.G.S. SYSTEM OF MEASUREMENTS. 107 
 
 it an acceleration of g (in the latitude of the Northern States, 980) centi- 
 meters per second. The force of gravity, therefore, acting on a unit of 
 mass is, according to definition, g (980) dynes. The weight of a mass of 
 one gram is in the gravitation system one gram. Hence the gram (gravi- 
 tation unit of weight) must be equal to g dynes, or, in the Northern United 
 States, to 980 dynes. The weight of a mass of one gram varies with the 
 latitude and hight above the earth's surface, while the mass of a gram and 
 the dyne are constant quantities; their value does not change with place. 
 
 93. Another Formula for Computing Kinetic Energy. 
 
 It is evident that the weight of a body is dependent upon its mass and 
 the force of gravity ; in other words, (W = M#) the weight of a body is 
 measured by the product of the acceleration which the force of gravity 
 produces into its units of mass. Hence the mass of a body is numerically 
 
 _ its weight. Substituting the value of W given above in the formula 
 g 
 
 (p. 103), E = -, we have E = When the latter formula is used, 
 
 it is evident that the mass of the moving body must be found by dividing 
 its weight in grams by 980, or its weight in pounds by 32.1 +. 
 
 The absolute system is used in all refined physical measurements, 
 but the gravitation system is more convenient and is universally used in 
 the ordinary affairs of life. 
 
 QUESTIONS. 
 
 [Designed for only those who may take up the absolute system.] 
 
 1. (a) Name some unit of force which is based upon the weight of 
 some definite mass. (6) Name some unit of force which is based upon the 
 amount of acceleration which a force can impart to a body of a given 
 mass in a given time, (c) Have both of these units absolute (unchange- 
 able) values? (d) What names do you employ in distinguishing these 
 two classes of units ? 
 
 2. (a) What are the fundamental units of the absolute system? 
 (6) Why are they called fundamental units ? 
 
 3. A force of 20s is equivalent to how many dynes ? 
 
 4. (a) A force of 20 dynes would perform how many ergs of work in 
 acting through a distance of 10 cm ? (6) How many ergs of work would a 
 force of 20 grams perform in acting through the same distance ? (c) How 
 many kilogrammeters of work would a force of 20 grams perform in acting 
 through the same distance ? 
 
 5. What is the weight of a mass of Is in dynes ? 
 
108 
 
 WOBK AND ENERGY. 
 
 Section III. 
 
 MACHINES. 
 
 94. Uses of Machines. 
 
 Experiment 74. Suspend, as in Figure 95, a fixed pulley, A, and 
 a movable pulley, B. The scale-pan C counterbalances the pulley B, 
 so that there will be equilibrium. Suspend from B two balls, LL, of 
 equal weight, and suspend on the side where the pan is, a single ball, 
 
 K, equal to one of the former. The 
 single ball supports the two balls ; 
 i.e. by the use of the machine, a force 
 of 1 is enabled to balance a force of 
 2. So far no work is done. (Why ?) 
 Place a very small weight in the pan, 
 and the balls LL begin to rise, and 
 work is done. 
 
 As the weight K plus a very small 
 weight causes the motion, we shall 
 regard this as the force (F) ; and as 
 the weights LL are the bodies moved 
 (the pulleys and pan being parts of 
 the machine may be disregarded), 
 they may be regarded as the re- 
 sistance (R) overcome, or the body 
 on which work is done. Measure 
 the respective distances through 
 which F acts and R moves during 
 the same time. R moves only one- 
 half as great a distance as that through which F acts ; i.e. if R rises 
 2 feet, F must act through 4 feet. Suppose that R is 2 pounds, then 
 F is 1 + pounds. Now 2 (pounds) X 2 feet = 4 foot-pounds of work 
 done on R. Again, 1 + (pounds) X 4 feet = a little more than 4 foot- 
 pounds of work (or energy) expended. 
 
 It thus seems that, although a machine will enable a 
 small force to balance a large force, when work is per- 
 
 Fig. 95. 
 
MACHINES. 109 
 
 formed, the work applied to the machine is greater, rather 
 than less, than the work which the machine transmits to 
 the resistance. The work applied is greater than the 
 work transmitted by the amount of work wasted in conse- 
 quence of friction and other extra resistances. So that 
 by the employment of a machine nothing is gained in work 
 which the force is required to do, but always something lost. 
 What, then, is the advantage gained in using this 
 machine? Suppose that R is 400 pounds, and that the 
 utmost force that a man can exert is a little more than 
 200 pounds. Then, without the machine, the services of 
 two men would be required to move the resistance; 
 whereas one man can move it with a machine, only that 
 he will be obliged to move twice as far as the resistance 
 moves, a matter of little consequence in comparison with 
 the advantage of being able to do the work alone. The 
 advantage gained in this instance seems to be one of con- 
 venience. Men, however, are accustomed to speak of it as 
 " a gain of force" (or more commonly and inaccurately, 
 " of power "), inasmuch as a small force overcomes a 
 large resistance. 
 
 Experiment 75. If instead of applying the small additional 
 weight to the pan, it be suspended from one of the balls LL, the weight 
 of these balls, together with the additional weight, becomes the cause 
 of motion, and K is the resistance. In this case there is a loss of 
 force, because the force employed is more than twice as great as the 
 force overcome. Measure the distances traversed respectively by F and 
 R in the same time. R moves twice as far as F, and of course with 
 twice the velocity. There is a gain of velocity at the expense of force. 
 
 It thus appears that, if it should be desirable to move a 
 resistance with greater velocity than it is possible or con- 
 venient for the force to act, it may be accomplished 
 through the mediation of a machine, by applying to it a 
 
110 
 
 WORK AND ENERGY. 
 
 force proportionally greater than the resistance. This 
 apparatus is one of many contrivances called machines. 
 A machine is a contrivance for transferring or transforming 
 energy. [Machines for transforming energy will be con- 
 sidered in future chapters.] Some of the many advan- 
 tages derived from the use of machines are : 
 
 (1) They may enable us to exchange intensity of force 
 for velocity, or velocity for intensity of force. A gain of in- 
 tensity of force or a gain of velocity is called a mechani- 
 cal advantage. 
 
 They may enable us to employ a force in a direction 
 more convenient than the direction in which the resist- 
 to be moved. 
 
 (3) They may enable us to employ other 
 forces than our own in doing work; e.g. 
 the strength of animals ; the forces of wind, 
 water, steam, etc. 
 
 How are the last two uses illustrated in 
 Figure 96 ? The pulleys employed are 
 called fixed pulleys, i.e. they have no motion 
 except that of rotation. Is any mechani- 
 cal advantage gained by fixed pulleys ? 
 What is the use of a fixed pulley ? Pulley 
 B (Fig. 94) is a movable pulley. What 
 kind of advantage is gained by 
 means of a movable pulley ? 
 
 (2) 
 that is 
 ance is 
 
 Fig. 96. 
 
 95. General Law of Machines. 
 
 From the experiments and dis- 
 cussion above we derive the following formula for r ma- 
 chines : 
 
 FS = RS' + w, 
 
MACHINES. Ill 
 
 in which F represents the force applied, and S the distance 
 through which F acts ; R represents the resistance over- 
 come, and S' the distance through which its point of ap- 
 plication is moved ; w represents the wasted work. A 
 machine in which there is no wasted work is a perfect 
 machine. Such a machine is purely ideal, as none exists. 
 If in our calculations we regard a machine as perfect 
 (though subsequently suitable allowance must be made 
 for the wasted work), then our formula becomes 
 
 FS - RS'. 
 
 Whence R : F : : S : S' ; i.e. the force and resistance vary 
 inversely as the distances which their respective points of ap- 
 plication move. In other words, the ratio of the resistance 
 to the force is the reciprocal of the ratio of the distances 
 which these points move. 
 
 R:F = 4, then S':S = J. 
 
 This law applies to every machine of whatever descrip- 
 tion ; hence it is called the G-eneral or Universal Law of 
 Machines. When R is greater than F, there is a gain of 
 
 r> 
 
 force, and = the ratio of gain of force. When S ; is 
 
 F 
 
 S 
 
 greater than S, there is a gain of velocity, and "^r = the 
 ratio of gain of velocity. 
 
 Experiment 76. Support a lever, as in Figure 97, so that there 
 shall be unequal arms. Move w until the lever is balanced in a hori- 
 zontal position. Suspend (say) 
 seven balls from the short arm 
 (say) one space from the ful- 
 crum. Then from the other 
 arm suspend a single ball from 
 such a place (in this case seven 
 equal spaces from the fulcrum) 
 that it will balance the seven 
 balls. There is now equilibrium between the two forces. Suppose 
 
112 
 
 WORK AND ENERGY. 
 
 the smaller force to be increased a little and to produce motion ; what 
 mechanical advantage (i.e. intensity of force or velocity) would be 
 gained by the use of the machine ? What is the ratio of gain neg- 
 lecting the small additional force? How does this ratio compare with 
 the ratio between the length of the two arms ? For convenience we 
 call the distance of the point of application of the force from the 
 fulcrum the force-arm, and the distance of the resistance from the 
 fulcrum the resistance-arm. 
 
 Suppose the small additional force is applied to the short arm; 
 what mechanical advantage would be gained ? What would be the 
 ratio of gain ? 
 
 While the general law of machines is always applica- 
 ble, a special law, one in 
 which the relation be- 
 tween the ratio of gain 
 and the ratio between 
 certain dimensions of 
 the machine is stated, is 
 often more convenient in 
 practice. For example, 
 in our experiment with 
 the lever we discover 
 that R : F : : force-arm : 
 resistance-arm, i.e. the 
 force and resistance vary 
 inversely as the lengths 
 of their respective arms. 
 Compare this special law 
 with the general law. 
 Place the fulcrum at other points in the lever, and thereby 
 vary the length of the arms, and verify by numerous 
 experiments the special law of levers. 
 
 Experiment 77. By means of a pulley, D, so arrange (Fig. 98) 
 that both F and R may be on the same side of the fulcrum. First, 
 
 Fig. 98. 
 
MACHINES. 
 
 113 
 
 place in the pan weights sufficient to produce equilibrium in the 
 machine (for example, in this case, one ball). Then suspend weights 
 at some point, as A, and place other weights in the pan to counter- 
 balance these. Verify the law of levers. If A is the resistance, what 
 mechanical advantage is gained ? What is the ratio of gain ? If B 
 is the resistance, what mechanical advantage will be gained ? 
 
 Experiment 78. Obtain 
 a toy carriage, place it on an 
 inclined plane, pass the cord 
 over a pulley, B (Fig. 99), 
 so adjusted that the cord 
 between the carriage and 
 pulley shall be parallel with 
 the plane. Suspend a small 
 bucket, P, and place sand in 
 it to balance the carriage. 
 Place in the carriage a weight W, and place weights in the bucket to 
 balance W. The weights placed in the bucket represent the force 
 
 Fig. 99. 
 
 Fig. loo. Fig. un- 
 
 applied ; then what advantage is gained in the use of an inclined plane 
 as a machine? W, in traversing the inclined plane AB, only rises 
 through the vertical hight CB, while P must move through a distance 
 equal to AB. Measure the distances AB and CB. How does the ratio 
 
114 
 
 WORK AND ENERGY. 
 
 between these distances compare with the ratio of gain ? Construct a 
 special law of the inclined plane. 
 
 Experiment 79. Place a "wheel and axle" (Fig. 100) on the 
 support A. Wind a cord around the wheel B, and another in the re- 
 verse direction around the axle C. Suspend a weight, D, from the 
 axle, and another, E, from the wheel, to balance it. If E be the 
 force applied, what advantage is gained ? What, if D is the force 
 applied ? What is the ratio of advantage in either case ? How does 
 the ratio of advantage compare with the ratio between the radius of 
 the wheel AC (Fig. 101) and the radius of the axle BC ? Construct a 
 special law of the wheel and axle . 
 
 Fig. 102. 
 EXERCfSES. 
 
 1. (a) When is a machine said to gain intensity of force? (b) When 
 is it said to gain velocity V 
 
MACHINES. 
 
 115 
 
 2. (a) Can any machine do work ? (6) Can we by the use of any 
 machine accomplish more work than the work performed upon the 
 machine ? What is the proof ? 
 
 3. How is intensity of force 
 gained by the use of a machine ? 
 
 4. What machine is used only 
 to change the direction of motion ? 
 
 5. (a) What is a mechanical 
 
 Fig. 1O3. 
 
 (6) Give a rule by which the mechanical advantage 
 
 Fig. 104. 
 
 advantage ? 
 
 that may be gained by any machine may be calculated. 
 
 6. Figure 102 repre- 
 sents a pile-driver, (a) 
 How can the energy or 
 the work which the weight 
 W can do when it is raised 
 a given distance be com- 
 puted ? (b) What benefit is derived from the use of the machine in 
 raising the weight ? (c) Suggest some simple attachment to the 
 machine which would enable one man to raise the weight, (e?) Sug- 
 gest some attachment by means of which a horse could be made to do 
 the work, (e) What 
 difference will it make 
 whether the weight is 
 raised 5 feet or 10 
 feet? (/) Illustrate, 
 by means of this ma- 
 chine, what you un- 
 derstand by force and 
 energy. (g} Which, 
 while the weight rises, 
 is constantly accumu- 
 lating, and which re- 
 
 Fig. 105. 
 
 mains nearly constant ? 
 (A) Which can be meas- 
 ured with an instrument, and what is the name of the instrument? 
 
 7. (a) What advantage is gained by a lever when its force-arm is 
 longer thin its resistance-arm? (b) What, when its resistance-arm is 
 longer? 
 
 8. (a) What advantage is gained by a nut-cracker (Fig. 103)? 
 (6) What is the ratio of gain ? 
 
116 
 
 WORK AND ENERGY. 
 
 Fig. 106. 
 
 9. (a) What advantage is gained by cutting far back on the blades 
 of shears near the fulcrum? Why? (b) Should shears for cutting 
 metals be made with short handles and long blades, or the reverse ? 
 (c) What is the advantage of long blades ? 
 
 10. Is work done when the 
 moment of the force applied 
 to a lever is equal to the mo- 
 ment of the resistance ? Why ? 
 
 11. (a) If P (Fig. 105), 
 weighing 1 pound, is suspend- 
 ed 15 spaces from the fulcrum 
 of the steelyard, what weight 
 (W), suspended 3 similar 
 spaces the other side of the 
 fulcrum, will balance it ? (&) 
 
 Where would you place the one-pound weight in order to weigh out 
 6 pounds of tea? 
 
 12. (a) If the circumference of the axle (Fig. 106) is 15 inches, 
 and the force applied to the crank acts through 15 feet during each rev- 
 olution, what force will be necessary 
 
 to raise the bucket of coal weighing 
 (say) 36 pounds? (b) Through how 
 many feet must the force act to raise 
 the bucket from a cavity 48 feet 
 deep? 
 
 13. The arm is raised by the con- 
 traction (shortening by muscular 
 force) of the muscle A (Fig. 107), 
 which is attached at one extremity 
 to the shoulder and at the other ex- 
 tremity B to the fore-arm, near the 
 
 elbow, (a) When the arm is used, as represented in the figure, to 
 raise a weight, what kind of a machine is it ? (b) What mechanical 
 advantage is gained by it ? (c) How can the ratio of gain be com- 
 puted ? (c?) For which purpose is the arm adapted, to gain intensity 
 of force or velocity ? 
 
 The lengths of the two arms of a balance, such as is used in finding 
 specific gravity (Fig. 60, page 61), should be exactly equal. The arms 
 may be of unequal length, and yet the beam may be in equilibrium 
 
 Fig. 107. 
 
MACHINES. 
 
 117 
 
 (i.e. take a horizontal position when no weights are applied), in conse- 
 quence of having more matter in the shorter arm, as in Figure 97, page 
 111. Such a balance is called a, false balance. 
 
 14. (a) How would you test a balance to ascertain whether it is 
 true or false ? (6) If you were buying diamonds, and the seller should 
 sell them to you by weight as obtained by placing them on the shorter 
 arm of a false balance, would you be the loser or gainer? 
 
 The true weight of a body may be found with a false balance by a 
 process called double weighing. The article to be weighed is placed in one 
 pan, and a counterpoise of sand in the other pan. The article is then 
 removed, and known weights placed in the pan until equilibrium is again 
 produced. These weights represent the correct weight of the article. In 
 this way the balances used in the school laboratory should be tested by 
 the pupil 
 
 Fig. 1O8. 
 
 Fig. 109. 
 
 15. During one revolution a screw advances a distance equal to 
 the distance between two threads, measured in the direction of the 
 axis of the screw. Suppose the screw in the letter-press (Fig. 108) to 
 advance \ inch at each revolution, and a force of 25 pounds to be 
 applied to the circumference of the wheel B, whose diameter is 14 
 inches. What pressure would be exerted on articles placed beneath 
 the screw? (The circumference of a circle is 3.1416 times its diame- 
 ter.) 
 
 16. The toggle-joint (Fig. 109) is a machine employed where great 
 pressure has to be exerted through a small space, as in punching and 
 
118 
 
 WORK AND ENERGY. 
 
 Fig. 110. 
 
 shearing iron, and in printing-presses, in pressing the types forcibly 
 
 against the paper. An illustration 
 
 may be found in the joints used to 
 
 raise carriage-tops. Force applied 
 
 to the joint C will cause the two 
 
 links AC and BC to be straight- 
 ened, or carried forward to e. If 
 
 point C moves 5 inches while G 
 
 moves | inch, then what pressure 
 
 will a force of 50 pounds applied 
 
 at C exert on the book below ? 
 17. Show that the hydrostatic 
 
 press (page 50) conforms in its 
 operation to the general law of machines. 
 
 18. A wedge may be regarded as two inclined 
 planes placed base to base, as dc (Fig. 110). 
 
 (a) What mechanical advantage is gained by it ? 
 
 (b) Suppose that the thickness db is 4 inches, 
 and the length dc is 8 inches, and that the aver- 
 age pressure exerted upon it by the blow of a 
 sledge is 100 pounds ; what will be the average 
 pressure exerted by the wedge tending to separate 
 the fibers of wood ? 
 
 A compound machine is one consisting of two or more machines 
 
 combined in one; e.g. com- 
 pound pulleys (Fig. Ill) and 
 compound wheels and axles 
 (Fig. 112). The mechanical 
 advantage that may be gained 
 by a compound machine may 
 be calculated by multiplying 
 continuously together the ra- 
 tios of the several machines. 
 
 19. (a) How great is the 
 advantage gained by one mov- 
 able pulley? (b) How great is 
 the advantage gained by the 
 Fig. 113. compound pulley (Fig. Ill) 
 
 consisting of three movable pulleys? 
 
MACHINES. 
 
 119 
 
 20. Suppose that the radii of the wheels , d, and/ (Fig. 112) are, 
 respectively, 20 inches, 16 inches, and 24 inches, and the radii of their 
 axles are, respectively, 2 inches, 4 inches, and 6 inches; how great 
 advantage may be gained by the compound machine? 
 
 Fig. 113. 
 
 21. How would you calculate the mechanical advantage gained by 
 a machine like that of Figure 113 ? (On the axle A is an endless screw, 
 by means of which motion is communicated from the axle to the 
 wheel W.) 
 
 22. (a) What kind of a machine is a claw-hammer (Fig. 114)? 
 (6) What mechanical advantage is gained by it ? 
 
 23. In its technical meaning, a " perpetual motion machine " is not 
 a machine that will run indefinitely, but a machine which can do work 
 without the expenditure of energy. Is such a machine possible? 
 
 24. A plank 12 feet long and weighing 24 pounds is supported by 
 two props, one 3 feet from one end, and the other 1 foot from the 
 other end. What is the pressure on each prop? 
 
 25. With a movable pulley what force will support a weight of 
 100 pounds ? 
 
 26. The gradient of a certain road on a hillside is one foot in ten 
 feet. What force must a horse exert on a carriage which weighs to- 
 gether with its load one ton, to prevent its descent ? 
 
 27. What must be the diameter of a wheel in order that a force of 
 20 pounds a,pplied at its circumference may be in equilibrium with a 
 resistance of 600 pounds applied to its axle, which is 3 inches in diam- 
 eter? 
 
120 WORK AND ENERGY. 
 
 28. Draw a straight line to represent a lever ; locate the fulcrum, 
 and locate the points of application of the force and resistance un- 
 equally distant from the fulcrum. Draw lines from the points of 
 application of the force and resistance so that they will make some 
 angle with each other (i.e. not parallel with each other) to represent 
 the directions in which the two forces respectively act. Ascertain the 
 ratio between the two forces when their moments are equal, i.e. when 
 the two forces are in equilibrium. 
 
UNIVERSITY OF CALIFORNIA 
 
 DEPARTMENT OF PHYSICS 
 
 * 
 
 CHAPTER V. 
 MOLECULAR ENERGY. HEAT. 
 
 Section I. 
 
 WHAT HEAT IS. SOME SOURCES OF HEAT. 
 
 96. Theory of Heat. A body loses motion in com- 
 municating it. The hammer descends and strikes the 
 anvil; its motion ceases, but the anvil is not sensibly 
 moved ; the only observable effect produced is heat. In- 
 stead of a motion of the hammer and anvil, there is now, 
 according to the modern view, an increased vibratory mo- 
 tion of the molecules that compose the hammer and anvil, 
 simply a change from molar to molecular motion. Of 
 course, this latter motion is invisible. According to this 
 view, heat is but a name for the energy of vibration of the 
 molecules of a body. A body is heated by having the 
 motion of its molecules quickened, and cooled by parting 
 with some of its molecular motion. One body is hotter 
 than another when the average kinetic energy of each mole- 
 cule in it is greater than in the other. 
 
 As late as the beginning of the present century heat was generally 
 regarded as " a sensation which the presence of fire " (an " igneous fluid" 
 " matter of heat," called sometimes " caloric ") " occasions in animate and 
 inanimate bodies." A text-book of that period makes this significant 
 statement : "There is fire in the wood, and there is air in the field, though 
 we do not perceive either while at rest. Kubbing two pieces of wood does 
 not create fire any more than the blowing of the wind creates air. Motion 
 renders both perceptible." The former and the more modern views are in 
 
122 MOLECULAR ENERGY. HEAT. 
 
 harmony in attributing the immediate cause of the sensation to motion. 
 According to the former view, the sensation is produced by putting an 
 imaginary fluid in motion ; according to the modern view it is produced by 
 quickening the motion of the molecules of a body. 
 
 97. Artificial Sources of Heat. As heat is energy, 
 so all heat must originate in some form of energy, i.e. by 
 the transformation of some other form of energy into heat. 
 
 Experiment 80. Place a ten-penny nail on a stone or a flat 
 piece of iron and hammer it briskly for a few minutes. It soon be- 
 comes too hot to be handled with comfort. Rub a desk with your fist ; 
 your coat-sleeve with a metallic button; both the rubbers and the 
 things rubbed become heated. 
 
 (1) Heat is generated at the expense of molar motion, 
 i.e. molar motion checked becomes molecular motion, or heat. 
 
 Experiment 81. Take a glass test-tube half full of cold water 
 and pour into it one-fourth its volume of strong sulphuric acid. The 
 liquid almost instantly becomes so hot that the tube cannot be held in 
 the hand. 
 
 When water is poured upon quicklime, heat is rapidly 
 developed. The invisible oxygen of the air combines with 
 the constituents of the various fuels, such as wood, coal,, 
 oils, and illuminating-gas, and gives rise to what we call 
 burning, or combustion, by which a large amount of heat is 
 generated. In all such cases the heat is generated by the 
 combination or clashing together of molecules of sub- 
 stances that have an affinity (i.e. an attraction) for one 
 another. Before union the energy of the molecules is of 
 the same kind as that of a stone on a shelf. When the 
 shelf is withdrawn, gravity converts the potential energy 
 of the stone into kinetic energy ; so affinity converts the 
 potential energy of the molecules into kinetic energy 
 of vibration ; i.e. into heat. 
 
WHAT HEAT IS. 123 
 
 (2) Molecular (or atomic) potential energy is transformed 
 in the act of chemical combination into heat. 
 
 98. The Sun as a Source of Heat and Energy. The 
 
 sun is the source of very nearly all the energy employed by 
 man in doing work. Our coal-beds, the results of the de- 
 posit of vegetable matter, are vast storehouses of the sun's 
 energy, rendered potential during the growth of the plants 
 many ages ago. The animal finds its food in the plant, 
 appropriates the energy stored in the plant, and converts 
 it into energy of motion in the form of animal heat and 
 muscular motion. Every rain-drop that rolls its way to the 
 sea, contributing its mite to the immense water-power of 
 the earth, derives its energy from the sun. 
 
 QUESTIONS. 
 
 1. On every hand we see what appears to be at least an almost 
 universal tendency to destruction of motion. Is the destruction 
 usually an annihilation of motion ? 
 
 2. What name is usually given to molecular energy? 
 
 3. How does it appear that heat is energy? 
 
 4. What do you mean when you say that one body is hotter than 
 another ? 
 
 5. How must all heat originate ? 
 
 6. State all the sources of heat with which you are now acquainted. 
 
 7. (a) Give an illustration of mechanical or visible motion trans- 
 formed into molecular motion. (6) Give an illustration of molecular 
 motion transformed into mechanical motion. 
 
 8. What kind of energy does coal and other fuel possess ? 
 
 9. A lump of coal is raised and placed upon a shelf, (a) How can 
 the potential energy of the lump be transformed into kinetic energy ? 
 (6) Will the kinetic energy resulting from the transformation be 
 mechanical or molecular ? (c) When the lump strikes the earth, what 
 transformation of energy occurs ? 
 
 10. Every lump of coal possesses molecular potential energy, (or) 
 How can its energy be transformed into kinetic energy ? (6) What 
 
124 MOLECULAR ENERGY. HEAT. 
 
 two varieties of potential energy does a lump of coal on the shelf 
 
 11. (a) How do bodies acquire energy? (b) From what source did 
 coal obtain its molecular potential energy ? (c) What does the entire 
 value of coal consist in? 
 
 12. How does animal energy originate ? 
 
 Section II. 
 
 TEMPERATURE. METHODS OF EQUALIZATION. 
 
 99. Temperature Defined. If body A is brought 
 in contact with body B, and A tends to impart heat 
 to B, then A is said to have a higher temperature than 
 B. Temperature is the state of a body with reference to 
 its tendency to communicate heat to, or receive heat from, 
 other bodies. The direction of the flow of heat deter- 
 mines which of two bodies has the higher temperature. 
 If the temperature of neither body rises at the expense 
 of the other, then both have the same temperature. 
 
 100. Temperature distinguished from Quantity of 
 Heat. The term temperature does not signify quantity 
 of heat. If we dip from a gallon of boiling water a cupful, 
 the cup of water is just as hot, i.e. has the same tempera- 
 ture, as the larger quantity, although of course there is a 
 great difference in the quantities of heat the two bodies of 
 water contain. Temperature depends upon the average ki- 
 netic energy of the individual molecule, while quantity of 
 heat depends upon the average kinetic energy of the indi- 
 vidual molecule multiplied by the number of molecules. 
 
TEMPERATURE. METHODS OF EQUALIZATION. 125 
 
 There is always a tendency to equalization of tempera- 
 ture; that is, heat has a tendency to pass from a warmer 
 body to a colder, or from a warmer to a colder part of the 
 same body, until there is an equality of temperature. 
 
 1O1. Conduction. 
 
 Experiment 82. Place one end of a wire about 10 inches long 
 in a lamp-flame, and hold the other end in the hand. Heat gradually 
 travels from the end in the flame toward the hand. Apply your fin- 
 gers successively at different points nearer and nearer the flame ; you 
 find that the nearer you approach the flame, the hotter the wire is. 
 
 The flow of heat through an unequally heated body, 
 from places of higher to places of lower temperature, is 
 called conduction ; the body through which it travels is 
 called a conductor. The molecules of the wire in the flame 
 have their motion quickened ; they strike their neighbors 
 and quicken their motion ; the latter in turn quicken the 
 motion of the next ; and so on, until some of the motion 
 is finally communicated to the hand, and creates in it the 
 sensation of heat. 
 
 Experiment 83. Figure 115 represents a board on which are 
 fastened, by means of staples, four wires : (1) 
 iron, (2) copper, (3) brass, and (4) German 
 silver. Place a lamp-flame where the wires meet. 
 In about a minute run your fingers along the 
 wires from the remote ends toward the flame, 
 and see how near you can approach the flame on 
 each without suffering from the heat. Make a 
 list of these metals, arranging them in the order Fi s- H5- 
 
 of their conduetibility. 
 
 You learn that some substances conduct heat much more 
 rapidly than others. The former are called good conduc- 
 tors, the latter poor conductors. Metals are the best con- 
 ductors, though they differ widely among themselves. 
 
MOLECULAR ENERGY. HEAT. 
 
 Experiment 84. Fill a test-tube full of water, and hold it some- 
 what inclined (Fig. 116), so that a flame may heat the part of the 
 tube near the surface of the water. Do 
 not allow the flame to touch the part of 
 the tube that does not contain water. 
 The water may be made to boil near its 
 surface for several minutes before any 
 change of the temperature at the bottom 
 will be perceived. 
 
 Liquids, as a class, are poorer 
 conductors than solids. Gases are 
 Fig. lie. much poorer conductors than liquids. 
 
 It is difficult to discover that pure, dry air possesses any 
 conducting power. The poor conducting power of our 
 clothing is due partly to the poor conducting power of 
 the fibers of the cloth, but chiefly to the air which is 
 confined by it. 
 
 Loose garments, and garments of loosely woven cloth, inasmuch as 
 they hold a large amount of confined air, furnish a good protection from 
 heat and cold. Bodies are surrounded with bad conductors, to retain heat 
 when their temperature is above that of surrounding objects, and to 
 exclude it when their temperature is below that of surrounding objects. 
 In the same manner double windows and doors protect from cold. 
 
 1O2. Convection in Gases. 
 
 Experiment 85. Hold your hand a little way 
 from a flame, beneath, on the side of, and above the 
 flame. At which place is the heat most intense ? 
 
 Experiment 86. Draw on thin glazed paper 
 an unfolding line, so that the windings shall be 
 about | inch apart. Cut along the line; give the 
 central portion a conical form ; place the cone on 
 a pointed end of a vertical wire, and allow the 
 remainder of the paper to fall spirally around the 
 wire as in Figure 117. Place the spiral over a flame 
 or hot stove. A continuous current of air, a mini- 
 
 Fig. 117. 
 
 ature wind, moving upward from the flame or stove causes the spiral 
 
TEMPERATURE. METHODS OF EQUALIZATION. 127 
 
 to rotate. This current tends only upward. The air having become 
 heated by contact with the surfaces of the flame or stove conveys, in 
 its ascent, heat to objects above. Heat is thus diffused by a process 
 called convection (conveying). 
 
 Experiment 87. Cover a candle-flame with a glass chimney (Fig. 
 118), blocking the latter up a little way so that there may be a circu- 
 lation of air beneath. Hold the spiral over the chimney; the rotation 
 is much quicker than before. Hold smoking touch-paper near the 
 bottom of the chimney; the smoke seems to be drawn with great 
 rapidity into the chimney at the bottom ; in other words, the office of 
 the chimney is to create what is called a draft of air. Notice whether 
 the combustion takes place any more rapidly with than without the 
 chimney. 
 
 Fig. 118. Fig. 119. 
 
 Experiment 88. Place a candle within a circle of holes cut in the 
 cover of a vessel, and cover it with a chimney, A (Fig. 119). Over 
 an orifice in the cover place another chimney, B. Hold a roll of 
 smoking touch-paper over B. The smoke descends this chimney, 
 passes through the vessel and out at A. This illustrates the method 
 often adopted to produce a ventilating draft through mines. Let the 
 interior of a tin vessel represent a mine deep in the earth, and the 
 chimneys two shafts sunk to opposite extremities of the mine. A fire 
 kept burning at the bottom of one shaft will cause a current of air 
 
128 
 
 MOLECULAR ENERGY. HEAT. 
 
 to sweep down the other shaft, and through the mine, and thus keep 
 up a circulation of pure air through the mine. 
 
 The cause of the ascending currents is evident. Air, on becoming 
 heated, expands rapidly and becomes much rarer than the surround- 
 ing colder air ; hence it rises much like a cork in water, while cold 
 air pours in laterally to take its place. In this manner winds are 
 created. 
 
 The so-called trade-winds originate in the torrid or heated zone of the 
 earth. The air over the heated surface of the earth rises, and the colder 
 air from the polar regions flows in on both sides, giving rise to a constant 
 southward wind in the northern hemisphere, and northward wind in the 
 southern hemisphere. 
 
 Chemistry teaches us the vital 
 importance of thorough ventilation. 
 Figure 120 represents a scheme for 
 heating a room by steam, and venti- 
 lating it by convection. Steam is 
 conveyed by a pipe from the boiler 
 to a radiator box just beneath the 
 floor of the room. The air in the 
 box becomes heated by contact with 
 and radiation from the coil of pipe 
 in the box, and rises through a pas- 
 sage opening by means of a register 
 into the room near the floor at C, a 
 supply of pure air being kept up by 
 means of a tubular passage opening 
 into the box from the outside of 
 the building. Thus the room is fur- 
 nished with pure warm air, which, 
 mingling with the impurities aris- 
 ing from the respiration of its occu- 
 pants, serves to dilute them, and 
 render them less injurious. At the 
 same time, the warm and partially 
 Fig. 120. vitiated air of the room passes 
 
 through the open ventilator, A, into the ventilating-flue, and escapes, so 
 that in a moderate length of time a nearly complete change of air is 
 effected. It is evident that on the coldest days of winter the convection 
 is most rapid ; indeed, it may be so rapid that the air cannot be heated 
 sufficiently to render the room neai 1 the floor comfortable. At such times 
 
TEMPERATURE. METHODS OF EQUALIZATION. 129 
 
 the ventilator A may be closed, while the ventilator B is always open. 
 The heated air rises to top of the room and, not being able to escape, 
 crowds the colder air- beneath out at the ventilator B. No system of 
 ventilation dependent wholly on convection is adequate to ventilate 
 properly crowded halls ; air is too viscous and sluggish in its movements. 
 In such cases ventilation should be assisted by some mechanical means, 
 such as a blower or fan, worked by steam or water power. 
 
 103. Convection in Liquids. 
 
 Experiment 89. Fill a small (6 ounce), thin glass flask with 
 boiling hot water, color it with a teaspoonful of ink, stopper the flask, 
 and lower it deep in a tub, pail, or other large vessel rilled with cold 
 water. Withdraw the stopper, and the hot, rarer, colored water will 
 rise from the flask, and the cold water will descend into the flask. 
 The two currents passing in and out of the nack of the flask are easily 
 distinguished. The colored liquid marks distinctly the path of the 
 heated convection currents through the colored liquid and makes clear 
 the method by which heat, when applied at the bottom of a body of 
 liquid, becomes rapidly diffused through the entire mass notwithstand- 
 ing that liquids are poor conductors. 
 
 Experiment 90. Fill again the flask with hot colored water, 
 stopper, invert, and introduce the mouth of the flask just beneath the 
 surface of a fresh pail of cold water. Withdraw the stopper with as 
 little agitation of the water as possible. What happens? Explain. 
 
 104. Radiation. In some way the sun is the cause 
 of a large amount of the heat which -the surface of the 
 earth possesses. On the other hand, the earth in some 
 way parts with a large amount of heat. It is quite 
 apparent that the earth does not receive heat from the 
 sun by conduction or convection, and that by neither 
 of these processes does it part with heat. It is also 
 apparent that there is another and a much more rapid 
 and effectual method by which bodies of higher tempera- 
 ture on the earth part with their heat, and other bodies of 
 lower temperature acquire heat at the expense of distant 
 bodies, than by either of the two comparatively slow pro- 
 cesses of diffusion so far described. This process is called 
 
130 MOLECULAR ENERGY. HEAT. 
 
 radiation. The process is a very peculiar one, and must 
 be reserved for discussion in its proper place in the chapter 
 on Radiant Energy. 
 
 QUESTIONS. 
 
 1. Why does more heat reach your hand above than at an equal 
 distance beside a flame ? 
 
 2. Why is loose clothing warmer than tight-fitting clothing? 
 
 3. (a) Which contains more heat, the Atlantic Ocean or a tea-kettle 
 full of boiling water? (6) Which is capable of giving heat to the 
 other? (c) Can a body have less heat than another and yet be hotter 
 than the other? 
 
 4. Why should heat be applied to the bottom of a body of water? 
 
 5. (a) How is equalization of temperature effected in solids? (6) In 
 liquids and gases ? 
 
 Section III. 
 
 EFFECTS OF HEAT. EXPANSION. 
 
 1O5. Expansion of Solids, Liquids, and Gases. 
 
 Experiment 91. The brass ring and ball (Fig. 121) are so 
 constructed that the latter will just pass through 
 the former when both have the same, or nearly the 
 same, temperature. Heat the ball quite hot in a 
 flame, and ascertain by trying to pass it through the 
 ring whether it has increased in size. Devise some 
 method of passing it through the ring without cooling 
 the ball. 
 
 Experiment 92. Figure 122 represents a thin 
 Fig. 121. brass plate and an iron plate of the same dimensions 
 riveted together so far as to form what is called a compound bar. 
 Place the bar edgewise in a flame, dividing the flame in halves (one- 
 
EFFECTS OF HEAT. EXPANSION. 131 
 
 half on each side of the bar) so that both metals may be equally 
 heated. The bar, which was at first straight, is now bent, owing to 
 the unequal expansion of the two metals on receiving equal 
 increments of heat. Which metal expands more rapidly? 
 Thrust the hot bar into cold water. What happens ? Cover 
 the bar with chips of ice. What happens? 
 
 Experiment 93. Fit stoppers (perforated rubber stop- 
 pers are best) tightly in the necks of two similar thin 
 glass flasks (or test-tubes), and through each stopper pass 
 a glass tube about 18 inches long. The flasks should be 
 nearly of the same size. Fill one flask with water and the 
 other with alcohol, and crowd in the stoppers so as to force 
 the liquids up the tubes a little way above the stoppers. 
 Set both flasks at the same time into a large basin of hot Fig 7"i22. 
 water in order that both may have the same opportunity to 
 acquire heat. Soon the liquids begin to expand and rise in the 
 tubes. Which liquid is more expansible ? 
 
 Experiment 94. Take a dry flask like that used in Experiment 
 89, insert the end of the tube in a bottle of 
 colored water (Fig. 123), and apply heat to the 
 flask ; the enclosed air expands and comes out 
 through the liquid in bubbles. After a few 
 minutes, withdraw the heat, keeping the end 
 of the tube in the liquid ; as the air left in the 
 flask cools, it loses some of its tension, and 
 the water is forced by atmospheric pressure up 
 the tube into the flask, and partially fills it. ^ 
 
 Experiment 95. Partly fill a foot-ball (see 
 Fig. 9, page 8) with cold air, close the orifice, 
 and place it near a fire. The air will expand 
 and distend the ball. 
 
 Different substances, both in the solid 
 and liquid states, expand unequally on Flg ' 
 
 experiencing equal changes of temperature. Except at 
 very low temperatures, all gases expand alike for equal 
 changes of temperature. Under uniform pressure (as is 
 very nearly the case in the experiment with the balloon) 
 
132 MOLECULAB ENERGY. HEAT. 
 
 the volume of any body of gas varies -^ its volume at 
 the freezing-point of water for every degree Centigrade, 
 or -jiy for every degree Fahrenheit, its temperature is 
 changed. But if the gas is confined in a vessel of rigid 
 sides, so that its volume is necessarily constant, then 
 its tension varies in the same ratio for every degree its 
 temperature is changed. 
 
 The force exerted by bodies in expanding or contracting is very great, 
 as shown by the following rough calculation : If an iron bar, 1 square inch 
 in section, is raised from C. (freezing-point of water) to 500 C. (a dull, 
 red heat), its length, if allowed to expand freely, will be increased from 
 1 to 1.006. Now, a force capable of stretching a bar of iron of 1 square 
 inch section this amount is about 90 tons, which represents very nearly the 
 force that would be necessary to prevent the expansion caused by heat. 
 It would require an equal force to prevent the same amount of contraction 
 if the bar is cooled from 500 to C. 
 
 Boiler plates are riveted with red-hot rivets, which, on cooling, draw the 
 plates together so as to form very tight joints. Tires are fitted on carriage- 
 wheels when red hot, and, on cooling, grip them with very great force. 
 
 1O6. Abnormal Expansion and Contraction of Water. 
 
 Water presents a partial exception to the general rule 
 that matter expands on receiving heat and contracts on 
 losing it. If a quantity of water at C., or 32 R, is 
 heated, it contracts as its temperature rises, until it reaches 
 4 C., or about 39 F., when its volume is least, and there- 
 fore it has its maximum density. If heated beyond this 
 temperature, it expands, and at about 8 C. its volume is 
 the same as at 0. On cooling, water reaches its maximum 
 density at 4 C., and expands as the temperature falls 
 below that point. [See treatment of Expansion-Coeffi- 
 cients, Section E, Appendix.] 
 
THERMOMETRY. 133 
 
 Section IV. 
 
 THERMOMETRY. 
 
 A thermometer primarily indicates changes in volume ; 
 but as changes of volume are caused by changes of tem- 
 perature, it is commonly used for the more important pur- 
 pose of indicating temperature. 
 
 1C 7. Construction of a Thermometer. A thermom- 
 eter generally consists of a glass tube of capillary bore, 
 terminating at one end in a bulb. The bulb and part of 
 the tube are filled with mercury, and the space in the tube 
 above the mercury is usually a vacuum. On the tube, or 
 on a plate behind the tube, is a scale to show the hight of 
 the mercurial column. 
 
 108. Standard Temperatures. That a thermometer 
 may indicate any definite temperature, it is necessary that 
 its scale should relate to some definite and unchangeable 
 points of temperature. Fortunately nature furnishes us 
 with two convenient standards. It is found that under 
 ordinary atmospheric pressure ice always melts at the 
 same temperature, called the melting-point, or, more com- 
 monly, the freezing-point (water freezes and ice melts at 
 the same temperature). Again, the temperature of steam 
 rising from boiling water under the same pressure is always 
 the same. 
 
 109. Graduation of Thermometers. The bulb of a 
 thermometer is first placed in melting ice (Fig. 124), and 
 allowed to stand until the surface of the mercury becomes 
 
134 
 
 MOLECULAR ENERGY. HEAT. 
 
 stationary, arid a mark is made upon the stem at that 
 point, and indicates the freezing-point. Then the instru- 
 ment is suspended in steam rising from boiling water (Fig. 
 125), so that all but the very top of the column is in the 
 steam. The mercury rises in the stem until its tempera- 
 ture becomes the same as that of the steam, when it again 
 becomes stationary, and another mark is placed upon the 
 stem to indicate the boiling-point. Then the space be- 
 
 Fig. 134. 
 
 Fig. 125. 
 
 tween the two points found is divided into a convenient 
 number of equal parts called degrees, and the scale is ex- 
 tended above and below these points as far as desirable. 
 
 Two methods of division are adopted in this country : 
 by one, this space is divided into 180 equal parts, and the 
 result is called the Fahrenheit scale, from the name of its 
 author ; by the other, the space is divided into 100 equal 
 parts, and the resulting scale is called centigrade, which 
 means one hundred steps. In the Fahrenheit scale, which 
 is generally employed in English-speaking countries for 
 ordinary household purposes, the freezing and boiling 
 
THERMOMETRY. 
 
 135 
 
 points are marked respectively 32 and 212. 
 The of this scale (32 below freezing- 
 point), which is about the lowest tempera- 
 ture that can be obtained by a mixture of 
 snow and salt, was incorrectly supposed to 
 be the lowest temperature attainable. The 
 centigrade scale, which is generally em- 
 ployed by scientists, has its freezing and 
 boiling points more conveniently marked, 
 respectively and 100. A temperature be- 
 low in either scale is indicated by a minus 
 sign before the number. Thus 12 F. in- 
 dicates 12 below (or 44 below freezing- 
 point), according to the Fahrenheit scale. 
 
 To reduce a Fahrenheit reading to a 
 centigrade reading, first subtract 32 from 
 the given number, and then multiply by ^. 
 Thus, 
 
 100 c 
 
 To change a centigrade reading to a Fah- 
 renheit reading, first multiply the given 
 number by -|, and then add 32. Thus, 
 
 Fig. 126. 
 
 11O. Absolute Zero. The zeros on the thermometric 
 scales which we have hitherto considered are provisional, 
 arbitrary. Absolute zero is the temperature corresponding 
 to total absence of heat. At the absolute zero the mole- 
 cules must be supposed to be at rest. At this temperature 
 gases (if they may be called such) exert no pressure, and 
 occupy no space save that which their molecules take up 
 when closely packed together. The point of absolute zero 
 is a point beyond which no cooling is conceivable. It is 
 independent of the conventions of man. 
 
136 MOLECULAR ENERGY. HEAT. 
 
 Now it has been found that the pressure in air increases 
 or diminishes by .00367 = (about) ^^ of its pressure at 
 for each centigrade degree of rise or fall of temperature, 
 the volume being maintained constant. If air were a per- 
 fect gas, and could be cooled down in this way to 273 
 C. ( 459.4 F.), it would exert no pressure. The reason 
 it would exert no pressure is that its particles possess no 
 kinetic energy, no motion. This is assumed, therefore, to 
 be the absolute zero of temperature. 
 
 111. Absolute Temperature. Absolute temperature 
 is that reckoned from the absolute zero, or 273 C. 
 Temperatures measured from absolute zero are proportional 
 to the pressure of a theoretically perfect gas of constant 
 volume or density. 
 
 The absolute temperature (based on the above theory) 
 of any body is found by adding 273 to its temperature as 
 indicated by a centigrade thermometer,, or 459.4 to its 
 temperature as indicated by a Fahrenheit thermometer. 
 
 EXERCISES. 
 
 1. Express the following temperatures of the centigrade scale in the 
 Fahrenheit scale: 100; 40; 56; 60; 0; -20; -40; 80; 150. 
 
 NOTE. In adding or subtracting 32, it should be done algebraically. 
 Thus to change 14 C. to its equivalent on the Fahrenheit scale : f X 
 ( 14) = 25.2; 25.2 + 32 = 6.8, the required temperature on the 
 Fahrenheit scale. Again, to find the equivalent of 24 F. in the centi- 
 grade scale :24 32= 8; 8X f = 4f ; hence, 24 F. is equivalent 
 to - 4.4 + C. 
 
 2. Express the following temperatures of the Fahrenheit scale in 
 the centigrade scale : 212; 32; 90; 77; 20; 10; - 10; - 20; 
 -40; 40; 59; 329. 
 
 3. Mercury freezes at 39 C. and boils at 350 C.; find, in both 
 centigrade and Fahrenheit degrees, the absolute temperatures at 
 which mercury freezes and boils. 
 
LIQUEFACTION AND VAPORIZATION. 137 
 
 Section V. 
 
 EFFECTS OF HEAT CONTINUED. LIQUEFACTION AND 
 VAPORIZATION. 
 
 112. Liquefaction. As previously stated (page 9), 
 whether a body exist in a solid, liquid, or gaseous state 
 depends upon its temperature and the pressure which it is 
 under. 
 
 Experiment 96. Take a lump of ice as large as your two fists, 
 put it into boiling water ; when reduced to about \ its original size 
 skim it out. Wipe the lump, and place one hand on it and the other 
 on a lump to which heat has not been applied. Do you perceive any 
 difference in their temperatures? Ice reduces the temperature of 
 victuals in our refrigerators ; do the victuals raise the temperature of 
 the ice? How does the heat which the victuals impart to the ice 
 affect it? 
 
 Experiments and experience teach that (1) the melting 
 or solidifying point (they are always the same for the same 
 substance) may vary widely for different substances, but 
 for the same substance it is invariable when under the same 
 pressure. 
 
 (2) The temperature of a solid or liquid remains con- 
 stant at the melting-point from the moment that melting or 
 solidification begins. 
 
 113. Vaporization. 
 
 Experiment 97. Place a test-tube (Fig. 127), 
 half filled with ether, in a beaker containing water at 
 a temperature of 60 C. Although the temperature of 
 the water is 40 below its boiling-point, it very quickly 
 raises the temperature of the ether sufficiently to cause 
 Fig. 137. it to boil violently. Introduce a chemical thermometer 1 
 into the test-tube, and ascertain the boiling-point of ether. 
 
 1 A chemical thermometer has its scale on tho glass stem, instead of a plate, and is 
 otherwise adapted to experimental use. 
 
138 
 
 MOLECULAR ENERGY. HEAT. 
 
 Experiment 98. Take two beakers half full of water. Kaise 
 both to the boiling-point. Dissolve pulverized saltpetre in one as 
 long as it readily dissolves. Suspend in both liquids chemical ther- 
 mometers, so that the bulb of each shall be within one inch of the 
 bottom. Does the boiling water, as you continue to apply heat, get 
 hotter? Is the boiling solution any hotter than the boiling water? 
 Does the solution get hotter as it becomes concentrated by loss of 
 water by vaporization ? 
 
 After a liquid begins to boil, the temperature remains con- 
 stant until the whole is vaporized, if the density of the liquid 
 and the pressure remain constant. 
 
 Experiment 99. Place a beaker, half full of water at 80 C., 
 under the receiver of an air-pump, and exhaust the air. The water, 
 though far below its usual boiling-point, boils violently. Readmit the 
 air, and test the temperature of the water which has just been boiling. 
 
 Fig. 138. Fig. 129. 
 
 Experiment 100. Half fill a thin glass flask with water. Boil 
 the water over a Bunsen burner; the steam will drive the air from 
 the flask. Withdraw the burner, quickly cork the flask very tightly, 
 invert the flask, and pour cold water upon the part containing steam, 
 as in Figure 128 ; the water in the flask, though cooled several degrees 
 
LIQUEFACTION AND VAPORIZATION. 139 
 
 below the usual boiling-point, boils again violently. The application 
 of cold water to the flask condenses some of the steam, and diminishes 
 the tension of the rest, so that the pressure upon the water is dimin- 
 ished, and the water boils at a reduced temperature. 
 
 If hot water is poured upon the flask, the water ceases to boil. 
 Why? 
 
 Experiment 101. Provide a tumbler of cold water, a test-tube 
 nearly filled with water, tightly stoppered, and having glass tubes ex- 
 tending through the stopper, as represented in Figure 129. Place the 
 exposed end of the bent tube in the tumbler of water, and apply heat to 
 the bottom of the test-tube, and boil the water for about five minutes. 
 Then remove the heat, leave the end of the tube in the tumbler of 
 water, and allow the water of the test-tube to cool for some time ; or, 
 
 better, to hasten the 
 
 d\\\ cooling, place the test- 
 
 tube in another tum- 
 bler of cold water. Ob- 
 serve carefully, and 
 explain all phenomena 
 which occur from the 
 beginning to the end 
 of the operation. 
 
 114. Distillation. 
 
 Experiment 102. 
 Vessel A (Fig. 130) 
 (called a condenser) 
 contains a coil (called 
 a worm) of copper 
 Fig ' 130> tube, terminating at 
 
 one extremity at a. The other end of the tube, b, projects through 
 the side of the vessel near its bottom. Near the top of the vessel 
 projects another tube, c (called the overflow), with which is con- 
 nected a rubber tube, e. This tube conveys the warm water which 
 rises from the surface of the heated worm away to a sink or other 
 convenient receptacle. 
 
 Take a glass flask of a quart capacity, fill it three-fourths full of pond 
 or bog water. Connect the flask by means of a glass delivery-tube with 
 the extremity a of the worm. Heat the water in the flask ; as soon as 
 
140 MOLECULAR ENERGY. HEAT. 
 
 it begins to boil, commence siphoning cold water through a small tube, 
 d, from an elevated vessel E into the condenser. Inasmuch as the worm 
 is constantly surrounded with cold water, the steam on passing through 
 it becomes condensed into a liquid, and the liquid (called the distillate} 
 trickles from the extremity b into a receiving vessel. The distillate 
 is clear, but the water in the flask acquires a yellowish brown tinge 
 as the boiling progresses, due to the concentration of impurities 
 (largely of vegetable matter) which are held in suspension and solu- 
 tion in ordinary pond water. The apparatus used is called a still, and 
 the operation distillation. 
 
 When a volatile liquid is to be separated from water, for example, 
 when alcohol is separated from the vinous mash after fermentation (see 
 Chemistry, page 184), the mixed liquid is heated to its boiling-point, which 
 is lower than that of water. Much more of the volatile liquid will be con- 
 verted into vapor than of the water, because its boiling point is lower. 
 Thus a partial separation is effected. By repeated distillations of the 
 distillate, a 95 per cent alcohol is obtained. 
 
 115. Evaporation. In boiling, the heat, applied at 
 the bottom, rapidly converts the liquid into vapor, which, 
 rising in bubbles and breaking at or near the surface, pro- 
 duces a violent agitation in the liquid, called boiling or 
 ebullition. Boiling takes place only at a definite tempera- 
 ture, which depends on the kind of liquid and the pressure 
 that is on it. Evaporation is that form of vaporization 
 which takes place quietly and slowly at the surface. Al- 
 though hastened by heat, the evaporation of water occurs 
 at any temperature, however low; even ice and snow 
 evaporate. 
 
 The rapidity of evaporation increases with the tempera- 
 ture, amount of surface exposed, dryness of the atmosphere, 
 and diminution of pressure. This vapor of water mixes 
 freely with the air, and diffuses rapidly through it, acting 
 like another gas. A given space, for example, a cubic 
 foot (it matters little whether there is air in the space or 
 whether it is a vacuum), can hold only a limited amount 
 
LIQUEFACTION AND VAPORIZATION. 141 
 
 of water vapor. This quantity depends on the tempera- 
 ture of the vapor. The capacity of a space for water 
 vapor increases rapidly with the temperature, being nearly 
 doubled by a rise of 10 C. When a space contains sucli 
 an amount of water vapor that it temperature cannot be 
 lowered without some of the water being precipitated in 
 the form of a liquid, the vapor is said to be saturated, 
 and the temperature at which this happens is called the 
 dew-point. 
 
 Experiment 103. Take a bright nickel-plated cup, such, for ex- 
 ample, as are used for lemonade-shakers ; pour into it a small quantity 
 of tepid water. Place in the water the bulb of a chemical thermome- 
 ter. Gradually reduce the temperature of the water by stirring into 
 it ice water until you discover a slight dimness of the luster of that 
 portion of the outside of the cup next the water. If the ice water 
 does not reduce the temperature sufficiently, add ice, keeping the mix- 
 ture briskly stirring. If the ice does not answer, pour out some of 
 the water and sprinkle salt on the ice, keeping the bulb of the ther- 
 mometer in the remaining water. Note the temperature of the water 
 at the instant that the first mist or dimness appears on the cup. 
 Wait until the dimness or mist disappears, and note the temperature 
 of the water when the last disappears. Take the mean of the two 
 temperatures for the dew-point. 
 
 The form in which the condensed vapor appears is, according to its 
 location, dew, fog, or cloud. 1 The atmosphere is said to be dry or humid, 
 not according to the quantity of water vapor which it at any time contains, 
 but according as it can contain much or little more than it has. The air 
 in summer months usually contains a large amount of water vapor, yet it 
 is usually very dry. The heat of a stove dries the air of a room without 
 destroying any of its water vapor. In such a room, the lips, tongue, 
 throat, and skin experience a disagreeable sensation of dryness, owing to 
 the rapid evaporation which takes place from their surfaces. This should 
 be taken as nature's admonition to keep water in the stove urns, and 
 tanks connected with furnaces. 
 
 1 A cloud is simply a fog in an elevated region of the atmosphere. It is composed of 
 minute spheres of water from 7^53 to TO \j C of an inch in diameter. 
 
142 MOLECULAR ENERGY. HEAT. 
 
 Section VI. 
 
 HEAT CONVERTIBLE INTO POTENTIAL ENERGY, AND VICE 
 
 VERSA. 
 
 116. Heat Units. It is frequently necessary to meas- 
 ure quantity of heat, and for this purpose a standard unit 
 of measurement is required. The heat unit generally 
 adopted is the amount of heat required to raise the tempera- 
 ture of one kilogram of water from 4 to 5 C. This unit is 
 called a calorie, or kilogram-centigrade. 
 
 Let it be required to find approximately the amount of 
 heat that disappears during the melting of one kilogram 
 of ice. 
 
 Experiment 104. Weigh out 200 of dry (dry it with a towel) 
 ice chips whose temperature in a room of ordinary temperature may 
 be safely assumed to be C. Weigh out 200& of boiling water, whose 
 temperature we assume to be 100 C. Pour the hot water upon the 
 ice, and stir until the ice is all melted. Test the temperature of the 
 resulting liquid. 
 
 Suppose its temperature is found to be 10 C. It is evident that 
 the temperature of the hot water in falling from 100 to 90 would 
 yield sufficient heat to raise an equal weight of water from to 10 
 C. Hence it is clear that the heat which the water at 90 yields in 
 falling from 90 to 10 - a fall of 80 in some manner disappears. 
 At this rate had you used l k of ice and l k of hot water, the amount of 
 heat lost would be 80 calories. Careful experiments, in which suit- 
 able allowances are made for loss or gain of heat by radiation and 
 conduction, have determined that 80 calories of heat are consumed in 
 melting 1 kilogram of ice. How near to this do the results of your ex- 
 periments approach ? 
 
 Next let it be required to find the amount of heat that disappears 
 during the conversion of 1 kilogram of water into steam. 
 
 Experiment 105. Take in a porcelain evaporating-dish 50 g of 
 
HEAT CONVERTIBLE INTO POTENTIAL ENERGY. 143 
 
 ice water at (say) 5 C. Place it over a flame, and, watch in hand, 
 note the time in seconds which elapses before it boils. Then note 
 the time which elapses before it is all converted into steam. Suppose 
 that it required 100 seconds to raise the water from 5 to its boiling- 
 point, which we assume is 100 a rise of 95 ; and that it requires 
 530 seconds to convert the water, after it commences to boil, into 
 steam. Then the latter operation consumes (530-^100=) about 5.3 
 times as much time as the former. But the heat applied to the water 
 while boiling does not raise its temperature (see Exp. 98, page 137) ; 
 then all the heat given to the water during the interval of time dis- 
 appears. Had you taken l k of water, it would have required 95 calo- 
 ries to raise the water from 5 to 100 C. Hence, in converting the 
 l k of water into steam, 95x5.3= (about) 503 calories disappear. 
 Accurate methods have determined that 537 calories disappear during 
 the conversion of l k of water into steam. 
 
 The heat which disappears in melting and boiling is 
 generally, but with our present knowledge of the subject, 
 rather objectionably, called latent (hidden) heat. The 
 error consists in calling that heat which has ceased to be 
 heat. The heat, i.e. kinetic energy, that disappears in 
 melting is consumed in doing interior (i.e. molecular) work. 
 The molecules that in the solid are held firmly in their 
 places by molecular forces, are moved from their places 
 during melting, and so work is done against these forces, 
 much as work is done against gravity when a stone is 
 raised. In both cases kinetic energy is consumed disap- 
 pears ; but this means simply that it is transformed into 
 potential energy. The so-called latent heat is simply a 
 misnomer for molecular potential energy. 
 
 When water is converted into steam, the larger portion of the heat, 
 which is rendered latent, is consumed in separating the molecules so far 
 that molecular attraction is no longer sensible ; a small portion about 
 x 1 ^ is consumed in overcoming atmospheric pressure. The amount of 
 work done in melting and boiling especially the latter is very great, 
 as shown by the amount of heat consumed. Hence it requires a long time 
 to acquire the requisite amount of heat. This is a protection against 
 
144 MOLECULAR ENERGY. HEAT. 
 
 sudden changes. For example, if snow and ice melted immediately on 
 reaching the melting-point, all the snow and ice would melt in a single 
 warm day in winter, creating most destructive freshets. 
 
 117. Potential Energy converted into Heat by the 
 Solidification of Liquids and the Liquefaction of 
 Vapors. If our theory be true that heat is converted 
 into potential energy during vaporization and melting, 
 then ought the energy to be restored to the kinetic state 
 (i.e. the heat which disappears during these operations 
 ought to be restored) when the molecules return to their 
 original positions, i.e. when vapor becomes liquid, or when 
 liquids solidify. 
 
 Experiment 106. Take in a beaker C (Fig. 131) l k of water at 
 (say) 12 C. Take about 
 500s of water in a flask A, 
 and raise it to the boiling- 
 point. As soon as it be- 
 gins to boil, connect the 
 flask with the beaker by 
 a delivery-tube B, carry- 
 ing the end of the tube 
 nearly to the bottom of the 
 beaker. When about one- 
 fifth of the water has boiled 
 away, remove the delivery 
 tube from C, and immedi- Flg * 131 " 
 
 ately test the temperature of the water in the beaker, and weigh it. 
 Assume that the temperature of the steam is 100 C., and we will 
 suppose, for illustration, that there are 1,100= of water now in the 
 beaker; then 100s of water have been converted into steam which 
 has passed into the beaker and been condensed or liquefied by the 
 cold water. Suppose, again, that the temperature of the water 
 in the beaker was raised thereby to 70 C. Now 100* of water at 
 100 C. (resulting from the condensation of the steam) in falling to 
 70 C. could yield (30-4-10=) only 3 calories; hence it could raise the 
 l k of water only 3; i.e. from 12 to 15 C. Then it is evident that 
 it must have acquired the balance of (70 15=) 55 calories, by the 
 
HEAT CONVERTIBLE INTO POTENTIAL ENERGY. 145 
 
 restoration of the latent heat to real heat when the steam is liquefied. 
 If the liquefaction of 100s of steam yields 55 calories, then the lique^ 
 faction of l k of steam would yield 550 calories. Accurate methods 
 give 537 calories. 
 
 Various phenomena show that heat is developed during the solidifica- 
 tion of liquids, but as the development is slow, and the loss by radiation 
 rapid, it is difficult to make measurements. There are good reasons for 
 assuming, however, that there are 80 calories of heat generated for every 
 kilogram of water that is frozen. Farmers sometimes turn to practical 
 use this well-known phenomenon. Anticipating a cold night, they carry 
 tubs of water into cellars to be frozen. The heat generated thereby, 
 although of a low temperature, is sufficient to protect vegetables which 
 freeze at a lower temperature than water. 
 
 Steam is a most convenient vehicle for the conveyance of latent heat. 
 For example, every kilogram of steam that is condensed in the radiator 
 box (Fig. 120, p. 128) contributes to the air which passes through the box 
 537 calories, or heat sufficient to raise 5.37 k of ice water to the boiling- 
 point. 
 
 118. Methods of Producing Artificial Cold. The 
 
 fact that heat must be consumed because work is done, in 
 the conversion of solids into liquids and liquids into 
 vapors, is turned to practical use in many ways for the 
 purpose of producing artificial cold. The following ex- 
 periments will illustrate. 
 
 119. Cold by Dissolving. Freezing Mixtures. 
 
 Experiment 107. Prepare a mixture of 2 parts, by weight, of 
 pulverized ammonium nitrate and 1 part of ammonium chloride. 
 Take about 75 CC of water (not warmer than 8 C.), and into it pour 
 a large quantity of the mixture, stirring the same, while dissolving, 
 with a test-tube containing a little cold water. The water in the 
 test-tube will be quickly frozen. A finger placed in the solution will 
 feel a painful sensation of cold, and a thermometer will indicate a 
 temperature. of about 10 C. 
 
 One of the most common freezing mixtures consists of 
 3 parts of snow or broken ice and 1 part of common salt. 
 The affinity of salt for water causes a liquefaction of the 
 
146 MOLECULAR ENERGY. HEAT. 
 
 ice, and the resulting liquid dissolves the salt, both opera- 
 tions requiring heat. 
 
 12O. Cold by Evaporation. 
 
 Experiment 108. Fill the palm of the hand with ether; the 
 ether quickly evaporates, and produces a painful sensation of cold. 
 
 Experiment 109. Place water at about 30 C. in a thin porous 
 cup, such as is used in the Grove's battery, and the same amount of 
 water, at the same temperature, in a glass beaker of as nearly as pos- 
 sible the same size as the porous cup. Introduce into each a chemi- 
 cal thermometer. The comparatively large amount of surface exposed 
 by means of the porous vessel will so hasten the evaporation in this 
 vessel, that, in the course of 10 to 15 
 minutes, quite a sensible difference of 
 temperature will be indicated by the 
 thermometers in the two vessels. 
 
 Experiment 110. Cover closely the 
 bulb of an air thermometer (Fig. 132) 
 with thin muslin, and partly fill the stem 
 with water. Let one person slowly drop 
 ether on the bulb, while another briskly 
 blows the air charged with vapor away 
 from the bulb with a bellows ; or, place 
 the bulb in a window whose sash is raised 
 a little way, so as to be in a draft. As 
 
 the air changes rapidly, it does not become saturated with vapor so 
 as to impede evaporation, and in 10 to 15 minutes the water in the 
 stern freezes, even in a warm room. 
 
 The evaporation of perspiration conduces to our health and comfort by 
 relieving us of surplus heat. We cool the fevered forehead by bathing it 
 with a volatile liquid, such as a solution of alcohol in water. Windy days 
 seem colder to us than still days, although the temperature of both is the 
 same, because evaporation of perspiration takes place more rapidly in a 
 changing air. Fanning in a similar way changes the air next our persons, 
 thereby quickening the evaporation of the perspiration, and cooling the 
 surface of the body. Ice is now manufactured in large quantities during 
 the summer season in warm climates by the evaporation of liquid ammo- 
 nia. Evaporation is the most efficient means of producing extremely 
 low temperatures. 
 
HEAT CONVERTIBLE INTO POTENTIAL ENERGY. 147 
 
 QUESTIONS. 
 
 1. How can water be made to boil at a low temperature ? 
 
 2. Upon what does the tension of steam depend ? 
 2. Why can you not make ice warm ? 
 
 4. Does ice always have the same temperature ; i.e. can it be made 
 colder than 32 F. ? 
 
 5. What is the lowest temperature any body can have ? 
 
 6. (a) Where does the " sweat " on ice-pitchers come from ? (6) Where 
 does dew on grass come from ? (c) How are clouds formed ? 
 
 7. (a) When the sweat on ice-pitchers is very abundant, what 
 does it indicate about dew-point ? (b) Does it forebode fair or rainy 
 weather ? 
 
 8. How will you easily show that ether boils at a lower tempera- 
 ture than water? 
 
 9. In which will vegetables cook quicker, in fresh or salt water ? 
 
 10. How could you separate the alcohol of rum or brandy from 
 the watery part ? 
 
 11. (a). On what kind of days do clothes dry fastest? (6) W T ill 
 frozen clothes dry? 
 
 12. (a) How does heat dry the air ? (b) How does heat dry clothes ? 
 
 13. Suppose that 10 k of steam, at 100 C., is condensed in the 
 steam-pipe in the radiator box, Figure 120, per hour ; how much heat 
 will it furnish to the surrounding air ? 
 
 14. How much heat will be produced by freezing one cubic foot 
 (about 29 k or 02.5 pounds) of water? 
 
 15. (a) When the barometric column stands at 760 mm , what 
 quantity of heat must be applied to 5 k of icer at 0C to convert it 
 into steam in an open vessel ? (7>) What will be the temperature of 
 the steam at the instant of generation ? (c) How much of the heat 
 applied is rendered latent during the conversion from ice to steam ? 
 
 16. Is there any reason why the boiling point of water in an open 
 vessel should be different on the top of a mountain from what it is 
 at its base ? 
 
 17. Why does ice melt slowly even in warm places? 
 
 18. 10 k of water at 100C will melt how much ice at 0? 
 
 19. The freezing of the water of lakes and other bodies of water 
 tends to produce what change in the temperature of the air ? 
 
 20. Why does not all the water in a tea-kettle flash into steam at 
 the instant it reaches its boiling point ? 
 
148 MOLECULAR ENERGY. HEAT. 
 
 Section VII. 
 
 HEAT CAPACITY. 
 
 121. Heat Capacity, Specific Heat. The expression 
 heat capacity applied to a body refers to the quantity of 
 heat necessary to raise the temperature of the body 1. 
 The expression specific heat l is applied only to some par- 
 ticular substance and refers to the quantity of heat required 
 to raise one kilogram of that substance from 4 to 5 C. 
 It is apparent that the specific heat of a substance is the heat 
 capacity of 1 unit of mass of that substance. 
 
 Experiment 111. Mix l k of water at with l k at 20; the 
 temperature of the mixture becomes 10. The heat that leaves l k of 
 water when it falls from 20 to 10 is just capable of raising l k of 
 water from to 10. 
 
 Experiment 112. Take (say) 300 g of sheet lead, make a loose 
 roll of it, and suspend it by a thread in boiling water for about five 
 minutes, that it may acquire the same temperature (100 C.) as the 
 water. Remove the roll from the hot water, and immerse it as 
 quickly as possible in 300 g of water at 0, and introduce the bulb of 
 a thermometer Note the temperature of the water when it ceases 
 to rise, which will be found to be about 3 (accurately 3.3 +). The 
 lead cools very much more than the water warms. The temperature 
 of lead falls about 33 for every degree an equal mass of water is 
 warmed. 
 
 From Experiment 111 we infer that a body in cooling a 
 certain number of degrees gives to surrounding bodies as 
 much heat as it takes to raise its temperature the same 
 
 1 The specific heat of a substance is often defined as the ratio of the heat capacity 
 of a body of that substance to the heat capacity of an equal mass of water. 
 
HEAT CAPACITY. 149 
 
 number of degrees. From Experiment 112 we learn that 
 the quantity of heat that raises l k of lead from 3.3 -)- to 
 100, when transferred to water, can raise l k of water only 
 from to 3.3. Hence we conclude that equal quantities 
 of heat, applied to equal masses of different substances, raise 
 their temperatures unequally. 
 
 If equal masses of mercury, alcohol, and water receive equal quantities 
 of heat, the mercury will rise 30, and the alcohol nearly 2, for every 
 degree the water rises. From this we infer that to raise equal masses of 
 each of these substances 1 requires 30 times as much heat for the water 
 as for the mercury, and twice as much as for the alcohol. Since a given 
 quantity of heat affects the temperature of a given mass of water less 
 than that of an equal mass of mercury or alcohol, water is said to have 
 greater specific heat than these substances. It is also apparent that a 
 given mass of water in cooling imparts to surrounding bodies more heat 
 than the same masses of mercury and alcohol would impart in cooling the 
 same number of degrees, in proportion to its greater specific heat. 
 
 " The vast influence which the ocean must exert as a moderator of cli- 
 mate here suggests itself. The heat of summer is stored up in the ocean, 
 and slowly given out during the winter. This is one cause of the absence 
 of extremes in an island climate." 
 
 j The high specific heat of water is utilized in heating buildings by hot 
 water. 
 
 122. Method of Measuring Specific Heat. A known mass 
 m (in kilograms) of the substance of which the specific heat is required 
 is taken, as in Experiment 112, and heated to a known temperature ti 
 (C.); then it is mixed with (or immersed in) a known mass of water w 2 at 
 a lower temperature t%, and as soon as thermal equilibrium is established 
 throughout, the temperature of the mixture t is taken. Let s represent the 
 specific heat of the substance sought. Then the quantity of heat lost by the 
 substance is m X 3 (ti t) calories ; while that gained by the water is m z 
 (t 2 ) calories. Now if no heat be lost during the operation, m X s 
 
 fa t) mz(t t 2 ) whence s =^-77 r'. For example, taking the 
 
 in \i>\ f ) 
 
 quantities obtained in Experiment 112, we find for lead (300 g==c=.3 k ) 
 
150 MOLECULAR ENERGY. HEAT. 
 
 Section VIII. 
 
 THERMO-DYNAMICS. 
 
 123. Therm o-dynamics Defined. Thermo-dynamics is 
 that branch of science that treats of the relation between heat 
 and mechanical work. One of the most important discov- 
 eries in science is that of the equivalence of heat and work; 
 that is, that a definite quantity of mechanical work, when 
 transformed "without waste, will yield a definite quantity of 
 heat; and conversely, this heat, if there were no waste, could 
 perform the original quantity of mechanical work. 
 
 124. Transformation, Correlation, and Conservation 
 of Energy. The proof of the facts just stated was one of 
 the most important steps in the establishment of the grand 
 twin conceptions of modern science : (1) That all kinds of 
 energy are so related to one another that energy of any kind 
 can be transformed into energy of any other kind, known 
 as the doctrine of CORRELATION OF ENERGY; (2) That 
 when one form of energy disappears, an exact equivalent of 
 another form always takes its place, so that the sum total of 
 energy is unchanged, known as the doctrine of CONSER- 
 VATION OF ENERGY. These two principles constitute the 
 corner-stone of physical science. Chemistry teaches that 
 there is a conservation of matter. 
 
 125. Joule's Experiment. The experiment to ascer- 
 tain the "mechanical value of heat," as performed by Dr. 
 Joule of England, was conducted about as follows. He 
 caused a paddle-wheel to revolve in water, by means of a 
 tailing weight attached to a cord wound around the axle 
 
THERMO-DYNAMICS. 151 
 
 of a wheel. The resistance offered by the water to the 
 motion of the paddles was the means by which the mechan- 
 ical energy of the weight was converted into heat, which 
 raised the temperature of the water. Taking a body of a 
 known weight, e.g. 80 k , he raised it a measured distance, 
 e.g. 53 m high; by so doing 4,240 kgm of work were performed 
 upon it, and consequently an equivalent amount of energy 
 was stored up in it ready to be converted, first into me- 
 chanical motion, then into heat. He took a definite 
 weight of water to be agitated, e.g. 2 k , at a temperature of 
 C. After the descent of the weight, the water was 
 found to have a temperature of 5 C. ; consequently the 
 2 k of water must have received 10 units of heat (careful 
 allowance being made for all losses of heat), which is the 
 amount of heat-energy that is equivalent to 4,240 kgm of 
 work, or one unit of heat is equivalent to 424*^ m of work. 
 
 126. Mechanical Equivalent of Heat. As a con- 
 verse of the above it may be demonstrated by actual ex- 
 periment that the quantity of heat required to raise l k of 
 water from 4 to 5 C. will, if converted into work, raise a 
 424 k weight l m high, or l k weight 424 m high. According 
 to the English system, the same fact is stated as follows : 
 The quantity of heat that will raise 1 pound of water 1 F. 
 will raise 772.55 pounds 1 foot high. The quantity, 424 kgm , 
 is called the mechanical equivalent of one calorie, or Joule's 
 equivalent (abbreviated simply J.). Or, we may say that 
 one calorie is the thermal equivalent of 424 kgm of work. 
 
152 MOLECULAR ENERGY. HEAT. 
 
 Section IX. 
 
 STEAM-ENGINE. 
 
 127. Description of a Steam-Engine. A steam-en- 
 gine is a machine in which the elastic force of steam is the 
 motive power. Inasmuch as the elastic force of steam is 
 entirely due to heat, the steam-engine is properly a heat en- 
 gine ; that is, it is a machine by means of which heat is 
 continuously transformed into work or mechanical motion. 
 
 The modern steam-engine consists essentially of an ar- 
 rangement by which steam from a boiler is conducted to 
 both sides of a piston alternately ; and then, having done 
 its work in driving the piston to and fro, is discharged 
 from both sides alternately, either into the air or into a 
 condenser. The diagram in Figure 133 will serve to illus- 
 trate the general features and the operation of a steam-en- 
 gine. The details of the various mechanical contrivances 
 are purposely omitted, so as to present the engine as nearly 
 as possible in its simplicity. 
 
 In the diagram, B represents the boiler, F the furnace, 
 S the steam-pipe through which steam passes from the 
 boiler to a small chamber VC, called the valve-chest. In 
 this chamber is a slide-valve V, which, as it is moved to 
 and fro, opens and closes alternately the passages M and 
 N leading from the valve-chest to the cylinder C, and thus 
 admits the steam alternately each side of the piston P. 
 When one of these passages is open, the other is always 
 closed. Though the passage between the valve-chest and 
 the space in the cylinder on one side of the piston is 
 closed, thereby preventing the entrance of steam into this 
 space, the passage leading from the same space is open 
 
STEAM-ENGINE. 
 
 153 
 
 through the interior of the valve, so that steam can escape 
 from this space through the exhaust-pipe E. Thus, in the 
 position of the valve represented in the diagram, the pas- 
 sage N is open, and steam entering the cylinder at the top 
 drives the piston in the direction indicated by the arrow. 
 At the same time the steam on the other side of the piston 
 escapes through the passage M and the exhaust-pipe E. 
 While the piston moves to the left, the valve moves to the 
 
 Fig. 133. 
 
 right, and eventually closes the passage N leading from 
 the valve-chest, opens the passage M into the same, and 
 thus the order of things is reversed. 
 
 Motion is communicated by the piston through the 
 piston-rod R to the crank G, and by this means the shaft 
 A is rotated. Connected with the shaft by means of the 
 
154 MOLECULAR ENERGY. HEAT. 
 
 crank H is a rod R' which connects with the valve V, so 
 that, as the shaft rotates, the valve is made to slide to and 
 fro, and always in the opposite direction to that of the 
 motion of the piston. 
 
 The shaft carries a fly-wheel W. This is a large, heavy 
 wheel, having the larger portion of its weight located near 
 its circumference; it serves as a reservoir of energy which 
 is needed to make the rotation of the shaft and all other 
 machinery connected with it uniform, so that sudden 
 changes of velocity resulting from sudden changes of the 
 driving power or resistances are avoided. By means of a 
 belt passing over the wheel W motion may be communi- 
 cated from the shaft to any machinery desirable. 
 
 128. Condensing and Non-Condensing Engines. 1 
 Sometimes steam, after it has done its work in the cylin- 
 der, is conducted through the exhaust-pipe to a chamber 
 Q, called a condenser, where, by means of a spray of cold 
 water introduced through a pipe T, it is suddenly con- 
 densed. This water must be pumped out of the condenser 
 by a special pump, called technically the air-pump ; thus 
 a partial vacuum is maintained. Such an engine is called 
 a condensing engine. The advantage of such an engine is 
 obvious, for if the exhaust-pipe, instead of opening into a 
 condenser, communicates with the outside air, as in the 
 non-condensing engine, the steam is obliged to move the 
 piston constantly against a resistance arising from atmos- 
 pheric pressure of 15 pounds for every square inch of the 
 surface of the piston. But in the condensing engine no 
 resistance arises from atmospheric pressure, and so with a 
 given steam pressure in the boiler the effective pressure 
 on the piston is considerably increased ; hence, condensing 
 engines are usually more economical in their working. 
 
 1 The terms, low-pressure and high-pressure engines, are not distinctive as applied to 
 engines of the present day. 
 
STEAM-ENGINE. 
 
 155 
 
 129. Compound Condensing Engine. This engine has two 
 cylinders, each like that of a simple engine. One, A (Fig. 134), called 
 the high-pressure cylinder, receives steam of very high pressure directly 
 from the boiler through the orifice V. The steam, after it has done work in 
 this cylinder, passes through the steam-port E into cylinder B, called the 
 low-pressure cylinder. Cylinder B is larger than cylinder A. The steam 
 which enters cylinder B possesses considerable pressure, and is therefore 
 capable of doing considerable work under suitable conditions. It should 
 be borne in mind that in order that steam may do work in any cylinder, it 
 is necessary that an inequality in the pressure of the steam each side of the 
 
 Fig. 134. 
 
 piston should be maintained ; just as an inequality of level, i.e. a head, is 
 essential to water-power. The steam, after it has done its work in cylin- 
 der B, passes through a port C into a condenser (not represented in the 
 figure), where it is suddenly condensed or let down to a very low pressure. 
 If a vertical glass tube were led from the condenser to a vessel of mercury 
 below, the mercury would ordinarily stand about 25 inches high in the 
 tube, which would show that the pressure of the steam against which the 
 steam when it enters cylinder B does work, is only about one-sixth of an 
 atmosphere. Much energy is economized by the compound engine. 
 
 13O. The Locomotive. The distinctive feature of the locomo- 
 tive engine is its great steam-generating capacity, considering its size 
 and weight, which are necessarily limited. To do the work ordinarily 
 required of it, from three to six tons of water must be converted into 
 
156 STEAM-ENGINE. 
 
 steam per hour. This is accomplished in two ways : viz., first, by a rapid 
 combustion of fuel (from a quarter of a ton to a ton of coal per hour) ; 
 second, by bringing the water in contact with a large extent (about 800 
 square feet) of heated surface. The fire in the "fire-box" A (Fig. 135, 
 Plate II.) is made to burn briskly by means of a powerful draft 
 which is created in the following manner : The exhaust steam, after it 
 has done its work in the cylinders B, is conducted by the exhaust-pipe C 
 to the smoke-box D, just beneath the smoke-stack E. The steam, as it 
 escapes from the blast-pipe F, pushes the air above it, and drags by fric- 
 tion the air around it, and thus produces a partial vacuum in the smoke- 
 box. The external pressure of the atmosphere then forces the air through 
 the furnace grate and hot-air tubes G, and thus causes a constant draft. 
 The large extent of heated surface is secured as follows : The water of 
 the boiler is brought not only in contact with the heated surface of the 
 fire-box, but it surrounds the pipes G (a boiler usually contains about 
 150). These pipes are kept hot by the heated gases and smoke, all of 
 which must pass through them to the smoke-box and smoke-stack. 
 
 The steam-engine, with all its merits and with all the 
 improvements which modern mechanical art has devised, 
 is an exceedingly wasteful machine. The best engine that 
 has been constructed utilizes only about twenty per cent of 
 the heat-power generated by the combustion of the fuel. 
 
 QUESTIONS. 
 
 1. What kind of engine (i.e. condensing or n on- condensing) is that 
 which produces loud puffs? What is the cause of the puffs? 
 
 2. Why does the temperature of steam suddenly fall as it moves 
 the piston ? 
 
 3. What do you understand by a ten horse-power steam-engine? 
 
 4. Upon what does the power of a steam-engine depend? 
 
 5. Is the compound engine a condensing or a non-condensing en- 
 gine ? Which is the locomotive engine ? 
 
 6. The area of a piston is 500 square inches, and the average unbal- 
 anced steam pressure is 30 pounds per square inch ; what is the total 
 effective pressure ? Suppose that the piston travels 30 inches at each 
 stroke, and makes 100 strokes per minute, allowing 40 per cent for 
 wasted energy, what power does the engine furnish, estimated in 
 horse-powers ? 
 
CHAPTER VI. 
 
 ELECTRO-STA TICS. 
 
 Section I. 
 
 INTRODUCTION. 
 
 131. Electrification. Certain bodies, when the con- 
 ditions are suitable, acquire by contact and subsequent 
 separation (or more readily by friction) the property of 
 attracting light bodies such as pieces of tissue paper, etc. 
 For example, glass rubbed with silk, and sealing-wax or 
 ebonite with woolen cloth, manifest this property by 
 picking up scraps of paper, etc. Bodies in this state are 
 said to be electrified or charged with electricity. 
 
 Experiment 113. Rub a rubber comb with a woolen cloth or 
 draw it a few times through your hair (if dry). Hold the comb 
 over a handful of bits of tissue paper ; the papers quickly jump to 
 the comb, stick to it for an instant, and then leap energetically from 
 it. The papers are first attracted to the comb, but in a short time 
 acquire some of its electrification, and then are repelled. 
 
 132. Two Kinds of Electrification. 
 
 Experiment 114. Suspend a ball of elder pith, C (Fig. 136), by 
 a silk thread. Electrify a glass rod D with a silk handkerchief and 
 present it to the ball; attraction at first occurs, followed by repulsion 
 soon after contact. Next excite a stick of sealing-wax or a rubber 
 comb with a woolen cloth and present it to the ball which is 
 
158 
 
 ELECTRO-STATICS. 
 
 repelled by the electrified glass ; the ball is attracted by the electrified 
 wax or rubber. 
 
 It is evident (1) 
 
 Fig. 136. 
 
 that there are two kinds or condi- 
 tions of electrification ; (2) 
 that bodies similarly elec- 
 trified repel one another, 
 bodies oppositely electri- 
 fied attract one another. 
 
 Glass rubbed with silk 
 is said to receive a charge 
 of vitreous electrification ; 
 the wax, after being 
 rubbed with woolen 
 cloth, on the other hand, is charged with resinous 
 electrification. Vitreous charges are said to be positive 
 (written +E), and resinous negative (written E). 
 
 Experiment 115. Once more electrify a stick of sealing-wax 
 with a woolen cloth, and present it to the pith ball, and after the ball 
 is repelled, bring the surface of the flannel which had electrified the 
 rod near the ball; the ball is attracted by it, showing that the rubber 
 is also electrified, and with the opposite kind to that which the 
 sealing-wax possesses. 
 
 One kind of electrification is never developed alone ; 
 when two substances are rubbed together, and one becomes 
 electrified, electrification of the opposite kind is always 
 developed in the other. 
 
 133. Electrification a Form of Potential Energy. - 
 
 When small pieces of glass and silk are rubbed together, 
 it is found that after they are pulled apart they attract 
 each other with a definite and measurable force ; and that 
 this force varies inversely as the square of the distance 
 
INTRODUCTION. 
 
 159 
 
 between them. When two bodies are pulled apart, energy 
 is expended upon them which will be restored when they 
 are allowed to approach each other. It is certain that 
 electrification is the result of work done, and is a form of 
 potential energy. 
 
 134. What is Electricity ? The student naturally 
 has already begun to ask the never-answered question, 
 "What is electricity?" and to inquire, " What is the 
 function of electricity in these operations ? " Provision- 
 ally we shall regard electricity as that which is transferred 
 from one body to another body when the two become 
 oppositely electrified. Electricity is not a form of energy. 
 It is quite true that electricity under pressure or in motion 
 possesses energy ; in the same sense do water and air 
 under like conditions possess energy, but no one presumes 
 to call them forms of energy. 
 
 135. Electroscope. This is an instrument used to 
 detect the presence of electrification in a body, and to 
 determine its kind. It usu- 
 ally consists of two strips of 
 
 gold foil, A B (Fig. 137), 
 suspended from a brass rod 
 within a glass jar. To the 
 upper end of the rod is fixed 
 a metal disk, C. On the 
 opposite sides of the interior 
 of the jar are two strips of 
 metal foil, D and E, of suf- 
 ficient hight to be touched 
 by the strips A and B on 
 their extreme divergence. Fig. 137. 
 
160 ELECTRO-STATICS. 
 
 (1) If an unelectrified body be brought near the 
 disk C, no change takes place in the two strips of foil A 
 and B, but if an electrified body be brought near the disk, 
 the strips diverge, thus indicating the existence of a 
 charge of electricity in the body. 
 
 (2) If the electroscope be charged by contact with an 
 excited body, the strips will remain in a divergent posi- 
 tion. While they are in this condition, if a body similarly 
 charged be brought near the disk, the strips will diverge 
 more; but if an unexcited body or a body oppositely 
 electrified be brought near the disk, the strips will collapse. 
 
 136. Conduction. 
 
 Experiment 116. a. Rub a brass tube, held in the hand, with 
 warm silk. Bring it near the disk of the electroscope ; the leaves 
 are unaffected, b. Wrap a piece of sheet rubber around one end of 
 the tube and hold this end in the hand, and rub as before. Bring it 
 near the disk of the electroscope ; notice that the leaves diverge. 
 c. Repeat the last operation ; but before bringing the tube near the 
 disk touch the tube with a finger. The leaves no longer show signs 
 of electrification. 
 
 In the first (a) and last (c) operations electricity escaped 
 through the hand and body to the earth ; in the second (b) 
 it was prevented from escaping by the intervening sheet 
 rubber. Substances which allow electricity to spread over 
 them, i.e. substances which offer little resistance to the 
 flow of electricity, are called conductors. Those which 
 offer great resistance to its passage are called non-con- 
 ductors, insulators, or dielectrics. 
 
 Some of the best insulating substances are dry air, 
 ebonite, shellac, resins, glass, silks, and furs. On the other 
 hand, metals are exceedingly good conductors. Moisture 
 
INDUCTION. 161 
 
 injures the insulation of bodies ; hence experiments suc- 
 ceed best on dry, cold days of winter, when moisture of 
 the air is least liable to be condensed on the surfaces of 
 apparatus, especially if the latter be kept warm. 
 
 Water cannot be retained in a reservoir unless its walls 
 be of sufficient strength ; so a body, in order to become 
 charged and to retain the charge, must be surrounded by 
 something that will offer sufficient resistance to the escape 
 of electricity. There is no limit to the quantity of electri- 
 city with which a body can be charged, provided the 
 charge can be retained. This entity which represents the 
 walls of the reservoir is termed the dielectric. It may be 
 the air or any of the so-called non-conductors of electricity. 
 A body thus surrounded is said to be insulated. 
 
 Section II. 
 
 INDUCTION. 
 
 137. Electricity acts across a Dielectric. 
 
 Experiment 117. Figure 138 represents an empty egg-shell cov- 
 ered with tin foil to make it a good conductor. It is suspended from 
 a glass rod by a silk thread, a. Electrify a glass rod and bring 
 it near the shell. The shell moves toward the rod. b. Next 
 introduce a glass plate between the rod and shell. The shell ap- 
 proaches the rod as before. 
 
 The chief lesson we learn from this experiment is that 
 electricity acts across a dielectric. In a the dielectric was 
 air ; in 6, air and glass. 
 
162 
 
 ELECTRO-STATICS. 
 
 138. To determine what actually happens on an 
 Insulated Conductor when an Electrified Body is 
 brought near. 
 
 Experiment 118. a. Suspend, as above, two shells so as to 
 
 touch each other, end to end, as 
 in Figure 139, thus making prac- 
 tically one conductor. Bring 
 near to one end of the shells a 
 sealing-wax rod, D, excited with 
 E. While the rod is in this 
 position carry a thin strip of tis- 
 sue paper, C, along the shells. 
 The- paper is attracted to the 
 shells, but most strongly at the 
 ends. In the middle of the con- 
 ductor, where the shells touch 
 each other, there is little if any 
 electrification. 
 
 b. While the rod D is still in 
 position, separate B from A, 
 then remove D. Test each shell 
 with the tissue paper ; both are found to be excited. 
 
 c. Charge an electroscope with + E. Then bring A near it ; the 
 leaves diverge, showing that A is charged with +E. Bring B near 
 the electroscope ; the leaves collapse, showing that B is charged with 
 -E. 
 
 d. Finally bring the two shells near each other ; they attract each 
 other. Allow them to touch each other, and then test each with the 
 tissue paper or the electroscope ; it will be found that both have 
 become discharged. 
 
 From the above operations we learn that when an electri- 
 fied body is brought near but not in contact with an insu- 
 lated conductor, the electrified body acts across the dielec- 
 tric upon the conductor, repelling electricity of the same 
 
 Fig. 138. 
 
INDUCTION. 
 
 163 
 
 kind to the remote side of the conductor, and attracting 
 the opposite kind to the side near to it. Such electrical 
 action is called induction. The electrified body which 
 
 Fig. 139. 
 
 produces the action is called the inducing body ; the 
 charge of electricity thus produced is called induced 
 electricity. 
 
 139. Charging 1 by Induction. 
 
 Experiment 119. Take a proof plane E (Fig. 140) (which 
 consists of an insulating handle of glass or gutta-percha, terminating 
 at one end with a thin metal disk, F, about the size of a 5-cent nickel), 
 and connect it with an electroscope, G, by a fine wire, H. Bring a 
 stick of sealing-wax electrified as before with E near the egg-shell 
 conductor. Holding the proof plane by the insulating handle, bring 
 the disk near the end of the conductor charged by induction with 
 E. The E will act inductively upon the continuous conductor 
 consisting of disk, wire, and electroscope, charging the end nearest 
 itself (i.e. the disk) with +E and the remote end (i.e. the leaves) 
 with E. The leaves of the electroscope show the presence of a 
 charge by their divergence. 
 
 Now while everything is in the position indicated by the cut, 
 touch with the finger any part of the continuous conductor ; the 
 
164 ELECTRO-STATICS. 
 
 leaves of the elec- 
 troscope instantly 
 collapse. The E 
 with which the 
 leaves had been 
 charged being/ree is 
 discharged through 
 your body. But the 
 + E concentrated 
 on the disk of the 
 Fig. 14O. proof plane is bound 
 
 by the attraction of 
 
 the charge of E on the end of the shell nearest it, and cannot escape. 
 
 Remove the finger from the electroscope and the proof plane from 
 
 the influence of the shell ; the leaves again diverge. 
 
 The last phenomenon is explained as follows : After 
 E had been discharged from the continuous conductor, 
 there was left an excess of -)- E ; but this excess was all 
 concentrated in the disk F so long as it remained near 
 the negative charge of the shell. But as soon as F was 
 removed from the influence of the shell, the charge spread 
 itself over the entire conductor, and the leaves, which 
 received a portion of the charge, diverged. The conductor 
 is said to be charged by induction. 
 
 Experiment 120. To electrify the shell by induction, bring the 
 excited wax near it, touch the shell with a finger, remove the finger, 
 and finally remove the rod. The proof plane being connected with 
 the electroscope and being charged with E, bring F near to the 
 shell A ; the leaves collapse, showing that the shell is charged with 
 + E, which draws the E away from the leaves. 
 
 Observe that when a body becomes charged by induc- 
 tion the charge which it receives is opposite in kind to that 
 of the inducing body. 
 
ELECTEICAL POTENTIAL. 
 
 165 
 
 140. Charging- by Conduction. 
 
 Experiment 121. Disconnect the proof plane from the electro- 
 scope. Charge the electroscope with E and the shell with +E ; 
 touch the shell with the disk of the proof plane, then hold the disk 
 near the electroscope ; the divergent leaves collapse, showing that 
 the disk bears +E which it received by conduction from the shell 
 when they were brought in contact. Of course the charge is the 
 same kind as that of the body which communicated it. 
 
 141. Induction precedes Attraction. When 
 ball is brought near an electrified glass rod, the 
 the rod A (Fig. 141) induces E on the 
 
 side of the ball B nearest A and repels 
 -j- E to the farther side. The -f- E of A and 
 the E of B therefore attract each other ; 
 likewise the + E of A and the + E of B 
 repel each other : but since the former 
 charges are nearer each other than the latter 
 are, the attraction exceeds the repulsion. 
 
 FIg - 141 
 
 Section III. 
 
 ELECTRICAL POTENTIAL. 
 
 142. Electro-statics and Electro-kinetics. Electric- 
 ity may be at rest, as in a charged body, or it may be in 
 motion, as in the case of a charged body connected by a 
 conductor with the earth, when it is discharged through 
 the conductor to the earth. It will be shown later on 
 that as long as a flow of electricity continues, the con- 
 ductor along which it flows has properties different from 
 
166 ELECTRO-STATICS. 
 
 those of a simple electrified body. That branch of electri- 
 cal science which treats of the properties of simple 
 electrified bodies is called Electro-statics, because in them 
 electricity is supposed to be at rest; and that branch 
 which treats of electricity in motion is called Electro- 
 kinetics. 
 
 143. Potential. The fundamental fact of electricity 
 is that we are able to place bodies in different electrical 
 conditions. A charge of electricity, which implies an 
 abnormal electrical condition, is the foundation of all 
 electrical phenomena. We are now to discuss the mean- 
 ing and use of the very important term potential, with 
 reference to electricity. 
 
 a. When a charged conductor is connected with the 
 earth, a transfer of electricity takes place between the 
 body and the earth. 
 
 b. If the body be charged with -{- E, we say arbitrarily 
 that electricity passes to the earth ; but if the body be 
 charged with E, electricity passes from the earth to 
 the body. 
 
 c. If two insulated charged conductors be connected 
 with each other, electricity may or may not pass from one 
 to the other. Now whether electricity passes from one to 
 the other, and in what direction it passes, if at all, depends 
 upon the so-called potentials of the conductors. 
 
 d. If two bodies have the same potential, no transfer of 
 electricity takes place between them when they are con- 
 nected by a conductor ; but if the two bodies have different 
 potentials, there will be a transfer, and the body from 
 which the electricity flows is said to be at a higher poten- 
 tial than the one to which it flows. 
 
ELECTRICAL POTENTIAL. 167 
 
 144. Definition of Potential. The potential of a 
 conductor may, therefore, be defined provisionally as the 
 electrical condition of that conductor which determines 
 the direction of the transfer of electricity. 
 
 The term potential is relative. It is important to have 
 a standard of reference whose potential is considered to 
 be zero, just as it is convenient in stating the elevations 
 or depressions of the earth's surface to give the distances 
 above or below sea-level, which is taken as the zero of 
 hight. For experimental purposes the earth is usually 
 assumed to be at zero potential. A body charged with 
 -J- E is understood to be one that has a higher potential 
 than that of the earth, and a body charged with E is 
 one that has a lower potential than that of the earth. 
 
 145. Analogies. Potential is analogous, in many 
 respects, to (1) temperature, and to (2) liquid level. 
 
 (1) When we say that the temperature of air is 20 or 
 10 C., we mean that its temperature is 20 above or 
 10 below the standard temperature of reference, viz. that 
 of melting ice. If two bodies at different temperatures 
 be placed in thermal communication, heat will pass from 
 the body at a higher temperature to the one at a lower, 
 and will continue to do so until both are at the same 
 temperature. 
 
 (2) If two vessels containing water at different levels 
 be put in communication at their bottoms by a pipe, water 
 will flow from the one at a higher level to the one at a 
 lower until the water is at the same level in both 
 vessels. 
 
 Temperature is not heat ; level is not water ; and 
 potential is not electricity, but merely the state of the 
 
168 ELECTRO-STATICS. 
 
 conductor which determines the direction of transfer of 
 electricity. 
 
 Section IV. 
 
 ATMOSPHERIC ELECTRICITY. 
 
 146. Lightning 1 . Franklin, by his historic series of 
 experiments, proved the exact similarity of lightning and 
 thunder to the light and crackling of the electric spark. 
 Certain clouds which have formed very rapidly are highly 
 charged, usually with +E, but sometimes with E. 
 The surface of the earth and objects thereon immediately 
 beneath the cloud are, of course, charged inductively 
 with the opposite kind of electricity. The opposite 
 charges on the earth and on the cloud hold each other 
 prisoners by their mutual attraction, the air serving as an 
 intervening dielectric. 
 
 As condensation progresses in the cloud its potential 
 rises (or sinks). This process continues till the difference 
 of potential between the cloud and the earth becomes 
 great enough to produce a discharge through the air. 
 
 It is the accumulation of induced charges on elevated 
 objects, such as buildings, trees, etc., that offers an 
 intensified attraction for the 'opposite electricity of the 
 cloud in consequence of their greater proximity, and 
 renders them especially liable to be struck by lightning. 
 
 The clouds gather electricity from the atmosphere. 
 Our knowledge of the method by which the atmosphere 
 becomes charged is very limited. 
 
169 
 
 CHAPTER VII. 
 ENERGY OF ELECTRIC FLOW. ELECTRO-KINETICS. 
 
 Section I. 
 
 VOLTAIC CELLS. ELECTRIC CIRCUITS. 
 
 147. Introductory Experiments. 
 
 APPARATUS REQUIRED. A tumbler $ full of water, into which have 
 been poured two or three tablespoonfuls of strong sulphuric acid ; a strip 
 of sheet-copper, and two pieces of rolled zinc, each about 5 inches long, 
 1 inches wide, and at least T \ of an inch thick (a piece of No. 16 copper 
 wire 12 inches long should be soldered to one end of each piece of metal, 
 and the soldering covered with asphaltum paint) ; 2 yds. of silk insulated 
 No. 18 copper wire ; two double 
 connectors (Fig. 142), which serve 
 to join two wires without the incon- 
 venience of twisting them together. 
 One of the zincs should be amal- 
 gamated as follows :. First dip the zinc, with the exception of inch at 
 the soldered end, into the acidulated water ; then pour mercury over the 
 wet surface, and finally rub the surface, now wet with mercury, with a 
 cloth. (To insure complete amalgamation, it is best to repeat this 
 operation.) 
 
 Experiment 122. a. Put the unamalgamated zinc into the tum- 
 bler containing acidulated water. Bubbles of hydrogen gas arise 
 from the surface of the immersed zinc. 
 
 6. Remove this zinc and introduce the amalgamated zinc. No 
 bubbles (or at least very few) arise from the latter, provided that the 
 zinc is properly amalgamated. 
 
 If a plate of metal be placed in a liquid of a class which 
 we shall term an electrolyte (i.e. one which is capable of 
 
170 ENERGY OF ELECTRIC FLOW. 
 
 being decomposed by a current of electricity), there is a 
 difference of electrical condition produced between them 
 so that the metal becomes either of higher or lower poten- 
 tial than the liquid, according to the nature of the metal 
 and liquid. 
 
 We know that if two conductors be at different poten- 
 tials, electricity tends to flow from the one whose potential 
 is higher to that whose potential is lower ; if, therefore, 
 two dissimilar metals be placed in the same electrolytic 
 liquid, it may be shown, by actual experiment, 1 that the 
 free end of the wire in connection with one plate is charged 
 with -f- E, and the free end of the other with E. Hence 
 we conclude that if the two oppositely charged bodies be 
 brought in contact, a current of electricity will flow from 
 the positively charged plate to the negatively charged one. 
 A current therefore flows through the connecting wire 
 from the copper (which is called the positive electrode) to 
 the wire leading from the zinc (which is called the nega- 
 tive electrode), when they are connected. 
 
 That difference in quality in virtue of which zinc and 
 copper placed in acidulated water can give rise to an elec- 
 trit current, is called their electro-chemical difference, and 
 the zinc is said to be electro-positive to the copper in the 
 liquid. 
 
 148. Voltaic Cell. Two electro-chemically different 
 solids (of which zinc is almost invariably one) placed in 
 an electrolytic liquid constitute what is called a galvanic 
 or voltaic 2 cell (or pair). One of these plates must be 
 more actively attacked by the liquid than the other ; the 
 
 1 See author's Principles of Physics, p. 463. 
 
 2 A single voltaic couple is usually termed a cell ; a combination of cells, a battery. 
 
VOLTAIC CELLS. ELECTRIC CIRCUITS. 171 
 
 plate most acted upon is called the electro-positive plate, 
 and the other the electro-negative one. 
 
 The greater the disparity between the two solid elements 
 with reference to the action of the liquid on them, the greater 
 the difference in potential ; hence, the greater the current. 
 
 In the following electro-chemical series the substances are so arranged 
 that the most electro-positive, or those most affected by dilute sulphuric 
 acid, are at the beginning, while those most electro-negative, or those 
 least affected by the acid, are at the end. The arrow indicates the 
 direction of the current through the liquid. 
 
 I 
 
 fe & 8 
 
 ^ a o 
 
 i 6 a *x 8* P 2 " 
 
 +1 f a f > I 1 s~ 
 
 NHH;OPHU 
 
 It will be seen that zinc and platinum are the two substances best 
 adapted to give a strong current. 
 
 When the wires from the two plates are joined, the dis- 
 charge of the two plates would produce electrical equilib- 
 rium were there not some means of maintaining a difference 
 of potential between the two plates. This is accomplished 
 by the chemical action be ween the liquid and the electro- 
 positive plate and at the expense of the chemical potential 
 energy of the electrolyte and plate. A voltaic cell is, there- 
 fore, a contrivance which converts chemical energy into 
 electrical energy. 
 
 149. Circuit. This term is applied to the entire path 
 along which electricity flows, and it comprises the battery 
 itself and the wire or other conductor connecting the bat- 
 tery-plates. 1 Bringing the two extremities of the wire in 
 
 1 It was an early discovery in telegraphic history that a complete metallic circuit 
 is not necessary, but that, in common parlance, the earth can be used as a " return 
 circuit." This type of circuit is represented by a battery with a wire leading from 
 
172 ENERGY OF ELECTRIC FLOW. 
 
 contact and separating them are called, respectively, clos- 
 ing and opening, QT making and breaking, the circuit. Open- 
 ing a circuit at any point and filling in the gap with an 
 instrument of any kind so that the current is obliged to 
 traverse it, is called introducing the instrument into the 
 circuit. 
 
 150. Importance of Amalgamating- the Zinc. Com- 
 mercial zinc contains impurities, such as carbon, iron, etc. Figure 143 
 
 represents a zinc element having on its surface a particle of 
 
 B^^^s. carbon a, purposely magnified. If such a plate be immersed 
 
 in dilute sulphuric acid, the particles of carbon will form 
 
 HlS with the zinc numerous voltaic circuits, and a transfer of 
 
 W oj electricity along the surface will take place. This transfer 
 
 ^fp between the zinc and the impurities on its surface diverts so 
 
 much from the regular battery current, and thereby weakens 
 
 it. In addition to this, it occasions a great waste of mate- 
 
 1 rials, because, when the regular circuit is broken, this local 
 
 action, as it is called, still continues. If mercury be rubbed 
 
 over the surface of the zinc it dissolves a portion of the zinc, 
 
 forming with it a semi-liquid amalgam, which covers up its 
 
 impurities. 
 
 151. Polarization of the Negative Element. 
 
 Experiment 123. Construct a voltaic cell composed of dilute 
 sulphuric acid and plates of copper and zinc. Introduce into the 
 circuit a galvanoscope ( 159) and note the deflection of the needle 
 when the circuit is first closed. Watch the needle for a time. Little 
 by little this deflection will decrease, and as it decreases bubbles of 
 gas collect on the copper plate. This accumulation of gas is called 
 " polarization of the negative element or plate." 
 
 We already understand that difference of potential is 
 indispensable to a flow of electricity. Accompanying a 
 difference of potential there seems to be something anal- 
 one plate to any convenient point of the earth, and a second wire leading from the 
 other plate to any other point of the earth, which may he many miles distant from 
 the first point. 
 
VOLTAIC CELLS. ELECTRIC CIRCUITS. 
 
 173 
 
 ogous to a force which causes the flow of electricity 
 through the circuit. The film of gas on the copper 
 reduces the electro-chemical difference between it and 
 the zinc plate, upon which the generation of this force 
 depends, and thereby diminishes the efficiency of the 
 battery. 
 
 The remedy for this is to prevent the deposit of hydro- 
 gen upon the negative plate. The usual method is to 
 employ in . addition to the dilute sulphuric acid (i.e. the 
 exciting liquid) some oxidizing substance which will com- 
 bine with the hydrogen as soon as it is liberated. A sub- 
 stance used for this purpose is termed a depolarizer. A 
 mixture of a solution of crystals of 
 bichromate of potassium in water 
 with a suitable quantity of dilute 
 sulphuric acid is used as a depo- 
 larizer in the so-called bichromate 
 batteries. 
 
 152. Grenet Cell. This is a bi- 
 chromate of potassium battery in which 
 two carbon plates, CC (Fig. 144), elec- 
 trically connected, and a zinc plate, Z, 
 suspended between them by a brass rod, 
 a, are immersed in the mixed liquid re- 
 ferred to above. 
 
 This combination furnishes a much 
 more energetic and constant current than 
 would be furnished if only dilute sulphuric 
 acid were used. 
 
 Fig. 144. 
 
 153. Bunsen Cell. A plan generally adopted to keep the oxi- 
 dizing liquid away from the zinc plate, where it is not wanted and only 
 does harm, is to place the carbon plate in an unglazed, porous, earthen 
 cup and to surround it with the oxidizing substance. This arrangement, 
 called a two-fluid cell, is that adopted by Bunsen (Fig. 145) and others. 
 
174 
 
 ENERGY OF ELECTRIC FLOW. 
 
 154, Ijeclanch^ Cell. There is a class of galvanic cells in which 
 the negative element is protected from polarization by means of metallic 
 oxides. Of these the best known is the Leclanche" cell (Fig. 146). In 
 this cell the carbon plate C is contained in a porous cup P, and packed 
 round with fragments of gas-retort coke and manganese peroxide. The 
 manganese compound has a strong affinity for the hydrogen. But the 
 
 Fig. 145. 
 
 Fig. 146. 
 
 chemical action of solids is sluggish and they quickly polarize when in 
 action. They need periodical rest to recover their normal condition. 
 Such are called open-circuit batteries, since they are suited for work only 
 on lines kept open or disconnected most of the time, such as in telephone 
 and bell-ringing circuits. The zinc rod Z is immersed in a solution of 
 ammonium chloride, which is the exciting liquid. 
 
EFFECTS PRODUCIBLE BY AN ELECTRIC CURRENT. 175 
 
 Section II. 
 
 EFFECTS PRODUCIBLE BY AN ELECTRIC CURRENT. 
 
 155. Summary of Effects. The several effects pro- 
 ducible by an electric current may be classified as (1) 
 electrolytic, (2) magnetic, (3) thermal, and (4) physiological. 
 
 156. (1) Electrolysis. 
 
 Experiment 124. Take a dilute 
 solution of sulphuric acid (1 part by 
 volume to 20), pour some of it into the 
 funnel (Fig. 147), so as to fill the 
 U-shaped tube when the stoppers are 
 removed. Place the stoppers which 
 support the platinum electrodes tightly 
 in the tubes. Connect with these 
 electrodes the battery l wires. Instantly 
 bubbles of gas arise from both elec- 
 trodes, accumulating in the upper part 
 of the tube and forcing the liquid back 
 into the tunnel. Introduce a glowing 
 splinter into the gas surrounding the 
 + electrode ; it relights and burns vigor- 
 ously, showing that the gas is oxygen. 
 Invert the tube, allow the gas which 
 had accumulated about the electrode 
 to escape at a, and apply a lighted match 
 to it : the gas burns ; it is hydrogen. 
 
 Fig. 147. 
 
 The volume of hydrogen is just double that of the 
 oxygen liberated in the same time. The process by which 
 
 l A battery consisting of not less than two Grenet or Bunsen cells connected ii 
 series will be required. 
 
176 ENERGY OF ELECTRIC FLOW. 
 
 a compound substance is separated into its constituents 
 is called electrolysis, and the compound thus treated is 
 called the electrolyte. The electrode by which the current 
 enters the electrolyte is called the anode; and that by 
 which the current leaves, the cathode. 
 
 When a chemical salt is electrolyzed, the base appears 
 at the cathode, and the acid at the anode. In general it 
 will be found that in both the battery and the decompos- 
 ing cell, hydrogen, bases, and metals appear at the plates 
 toward which the current flows. 
 
 Experiment 125. Dissolve about three grains of pulverized 
 potassium iodide in a teaspoonful of water. Make a paste by 
 boiling pulverized starch in water. Take a portion of this paste 
 
 about the size of a pea, and 
 stir it into the solution. Wet a 
 piece of writing-paper with the 
 liquid thus prepared. Spread the 
 wet paper smoothly on a piece of 
 tin, e.g. on the bottom of a tin 
 basin (Fig. 148). Press the nega- 
 tive electrode of the battery against 
 Fig. 148. an uncovered part of the tip. Draw 
 
 the positive electrode over the 
 
 paper. A mark is produced upon the paper as if the electrode were 
 wet with a purple ink. In this case the potassium iodide is decom- 
 posed, and the iodide combining with the starch forms a purplish- 
 blue compound. 
 
 157. (2) Magnetic Action and Magnetic Field of a 
 Straight Current. Magnetic Lines of Force. 
 
 Experiment 126. Construct a low resistance battery of (say) 
 four cells. Close the circuit and dip the wire into a little heap of 
 filings of soft iron. On raising the wire you will find filings adher- 
 ing in a cluster to it (Fig. 149). 
 
EFFECTS PRODUCIBLE BY AN ELECTRIC CURRENT. 177 
 
 If a wire bearing a very strong current be passed vertically through 
 the center of a board on which have been sifted some very fine iron fil- 
 ings, the filings will arrange themselves in circular lines round the 
 
 Fig. 149. 
 
 current-carrying wire (Fig. 150), thus 
 furnishing a graphic representation of 
 the magnetic field set up by a current. 
 If a small pocket compass be carried 
 around and near the wire, the needle 
 will at every point take a position 
 tangent to these circular lines of fil- Fig. 150. 
 
 ings, whichever way the current passes. 
 
 If the current be reversed, however, the position of the n and s poles of 
 the needle will be reversed. This clearly indicates that there is a differ- 
 ence of direction of these circular lines according as the current flows in 
 one direction or in the other. These circular lines represent the so-called 
 magnetic lines of force which occupy a limited space or field round a 
 current-bearing wire. 
 
 158. Deflection of the Magnetic Needle by a Current. 
 
 Experiment 127. a. Place the apparatus ^(Fig. 151) so that the 
 magnetic needle, which points (nearly) north and south, shall be 
 parallel with the wires W l and W 2 . Introduce the + electrode of a 
 battery into screw-cup T 2 , and the electrode into screw-cup T v 
 and pass a current through the upper wire. At the instant the 
 circuit is closed the needle swings on its axis, and after a few oscilla- 
 tions comes to rest in a position which forms an angle with the wire 
 bearing the current. 
 
 b. Break the circuit by removing one of the wires from the screw- 
 cup. The needle, under the influence of the magnetic action of the 
 earth, returns to its original position. 
 
 c. Reverse the current by inserting the + electrode of the battery 
 into screw-cup T x , and the electrode into screw-cup T 2 . Again 
 
ITS 
 
 ENERGY OF ELECTKIC FLOW. 
 
 there is a deflection of the needle, but the direction of the deflection 
 is reversed ; that is, the north-pointing pole (N-pole), which before 
 turned to the west, is now deflected toward the east. 
 
 d. Place your right hand above the wire with the palm towards 
 
 Fig. 151. 
 
 the wire, and with the fingers pointing in the same direction as that 
 in which the current is flowing, and extend your thumb at right 
 angles to the direction of the current (Fig. 152). You observe that 
 
 Fig. 152. Right hand above the wire; 
 needle below it. 
 
 Fig. 153. Right hand below the 
 wire ; needle above it. 
 
 your thumb points in the same direction as the N-pole of the needle 
 under the current-bearing wire. 
 
 e. Reverse the current again (so that it will flow northward), place 
 your right hand as before (viz. with the palm towards the wire and 
 with the fingers pointing in the same direction as the current) ; your 
 outstretched thumb still points in the same direction as the N-pole of 
 the needle. 
 
EFFECTS PRODUCIBLE BY AN ELECTRIC CURRENT. 179 
 
 /. Introduce the + electrode of the battery into screw-cup T 3 and 
 the electrode into screw-cup T 4 so that the current will flow north- 
 ward under the needle. Place the right hand as directed before, 
 except that it must be under the wire, so that the wire shall be 
 between the hand and the needle ; the thumb will point in the same 
 direction as the N-pole (Fig. 153). Reverse the direction of the 
 current in this wire, and apply the same test ; the same rule holds. 
 
 The rule for determining the direction of the deflection 
 of the N-poles of a needle when the direction of the 
 current is known is this : Place the outstretched right hand 
 over or under the wire so that the wire shall be between the 
 hand and the needle, with the palm towards the needle, the 
 fingers pointing in the direction of the current and the thumb 
 extended laterally at right angles to the direction of the cur- 
 rent; then the extended thumb will point in the direction of 
 the deflection of the N-pole. 
 
 It will be observed that a deflection is reversed either 
 by reversing the current or by changing the relative posi- 
 tions of the wire and needle, e.g. by carrying the needle 
 from above the wire to a position below it. 
 
 The force exerted by the current upon the needle in 
 deflecting it is called an electro-magnetic force. 
 
 159. Simple Galvaiioscope or Current Detector. 
 
 Experiment 128. Introduce the + electrode of the battery into 
 screw-cup T 2 (Fig 151) and the electrode into screw-cup T 3 , so 
 that the current will pass above the wire in one direction and below 
 it in the opposite direction, as indicated by the arrows. A larger 
 deflection is obtained than when the current passes the needle only once. 
 
 If the right-hand test be applied, it will be seen that 
 the tendency of the current, both when passing the needle 
 in one direction above and in the opposite direction below, 
 is to produce a deflection in the same direction, and con- 
 
180 ENERGY OF ELECTRIC FLOW. 
 
 sequently the two parts of the current assist each other 
 in producing a greater deflection. 
 
 If a more sensitive instrument, i.e. one which will 
 produce considerable deflections with weak currents, be 
 required, then it will be necessary to pass the current 
 through an insulated wire wound many times around the 
 needle. Such an instrument is called a galvanoscope or 
 current detector, since one of its important uses is to detect 
 the presence of a current. 
 
 16O. Magnetizing- Effect of an Electric Current. 
 Electro-magnets. 
 
 Experiment 129. a. Wind an insulated copper wire in the form 
 of a spiral round a rod of soft iron (Fig. 154). Pass a current of 
 electricity through the spiral, and hold an iron nail near the end of 
 the rod. Observe, from its attraction for the nail, that the rod is 
 magnetized. A magnet may be provisionally denned as a body 
 which attracts iron. 
 
 b. Break the circuit ; the rod loses its magnetism and the nail drops. 
 
 The iron rod is called a core, the coil of wire a helix, and 
 both together are called an electro-magnet. 
 In order to take advantage of the attraction 
 of both ends or poles of the magnet, the rod 
 is most frequently bent into a U-shape (A, 
 Fig. 155). More frequently two iron rods 
 are used, connected by a rectangular piece 
 of iron, as a in B of Figure 155. The 
 method of winding is such that if the iron 
 core of the U-magnet were straightened, 
 or the two spools were placed together 
 end to end, one would appear as a con- 
 Fig. 154. tinuation of the other. A piece of soft 
 
EFFECTS PRODUCIBLE BY AN ELECTRIC CURRENT. 181 
 
 iron, 5, placed across the ends and attracted by them is 
 called an armature. The piece of iron a is called a yoke. 
 
 161. (3) Thermal and Luminous Effects of the 
 Electric Current. 
 
 Experiment 130. Construct a low resistance battery ( 181) of 
 four to six cells, and introduce into the circuit a platinum wire, No. 
 30, about \ inch long. The wire very quickly becomes white hot, i.e. 
 it emits white light, which indicates a temperature of approximately 
 1900 C. 
 
 This experiment illustrates the conversion of the energy 
 of an electric current into heat energy. In this case the 
 energy of the current is said to be consumed in over- 
 coming the resistance which 
 the conductor or the cir- 
 cuit offers to its passage. 
 Heat is developed by a 
 current in every part of 
 the circuit, because all 
 substances offer some resistance to a current ; in other 
 words, there are no perfect conductors. The small platinum 
 wire offers much greater resistance than an equal length 
 of a larger copper wire ; whence the greater quantity of 
 heat generated in this part of the circuit. All of the 
 energy in any electric current that is not consumed in 
 doing other kinds of work is changed into heat. 
 
 162. (4) Physiological Effects. 
 
 Experiment 131. Place one of the copper electrodes of a single 
 voltaic cell on each side of the tip of the tongue. A slight stinging 
 (not painful) sensation is felt, followed by a peculiar acrid taste. 
 
182 ENEKGY OF ELECTRIC FLOW. 
 
 Section III. 
 
 ELECTRICAL QUANTITIES AND UNITS. OHM'S LAW. 
 
 163. Strength of Current. The Ampere and the 
 Coulomh. The magnitude of the effects produced by an 
 electric current depends, among other things, upon the 
 magnitude of the current. Any one of the effects pro- 
 ducible by a current may be made the basis of a system of 
 measurement of currents. For example, the quantity of 
 hydrogen gas or of any metal liberated at the cathode in 
 a given time, by electrolysis, is strictly proportional to the 
 magnitude of the current, or as it is technically termed 
 the strength of the current. 
 
 By current strength is meant the number of units of 
 electricity which flows in a given time, or, briefly, it is 
 the "rate of flow." The practical unit of current (i.e. the 
 unit of current strength) is the ampere. It is the current 
 which passed through a solution of nitrate of silver ( u in 
 accordance with standard specifications "), deposits silver 
 at the rate of 0.001118 gram per second. The quantity 
 of electricity transferred by a current of one ampere in 
 one second is called a coulomb. 1 The coulomb, then, is 
 the unit of quantity of electricity. When the quantity 
 of electricity conveyed by a current in one second is one 
 coulomb, its strength is one ampere. 
 
 164. Electro-Motive Force. The Volt. - Water 
 flows from one place to another in virtue of a difference 
 
 1 The definitions of the coulomb and the ampere here given are those of the so- 
 called international units, which were adopted as the legal units by act of the United 
 States Congress in July, 1864. 
 
ELECTRICAL QUANTITIES AND UNITS. 183 
 
 of pressure between the two places, and the flow takes 
 place from the place of high pressure to the place of low 
 pressure. For instance, when water flows from a reservoir 
 or cistern the pressure at any point in the pipe is due to 
 the "head" of water above it. If it be set flowing by a 
 force pump, we might say the flow of water is due to a 
 water-motive force which could be expressed as equal to 
 a " head " of a certain number of feet of water. 
 
 Similarly, electricity flows in a conductor only when 
 there is a difference of what may be termed electrical 
 pressure between its ends. If such be maintained between 
 two points connected by a conductor, it obviously repre- 
 sents a kind of current-producing force, one which can 
 keep electricity in motion against resistance. It is for 
 this reason called electro-motive force (E.M.F.). Electro- 
 motive force is that which maintains or tends to maintain 
 a current of electricity through a conductor. That which 
 hinders the current is called resistance. 
 
 Difference in electrical pressure we have hitherto 
 assumed to be due to difference of potential. It is this 
 difference of electrical pressure which sets up a current in 
 the conductor. Potential difference may be due to con- 
 tact of dissimilar substances, as in the voltaic cell, or to 
 the movement of a part of the conductor in a magnetic 
 field, as in the dynamo (p. 223). 
 
 The volt is the name chosen for the practical unit of 
 E.M.F. and difference of potential. It is the electrical 
 pressure required to maintain a current of one ampere 
 against a resistance of one ohm ( 165). For purposes 
 where great accuracy is not required, it will answer to 
 consider a volt as the E.M.F. of a Daniell's cell, i.e. it is 
 
184 ENERGY OF ELECTRIC FLOW. 
 
 about the difference of potential between the zinc and 
 copper of this cell, the E.M.F. of a standard Daniell cell 
 being approximately 1.07 volts. 
 
 165. Electrical Resistance. The Ohm. - - Every 
 substance offers resistance to the passage of a current. 
 Those substances which offer a very powerful barrier are 
 called insulators. The unit of resistance is called the ohm. 
 
 The international ohm is " the resistance offered to an 
 unvarying electric current by a column of mercury at the 
 temperature of melting ice, 14.421 grams in mass, of a 
 constant cross-sectional area, and of the length of 106.3 
 centimeters " ; or about the resistance of 9.3 ft. of No. 30 
 (American gauge) copper wire (.01 in. diam.). 
 
 166. Electrical Work and Electrical Power. The 
 Joule and the Watt. If a coulomb of electricity flow 
 between two points in a conductor whose difference of 
 potential is one volt, then one joule or volt-coulomb of 
 work is done thereby. The volt-coulomb is analogous to 
 the foot-pound. 
 
 If a conductor be traversed by a current of one ampere 
 (i.e. a coulomb per second) and there be two points in the 
 conductor whose difference of potential is one volt, then 
 the rate at which work is done in that portion is one watt 
 = one joule per second. The joule and the watt are 
 units of electrical work (or energy) and electrical power 
 respectively. 
 
 167. Re'sume'. A unit current is a current maintained 
 by a unit E.M.F. against a unit resistance. 
 
 A unit E.M.F. is the E.M.F. required to maintain a unit 
 current against a unit resistance. 
 
ELECTRICAL QUANTITIES AND UNITS. 185 
 
 A conductor has a unit resistance when a unit E.M.F. (or 
 a unit difference of potential between its two ends) causes a 
 unit current to pass through it. 
 
 A unit of electric power is the power of a unit current 
 maintained by a unit difference of potential. 
 
 168. Ohm's L,aw. The three factors, current (C), 
 electro-motive force (E), and resistance (R), are evidently 
 interdependent. Their relations to one another are stated 
 in the well-known Ohm's Law thus : The current is equal 
 to the electro-motive force divided by the resistance; or 
 
 E E 
 
 C = 77 ; whence E = R C, and R = -^ 
 it u 
 
 Hence the strength of a current is directly proportional to 
 the E.M.F. and inversely proportional to the resistance. 
 This famous law is the basis of a large portion of electrical 
 measurements commonly made. 1 
 
 EXERCISES. 
 
 1. What E.M.F. is required to maintain a current of one ampere 
 against a resistance of one ohm ? 
 
 2. An E.M.F. of 10 volts will maintain a current of 5 amperes 
 against what resistance? 
 
 3. What current ought an E.M.F. of 20 volts to maintain against 
 a resistance of 5 ohms? 
 
 4. A volt-meter applied each side of an electric lamp shows a 
 difference of potential of 40 volts ; what current flows through the 
 lamp, if it has a resistance of 10 ohms ? 
 
 1 The following formulas relating to the electric current will be found convenient 
 for reference : (1) P (watts) = C (amperes) x E (volts). (2) The watt OTIS horse- 
 
 O F 1 
 power. Hence =power in horse-power. (3) Substituting in (1) the value of 
 
 E 2 
 
 C (Ohm's formula), we have P = . Or, (4) substituting in (1) the value of E (Ohm's 
 
 formula), we have P = C*R. 
 
186 
 
 ENERGY OF ELECTRIC FLOW. 
 
 5. The resistance between two points in a circuit is 10 ohms. An 
 ammeter (an instrument which measures the strength of a current in 
 amperes) shows that there is a current strength in the circuit of 0.5 
 ampere ; what is the difference in potential between the points ? 
 
 Section IV. 
 
 GALVANOMETER COIL 
 
 INSTRUMENTS FOR MEASUREMENT OF ELECTRIC 
 CURRENTS. 
 
 169. Galvanometer. This is an instrument for meas- 
 uring current-strength by means of the deflection of a 
 magnetic needle when placed in the field of the current. 
 It is so constructed that either the deflection angle itself, 
 or some function of it, is proportional to the current- 
 strength. 
 
 A very simple form of this instrument is represented in sectional 
 
 elevation and plan in Figure 156. It 
 consists of an insulated wire wound 
 many times around a magnetic 
 needle. A card graduated like that 
 of a mariner's compass is placed 
 beneath the needle so that the 
 number of degrees of deflection may 
 be read from it. This form of 
 instrument is much used to detect 
 the presence of a current, to locate 
 faults, etc. 
 
 17O. Tangent Galvanom- 
 eter. A tangent galvanom- 
 eter is one so constructed that 
 Fig. ise. the current passing through 
 
MEASUREMENT OF ELECTRIC CURRENTS. 
 
 187 
 
 it is proportional to the tangent of the angle of deflection 
 produced. To this end it is necessary that the needle be 
 very short (not more than -fa) in comparison with the 
 diameter of the coil. 
 
 It consists of a large vertical coil (C, Fig. 157) in the 
 center of which is either a small compass needle or a 
 needle suspended by a silk fiber. 
 
 A needle thus placed in the field of a current is acted 
 on by a mechanical couple tending to place it at right 
 angles to the plane of the coil, and it is deflected until 
 this couple is balanced by the return couple due to the 
 earth's magnetism. 
 
 When the scale is divided into degrees, the correspond- 
 ing tangents are found by consulting a table of tangents 
 (see Appendix). In some instru- 
 ments the scale is graduated direct- 
 ly in tangents. 
 
 If the strengths of two currents 
 are to be compared, it is only nec- 
 essary to obtain deflections with 
 each current, and compare the 
 tangents of the angles. 
 
 171. Ammeter. If the gal- 
 vanometer be calibrated so as to 
 read in amperes, we shall have a 
 direct^reading ampere -meter, or 
 ammeter as it is more commonly 
 called. There is a great variety 
 of ammeters in use, for a description of which the student 
 is referred to technical works on the subject. 
 
 Fig. 157. 
 
188 ENERGY OF ELECTRIC FLOW. 
 
 Section V. 
 
 RESISTANCE OF CONDUCTORS. 
 
 172. External and Internal Resistance. For con- 
 venience the resistance of an electric circuit is divided 
 into two parts, the external and the internal. External 
 resistance includes all the resistance of a circuit except 
 that of the generator, while the latter is termed internal 
 resistance. 
 
 When the external resistance in a circuit is considered 
 separately from the internal, Ohm's formula must be con- 
 verted thus (calling the former R, and the latter r}: 
 
 r- E 
 ~RT? 
 
 If a cell have E = 1 volt, and r = 1 ohm, and the con- 
 necting wire be short and stout, so that R may be dis- 
 regarded, then the cell yields a current of one ampere. 
 If by any means the internal resistance of this cell can be 
 decreased one-half, it will then be capable of yielding a 
 two-ampere current under the same conditions. 
 
 173. External Resistance. 
 
 Experiment 132. Introduce into a circuit a galvanometer, 1 and 
 note the number of degrees the needle is deflected. Then introduce 
 into the same circuit the wire on the spool numbered 4 on the plat- 
 form 2 S (Fig. 158). (The wire on any one of the five spools on this 
 
 1 The galvanometer represented in the cut is a form of galvanometer chiefly used 
 hy the author in elementary laboratory work. 
 
 2 The platform of spools containing wire of different (known) sizes, lengths, and 
 material, so arranged that any one, two, or more can he introduced into the circuit 
 for the purpose of measurement of resistance, is an instrument of great convenience 
 in a school laboratory. 
 
RESISTANCE OF CONDUCTORS. 
 
 189 
 
 platform can at any time be introduced into a circuit, by connecting 
 the battery wires with the binding screws on each side of the spool 
 to be introduced.) 
 
 The deflection is now less than before. The copper wire on this 
 spool is 16 yards in length ; its size is No. 30 of the Brown and 
 Sharpe wire gauge. When this spool is in circuit, the circuit is 16 
 
 Fig. 158. 
 
 yards longer than when the spool is out. The effect of lengthening 
 the circuit is to weaken the current, as shown by the diminished 
 deflection. 
 
 Experiment 133. Next, substitute Spool 2 for Spool 4. This 
 contains 32 yards of the same kind of wire as that on Spool 4. The 
 deflection is still smaller. 
 
 The weakening of the current by introducing these wires is caused 
 by the resistance which the wires offer to the current, much as the 
 friction between water and the interior of a pipe impedes, to some 
 extent, the flow of water through it. The longer the pipe the greater 
 is the resistance to the flow. 
 
 If the wire on the spools had been the only resistance in the cir- 
 cuit, then, when Spool 2 was in the circuit, the resistance would have 
 been double what it was when Spool 4 was in the circuit, and the 
 current, with double the resistance, would have been half as strong. 
 
 (1) Other things being equal, the resistance of a conductor 
 varies as its length. 
 
190 ENERGY OF ELECTRIC FLOW. 
 
 Experiment 134. Next substitute Spool 1 for Spool 2. This 
 spool contains 32 yards of No. 23 copper wire, a thicker wire than 
 that on Spool 2, but the length of the wire is the same. The deflec- 
 tion is now greater than it was when Spool 2 was in circuit. This 
 indicates that the larger wire offers less resistance. 
 
 Careful experiments show that (2) the resistance of all 
 conductors varies inversely as the areas of their cross-sections. 
 If the conductors be cylindrical, it varies inversely as the 
 squares of their diameters. 
 
 Experiment 135. Substitute Spool 5 for Spool 1, and compare 
 the deflection with that obtained when Spool 4 was in the circuit. 
 The deflection is smaller than when Spool 4 was in circuit. The 
 wire on these two spools is of the same length and size, but the wire 
 of Spool 5 is German-silver. It thus appears that German-silver 
 offers more resistance than copper. 
 
 (3) In obtaining the resistance of a conductor, the specific 
 resistance of the substance must enter into the calculation. 
 (See table of specific resistances in the Appendix.) 
 
 The resistance of metal conductors increases slowly 
 with the temperature of the conductor. The resistance of 
 German-silver is affected less by changes of temperature 
 than that of most metals ; hence its general use in 
 standards of resistance. 
 
 174. Internal Resistance. 
 
 Experiment 136. Connect with the galvanometer the copper 
 and zinc strips used in Experiment -122, and introduce the strips into 
 a tumbler nearly full of acidulated water. Note the deflection. 
 Then raise the strips, keeping them the same distance apart, so that 
 less and less of the strips will be submerged. As the strips are 
 raised, the deflection becomes smaller. This is caused by the 
 increase of resistance in the liquid part of the circuit, as the cross- 
 section of the liquid lying between the two strips becomes smaller. 
 
MEASUREMENT OF RESISTANCE. 
 
 191 
 
 (4) The internal resistance of a circuit, other things being 
 equal, varies inversely as the area of the cross-section of the 
 liquid between the two elements. 
 
 In a large cell the area of the cross-section of the liquid 
 between the elements is larger than in a small cell, con- 
 sequently the internal resistance is less. This is the only 
 way in which the size of the cell affects the current. 
 
 Obviously the resistance of the battery would be increased by any 
 increase of the distance between the elements, since this increases the 
 length of the liquid conductor ; but as this distance is usually made as 
 small as convenient, and is kept invariable, it demands little of our 
 attention. 
 
 Section VI. 
 
 MEASUREMENT OF RESISTANCE. 
 
 1 75. Description of the Resistance Box. 
 
 Figure 159 represents a wooden box containing what is equivalent to a 
 series of coils of German-silver wire, whose resistance ranges from 0.1 ohm 
 to 100 ohms. Each of 
 these coils is connected 
 with a brass stud on the 
 top of the box. 
 
 Three switches, A, 
 B, and C, so connect 
 the coils with the bind- 
 ing screws a and 6 that 
 a current can be sent 
 through any three coils 
 at the same time by 
 moving the switches on 
 to the proper studs. 
 The resistance in ohms of each coil is marked on the box near its stud. 
 
192 
 
 ENERGY OF ELECTRIC FLOW. 
 
 When the three switches rest upon studs marked 0, the current meets 
 with no appreciable resistance in passing through the box, but any 
 desired resistance within the range of the instrument can be introduced 
 by moving the 'switches on to the studs, the sum of whose resistances is 
 the resistance required. This instrument we shall call a resistance box. 
 
 G G X 
 
 Fig. 160. 
 
 176. Wheatstone Bridge. 
 
 Figure 160 represents a perspective view of the bridge (as modified by 
 the author), and Figure 161 represents a diagram of the essential electri- 
 cal connections. The battery wires are connected with the bridge at the 
 
 binding screws B B'. A gal- 
 vanometer, G, is connected at 
 G G', a resistance box, r, at 
 R R, and the conductor, x, 
 whose resistance is sought, at 
 XX. 
 
 When the circuit is closed 
 by means of the key T, the 
 current, we will suppose, 
 enters at B ; on reaching the point A it divides, one part flowing via the 
 branch A G B', and the other via the branch A D B'. If points D and G 
 in the two branches be at 
 different potentials and a 
 connection be made between 
 them through the galvanom- 
 eter, G, by closing the key 
 S, there will be a current 
 through this wire and through 
 the galvanometer, and a de- 
 flection of the needle will be 
 produced. But if the points 
 D and G be at the same 
 potential, there will be no 
 cross current through the 
 bridge wire and no deflection. 
 Now it can be demonstrated 
 that points D and G will be at 
 the same potential when R 
 (the resistance) of A D : R of D B 7 :: R of A G : R (the unknown resist- 
 ance) of G B'. Between A and T) and A and G there are three coils of 
 
MEASUREMENT OF RESISTANCE. 193 
 
 wire having resistances respectively of 1, 10, and 100 ohms. One or 
 more of these coils are introduced into the circuit by removing the 
 corresponding plugs a, 6, c, d, e, and /. As the other connections 
 between A and D, and A and G, have no appreciable resistance, being 
 for the most part short brass bars, the only practical resistance between 
 these points is that introduced at will through the coils. Similarly 
 between points D and B', the only practical resistance is that introduced 
 at will through the resistance box, and between the points G and B' the 
 resistance is the resistance (x) sought. 
 
 It is apparent, then, that in using the bridge after the connections are 
 properly made through the several instruments and certain known 
 resistances are introduced between A and D, and A and G, we have 
 simply to regulate the resistance through the resistance box so that there 
 will be no deflection in the galvanometer; then we are sure that the 
 above proportion is true. The first three terms of the proportion being 
 known, the fourth term, which is the resistance sought, is computable. 1 
 
 If the same resistance be introduced between points A and G as 
 between A and D, it is evident that the resistance in the resistance box r 
 must be made equal to the unknown resistance x in order that there may 
 be no deflection in the galvanometer. Consequently when this result is 
 obtained the resistance of x may be read from the resistance box. 
 
 Experiment 137. Measure the resistance of each of the several 
 spools of wire used above, electro-magnets, electric lamps, etc., 
 using the bridge. Place the switches of the resistance box on the 
 zero studs. Make connections as in the description above. Then 
 close the circuit at T, and afterwards the bridge at S. There will 
 probably be a deflection in the galvanometer, Regulate the resist- 
 ance through the resistance box, throwing in or taking out resistance 
 according as one or the other tends to reduce the deflection (the 
 process is much like that of weighing), until there is no deflection. 
 Then compute the resistance sought according to the above proportion. 
 
 
 
 1 The accuracy of the results obtained largely depends upon so choosing resist- 
 ances of the bridge as to make the arrangement have maximum sensibility, and upon 
 the sensitiveness of the galvanometer. In using the bridge the following directions 
 should be observed : (1) Always close the circuit at T before closing the bridge at S, 
 and in breaking the circuit reverse this order. (2) Introduce between A and D, and 
 A and G, resistance as nearly equal to the resistance sought (x) as practicable. If 
 you have no conception what the unknown resistance is, it is best to begin by using 
 high resistances. (3) Use a sensitive galvanometer, e.g. a mirror galvanometer, or 
 the galvanometer shown in Figure 158, substituting the astatic needle for the tangent 
 needle. 
 
194 
 
 ENERGY OF ELECTRIC FLOW. 
 
 B' 
 
 177. Measurement of Galvanometer Resistance. 
 Lord Kelvin's Method. 
 
 The bridge may be used for measuring 
 the resistance of the galvanometer actually 
 in use. The bridge is arranged as in Figure 
 162. The resistance in the resistance box 
 K is then varied until the deflection of G 
 does not change when the key S is closed ; 
 then 
 
 in which r is the resistance of the galva- 
 nometer, R is the resistance in the resistance 
 box, and a and 6 are the resistances in 
 the arms A G' and A D respectively. If 
 Fig. 162. a = 6, then r = R. 
 
 Section VII. 
 
 E.M.F. OF DIFFERENT CELLS. DIVIDED CIRCUITS. 
 METHODS OF COMBINING VOLTAIC CELLS. 
 
 178. Electro-Motive Force of Different Cells. If 
 
 a galvanometer be introduced into a circuit with different 
 battery cells, e.g. Bunsen, Daniell, Greiiet, etc., very 
 different deflections will be obtained, showing that the 
 different cells yield currents of different strengths. This 
 may be in some measure due to a difference in their 
 internal resistance, but it is chiefly due to the difference 
 in their electro-motive forces. We have learned that 
 difference of electro-motive force is due to the difference 
 of the chemical action on the two plates used, and this 
 depends upon the nature of the substances used. It is 
 
E.M.F. OF DIFFERENT CELLS, ETC. 195 
 
 wholly independent of the size of the plates ; hence the 
 electro-motive force of a large battery cell is no greater 
 than that of a small one of the same kind. Consequently 
 any difference in strength of current yielded by battery 
 cells of the same kind, but of different sizes, is due wholly 
 to a difference in their internal resistances. 
 
 The electro-motive forces of the Bunsen, Daniell, and 
 Grenet cells are respectively about 1.8, 1, and 2 volts. 
 
 179. Divided Circuits; Shunts. 
 
 Experiment 138. Make a divided circuit as 
 in Figure 163 (using double connectors a and 5). 
 Insert a galvanometer, G, in one branch and a 
 resistance box, R, in the other. When the cur- 
 rent reaches a, it divides, a portion traversing one 
 branch through the galvanometer, and the remainder 
 passing through the other branch and the resistance FI s- 163 ' 
 box. The branch a R b is called a shunt or derived circuit. Increase 
 gradually the resistance in the resistance box. The result is that 
 it throws more of the current through the galvanometer, as shown 
 by the increase of deflection. 
 
 In a divided circuit the current divides between the paths 
 inversely as their resistances. For example, if the resist- 
 ance of the resistance box above be 4 ohms, and the 
 resistance in the galvanometer be 1 ohm, then four-fifths 
 of the current will traverse the latter and one-fifth the 
 former. 
 
 Suppose that the resistance box and galvanometer be 
 removed from the shunts, and that the shunts be of the 
 same length, size, and kind of wire, and consequently 
 have equal resistances. Using the two wires instead of 
 one to connect a and b is equivalent to doubling the size 
 of this portion of the conductor ; consequently the re- 
 sistance of this portion is reduced one-half. 
 
196 ENERGY OF ELECTRIC FLOW. 
 
 Generally, the joint resistance of two branches of a circuit 
 is the product of their respective resistances divided by their 
 sum. 
 
 If any portion of a circuit be divided into three or more 
 branches whose resistances are respectively r v r%, r^ etc., 
 it may be demonstrated 1 that, 
 
 E^n^^n"* 
 
 in wliich R represents the joint resistance of the several 
 branches. That is, the reciprocal of the joint resistance of 
 any number of branches is equal to the sum of the reciprocals 
 of the resistances of the several branches. 
 
 ISO. Combining- Cells. Batteries. 
 
 A number of cells connected in such a manner that the 
 currents generated by all have the same direc- 
 tion constitutes a voltaic battery. The object 
 of combining cells is to get a stronger current 
 than one cell will afford. We learn from 
 Ohm's law that there are two, and only two, 
 ways of increasing the strength of a current. 
 It must be done either by increasing the 
 E.M.F. or by decreasing the resistance. So 
 we combine cells into batteries, either to secure 
 greater E.M.F. or to diminish the internal re- 
 sistance. Unfortunately, both purposes cannot 
 y be accomplished by the same method. 
 
 I 181. Batteries of Low Internal Resist- 
 
 ance. Figure 164 represents three cells 
 Fig. 164. having all the carbon (-}-) plates electrically 
 
 i See the author's Principles of Physics, p. 509. 
 
 ' i 
 
 if 
 \( 
 
E.M.F. OF DIFFERENT CELLS, ETC. 197 
 
 connected with one another, and all the zinc ( ) plates 
 connected with one another, and the triplet carbons are 
 connected with the triplet zincs by the leading-out wires 
 through a galvanometer G. 
 
 It is easy to see that through the battery the circuit 
 is divided into three parts, and consequently the conduc- 
 tivity in this part of the circuit, according to the principle 
 stated in 179, must be increased threefold ; in other 
 words, the internal resistance of the three cells is one-third 
 of that of a single cell. This is called connecting cells 
 " in multiple arc," and the battery is called a " battery of 
 low internal resistance." The resistance of the battery is 
 decreased as many times as there are cells connected in 
 multiple are, but the E.M.F. is that of one cell only. 
 
 The formula for the current-strength in this case is 
 
 written thus : 
 
 E 
 
 in which n represents the number of cells. It is evident 
 from this formula that when R is so great that - is a 
 
 v 7Z* 
 
 small part of the whole resistance of the circuit, little is 
 added to the value of C by increasing the number of cells 
 in multiple arc. 
 
 182. Batteries of High Internal Resistance and 
 Great E.M.F. Figure 165 represents four cells having 
 the carbon or -|- plate of one connected with the zinc or 
 plate of the next, and the -j- plate at one end of the series 
 connected by leading-out wires through a galvanometer 
 with the plate at the other end of the series. It is evi- 
 
198 ENERGY OF ELECTRIC FLOW. 
 
 dent that the current in this series traverses the liquid 
 four times, which is equivalent to lengthening the liquid 
 
 conductor four times, and of 
 course increasing the internal 
 resistance fourfold. But, 
 while the internal resistance 
 |+ is increased, the E.M.F. of 
 the battery is increased as 
 Fig. 165. many times as there are cells 
 
 in series. The gain by increasing the E.M.F. more than 
 offsets, in many cases (always when the internal resistance 
 is a small part of the whole resistance of the circuit), the 
 loss occasioned by increased resistance. 
 
 The formula for current-strength in this case becomes 
 
 XV, T? 
 
 c== 
 
 It is evident that C is increased most by adding cells in 
 series when n r is smallest in comparison with R. 
 
 183. Rule for Combining- Cells. 
 
 When the external resistance is large, connect cells in 
 series ; when the external is less than the internal resistance, 
 connect cells in multiple arc. 
 
 EXERCISES. 
 
 1. What E.M.F. is required to maintain a current of one ampere 
 through a resistance of one ohm ? 
 
 2. Through what resistance will an E.M.F. of ten volts maintain 
 a current of 5 amperes ? 
 
 3. What current ought an E.M.F. of 20 volts to maintain through 
 a resistance of 5 ohms ? 
 
EXERCISES. 199 
 
 4. A voltmeter applied each side of an electric lamp shows a differ- 
 ence of potential of 40 volts ; "what current flows through the lamp, 
 if it have a resistance of 10 ohms ? 
 
 5. The resistance between two points in a circuit is 10 ohms. 
 An ammeter shows that there is a current-strength in the circuit of 
 0.5 ampere ; what is the difference in potential between the points ? 
 
 6. What current will a Bunsen cell furnish when r = 0.9 ohm 
 (about the resistance of a quart cell), E = 1.8 volts, and R = 0.01 
 ohm (about the resistance of 3 ft. of No. 16 wire) ? 
 
 [In the following exercises, whenever a Bunsen cell is mentioned 
 it may be understood to be a quart cell, having a resistance of about 
 0.9 ohm. Its E.M.F. is about 1.8 volts.] 
 
 7. a. When is a large cell considerably better than a small one ? 
 b. When does the size of the cell make little difference in the 
 current ? 
 
 8. If you have a dozen quart cells, how can you make them 
 equivalent to one 3-gallon cell ? 
 
 9. If a battery of 10 cells have an E.M.F. 10 times greater than 
 that of a single cell, why will not the battery yield a current ten 
 times as strong ? 
 
 10. a. The internal resistance of ten cells, connected in multiple 
 arc, is what part of that of a single cell ? b. If the cells were con- 
 nected in series, how would the resistance of the battery compare 
 with that of one of its cells ? c. How would the E.M.F. of the latter 
 battery compare with that of a single cell ? 
 
 11. What current will a single Bunsen cell furnish through an 
 external resistance of 10 ohms ? 
 
 12. What current will 8 Bunsen cells, in series, furnish through 
 the same resistance ? 
 
 SOLUT.ON : = ~~ = 0.83+ ampere. 
 
 13. What current will 8 Bunsen cells, in multiple arc, furnish 
 through the same external resistance ? 
 
 14. What current will a Bunsen cell furnish through an external 
 resistance of 0.4 ohm ? 
 
200 ENERGY OF ELECTRIC FLOW. 
 
 15. What current will a battery of two Bunsen cells, in series, 
 furnish through the same resistance as the last ? 
 
 16. What current will two cells, in multiple arc, furnish through 
 the same resistance ? 
 
 17. A coil of wire having a resistance of 10 ohms carries a current 
 of 1.5 amperes. Required the difference of potential at its ends. 
 
 18. a. The resistance between two points, A and B, of a con- 
 ductor is 2.5 ohms ; the resistance of a shunt between the same 
 points is 1.5 ohms ; what is the joint resistance between these points? 
 b. If a current of 10 amperes be maintained between these points, 
 what will be the strength of current in each branch ? c. How will 
 the strength of current between these points be affected if the shunt 
 be removed and the same fall of potential be preserved ? Why ? 
 
 Section VIII. 
 
 MAGNETS AND MAGNETISM. 
 
 184. Law of Magnets. Suspend by fine threads in 
 a horizontal position two stout darning-needles which 
 have been drawn in the same direction (e.g. from eye to 
 point) several times over the same pole of a powerful 
 electro-magnet. These needles, separated a few feet from 
 each other, take positions parallel with each other, and 
 both lie in a northerly and southerly direction with the 
 points of each turned in the same direction. 
 
 That point in the Arctic zone of the earth towards 
 which magnetic needles point is called the north magnetic 
 pole of the earth. That end of a needle which points 
 toward the north magnetic pole of the earth is called the 
 north-seeking, marked, or -\-pole; this is the end that is 
 
MAGNETS AND MAGNETISM. 201 
 
 always marked for the purpose of distinguishing one from 
 the other. That end of the needle which points south- 
 ward is called the south-seeking, unmarked, or pole. 
 
 Experiment 139. Bring both points near each other ; there is 
 a mutual repulsion. Bring both eyes near each other ; there is a 
 mutual repulsion. Bring a point and an eye near each other ; there 
 is a mutual attraction. 
 
 Like poles of magnets repel, unlike poles attract each other. 
 
 185. Magnetic Transparency and Induction. 
 
 Experiment 140. Interpose a piece of glass, paper, or wood- 
 shaving between the two magnets. These substances are not them- 
 selves perceptibly affected by the magnets, nor do they in the least 
 affect the attraction or repulsion between the two magnets. 
 
 Substances that are not susceptible to magnetism are 
 said to be magnetically transparent. When a magnet causes 
 another body, in contact with it or in its neighborhood, 
 to become a magnet, it is said to induce magnetism in that 
 
 Fig. 166. 
 
 body. As attraction, and never repulsion, occurs between 
 a magnet and an unmagnetized piece of iron or steel, it 
 must be that the magnetism induced in the latter is such 
 that opposite poles are adjacent : that is, a N or -f- pole 
 induces a S or pole next itself, as shown in Figure 
 166. 
 
 186. Polarity. 
 
 Experiment 141. Strew iron filings on a flat surface, and lay 
 a bar magnet on them. On raising the magnet it is found that large 
 
202 ENERGY OF ELECTRIC FLOW. 
 
 tufts of filings cling to the poles, as in Figure 167, especially 
 to the edges ; but the tufts diminish regularly in size from 
 each pole towards the center, where none are found. 
 
 Magnetic attraction is greatest at the poles, and 
 diminishes towards the center, where it is nothing; 
 i.e. the center of the bar is neutral. This dual 
 character of the magnet, as exhibited at its opposite 
 extremities, is called polarity. If a magnet be 
 broken, each piece becomes a magnet with two 
 poles and a neutral line of its own. 
 
 187. Retentivity and Resistance. 
 
 It is more difficult to magnetize steel then iron ; 
 on the other hand, it is difficult to demagnetize steel, 
 while soft iron loses nearly all its magnetism as soon as 
 it is removed from the influence of the inducing body. 
 That quality of steel by which it resists the escape of 
 magnetism which it has once acquired is called its reten- 
 tivity. The greater the retentivity of a magnetizable body, 
 the greater is the resistance which it offers to becoming 
 magnetized. The harder steel is, the greater is its retentivity. 
 Hence, highly tempered steel is used for permanent mag- 
 nets. Hardened iron possesses considerable retentivity ; 
 hence the cores of electro-magnets should be made of the 
 softest iron, that they may acquire and part with magnetism 
 instantaneously. 
 
 188. Forms of Artificial Magnets. Artificial magnets, 
 including permanent magnets and electro-magnets, are usually made in 
 the shape either of a straight bar or of the letter U, according to the use 
 to be made of them. If we wish, as in the experiments already described, 
 to use but a single pole, it is desirable to have the other as far away as 
 possible ; then, obviously, the bar magnet is most convenient. But if 
 
LINES OF MAGNETIC FORCE. 
 
 203 
 
 the magnet is to be used for lifting or holding weights, the U-form (see 
 Fig. 155) is far better, because the attraction of both poles is conveniently 
 available. 
 
 Section IX. 
 
 LINES OF MAGNETIC FORCE. THE MAGNETIC CIRCUIT. 
 
 189. Lines of Magnetic Force. These lines are 
 easily studied by the use of iron filings. The field of 
 force around a magnet is shown by placing a paper over 
 
 Fig. 168. 
 
 it, dusting filings upon the paper, and tapping it. The 
 filings take symmetrical positions, form curves between 
 the poles of the magnet or magnets, and show that the 
 lines of force connect the opposite poles of the magnet. The 
 fact is, that each filing, when brought within the influence 
 
204 
 
 ENERGY OF ELECTRIC FLOW. 
 
 of the magnetic field, 1 becomes a magnet by induction, 
 and of necessity tends to take a definite position which 
 represents the resultant of the forces acting upon it from 
 
 
 ;:> /l\\<:<: : 5^ 
 
 / ; \ \X .-- ' W 
 
 Fig. 169. 
 
 each pole of the system. A line of magnetic force is a line 
 drawn in such a manner that the tangent to it at any 
 point indicates the direction of the resultant magnetic 
 
 
 ^~^//p\M$ 
 N::---X/// vi\\N 
 
 x ^ **'/! \ \ \ \ 
 
 . ---^"- / / ! ; \ ^ 
 
 Fig. 17O. 
 
 force at that point. Figure 168 represents a magnetic 
 field photographed from a specimen paper, and Figure 169 
 is a graphical representation of the same. In this illustra- 
 
 1 A portion of space throughout which magnetic effects are exerted is called a 
 magnetic field. 
 
LINES OF MAGNETIC FORCE. 
 
 205 
 
 Fig. 171. 
 
 tion the unlike poles of two magnets are placed opposite 
 each other. Figure 170 is a diagram of paths of lines of 
 force of a bar magnet, and Figure 171 of a U-shaped magnet. 
 
 19O. Magnetic Circuit. - - A 
 
 line of force is assumed arbitrarily 
 to start from the N-pole and to pass 
 through the surrounding medium 
 (e.g. the air), entering the magnet 
 by the S-pole, and completing its 
 path through the magnet itself to ^ 
 its starting-point (the N-pole), thus '^ 
 forming a complete circuit (Fig. / , 
 170). These lines do not all ( 
 emerge, however, from the extrem- 
 ities. A multitude of lines start 
 from all parts of the magnet and 
 enter at corresponding points on the other side of its 
 central or neutral line. No magnetic line of force can 
 exist without completing its own circuit, and lines of force 
 never cross or merge into one another, consequently a 
 magnet cannot have a single pole. 
 
 Lines of force possess several peculiar characteristics. One is that in 
 air and most other mediums they tend to separate from one another, but 
 at the same time tend to become as short as possible. The strain is as if 
 these lines were stretched elastic threads endowed with the property of 
 repelling one another as well as of shortening themselves; in other words, 
 there is tension along the lines and pressure at right angles to them. If 
 the N-pole of one magnet be placed opposite the S-pole of another (Fig. 
 169), the lines of force issuing from the former will enter the latter, and, 
 tending to shorten, will produce attraction. If the similar ends be opposed 
 (Fig. 172), the lines of force will be turned away from each pole in all 
 directions, and will complete their circuits independently. Thus becom- 
 ing parallel they will repel one another ; for this reason like magnetic 
 poles repel each other. 
 
206 
 
 ENERGY OF ELECTRIC FLOW. 
 
 Air is a poor conductor for lines of force, or its permeability is low ; 
 on the other hand, iron has high permeability for lines of force, and if a 
 piece of iron be brought within a magnetic field, a portion of the lines of 
 
 Fig. 173. 
 
 force will crowd together into it, leaving their normal paths through the 
 air for a medium of greater permeability. 
 
 191. Law of Inverse Squares. It may be demon- 
 strated experimentally 1 that the force exerted between two 
 magnetic poles varies inversely as the square of the distance 
 between them. 
 
 Section X. 
 
 TERRESTRIAL MAGNETISM. 
 
 192. The Earth a Magnet. 
 
 Experiment 142. Place a dipping-needle 2 over the + pole of a 
 bar magnet (Fig. 173). The needle takes a vertical position with 
 its pole down. Slide the supporting stand along the bar ; the 
 
 pole gradually rises 
 until the stand reaches 
 the middle of the bar, 
 where the needle becomes 
 horizontal. Continue 
 .Fig. 173. moving the stand toward 
 
 1 See tlie author's Principles of Physics, p. 528. 
 
 2 A magnetic needle so supported that it can rotate in a vertical plane is called a 
 dipping-needle. 
 
TERRESTRIAL MAGNETISM. 
 
 207 
 
 the pole of the bar ; after passing the middle of the bar the 
 + pole begins to dip, and the dip increases until the needle reaches 
 the end of the bar, when the needle is again vertical with its + pole 
 down. 
 
 If the same needle be carried northward or southward along the 
 earth's surface, it will dip in the same way as it approaches the polar 
 regions, and be horizontal only at or near the equator. 
 
 The experiment presents a true exhibition, on a small 
 scale, of what the earth does on a large one, and thereby 
 
 Fig. 174. 
 
 presents one of many phenomena which lead to the con- 
 clusion that the earth is a magnet. In other words, these 
 phenomena are just what we should expect if a huge 
 magnet were thrust through the earth, as represented in 
 Figure 174, having its N-pole near the S geographical 
 pole, and its S-pole near the N geographical pole ; or if 
 the earth itself were a magnet. 
 
208 ENERGY OF ELECTRIC FLOW. 
 
 193. Magnetic Poles of the Earth. Points on the 
 earth's surface where the dipping-needle assumes a vertical 
 position are called the magnetic poles of the earth. A point 
 was found on the western coast of Boothia, by Sir James 
 Ross, in the year 1831, where the dipping-needle lacked 
 only one-sixtieth of a degree of pointing directly to the 
 earth's center. The same voyager subsequently reached a 
 point in Victoria Land where the opposite pole of the 
 needle lacked only 1 20 ' of pointing to the earth's center. 
 
 It will be seen that, if we call that end of a magnetic needle which 
 points north the N-pole, we must call that magnetic pole of the earth 
 which is in the northern hemisphere the S-pole, and vice versa. (See 
 Fig. 174.) Hence, to avoid confusion, many careful writers abstain from 
 the use of the terms north and south poles, and substitute for them the 
 terms positive and negative, or marked and unmarked poles. 
 
 194. Variation of the Needle. Inasmuch as the 
 magnetic poles of the earth do not coincide with the 
 geographical poles, it follows that the needle does not in 
 most places point due north and south. The angle which 
 the vertical plane through the axis of a freely suspended 
 needle makes with the geographical meridian of the place 
 is known as the angle of declination. In other words the 
 angle of declination is the angle formed by the magnetic 
 and geographical meridians. This angle differs at different 
 places. The magnetic axis of a needle is a straight line 
 connecting its two poles. 
 
 195. Isogfonic curves. These are lines connecting all points 
 of equal declination on the earth's surface. The line of no declination, 
 or isogonic of (Fig. 175), commences at the N. magnetic pole about lat. 
 70, long. 96, passes in a southeasterly direction across Lake Erie and 
 Western Pennsylvania, and enters the Atlantic Ocean near the boundary 
 between the Carolinas. Pursuing its course through the south polar 
 regions, it reappears in the eastern hemisphere and crosses Western 
 
MAGNETIC RELATIONS OF THE CURRENT. 
 
 209 
 
 Australia, the Caspian Sea, and thence to the Arctic Ocean. There is 
 also a detached line of no declination inclosing an oval area in Eastern 
 Asia and the Pacific Ocean. In the eastern (or Atlantic) hemisphere, 
 bounded by the line of no declination, the declination is westward, as 
 
 Fig. 175. 
 
 indicated by continuous lines in the figure. In the western (or Pacific) 
 hemisphere the declination is eastward, as indicated by dotted lines. 
 
 The magnetic poles are not fixed objects that can be located like an 
 island or cape, but are constantly changing. They appear to swing, 
 something like a pendulum, in an easterly and westerly direction, each 
 swing requiring centuries to complete it. The north magnetic pole is 
 now on its westerly swing. 
 
 Section XI. 
 
 MAGNETIC RELATIONS OF THE CURRENT. 
 
 ELECTRO-MAGNETS. 
 
 196. Magnetic Field due to a Circular Current. 
 
 If a wire be bent into the form of a circle of about 10 in. 
 diameter, and placed vertically in the magnetic meridian, 
 
210 
 
 ENERGY OF ELECTRIC FLOW. 
 
 and a cardboard be placed at right angles to the circle so 
 that its horizontal diameter is coincident with the upper 
 surface of the cardboard, and a very strong current be 
 sent through the wire in the direction indicated by the 
 arrow-head in the wire, iron filings sifted upon the card 
 will arrange themselves as shown in Figure 176. And if 
 a freely suspended test-needle be carried inside and out- 
 
 
 Fig. 176. 
 
 side the circle, the several positions taken by the needle, 
 as indicated in the figure by arrows, corroborate the direc- 
 tions of the lines of force as indicated by the filings. If 
 the direction of the current be reversed, the direction of 
 the needle will be reversed wherever it may be placed. 
 
 In fact, when a current traverses a wire (or other con- 
 ductor) lines of force encircle the electric current at right 
 angles to it. 1 The electric current and its encircling lines 
 of force always coexist, and one varies directly as the 
 other when there is no magnetic substance near the wire. 
 
 1" Every conducting wire is surrounded by a sort of magnetic whirl. A great 
 part of the energy of the so-called electric current in the wire consists in these 
 external magnetic whirls. To set them up requires an expenditure of energy ; and 
 to maintain them requires a constant expenditure of energy. It is these magnetic 
 whirls which act on magnets, and cause them to set, as galvanometer needles do, at 
 right angles to the conducting wire." S. P. THOMPSON. 
 
MAGNETIC RELATIONS OF THE CURRENT. 
 
 211 
 
 Fig. 177. 
 
 197. Solenoid. If instead of a single circle of wire 
 an insulated wire be wound into a helix of several turns, 
 it is called a solenoid. The intensity of the magnetic field 
 is greatly increased by the joint action of the many cur- 
 rent turns. The passage of an electric current through 
 a solenoid gives it all 
 
 the properties of a mag- 
 net. The magnetic field 
 within the solenoid is 
 nearly uniform in 
 strength, and the lines 
 of force to within a 
 short distance of its ends are parallel with its axis, as 
 shown in Figure 177. 
 
 A solenoid encircling an iron core constitutes an electro- 
 magnet. 
 
 The iron core greatly increases the number of lines of 
 force which pass through the solenoid by reason of its 
 permeability. Hence the magnetic strength of a solenoid 
 is greatly increased by the presence of an iron core. 
 
 198. Magnetic Polarity of Electro-Magnetic Solenoid. 
 
 Figure 178 represents a small battery floating on water. The leading 
 
 wire of the cell is wound 
 into a horizontal solenoid. 
 Slowly after the cell is 
 floated it will take a posi- 
 tion so that the axis of 
 the solenoid will point 
 north and south like a 
 magnetic needle. Hold 
 (say) the S-pole of a bar 
 magnet near that end of 
 
 the solenoid which points north ; the solenoid is attracted by the magnet. 
 
 Hold the N-pole of the magnet near the north-pointing end of the 
 
 solenoid; the magnet repels the solenoid. 
 
 Fig. 178. 
 
212 
 
 BNBEGY OF ELECTRIC FLOW. 
 
 Fig. 179. 
 
 Repeat the above, using in place of 
 the bar magnet another current-bear- 
 ing solenoid (Fig. 179) ; there will be a 
 repetition of the same phenomena as 
 obtained with the bar magnet. Intro- 
 duce a rod of soft iron into the solenoid 
 held in the hand, thereby making of it 
 an electro-magnet; the only change 
 observed is that the force of attraction 
 and repulsion is greatly increased. 
 
 Place the wire of another battery over and parallel with the coil 
 (Fig. 180), so that the 
 two currents will flow 
 in planes at right an- 
 gles to each other. The 
 coil is deflected like a 
 magnetic needle (Fig. 
 181). 
 
 Reverse the direc- 
 tion of the current Fisr ' 18 * 
 above and the deflection is reversed. 
 
 Fig. 181. 
 
 We thus prove that a solenoid bearing a current pos- 
 sesses polarity as if it were a magnet, and that there can 
 be produced by a current-bearing solenoid a magnetic field 
 of the same character as that produced by a permanent 
 magnet. There is no essential difference between a per- 
 manent magnet, a current-bearing solenoid, and an electro- 
 magnet, except that the last may be made much stronger 
 than either of the others. 
 
 199. Given the Direction of the Current in a Sole- 
 noid, to find the N- and S-poles of the Solenoid, and 
 vice versa. 
 
 RULE 1. Place the palm of the right hand against the 
 side of the solenoid so that the fingers will point in the direc- 
 tion of the current passing through the windings (as shown 
 
ELECTRODYNAMICS. 
 
 213 
 
 in Fig. 182); the 
 thumb will point in 
 the direction of the 
 N-pole of the solenoid 
 or electro-magnet. 1 
 
 RULE 2. Ascer- 
 tain the N-pole of the 
 solenoid or electro- 
 magnet with a mag- 
 netic needle, and place 
 the palm of the right hand upon the solenoid so that the 
 outstretched thumb points in the direction of the N-pole; 
 the fingers will point in the direction in which the current 
 passes in the windings. 
 
 Fig. 183. 
 
 Section XII. 
 
 ELECTRODYNAMICS. AMPERE S THEORY OF MAGNETISM. 
 
 2OO. Mutual Action of Currents on One Another. 
 
 If we suppose that a test-needle be moved up or down 
 just back of the current-bearing wires (Fig. 183), the N- 
 and S-poles will take the positions indicated by n and s. 
 We may readily predict from inspection of the polarity 
 developed, that if the wires were so suspended as to be 
 
 1 The following suggestion will often prove of practical value : that is the south 
 pole of a helix where the current corresponds to the motion of the hands of a watch, 
 S, and that is the north pole where the current is in the reverse direction, N! 
 
214 
 
 ENERGY OF ELECTRIC FLOW. 
 
 free to move either toward or from each other, the pair 
 of wires in which the currents flow parallel to each 
 other and in the same direction, A, would attract each 
 other, and the pair of wires in which the currents flow in 
 opposite directions, B, would repel each other; but if the 
 
 ft II 
 
 Fig. 183. 
 
 Fig. 184. 
 
 currents be inclined to each other, as in Figure 184, they 
 will tend to move into a position in which they will be 
 parallel and in the same direction. That such actually 
 takes place may be shown by the following experiments:- 
 
 Experiment 143. Figure 185 represents a portion of a divided 
 circuit. The lower ends of the wires dip about one-sixteenth of an 
 inch into mercury, and the wires are so suspended that they are free 
 to move toward or from each other. Send a current of a battery of 
 three or four Bun sen cells, in multiple arc, through this divided cir- 
 cuit. The two portions of the current travel in the same direction 
 and parallel with each other, and the two wires at the lower extremi- 
 ties move toward each other, showing an attraction. 
 
 Experiment 144 Make the connections (Fig. 186) so that the 
 
 current will go down one wire and up the other. They repel each 
 other. 
 
ELECTRODYNAMICS. 
 
 215 
 
 Fig. 185. 
 
 Fig. 186. 
 
 In the experiment with the floating cell and current- 
 bearing wire placed over and 
 parallel to the solenoid (Fig. 
 180), a careful examination 
 will disclose the fact that not 
 only do the planes in which 
 the current flows in the coil 
 tend to become parallel to the 
 current above, but that the 
 current in the upper half of 
 the coil, where the influence 
 due to proximity is greatest, 
 tends to place itself so as to flow in the same direction as 
 that of the current above. 
 
 201. Ampere's Laws. LAW 1. Parallel currents, if 
 in the same direction, attract one another ; and if in oppo- 
 site directions, they repel one another. 
 
 LAW 2. Currents that are not parallel tend to become 
 parallel and flow in the same direction. 
 
 202. Ampere's Theory of Magnetism. This cele- 
 brated theory briefly stated is that magnets and solenoid 
 systems are fundamentally the same; that magnetism is 
 simply electricity in rotation, and that a magnetic field 
 is a sort of whirlpool of electricity. Not, of course, that 
 a steel magnet contains an electric current circulating 
 round and round it as does an electro-magnet, but that 
 every molecule of iron, steel, or other magnetizable sub- 
 stance is the seat of a separate current circulating round 
 it continuously and without resistance, and thus every 
 molecule is a magnet. 
 
216 
 
 ENERGY OF ELECTRIC FLOW. 
 
 According to the theory, in an unmagnetized bar these currents lie in 
 all possible planes, and, having no unity of direction, they neutralize one 
 another, and so their effect as a system is zero. But if a current of elec- 
 tricity or a magnet be brought near, the effect of the induction is to turn 
 the currents into parallel planes, and in the same direction, in conformity 
 to Ampere's Second Law. If the retentivity be strong enough, this 
 parallelism will be maintained after the removal of the inducing cause, 
 and a permanent magnet is the result. 
 
 Intensity of magnetization depends on the degree of parallelism, and 
 the latter depends on the strength of the influencing magnet. When 
 these currents have become quite parallel, the body has received all the 
 magnetism that it is capable of receiving, and is said to be saturated. 
 
 The hypothetical currents that circulate round a magnetic molecule 
 we shall call amperian currents, to distinguish them from the known 
 
 Fig. 187. 
 
 current that traverses the solenoid. In strict accordance with this theory, 
 the poles of the electro-magnet are determined by the direction of the 
 current in the helix. The inductive influence of the electric current 
 causes the amperian currents to take the same direction with itself, as 
 represented in Figure 187. 
 
 Section XIII. 
 
 ELECTRO-MAGNETIC INDUCTION. 
 
 2O3. Description of Apparatus. A (Fig. 188) is a 
 short coil of coarse wire (i.e. the wire which it contains is 
 comparatively short), and has, of course, little resistance. 
 B is a long coil of fine wire having many turns. Coil 
 
ELECTRO-MAGNETIC INDUCTION. 
 
 217 
 
 A is in circuit with two 
 Bunsen cells in multiple 
 arc. This circuit we call 
 the primary circuit, the 
 current in this circuit 
 the primary or inducing 
 current, and the coil the 
 primary coil. Another 
 circuit, having in it no 
 battery or other means of 
 generating a current, con- 
 tains coil B and a galvano- 
 scope with an astatic needle. 1 This circuit is called the 
 secondary circuit, the coil the secondary coil, and the cur- 
 rents which circulate through this circuit are called 
 secondary or induced currents. 
 
 Experiment 145. Lower the primary coil quickly into the 
 secondary coil, watching at the same time the needle of the galvano- 
 
 Fig. 188. 
 
 Fig. 189. 
 
 1 This needle consists of two needles of about the same intensity with their poles 
 reversed, fixed parallel with each other. Though the needles nearly neutralize each 
 other and are therefore little affected by the field of the earth's magnetism, they are 
 especially sensitive to the influence of the electric current properly situated. 
 
218 ENERGY OF ELECTRIC FLOW. 
 
 scope to see whether it moves, and, if so, in what direction. Simul- 
 taneously with this movement there is a movement of the needle, 
 showing that a current must have passed through the secondary 
 circuit. Let the primary coil rest within the secondary, until the 
 needle comes to rest. After a few vibrations the needle settles at 
 zero, showing that the secondary current was a temporary one. Now, 
 watching the needle, quickly pull the primary coil out ; another 
 deflection in the opposite direction occurs, showing that a current in 
 the opposite direction is caused by withdrawing the coil. 
 
 It is evident that in this case the current does not by its 
 mere presence cause an induced current, but that a change 
 in the relative positions of the two circuits, one of which 
 bears a current, is necessary. 
 
 Instead of a current-bearing coil a bar magnet may be 
 introduced into the secondary coil, and afterwards with- 
 drawn from it. The needle is deflected at each act as 
 before. 
 
 Experiment 146. Place the primary coil within the secondary. 
 Open the primary wire at some point and then close the circuit (Fig. 
 189) by bringing in contact the extremities of the wires. A deflec- 
 tion is produced. As soon as the needle becomes quiet, break the 
 circuit by separating the wires ; a deflection in the opposite direction 
 occurs. 
 
 The same phenomena occur when the primary current 
 is by any means suddenly strengthened or weakened. 
 
 An examination of the direction of these currents enables 
 us to state the facts as follows : Starting a current in a 
 primary, increasing the strength of the primary current, 
 or moving the primary nearer while the current is steady, 
 produces a transitory current in the opposite direction in 
 the secondary. Stopping the primary, diminishing the 
 strength of the primary current, or moving the primary 
 
ELECTRO-MAGNETIC INDUCTION. 
 
 219 
 
 away while the current is kept steady, causes a transitory 
 current in the same direction in the secondary. 
 
 It is evident, therefore, that the conditions under which 
 a current in the primary coil can cause a current in a 
 neighboring secondary depend upon some change either in 
 the strength of the primary current or in the relative posi- 
 tions of the primary and secondary circuits. 
 
 The act by which the primary, or a magnet, causes a 
 current in a neighboring secondary is called magneto- 
 electric induction. 
 
 204. Faraday's Law of Induction. If any conducting 
 circuit be placed in the magnetic field, then, if a change of 
 relative position or change of strength of the primary current 
 cause a change in the number of lines of force passing through 
 the secondary, an electro-motive force is set up in the sec- 
 ondary proportional to the rate at which the number of lines 
 of force included by the sec- 
 ondary is varying. 
 
 Consider the case of induction 
 by a magnet. Let S (Fig. 190) be a 
 secondary circuit and N a magnet 
 projecting a certain number of 
 lines of force through the circuit. 
 If S be moved nearer to the mag- 
 net, say to S', a much greater 
 number of lines of force of the 
 magnet pass through the circuit 
 than when in its former position, 
 owing to the divergence of the lines as they recede from the pole. 
 
 205. Lenz's Law. The law by which the direction 
 of the induced current is determined is known as Lenz's 
 law, and may be expressed as follows : "In all cases of 
 
 Fig. 190. 
 
220 ENERGY OF ELECTRIC FLOW. 
 
 induction the direction of the induced current is such as 
 to oppose the motion which produces it." Thus approach 
 develops an opposite current, since opposite currents resist 
 approach, while recession develops a current of similar 
 direction, since similarly directed currents attract one 
 another and thus resist recession. 
 
 It is, then, apparent that the current developed in the 
 secondary circuit is at the expense of mechanical energy, 
 and that mechanical energy is, therefore, transformed into 
 electric energy. 
 
 206. Self-induction. " Extra Currents." Not only 
 does a current at starting and stopping or changing strength 
 act on neighboring conductors, generating currents in them, 
 but it acts upon itself by a process which is called self- 
 induction. A current starting or increasing creates an 
 oppositely directed current not only in its neighbor, but 
 also in its own wire. 
 
 Likewise at the instant a circuit is broken a current is 
 generated in the same direction as the retiring current, 
 and this induced current causes the spark seen on break- 
 ing a circuit. 
 
 If a current pass through the helix of an electro-magnet, owing to the 
 permeability of the iron a far larger number of lines of force traverse its 
 circuit than if the core were removed ; and hence, at the stoppage of the 
 current, a correspondingly greater impulse operates in the wire and 
 creates a correspondingly more powerful spark. For a similar reason 
 the self-induction is much greater in a coil of wire than if the same wire 
 were laid out straight. 
 
 20 7. Induction Coils. If a core of iron, or, still 
 better, a bundle of wires (A A, Fig. 191), be inserted in 
 the primary coil, it is evident that it will be magnetized 
 
ELECTRO-MAGNETIC INDUCTION. 
 
 221 
 
 and demagnetized every time the primary is made and 
 broken. The starting and cessation of amperian currents 
 in the core in the same direction as the primary current, 
 and simultaneously with the commencement and ending 
 of the primary current, greatly intensifies* the secondary 
 current. To save the trouble of making and breaking by 
 
 B 
 
 Fig. 191. 
 
 hand the core is also utilized in the -construction of an 
 automatic make-and-break piece. A soft iron hammer b 
 is connected with the steel spring <?, which is in turn con- 
 nected with one of the terminals of the primary wire. 
 The hammer presses against the point of a screw t?, and 
 thus, through the screw, closes the circuit. But when a 
 current passes through the primary wire, the core becomes 
 magnetized, draws the hammer away from the screw, and 
 breaks the circuit. The circuit broken, the core loses its 
 magnetism, and the hammer springs back and closes the 
 
222 ENERGY OF ELECTRIC FLOW. 
 
 circuit again. Thus the spring and hammer vibrate, and 
 open and close the primary circuit with great rapidity. 
 An instrument made on these principles is called an 
 induction coil. 
 
 2O8. Ruhmkorff's Coil. This instrument has the 
 important addition to the parts already explained of a 
 condenser, B B. This consists of two sets of layers of tin- 
 foil separated by paraffined paper ; the layers are con- 
 nected alternately with one and the other electrode of the 
 battery, as the figure shows, so that they serve as a sort of 
 expansion of the primary wire. When the circuit is 
 broken, the extra current tends to jump across at 5, and to 
 vaporize the points of contact, and to form with the vapor 
 of metal a bridge that would prolong the time of breaking. 
 But, when the condenser is attached, the extra current 
 finds an escape into it easier than to jump across at 5, so 
 the vaporizing of the contact is avoided, and the time of 
 breaking being much shortened, the secondary is much 
 more intense. 
 
 The secondary current is, as we ought to expect from 
 the extreme rapidity with which the primary, circuit is 
 broken, distinguished from the primary, or galvanic cur- 
 rent, by its vastly greater E.M.F., or power to overcome 
 resistances. A coil constructed for Mr. Spottiswoode of 
 London has two hundred and eighty miles of wire in its 
 secondary coil. With five Grove cells this coil gives a 
 secondary spark forty-two inches long, and perforates 
 glass three inches thick. Many brilliant experiments may 
 be performed with these coils. 
 
DYNAMO-ELECTRIC MACHINES. 223 
 
 Section XIV. 
 
 DYNAMO-ELECTRIC MACHINES. 
 
 2O9. Principles of the Dynamo. The dynamo is a 
 device for transforming mechanical energy into electric 
 energy. In the most improved types of dynamos this is 
 done with a loss of less than five per cent of the energy. 
 
 The action of the dynamo depends upon the principle 
 that when lines of magnetic force are cut by a wire a 
 difference of potential is produced in the wire, and hence 
 a current flows through the wire, if its ends be connected 
 so as to form a closed circuit. This is illustrated by the 
 following experiment. 
 
 Experiment 147. Connect a flat coil of about two inches in 
 diameter, having several turns of wire, with a delicate galvanometer, 
 
 and rotate the coil at one of the poles of a strong magnet on an axis 
 at right angles to the axis of the magnet and the lines of force, as 
 illustrated in Figure 192. 
 
 The horizontal arrow a indicates the direction of the 
 magnetic lines of force, the horizontal arrow b the direc- 
 
224 ENERGY OF ELECTRIC FLOW. 
 
 tion of motion of the end of the coil of wire, and the 
 vertical arrow c the direction of the current induced in 
 the coil of wire from the movement of the coil across the 
 field of magnetic force in such a manner as to cut lines 
 of force. 
 
 If the coil be moved rapidly in front of the magnet, 
 the current is stronger, and hence the E.M.F. must be 
 greater than if it be moved slowly. 
 
 Also if the number of turns of wire be increased the 
 E.M.F. is correspondingly increased, as will be shown by 
 the increased strength of current. 
 
 We may continue our experiment still further by in- 
 serting a bar or disk of soft iron into the coil and again 
 moving the end of the coil through the field of force in 
 front of the north pole of the magnet. A very decided 
 increase in the strength of current is observed. If, fur- 
 ther, another bar magnet be placed so that its south end 
 faces the other end of the coil, and the coil be fixed at its 
 center while its two ends are made to rotate past the two 
 poles, more lines of force are cut and greater E.M.F. is 
 developed, as is seen from the increased strength of cur- 
 rent. A powerful electro-magnet is preferable as an 
 inducer to a permanent magnet, as its strength or magnetic 
 density can be made much greater. 
 
 We have now found that the strength of current and 
 E.M.F. depend upon (1) the rapidity of motion of the wire 
 through the field ; (2) the number of turns of the wire; 
 and (3) the number of lines of force cut, or the strength 
 of field. 
 
DYNAMO-ELECTBIC MACHINES. 
 
 225 
 
 DIRECTION OF FORCB 
 
 210. Rule for Determining- the Direction of the 
 Induced Current. Place the right hand (Fig. 193) so 
 that the direction of 
 
 the forefinger coin- 
 cides with the direc- 
 tion of the lines of 
 force (as indicated 
 by a test needle), 
 and the thumb points 
 in the direction of mo- 
 tion of the part of the 
 conductor under con- 
 
 . 7 . 7 .-. Fi S> 193. 
 
 sideration ; the mid- 
 dle finger will indicate the direction of the induced 
 current. 
 
 211. The Dynamo. We are now prepared to study 
 the action of the dynamo. Our inducing magnet, which 
 is commonly an electro-magnet, is called the field magnet, 
 
 and our coil or series of coils 
 of wire, which is generally 
 made to move in front of 
 the poles of the field magnet, 
 is called the armature. The 
 armature is that part of the 
 electric circuit in which the 
 induced current is generated. 
 Like the battery, it may be 
 considered as the source of 
 the current. The number of 
 lines of force passing through a circuit may in general be 
 changed in two ways: either (1) by moving the circuit 
 
 Fig. 194. 
 
226 
 
 ENERGY OF ELECTRIC FLOW. 
 
 =>v 
 
 Fig. 195. 
 
 through a field in which the 
 
 density of the lines of force 
 
 varies, as represented in 
 ' Figure 194 ; or (2) by rotat- 
 ing the plane of the circuit 
 so as to change the angle 
 which it makes with the line 
 HZ of force, thus increasing or 
 decreasing the number which 
 the circuit encloses (Fig. 
 
 195). A common simple form of dynamo is illustrated 
 in Figure 196. A large mass or bar of soft iron of the U 
 form, surrounded 
 with a coil of in- 
 sulated wire, and 
 terminating in the 
 pole pieces N and 
 S, forms the field 
 magnet. The ar- 
 mature consists of 
 a single rectangu- 
 lar loop of wire 
 fixed to a horizon- Fig ' 196 ' 
 
 tal axis and terminating in two rings of metal, a and 6, 
 which are fixed to the axle, but insulated from it. 
 
 When a current passes through the field coils, and the 
 core becomes magnetized, lines of force will cross and fill 
 the space between the pole pieces of the field magnet. 
 As these lines are cut by the horizontal parts of the 
 rotating wire, an E.M.F. is generated in these parts, and 
 a current flows in the direction indicated by the arrows. 
 
DYNAMO-ELECTRIC MACHINES. 227 
 
 A metallic or carbon brush m touches, and carries off 
 the current from, the lower horizontal segment of the 
 rectangular coil. This current flows through the external 
 resistance R, and completes the circuit through the brush 
 n to the ring 6, and the upper half of the loop. The 
 current will continue to flow in this direction while the 
 loop moves through one half of a revolution. Since 
 the lines of force are cut in the opposite direction in the 
 next half revolution, the current will be reversed in the 
 armature wire and also through the external circuit. Thus 
 with each half revolution of the armature a reversal of 
 the current takes place. This, then, would be called an 
 alternating current dynamo. 
 
 212. The Commutator. The alternating current is 
 not adapted to all uses, and for many purposes it is desir- 
 able to have the current continuously flowing in the same 
 direction. To accomplish this a commutator is attached to 
 the axis of the armature. 
 
 In Figure 197 the two brass rings a and 6 are replaced by a single 
 brass tube divided into two parts by cutting it lengthwise. These two 
 segments are attached to but insulated from the axis, and are connected 
 with the separate ends of the 
 armature wire. When the 
 plane of the armature coil is 
 perpendicular to the line of 
 force passing from N to S, as 
 in Figure 197, no lines of force 
 are being cut, and hence no 
 E.M.F. is developed and no 
 current flows through the 
 loop. But the instant it moves 
 out of the vertical in the direc- 
 tion of the arrow, lines of force will be cut, and as the lower segment of 
 the loop is moving upward past the pole S, and the other segment is mov- 
 
228 ENERGY OF ELECTRIC FLOW. 
 
 ing downward in front of the pole N, a positive current flows from the 
 loop through the segment a, the brush w?, the resistance R, the brush ?i, 
 and the strip of the commutator 6. During the next half of a revolution 
 the lines of force will be cut from an opposite direction by each of the 
 horizontal segments of the armature loop, and hence the current will be 
 reversed. But the segment b of the commutator will now be in contact 
 with the brush m ; and although the current is reversed in the armature it 
 will flow off at the brush m as before. Inasmuch as no E.M.F. is 
 developed when the plane of the loop is perpendicular to the lines of 
 force, it is at this point that the brushes pass from one segment to the 
 other. 
 
 Thus by means of the commutators and brushes, reversal 
 of the current is prevented in the external circuit, although 
 the current in the armature reverses with each half revolu- 
 tion. This arrangement will constitute a direct-current 
 dynamo. We may have two turns of wire before connect- 
 ing with the commutator strips, giving twice the E.M.F., 
 or three turns, giving three times the E.M.F. ; i.e. the 
 E.M.F. will be proportional to the number of turns of 
 wire in the coil. Again, instead of having only one coil 
 we may have two or any number of coils, each separate 
 from the others, and terminating in strips or segments 
 which are on opposite sides of the commutator. Generally 
 the coils are connected in series, thus making any segment 
 a terminal of one coil and the beginning of the next. 
 
 213. Classes of Dynamos. 1 Dynamos may be divided 
 into different classes according to the method by which 
 their field magnets are excited. Figure 198 illustrates a 
 magneto-electric machine, where the field magnet is a per- 
 manent steel magnet. This form of machine is seldom 
 
 1 For the characteristics of the various classes of dynamos, as well as for a most 
 lucid and comprehensive treatment of dynamos generally, see Dynamo-Electric 
 Machinery, by S. P. Thompson. 
 
DYNAMO-ELECTKIC MACHINES. 
 
 229 
 
 used, since a permanent steel magnet cannot be made as 
 powerful as an electro-magnet having a soft iron core of 
 equal mass. 
 
 Figure 196 illustrates a separately 
 excited dynamo, where the field magnet 
 coils receive their currents from a sepa- 
 rate generator, e.g. a battery, and not 
 from the armature coils. Since an alter- 
 nating current dynamo does not produce 
 a constant magnetic field, alternating 
 d}^namos, in general, are separately 
 excited. 
 
 Fig. 198. 
 
 In a 
 
 series 
 
 dynamo the coils of the 
 field magnet are joined in 
 series with the armature 
 so that the entire current 
 passes through these coils. 
 
 Figure 199 illustrates a 
 shunt machine, where the 
 field-coil serves as a shunt 
 to the external circuit. L is 
 the main wire and I is the 
 shunt wire. In the shunt 
 machine only a part of the 
 current generated in the 
 armature passes through 
 the field-coils. 
 
 A dynamo is said to be 
 " self -exciting " when the whole or any part (Fig. 199) of 
 
 Fig. 199. 
 
230 ENERGY OF ELECTRIC FLOW. 
 
 the current which is produced is used to magnetize the 
 field magnets. Such are the Edison incandescent 
 dynamos. 
 
 The fields, after being once excited from any source, 
 e.g. another dynamo, always retain a little residual 
 magnetism, so that when the armature begins to rotate, a 
 slight current is at once induced in it. This strengthens 
 the field, and the stronger field reacts to increase the 
 current, so that the current soon rises to its normal 
 strength. For further treatment of the dynamo, see 
 Appendix, Section G. 
 
 Section XV. 
 
 ELECTRIC MOTOR. 
 
 214. Reversibility of the Dynamo. If a current 
 from an external source, e.g. a battery or another dynamo, 
 be passed through the armature and field magnet of a 
 direct-current dynamo, it will excite the armature and 
 make of it an electro-magnet x and will also excite the 
 fields. The current will enter at the terminals and will 
 pass through the commutator into the armature. The 
 relation of parts is such that in doing this it will develop 
 N and S poles in parts of the periphery of the armature 
 distant from the N and S poles of the fields. Hence there 
 will be set up between the armature and the poles of the 
 field magnet a stress tending to move the former a little 
 
ELECTRIC MOTOR. 231 
 
 in the opposite direction to that in which it is compelled 
 to move when generating a current. But as soon as it 
 has turned a short distance, the action of the commutator 
 shifts the current, and new poles are established in the 
 armature back of the first and in the same relative posi- 
 tions which they at first occupied. The armature con- 
 tinues to rotate as the new poles are attracted and repelled, 
 and the action goes on so long as a current is supplied. 
 Obviously if there were no commutator the poles of the 
 armature would be fixed, and it never could rotate through 
 a greater angle than 180. 
 
 It is evident, then, that if two dynamos be connected 
 by wires in the same circuit and the armature of one be 
 rotated, the armature of the other will rotate in a reverse 
 direction as soon as the current transmitted from the first 
 attains a certain intensity. 
 
 The dynamo, then, is a reversible machine, in which 
 mechanical energy can be changed directly into electrical 
 energy or electrical energy into mechanical energy. When 
 the dynamo is used for the latter transformation, it is 
 commonly known as an electric motor. In other words a 
 modern motor is a dynamo reversed. * The discovery of 
 the reversibility of the dynamo is considered to be one of 
 high importance. For further treatment of the electric 
 motor, see Appendix, Section H. 
 
232 ENERGY OF ELECTRIC FLOW. 
 
 Section XVI. 
 
 THE TRANSFORMER. 
 
 215. The Induction Coil Reversible. An induction 
 coil is in a certain sense a reversible machine. If a cur- 
 rent of considerable strength circulate under small E.M.F. 
 in the primary, then variations in its strength give rise to 
 very weak currents of exceedingly high E.M.F. in the 
 secondary. Conversely, if we cause to circulate in the 
 secondary weak currents under very high E.M.F., by their 
 fluctuations there will be generated in the primary strong 
 currents of small E.M.F. We do not in either case create 
 electric energy. Electric power is the product of two 
 factors, current and electro-motive force. The induction 
 coil enables us to increase one of these factors at the 
 expense of the other, and to transform electric energy in 
 form much as a mechanical power (e.g. a lever) enables us 
 to convert a quantity of work which consists of small 
 stress exerted through a great distance into a large stress 
 exerted through a small distance. 
 
 The transformer sometimes called a converter is 
 merely an induction coil used to change the relation of 
 the number of volts to the number of amperes of any 
 current. In a perfect transformer the number of watts in 
 the primary equals the number of watts in the secondary. 
 
 The Ruhmkorff coil as ordinarily used may be regarded 
 as a "step up" transformer from low potential to high 
 potential. But if the coil of long thin wire be used as the 
 primary, it becomes a "step down " transformer from high 
 potential to low potential. 
 
THE TRANSFORMER. 
 
 233 
 
 Figure 200 represents the coils of a transformer used in the incan- 
 descent lamp service, and Figure 201 represents the same enclosed in a 
 case. These transformers are usually supported on the street poles. 
 
 The transformer is applied in the welding of metals, i.e. to fuse the 
 ends of metals that are to be joined together, where many hundred or 
 
 Fig. 2OO. 
 
 Fig. 201. 
 
 even thousand amperes of current, and only a fraction of a volt, would 
 be required for an instant. 
 
 A still wider application of transformers is in the transmission of 
 electric power. Since the rate at which a current performs work equals 
 the volts times the amperes (Ex C), then according to Ohm's law the 
 work done per second by a current passing through a conductor equals 
 C2R. 1 That is, when the current strength is doubled there will be four 
 times as much energy transformed per second. We see, then, that to 
 transfer electric energy to a great distance it may be desirable to have a 
 high E.M.F. with a small current passing through the mains, and then to 
 reduce the E.M.F. and increase the current by a transformer at the place 
 where the energy is to be used. By this means the expense involved in 
 the copper conductors is much reduced. 
 
 For electric lighting in private houses transformers are used to bring 
 down the high potential of the mains to the safe limit of about 100 volts. 
 
 1 P (watts) Ex C. E=rCR (Ohm's formula); by substituting this value of E 
 the first formula becomes P = C 2 R. 
 
234 ENERGY OF ELECTRIC FLOW. 
 
 Section XVII. 
 
 SECONDARY OR STORAGE BATTERIES. 
 
 216. Reversibility of Electrolysis. If water be 
 
 decomposed for a time between neutral electrodes such 
 as platinum plates and then the battery or other generator 
 be withdrawn from the circuit and replaced by a sensitive 
 galvanometer, a deflection of the needle shows that a 
 transitory current flows in the opposite direction to the 
 primary or electrolyzing current. It is evident that the 
 electrolyzing current polarizes the electrodes in the 
 electrolyte, and that energy is thus stored in the cell. 
 Polarization is of the nature of a counter E.M.F. It is 
 precisely this polarization which we have to contend with 
 in nearly all voltaic cells, and which we seek to neutralize 
 by means of depolarizing substances. 
 
 Devices for thus storing up energy by electrolysis are 
 called storage or secondary batteries, and sometimes accumu- 
 lators. Note that the process is an electrical storage of 
 energy, not a storage of electricity. The energy of the 
 charging current is transformed into the potential energy 
 of chemical separation in the storage cell. When the 
 circuit of the storage cell is closed this energy is recon- 
 verted into the energy of an electric current in precisely 
 the same way as with an ordinary voltaic cell. 
 
 A common form of storage cell consists of large lead plates (for 
 electrodes) covered with a paste of red lead dipping into dilute sulphuric 
 acid. Connected with a dynamo the positive electrode becomes by 
 electrolysis peroxydized and the negative electrode deoxydized. 
 
 The storage battery offers a means of accumulating energy at one time 
 or place, and using it at some other time or place. For example, energy 
 
THERMO-ELECTRIC CURRENTS. 235 
 
 of a dynamo current may be stored during the daytime when the current 
 is not needed for illuminating purposes ; and this energy reconverted into 
 electric energy may feed incandescent lamps at night at any convenient 
 place; or the charged cells may be transported to lecture-halls, work- 
 shops, electric cars, etc., where powerful currents may be needed. 
 
 Section XVIII. 
 
 THERMO-ELECTRIC CURRENTS. 
 
 217. Heat Energy Transformed Directly into Elec- 
 tric Energy. 
 
 Experiment 148. Insert in one screw-cup of a sensitive 
 galvanometer an iron wire, and in the other cup a copper, or better, 
 a German-silver wire. Twist the other ends of the wire together, 
 and heat them at their junction in a flame; a deflection of the 
 needle shows that a current of electricity is traversing the wire. 
 Place a piece of ice at their junction ; a deflection in the opposite 
 direction shows that a current now traverses the wire in the opposite 
 direction. 
 
 These currents are named, from their origin, thermo- 
 electric. Apparatus required for the generation of these 
 currents is very simple, consisting merely of bars of two 
 different metals joined at one extremity, and some means 
 of raising or lowering the temperature at their junction, 
 or of raising the temperature at one extremity of the pair 
 and lowering it at the other ; for the electro-motive force, 
 and consequently the strength of the current, is nearly 
 proportional to the difference in temperature of the two 
 extremities of the pair. The strength of the current is 
 
236 ENERGY OF ELECTRIC FLOW. 
 
 also dependent, as in the voltaic pair, on the thermo- 
 electromotive force of the metals employed. 
 
 218. Thermo-Electric Batteries. A combination of 
 the metals antimony and bismuth makes the most effective 
 thermo-electric pair. The E.M.F. of such a pair is small 
 in comparison with that of a voltaic pair ; hence the greater 
 necessity of combining a large number of pairs with one 
 another in series. Such contrivances for generating 
 electric currents are called thermo-electric batteries. They 
 are seldom used, inasmuch as the best transform less than 
 one per cent of the heat energy employed. 
 
 Section XIX. 
 
 THE ELECTRIC LIGHT. 
 
 219. Electric Light : Voltaic Arc. If the terminals 
 of wires from a powerful dynamo or galvanic battery be 
 brought together, and then separated 1 or 2 mm , the 
 current does not cease to flow, but volatilizes a portion of 
 the terminals. The vapor formed becomes a conductor of 
 high resistance, and, remaining at a very high temperature, 
 produces intense light. The heat is so great that it fuses 
 the most refractory substances. Metal terminals quickly 
 melt and drop off like tallow, and thereby become so 
 far separated that the electro-motive force is no longer 
 sufficient for the increased resistance, and the light is 
 extinguished. Hence, pencils of carbon (prepared from 
 
THE ELECTRIC LIGHT. 
 
 237 
 
 the coke deposited in the distillation of coal inside of gas 
 retorts), being less fusible, are used for terminals. 
 
 The light is too intense to admit 
 of examination with the naked eye; 
 but if an image of the terminals be 
 thrown on a screen by means of a 
 lens or a pin-hole in a card, an 
 arch-shaped light is seen extending 
 from pole to pole, as shown in 
 Figure 202. 
 
 The heated air containing the 
 glowing particles of carbon forms 
 what is called the electric arc. 
 
 The larger portion of the light, 
 however, emanates from the tips of 
 the two carbon terminals, which are 
 heated to an intense whiteness, al- 
 though some emanates from the arc. 
 The -f- pole is hotter than the - 
 pole, as is shown by its glowing 
 longer after the current is stopped. Flg * 303 ' 
 
 The carbon of the -f- pole becomes volatilized, and the 
 light-giving particles are transported from the -(- pole 
 to the pole, forming a bridge of luminous vapor 
 between the poles. -What we see is not electricity, but 
 luminous matter. 
 
 22O. Electric Lamp. It is apparent that the + pole 
 is subject to a wasting away ; so also the pole wastes 
 away, but not so fast. At the point of the former a 
 conical-shaped cavity is formed, while around the point 
 of the latter warty protuberances appear. When, 
 
238 
 
 ENERGY OF ELECTRIC FLOW. 
 
 in consequence of the wearing away of 
 the -f- pole, the distance between the two 
 pencils becomes too great for the electric 
 current to span, the light goes out. 
 Numerous self-acting regulators for main- 
 taining a uniform distance between the 
 poles have been devised. Such an ar- 
 rangement (Fig. 203) is called an electric 
 lamp. The movements of the carbons are 
 accomplished automatically by the action 
 of the current itself. 
 
 221. Incandescent Electric Lamps. 
 
 The incandescent (or " glow ") light is 
 produced by the heating of some refractory 
 body to a state of incandescence by the 
 passage of an electric current. Carbon 
 filaments are now al- 
 most exclusively used 
 in incandescent lamps. 
 
 TThe filament of the 
 Edison lamp is carbon- 
 ized bamboo. It is es- 
 Fig. 203. sential that the oxygen 
 of the air be removed from these bulbs, 
 otherwise the carbons would be quickly 
 burned out ; hence very high vacua are 
 produced in the bulbs with a mercury 
 pump. 
 
 Figure 204 represents an Edison lamp. The 
 loop or filament of carbon, L, is joined at n n to 
 two platinum wires which pass through the closed end of the glass tube, 
 
ELECT ROT YPING AND ELECTROPLATING. 
 
 239 
 
 T. One of these wires is connected with the brass ring, B, and the 
 other with the brass button, D, at the bottom of the lamp. When the 
 lamp is screwed into its socket, connection is made with the line through 
 pieces of brass in the socket which are insulated from each other. 
 
 An Edison 16 candle-power lamp has a resistance (when hot) of about 
 
 ^Negative 
 
 Fig. 205. 
 
 140 ohms, the difference of potential at its terminals is about 110 volts, 
 and it requires a current of 0.75 ampere. Each lamp consumes about 
 one-tenth of a horse-power. 
 
 Incandescent lamps are usually introduced into the circuit in multiple 
 arc (Fig. 205), the current being equally divided by properly regulating 
 the resistance between all the lamps in the circuit. 
 
 Section XX. 
 
 ELECTROTYPING AND ELECTROPLATING. 
 
 222. Electrotypiiig". This book is printed from 
 electrotype plates. A molding-case of brass, in the 
 shape of a shallow pan, is filled to the depth of about 
 one-quarter of an inch with melted wax. A few pages 
 are set up in common type, and an impression or mold 
 is made by pressing these into the wax. The type is 
 
240 
 
 ENERGY OF ELECTRIC FLOW. 
 
 then distributed, and again used to set up other pages. 
 Powdered plumbago is applied by brushes to the surface 
 of the wax mold to render it a conductor. The case is 
 then suspended in a bath of copper sulphate dissolved in 
 dilute sulphuric acid. The pole of a galvanic battery 
 or dynamo machine is applied to it ; and from the -f- pole 
 is suspended in the bath a copper plate opposite and near 
 to the wax face. The salt of copper is decomposed by 
 
 Fig. 306. 
 
 the electric current, and the copper is deposited on the 
 surface of the mold. The sulphuric acid appears at the 
 -f- pole, and, combining with the copper of this pole, 
 forms new molecules of copper sulphate. When the 
 copper film has acquired about the thickness of an 
 ordinary visiting card, it is removed from the mold. This 
 shell shows distinctly every line of the types or engraving. 
 It is then backed, or filled in, with melted type-metal, to 
 give firmness to the plate. The plate is next fastened on 
 
THE ELECTRIC TELEGRAPH. 241 
 
 a block of wood, and thus built up type-high, and is now 
 ready for the printer. (For full directions which will 
 enable a pupil to electrotype in a small way, see the 
 author's Physical Technics.) 
 
 223. Electroplating". The distinction between elec- 
 troplating and electrotyping is that with the former the 
 metallic coat remains permanently on the object on which 
 it is deposited, while with the latter it is intended to be 
 removed. The processes are, in the main, the same. 
 The articles to be plated are first thoroughly cleaned and 
 suspended on the pole of a battery, and then a plate of 
 the same kind of metal that is to be deposited on the 
 given articles is suspended from the -f- pole (Fig. 206). 
 The bath used is a solution of a salt of the metal to be 
 deposited. The cyanides of gold and silver are generally 
 used for gilding and silvering. 
 
 Section XXI. 
 
 THE ELECTRIC TELEGRAPH. 
 
 224. Morse Telegraph. First, it should be under- 
 stood that, instead of two lines of wires (one to convey 
 the electric current far away from the battery, and another 
 to return it to the battery), if the distant pole be connected 
 with a large metallic plate buried in moist earth, or, still 
 better, with a gas or water pipe that leads to the earth, 
 and the other pole near the battery be connected in like 
 manner with the earth, so that the earth forms about one- 
 
242 ENERGY OF ELECTRIC FLOW. 
 
 half of the circuit, there will be needed only one wire to 
 connect telegraphically two places that are distant from 
 each other. 
 
 Let B (Fig. 207, Plate III) represent the message sender, or operator's 
 key ; Y, the message receiver. It may be seen that the circuit is broken 
 at B. Let the operator press his finger on the knob of the key. He 
 closes the circuit, and the electric current instantly fills the wire from 
 Boston to New York. It magnetizes a ; a draws down the lever 6, and 
 presses the point of a style on a strip of paper, c, that is drawn over a 
 roller. The operator ceases to press upon the key, the circuit is broken, 
 and instantly b is raised from the paper by a spiral spring, d. Let the 
 operator press upon the key only for an instant, or long enough to count 
 one : a simple dot or indentation will be made in the paper. But if he 
 press upon the key long enough to count three, the point of the style will 
 remain in contact with the paper the same length of time ; and, as the 
 paper is drawn along beneath the point, a short straight line is produced. 
 This short line is called a dash. These dots and dashes constitute the 
 alphabet of telegraphy. 
 
 225. The Sounder. If the strip of paper be removed, and the 
 style be allowed to strike the metallic roller, a sharp click is heard. 
 Again, when the lever is drawn up by the spiral spring it strikes a screw 
 point above (not represented in the figure), and another click, differing 
 slightly in sound from the first, is heard. A listener is able to distinguish 
 dots from dashes by the length of the intervals of time that elapse 
 between these two sounds. Operators generally read by ear, giving heed 
 to the clicking sounds produced by the strokes of a little hammer. A 
 receiver so used is called a sounder, a common form of which is repre- 
 sented in the lower central part of Plate III. 
 
 226. The Relay. The strength of the current is diminished, of 
 course, as the line is extended and the number of instruments in the 
 circuit is increased. Hence, a battery that would give a current sufficient 
 to move the parts of a single sounder audibly, on a short line, would not 
 move the same parts of many sounders on a long line with sufficient force 
 to render the message audible. Resort is had to relays. 
 
 In Figure 208, Plate III, R represents a relay and S a sounder. 
 Suppose a weak current arrives at New York from Boston, and has 
 sufficient strength to attract the armature of the relay at that station. 
 This, as may be seen by examination of the diagram, will close another 
 
Plate III. 
 
THE TELEPHONE. 243 
 
 short circuit, called the local circuit, and send a current from a local 
 battery located in the same office through the sounder at that station. 
 The sounder, being operated by a battery in a circuit of only a few feet 
 in length, delivers the message audibly. 
 
 Section XXII. 
 
 THE TELEPHONE. 
 
 227. Bell Telephone. Figure 209 represents a sectional and a 
 perspective view of this instrument. It consists of a steel magnet, A, 
 encircled at one extremity by a spool of very fine insulated wire, B, the 
 ends of which are connected with the binding screws D D. Immediately 
 in front of the magnet is a thin circular iron disk, E E. The whole is 
 enclosed in a wooden or rubber case, F. The conical-shaped cavity G 
 serves the purpose of either a mouth-piece or an ear-trumpet. There is 
 no difference between the transmitting and the receiving telephone ; con- 
 sequently, either instrument may be employed as a transmitter, while 
 the other serves as a receiver. Two magneto-telephones in a circuit are 
 virtually in the relation of a dynamo and a motor. The transmitter 
 being in itself a diminutive dynamo, no battery is required in the circuit. 
 Connect in circuit two such telephones, and the apparatus is ready for 
 use. 
 
 A person talking near the disk of the transmitter, throws it into rapid 
 vibration. The disk, being quite close to the magnet, is magnetized by 
 induction ; and as it vibrates, its magnetic power is constantly changing, 
 being strengthened as it approaches the magnet, and enfeebled as it 
 recedes. This fluctuating magnetic force will of course induce currents 
 in alternate directions in the neighboring coil of wire. These currents 
 traverse the whole length of the wirje, and so pass through the coil of the 
 distant instrument. When the direction of the arriving current is such 
 as to increase the intensity of the magnetic field of the receiver, the 
 magnet attracts the iron disk in front of it more strongly than before. 
 When the current is in the opposite direction, the disk is less attracted, 
 and flies back. Hence the disk of the receiving telephone is forced to 
 repeat whatever movement is imparted to the disk of the transmitting 
 
244 
 
 ENERGY OF ELECTRIC FLOW. 
 
 telephone. The vibrations of the former disk become sound in the same 
 manner as the vibrations of a tuning-fork or of the head of a drum. 
 
 The above is a description of the original and simplest form of the 
 Bell telephone. It is apparent that the original energy (i.e. that of the 
 
 Fig. 3O9. 
 
 voice) applied at the transmitter must, during its successive transforma- 
 tions and especially during its transmission in the form of electric energy 
 through large resistances, become very much enfeebled, so that when it 
 reappears as sound, the sound is quite feeble and frequently inaudible. 
 
 Fig. 21O. 
 
 The first grand improvement on the original consists in introducing a 
 battery into the circuit, and so arranging that the voice, instead of being 
 obliged to generate currents, shall be required only to render a current, 
 already generated by a voltaic cell, fluctuating or undulating. 
 
THE TELEPHONE. 
 
 245 
 
 The fluctuations are caused by a varying resistance in the circuit. 
 The pupil must have learned by experience ere this that the effect of a 
 loose contact between any two parts of a circuit is to increase the 
 resistance and thereby weaken the current; but the effect of a slight 
 variation in pressure is especially noticeable when either or both of the 
 parts are carbon. Figure 210 illustrates a simple telephonic circuit in 
 which are included a variable resistance transmitter, T, and a battery, B. 
 One of the electrodes, a platinum point, touches the center of the trans- 
 
 Fig. 313. 
 
 mitter disk; the other electrode, a carbon 
 button, a, is pressed by a spring gently 
 against the platinum point. Every vibration 
 of the disk, however minute, causes a varia- 
 tion in the pressure between the two elec- 
 trodes and a corresponding variation in the 
 circuit resistance. As the resistance changes, 
 so changes the current strength, and thus the 
 current is rendered undulatory. 
 
 The next improvement of considerable 
 importance consists in* the adoption of an 
 induction coil (C, Fig. 210), which, we have 
 learned, may produce a current of much 
 greater electro-motive force than is possessed 
 by the original battery current. Since the 
 battery current traverses only a local circuit, 
 as may be seen by reference to Figure 210, a 
 single Leclanche" cell is generally sufficient to 
 operate it. The currents induced by the 
 fluctuating primary current traverse the line 
 
 wire and generate sonorous vibrations in the disk of the receiver K, in 
 
 the same manner as in the original telephone. 
 
 Figure 211 represents the entire telephonic apparatus required at any 
 
 single station. The box A contains a small hand-dynamo, such as is 
 
 Fig. 211. 
 
246 
 
 ENERGY OF ELECTRIC FLOW. 
 
 represented in Figure 212. A person turning the crank F generates a 
 current which rings a pair of electric bells G, both at his own and at a 
 distant station, and thus attracts attention. He next takes the receiver 
 B off the supporting hook and places it at his ear. When the weight is 
 removed from the hook, the hook rises a little and throws the dynamo 
 and bells out of the circuit, and at the same time introduces the receiver 
 B, the transmitter C, and the battery D, so that the circuit stands as 
 represented in Figure 210. The box C contains the induction coil. E is 
 a "lightning arrester." 
 
 In Figure 212a, A and B are buttons of carbon ; the former is attached 
 to a sounding-board of thin pine wood, the latter to a steel spring C, and 
 both are connected in circuit with a battery and a telephone used as a 
 receiver. The spring presses B against A, and any slight jar will cause a 
 variation in the pressure and corresponding variations in the current 
 strength. 
 
 A- 
 
 Fig. 312a. 
 
 By means of this instrument, called the microphone, any little sounds, 
 as its name indicates, such as the ticking of a watch or the footfall of an 
 insect, may be reproduced at a considerable distance, and be as audible 
 as though the original sounds were made close to the ear. 
 
THE TELEPHONE. 247 
 
 REVIEW EXERCISES. 
 
 1. How is a body charged by conduction ? How by induction ? 
 
 2. In a circuit of large resistance which would be more sensitive, 
 a long-coil or a short-coil galvanometer ? Why ? 
 
 3. How does the condition of a wire and its surroundings when 
 traversed by a current differ from that of a wire when not traversed 
 by a current ? 
 
 4. What conditions are prerequisite to a current of electricity ? 
 
 5. If a current be sent through the armature of a dynamo, what 
 happens? Why? 
 
 6. Upon what conditions does the strength of a current furnished 
 by a dynamo depend ? 
 
 7. You wish to make an electro-magnet of an iron rod with a 
 certain end as an N-pole. Explain the method by a diagram. 
 
 8. What is the strength of a current which falling 15 volts yields 
 .002 horse-power ? 
 
 9. When would you wind an electro-magnet with fine wire ? 
 
 10. If the difference of potential between the terminals of an arc 
 lamp supplied with a 10-ampere current be 50 volts, what is the 
 power consumed in the lamp? 
 
 11. A difference of potential of 5.5 volts is maintained at the 
 terminals of a wire of 0.1 ohm resistance, (a) What current flows ? 
 (&) What is the power of the current ? 
 
 12. To which electrode must an article to be electroplated be 
 attached ? Why ? 
 
 13. Explain, in accordance with Ampere's theory of magnetism, 
 the deflection of a magnetic needle by an electric current. 
 
 14. What length of copper wire .012 in. in diameter will offer a 
 resistance of 1 ohm ? 
 
 15. What currents are difficult to insulate ? Why ? 
 
 16. Upon what does the E.M.F. of a dynamo depend 
 
 17. (a) How does a storage cell differ from a voltaic cell? 
 (6) What can you say as to the direction of the current produced 
 by each? 
 
 18. What pole of an electro-magnet is that where the direction of 
 the current in the coil is anti-clockwise ? 
 
CHAPTER VII. 
 SOUND. 
 
 Section I. 
 
 STUDY OF VIBRATIONS AND WAVES. 
 
 The subjects of Sound-waves and Light-waves, which we are about to 
 study, have two important characteristics in common that distinguish them 
 from the subjects already studied. First, each of them affects its peculiar 
 organ of sense, the ear or the eye. Secondly, both originate in vibrating 
 bodies, and reach us only by the intervention of some medium capable 
 of being set in vibration. 
 
 228. Period of Vibration. 
 
 Experiment 149. Suspend an iron ball by a string, as in Experi- 
 ment 71, cause it to vibrate, and, watch in hand, ascertain the num- 
 ber of vibrations made in a given number of seconds; e.g. 60 seconds. 
 Then, remembering that all the vibrations are made in equal intervals 
 of time, ascertain the period of vibration of this pendulum ; i.e. the 
 time it takes to make each vibration, using the formula 
 
 s 
 
 <=-> 
 n 
 
 in which t = the period, and n = the number of vibrations made in s 
 seconds. 
 
 229. Direction of Vibration. 
 
 Experiment 150. Grasp one end of a small rod or yardstick in 
 a vice, pull the free end one side, and set it in vibration. Pluck a 
 string of a piano or violin. Note that the motions of all the bodies 
 which thus far we have caused to vibrate are at right angles to their 
 length. These are called transverse vibrations. 
 
 Experiment 151. Hang up a spiral spring or elastic cord with a 
 small weight attached at the lower end; lift the weight, and, drop- 
 
STUDY OF VIBRATIONS AND WAVES. 249 
 
 ping it, notice that the cord vibrates lengthwise. This is a case of 
 Longitudinal vibration. There may also be torsional vibrations, for ex- 
 ample children often amuse themselves by producing these by twist- 
 ing a window cord and tassel. 
 
 230. Propagation of Vibration ; Waves. 
 
 Experiment 152. Take a rubber cord about the size of an ordi- 
 nary lead'pencil and 12 feet long. Attach at intervals a few glass 
 beads and fasten one end of the cord to the wall of the room. Hold 
 the free end in the hand and draw the cord out so as to be nearly 
 horizontal. By quick movements of the hand in a horizontal or a 
 vertical direction set this end in vibration. Notice that these vibra- 
 tions are communicated from point to point along the cord, and that 
 each point in the cord successively goes through a vibration precisely 
 similar to that held in the hand. Fix the eyes upon any one of the 
 beads ; it simply vibrates transversely. Observe the cord as a whole ; 
 waves traverse it from end to end, but it is easy to see that it is only 
 a form that traverses it ; the beads and all other points of the cord 
 move transversely. These successive transverse movements give rise 
 to the wave-line into which the cord is thrown. 
 
 231. Wave-Length and Amplitude. Imagine an in- 
 stantaneous photograph taken of the cord along which con- 
 tinuous waves are passing. It 
 
 would appear much like the 
 
 curved line CD (Fig. 213). c 
 
 This curved line represents 
 
 what is known as a simple 
 
 wave-line. The distance from any vibrating point to the 
 
 nearest point which is in exactly the same stage of its 
 
 vibration is called a wave-length, as wx, uv, or en. 
 
 The distance between the extreme positions of a vibrat- 
 ing point or the length of its journey is called the ampli- 
 tude of the wave or the amplitude of vibration. 
 
 232. Reflection of Waves ; Interference. 
 Experiment 153. Stretch the cord horizontally between two 
 
250 
 
 SOUND. 
 
 elevated points, and pluck it with the hand or strike it with a stick 
 near one end, and send along it a single pulse, forming a crest on the 
 
 rope (A, Fig. 214). This 
 travels to the other end, 
 and there we see it re- 
 flected and inverted (B). 
 Experiment 154. 
 Just at the instant of re- 
 flection, start a second 
 crest ; these two, the crest 
 and the returning inverted 
 
 214 - crest or trough (C), are 
 
 now travelling along the rope in opposite directions, and must meet 
 at some point. This point will be urged upward by the crest and 
 downward by the trough, and so its motion will be due to the differ- 
 ence of the two forces. 
 
 Experiment 155. Send along the rope, first a trough, then a 
 crest;. now two crests (D) will meet near the middle of the rope, and 
 the motion here will be due to two forces acting in the same direc- 
 tion, so that the resulting crest will be greater than either of the origi- 
 nal ones. 
 
 This action on a single point of two pulses, or two trains 
 of waves, no matter if from different sources, is termed 
 interference. The resulting motion may be greater or less 
 than that due to either pulse alone, or it may be zero. 
 
 233. Stationary Vibrations, Nodes, etc. 
 
 Experiment 156. Hold one end of the cord while the other is 
 fixed, and send along it a regular succession of equal pulses from the 
 
 Fig. 315. 
 
 vibrating hand; it will be easy, by varying the tension and rate a 
 little, to obtain a succession of hazy spindles (Fig. 215), separated by 
 points that are nearly or quite at rest. Unlike the earlier experiments, 
 
STUDY OF VIBRATIONS AND WAVES. 251 
 
 the waves here do not appear to travel along the tube ; yet in reality 
 they do traverse it. The deception is caused by stationary points being 
 produced by the interference of the advancing and retreating waves. 
 
 This interference of direct and reflected waves gives 
 rise to the important class of so-called stationary vibrations. 
 The points of least motion, as a and 6, are called nodes ; 
 the points of greatest motion, c and d, are called antinodes ; 
 and the portion of the rope between two nodes, as ab^ is 
 a ventral segment. 
 
 234. L/ongitudinal Waves. 
 
 Experiment 157. Figure 216 represents a brass wire wound in 
 the form of a spiral spring, about 12 feet long. Attach one end to a 
 cigar-box, and fasten the box to a table. Hold the other end H of 
 the spiral firmly in one hand, and with the other hand insert a knife- 
 blade between the turns of the wire, and quickly rake it for a short 
 distance along the spiral toward the box, thereby crowding closer 
 together for a little distance (B) the turns of wire in front of the 
 hand, and leaving 
 the turns behind 
 pulled wider apart 
 (A) for about an 
 
 equal distance. The Fi s- 
 
 crowded part of the spiral may be called a condensation, and the 
 stretched part a rarefaction. The condensation, followed by the rare- 
 faction, runs with great velocity through the spiral, strikes the 
 box, producing a sharp thump ; ic reflected from the box to the 
 hand, and from the hand again to the box, producing a second 
 thump ; and by skilful manipulation three or four thumps will be 
 produced in rapid succession. If a piece of twine be tied to some 
 turn of the wire, it will be seen, as each wave passes it, to receive a 
 slight jerking movement forward and backward in the direction of 
 the length of the spiral. 
 
 How is energy transmitted through the spring so as to 
 deliver the blow on the box ? Certainly not by a bodily 
 movement of the spiral as a whole, as might be the case if 
 it were a rigid rod. The movement of the twine shows 
 
252 SOUND. 
 
 that the only motion which the coil undergoes is a vibra- 
 tory movement of its turns. Here, as in the case of 
 water-waves, energy is transmitted through' a medium by 
 the transmission of vibrations. 
 
 There are two important distinctions between these 
 waves and those which we have previously studied : the 
 former consist of condensations and rarefactions; the 
 latter, of elevations and depressions. In the former, the 
 vibration of the parts is in the same line with the path 
 of the wave, and hence these are called longitudinal waves ; 
 in the latter, the vibration is across its path ; they are 
 therefore called transverse waves. 
 
 A wave cannot be transmitted through an inelastic soft 
 iron spiral. Elasticity is essential in a medium, that it may 
 transmit waves composed of condensations and rarefactions ; 
 and the greater the elasticity, the greater the facility and 
 rapidity with which a medium transmits waves. 
 
 235. Air as a Medium of Wave-Motion. May not 
 
 air and other gases, which are elastic, serve as media for 
 waves ? 
 
 Fig. 317. 
 
 Experiment 158. Place a candle flame at the orifice a of the 
 tube (Fig. 217), and strike the table a sharp blow with a book near 
 the orifice b. Instantly the candle flame is quenched. The body of 
 air in the tube serves as a medium for transmission of motion to the 
 candle. 
 
 Was it the motion of a current of air through the tube, a rninia- 
 
STUDY OF VIBRATIONS AND WAVES. 253 
 
 ture wind, or was it the transfer of a vibratory motion ? Burn touch- 
 paper 1 at the orifice b, so as to fill this end of the tube with smoke, 
 and repeat the last experiment. 
 
 Evidently, if the body of the air is moved along through the tube, 
 the smoke will be carried along with it. The candle is blown out as 
 before, but no smoke issues from the orifice a. It is clear that there is no 
 translation of material particles from one end to the other, nothing 
 like the flight of a rifle bullet. The candle flame was struck by some- 
 thing like a pulse of air, not by a wind. 
 
 236. How a Wave is propagated through a Medium. 
 
 The effect of applying force with the hand to the spiral 
 spring is to produce in a certain section (B, Fig. 216) of 
 the spiral a crowding together of the turns of wire, and 
 at A a separation ; but the elasticity of the spiral instantly 
 causes B to expand, the effect of which is to produce a 
 crowding together of the turns of wire in front of it, in 
 the section C, and thus a forward movement of the con- 
 densation is made. At the same time, the expansion of B 
 causes a filling up of the rarefaction at A, so that this 
 section is restored to its normal state. This is not all: 
 the folds in the section B do not stop in their swing when 
 they have recovered their original position, but, like a 
 pendulum, swing beyond the position of rest, thus produc- 
 ing a rarefaction at B, where immediately before there 
 was a condensation. Thus a forward movement of the 
 rarefaction is made, and thus a pulse or wave is trans- 
 mitted with uniform velocity through a spiral spring, air, 
 or any elastic medium. 
 
 237. Graphical Method of Studying Vibrations. 
 Experiment 159. Attach, by means of sealing-wax, a bristle or 
 
 a fine wire to the end of one of the prongs of a large steel fork (like 
 
 1 To prepare touch-paper, dissolve about a teaspoonful of saltpetre in a half-teacupful 
 of hot water, dip unsized paper in the solution, and then allow it to dry. The paper 
 produces much smoke in burning, but no flame. 
 
254 SOUND. 
 
 a tuning-fork, but larger) called a diapason. Set the fork in vibra- 
 tion, and quickly draw the point of the bristle lightly over a smoked 
 
 glass (A, Fig. 218). A 
 beautiful wavy line will be 
 traced on the glass, each 
 
 Fig. 318. . 
 
 wave corresponding to a 
 vibration of the prong when vibrating as a whole. 
 
 Next, tap the fork, near its stem, on the edge of a table, and trace 
 its vibrations on a smoked glass as before. You will generate a 
 similar set of waves, but, running over these, is another set, of much 
 shorter period, like No. 3 of Figure 233, showing that the prong 
 vibrates, not only as a whole, but in parts. The serrated wavy line 
 produced represents the resultant of the combined vibrations, and 
 may be called a complex wave-line. 
 
 QUESTIONS. 
 
 1. In what kind of motion does all wave-motion originate ? 
 
 2. Watch the waves of the ocean moving landward; what is it 
 that advances? 
 
 3. Throw a cord into wavy motion by the movement of your 
 hand ; upon what do the number and the length of the waves which 
 traverse the cord at any given time depend? 
 
 4. How is a node produced ? 
 
 5. How do the vibrations in longitudinal waves differ from the 
 vibrations in transverse waves? 
 
 6. Are the vibrations in air-waves longitudinal or transverse? 
 
 Section II. 
 
 SOUND-WAVES. 
 
 238. How Sound-waves Originate. Listen to a 
 sounding church-bell. It produces a sensation ; it is 
 heard. The ear is the organ through which the sensation 
 
SOUND-WAVES. 255 
 
 of hearing is produced. The bell is at such a distance 
 that it cannot act directly on the ear ; yet something 
 must act on the ear, and it must be the bell which causes 
 that something to act. 
 
 Commencing at the origin of sound, let the first in- 
 quiry be, How does a sounding body differ from a silent 
 body? 
 
 Experiment 160. Strike a bell or a glass bell-jar, and touch the 
 edge with a small cork ball suspended by a thread ; you not only hear 
 the sound, but, at the same time, you see a tremulous motion of the 
 ball, caused by a motion of the bell. Touch the bell gently with a 
 finger, and you feel a tremulous motion. Press the hand against the 
 bell ; you stop its vibratory motion, and at that instant the sound 
 ceases. Strike the prongs o'f a tuning-fork, press the stem against a 
 table : you hear a sound. Thrust, the ends of the prongs just beneath 
 the surface of water ; the water is thrown off in a fine spray on either 
 side of the vibrating fork. Watch the strings of a piano, guitar, or 
 violin, or the tongue of a jews-harp, when sounding. You can see that 
 they are in motion. 
 
 Sound-waves originate in a vibrating body. 
 
 239. How Sound-waves Travel. How can a bell, 
 sounding at a distance, affect the ear? If the bell while 
 sounding possesses no peculiar property except motion, 
 then it has nothing to communicate to th'e ear but motion. 
 But motion can be communicated by one body to another 
 at a distance only through some medium. 
 
 Do sound-waves require a medium for their communi- 
 cation ? 
 
 Experiment 161. Lay a thick tuft of cotton-wool on the plate 
 of an air-pump, and on this, face downward, place a loud-ticking 
 watch, and cover with the receiver. Notice that the receiver, inter- 
 posed between the watch and your ear, greatly diminishes the sound, 
 or interferes with the passage of something to the ear. Take a few 
 strokes of the pump and listen ; the sound is more feeble, and con- 
 
256 SOUND. 
 
 tinues to grow less and less distinct as the exhaustion progresses, 
 until either no sound can be heard when the ear is placed close to the 
 receiver, or an extremely faint one, as if coming from a great dis- 
 tance. The removal of air from a portion of the space between the 
 watch and your ear destroys the sound. Let in the air again, and the 
 sound is restored. 
 
 Sound-waves cannot travel through a vacuum, i.e. with- 
 out a medium. 
 
 Boys often amuse themselves by inflating paper bags, 
 and with a quick blow bursting them, producing with 
 each a single loud report. First the air is suddenly and 
 greatly condensed by the blow, and the bag is burst ; the 
 air now, as suddenly and with equal force, expands, and 
 by its expansion condenses the air for a certain distance 
 all around it, leaving a rarefaction where just before had 
 been a condensation. If many bags were burst at the 
 same spot in rapid succession, the result would be that 
 alternating shells of condensation and rarefaction would 
 be thrown off, all having a common center, enlarging as 
 they advance, like the waves formed by stones dropped 
 into water ; except that, in this case, the waves are not 
 like rings, but hollow globes ; not circular, but spherical. 
 In this manner sound-waves produced by the vibration 
 of a sounding body travel through the air. 
 
 As a wave advances, each individual air-particle con- 
 cerned in its transmission performs a short excursion to 
 and fro in the direction of a straight line radiating from 
 the center of the shells or hollow globes. A sound-wave 
 travels its own length in the time that a particle occupies 
 in going through one complete vibration so as to be ready 
 to start again. 
 
 Experiment 162. Take a strip of black cardboard 4.5 inches X 
 1 inch. Cut a slit about one-sixteenth of an inch wide lengthwise 
 and centrally through the strip nearly, from end to end. Place the 
 
SOUND-WAVES. 
 
 257 
 
 slit over the dotted line at the bottom of Figure 219, and draw the 
 book along underneath in the direction of the arrow. Imagine that 
 the short white dashes seen through the slit represent a series of air- 
 particles, and the slit itself represents the direction in which a series 
 of sound-waves are travelling. It will be seen that each air-particle 
 moves a little to and fro in the direction in which the sound travels 
 and comes back to its starting-point; but the condensations and rare- 
 factions, represented by a group (half a wave-length) of dots being 
 alternately closer together or farther apart, are transmitted through 
 the whole series of air-particles. 
 
 Fig. 219. 
 
 240. What Sound Is. Sound is a sensation caused 
 usually by waves of air beating upon the organ of hearing. 
 
 241. Solids and Liquids as Media for transmitting- 
 Sound-waves. 
 
 Experiment 163. Lay a watch, with its back downward, on a 
 
258 SOUND. 
 
 long board (or table), near to one of its ends, and cover the watch 
 with loose folds of cloth till its ticking cannot be heard through the 
 air in any direction at a distance equal to the length of the board. 
 Now place the ear in contact with the farther end of the board, and 
 you will hear the ticking of the watch very distinctly. 
 
 Experiment 164. Place one end of a long pole on a cigar box, 
 and apply the stem of a vibrating diapason to the other end ; the 
 sound-vibrations will be transmitted through the pole to the box, and 
 a loud sound will be given out by the box, as though that, and not the 
 tuning-fork, were the origin of the sound. 
 
 Experiment 165. Place the ear to the earth, and listen to the 
 rumbling of a distant carriage ; or put the ear to one end of a long 
 stick of timber, and let some one gently scratch the other end with a 
 pin. 
 
 Solids and liquids, as well as gases, transmit sound- 
 vibrations. 
 
 Section III. 
 
 VELOCITY OF SOUND-WAVES. 
 
 242. The Velocity of Sound-waves tlepends on the 
 Elasticity and Density of the Medium. The relation 
 of velocity to the density and elasticity of gases, as ascer- 
 tained by careful experiment, is as follows: the velocity 
 of sound-waves in gases is directly proportional to the square 
 root of their elasticity, and inversely proportional to the 
 square root of their respective densities. 
 
 The velocity of sound-waves in air at C. is (332.4 m ) 
 nearly 1091 feet per second. The velocity increases nearly 
 two feet for each degree centigrade. At the temperature 
 of 16 C. (60 F.) we may reckon the velocity of sound- 
 waves at about (342 m ) 1125 feet per second. 
 
REFLECTION OF SOUND-WAVES. ECHOES. 259 
 
 The greater density of solids and liquids, as compared 
 with gases, tends, of coarse, to diminish the velocity of 
 sound-waves ; but their greater incompressibility more 
 than compensates for the decrease of velocity occasioned 
 by the increase of density. As a general rule, solids are 
 more incompressible than liquids; hence, sound-waves 
 generally travel faster in the former than in the latter. 
 For example, sound-waves travel in water about 4 times 
 as fast as in air, and in iron and glass 16 times as fast. 
 
 Section IV. 
 
 EEFLECTION OF SOUND-WAVES. ECHOES. 
 
 243. Reflection. In the experiment with the spiral 
 spring, waves were reflected from the box to the hand, and 
 from the hand to the box. When a sound-wave meets an 
 obstacle in its course, it is reflected; and the sound re- 
 sulting from the reflected waves is often called an echo, 
 or, when they are many times reflected sb that the sound 
 becomes nearly contin- 
 uous, a reverberation. 
 
 244. Sound-waves 
 reflected by Concave 
 Mirrors. 
 
 Experiment 166. Place 
 
 a watch at the focus A (Fig. Flg * 
 
 220) of a concave mirror G. At the focus B of another concave 
 mirror H, place the large opening of a small tunnel, and with a 
 rubber connector attach the bent glass tube C to the nose of the 
 
260 SOUND. 
 
 tunnel. The extremity D being placed in the ear, the ticking of the 
 watch can be heard very distinctly, as though it were somewhere near 
 the mirror H. Though the mirrors be 12 feet apart, the sound will 
 be louder at B than at an intermediate point E. 
 
 How is this explained ? Every air-particle in a certain 
 radial line, as Ac, receives and transmits motion in the 
 direction of this line ; the last particle strikes the mirror 
 at , and being perfectly elastic, bounds off in the direc- 
 tion cc\ communicating its motion to the particles in this 
 line. At c' a similar reflection gives motion to the air 
 particles in the line c'B. In consequence of these two re- 
 flections, all divergent lines of motion as Ad, Ae, etc., that 
 meet the mirror G, are there rendered parallel, and after- 
 wards rendered convergent at the mirror H. The prac- 
 tical result of the concentration of this scattering energy 
 is, that a sound of great intensity is heard at B. The 
 points A and B are called the foci of the mirrors. The 
 front of the wave as it leaves A is convex, in passing 
 from G to H it is plane, and from H to B concave. If 
 you fill a large circular tin basin with water, and strike 
 one edge with a knuckle, circular waves with concave 
 fronts will close in on the centre, heaping up the water 
 at that point. 
 
 Long u whispering-galleries " have been constructed on this principle. 
 Persons stationed at the foci of the concave ends of the long gallery can 
 carry on a conversation in a whisper which persons between cannot hear. 
 
 The external ear is a wave-condenser. The hand held concave behind 
 the ear, by its increased surface, adds to its efficiency. An ear-trumpet, 
 by successive reflections, serves to concentrate, at the small orifice open- 
 ing into the ear, the sound-waves that enter at the large end. 
 
INTENSITY OF SOUND. 261 
 
 Section V. 
 
 INTENSITY OF SOUND. 
 
 245. Intensity depends on the Amplitude of Vibra- 
 tion. Gently tap the prongs of a tuning-fork and dip 
 them into water, the water is scarcely moved by them ; 
 increase the force of the blow, the vibrations become 
 wider, and the water spray is thrown with greater force 
 and to a greater distance. The same thing occurs when the 
 fork vibrates in the air ; though we do not see the air-par- 
 ticles as they are batted by the moving fork, yet we feel the 
 effects as a sound sensation, and we judge of their energy 
 by the intensity of the sensation which they produce. 
 Loudness of sound refers to the intensity of a sensation. 
 We have no standard of measurement for a sensation, so 
 we are compelled to measure the intensity of the sound- 
 wave, knowing at the same time that loudness is not pro- 
 portional to this intensity. Unfortunately, the expressions 
 loudness and intensity of sound-wave are often inter- 
 changed. The intensity of a vibration is measured by 
 the energy of the vibrating particle. It is clear that if 
 the amplitude of vibration of a particle is doubled while 
 its period remains constant, its velocity is doubled, and 
 its energy is increased fourfold. Hence, (1) measured 
 mechanically, the intensity of a sound-wave is proportional 
 to the square of the amplitude of the vibrations of the 
 vibrating body. 
 
 246. Intensity depends upon the Density of the Me- 
 dium. In the experiment with the watch under the 
 receiver of the air-pump (page 255), the sound grew 
 
262 SOUND. 
 
 feebler as the air became rarer. Aeronauts are obliged to 
 exert themselves more to make their conversation heard 
 when they reach great hights than when in the denser 
 lower air. (2) The intensity of sound-waves increases with 
 the density of the medium in which they are produced. 
 
 247. Intensity depends on Distance. It is a mat- 
 ter of e very-day observation that the loudness of a sound 
 diminishes very rapidly as the distance from the source 
 of the waves to the ear increases. As a sound-wave ad- 
 vances in an ever-widening sphere, a given amount of 
 energy becomes distributed over an ever-increasing sur- 
 face ; and as a greater number of particles partake of the 
 motion, the individual particles receive proportionately 
 less energy ; hence it follows, as a consequence of the 
 geometrical truth, that " the surface of a sphere varies 
 as the square of its radius," - that (3) the intensity of 
 a sound-wave varies inversely as the square of the distance 
 from its source. For example, if two persons, A and B, 
 are respectively 500 and 1000 rods from a gun when it 
 is discharged, the waves that reach A will be four times 
 as intense as the same when they reach B. 
 
 248. Speaking-Tubes. 
 
 Experiment 167. Place a watch at one end of the long tin tube 
 (Fig. 217), and the ear at the other end. The ticking sounds very 
 loud, as though the watch were close to the ear. 
 
 Long tin tubes, called speaking-tubes, passing through many apartments 
 in a building, enable persons at the distant extremities to carry on conver- 
 sation in a low tone of voice, while persons in the various rooms through 
 which the tube passes hear nothing. The reason is that the sound-waves 
 which enter the tube are prevented from expanding, consequently the 
 intensity of sound is not affected by distance, except as its energy is wasted 
 by friction of the air against the sides of the tube. 
 
REENFORCEMENT OF SOUND-WAVES. 
 
 263 
 
 Section VI. 
 
 REENFOKCEMENT OF SOUND-WAVES AND INTERFERENCE 
 OF SOUND-WAVES. 
 
 249. Reenforcement of Sound-waves. 
 
 Experiment 168. Set a diapason in vibration ; you can scarcely 
 hear the sound unless it is held near the ear. Press the stem against 
 a table ; the sound rings out loud, but the waves seem to proceed 
 from the table. 
 
 When only the fork vibrates, the prongs presenting 
 little surface cut their way through the air, producing very 
 slight condensations, and consequently waves of little in- 
 tensity. When the fork rests upon the table, the vibrations 
 are communicated to the table ; the table with its larger 
 surface throws a larger mass of air into vibration, and 
 thus greatly intensifies the sound-waves. The strings of 
 the piano, guitar, and violin 
 owe as much of their loud- 
 ness of sound to their elas- 
 tic sounding-boards, as the 
 fork does to the table. A 
 
 25O. Keenforcement by 
 Bodies of Air ; Resona- 
 tors. 
 
 Experiment 169. Take a 
 glass tube A (Fig. 219), 16 inches 
 long and 2 inches in diameter; 
 thrust one end into a vessel of 
 water C, and hold over the other 
 end a vibrating diapason B that makes (say) 256 vibrations in a 
 second. Gradually lower the tube into the water, and when it reaches 
 
 Fig. 331. 
 
264 SOUND. 
 
 a certain depth, i.e. when the column of air oc attains a certain length, 
 the sound of the fork becomes very loud; continuing to lower the 
 tube, the sound rapidly dies away. 
 
 Columns of air are thus found to serve, as well as sound- 
 ing-boards, to reenforce sound-waves. The instruments 
 which enclose the columns of air are called resonators. 
 Unlike sounding-boards, they can respond loudly to only 
 one tone, or to a few tones of widely different pitch. 
 
 How is this reinforcement effected ? When the prong 
 a moves from one extremity of its arc a' to the other a", 
 it sends a condensation down the tube ; this condensation 
 striking the surface of the water, is reflected by it up the 
 tube. Now suppose that the front of this reflected con- 
 densation should just reach the prong at the instant it is 
 starting on its retreat from a" to a' ; then the reflected 
 condensation will conspire with the condensation formed by 
 the prong in its retreat to make a greater condensation in 
 the air outside the tube. Again, the retreat of the prong 
 from a' 1 to a' produces in its rear a rarefaction, which also 
 runs down the tube, is reflected, and will reach the prong 
 at the instant it is about to return from a' to a", and to 
 cause a rarefaction in its rear; these two rarefactions 
 moving in the same direction conspire to produce an in- 
 tensified rarefaction. The original sound-waves thus com- 
 bine with the reflected, to produce resonance ; but this can 
 only happen when the like parts of each wave coincide 
 each with each ; for if the tube were somewhat longer or 
 shorter than it is, it is plain that condensations would 
 meet rarefactions in the tube, and tend to destroy one 
 another. 
 
 The loudness of sound of all wind instruments is due to the resonance 
 of the air contained within them. A simple vibratory movement at the 
 mouth or orifice of the instrument, scarcely audible in itself, such as the 
 
KEENFORCEMENT OF SOUND-WAVES. 
 
 265 
 
 vibration of a reed in reed pipes, or a pulsatory movement of the air pro- 
 duced by the passage of a thin sheet of air over a sharp wooden or metallic 
 edge, as in organ pipes, flutes, and flageolets, or more simply still by the 
 friction of a gentle stream of breath from the lips sent obliquely across 
 the open end of a closed tube, bottle, or pen-case, is. sufficient to set the 
 large body of enclosed air in the instrument into vibration, and thus re- 
 enforced, the sound becomes audible at long distances. 
 
 Experiment 170. Attach a rose gas-burner A (Fig. 222) to a 
 metal gas-tube about l m in length, and connect this by a rubber tube 
 with a gas-burner. Light the gas at the rose burner, 
 and you will hear a low, rustling noise. Remove the 
 conical cap from the long tin tube (Fig. 217), support 
 the tube in a vertical position, and gradually raise the 
 burner into the tube ; when it reaches a certain point 
 not far up, the body of air in the tube will catch up 
 the vibrations, and give out deafening sound-waves 
 that will shake the walls and furniture in the room. 
 
 t 
 
 251. Measuring Wave-Lengths and the 
 Velocity of Sound-waves. Experiments 
 like that described on page 263 enable us read- 
 ily to measure the wave-length produced by a 
 fork that makes a given number of vibrations 
 in a second, and also to measure the velocity 
 of sound-waves. It is evident that if a con- rig. 222. 
 densation generated by the prong of the fork in which its 
 forward movement from a' to a" (Fig. 221) met with no 
 obstacle, its front, meantime, would traverse the distance 
 od, or twice the distance oc ; hence the length of the 
 condensation is the distance od. But a condensation is 
 only one-half of a wave, and the passage of the prong 
 from a f to a" is only one-half of a vibration ; conse- 
 quently the distance od is one-half of a wave-length, and 
 the distance oc is one-fourth of a wave-length. The 
 measured distance of oc in this case is about 13.13 inches ; 
 hence the length of wave produced by a C'-fork making 
 
266 
 
 SOUND. 
 
 256 vibrations in a second is (13.13 inches x 4 =) 52.5 
 inches = 4.38 feet. And since a wave from this fork 
 travels 4.38 feet in ^TG of a second, it will travel in an 
 entire second (4.38 feet X 256 =) 1121 feet. The dis- 
 tance oc varies with the temperature of the air. 
 
 It is evident that the three quantities expressed in the 
 formula 
 
 velocity 
 
 wave-length = 
 
 number of vibrations 
 
 bear such a relation to one another that if any two are 
 known, the remaining quantity can be computed. It 
 will further be observed that with a given velocity the wave- 
 length varies inversely as the number of vibrations ; i.e. the 
 greater the number of vibrations per second, the shorter 
 the wave-length. 
 
 252. Interference of Sound- Waves. 
 
 Experiment 171. Hold a vibrating diapason over a resonance- 
 jar as in Figure 223. Roll the 
 diapason over slowly in the fin- 
 gers. At certain points, a quarter 
 of a revolution apart, when the 
 diapason is in an oblique posi- 
 tion with reference to the edge 
 of the jar as represented in the 
 figure, the reinforcement from 
 the tube almost entirely dis- 
 appears, but reappears at the 
 intermediate points. Return to 
 the position where there is no 
 resonance, and enclose in a loose 
 roll of paper, the prong farthest 
 from the tube, without touching the diapason, so as to prevent the 
 sound-waves produced by that prong from passing into the tube; the 
 resonance resulting from the vibrations of the other prong immediately 
 appears. 
 
 Fig. 233. 
 
REENFORCEMENT OF SOUND-WAVES. 
 
 267 
 
 Experiment 172. Select two of the tubes (Fig. 237) of nearly 
 the same length, blow through them, and notice the peculiar throbbing 
 sound produced by the interference of the two sounds. 
 
 Experiment 173. Stop one of the orifices of a 
 bicyclist's whistle (Fig. 224), and sound one whistle at a 
 time. The sound of each is clear and smooth. Sound 
 both whistles at the same time, and you obtain the usual 
 rough and discordant sound. 
 
 The two whistles of unequal length give out waves of 
 slightly different length, so that at certain short inter- 
 vals the same phases of both sets will coincide (i.e. con- 
 densation with condensation) and produce intensified 
 sounds which are heard at long distances, while at other 
 intervals opposite phases coincide (i.e. condensation with 
 rarefaction), and the result of their mutual destruction 
 is to cause the otherwise smooth sound to become broken 
 or rattling. 
 
 Two sound-ivaves may unite to produce a sound louder or 
 weaker than either alone would produce, or even cause silence. 
 
 253. Forced and Sympathetic Vibrations. 
 
 Experiment 174. Suspend from a frame several pendulums, A, 
 
 B, C, etc. (Fig. 225). A and D are each 3 feet long, C a little longer, 
 and B and E are shorter. Set A in vibration, and slight impulses 
 will be communicated through the frame to 
 
 D and cause it to vibrate. The vibration- 
 period of D being the same as that of A, 
 all the impulses tend to accumulate motion 
 in D, so that it soon vibrates through arcs 
 as large as those of A. On the other hand, 
 
 C, B, and E, having different rates of vibra- 
 tion from that of A, will at first acquire a 
 slight motion, but soon their vibrations will 
 be in opposition to those of A, and then the 
 impulses received from A will tend to destroy 
 the slight motion they had previously acquired. 
 
 Experiment 175. Press down gently one of the keys of a piano 
 so as to raise the damper without making any sound, and then sing 
 
-268 SOUND. 
 
 loudly into the instrument the corresponding note. The string cor- 
 responding to this note will be thrown into vibrations that can be 
 heard for several seconds after the voice ceases. If another note be 
 sung, this string will respond only feebly. 
 
 Raise the dampers from all the strings of the piano by pressing the 
 foot on the right-hand pedal, and sing strongly some note into the 
 piano. Although all the strings are free to vibrate, only those will 
 respond loudly that correspond to the note you sing, i.e. those that are 
 capable of making the same number of vibrations per second as are 
 produced by your voice. 
 
 These experiments show that a vibrating body tends to 
 make other bodies near it vibrate even if their periods of 
 vibrations are different. Vibrations of this kind, such, for 
 example, as those of B, C, and E in Experiment 174 and 
 those generated in the sounding-boards of pianos, violins, 
 etc., are called forced vibrations. But if the period of the 
 incident waves of air is the same as that of the body which 
 they cause to vibrate, the amplitude and intensity of the 
 vibrations become very great, like that of the pendulum D, 
 and those of the piano strings which gave forth the loud 
 sounds. Such are called sympathetic vibrations. 
 
 QUESTIONS. 
 
 1. Why do not sound-waves travel with the same velocity through 
 all bodies? 
 
 2. How are echoes produced ? 
 
 3. On a day when sound-waves travel through the air at the rate of 
 1120 feet per second, what is the length of the sound-waves that pro- 
 ceed from a church bell which makes 192 vibrations in a second? 
 
 4. With what velocity do sound-waves travel when a jar whose 
 depth is 10 inches gives the maximum reenforcement for a diapason 
 which makes 256 vibrations in a second? 
 
 5. Great danger often arises from vibrations of the walls of a 
 building caused by certain vibratory movements of machinery within. 
 The danger in such cases can frequently be greatly diminished by 
 changing the rate of motion in the machinery. Explain. 
 
PITCH OF MUSICAL SOUNDS. 
 
 269 
 
 Section VII. 
 
 PITCH OF MUSICAL SOUNDS. 
 
 254. On What Pitch Depends. 
 
 Experiment 176. Draw the finger-nail or a card slowly, and 
 then rapidly, across the teeth of a comb. The two sounds produced 
 are commonly described as low or 
 grave, and high or acute. The hight 
 of a musical sound is its pitch. 
 
 Experiment 177. Cause the cir- 
 cular sheet-iron disk A (Fig. 226) to 
 rotate, and hold a corner of a visiting- 
 card so that at each hole an audible 
 tap shall be made. Notice that when 
 the separate taps cease to be distin- 
 guishable, the pitch of the sound 
 depends upon the rapidity of the 
 rotation, i.e. upon the frequency of 
 the taps. 
 
 Experiment 178. Hold the ori- 
 fice of a tube B so as to blow through 
 the holes as they pass. When the ear 
 is no longer able to detect the separate 
 puffs, the sound becomes quite musi- 
 cal, and the pitch rises or falls with 
 the speed. 
 
 fitch depends upon the number of sound-waves striking 
 the ear per second, or upon the frequency of vibration. The 
 greater the number of vibrations per second, or the shorter 
 the wave-length, the higher is the pitch. 
 
 255. Musical Scale. Suppose a body, e.g. a tuning fork, to 
 make 201 vibrations per second, the sound produced is recognized by our 
 
 Fig. 236. 
 
270 
 
 SOUND. 
 
 musical sense as the note 
 
 which corresponds with the so- 
 
 called middle C (c') of a piano tuned to the national standard pitch. 
 
 The pitch of a sound produced by twice as many vibrations as that of 
 another sound is called the octave of the latter. Between two such 
 sounds the voice rises or falls, in a manner very pleasing to the ear, by a 
 definite number of steps called musical intervals. This gives rise to the 
 so-called diatonic scale, or gamut. 
 
 The successive tones of the diatonic scale of C are related to one 
 another with respect to vibration frequency as follows : 
 
 No. of vi- 
 brations 
 Ratios 
 
 or 
 
 256 
 1 
 
 d' 
 
 293.62 
 288 : 
 
 9 
 
 e' 
 
 326.25 
 320 : 
 
 r 
 
 348 
 341.3 
 
 I 
 
 391.5 
 
 : 384 : 
 
 a 
 
 435 
 426 
 
 f 
 
 b' c" 
 
 489.37 522 
 
 480 : 512 
 
 Section VIII. 
 
 VIBRATION OF STRINGS. 
 
 256. Sonometer. 
 
 Experiment 179. Stretch an elastic wire a over the bridges of 
 the sonometer (Fig. 228), so that the portion between will be free to 
 
 Fig. 228. 
 
 vibrate. Pluck the string at its middle with the thumb and finger, 
 causing it to vibrate, and observe the pitch. Next place a movable 
 bridge d half-way between the two fixed bridges and cause the portion 
 
UNIVERSITY OF CALIFORNIA 
 
 DEPARTMENT OF PHYSICS 
 
 VIBRATION OF STRINGS. 
 
 271 
 
 between either fixed bridge and the movable bridge to vibrate, and 
 observe the change in pitch. How is the vibration period changed? 
 
 Experiment 180. Stretch another wire b, either thicker or thin- 
 ner than the last, employing the same length and tension as before, 
 and notice the change in pitch due to the difference of weight of 
 the wire. How is the vibration period changed? 
 
 Experiment 181. Increase the tension of either wire by turning 
 the pin, to which one end of the wire is attached, with a wrench C, 
 and observe the change in pitch caused by change of tension. How 
 does an increase of tension affect the vibration period? 
 
 Careful experiments show that the vibration numbers of 
 strings of the same material vary inversely as their lengths 
 and the' square roots of their weights, and directly as the 
 square roots of their tension. 
 
 257. Beats. 
 
 Experiment 182. Strike simultaneously the lowest note of a 
 piano and its sharp (black key next above), and listen to the result- 
 ing sound. 
 
 You hear a peculiar wavy or throbbing sound, caused 
 by an alternate rising and sinking in loudness. These 
 alternations in loudness are called beats. 
 
 Fig. 229. 
 
 Let the continuous curve line AC (Fig. 229) represent a 
 series of waves caused by striking the lower key, and the 
 dotted line a series of waves proceeding from the upper 
 key. Now the waves from both keys may start together 
 at A ; but as the waves from the lower key are given less 
 
272 SOUND. 
 
 frequently, so are they correspondingly longer ; and at 
 certain intervals, as at B, condensations will correspond 
 with rarefactions, producing by their interference momen- 
 tary silence, too short, however, to be perceived ; but the 
 sound as perceived by the ear is correctly represented in 
 its varying loudness by the curved line in the lower part 
 of the figure. 
 
 The number of heats per second due to two simple tones is 
 equal to the difference of their respective vibration numbers. 
 The sensation produced on the ear by such a throbbing 
 sound, when the beats are sufficiently frequent, is un- 
 pleasant, much as the sensation produced by flashes of 
 light that enter the eye, when you walk on the shady 
 side of a picket fence, is unpleasant. The unpleasant 
 sensation, called by musicians discord, is due to beats. 
 
 Section IX. 
 
 OVERTONES AND HARMONICS. 
 
 258. Vibration in Parts. 
 
 Experiment 183. Hang up a rubber cord AC (Fig. 230) 4 feet 
 long, and fasten both ends. Pluck it near the middle, and it will 
 swing to and fro as a whole (2), at a rate dependent on its length, 
 tension, etc. Hold it fast at B (3), and pluck it at a point half-way 
 between A and B. Both halves are thrown into independent vibra- 
 tions, and continue so to vibrate for a brief time after the hand is 
 withdrawn from B. Again hold it fast at B, one-third its length 
 above A (4), and pluck it half-way between A and B ; the length BC 
 instantly divides itself at B' into two equal parts, and on withdraw- 
 ing the hand from B, the whole cord is seen to vibrate in three dis- 
 tinct and equal sections. In a similar manner it may be made to 
 vibrate in four, five, etc., sections. 
 
OVERTONES AND HARMONICS. 273 
 
 Sounds coming from a string or other body that vibrates 
 in parts are called overtones. If, as is the case with a 
 string, the vibration num- 
 ber of the overtone is 
 just two, three, four, etc., 
 times that of the funda- 
 mental or lowest tone, 
 the sound is called a har- 
 monic. Many overtones 
 can be produced from a 
 steel bar or a metallic 
 plate, but no harmonics. 
 This distinction is of 
 great importance, for, 
 practically, no musical 
 instruments are of much 
 use unless their vibrat- 
 ing parts furnish harmon- 
 ics- Fig. 230. 
 
 Experiment 184. Press down the C'-key (middle C) of a piano 
 gently, so that it will not sound ; and while holding it down, strike 
 the C-wire strongly. In a few seconds release the key, so that its 
 damper will stop the vibrations of the string that was struck, and 
 you will hear a sound which you will recognize by its pitch as com- 
 ing from the C'-wire. Place your finger lightly on the C'-wire, and 
 you will find that it is indeed vibrating. Press down the right pedal 
 with the foot, so as to lift the dampers from all the wires, strike the 
 C-key, and touch with the finger the C'-wire ; it vibrates. Touch the 
 keys next to C', viz. B and D r ; they have only a slight forced vibra- 
 tion. Touch G' ; it vibrates. 
 
 Now it is evident that the vibrations of the C' and G'- 
 wires are sympathetic. A C-wire vibrating as a whole 
 cannot cause sympathetic vibrations in a C'-wire ; but if 
 it vibrates in halves, it may. Hence we conclude that 
 
274 SOUND. 
 
 when the C-wire was struck, it vibrated, not only as a 
 whole, giving a sound of its own pitch, but also in halves ; 
 and the result of this latter set of vibrations was, that an 
 additional sound was produced by this wire, just an octave 
 higher than the first-mentioned sound. 
 
 Again, the G'-wire makes three times as many vibra- 
 tions as are made by the C-wire ; hence the latter wire, 
 in addition to its vibrations as a whole and in halves, must 
 have vibrated in thirds, inasmuch as it caused the G'-wire 
 to vibrate. It thus appears that a string may vibrate at 
 the same time as a whole, in halves, thirds, etc., and the 
 result is that a sound is produced that is compounded of 
 several sounds of different pitch. 
 
 Not only do stringed instruments produce compound 
 tones, but no ordinary musical instrument is capable of 
 producing a simple tone, i.e. a sound generated by vibra- 
 tions of a single period. In other words, when any note of 
 any musical instrument is sounded, there is produced, in 
 addition to the primary tone, a number of other tones in a 
 progressive series, each tone of the series being usually of 
 less intensity than the preceding. The primary or lowest 
 tone of a note is usually sufficiently intense to be the most 
 prominent, and hence is called the fundamental tone. 
 
 That two notes sounded together may harmonize, it is 
 essential not only that the pitch of their fundamental tones 
 be so widely different that they cannot produce audible beats, 
 but that no beat shall be formed by their overtones, or by an 
 overtone and a fundamental. Not only is there perfect 
 agreement among the overtones of two notes an octave 
 apart when sounded together, as when male and female 
 voices unite in singing the same part of a melody, but 
 the richness and vivacity of the sound is much increased 
 thereby. 
 
QUALITY OP SOUND. 275 
 
 Section X. 
 
 QUALITY OF SOUND. 
 
 259. How Sounds from Different Sources are Distin- 
 guished. We easily learn to distinguish by certain pecu- 
 liarities the voices of our acquaintances. So we readily 
 distinguish sounds emanating from various musical instru- 
 ments, e.g. a piano, violin, harp, and cornet. It is not 
 necessarily by the loudness or pitch of the sounds that we 
 recognize them. It is by another property of sound called 
 quality. Two sounds can differ from each other in only 
 three particulars, viz. intensity, pitch, and quality. 
 
 Pitch depends on frequency of vibrations, loudness on 
 their amplitude ; on what does quality depend ? 
 
 260. Analysis of Sounds. The unaided ear is unable, 
 except to a very limited 
 
 extent, to distinguish the 
 individual tones that com- 
 pose a note. Helmholtz ar- 
 ranged a series of resona- 
 tors consisting of hollow 
 spheres of brass, each hav- 
 ing two openings : one (A, 
 Fig. 231) large, for the re- 
 ception of the sound-waves, rig. 331. 
 and the other (B) small and funnel-shaped, and adapted 
 for insertion into the ear. Each resonator of the series 
 was adapted by its size to resound powerfully to only a 
 single tone of a definite pitch. When any musical sound 
 is produced in front of these resonators, the ear, placed at 
 the orifice of any one, is able to single out from a collec- 
 tion that overtone, if present, to which alone this resonator 
 
276 
 
 SOUND. 
 
 is capable of responding. In this manner a complete 
 analysis of any musical sound may be made, and the pitch 
 and intensity of each of its components determined. 
 
 It is found that when a note is produced on a given instrument, not 
 only is there a great variety of intensity represented by the overtones, but 
 all the possible overtones of the series are by no means present. Which 
 are wanting depends very much, in stringed instruments, upon the point of 
 the string struck. For example, if a string is struck in its middle, no node 
 can be formed at that point ; consequently, the two important overtones 
 produced by 2 and 4 times the number of vibrations of the fundamental 
 will be wanting. Strings of pianos, violins, etc., are generally struck near 
 one of their ends, and thus they are deprived of only some of their higher 
 and feebler overtones. 
 
 261. Synthesis of Sounds. The sound of a tuning- 
 fork, when its fundamental is reenforced by a suitable 
 resonance-cavity, is very nearly a simple tone. By sound- 
 ing simultaneously several forks of different but appropri- 
 ate pitch, and with the requisite relative intensities, Helm- 
 holtz succeeded in producing sounds peculiar to various 
 musical instruments, and even in imitating most of the 
 vowel sounds of the human voice. 
 
 Fig. 232. 
 
 Thus it appears that he has been able to determine, 
 both analytically and synthetically, that the quality of a 
 given sound depends upon what overtones combine with its 
 fundamental tone, and on their relative intensities; or, we 
 may say more briefly, upon the form of vibration, since the 
 form must be determined by the character of its components. 
 
COMPOSITION OF SONOROUS VIBRATIONS. 
 
 277 
 
 Section XI. 
 
 COMPOSITION OF SONOROUS VIBRATIONS, AND THE 
 RESULTANT WAVE-FORMS. 
 
 262. Method of Representing Sound-Vibrations 
 Graphically. It is evident that there must be a particular aerial 
 wave-form corresponding to each compound vibration, otherwise the ear 
 would not be able to appreciate a difference in the quality of sounds to 
 which these combination forms give rise. Every particle of air engaged in 
 
 Fig. 234. 
 
 transmitting a compound sound-wave is simultaneously acted upon by 
 several sets of vibratory movements, and it remains to investigate what 
 its motion will be under their joint influence. 
 
 The light wave-lines AB (Fig, 232) represent typically two series of 
 
278 
 
 SOUND. 
 
 aerial sound-waves, corresponding respectively to a fundamental tone and its 
 first overtone. The heavy line represents the form of the joint wave which 
 results from the combination of the two constituents. If we suppose lines 
 perpendicular to the axis, that is, to the dotted line, or line of repose, to 
 be drawn to each point in this line, as ab, cc?, eF, etc., they will represent 
 by their varying lengths the displacement of any particle in a vibrating 
 body, or any particle of air traversed by sound-waves, from its normal 
 position. 
 
 The rectangular dia- 
 gram CD is intended 
 to represent a portion 
 of a transverse section 
 of a body of air trav- 
 ersed by the joint wave 
 represented by the 
 heavy wave-line above. 
 The depth of shading 
 in different parts in- 
 dicates the degree of 
 condensation at those 
 parts. 
 
 Figure 233 repre- 
 sents wave-lines drawn 
 by an instrument call- 
 ed a vibrograph (Fig. 
 234). The second line 
 represents a sound two 
 octaves above that 
 which the first line rep- 
 resents, and the third 
 line shows the result of 
 the combination of the 
 Fig. 235. two sets of vibrations. 
 
 263. Manometric Flames. Apparatus like that shown in 
 Figure 235 will serve to illustrate in a pleasing manner many facts per- 
 taining to sound vibrations. 
 
 The cylindrical box A is divided by a membrane a into two compart- 
 ments c and b. Illuminating-gas is introduced into the compartment c, 
 through the rubber tube n, and burned at the orifice d. CD is a frame 
 holding two mirrors, M, placed back to back, so that whichever side is 
 turned toward the flame there is a reflection of the flame. 
 
COMPOSITION OF SONOKOUS VIBRATIONS. 
 
 279 
 
 When the mirror is at rest, an image of the flame will appear in the 
 mirror as represented by A (Fig. 236). If the mirror is rotated, the 
 flame appears drawn out in a band of light, as shown in B of the same 
 figure. 
 
 Fig. 336. 
 
 Sing into the cone B (Fig. 236) the sound of oo in tool, and waves of 
 air will run down the tube, beat against the membrane a, causing it to 
 vibrate, and the membrane in turn acts upon the gas in the compartment c, 
 throwing it into vibration. The result is, that instead of a flame appear- 
 ing in the rotating mirror as a continuous band of light, as B, Figure 236, 
 
280 SOUND. 
 
 it is divided up into a series of tongues of light, as shown in C, each con- 
 densation being represented by a tongue, and each rarefaction by a dark 
 interval between the tongues. If a note an octave higher than the last is 
 sung, we obtain, as we should expect, twice as many tongues in the same 
 space, as shown in D. E represents the result when the two tones are 
 produced simultaneously, and illustrates in a striking manner the effect of 
 interference. F represents the result when the vowel e is sung on the key 
 of C' ; and G, when the vowel o is sung on the same key. These are called 
 manometric flames. 
 
 Section XII. 
 
 MUSICAL INSTRUMENTS. 
 
 264. Classification of Musical Instruments. Musi- 
 cal instruments may be grouped into three classes : (1) 
 stringed instruments; (2) wind instruments, in which 
 the sound is due to the vibration of columns of air con- 
 fined in tubes; (3) instruments in which the vibrator 
 is a membrane or plate. The first class has received its 
 share of attention ; the other two merit a little further 
 consideration. 
 
 265. Wind Instruments. 
 
 Experiment 185. Figure 237 represents a set of Quinke's 
 whistles. The tubes are of the same size, but of varying length. 
 Blow through the small tube across the lips of the large tube of each 
 whistle in the order of their lengths, commencing with the longest. 
 
 Repeat the experiment, closing the end of the whistle farthest 
 from you with a finger, so as to make what is called a " closed pipe." 
 
 The pitch of vibrating air-columns, as well as of strings, 
 varies with the length, and in both stopped and open pipes 
 
MUSICAL INSTRUMENTS. 
 
 281 
 
 the number of vibrations is inversely proportional to the 
 length of the pipe. An open pipe gives a note an octave 
 higher than a closed pipe of the same length. 
 
 Fig. 237. 
 
 Experiment 186. Take some of the longer whistles, blow as 
 before, gradually increasing the force of the current. It will be found 
 that only the gentle current will give the full musical fundamental 
 tone of the tube, a little stronger current produces a mere rustling 
 sound ; but when the force of the current reaches a certain limit, an 
 overtone will break forth ; and, on increasing still further the power 
 of the current, a still higher overtone may be reached. 
 
 Figure 238 represents an open organ-pipe provided with a glass 
 window A in one of its sides. A wire hoop B has stretched over it a 
 membrane, and the whole is suspended by a thread within the pipe. If 
 the membrane is placed near the upper end, a buzzing sound proceeds 
 
282 
 
 SOUND. 
 
 from the membrane when the fundamental tone of the pipe is sounded ; 
 and sand placed on the membrane will dance up and down in a lively 
 manner. On lowering the membrane, the buzzing sound becomes 
 fainter, till, at the middle of the tube, it ceases entirely, and the sand 
 becomes quiet. Lowering the membrane still further, the sound and 
 dancing recommence, and increase as the lower end is approached. 
 
 When the fundamental tone of an open pipe is produced, 
 its air-column divides itself into two equal vibrating sections, 
 with the anti-node at the extremities of the 
 tube, and a node in the center. 
 
 Fig. 338. Fig. 239. 
 
 If the pipe is stopped, there is a node at the stopped 
 end ; if it is open, there is an anti-node at the open 
 end; and in both cases there is an anti-node at the end 
 where the wind enters, which is always to a certain 
 extent open. 
 
 A, B, and C of Figure 239 show respectively the posi- 
 tions of the nodes and anti-nodes for the fundamental tone 
 
MUSICAL INSTRUMENTS. 
 
 283 
 
 and first and second overtones of a closed pipe ; and 
 A', B', and C' show the positions of the same in an 
 open pipe of the same length. The distance between the 
 dotted lines shows the relative amplitudes of the vibra- 
 tions of the air-particles at various points along the tube. 
 Now the distance between a node and the nearest anti 
 node is a quarter of a wave-length. Comparing, then, 
 A and A', it will be seen that the wave-length of the 
 fundamental of the closed pipe must be twice the wave- 
 length of the fundamental of the open pipe ; hence the 
 vibration period of the latter is half that of the former; 
 consequently the fundamental of the open pipe must be 
 an octave higher than that of the closed pipe. 
 
 Fig. 240. 
 
 266. Sounding Plates, etc. 
 
 Experiment 187. Fasten with a screw the elastic brass plate A 
 (Fig. 240) on the upright support. Strew writing-sand over the plate, 
 and draw a rosined bass bow steadily and firmly over one of its 
 edges near a corner ; and at the same time touch the middle of one 
 
284 
 
 SOUND. 
 
 of its edges with the tip of the finger; a musical sound will be 
 produced, and the sand will dance up and down, and quickly collect 
 in two rows, extending across the plate at right angles to one an- 
 other. Draw the bow across the middle of an edge, and touch with a 
 finger one of its corners ; the sand will arrange itself in two diagonal 
 rows (2) across the plate, and the pitch of the note will be a fifth 
 higher. Touch, with the nails of the thumb and forefinger, two 
 points a and b (3) on one edge, and draw the bow across the middle 
 c of the opposite edge, and you will obtain additional rows and a 
 shriller note. 
 
 r!"\ulun*Trii-MjrrimiL'"-' 
 
 *,Ti-v-w>*i''v.vjrMO. 
 
 Fig. 341. 
 
 By varying the position of the point touched and bowed, 
 a great variety of patterns can be obtained, some of which 
 are represented in Figure 241. It will be seen that the 
 effect of touching the plate with a finger is to prevent 
 vibration at that point, and consequently a node is there 
 produced. The whole plate then divides itself up into 
 segments with nodal division lines in conformity with the 
 
MUSICAL INSTBTJMENTS. 285 
 
 node just formed. The sand rolls away from those parts 
 which are alternately thrown into crests and troughs, to 
 the parts that are at rest. 
 
 267. Interference. 
 
 Experiment 188. C (Fig. 240) is a tin tube made in two parts to 
 telescope one within the other. The extremity of one of the parts ter- 
 minates in two slightly smaller branches. Bow the plate, as in the first 
 experiment (1), place the two orifices of the branches over the segments 
 marked with the + signs, and regulate the length of the tube so as to 
 reenforce the note given by the plate, and set the plate in vibration. 
 Now turn the tube around, so that one orifice may be over a + seg- 
 ment, and the other over a segment ; the sound due to resonance 
 entirely ceases. It thus appears that the two segments marked + 
 pass through the same phases together ; likewise the phases of seg- 
 ments correspond with one another ; i.e. when one + segment is 
 bent upward, the other is bent upward, and at the same time the two 
 segments are bent downward; for, when the two orifices of the 
 tube are placed over two + segments or two segments, two condensa- 
 tions followed by two rarefactions pass up these branches and unite 
 at their junction to produce a loud sound ; but when one of the 
 orifices is over a + segment, and the other over a segment, a con- 
 densation passes up one branch at the same time that a rarefaction 
 passes up the other, and the two destroy one another when they corne 
 together; i.e. the two sound-waves combine to produce silence. 
 
 268. Bells. A bell or goblet is sub- 
 ject to the same laws of vibration as a 
 plate. 
 
 Experiment 189. Nearly fill a large goblet 
 with water, strew upon the surface lycopodium 
 powder, and draw a rosined bow gently across the 
 edge of the glass. The surface of the water will 
 become rippled with wavelets (Fig. 242) radiating 
 from four points 90 apart, corresponding to the 
 centers of four ventral segments into which the Fig ' 
 
 goblet is divided, and the powder will collect in lines proceeding from 
 the nodal points of the bell. By touching the proper points of a 
 
286 
 
 SOUND. 
 
 bell or glass with a finger-nail, it may be made to divide itself, like a 
 plate, into 6, 8, 10, etc. (always an even number), vibrating parts. 
 
 Experiment 190. Remove the brass plate (Fig. 240) from its 
 support, and fasten the bell B (Fig. 243) on the support. Bow the 
 
 edge of the bell at some point, and 
 hold the open tube C in a horizon- 
 tal position with the center of one 
 of its walls near that point of the 
 edge of the bell which is opposite 
 the point bowed. The tube loudly 
 reenforces the sound of the bell. 
 Move the tube around the edge of 
 
 Fig. 243. 
 
 the bell and find its nodes. 
 
 Thrust the plunger D into the open end E of the tube, and find 
 what part of the length of an open tube a closed tube should be to 
 reenforce a sound of a given pitch. 
 
 269. Vocal Organs. It is difficult to say which is 
 more to be admired, the wonderful capabilities of the 
 human voice or the extreme sim- 
 plicity of the means by which it is 
 produced. The organ of the voice 
 is a reed instrument situated at the 
 top of the windpipe, or trachea. A 
 pair of elastic bands aa (Fig. 244), 
 called the vocal chords, is stretched 
 across the top of the windpipe. The 
 air-passage 6, between these chords, 
 is open while a person is breathing ; 
 Fig. 344. k^ wnen he speaks or sings, they 
 
 are brought together so as to form a narrow, slit-like 
 opening, thus making a sort of double reed, which vibrates 
 when air is forced from the lungs through the narrow 
 passage, somewhat like the little tongue of a toy trum- 
 pet. The sounds are grave or high according to the 
 tension of the chords, which is regulated by muscular 
 
SOME SOUND-WAVE RECEIVERS. 287 
 
 action. The cavities of the mouth and the nasal passages 
 form a compound resonance-tube. This tube adapts it- 
 self, by its varying width and length, to the pitch of the 
 note produced by the vocal chords. Place a finger on 
 the protuberance of the throat called " Adam's apple," 
 and sing a low note ; then sing a high note, and you will 
 observe that the protuberance rises in the latter case, thus 
 shortening the distance between the vocal chords and the 
 lips. Set a tuning-fork in vibration, open the mouth as if 
 about to sing the corresponding note, place the fork in 
 front of it, and the cavity of the mouth will resound to 
 the note of the fork, but will cease to do so when the 
 mouth adapts itself to the production of some other note. 
 The different qualities of the different vowel sounds are 
 produced by the varying forms of the resonating mouth- 
 cavity, the pitch of the fundamental tones given by the 
 vocal chords remaining the same. This constitutes articu- 
 lation. 
 
 Section XIII. 
 
 SOME SOUND-WAVE RECEIVERS. 
 
 27O. The Phonograph. Figure 245 represents the Edison 
 phonograph. A metallic cylinder A is rotated by means of a crank. On 
 the surface of the cylinder is cut a shallow helical groove running around 
 the cylinder from end to end, like the thread of a screw. A small metallic 
 point, or style, projecting from the under side of a thin metallic disk D 
 (Fig. 246), which closes one orifice of the mouth-piece B, stands directly 
 over the thread. By a simple device the cylinder, when the crank is 
 turned, is made to advance just rapidly enough to allow the groove to 
 keep constantly under the style. The cylinder is covered with tinfoil. 
 The cone F is usually applied to the mouth-piece to concentrate the sound- 
 waves upon the disk D. 
 
288 
 
 SOUND. 
 
 Now, when a person directs his voice toward the mouth-piece, the aerial 
 waves cause the disk D to participate in every motion made by the parti- 
 cles of air as they beat against it, and the motion of the disk is communi- 
 
 Fig. 245. 
 
 cated by the style to the tinfoil, producing thereon impressions or indenta- 
 tions as it passes on the rotating cylinder. The result is that there is left 
 upon the foil an exact representation in relief of every movement made by 
 the style. Some of the indentations are quite perceptible to the naked 
 eye, while others are visible only with 
 the aid of a microscope of high power. 
 Figure 247 represents a piece of the foil 
 as it would appear inverted after the in- 
 dentations (here greatly exaggerated) 
 have been imprinted upon it. Fig. 246. 
 
 The words addressed to the phonograph having been thus impressed 
 upon the foil, the mouth-piece and style are temporarily removed, while 
 the cylinder is brought back to the position it had 
 when the talking began, and then the mouth-piece 
 is replaced. Now, evidently, if the crank is turned 
 Fig. 247. j n ^ ne same direction as before, the style, resting 
 
 upon the foil beneath, will be made to play up and down as it passes 
 over ridges and sinks into depressions; this will cause the disk D to 
 
SOME SOUND-WAVE RECEIVERS. 
 
 289 
 
 reproduce the same vibratory movements that caused the ridges and 
 depressions in the foil. The vibrations of the disk are communicated 
 to the air, and through the air to the ear ; thus the words spoken to the 
 apparatus may be, as it were, shaken out into the air again at any subse- 
 quent time, even centuries after, accompanied by the exact accents, into- 
 nations, and quality of sound of the original. 
 
 271. The Ear. In Figure 248, A represents the external ear-passage; 
 a is a membrane, called the tympanum, stretched across the bottom of the 
 passage, and thus closing the orifice of a cavity b, called the drum ; c is a 
 
 Fig. 348* 
 
 chain of small bones stretching across the drum, and connecting the 
 tympanum with the thin membranous wall of the vestibule e; ff are a 
 series of semicircular canals opening into the vestibule; g is the open- 
 ing into another canal in the form of a snail-shell /, hence called the 
 cochlea (this is drawn on a reduced scale) ; d is a tube (the Eustachian 
 tube'} connecting the drum with the throat; and h is the auditory nerve. 
 The vestibule and all the canals opening into it are filled with a trans- 
 parent liquid. The drum of the ear contains air, and the Eustachian tube 
 forms a means of ingress and egress for air through the throat. 
 
 Now how does the ear hear ? and how is it able to distinguish between 
 the infinite variety of form, rapidity, and intensity of aerial sound-waves 
 
290 SOUND. 
 
 so as to interpret correctly the corresponding quality, pitch, and loudness 
 of sound 1 Sound-waves enter the external ear-passage A as ocean-waves 
 enter the bays of the seacoast, are reflected inward, and strike the tym- 
 panum. The air-particles, beating against this drum-head, impress upon 
 it the precise wave-form that is transmitted to it through the air from the 
 sounding body. The motion received by the drum-head is transmitted 
 by the chain of bones to the membranous wall of the vestibule. From 
 the walls of the spiral passage of the cochlea project into its liquid con- 
 tents thousands of fine elastic threads or fibres, called " rods of Corti." 
 As the passage becomes smaller and smaller, these vibratile rods become 
 of gradually diminishing length and size (such as the wires of a piano 
 may roughly represent), and are therefore suited to respond sympatheti- 
 cally to a great variety of vibration-periods. This arrangement is some- 
 times likened to a "harp of three thousand strings" (this being about 
 the number of rods). The auditory nerve at this extremity is divided 
 into a large number of filaments, like a cord unravelled at its end, and 
 one of these filaments is attached to each rod. Now, as the sound- 
 waves reach the membranous wall of the vestibule, they set it, and by 
 means of it the liquid contents, into forced vibration, and so through the 
 liquid all the fibres receive an impulse. Those rods whose vibration 
 periods correspond with the periods of the constituents forming the com- 
 pound wave are thrown into sympathetic vibration. The rods stir the 
 nerve filaments, and the nerve transmits to the brain the impressions re- 
 ceived. Just as a piano when its dampers are raised and a person sings 
 into it, may be said to analyze each sound-wave, and show by the vibrat- 
 ing strings of how many tones it is composed, as well as their respective 
 pitch, and by the amplitude of their vibrations their respective intensi- 
 ties ; so, it is thought, this wonderful harp of the ear analyzes every com- 
 plex sound-wave into a series of simple vibrations. Tidings of the dis- 
 turbances are communicated to the brain, and there, in some mysterious 
 manner, these disturbances are interpreted as sound of definite quality, 
 pitch, and intensity. 
 
CHAPTER VIII. 
 RADIANT ENERGY, ETHER-WAVES, LIGHT. 
 
 Section I. 
 
 INTRODUCTION. 
 
 272. Energy Received from the Sun. Exposed to 
 the sun, the skin is warmed, the sense of touch is 
 affected; it is illuminated, thereby the 
 sense of sight is affected ; it is tanned, 
 its chemical condition is changed. It is 
 evident that we receive something which 
 must come to us from the sun. To the 
 sense of touch it appears to be heat; in 
 the eye it produces the sensation of light ; 
 in certain substances it has the power to 
 produce chemical changes. What is it that 
 we receive from the sun? 
 
 Figure 249 represents an instrument 
 called a radiometer. The moving part is 
 a small vane resting on the point of a 
 needle. It is so nicely poised on this pivot 
 that it rotates with the greatest freedom. Fig - 249 * 
 To the extremities of each of the four arms of the vane 
 are attached disks of aluminum, which are white on one 
 side and black on the other. The whole is enclosed in a 
 glass bulb, and the air within is reduced to less than one- 
 millionth its usual density. If the instrument is exposed 
 
292 KADIANT ENERGY. 
 
 to the sun the wheel will rotate with the white faces in 
 advance. 
 
 In just what manner it is caused to rotate does not con- 
 cern us at present ; but the fact that it rotates, and that 
 it is caused to rotate directly or indirectly by something 
 that comes from the sun, is pertinent to the question be- 
 fore us. Whenever a body is caused to move or increase 
 its rate of motion, energy must be imparted to it; hence 
 energy must be imparted to the radiometer-vane by the sun. 
 
 That which we receive from the sun, whether it affects 
 the sense of touch or of sight, or produces chemical changes, 
 is in reality some form of energy and is one and the same 
 form whatever the effect. 
 
 273. The Ether. If we receive the energy of 
 motion, what moves ? Our atmosphere is but a thin 
 mantle covering the earth, while the great space that 
 separates us from the sun contains no air or other known 
 substance. But empty space cannot communicate motion. 
 It is assumed it is necessary to assume that there is 
 some medium filling the interplanetary space ; in fact, 
 filling all space otherwise unoccupied, a medium by which 
 motion can be communicated from one point to another. 
 This medium has received the name of the ether. 
 
 We cannot see, hear, feel, taste, smell, weigh, nor meas- 
 ure it. What evidence, then, have we that it exists? 
 This : phenomena occur just as they would occur if all 
 space were filled with an ethereal medium capable of 
 transmitting motion ; we have been able to account for 
 these phenomena on no other hypothesis, hence our belief 
 in the existence of the medium. 
 
 The transmission of energy through the medium of the 
 ether is called radiation; energy so transmitted is called 
 

 UNDULATORY THEORY. 293 
 
 radiant energy, and the body emitting energy in this 
 manner is called a radiator. 
 
 274. Undulatory Theory; the Sensation of Sight. 
 
 All evidence points to one conclusion : that we receive 
 energy from the sun in the form of vibrations or waves; 
 that a portion of these waves having suitable wave-length 
 are capable of causing through the eye the sensation of 
 sight. Such as affect the sense of sight are called light- 
 waves. 1 This is known as the undulatory theory of light. 
 The term light is commonly applied to those ether-waves 
 which are capable of producing the sensation of sight ; 
 hence light is that vibration of the ether which may be 
 appreciated by the organ of sight. 
 
 275. Sources of Light- waves, Incandescence and 
 Phosphorescence. Every form of matter when suffi- 
 ciently heated emits light-waves ; in other words, when 
 the vibration period of its molecules becomes such as to 
 create ethereal waves that are capable of affecting the 
 sense of sight, the body is said to be luminous. This con- 
 dition is termed incandescence. The sun and fixed stars 
 are in a condition of intense incandescence. Nearly all 
 the artificial sources of light-waves, such as lamp and gas 
 flames and electric lamps, depend upon the development 
 of light-waves mainly through the incandescence of carbon. 
 
 1 It will be shown further on, that not all ether-way es are capable of affecting 
 the sight, hence for the purpose of distinction we apply the term light- waves to those 
 ether-waves only which are capable of producing vision. It is strongly recommended 
 that the student in beginning this branch of science make use of the term light-waves 
 instead of light except when such usage would lead to an inconvenient circumlocu- 
 tion, in order that he may have strongly impressed upon his mind the fact that when 
 he is dealing with light he is dealing with waves. 
 
294 
 
 RADIANT ENERGY. 
 
 There is a class of substances, such as the sulphides of 
 calcium, strontium, etc., which, after several hours' expos- 
 
 ure to light-waves, absorb their 
 
 energy (i.e. their molecules ac- 
 quire sympathetic vibrations) 
 without becoming hot, and in 
 turn emit light-waves, which are 
 quite perceptible in a dark room 
 for several hours after the ex- 
 posure. This property of shining 
 in the dark after having been 
 . exposed to light-waves is termed 
 phosphorescence. A so-called lumi- 
 nous paint is prepared and ap- 
 Fig. 250. plied to certain parts of bodies 
 
 that are exposed to sunshine during the day; at night 
 those parts to which the paint is applied are alone lumi- 
 nous. This paint may be used for a variety of purposes, 
 such as rendering luminous danger signals, door numbers 
 and plates (Fig. 250), etc. 
 
 276. Light-waves travel in Straight Lines. The 
 
 path of light-waves admitted into a darkened room through 
 a small aperture, as indicated by the illuminated dust, is 
 perfectly straight. An object is seen by means of light- 
 waves which it sends to the eye. A small object placed in 
 a straight line between the eye and a luminous point 
 may intercept the light-waves in that path, and the point 
 become invisible. Hence we cannot see around a corner, 
 or through a bent tube. 
 
 277. Ray, Beam, Pencil. Any line RR, Figure 251, 
 which pierces the surface of an ether-wave ab perpen- 
 
RAY, BEAM, PENCIL. 295 
 
 dicularly is called a ray. The term "ray" is but an 
 
 expression for the*direction in which motion is propagated, 
 
 and along which the successive effects of ether-waves occur. 
 
 If the wave-surface a'b' is a plane, 
 
 the rays R/R' are parallel, and a 
 
 collection of such rays is called a 
 
 beam. If the wave-surface a n b" 
 
 is spherical or concave, the rays 
 
 R"R" have a common point at 
 
 the center of curvature ; and a 
 
 collection of such rays is called 
 
 a pencil. 
 
 278. Transparent, Translu- 
 cent, and Opaque Bodies. 
 
 Bodies are transparent, translu- 
 cent, or opaque, according to 
 the manner in which they act 
 upon the light-waves which pass 
 through them. Generally speak- 
 ing, those objects are transparent that allow other objects 
 to be seen through them distinctly, e.g. air, glass, and 
 water. Those objects are translucent . that allow light- 
 waves to pass, but in such a scattered condition that 
 objects are not seen distinctly through them, e.g. fog, 
 ground glass, and oiled paper. Those objects are opaque 
 that apparently cut off all the light-waves and prevent 
 objects from being seen through them. 
 
 279. Luminous and Illuminated Objects. Some 
 bodies are seen by means of light-waves which they emit, 
 e.g. the sun, a candle flame, and a " live " coal ; they are 
 called luminous bodies. Other bodies are seen only by 
 
296 RADIANT ENERGY. 
 
 means of light-waves which they receive from luminous 
 ones; and when thus rendered visible are said to be 
 
 illuminated, e.g. the moon, a 
 man, a cloud, and a "dead" 
 coal. 
 
 Every point of a luminous 
 body is an independent source of 
 light-waves, and emits light-ivaves 
 in every direction. Such a point 
 is called a luminous point. In 
 Figure 252 there are represented 
 a few of the infinite number of 
 Fig. 353. pencils emitted by three lumi- 
 
 nous points of a candle flame. Every point of an illumi- 
 nated object, db, receives light-waves from every luminous 
 point. 
 
 28O. Images formed through Small Apertures. 
 
 Experiment 191. Cut a hole about 4 inches square in one side of 
 a box ; cover the hole with tin-foil, and prick a hole in the foil with a 
 pin. Place the box in a darkened room, and a candle flame in the box 
 near to the pin-hole. Hold an oiled-paper screen before the hole in 
 the foil ; an inverted image of the candle flame will appear upon the 
 translucent paper. 
 
 An image is a kind of picture of an object. If light- 
 waves from objects illuminated by the sun, e.g. trees, 
 houses, clouds, or even an entire landscape, are allowed 
 to pass through a small aperture in a window shutter 
 and strike a white wall in a dark room, inverted im- 
 ages of the objects in their true colors will appear upon 
 it. The cause of these phenomena is easily understood. 
 When no screen intervenes between the candle and the 
 screen A, Figure 253, every point of the screen receives 
 
SHADOWS. 297 
 
 light-waves from every point of the candle ; consequently, 
 on every point on A, im- 
 ages of the infinite num- 
 ber of points of the candle 
 are formed. The result 
 of the confusion of images 
 is equivalent to no image. 
 But let the screen B, 
 containing a small hole, 
 be interposed ; then, since Fig. 253. 
 
 light- waves travel only in straight lines, the point Y' 
 can only receive an image of the point Y, the point Z' 
 only of the point Z, and so for intermediate points; 
 hence a distinct image of the object must be formed on 
 the screen A. 
 
 That an image may be distinct, the rays from different 
 points of the object must not mix on the image, but all rays 
 from each point on the object must be carried to its own 
 point on the image. 
 
 281. Shadows. 
 
 Experiment 192. Procure two pieces of tin or cardboard, one 
 18 cm square, the other 3 cm square. Place the.first between a white 
 wall and a candle flame in a darkened room. The opaque tin inter- 
 cepts the light-waves that strike it, and thereby excludes light-waves 
 from a space behind it. 
 
 This space is called a shadow. That portion of the sur- 
 face of the wall that is darkened is a section of the shadow, 
 and represents the form of a section of the body that 
 intercepts the light-waves. A section of a shadow is fre- 
 quently for convenience called a shadow. Notice that the 
 shadow is made up of two distinct parts, a dark center 
 bordered on all sides by a much lighter fringe. The 
 
298 RADIANT ENEEGY. 
 
 dark center is called the umbra, and the lighter envelope 
 is called the penumbra. 
 
 Experiment 193. Carry the tin nearer the* wall, and notice that 
 the penumbra gradually disappears and the outline of the umbra be- 
 comes more distinct. Employ two candle flames, a little distance apart, 
 and notice that two shadows are produced. Move the tin toward the 
 wall, and the two shadows approach one another, then touch, and 
 finally overlap. Notice that where they overlap the shadow is deepest. 
 This part gets no light-waves from either flame, and is a section of 
 the umbra; while the remaining portion gets light-waves from one 
 or the other, and is a section of the penumbra. Or move the eye 
 across the shadow from side to side and see parts of the flame in the 
 penumbra, but none in the umbra. 
 
 Just so the umbra of every shadow is the part that gets no 
 light-waves from a luminous body, while the penumbra is 
 the part that gets light-waves from some portion of the body, 
 but not from the whole. 
 
 Experiment 194. Repeat the above experiments, employing the 
 smaller piece of tin, and note all differences in phenomena that occur. 
 Hold a hair in the path of the sun's waves, about a quarter of an inch 
 in front of a fly-leaf of this book, and observe the shadow cast by 
 the hair. Then gradually increase the distance between the hair 
 and the leaf, and note the change of phenomena. 
 
 If the source of light-waves were a single luminous point, as A (Fig. 
 
 _, 254), the shadow of an opaque body B 
 
 " =as ^ ^ would be of infinite length, and would 
 
 consist only of an umbra. But if the 
 source of light-waves has a sensible size, 
 254. the opaque body will intercept just as 
 
 many separate pencils as there are luminous points, and consequently will 
 cast an equal number of independent shadows. 
 
 Let AB (Fig. 255) represent a luminous body, and CD an opaque body. 
 The pencil from the luminous point A will be intercepted between the 
 lines CF and DG, and the pencil from B will be intercepted between the 
 
INTENSITY OF ILLUMINATION, ETC. 
 
 299 
 
 wave-lines CE and DF. Hence the light-waves will be wholly excluded 
 only from the space between the lines OF and DF, which enclose the 
 
 Fig. 355. 
 
 umbra. The enveloping penumbra, a section of which is included between 
 the lines CE and CF, and between DF and DG, receives light-waves from 
 certain points of the luminous body, but not from all. 
 
 , QUESTIONS. 
 
 1. What do you understand by radiant energy ? 
 
 2. State some of the immediate effects which radiant energy is 
 capable of producing. 
 
 3. How do light-waves originate ? 
 
 4. a. Has a ray of light a physical existence? b. What is a 
 light-wave ? 
 
 5. a. Does a " dead " coal emit ether-waves ? b. Does it emit 
 light-waves ? 
 
 6. a. When is a body said to be incandescent ? b. How may a 
 non-luminous body be rendered incandescent ? 
 
 7. Why are images formed through apertures inverted ? 
 
 8. Why is the size of the image dependent on the distance of the 
 screen from the aperture ? 
 
 9. Why does an image become dimmer as it becomes larger? 
 
 10. Why do we not perceive an image of our persons on every 
 object in front of which we stand ? 
 
300 RADIANT ENERGY. 
 
 11. Upon what fact does a gunner rely in taking sight? 
 
 12. Explain the umbra and penumbra cast by the opaque body 
 H I, Figure 255. 
 
 13. When will a transverse section of the umbra of an opaque 
 body be larger than the object itself ? 
 
 14. When has an umbra a limited length ? 
 
 15. What is the shape of the umbra cast by the sphere C D, 
 Figure 255 ? 
 
 16. If C D should become the luminous body, and A B a non- 
 luminous opaque body, what changes would occur in the umbra and 
 the shadow cast ? 
 
 17. Why is it difficult to determine the exact point on the ground 
 where the umbra of a church-steeple terminates ? 
 
 18. What is the shape of a section of the shadow cast by a 
 circular disk placed obliquely between a luminous body and a screen ? 
 What is its shape when the disk is placed edgewise ? 
 
 19. Describe the shadow cast by the earth. 
 
 Section II. 
 
 INTENSITY OF ILLUMINATION, PHOTOMETRY, VELOCITY 
 OF LIGHT-WAVES. 
 
 282. Unit of Measurement. The unit generally 
 employed for the measurement of the intensity of the 
 light emitted by a luminous body is the British candle 
 power. It is the intensity of light emitted by a sperm 
 candle J in. in diameter, burning 120 grains to the hour. 
 
 283. Diminution of Intensity of Illuminating Capac- 
 ity with Distance. Application of the Law of Inverse 
 Squares to Light. Light diminishes in intensity, and 
 
INTENSITY OF ILLUMINATION, ETC. 301 
 
 hence in its power to illuminate objects which it strikes, 
 as it recedes from its source. The intensity of light 
 diminishes as the square of the distance from its source 
 increases. Calling the quantity of light falling upon a 
 visiting card at a distance of 2 feet from a lamp flame 1, 
 the quantity falling upon the same card at a distance of 
 4 feet is J, at a distance of 6 feet it is l, and so on. This 
 is the meaning of the law of inverse squares, as applied to 
 light. 
 
 This law may be illustrated thus : A square card placed (say) 1 foot 
 from a certain point in a candle flame, as at A (Fig. 256), receives from 
 this point a certain quantity of light. The 
 same light if not intercepted would go on to 
 
 B, at a distance of 2 feet, and would there 
 illuminate four squares, each of the size of the 
 card, and being spread over four times the 
 area can illuminate each square with only one 
 
 fourth the intensity. If allowed to proceed to ' Fi 
 
 C, 3 feet distant, it illuminates nine such 
 
 squares, and has but one ninth its intensity at A. The law is strictly 
 true only when distance from individual points is considered. 
 
 284. Photometry. The law just established enables 
 us to compare the illuminating power of one light with 
 that of another, and to express by numbers their relative 
 illuminating powers. The process is called photometry 
 (light-measuring) ; and the instrument employed, a 
 photometer. 
 
 285. The Bunsen Photometer (Fig. 257) has a screen 
 of paper S, mounted in a box B, open in front and at 
 the two ends. The box slides on a graduated bar. The 
 screen has a circular central spot saturated with paraffine, 
 which renders the spot more translucent than other por- 
 
302 
 
 RADIANT ENERGY. 
 
 tions of the screen. One side of the screen is illuminated 
 by the light L, whose intensity is to be measured, and 
 the other side by a standard candle L'. When the screen 
 
 Fig. 257. 
 
 is so placed that the two sides are equally illuminated 
 by the two lights, the paraffined spot becomes nearly 
 invisible. When one side is more strongly illuminated 
 than the other, the spot appears dark on that side and 
 
 light on the other. The 
 candle power of the two 
 * lights is directly propor- 
 
 tional to the square of 
 their respective distances 
 from the screen when it 
 is equally illuminated on 
 both sides. 
 
 Fig. 358. 
 
 In order to render both sides of the disk simultaneously visible, two 
 mirrors, m and m' (Fig. 258), are placed in the box in a vertical position, 
 so as to reflect images of the circular spot in the screen S to the eyes at 
 E, EL 
 
 QUESTIONS. 
 
 1. Suppose that a lighted candle is placed in the center of each of 
 three cubical rooms, respectively 10, 20, and 30 feet on a side ; would 
 a single wall of the first room receive more light than a single wall 
 of either of the other rooms, or less ? 
 
INTENSITY OF ILLUMINATION, ETC. 303 
 
 2. Would one square foot of a wall of the third room receive as 
 much light as would be received by one square foot of a wall of the 
 first room? If not, what difference would there be, and why the 
 difference ? 
 
 3. Give a reason for the law of inverse squares. 
 
 4. To what besides light has this law been found applicable? 
 
 286. Visual Angle. We see an object by means of its 
 image formed on the retina of the eye ; and its apparent 
 magnitude is determined by the extent of the retina 
 covered by its image. Rays proceeding from opposite 
 extremities of an object, as AB (Fig. 259), meet and cross 
 
 Fig. 259. 
 
 one another in the window of the eye, called the pupil. 
 Now, as the distance between the points of the blades of a 
 pair of scissors depends upon the angle that the handles 
 form with one another, so the size of the image formed on 
 the retina depends upon the size of the * angle, called the 
 visual angle, formed by these rays as they enter the eye. 
 But the size of the visual angle diminishes as the distance 
 of the object from the eye increases, as shown in the 
 diagram ; e.g. at twice the distance the angle is one-half 
 as great ; at three times the distance the angle is one- 
 third as great ; and so on. Hence, distance affects the 
 apparent size of an object. Our judgment of size is, 
 however, influenced by other things besides the visual 
 angle which the object subtends. 
 
304 RADIANT ENERGY. 
 
 287. Velocity of Light- Waves. By several ingenious 
 methods it has been ascertained that light-waves travel at 
 the rate of about 186,000 miles in a second, a velocity 
 which would enable them to go around the earth about 
 seven times in a second. Sound-waves travel in air at the 
 rate of only about one-fifth of a mile per second. This 
 great difference can be accounted for only on the suppo- 
 sition that the rarity and elasticity of ether are enormously 
 greater than that of air. 
 
 Section III. 
 
 REFLECTION OF LIGHT-WAVES. 
 
 288. Law of Reflection. 
 
 Experiment 195. Look through the hole in the metal band (Fig. 
 260), marked zero, at the mirror. You see in the mirror an image of 
 
 the hole through which you 
 are looking, but you do not 
 see the image of any of 
 the other holes. Rays that 
 pass through this hole strike 
 the mirror perpendicularly, 
 Fig. 260. an( j are ca i} e d incident rays. 
 
 The reflected rays are thrown back in the same line and through the 
 same hole that the incident rays travel to the eye. 
 
 Hold a candle flame at one of the other holes (or stop it with a fin- 
 ger), e.g. at the hole marked 10. You can see the reflected rays of the 
 candle flame only through the hole of the same number on the other 
 side, i.e. for example, incident rays making an angle of 10 (called the 
 angle of incidence) with the perpendicular to the surface of the mirror 
 is reflected at an angle of 10 (called the angle of reflection) with the 
 perpendicular. The angle of reflection is always equal to the angle of 
 incidence. 
 
REFLECTION OF LIGHT-WAVES. 305 
 
 289. Reflection from Plane Mirrors; Virtual Im- 
 ages. MM (Fig. 261) represents 
 a plane mirror, and AB a pencil of 
 divergent rays proceeding from the 
 point A of an object AH. Erect- 
 ing perpendiculars at the points of 
 incidence, or the points where these 
 rays strike the mirror, and mak- 
 ing the angles of reflection equal 
 to the angles of incidence, the 
 paths BC and EC of the reflected 
 rays are found. Fi s- 
 
 It appears that divergent incident rays remain divergent 
 after reflection from a plane mirror. (In like manner con- 
 struct a diagram, and show that parallel incident rays are 
 parallel after reflection.) Construct another diagram, and 
 show that convergent incident rays are convergent after re- 
 flection, i.e. reflection from a plane surface does not alter 
 the angle between rays. To an eye placed at C, the points 
 from which the rays appear to come are of course in the 
 direction of the rays as they enter the eye. These points 
 may be found by continuing the rays CB and CE behind 
 the mirror, till they meet at the points D* and N. Every 
 point of the object AH sends out its pencil of rays ; and 
 those that strike the mirror at a suitable angle to be 
 reflected to the eye, produce on the retina of the eye an 
 image of that point, and the point from which the light- 
 waves appear to emanate is found, as previously described. 
 Thus, the pencils EC and BC appear to emanate from the 
 points N and D ; and the whole body of light-waves re- 
 ceived by the eye seems to come from an apparent object 
 ND behind the mirror. This apparent object is called an 
 image; but as, of course, there can be no real image 
 
306 RADIANT ENERGY. 
 
 formed there, it is called a virtual or an imaginary image. 
 It will be seen, by construction, that an image in a plane 
 mirror appears as far behind the mirror as the object is in 
 front of it, and is of the same size and shape as the object. 
 
 29O. Reflection from Concave Mirrors. Let MM' 
 
 (Fig. 262), represent a section of a concave mirror, which 
 may be regarded as a small part of a hollow spherical 
 shell having a polished interior surface. The distance 
 MM' is called the diameter of the mirror. C is the center 
 
 of the sphere, and is 
 called the center of 
 curvature. G is the 
 vertex of the mirror. 
 A straight line DG 
 drawn through the 
 center of curvature 
 and the vertex is 
 Fig. 262. called the principal 
 
 axis of the mirror. A concave mirror may be considered 
 as made up of an infinite number of small plane surfaces. 
 All radii of the mirror, as CA, CG, and CB, are perpen- 
 dicular to the small planes which they strike. If C be a 
 luminous point, it is evident that all light-waves emanating 
 from this point, and striking the mirror, will be reflected 
 to its source at C. 
 
 Let E be any luminous point in front of a concave 
 mirror. To find the direction that rays emanating from 
 this point take after reflection, draw any two lines from 
 this point, as EA and EB, representing two of the infi- 
 nite number of rays composing the divergent pencil that 
 strikes the mirror. Next, draw radii to the points of inci- 
 dence A and B, and draw the lines AF arid BF, making 
 
REFLECTION OF LIGHT-WAVES. 307 
 
 the angles of reflection equal to the angles of incidence. 
 Place arrow-heads on the lines representing rays to indi- 
 cate the direction of the motion. The lines AF and BF 
 represent the direction of the rays after reflection. 
 
 It will be seen that the rays after reflection are con- 
 vergent, and meet at the point F, called the focus. This 
 point is the focus of all reflected rays that emanate from 
 the point E. It is obvious that if F were the luminous 
 point, the lines AE and BE would represent the reflected 
 rays, and E would be the focus of these rays. Since the 
 relation between the two points is such that light-waves 
 emanating from either one are brought by reflection to a 
 focus at the other, these points are called conjugate foci. Con- 
 jugate foci are two points so related that the image of either is 
 formed at the other. The rays EA and EB emanating from 
 E are less divergent than rays FA and FB, emanating from 
 a point F less distant from the mirror, and striking the 
 same points. Rays emanating from D, and striking the 
 same points A and B, will be still less divergent ; and if 
 the point D were removed to a distance of many miles, 
 the rays incident at these points would be very nearly 
 parallel. Hence rays may be regarded 
 as practically parallel when their source. 
 is at a very great distance, e.g. the sun's 
 rays. If a sunbeam, consisting of a 
 bundle of parallel rays, as EA, DG, 
 and HB (Fig. 263), strike a concave Fig. 
 
 mirror parallel with its principal axis, these rays become 
 convergent by reflection, and meet at a point (F) in the 
 principal axis. This point, called the principal focus, is 
 just half-way between the center of curvature and the 
 vertex of the mirror. 
 
 On the other hand, it is obvious that divergent rays 
 
308 
 
 RADIANT ENERGY. 
 
 emanating from the principal focus of a concave mirror 
 become parallel by reflection. 
 
 If a small piece of paper is placed at the principal focus 
 of a concave mirror, and the mirror is exposed to the par- 
 allel rays of the sun, the paper will quickly burn. 
 
 Construct a diagram, and show that rays proceeding 
 from a point between the principal focus and the mirror 
 are divergent after reflection, but less divergent than the 
 incident rays. Reversing the direction of the rays the 
 same diagram will show that convergent rays are rendered 
 more convergent by reflection from concave mirrors. 
 
 The general effect of a concave mirror is to increase the 
 
 convergence or to 
 decrease the diver- 
 gence of incident 
 rays. 
 
 The statement, that 
 parallel rays after re- 
 flection from a concave 
 mirror meet at the prin- 
 cipal focus, is only ap- 
 proximately true. The 
 
 Fig. 264. smaller the diameter of 
 
 the mirror, the more nearly true is the statement. It is strictly true only 
 of parabolic mirrors. Such are used m the head-lights of locomotives. 
 
 291. Formation of Images. 
 
 Experiment 196. Hold some object, e.g. a rose, as ab (Fig. 264), 
 a few feet in front of a concave mirror. Looking in the direction of 
 the axis of the mirror you see a small inverted image AB of the object 
 between the center of curvature, C, of the mirror and its principal 
 focus F. 
 
 Evidently if AB represent an object placed between the principal 
 focus and center of curvature, then ab will represent the image of the 
 object. The image in this case may be projected upon a screen, but 
 it will not be so bright as in the former case, because the light-waves 
 are spread over a larger surface. 
 
KEFLECTION OF LIGHT-WAVES. 309 
 
 Experiment 197. Place a candle in an otherwise dark room 20 
 feet from the mirror, catch the focused light-waves upon a paper 
 screen, and show that the focus is half-way between the vertex and 
 the center of curvature of the mirror. 
 
 Experiment 198. Advance the distant candle flame toward the 
 mirror, moving it up and down. (1) Show that the focus advances to 
 meet the flame, and that when the flame is raised, the focus is depressed, 
 and the converse. (2) Show that when the flame is at the center of 
 curvature, there also is the focus. (3) Show that when the flame is be- 
 tween the center of curvature and the principal focus, the focus of the 
 flame is farther away than the center of curvature. (4) Show that 
 when the flame is at the principal focus, the reflected rays are parallel, 
 or the focus is at an infinite distance. (5) Show that when the flame is 
 still nearer, the reflected rays diverge and appear to come from a point 
 behind the mirror. (6) Notice that in all cases except the last the im- 
 ages are real and inverted, and that in all cases where a real image is 
 formed, the flame and the image may change places. 
 
 Experiment 199. Form a real image of the flame between your- 
 self and the mirror ; view the 
 image through a convex lens 
 (Fig. 284) ; show that the im- 
 age can be magnified by a 
 convex lens, and thereby illus- 
 trate the principle of an astro- 
 nomical reflecting telescope. 
 
 Construct the image of 
 an object placed between m s- 
 
 tbe principal focus and the mirror, as in Figure 265. It 
 will be seen in this case that a pencil of rays proceeding 
 from any point of an object, e.g. D, has no actual focus, 
 but appears to proceed from a virtual focus D', back of the 
 mirror ; and so with other points, as E. The image of an 
 object placed between the principal focus and the mirror is 
 virtual, erect, larger than the object, and is back of the mirror. 
 
 292. Convex Mirrors. The general effect of convex 
 mirrors is to separate incident rays. In them all images 
 are virtual, erect, and smaller than the objects. 
 
310 RADIANT ENERGY. 
 
 Section IV. 
 
 KEF R ACTION. 
 
 293. Introductory Experiments. 
 
 Experiment 200. Into a darkened room admit a sunbeam so 
 that its rays may fall obliquely on the bottom of the basin (Fig. 266), 
 
 and note the place on the bottom 
 where the edge of the shadow DE 
 cast by the side of the basin DC 
 meets the bottom at E. Then, 
 without moving the basin, fill it 
 even full with water slightly clouded 
 with milk or with a few drops of a 
 solution of mastic in alcohol. It 
 will be found that the edge of the 
 shadow has moved from I)E to DF, 
 and meets the bottom at F. Beat 
 a blackboard rubber, and create a 
 cloud of dust in the path of the beam in the air, and you will dis- 
 cover that the rays GD that graze the edge of the basin at D be- 
 come bent at the point where they enter the water, and now move 
 in the bent line GDF, instead of, as formerly, in the straight line GE. 
 The path of the line in the water is now nearer to the vertical side DC ; 
 in other words, this part of the beam is more nearly vertical than before. 
 Experiment 201. Place a coin (A, Fig. 267) on the bottom of 
 an empty basin, so that, as you look through a small hole in a card 
 BC over the edge of the vessel, the coin is 
 just out of sight. Then, without moving the 
 card or basin, fill the latter with water. Now, 
 on looking through the aperture in the card, 
 the coin is visible. The beam AE, which 
 formerly moved in the straight line AD, is 
 now bent at E, where it leaves the water, 
 and, passing through the aperture in the card, 
 enters the eye. Observe that, as the beam 
 passes from the water into the air, it is turned farther from a verti- 
 
BEFR ACTION. 311 
 
 cal line EF ; in other words, the beam is farther from the vertical than 
 before. 
 
 Experiment 202. From the same position as in the last experi- 
 ment, direct the eye to the point G in the basin filled with water. 
 Reach your hand around the basin, and place your finger where that 
 point appears to be. On examination, it will be found that your 
 finger is considerably above the bottom. Hence, the effect of the bend- 
 ing of rays, as they pass obliquely out of water, is to cause the bottom to 
 appear more elevated than it really is ; in other words, to cause the water 
 to appear shallower than it is. 
 
 Experiment 203. Thrust a pencil obliquely into water ; it will 
 appear shortened, bent at the surface of the water, and the immersed 
 portion elevated. 
 
 Experiment 204. Place a piece of wire (Fig. 268) vertically in 
 front of the eye, and hold a narrow strip of thick plate glass horizon- 
 tally across the wire, so that the light-waves from the wire 
 may pass obliquely through the glass to the eye. The wire 
 will appear to be broken at the two edges of the glass, and 
 the intervening section will appear to the right or left accord- 
 ing to the inclination of the glass ; but if the glass is not 
 inclined to the one side or the other, the wire does not 
 
 Fig. 368. 
 
 appear broken. 
 
 Experiment 205. Partly fill a cell 1 with parallel glass sides 
 with carbon bisulphide, then add water. Place the cell in the path 
 of a beam reflected from a porte lumiere. Place vertically in front of 
 the cell a wire, and project with a lens a shadow of the wire on a 
 screen. Turn the cell obliquely, as in the last experiment, and 
 notice the difference in the refracting power of the two liquids. 
 
 Experiment 206. Partly fill the same cell with water. Focus 
 it on the screen so that the surface of the water will be visible. 
 Add a lump of ice on the water. Observe the streakiness caused by 
 difference in the density of water at different temperatures. 
 
 Experiment 207. Project with a lens a luminous circle on a 
 screen. Hold, a few feet in front of the screen, a candle flame in the 
 path of the light-waves. Observe the wavy streakiness arising from 
 the changing density of the air and convection currents. 
 
 1 These cells, used with stereopticons for projecting liquids, can be procured of 
 apparatus dealers. 
 
312 RADIANT ENERGY. 
 
 When a light-beam passes from one medium into another of different 
 density, it is bent or refracted at the boundary plane between the two 
 media, unless it falls exactly perpendicularly on this plane. If it, pass 
 into a denser medium, it is refracted toward a perpendicular to this plane ; 
 if into a rarer medium, it is refracted from the perpendicular. The angle 
 
 GDO (Fig. 266) is called the angle 
 of incidence ; FDN, the angle of re- 
 fraction; and EDF, the angle of 
 deviation. 
 
 294. Cause of Refraction. 
 
 Careful experiments have proved that 
 the velocity of light-waves is less in a 
 dense than in a rare medium. Let the 
 series of parallel lines AB (Fig. 269) 
 represent a series of wave-fronts leav- 
 ing an object C, and passing through 
 a rectangular piece of glass DE, and 
 constituting a beam. Every point 
 in a wave-front moves with equal 
 Fig. 269. velocity as long as it traverses the 
 
 same medium ; but the point a of a given wave ab enters the glass first, 
 and its velocity is impeded, while the point 6 retains its original velocity ; 
 so that, while the point a moves to a', b moves to b f , and the result is 
 that the wave-front assumes a new direction (very much in the same 
 manner as a line of soldiers execute a wheel), and a ray or a line drawn 
 perpendicularly through the series of waves is turned out of its original 
 direction on entering the glass. Again, the extremity c of a given wave- 
 front cd first emerges from the glass, when its velocity is immediately 
 quickened ; so that, while d advances to d f , c advances to c', and the 
 direction of the ray is again changed. The direction of the ray, after 
 emerging from the glass, is parallel to its direction before entering it, but 
 it has suffered a lateral displacement. Let C represent a section of the 
 wire used in Experiment 262, and the cause of the phenomenon observed 
 will be apparent. If the beam strike the glass perpendicularly, all points 
 of the wave will be checked at the same instant on entering the glass ; 
 consequently it will suffer no refraction. 
 
 295. Index of Refraction. The deviation of light- 
 waves, in passing from one medium to another, varies 
 with the medium and with the angle of incidence. It 
 
UNIVERSITY OF 
 
 OF PHYSfCS 
 
 REFRACTION. 
 
 318 
 
 diminishes as the angle of incidence diminishes, and is 
 zero when the incident ray is normal (i.e. perpendicular 
 to the surface of the medi- 
 um). It is highly impor- 
 tant, knowing the angle 
 of incidence, to be able to 
 determine the direction 
 which a ray will take on 
 entering a new medium. 
 Describe a circle around 
 the point of incidence A 
 (Fig. 270) as a center; 
 through the same point 
 draw IH perpendicular to Fi s- 3>?0 - 
 
 the surfaces of the two media, and to this line drop per- 
 pendiculars BD and CE from the points where the circle 
 cuts the ray in the two media. Then suppose that the 
 perpendicular BD is -$ of the radius AB ; now this frac- 
 tion y^- is called (in trigonometry) the sine of the angle 
 DAB. Hence, T 8 7 is the sine of the angle of incidence. 
 Again, if we suppose that the perpendicular CE is T % of 
 the radius, then the fraction -f$ is the sine of the angle of 
 refraction. The sines of the two angles are to one another 
 as T V : T %, or as 4 : 3. The quotient (in this case f = 1.33+) 
 obtained by dividing the sine of the angle of incidence by 
 the sine of the angle of refraction is called the index of 
 refraction. It can be proved to be the ratio of the velocity 
 of the incident to that of the refracted light-waves. It is 
 found that for the same media the index of refraction is 
 a constant quantity ; i.e. the incident ray might be more 
 or less oblique, still the quotient would be the same. 
 
 296. Indices of Refraction. The index of refraction for light- 
 waves in passing from air into water is approximately |, and from air into 
 
314 
 
 RADIANT ENERGY, 
 
 glass f ; of course, if the order is reversed, the reciprocal of these frac- 
 tions must be taken as the indices ; e.g. from water into air, the index is f ; 
 from glass into air, f . When a ray passes from a vacuum into a medium, 
 the refractive index is greater than unity, and is called the absolute index 
 of refraction. The relative index of refraction, from any medium A into another 
 B, is found by dividing the absolute index of B by the absolute index of A. 
 
 The refractive index varies with wave-length. The following table is 
 intended to represent mean indices : 
 
 TABLE OF ABSOLUTE INDICES. 
 
 Air at C., and 760mm pressure . 1.000294 
 
 Pure water 1.33 
 
 Alcohol 1.37 
 
 Spirits of turpentine 1.48 
 
 Humors of the eye (about) . . . 1.35 
 
 Carbon bisulphide 1.641 
 
 Crown glass (about) 1.53 
 
 Flint glass (about) 1.61 
 
 Diamond (about) 2.5 
 
 Lead chromate 2.97 
 
 297. Critical Angle; Total Reflection. Let SS' 
 
 (Fig. 271) represent the boundary surface between two 
 media, and AO and BO incident rays in the more refractive 
 medium (e.g. glass) ; then OD and OE may represent the 
 same rays respectively after they enter the less refractive 
 
 Fig. 371. 
 
 medium (e.g. air). It will be seen that, as the angle of 
 incidence is increased, the refracted ray rapidly approaches 
 the surface OS. Now, there must be an angle of incidence 
 (e.g. COM) such that the angle of refraction will be 90 ; 
 
REFRACTION. 
 
 315 
 
 in this case the incident ray CO, after refraction, will just 
 graze the surface OS. This is called the critical or limiting 
 angle. Any incident ray, as LO, making a larger angle 
 with the normal than the critical angle, cannot emerge from 
 the medium, and consequently is not refracted. Experi- 
 ment shows that all such rays undergo internal reflection ; 
 e.g. the ray LO is reflected in the direction ON. Reflec- 
 tion in this case is perfect, and hence is called total reflec- 
 tion. Total reflection occurs when rays in the more refractive 
 medium are incident at an angle greater than the critical angle. 
 
 Surfaces of transparent media, under these circumstances, constitute the 
 best mirrors possible. The critical angle diminishes as the refractive index 
 increases. For water it is about 48}; for flint glass, 38 41' ; and for the 
 diamond, 23 41'. Light-waves cannot, therefore, pass out of water into 
 air with a greater angle of incidence than 48|. The brilliancy of gems, 
 particularly the diamond, is due in part to their extraordinary power of 
 internal reflection, arising from their large indices of refraction. 
 
 298. Illustrations of Refraction and Total Reflection. 
 
 Experiment 208. Observe the image of a candle flame reflected 
 by the surface of water in a glass beaker, as in Figure 272. 
 
 Experiment 209. Thrust the closed end of a glass test-tube 
 (Fig. 273) into water, and incline the tube. Look down upon the 
 immersed part of the tube, and its upper surface will look like bur- 
 
 Fig. 273. Fig. 273. 
 
 nished silver, or as if the tube contained mercury. Fill the test-tube 
 with water, and immerse as before ; the total reflection which before 
 occurred at the surface of the air in the submerged tube now 
 disappears. Explain. 
 
316 
 
 RADIANT ENERGY. 
 
 Section V. 
 
 DOUBLE REFRACTION. 
 
 299. Double Kefraction. 
 
 Experiment 210. Through a card make a pin-hole, and hold 
 the card so that you may see the sky 
 through the hole. Now bring a crystal of 
 Iceland spar (Fig. 274) between the eye 
 and the card, and look at the hole through 
 two parallel surfaces of the crystal. There 
 will appear to be two holes, with light- 
 waves passing through each. Cause the 
 crystal to rotate in a plane parallel with 
 the card, and one of the holes will appear 
 to remain nearly at rest, while the other 
 rotates around the first. A ray, PQ, 
 immediately on entering the crystal is 
 divided into two parts, one of which, QO, 
 obeys the regular law of refraction ; the other, QE, does not. The 
 former is called the ordinary ray ; the latter, the extraordinary ray. 
 The rays issue from the crystal parallel with each other. 
 
 In every direction in which one looks through the 
 crystal, except that parallel to its optical axis, objects seen 
 through it appear double. (See Figure 275.) The optic 
 
 Fig. 274. 
 
 Fig. 275. 
 
 axis of a crystal is a line around which the molecules 
 of the crystal appear to be arranged symmetrically. A 
 crystal is called uniaxial when it has only one optic axis, 
 
PRISMS AND LENSES. 317 
 
 and biaxial when it has two such axes. By far the largei 
 number of crystals of other substances possess the prop- 
 erty of causing objects seen through them to appear 
 double. This phenomenon is called double refraction. 
 
 Section VI. 
 
 PRISMS AND LENSES. 
 
 300. Optical Prisms. An optical prism is a trans- 
 parent, wedge-shaped body. Figure 276 represents a 
 transverse section of such a prism. Let AB be a ray 
 incident upon one of its surfaces. On entering the prism 
 it is refracted toward the normal, and takes the direc- 
 tion BC. On emerging from the prism it is again re- 
 fracted, but now from the normal in the direction CD. 
 The object that emits the 
 
 ray will appear to be at F. 
 Observe that the ray AB, 
 at both refractions, is bent 
 toward the thicker part, or 
 base, of the prism. 
 
 301. Lenses. Any trans- ms ' 276 ' 
 
 parent medium bounded by two curved surfaces, or by 
 one plane and the other curved, is a lens. 
 
 Experiment 211. Procure a couple of lenses thicker in the 
 middle than at the edge : strong spectacle glasses, or the large lenses 
 in an opera glass will answer. Hold one of the lenses in the sun's 
 rays, and notice the path of the beam in dusty air (made so by strik- 
 ing together two blackboard rubbers), after it passes through the lens ; 
 
318 RADIANT ENERGY. 
 
 also, that on a paper screen all the rays may be brought to a small 
 circle, or even to a point, not far from the lens. This point is called 
 the focus, and its distance from the lens, the focal length of the 
 lens. 
 
 Find the focal length of this lens, then of the second, and then of 
 the two together. You find the focal length of the two combined is 
 less than of either alone, and learn that the more powerful a lens or 
 combination of them is, the shorter the focal length ; that is, the more 
 quickly are the parallel rays that enter different parts of the lens 
 brought to cross one another. 
 
 Experiment 212. Procure a lens thinner in the middle than at 
 its edge. One of the small lenses or eye-glasses of an opera glass will 
 answer. Repeat the above experiment with this lens, and notice that 
 the rays emerging from the lens, instead of coming to a point, become 
 spread out. 
 
 Lenses are of two classes, converging and diverging, 
 according as they collect rays or cause them to diverge. 
 Each class comprises three kinds (Fig. 277) : 
 
 CLASS I. CLASS H. 
 
 1. Double-convex "j Converging, or convex 
 
 2. Plano-convex 1 lenses thicker in 
 
 3. Concavo-convex. [ the middle than at 
 
 (or meniscus) } the edges. 
 
 4. Double-concave J c '^ g S e r 
 
 MSsaM'SiSas? 
 
 A straight line, as AB, normal to both surfaces of a 
 leus, and passing through its center of curvature, is called 
 
 its principal axis. 
 In every thin lens 
 there is a point in 
 the principal axis 
 called the optical 
 Fig. 377. center. Every ray 
 
 that passes through it has parallel directions at incidence 
 and emergence, i.e. can suffer at most only a slight lateral 
 displacement. In lenses 1 and 4 it is half-way between 
 their respective curved surfaces. A ray, drawn through 
 
PRISMS AND LENSES. 319 
 
 the optical center from any point of an object, as Aa 
 (Fig. 286), is called the secondary axis of this point. 
 
 3O2. Effect of Lenses. We may, for convenience of 
 illustration, regard a convex lens as composed, approxi- 
 mately, of two prisms placed base to base, as A (Fig. 
 278), and a concave lens as composed of two prisms with 
 their edges in contact, as B. Inasmuch as a beam ordi- 
 narily strikes a lens in such a manner 
 that it is bent toward the thicker parts 
 or bases of these approximate prisms, 
 it is obvious that the lens A tends to 
 bend the transmitted rays toward one 
 another, while the lens B tends to 
 separate them. The general effect of all ^s- 378. 
 
 convex lenses is to converge transmitted rays ; that of con- 
 cave lenses, to cause them to diverge. Incident rays parallel 
 with the principal axis of a convex lens are brought to 
 
 a focus F (Fig. 279) 
 at a point in the prin- 
 cipal axis. This point 
 is called the principal 
 focus, i.e. it is the focus 
 of incident rays par- 
 allel with the principal 
 Fig ' 379 - axis. It may be found 
 
 by holding the lens so that the rays of the sun may fall 
 perpendicularly upon it, and then moving a sheet of paper 
 back and forth behind it until the image of the sun 
 formed on the paper is brightest and smallest. Or, in a 
 room, it may be found approximately, by holding a lens at 
 a considerable distance from a window, regulating the 
 distance so that a distinct image of the window will be 
 
320 
 
 RADIANT ENERGY. 
 
 projected upon the opposite wall, as in Figure 280. The 
 focal length is the distance of the optical center of the lens 
 
 Fig. 380. 
 
 to the center of the image on the paper. The shorter 
 this distance the greater is the power of the lens. 
 
 If the paper is kept at the principal focus for a short time, 
 it will take fire. The reason is apparent why convex lens- 
 es are sometimes 
 called " burning 
 glasses." A pencil 
 of rays emitted 
 from the princi- 
 pal focus F (Fig. 
 279), as a lumi- 
 nous point, be- 
 
 88i. comes parallel on 
 
 emerging from a convex lens. If the rays emanate from 
 a point nearer the lens, they diverge after egress, but the 
 divergence is less than before ; if from a point beyond 
 the principal focus, the rays are rendered convergent. A 
 
PRISMS AND LENSES. 
 
 321 
 
 concave lens causes parallel incident rays to diverge as 
 if they came from a point, as F (Fig. 281). This point is 
 therefore its principal focus. It is, of course, a virtual 
 focus. 
 
 3O3. Conjugate Foci. When a luminous point S (Fig. 
 282) sends 
 rays to a con- 
 vex lens, tho 
 emerge n trays 
 converge to 
 another point 
 
 S'; rays sent Fig . 383 . 
 
 from S' to the lens would converge to S. Two points 
 thus related are called conjugate foci. The fact that rays 
 which emanate from one point are caused by convex 
 lenses to collect at one point, gives rise to real images, as 
 in the case of concave mirrors. 
 
 Fig. 283. 
 
 3O4. Images Formed. Fairly distinct images of objects 
 may be formed through very small apertures (Fig. 253); 
 but owing to the small amount of radiant energy that passes 
 through the aperture, the images are very deficient in bril- 
 liancy. If the aperture is enlarged, brilliancy is increased 
 
322 RADIANT ENERGY. 
 
 at the expense of distinctness. A convex lens enables us to 
 obtain both brilliancy and distinctness at the same time. 
 
 Experiment 213. By means of a porte lumiere A (Fig. 283) in- 
 troduce a horizontal beam into a darkened room. In its path place 
 some object, as B, painted in transparent colors or 
 photographed on glass. (Transparent pictures are 
 cheaply prepared by photographers for sun-light and 
 lime-light projections.) Beyond the object place a 
 convex lens L (such as represented in Figure 283), and 
 beyond the lens a screen S. The object being illu- 
 minated by the beam, all the rays diverging from 
 any point a are bent by the lens so as to come to- 
 gether at the point a 1 . In like manner, all the rays 
 proceeding from c are brought to the same point c' ; 
 and so also for all intermediate points. Thus, out of 
 Fig. 284. fa e innumerable rays emanating from each of the in- 
 numerable points on the object, those that reach the lens are guided 
 by it, each to its own appropriate point in the image. It is evident 
 that there must result an image, both bright and distinct, provided the 
 screen is suitably placed, i.e. at the place where the rays meet. But if 
 the screen is placed at S' or S", it is evident that a blurred image 
 will be formed. Instead of moving the screen back and forth, in order 
 to "focus" the rays properly, it is customary to move the lens. 
 
 Experiment 214. Make a series of experiments similar to those 
 (Experiment 198) with the concave mirror. Ascertain the focal length 
 of the convex lens. Place the lens a distance from a white wall about 
 equal to its focal length. Place a candle flame (better the flame of 
 a fish-tail burner) at such a distance the other side of the lens that it 
 will produce a distinct and well-defined image on the wall (Fig. 285). 
 
 (1) Observe and note on paper the size and kind of image. Advance 
 the flame toward the lens, regulating at the same time the distance 
 between the lens and wall, so as to preserve a distinctness of image. 
 
 (2) Note the changes which the image undergoes. (3) When the 
 image and flame become of the same size, measure and note the dis- 
 tances of each from the lens. (4) Advance the flame still nearer, 
 and note the changes in the image, until it is impossible to obtain an 
 image on the wall. Measure the distance of the flame from the lens, 
 and compare this distance with the focal length of the lens. (5) Move 
 
PRISMS AND LENSES. 
 
 323 
 
 the flame still nearer. Note whether the rays, after emerging from 
 the lens, are divergent or convergent. (6) See whether an image and 
 
 Fig. 285. 
 
 an object may change places. (7) Form images of the flame on the 
 wall at different distances from the lens ; measure the distances, also 
 the linear dimensions (e.g. the width, or the vertical hight) of the 
 images, and determine whether the linear dimensions of images are 
 proportional to their distances from the lens. 
 
 305. To Construct the Image .Formed by a Convex 
 Lens. Given the 
 lens L (Fig. 286), 
 whose principal fo- 
 cus is at F (or F', for 
 rays coming from the 
 other direction), and 
 object AB in front of 
 it ; any two of the 
 many rays from A will determine where its image a is formed. The two 
 that can be traced easily are the one along the secondary axis AOa, and 
 the one parallel to the principal axis A A': the latter will be deviated so 
 as to pass through the principal focus F, and will afterward intersect the 
 principal axis at some point a ; so this is the conjugate focus of A ; 
 similarly for B, and all intermediate points along the arrow. Thus, a 
 real inverted image is formed at ab. 
 
 286. 
 
324 
 
 RADIANT ENERGY. 
 
 3O6. Virtual Images ; Simple Microscope. Since 
 rays that emanate from a point nearer the lens than the 
 principal focus diverge after egress, it is evident that 
 their focus must be virtual and on the same side of the 
 
 A' 
 
 Fig. 287. 
 
 lens as the object. Hence, the image of an object placed 
 nearer the lens than the principal focus is virtual, magnified, 
 and erect, as shown in Figure 287. A convex lens used 
 in this manner is called a simple microscope. 
 
 Since the effect of concave lenses is to scatter trans- 
 mitted rays, pencils of rays emitted from A and B 
 
 Fig. 288. 
 
 (Fig. 288), after refraction, diverge as if they came from 
 A' and B', and the image will appear to be at A' B'. 
 Hence, images formed by concave lenses are virtual, erect, 
 and smaller than the object. 
 
PRISMS AND LENSES. 325 
 
 3O7. Spherical Aberration. In all ordinary convex 
 lenses the curved surfaces are spherical, and the angles 
 which incident rays make with the little plane surfaces of 
 which we may imagine the spherical surface to be made 
 
 P. 
 
 F' 
 
 up, increase rapidly toward the edge of the lens. Thus, 
 while those rays from a given point of an object, as A 
 (Fig. 289), which pass through the central portion, meet 
 approximately at the same point F, those which pass 
 through the marginal portion are deviated so much that 
 they cross the axis at nearer points, e.g. at F'; so a blurred 
 image results. This wandering of the rays from a single 
 focus is called spherical aberration. The. evil may be 
 largely corrected 1 by interposing a diaphragm DD', pro- 
 vided with a central aperture, smaller than the lens, so as 
 to obstruct those rays that pass through the marginal part 
 of the lens. 
 
 Experiment 215. (Illustrating spherical aberration.) Cut a 
 cardboard disk as large as the convex lens (Fig. 284). Cut a ring 
 of holes near the circumference, and also a ring near the center. 
 Support the disk close to the lens, so as to cover one of its surfaces. 
 Place the whole in a beam from a porte lumiere. Catch refracted 
 beams on a screen. Move the screen away from the lens. The beams 
 through the outer ring of spots are the first to cross one another and 
 form an image. Further away, the inner beams coincide, forming 
 an image. The outer ones, having crossed, form a ring of spots. 
 
 1 It can be wholly corrected only by modifying the curvature of the surfaces of 
 the lens. A lens having surfaces thus modified is said to be aplanatic. 
 
326 
 
 RADIANT ENERGY. 
 
 Section VII. 
 
 PRISMATIC ANALYSIS OF LIGHT- WAVES. SPECTRA. 
 
 3O8. Analysis of Light-Waves which Produce the 
 Sensation of White. 
 
 Experiment 216. Place the disk with adjustable slit in the aper- 
 ture of a porte lumiere, so as to exclude all light-waves from a darkened 
 room except those which pass through the slit. Near the slit inter- 
 pose a double-convex lens of (say) 10-inch focus. A narrow sheet of 
 light will traverse the room and produce an image AB (Fig. 290) of 
 the slit on a white screen placed in its path. Now place a glass prism 
 C in the path of the narrow sheet of light-waves and near to the lens 
 with its edge vertical. (1) The light-waves now are not only turned 
 
 Fig. 290. 
 
 from their former. path, but that which before was a narrow sheet, is, 
 after emerging from the prism, spread out fan-like into a wedge-shaped 
 body, with its thickest part resting on the screen. (2) The image, 
 before only a narrow, vertical band, is now drawn out into a long 
 
PRISMATIC ANALYSIS OF LIGHT-WAVES. 327 
 
 horizontal ribbon, DE. (3) The image, before white, now presents all 
 the colors of the rainbow, from red at one end to violet at the other ; 
 it passes gradually through all the gradations of red, orange, yellow, 
 green, blue, and violet. (The difference in deviation between the red 
 and the violet is purposely much exaggerated in the figure.) 
 
 From this experiment we learn (1) that white waves (i.e. 
 those waves which are capable of producing the sensation 
 of white) are not simple in their composition, but the result 
 of a mixture. (2) The color waves of which white waves are 
 composed may be separated by refraction. (3) The cause of 
 the separation is due to the different degrees of deviation 
 which they undergo by refraction. Red waves, which are 
 always least turned aside from a straight path, are the 
 least refrangible. Then follow orange, yellow, green, blue, 
 and violet in the order of their refrangibility. The many- 
 colored ribbon DE is called the solar spectrum. This 
 separation of white waves into their constituents is called 
 dispersion. The variety of color waves of which white 
 waves are composed is really infinite ; but we name the 
 seven principal ones as follows: red, orange (or citron), 
 yellow, green, cyan-blue, ultramarine-blue, and violet; these 
 are called the prismatic colors. The names of the blues 
 are derived from the names of the pigments which most 
 closely resemble them. 
 
 3O9. The Kainbow. The rainbow is an illustration of a solar 
 spectrum on a grand scale. It is the result of refraction, reflection, and dis- 
 persion of sunlight by falling raindrops. Let spheres 1 and 2 (Fig. 291) 
 represent drops at the extreme opposite edges of the bow. The eye is in a 
 position to receive after the dispersion and internal reflection of the light- 
 waves within 1 drop, only the red waves ; consequently this part of the 
 bow appears red. So, likewise, from drop 2, the eye receives only violet ; 
 consequently this edge appears violet. In like manner, the intermediate 
 colors of the bow are sifted out. 
 
 Outside the primary bow a secondary bow (Fig. 292) is sometimes seen. 
 Drops 3 and 4 (Fig. 291) are supposed to be at the opposite edges of the 
 
328 
 
 RADIANT ENERGY. 
 
 Fig. 291. 
 
 secondary bow. It will be seen that the light-waves undergo two internal 
 reflections within the drops which produce this bow. The colors of this 
 bow are in reverse order of those of the primary bow, and less brilliant. 
 
 Fig. 393. 
 
 31O. Synthesis of White Waves. The composition 
 of white waves has been ascertained by the process of anal- 
 ysis ; can it be verified by synthesis ? i.e. can the colors 
 
PRISMATIC ANALYSIS OF LIGHT-WAVES. 329 
 
 after dispersion be reunited ? and, if so, will white be re- 
 stored ? 
 
 Experiment 217. Place a second prism (2) in such a position 
 (Z^7) that light-waves which have passed through one prism (1), and 
 been refracted and decomposed, may be refracted back, and the colors 
 will be reblended, and a white image of the slit will be restored on 
 the screen. 
 
 Experiment 218. Place a large convex lens, or a concave mirror, 
 so as to receive the colors after dispersion by a prism, and bring the rays 
 to a focus on a screen. The image produced will be white. 
 
 311. Cause of Color Revealed by Dispersion. Color 
 is determined solely by the number of waves emitted by a 
 luminous body in a second of time, or by the corresponding 
 wave-length. In a dense medium, the short waves are more 
 retarded than the longer ones ; hence they are more re- 
 fracted. This is the cause of dispersion. The ether waves 
 diminish in length from the red to the violet. As pitch 
 depends on the number of aerial waves which strike the 
 ear in a second, so color depends on the number of ethereal 
 waves which strike the eye in a second. 
 
 From well-established data, determined by a variety of methods (see 
 larger works), physicists have calculated the number of waves that suc- 
 ceed one another for each of the several prismatic colors, and the corre- 
 sponding wave-lengths ; the following table contains the results. The let- 
 ters A, C, D, etc., refer to Fraunhofer's lines (see Plate I.). 
 
 Length of waves Number of waves 
 
 in millimeters. per second. 
 
 Dark red A 000760 395,000,000,000,000 
 
 Orange C 000656 458,000,000,000,000 
 
 Yellow D 000589 510,000,000,000,000 
 
 Green E 000527 570,000,000,000,000 
 
 C. Blue F 000486 618,000,000,000,000 
 
 U. Blue G 000431 697,000,000,000,000 
 
 Violet H 000397 760,000,000,000,000 
 
 There is a limit to the sensibility of the eye as well as of the ear. The 
 limit in the number of vibrations appreciable by the eye lies approximately 
 
330 KADIANT ENERGY, 
 
 within the range of numbers given in the above table ; i.e. if the succes- 
 sion of waves is much more or less rapid than indicated by these numbers, 
 they do not produce the sensation of sight. 
 
 312. Continuous Spectra. All luminous solids and 
 liquids give continuous spectra. If the spectrum is not 
 complete, as when the temperature is too low, it will begin 
 with red, and be continuous as far as it goes. 
 
 313. Spectroscope. A small instrument called a pocket spectro- 
 scope l will answer for all experiments given in this book. More elaborate 
 experiments require more elaborate apparatus, a description of which 
 must be sought for in larger works on this subject. This instrument con- 
 tains three or more prisms, A, B, and C (Fig. 293). The prisms are en- 
 closed in a brass tube D, and this tube in another tube E. F is a convex 
 lens, and G is an adjustable slit. By moving the inner tube back and 
 forth, the instrument may be so focused that parallel rays will fall upon 
 
 Fig. 393. 
 
 prism A. By varying the kind of glass used in the different prisms, 2 as 
 well as their structure, the deviation of light-waves from a straight path, 
 in passing through them, is overcome, while the dispersion is preserved. 
 On account of the directness of the path of light-waves through it, this 
 instrument is called a direct-vision spectroscope. 
 
 314. Bright Line, Absorption, or Reversed Spectra. 
 
 Experiment 258. Open the slit about one-sixteenth of an inch 
 wide, by turning the milled ring M (Fig. 
 294), and look through the spectroscope at 
 the sky (not at the sun, for its light-waves 
 are too intense for the eye), and you will see 
 a continuous spectrum. 
 
 1 It is expected that the pupil will be provided with a pocket spectroscope, the cost of 
 which need not exceed ten dollars. 
 
 2 A and C are crown-glass, and B is flint-glass. 
 
PRISMATIC ANALYSIS OF LIGHT- WAVES. 331 
 
 Experiment 219. Repeat the last experiment with a candle, 
 kerosene, or ordinary gas flame, and you will obtain similar results. 
 
 Experiment 220. Take a piece of platinum wire 16 inches long. 
 Seal one end by fusion to a short glass tube for a handle. Bend the 
 wire at a right angle. Dip a portion of the wire into a strong solution 
 of common salt, and support it by a clamp in the midst of the almost 
 invisible and colorless flame of a Bunsen burner or 
 alcohol lamp (Fig. 295). Instantly the flame becomes 
 luminous and colored a deep yellow. Examine it with 
 a spectroscope, and you will find, instead of a continuous 
 spectrum beginning with red, only a bright, narrow 
 line of yellow, in the yellow part of the spectrum, next 
 the orange. Your spectrum consists essentially of a 
 single bright yellow line on a comparatively dark 
 ground (see Sodium, Plate L, frontispiece). 
 
 Experiment 221. Heat the platinum wire until it ceases to color 
 the flame, then dip it into a solution of chloride of lithium, and repeat 
 the last experiment. You obtain a carmine-tinted flame, and see 
 through the spectroscope a bright red line and a faint orange line 
 (see Lithium, Plate I.). 
 
 Experiment 222. Use potassium hydrate, and you obtain a 
 violet-colored flame, and a spectrum consisting of a red line and a 
 violet line (the latter is very difficult to see even with the best instru- 
 ments). Use strontium nitrate, and obtain a crimson flame, and a 
 spectrum consisting of several lines in the red and the orange, and a 
 blue line (see Potassium and Strontium, Plate L). 
 
 Experiment 223. Use a mixture of several of the above chemi- 
 cals, and you will obtain a spectrum containing all the lines that char- 
 acterize the several substances. 
 
 Every chemical compound used in the above experiments 
 contains a different metal, e.g. common salt contains the 
 metal sodium ; the other substances used successively con- 
 tain respectively the metals lithium, potassium, and stron- 
 tium. These metals, when introduced into the flame, are 
 vaporized, and we get their spectra when in a gaseous 
 state. All incandescent gases, unless under great pressure, 
 give discontinuous, or bright line, spectra, and no two gases 
 give the same spectra. 
 
332 RADIANT ENERGY. 
 
 315. Dark-line Spectra. 
 
 Experiment 224. Close the slit of the spectroscope so that the 
 aperture will be very narrow; direct it once more to the sky, and 
 slowly move the inner tube back and forth, and you will find, with a 
 certain suitable adjustment which may be obtained by patient trial, 
 that the solar spectrum is not in reality continuous, but is crossed by 
 several dark lines (see Solar Spectrum, Plate I.). 
 
 Remark. In general it is best to focus either the D line in the orange, 
 or the E line in the green. The inner sliding tube ought to be drawn out 
 a little when examining the blue end of the spectrum, and pushed in for 
 focusing the lines in the red. 
 
 Experiment 225. Put a few copper turnings in a test-tube, add 
 a little nitric acid. Hold the tube causing the colored vapor before 
 the slit, and notice the black bands. 
 
 Experiment 226. The electric light is now in so common use 
 that it may be possible to perform this experiment. Between the 
 electric light and the spectroscope introduce the flame of a Bunsen 
 burner, and color it yellow with salt. Examine the spectrum formed 
 through this yellow flame. 
 
 In the last experiment you would naturally expect to 
 find the yellow part of the spectrum uncommonly bright, 
 for there would apparently be added to the yellow waves 
 of the electric light the yellow waves of the salted flame. 
 But precisely where you would look for the brightest 
 yellow, there you discover that the spectrum is crossed 
 by a dark line. If you use salts of lithium, potassium, 
 and strontium in a similar manner, you will find in every 
 case your spectrum crossed by dark lines where you would 
 expect to find bright lines. Remove the Bunsen flame, 
 and the dark lines disappear. It thus appears that the 
 vapors of different substances absorb or quench the very 
 same waves that they are capable of emitting ; very much, 
 it would seem, as a given tuning-fork selects from various 
 sound-waves only those of a definite length corresponding 
 
PRISMATIC ANALYSIS OF LIGHT-WAVES. 333 
 
 to its own vibration-period. The dark places of the spec- 
 trum are illuminated by the salted flame ; but these places 
 are so feebly illuminated in comparison with those places 
 illuminated by the electric light, that the former appear 
 dark by contrast. Light-waves transmitted through cer- 
 tain liquids (as sulphate of quinine and blood) and certain 
 solids (as some colored glasses) produce dark-line spectra. 
 These spectra are obtained only when light-waves pass 
 through media capable of absorbing waves of certain 
 length; hence they are commonly called absorption spec- 
 tra. Since a given vapor causes dark lines precisely where, 
 if it were itself the only radiator of light-waves, it would 
 cause bright lines, dark-line spectra are frequently called 
 reversed spectra. There are then three kinds of spectra: 
 continuous spectra, produced by luminous solids, liquids, 
 or, as has been found in a few instances, gases under great 
 pressure; bright-line spectra, produced by luminous vapors; 
 and absorption spectra, produced by light-waves that have 
 been sifted by certain media. 
 
 316. Spectrum Analysis. More elaborate spectroscopes contain 
 many prisms, by which the purity of the spectrum is greatly increased. 
 (By purity is meant a freedom from the overlapping of images of the slit, 
 by which many lines of the spectrum are obscured.) They also contain an 
 illuminated scale which may be seen adjacent to the spectrum, by which the 
 exact position of the lines and their relative distances from one another 
 can be accurately determined, and a telescope by which the spectrum and 
 scale may be magnified. The positions of some of the prominent lines of 
 the solar spectrum were first determined, mapped, and distinguished from 
 one another by certain letters of the alphabet, by Fraunhofer; hence the 
 dark linos of the solar spectrum are commonly called Fraunhofer's lines. 
 So far as discovered, no two substances have a spectrum consisting of the 
 same combination of lines ; and, in general, different substances but very 
 rarely possess lines appearing to be common to both. Hence, when we have 
 once observed and mapped the spectrum of any substance, we may ever 
 after be able to recognize the presence of that substance when emitting 
 light-waves, whether it is in our laboratory or in a distant heavenly body. 
 
334 RADIANT ENEKGY. 
 
 The spectroscope, therefore, furnishes us a most efficient means of detect- 
 ing the presence (or absence) of any elementary substance, even when 
 it is combined or mixed with other substances. It is not necessary that 
 the given substance should exist in large quantities; for example, a 
 fourteen-millionth of a milligram of sodium can be detected by the spec- 
 troscope. 
 
 317. Celestial Chemistry and Physics. The spectrum of 
 iron has been mapped to the extent of 460 bright lines. The solar spec- 
 trum furnishes dark lines corresponding to nearly all these bright lines. 
 Can there be any doubt of the existence of iron in the sun ? By exami- 
 nation of the reversed spectrum of the sun, we are able to determine 
 with certainty the existence there of sodium, calcium, coppery zinc, 
 magnesium, hydrogen, and many other known substances. The moon 
 and other heavenly bodies that are visible only by reflected sunlight give 
 the same spectra as the sun, while those that are self-luminous give spectra 
 which differ from the solar spectrum. 
 
 318. Relative Heating- and Chemical Effects of 
 Ether- Waves of Different Lengths. If a sensitive thermome- 
 ter is placed in different parts of the solar spectrum, it will indicate heat in 
 all parts ; but the heat generally increases from the violet toward the red. 
 It does not cease, however, with the limit of the visible spectrum ; indeed, 
 if the prism is made of flint glass, the greatest heat is just beyond the red. 
 A strip of paper wet with a solution of chloride of silver suffers no change in 
 the dark ; in the light-waves it quickly turns black ; exposed to the light- 
 waves of the solar spectrum, it turns dark, but quite unevenly. The change 
 is slowest in the red, and constantly increases, till about the region indicated 
 by G (see Solar Spectrum, Plate I.), where it attains its maximum ; from 
 this point it falls off, and ceases at a point considerably beyond the limit of 
 the violet. It thus appears that the solar spectrum is not limited to the 
 visible spectrum, but extends beyond at each extremity. Those waves 
 that are beyond the red are usually called the infra-red waves, while those 
 that are beyond the violet are called the ultra-violet waves. The infra-red 
 waves are of longer vibration-period, and the ultra-violet of shorter period, 
 than the light-waves. 
 
 319. Only one Kind of Kadiation. The fact that radiant 
 energy produces three distinct effects viz. luminous, heating, and 
 chemical formerly gave rise to a prevalent idea that there are three 
 distinct kinds of radiation. There is, however, absolutely no proof that 
 these different effects are produced by different kinds of radiation, 
 
PRISMATIC ANALYSIS OF LIGHT-WAVES. 335 
 
 Science recognizes in radiations no distinctions but periods, wave lengths, 
 and wave forms. The same radiation that produces vision can generate 
 heat and chemical action. The fact that the infra-red and ultra-violet 
 rays do not affect the eye does not argue that they are of a different 
 nature from those that do, but it does show that there is a limit to the 
 susceptibility of the eye to receive impressions from radiation. Just as 
 there are sound-waves of too long, and others of too short period to affect 
 the ear, so there are ethereal waves, some of too long, and others of too 
 short period to affect the eye. 
 
 While waves traverse the ether there is neither heat nor light (i.e. 
 sensation) ; hence the propriety of applying either of these terms to a 
 train of waves traversing the ether may well be called in question. Yet 
 this is all that traverses the space between the sun and the earth. 
 
 32O. Chromatic Aberration. There is a serious de- 
 fect in ordinary convex lenses, to which we have not before 
 alluded, called chromatic aberration, which has required 
 the highest skill to correct. The convex lens both 
 refracts and disperses the light-waves that pass through it. 
 The tendency, of course, is to bring the more refrangible 
 rays, as the violet, to a focus much sooner than the less 
 refrangible rays, such as the red. The result is a disagree- 
 able coloration of the images that are formed by the lens, 
 especially by that portion of the light-waves that passes 
 through the lens near its edges. This evil has 
 been overcome very effectually by combining with 
 the convex lens a plano-concave lens. Now, if a 
 crown-glass convex lens is taken, a flint-glass 
 concave lens may be prepared that* will correct the 
 dispersion of the former without neutralizing all Flgt 396 ' 
 its refraction. 1 A compound lens, composed of these two 
 lenses (Fig. 296) cemented together, constitutes what is 
 called an achromatic lens. 
 
 1 The refractive and dispersive powers of the two lenses are not proportional. 
 
336 RADIANT ENERGY. 
 
 Section VIII. 
 
 COLOR. 
 
 321. Color by Absorption. Color is a sensation ; it 
 has no material existence. The term "yellow light" 
 means, primarily, a particular sensation ; secondarily, it 
 means the physical cause of this sensation, i.e. a train of 
 ether-waves of a particular frequency. " All objects are 
 black in the dark"; this is equivalent to saying that 
 without light there is no color. 
 
 Experiment 227. By means of a porte lumiere introduce a beam 
 of sunlight into a dark room. With the slit and prism form a solar 
 spectrum. Between the slit and prism introduce a deep red glass ; 
 all the colors of the spectrum except the red are much reduced in 
 intensity. 
 
 It thus appears that the color of a colored transparent 
 object, as seen by transmitted light, arises from the 
 unequal absorption of the different colors of white light 
 incident upon it. A red glass absorbs less red light than 
 light of other colors. The color produced by absorption 
 is rarely very pure, the particular hue of the transmitted 
 light being due merely to a predominance of certain colors, 
 and not to the absence of all others. As the absorbing 
 layer is thicker, the resulting color is purer but less 
 intense. 
 
 Experiment 228. We have found that common salt introduced 
 into a Bunsen flame renders it luminous, and that the light when 
 analyzed with a prism is found to contain only yellow. Expose 
 papers or fabrics of various colors to this light in a darkened room. 
 JVo one of them except yellow exhibits its natural color. 
 
COLOR. 
 
 337 
 
 Experiment 229. Hold a narrow strip of red paper or ribbon in 
 the red portion of the solar spectrum ; it appears red. Slowly move 
 it toward the other end of the spectrum ; on leaving the red it 
 becomes darker, and when it reaches the green it is quite black or 
 colorless, and remains so as it passes the other colors of the spectrum. 
 Repeat the experiment, using other colors, and notice that only in 
 light of its own color does each strip of paper appear of its natural 
 color, while in all other colors it is dark. 
 
 These experiments show that the color of a body seen by 
 light reflected from it depends both upon the color of the 
 light incident upon it and upon the nature of the body. 
 
 If a piece of colored glass, A B (Fig. 297), be held near a window so 
 as to receive, obliquely, rays of sunlight, a portion of the light will be 
 reflected by the anterior surface of the glass, and, falling upon the white 
 ceiling, will illuminate 
 it with white light. 
 Another portion of the 
 light will enter the 
 glass and be reflected 
 from the posterior sur- 
 face ; this light, having 
 entered the glass and 
 traveled in it a distance 
 a little greater than 
 twice its thickness, will suffer an unequal absorption of its rays, and 
 after emerging from the glass will, if the glass be blue, illuminate a 
 neighboring portion of the ceiling with blue light. This illustrates the 
 method by which pigments afford color. Thus, the first surface of a 
 water-color drawing reflects the white daylight. Most of the light 
 reflected to the eye has, however, passed through the pigment to the 
 white paper beneath, and being reflected from this, again passes through 
 the layer of pigment before reaching the eye. With less transparent 
 pigments the light may be reflected merely by particles of pigment 
 beneath the surface. The color of paints and pigments is, therefore, due 
 to the rays which they absorb least readily. When we paint our houses 
 we do not apply color to them ; we apply substances which have the 
 property of absorbing or subtracting from white light largely all the 
 
 Fig. 297. 
 
338 RADIANT ENERGY, 
 
 colors except those which we would have our houses appear. This is 
 technically called selective absorption. 
 
 The color of bodies thus depends generally upon their molecular 
 structure. Different bodies quench different portions of the complex 
 sunlight. The unquenched light determines the color of a body. 
 
 322. Mixing- Colors. A mixture of all the prismatic 
 colors in the proportion found in sunlight produces white. 
 Can white be produced in any other way ? 
 
 Experiment 230. On a black surface, A (Fig. 298), lay two 
 small rectangular pieces of paper, one yellow and the other blue, 
 about two inches apart. In a vertical position 
 between these papers, and from 3 inches to 6 inches 
 above them, hold a slip of plate glass, C. Looking 
 obliquely down through the glass you may see the 
 blue paper by transmitted light-waves and the 
 yellow paper by reflection. That is, you see the 
 object itself in the former case, and the image of 
 the object in the latter case. By a little manipula- 
 tion the image and the object may be made to 
 overlap each other, when both colors will apparently 
 Fig. 398. disappear, and in their place the color which is 
 the result of the mixture will appear. In this case it will be white, 
 or rather, gray, which is white of a low degree of luminosity. If the 
 color be yellowish, lower the glass ; if bluish, raise it. 
 
 Experiment 231. With the rotating apparatus, rotate the disk 
 (Fig. 299) which contains only yellow and blue. The colors (i.e. the 
 sensations) so blend in the eye as to produce the sensation of gray. 
 
 X 
 
 Fig. 399. Fig. 30O. Fig. 3O1. 
 
COLOR. 339 
 
 Figure 300 represents " Newton's disk," which contains 
 the seven prismatic colors arranged in a proper proportion 
 to produce gray when rotated. 
 
 In like manner, you may produce white by mixing 
 purple and green ; or, if any color on the circumference 
 of the circle (see Complementary Colors, Plate I) be mixed 
 with the color exactly opposite, the resulting color will be 
 gray. Green mixed with red, in varying proportions, will 
 produce any of the colors in a straight line between these 
 two colors in the diagram (Plate I), green mixed with 
 violet will produce any of the colors between them ; and 
 violet mixed with red gives purple. The three colors, red, 
 green, and violet, mixed (Fig. 301), give gray (see 324). 
 
 All colors are represented in the spectrum, except the purple hues. 
 The latter form the connecting link between the two ends of the 
 spectrum. Our color chart (Plate I) is intended to represent the sum 
 total of all the sensations of color. By means of this chart we may 
 determine the result of the (optical) mixture of any two colors, as 
 follows : Find the places occupied upon the chart by the two colors 
 which are to be mixed, and unite the two points by a straight line. The 
 color produced by the mixture will invariably be found at the center of 
 this line. 
 
 323. Mixing- Pigments. 
 
 Experiment 232. Mix a little of the two pigments, chrome 
 yellow and ultramarine blue, and you obtain a green pigment. 
 
 The last three experiments show that mixing certain 
 colors, and mixing pigments of the same name, may pro- 
 duce very different results. In the first experiments you 
 mixed colors ; in the last experiment you did not mix 
 colors, and we must seek an explanation of the result 
 obtained. If a glass vessel with parallel sides containing 
 a blue solution of sulphate of copper be interposed in the 
 
340 RADIANT ENERGY. 
 
 path of the lightwaves which form a solar spectrum, it 
 will be found that the red, orange, and yellow waves are 
 cut out of the spectrum, i.e. the liquid absorbs these 
 waves. And if a yellow solution of bichromate of potash 
 or picric acid be interposed, the blue and violet waves will 
 be absorbed. It is evident that, if both solutions be inter- 
 posed, all the colors will be destroyed except the green, 
 which alone will be transmitted ; thus : 
 
 Cancelled by the blue solution, $ ^ G B V. 
 
 Cancelled by the yellow solution, R O Y G 
 
 Cancelled by both solutions, $ V G 
 
 In a similar manner, when white light strikes a mixture of yellow and 
 blue pigments on the palette, it penetrates to some depth into the 
 mixture ; and, during its passage in and out, all the colors except the 
 green are destroyed ; so the mixed pigments necessarily appear green. 
 But when a mixture of yellow and blue waves enters the eye, we get, as 
 the result of the combined sensations produced by the two colors, the 
 sensation of white ; hence a mixture of yellow and blue gives white. 
 
 The color square 3 (Plate I) represents the result of the mixture of 
 pigments 1 and 2 ; while 4 represents the result of the optical mixture of 
 the same colors. 
 
 324. Theory of Color Vision. The generally accepted 
 theory of color vision is that of Dr. Young (1801-2), verified by Maxwell 
 and Helmholtz. It supposes the existence of three color sensations, red, 
 green, and violet. These excited simultaneously, and with proper inten- 
 sities, produce the sensation of white light. Combined in twos, they 
 produce the remaining color sensations. Thus red and green sensations 
 combined give yellow or orange ; green and violet give blue, etc. The 
 longer light- waves excite the sensation of red ; together with those some- 
 what shorter, they excite both red and green, thus giving yellow, and so 
 on. Strictly speaking, light-waves of any length excite all three sen- 
 sations ; but usually either one or two of them greatly predominate. 
 
 325. Complementary Colors. 
 
 Experiment 233. On a piece of gray paper lay a circular piece 
 of blue paper 15 mm in diameter. Attach one end of a piece of 
 
COLOR. 341 
 
 thread to the colored paper, and hold the other end in the hand. 
 Place the eyes within about 15 cm of the colored paper, and look 
 steadily at the center of the paper for about fifteen seconds ; then, 
 without moving the eyes, suddenly pull the colored paper away, and 
 instantly there will appear on the gray paper an image of the colored 
 paper, but the image will appear to be yellow. This is usually called 
 an after-image. If yellow paper be used, the color of the after-image 
 will be blue ; and if any other color given in the diagram (Plate I.), 
 the color of its after-image will be the color that stands opposite to it. 
 
 This phenomenon is explained as follows : When we 
 look steadily at blue for a time, the eyes become fatigued 
 by this color, and less susceptible to its influence, while 
 they are fully susceptible to the influence of other colors ; 
 so that when they are suddenly brought to look at white, 
 which may be regarded as a compound of yellow and blue, 
 they receive a vivid impression from the former, and a 
 feeble impression from the latter ; hence the predominant 
 sensation is yellow. Any two colors which together pro- 
 duce white are said to be complementary to each other. 
 The opposite colors in the diagram (Plate I.) are comple- 
 mentary to one another. 
 
 The complement of green is purple, a compound color 
 not existing in the spectrum. 
 
 326. Effect of Contrast. When different colors are seen at 
 the same time, their appearance differs more or less from that observed 
 when they are seen separately. Thus a red object (e.g. a red rose) 
 appears more brilliant if a green object be seen in juxtaposition with it. 
 Such effects are said to be due to contrast. 
 
 When any two colors given in the circle (Plate I.) are brought in 
 contrast, as when they are placed next each other, the effect is to move 
 them farther apart in the color scale. For example, if red and orange be 
 brought in contrast, the orange assumes more of a yellowish hue, and the 
 red more of a purplish hue. Colors that are already as far apart as 
 possible, e.g. yellow and blue, do not change their hue, but merely cause 
 each other to appear more brilliant. 
 
342 RADIANT ENERGY. 
 
 327. Color-blindness. In this defect in vision, one of the 
 three color sensations is either wanting or deficient, usually that of red ; 
 so that the colors perceived are reduced to those furnished by the remain- 
 ing two sensations, viz. green and violet. This causes the red-blind 
 person to confound reds, greens, and grays. In some rare cases the 
 sensation of green or violet is the one deficient. 
 
 Section IX. 
 
 THERMAL EFFECTS OF RADIATION. 
 
 328. Heat not transmitted by Radiation. We have 
 learned that heat may travel through matter (by con- 
 duction), and with matter (by convection), and it is some- 
 times stated that there is a third method by which it 
 travels, viz. "radiation." Heat itself is not transferred 
 by radiation ; heat generates radiation (i.e. ether waves) at 
 one place, and radiation is transformed into heat at 
 another. Radiation travels, not heat. Heat can flow 
 only one way, viz. from a given point to a point that is 
 colder ; radiation travels in all directions. The sun 
 sends us no heat; it sends radiations which the earth 
 transforms into heat ; but it should be borne in mind that 
 while it is radiation it is not heat, and vice versa. Tem- 
 perature is a condition of bodies, not of radiations ; 
 wave-lengths belong to radiations, not to heat which 
 produces them. 
 
 329. Diathermancy and Athermancy. What be- 
 comes of radiations which strike a body depends largely 
 upon the character of the body. If the nature of the 
 
THERMAL EFFECTS OF RADIATION. 
 
 343 
 
 body be such that its molecules can accept the motion of 
 the ether, the vibrations of the ether are said to be 
 absorbed by the body, and the body is thereby heated, 
 i.e. the undulations of the ether are transformed into 
 molecular energy or heat. Glass* for instance, allows the 
 sun's radiations to pass very freely through it, and very 
 little is transformed into heat. But if the glass be 
 covered with the soot of a candle flame, the soot will 
 absorb the radiations and the glass become heated. 
 Observe how cold window-glass may remain, while radia- 
 tions pour through it and heat objects in the room. Only 
 those radiations that a body absorbs heat it; those that pass 
 through it do not affect its temperature. 
 
 Bodies that transmit radiations freely are said to be 
 diathermanous, while those that absorb them largely are 
 called athermanous. The most diathermanous substance 
 known is rock salt. A solution of iodine in carbon 
 bisulphide absorbs almost completely the rays of the 
 visible spectrum, but transmits almost completely all of 
 longer wave-length than the red end of the spectrum. A 
 plate of alum acts in the reverse man- 
 ner, transmitting the visible and absorb- 
 ing the invisible. Among liquids carbon 
 bisulphide is exceptionally transparent 
 to all forms of radiation; while water, 
 transparent to short waves, absorbs the 
 longer waves, and is thus quite ather- 
 manous. 
 
 Experiment 234. Prepare a differential 
 thermometer with two glass flasks and a glass 
 tube, as represented in Figure 302. Cover one 
 
 Fig. 303. 
 
344 RADIANT ENERGY. 
 
 of the flasks with lamp-black by holding it above a smoking kerosene 
 flame. Place colored liquid in the bend A. Stopper both vessels 
 tightly and expose the apparatus to the direct rays of the sun. The 
 rays pass through the clean glass and through the air within, 
 affecting the temperature of either but little. But the lamp-black 
 absorbs the radiations, the 'flask becomes heated, the enclosed air 
 becomes heated by contact with the heated flask, the heated air 
 expands and pushes the liquid in the tube toward the cooler flask. 
 
 Dry air is almost perfectly diathermanous. All of the sun's radiations 
 that reach the earth pass through the atmosphere, which contains a vast 
 amount of aqueous vapor. This vapor, like water, is comparatively 
 opaque to long waves. 
 
 This fact has great influence in modifying the climate of the earth. 
 For the earth, warmed by the sun's radiations, tends also to part with its 
 heat by radiation. But the character of the radiations emitted by the 
 earth is quite different from that of the radiations which it receives. 
 The earth at a low temperature emits chiefly long ether waves, but it is 
 heated chiefly by short waves. But it is exactly these long waves which 
 are most readily stopped by the atmosphere ; hence, the atmosphere, or 
 rather the aqueous vapor of the atmosphere, acts as a sort of trap for the 
 energy which comes to us from the sun. 
 
 Remove the watery vapor (which serves as a " blanket " to the earth) 
 from our atmosphere, and the chill resulting from the rapid escape of heat 
 by radiation would probably put an end to all animal and vegetable life. 
 
 33O. Provost's Theory of Exchanges. Hot bodies usually 
 part with their heat much more rapidly by radiation than by all other 
 processes combined. But cold bodies, like ice, emit radiations even when 
 surrounded by warm bodies. This must be so from the nature of the case, 
 for the molecules of the coldest bodies possess some motion, and being 
 surrounded by the ether they cannot move without imparting some of 
 their motion to the ether, and to that extent becoming themselves colder. 
 
 Let us suppose that we have two bodies, A and B, at different 
 temperatures, A warmer than B. Radiation takes place not only from 
 A to B, but from B to A ; but, in consequence of A's excess of tempera- 
 ture, more radiation passes from A to B than from B to A, and this 
 continues until both bodies acquire the same temperature. At this point 
 radiation by no means ceases, but each now gives as much as it receives, 
 and thus equilibrium is kept up. This is known as "Provost's Theory 
 of Exchanges." 
 
THERMAL EFFECTS OF RADIATION. 345 
 
 331. Good Absorbers, Good Radiators. As bodies 
 differ widely in their absorbing power, so they do in their 
 radiating power, and it is found to be universally true 
 that good absorbers are good radiators, and bad absorbers 
 are bad radiators. Much, in both cases, depends upon 
 the character of the surface as well as of the substance. 
 Bright, polished surfaces are poor absorbers and poor 
 radiators ; while tarnished, dark, and roughened surfaces 
 absorb and radiate rapidly. Dark clothing absorbs and 
 radiates more rapidly than light clothing. 
 
 QUESTIONS. 
 
 1. What objections can you raise to the term " radiant heat "? 
 
 2. Explain why the temperature of a hotbed is above that of the 
 surrounding air. 
 
 3. How could you separate the dark radiation of an electric arc 
 lamp from the luminous radiation ? 
 
 4. How can you demonstrate the existence of ether waves of 
 greater length than the light-giving waves ? 
 
 5. Ice appears to radiate cold. Explain the phenomenon by 
 Provost's theory. 
 
 6. What parts of the spectrum are invisible to the eye ? 
 
 7. On what does the color of bodies primarily depend? 
 
 8. What agency does a body perform in determining its own 
 color when illuminated with white light ? 
 
 9. a. Why is grass green ? b. Snow white ? c. Soot black ? 
 
 10. What utility is there in keeping certain parts of a steam- 
 engine very bright ? 
 
 11. When red and green sensations coexist, what is the resulting 
 sensation ? 
 
 12. Describe the surface which a hot-water vessel should have in 
 order to retain its heat well. 
 
346 
 
 RADIANT ENERGY. 
 
 Section X. 
 
 SOME OPTICAL INSTRUMENTS. 
 
 332. Compound Microscope. When it is desired to 
 magnify an object more than can be done conveniently 
 and with distinctness by a single lens, two convex lenses 
 are used, one, O (Fig. 303), called the objective, to form 
 a magnified real image a' b f of the object a b ; and the 
 other E, called the eye-piece, to magnify this image so 
 that the image a' b' appears of the size a" b". Instead of 
 looking at the object as when we use a simple lens, we 
 look at the real inverted image a' b' of the object. 
 
 This represents the simplest possible form of the compound microscope. 
 
 In practice, however, the construction 
 is more complicated. 
 
 Figure 304 represents a perspective 
 and a sectional view of a simple form 
 of a modern compound microscope. 
 The body of the instrument consists of 
 a series of brass tubes movable one 
 within another. In the upper end H 
 is the ocular or eye-piece. It consists 
 of two plano-convex lenses o and ?i, 
 the former called the eye lens, the latter 
 called the field lens. This combination 
 tends to diminish both the spherical 
 and the chromatic aberration as well 
 as to increase the size and flatness of the field of view. 
 
 All microscopes, however, should be furnished with an achromatic 
 objective. This consists of two to four achromatic lenses (the achromatic 
 triplet, the most common form, is represented on an enlarged scale at L 
 in Figure 304), combined so as to act as a single lens of short focus. By 
 the use of several lenses, the aberrations can be better corrected than 
 with a single lens. 
 
 Fig. 303. 
 
SOME OPTICAL INSTRUMENTS. 
 
 347 
 
 The object to be examined is placed on a stage S, and if the object 
 be transparent, it is strongly illuminated by focusing light upon it by 
 means of a concave mirror M. If the object be opaque, it is illuminated 
 by light directed upon it obliquely from above by the converging lens N. 
 
 Fig. 304. 
 
 333. Magnifying Power. The magnifying power of 
 a compound microscope is the product of the respective 
 magnifying powers of the object-glass and the eye-piece ; 
 that is, if the first magnify 20 times and the other ten 
 times, the total magnifying power is 200. The magnify- 
 
348 RADIANT ENERGY. 
 
 ing power is determined experimentally by means of a 
 micrometer scale, for a description of which the student is 
 referred to technical works on microscopy. 
 
 334. Telescopes. Telescopes are used to view (scope) 
 objects afar off (tele). They are classified as astronomical 
 or terrestrial, according as they are designed to be used in 
 viewing heavenly bodies or terrestrial objects ; reflecting 
 or refracting, according as the objective is a concave 
 mirror or a converging lens. The terrestrial telescope 
 differs from the astronomical in producing images in their 
 true position without inversion. This is effected by means 
 of an extra object lens, which corrects the inversion of the 
 main object lens. The matter of inversion is of little or 
 no consequence in viewing heavenly bodies. 
 
 The refracting astronomical telescope consists essentially, like the 
 
 Fig. 305. 
 
 compound microscope, of two lenses. The object-glass (O, Fig. 305) forms 
 a real diminished image (a, 6) of the object A, B; this image, seen 
 through the eye-glass E, appears magnified and of the size c, d. The 
 object-glass is of large diameter, in order to collect as much light as 
 possible from a distant object for a better illumination of the image. 
 
 This telescope is analogous to the microscope, but the two instruments 
 differ in this respect : in the microscope, the object being very near the 
 object-glass, the image is formed much beyond the principal focus, and is 
 greatly magnified, so that both the object-glass and the eye-piece 
 magnify ; while in the telescope, the heavenly body being at a great 
 distance, the incident rays are practically parallel, and the image formed 
 by the object-glass is much smaller than the object. The use of the 
 
SOME OPTICAL INSTRUMENTS. 
 
 349 
 
 object-glass is to collect as large a number as possible of the greatly 
 scattered rays, so as to increase the brilliancy of the image. The only 
 magnification which can occur is produced by the eye-piece, which 
 ought therefore to be of high power. The magnifying power of this 
 instrument equals approximately the focal length of the object-glass divided 
 by the focal length of the eye-piece. 
 
 335. The Human Eye. Fig. 306 represents a hori- 
 zontal section of this wonderful organ. Covering the 
 front of the eye, like a watch- 
 crystal, is a transparent coat 
 1, called the cornea. A tough 
 membrane 2, of which the 
 cornea is a continuation, forms 
 the outer wall of the eye, and 
 is called the sclerotic coat, or 
 " white of the eye." This coat 
 is lined on the interior with a 
 delicate membrane 3, called 
 the choroid coat; the latter 
 consists of a black pigment, which prevents internal 
 reflection. The inmost coat 4, called the retina, is formed 
 by expansion of the optic nerve O. The muscular tissue 
 i, i is called the iris; its color determines the so-called 
 " color of the eye." In the center of the iris is a circular 
 opening 5, called the pupil, whose function is to regulate, 
 by involuntary enlargement and contraction, the quantity 
 of light-waves admitted to the posterior chamber of the eye. 
 Just back of the iris is a tough, elastic, and transparent 
 body 6, called the crystalline lens. This lens divides the 
 eye into two chambers ; the anterior chamber 7, is filled 
 with a limpid liquid, called the aqueous humor; the 
 posterior chamber 8, is filled with a jelly-like substance, 
 
350 RADIANT ENERGY. 
 
 called the vitreous humor. The lens and the two humors 
 constitute the refracting apparatus. 
 
 The eye may be likened to a photographer's camera, in 
 which the retina takes the place of the sensitized plate. 
 Images of outside objects are projected by means of the 
 crystalline lens, assisted by the refraction of the humors, 
 upon this screen, and the impressions thereby made on 
 this delicate network of nerve filaments are conveyed by 
 the optic nerve to the brain. 
 
 With the ordinary camera, the distance of the lens from 
 the screen must be regulated to adapt itself to the varying 
 distances of outside objects, in order that the images may 
 be properly focused on the screen. In the eye this is 
 accomplished by changing the convexity of the lens. We 
 can almost instantly and unconsciously change the lens of 
 the eye, so as to form on the retina a distinct image of an 
 object miles away, or only a few inches distant. The 
 nearest limit at which an object can be placed so as to 
 form a distinct image on the retina is about five inches. 
 On the other hand, the normal eye in a passive state is 
 adjusted for objects at an infinite distance. 
 
 336. Defects of Vision. Myopia (short-sightedness) is caused 
 by the excessive length of the globe from front to back, so that the 
 images of all but near objects are formed in front of the retina. 
 Remedy : use diverging lenses. Hypermetropia (long-sightedness) occurs 
 when the axis of the globe is so short that the image of an object is back 
 of the retina unless the object is held at an inconvenient distance, in 
 which case it tends to become indistinct. Remedy : use converging 
 lens. Presbyopia is due to loss of accommodation power, so that while 
 vision for distant objects remains clear, that for near objects is indistinct. 
 This defect is incident to advancing years, and is due to progressive loss 
 of elasticity of the crystalline lens. Remedy : converging lenses. Astig- 
 matism is caused by an inequality in the curvature of the cornea in 
 
SOME OPTICAL INSTRUMENTS. 
 
 351 
 
 different meridians, so that when, for example, a diagram like Figure 307 
 is held at a distance, vertical lines will be in focus and horizontal lines 
 will be out of focus and will appear blurred 
 and indistinct, or vice versa. Remedy : 
 lenses of cylindrical curvature. But, for 
 this, as well as for all other defects or 
 troubles of the eyes, consult a skilled ocu- 
 list, and the earlier the better. 
 
 Advice to all : Do not overstrain or over- 
 tax the eyes, or use them in insufficient or 
 excessive light, in flickering light such as 
 that of a gas-jet, or in unsteady light such 
 as that in a moving vehicle ; and avoid so 
 far as practicable sudden changes of light, 
 such as lightning flashes, etc. 
 
 337. Stereopticon. This instrument is extensively 
 employed in the lecture-room for producing on a screen 
 magnified images of small, transparent pictures on glass, 
 called slides ; also for rendering a certain class of experi- 
 ments visible to a large audience by projecting them on a 
 screen. 1 The lime light is most commonly used, though 
 the electric light is preferred for a certain class of pro- 
 jections. The flame of an oxyhydrogen blow-pipe, A 
 (Fig. 308), is directed against a stick of lime B, and 
 
 Fig. 307. 
 
 Fig. 308. 
 
 1 For useful information relating to the operation of projection, especially for 
 scientific illustrations, see Wright's Light, and Dolbear's Art of Projecting. 
 
352 RADIANT ENERGY. 
 
 raises it to a white heat. The radiations from the lime 
 are condensed by means of a convex lens <?, called the con- 
 densing lens (usually two plano-convex lenses are used), so 
 that a larger quantity of radiations will pass through the 
 convex lens E, called the projecting lens. The latter lens 
 produces (or projects) a real, inverted, and magnified 
 image of the picture on the screen S. The mounted lens 
 E may slide back and forth on the bar F, so as properly to 
 focus the image. 
 
 EXERCISES. 
 
 1. What is light? 
 
 2. State points of resemblance and points of difference between 
 light-waves and sound-waves. Which can traverse a vacuum (as 
 regards matter)? 
 
 3. Two books are held, respectively, 2 feet and 7 feet from the 
 same gas-flame. Compare the intensities of the illumination of their 
 respective pages. 
 
 4. What is the general effect of a concave mirror on light-waves ? 
 What kind of lens produces a similar effect ? 
 
 5. How can a beam of light be bent ? 
 
 6. State different ways by which the colors which compose white 
 light may be revealed. 
 
 7. How do you account for the color of flowers? How do you 
 account for the colors seen on a soap-bubble ? 
 
 8. Why do white surfaces appear gray at twilight ? 
 
 9. How are objects heated by the sun ? 
 
 10. What evidences can you give that the earth receives energy 
 from the sun ? 
 
 11. What phenomenon shows that ether-waves do not traverse all 
 substances with equal speed ? 
 
REVIEW QUESTIONS. 853 
 
 REVIEW QUESTIONS. 
 
 1. Show that a spring balance is, strictly speaking, a force- 
 measurer, and not a mass-measurer. 
 
 2. A body weighs 100 Ibs. at the earth's surface. Where would 
 it weigh on a spring balance 50 Ibs. ? 
 
 3. What way of measuring force is suggested by Newton's 
 Second Law of Motion ? 
 
 4. Determine the available water pressure (in pounds per square 
 inch) in a laboratory which is supplied from a tank at a hight of 
 45ft. 
 
 5. What is the atmospheric pressure in pounds per square inch 
 when the barometric height is 27.5 in.? 
 
 6. What should be the horse-power of an engine intended to 
 pump 200 gallons of water per minute to a hight of 50 yds. ? 
 (Assume 1 gall. =c= 10 Ibs.) 
 
 7. A cube, the edge of which is one decimeter, is suspended in 
 water with its upper surface l m below the surface of the water. 
 Find the pressure on each of its faces. 
 
 8. A sailor climbs a mast at a uniform rate of 5 ft. a minute, 
 while the vessel moves forward at the rate of 15 ft. a minute ; what 
 is his actual velocity ? 
 
 9. If the masses of a rifle and a bullet be respectively 25 Ibs. arid 
 1 oz. (y^ lb.), and the rifle at its discharge acquire a maximum 
 velocity of 3 ft. per second, what, at that instant, is the velocity of 
 the bullet ? 
 
 10. If the motion of the moon in its orbit about the earth were 
 to cease, these bodies would approach each other. The mass of the 
 earth is about 80 times that of the moon. What part of the whole 
 distance between them would the moon move before collision ? 
 
 11. A constant force acts on an otherwises freely moving body in a 
 direction opposite to that in which it is moving ; how is the body's 
 motion affected thereby ? Give an illustration. 
 
 12. State and explain the posture of a bicycle-rider in turning 
 a curve. 
 
354 RADIANT ENERGY. 
 
 13. Account for the curvilinear orbits of the planets. 
 
 14. A pebble is suspended by a thread 2 ft. long ; required the 
 number of vibrations it will make in a minute. 
 
 15. Suppose that in bending a bow an average force of 25 Ibs. is 
 exerted through a space of 10 inches ; what amount of energy will 
 be stored in the bow ? 
 
 16. A projectile of a mass of 50 k is thrown vertically upward 
 with an initial velocity of 29.4 ra per second. How much energy 
 has it ? 
 
 17. How many and what transformations of energy take place 
 during a single swing of a pendulum ? 
 
 18. Supply the following ellipses by selecting appropriate words 
 from the following, viz.: Force, work, energy, power. When 
 
 acts through space is performed, and is imparted. The 
 
 rate at which work is performed determines the of the agent. 
 
 The of a bullet flying through vacant space. What must 
 
 a bullet of mass 1 ounce have that it may rise 4 seconds ? What 
 
 is consumed by a steamer in crossing the ocean ? What is 
 necessary that it may traverse 300 knots per day, and what must be 
 
 the average exerted to overcome the resistances at the required 
 
 rate? 
 
 1 9. Change of momentum is proportional to what ? Change of 
 energy is proportional to what ? 
 
 20. A building is heated by steam-pipes. How does heat get 
 from the furnace to objects in the building? 
 
 21. A mass of 93.3s of copper at 80 C. is immersed in 560 of 
 water at 10, and raises the temperature of the water to 20; find 
 the specific heat of copper. 
 
 22. How much ice at will be melted by 400 of water at 90 C ? 
 
 23. Copper wire ^ in. in diameter offers a resistance of 8 ohms 
 per mile ; what is the resistance of a mile of copper wire -fa in. in 
 diameter ? 
 
 24. a. How many volts are required to maintain a 5-ampere 
 current in a circuit whose resistance is 2 ohms ? b. What power is 
 consumed in the circuit ? 
 
 25. Determine the amperage of a battery of 5 cells joined in 
 multiple arc, each having an E.M.F. of 2 volts and an internal 
 
REVIEW QUESTIONS. 355 
 
 resistance of .5 ohm, (a) when the external resistance is .1 ohm ; 
 (6) when the external resistance is 500 ohms. 
 
 26. What are induced currents ? how produced ? how made 
 continuous- ? 
 
 27. Upon what does the E.M.F. of a dynamo depend? 
 
 28. A dynamo feeds 16 arc lamps that have an average resistance 
 of 4.56 ohms. What current does the dynamo yield with an E.M.F. 
 of 838.44 volts ? 
 
 29. What is the length of sound-waves yielded by a c' fork when 
 the temperature of the air is 18 C. ? 
 
 30. A string sounding the tone c' is 18 in. long. What must be 
 its length to sound cf ? 
 
 31. If you hold a sheet of paper with a greased spot on it between 
 you and a gas-flame in a darkened room, will the spot appear lighter 
 or darker than the rest of the sheet ? Why ? 
 
 32. The focal length of a convex lens being 8 in., determine the 
 position of the conjugate focus of a point 15 in. from the lens. 
 
 33. Why is pulverized glass opaque? 
 
 34. Under what conditions will a spectrum be continuous ? bright- 
 line ? dark-line ? 
 
 35. A person whose distance of most distinct vision is 20 cm uses 
 a lens of 5 cm focal length as a reading-glass, a. At what distance 
 from a book ought he to hold it ? b. What will be its magnifying 
 power ? 
 
Inches 
 
 
 i 
 
 
 2 |3 
 
 lUlll] llll \2 
 
 
 |3 14 
 
 Ic 
 
 7 Is 9 
 
 1C 
 
 Millimeters 
 
 Centimeters 
 
 Mil lil'lte 
 
 Cubic Centimeter 
 
 The area of this figure is a square decimeter. 
 A cube of water, one of whose sides has this 
 area, is a cubic decimeter or a liter of water, 
 and at the temperature of 4 C. has a mass of 
 a kilogram. The same volume of air at C., 
 and under a pressure of one atmosphere, has a 
 mass of 1.293 grams. The gram is the mass 
 of 1 cc of pure water at 4 C. 
 
 Square j 
 Centimeter- 
 
 Square Inch 
 
 12 345 67 8 9 10 
 
 10 Centimeters 
 
 1 
 
 \ \ 
 
 
 
 
 
 1 
 
 I 
 
 
 
 I 
 
 \ \ 
 
 1 
 
 1 
 
 iHQJ] S2 IM 
 
 iMMIl 
 
 !! ill III I! PI 
 
 ! i i 
 
 MM 
 
 mL ttHL 
 
 1.1, iii." 
 
 :NN|'L 
 
 100 Millimeters 
 
-^, JFO 
 
 DEPARTMENT OF PHYSICS 
 
 APPENDIX. 
 
 SECTION A. 
 
 Metric system of measures. The term metric is derived from 
 the word meter, which is the name of the fundamental unit employed 
 in this system for measuring length, and from which all other units 
 of the system are derived. The meter is, approximately, the ten- 
 millionth part of the distance from the Equator to the North Pole. 
 Defined by law, it is the distance at C. between two lines engraved 
 on a platinum bar kept in the Paris Observatory. The gram is theo- 
 retically the mass of Ice o f distilled water at 4 C. By law it is y^ 
 of the mass of a piece of platinum preserved in the same observatory. 
 At Washington are kept exact copies of the meter and other metric 
 measures. 
 
 The following tables contain all the requirements of this book. The 
 pupil will find more complete tables in any good arithmetic. 
 
 TABLE OF LENGTHS. 
 
 10 millimeters ( mm ) = 1 centimeter ( cm ). 
 10 centimeters = 1 decimeter ( dm ). 
 10 decimeters = 1 meter ( m ). 
 
 1000 meters = 1 kilometer ( km ). 
 
 TABLE OF AREAS. 
 
 100 square millimeters (qnm) = 1 square centimeter (Q" ). 
 100 square centimeters = 1 square decimeter (q dm ). 
 
 100 square decimeters = 1 square meter (q n ). 
 
 1,000,000 square meters 1 square kilometer (Q*m). 
 
358 APPENDIX. 
 
 TABLE OF VOLUMES. 
 
 1000 cubic millimeters (cm) = 1 cubic centimeter ( ccm or cc ). 
 1000 cubic centimeters = 1 cubic decimeter ( cdm ). 
 
 1000 cubic decimeters = 1 cubic meter ( cbm ). 
 
 The volumes of liquids and gases are either expressed in the units 
 of the above table or in liters. The liter is l cdm , or 1000 CC . 
 
 TABLE OF MASSES OR WEIGHTS. 
 
 10 milligrams ( m s) = 1 centigram ( c g). 
 10 centigrams = 1 decigram ( d ). 
 10 decigrams = 1 gram (s). 
 
 1000 grams = 1 kilogram or kilo ( k ). 
 
 TABLE OF EQUIVALENTS. 
 
 1 inch = 0.0254 meter, or about 2| centimeters. 
 1 foot = 0.3048 meter, or about 30 centimeters. 
 1 yard 0.9144 meter, or about | meter. 
 1 mile = 1609.0000 meters, or about 1 T % kilometers. 
 
 i TT J liquid rtlll , t i 0.94G liter, 
 1U.S.-J d ^ y quart H ^oi liters, 
 
 1 U.S. gallon = 3.785 liters, or about 3 r % liters. 
 
 , i avoirdupois i 0.02835 kilo, , i less 
 
 H Troy and apothecaries' ounce = ^ 0.03110 kilo, orrather 1 mor e 
 than 30 grams. 
 
 1 avoirdupois pound = 0.45359 kilo, or about ^ kilo. 
 
 When great accuracy is not required, it will be found convenient to, 
 remember that 
 
 centimeters X f = inches (nearly) ; 
 inches X f centimeters (nearly) ; 
 
 5 meters = 1 rod (nearly) ; 
 
 also, kilos X ^ pounds (nearly) ; 
 
 pounds X fV = kilos (nearly). 
 
APPENDIX. 
 
 359 
 
 SECTION B. 
 
 TABLES OF SPECIFIC GRAVITIES OF BODIES. 
 [The standard employed in the tables of solids and liquids is distilled water at 4 C.] 
 
 I. Solids. 
 
 Antimony 6.712 
 
 Bismuth 9.822 
 
 Brass 8.380 
 
 Copper, cast 8.790 
 
 Iridium 23.000 
 
 Iron, cast 7.210 
 
 Iron, bar 7.780 
 
 Gold 19.360 
 
 Lead, cast 11.350 
 
 Platinum 22.069 
 
 Silver, cast 10.470 
 
 Tiu,cast 7.290 
 
 Zinc, cast 6.860 
 
 Anthracite coal 1.800 
 
 Bituminous coal. . 1.250 
 
 Diamond 3.530 
 
 Glass, flint 3.400 
 
 Human body 0.890 
 
 Ice 0.920 
 
 Quartz 2.650 
 
 Rock salt 2.257 
 
 Saltpetre 1.900 
 
 Sulphur, native 2.033 
 
 Tallow 0.942 
 
 Wax 0.969 
 
 Cork 0.240 
 
 Pine 0.650 
 
 Oak 0.845 
 
 Beech 0.852 
 
 Ebony 1.187 
 
 II. Liquids. 
 
 Alcohol, absolute 0.800 
 
 Bisulphide of carbon 1.293 
 
 Ether 0.723 
 
 Hydrochloric acid 1.240 
 
 Mercury 13.598 
 
 Milk 1.032 
 
 Naphtha 0.847 
 
 Nitric acid 1.420 
 
 Oil of turpentine 0.870 
 
 Olive oil 0.915 
 
 Sea water 1 .026 
 
 Sulphuric acid 1.841 
 
 Water, 4 C. , distilled ... 1 .000 
 
 Water, C. , distilled . . 0.999 
 
 III. Gases. 
 [Standard : air at C. ; barometer, 
 
 Air 1.0000 
 
 Ammonia 0.5367 
 
 Carbonic acid 1.5290 
 
 Chlorine 3.4400 
 
 Hydrochloric acid 1.2540 
 
 Hydrogen 0.0693 
 
 Nitrogen 0.9714 
 
 Oxygen 1.1057 
 
 Sulphuretted hydrogen.. 1.1912 
 Sulphurous acid 2.2474 
 
360 
 
 APPENDIX. 
 
 SECTION C. 
 
 TABLE OF NATURAL TANGENTS. 
 
 Deg. 
 
 Tangent. 
 
 Deg. 
 
 Tangent. 
 
 Deg. 
 
 Tangent. 
 
 Deg. 
 
 Tangent. 
 
 1 
 
 .017 
 
 24 
 
 .445 
 
 47 
 
 1.07 
 
 70 
 
 2.75 
 
 2 
 
 .035 
 
 25 
 
 .466 
 
 48 
 
 1.11 
 
 71 
 
 2.90 
 
 3 
 
 .052 
 
 26 
 
 .488 
 
 49 
 
 1.15 
 
 72 
 
 3.08 
 
 4 
 
 .070 
 
 27 
 
 .510 
 
 50 
 
 1.19 
 
 73 
 
 3.27 
 
 5 
 
 .087 
 
 28 
 
 .532 
 
 51 
 
 1.23 
 
 74 
 
 3.49 
 
 C 
 
 .105 
 
 29 
 
 .554 
 
 52 
 
 1.28 
 
 75 
 
 3.73 
 
 7 
 
 .123 
 
 30 
 
 .577 
 
 53 
 
 1.33 
 
 76 
 
 4.01 
 
 8 
 
 .141 
 
 .31 
 
 .601 
 
 54 
 
 1.38 
 
 77 
 
 4.33 
 
 9 
 
 .158 
 
 32 
 
 .625 
 
 55 
 
 1.43 
 
 78 
 
 4.70 
 
 10 
 
 .176 
 
 33 
 
 .649 
 
 56 
 
 1.48 
 
 79 
 
 5.14 
 
 11 
 
 .194 
 
 34 
 
 .675 
 
 57 
 
 1.54 
 
 80 
 
 5.67 
 
 12 
 
 .213 
 
 35 
 
 .700 
 
 58 
 
 1.60 
 
 81 
 
 6.31 
 
 13 
 
 .231 
 
 36 
 
 .727 
 
 59 
 
 1.66 
 
 82 
 
 7.12 
 
 14 
 
 .249 
 
 37 
 
 .754 
 
 60 
 
 1.73 
 
 83 
 
 8.14 
 
 15 
 
 .268 
 
 38 
 
 .781 
 
 61 
 
 1.80 
 
 84 
 
 9.51 
 
 16 
 
 .287 
 
 39 
 
 .810 
 
 62 
 
 1.88 
 
 85 
 
 11.43 
 
 17 
 
 .306 
 
 40 
 
 .839 
 
 63 
 
 1.96 
 
 86 
 
 14.30 
 
 18 
 
 .325 
 
 41 
 
 .869 
 
 64 
 
 2.05 
 
 87 
 
 19.08 
 
 19 
 
 .344 
 
 42 
 
 .900 
 
 65 
 
 2.14 
 
 88 
 
 28.64 
 
 20 
 
 .364 
 
 43 
 
 .933 
 
 66 
 
 2.25 
 
 89 
 
 57.29 
 
 21 
 
 .384 
 
 44 
 
 .966 
 
 67 
 
 2.36 
 
 90 
 
 Infinite. 
 
 22 
 
 .404 
 
 45 
 
 1.000 
 
 68 
 
 2.48 
 
 
 
 23 
 
 .424 
 
 46 
 
 1.036 
 
 69 
 
 2.61 
 
 
 
APPENDIX. 361 
 
 SECTION D. 
 
 SIMPLE PENDULUM. CENTER OF OSCILLATION. 
 
 A simple pendulum is a material particle supported by a weightless 
 thread. Such a pendulum can sxist only in the imagination, but the 
 conception is useful. Every real pendulum is a compound pendulum, 
 which may be supposed to be composed of as many simple pendulums 
 bound together as there are particles in the pendulum. Those particles 
 nearest the point of suspension tend to quicken, and those farthest away 
 tend to check, the motion of the combination. It is apparent that there 
 must be in every compound pendulum a particle so situated that its 
 motion is neither quickened nor checked by the combined action of the 
 particles above and below it. The location of this particle is called 
 the center of oscillation. The real length of a compound pendulum is the 
 distance of this point from the point of suspension, and it is this length 
 that is referred to in the laws of the pendulum, page 96. 
 
 The center of oscillation of a pendulum may be found approximately 
 as follows : A small lead ball suspended by a thread is a near approxima- 
 tion to a simple pendulum, and the distance from the center of the ball to 
 the point of suspension may be taken as the length of this pendulum. 
 Suspend from the same support this pendulum and the pendulum whose 
 center of oscillation is to be found. For example, let the pendulum 
 be a lath (Fig. 309) suspended at its upper extremity A. 
 Lengthen or shorten the ball pendulum till it swings in the 
 same time as the lath. Then the true lengths, of the two 
 pendulums must be the same. Lay off on the lath from its 
 point of suspension a distance equal to the distance from 
 the point of suspension to the center of the ball, and this 
 will give the center of oscillation of the lath pendulum. 
 This point, in case the lath be of uniform dimensions and 
 density throughout, will be at C, about two-thirds the length 
 of the lath from its point of suspension A. 
 
 If a weight (or " bob ") be attached to the lower end of 
 A B, its center of oscillation is moved lower and the period Fig 3O9 
 of vibration is lengthened. If the bob of a pendulum be 
 raised (usually by turning a thumb-screw just beneath it) the pendulum 
 is shortened and its rate of vibration is increased. 
 
362 APPENDIX. 
 
 The isochronism of the pendulum is utilized in the measurement of 
 time, i.e. in subdividing the solar day into hours, minutes, and seconds. 
 The office of the pendulum in clocks is to regulate the rate of motion of 
 the works. The balance-wheel replaces the pendulum in watches and 
 some clocks. 
 
 The three laws of the pendulum (pp. 95 and 96) are comprised in the 
 formula 
 
 t= tf-y-> whence g > 
 
 in which Z = length of pendulum ; t = time of one vibration in seconds. 
 The development of this formula may be found in Chapter VII. of 
 Maxwell's "Matter and Motion." 
 
APPENDIX. 363 
 
 SECTION B. 
 
 EXPANSION-COEFFICIENTS. 
 
 The expansion which attends a rise of temperature depends not only 
 upon the size of the body, and upon the number of temperature degrees 
 through which it is heated, but upon a quantity peculiar to the substance 
 itself called its expansion-coefficient. This term is applied to the increase 
 of unit-length per degree rise of temperature. 
 
 Suppose that a rod of length I at C. be heated through t degrees, so 
 that its length becomes li ; then, representing the linear expansion- 
 coefficient by c, we have 
 
 c 1 , whence li = l(l + ct). 
 
 IT; 
 
 The expression 1 + ct, called the expansion-factor, is evidently the 
 ratio of the final to the original length. Hence l\ I (1 + ct) ; that is, 
 multiplying the length of a solid at C. by the expansion factor gives 
 its length at t degrees above zero. Conversely, dividing its length at t 
 by the expansion factor gives its length at 0. 
 
 TABLE OF MEAN COEFFICIENTS ON LINEAR EXPANSION BETWEEN AND 100 C. 
 
 Platinum 
 
 00000085 
 
 Brass . 
 
 0000019 
 
 Steel 
 Wrought iron 
 
 0.000012 
 0.000012 
 0000011 
 
 Silver 
 Tin . 
 Lead 
 
 0.000019 
 0.000022 
 000029 
 
 Gold. 
 
 0.000015 
 
 Zinc . 
 
 0.000029 
 
 In the expansion of fluids we have to do only with increase of volume, 
 called volume or cubical expansion. A volume-expansion-coefficient is the 
 increase of unit-volume per degree rise of temperature. This is approxi- 
 mately 3 c, or three times the linear expansion-coefficient, and may be 
 taken as such for most practical purposes. Likewise, the surface or 
 superficial expansion-coefficient is approximately 2 c. 
 
 Not only do the expansion-coefficients of liquids and solids vary with 
 the substance, but the coefficient for the same substance varies with the 
 temperature, being greater at high than at low temperatures. Hence, in 
 giving the expansion-coefficient of any substance it is customary to give 
 the mean coefficient through some definite range of temperature, as from 
 to 100 C. 
 
364 APPENDIX. 
 
 SECTION F. 
 
 TABLE OF ELECTRICAL RESISTANCE OF WIRE. 
 
 Chemically pure, one meter long, one millimeter in diameter, 
 
 at C. (Jenkin). 
 
 Relative 
 Resistances. 
 
 Silver, annealed 01937 ohm 1.000 
 
 " hard drawn 02103 " 1.080 
 
 Copper, " . . . . .02104 " 1.086 
 
 Zinc, pressed 07244 " 3.741 
 
 Platinum 11660 " 0.022 
 
 Iron, annealed ,12510 " 6.400 
 
 Lead, pressed 25270 " 13.050 
 
 German-silver , .26950 " 13.920 
 
APPENDIX. 
 
 365 
 
 SECTION G. 
 
 DYNAMOS CONTINUED. 
 
 All figures given in preceding pages have been diagrammatic repre- 
 sentations of dynamos. Figure 310 represents a modern typical dynamo, 
 the Weston. Large field magnets, A and B, are placed each side of the 
 revolving armature. A steam-engine communicates motion to the 
 
 . 310. 
 
 armature by means of a belt passing over the circumference of the wheel 
 W. The magnets are shunt- wound. 
 
 Figure 311 represents one of the most common forms of the Edison 
 dynamo, and Figure 312 is a skeleton diagram corresponding in most 
 particulars with the first. It will be seen by the latter figure that it is a 
 shunt-wound dynamo. The terminals of an automatic regulator for 
 regulating the intensity of the current are inserted in the binding screws 
 a a. P is a so-called pilot-lamp joined in multiple arc to the field-coils. 
 F F are leading wires ; and b b are points for the attachment of fuses. 
 
366 
 
 APPENDIX. 
 
 These fuses are to the dynamo what the safety-valve is to the steam 
 boiler ; they protect the dynamo from injury by overpressure, since an 
 overload is sure to cause them to melt and thus interrupt the current. 
 
 Fig. 311. 
 
 Classes of Armatures. 1 (1) In ring-armatures the coils are 
 wound round a ring-shaped core. Example : the Gramme and the 
 Brush. 
 
 (2) In drum-armatures the coils are wound longitudinally over a 
 cylinder or drum, as in Figure 313. Examples : the Edison, the Weston, 
 and the Siemens. 
 
 (3) In pole or radial armatures the coils are wound on separate poles 
 that project radially from a cylinder (Fig. 314). 
 
 1 The Thomson-Houston armature cannot be classified, as it is unique among 
 armatures. It is spheroidal in shape. 
 
APPENDIX. 
 
 367 
 
 In alternating-current dynamos, in order to obtain the rapid reversals 
 (in some machines as many as 200 per second) of currents in opposition 
 to resistance offered by self-induction, a number of poles of alternate 
 polarity are employed. 
 
 Fig. 313. 
 
 Fig. 313. 
 
 The separate coils may be coupled either in series or in multiple arc. 
 When low E.M.F. is desired, as for incandescent lamps in multiple arc, 
 the separate coils are united in multiple arc ; but where great F/.M.F. is 
 required, they are connected in series, as shown in Figures 314 and 315. 
 
 Fig. 315. 
 
 (4) Disk-armatures are usually composed of a number of separate coils 
 set side by side in the circumference of a disk (Fig. 315). Mechanical 
 difficulties in their construction have not permitted them as yet to 
 compete successfully with the first two types named above. 
 
368 
 
 APPENDIX. 
 
 SECTION H. 
 
 ELECTRIC MOTORS CONTINUED. 
 
 316. 
 
 The Action of the Dynamo-Motor. This may be under- 
 stood by referring to Figure 316, and imagining a generator to replace 
 the external resistance R. Suppose the current from the generator enters 
 at the brushes and flows in the loop in the direction of the arrows; then 
 the upper face of the loop will have S polarity and the under face N 
 g polarity. Then by the mutual 
 
 action between this field and 
 that of the magnet N S, a rota- 
 tion of the loop will take place 
 clockwise till it comes into 
 a vertical position. When it 
 reaches this position, however, 
 the brushes are so arranged 
 with reference to the commu- 
 tator segments that the current 
 in the loop and hence its polarity is reversed. Even if there were 
 only one loop its inertia would be sufficient to carry it by this critical 
 position, and the loop would continue to rotate in the attempt again to 
 bring its field parallel to that of N S ; but as a matter of fact the other 
 loops in the armature are never in the critical position at the same time 
 as the one considered, and those on each side of it conspire to produce a 
 continuous rotation in the same direction. 
 
 If the armature contain a soft iron core, as is usually the case, the 
 intensity of the field will 
 be much greater and the 
 mechanical effect corre- 
 spondingly increased. 
 
 Figure 317 represents a 
 modern form of motor 
 weighing only two or three 
 pounds, and capable, when 
 worked with four or five 
 Bunsen cells, of operating 
 a sewing-machine or run- 
 
 Fig. 317. 
 
APPENDIX. 
 
 369 
 
 Fig. 318. 
 
 ning a small saw. It consists of a movable coil within a fixed coil. The 
 wires of each coil are wound on an iron frame-work, the two opposite 
 edges of the iron being north 
 and south poles when the 
 current is passing. 
 
 The inner coil is fur- 
 nished with a commutator, 
 which reverses the current 
 as soon as opposite poles of 
 the inner and outer coils are 
 opposed. A represents the 
 
 outer coil of wires, B one pole of the fixed electro-magnet made by it, and 
 C the commutator by which the inner coil has the current reversed each 
 
 half revolution. Figure 318 shows 
 the inner coil D, whose terminals are 
 attached to the two halves of the spin- 
 dle E, which are carefully insulated 
 from each other. In Figure 319 the 
 commutator is shown in plan. The 
 current enters the inner coil through 
 the spring H, which carries a friction 
 roller working on the commutator E ; 
 after traversing the coil it returns to 
 the upper half of E, and thence passes by the spring G to K, from K 
 through the outer coil to L, and from L back to the battery. 
 
 The dynamo as a generator and the dynamo as a motor have already 
 revolutionized electrical economics and relegated the battery to an 
 honored position among things of the past. The electric motor is now 
 extensively used in large towns and cities, in factories where power is 
 not continuously needed. Its widest application at present is in the 
 propulsion of street cars. The current is generated by dynamos at some 
 central power house and thence distributed to the motors at various 
 points on the circuit. 
 
 Fig. 319. 
 
INDEX. 
 
 [Numbers refer to pages.] 
 
 Aberration, Chromatic, 335; Spheri- 
 cal, 325. 
 
 Absolute temperature, 136; zero, 
 135. 
 
 Accelerated motion, Laws of, 89. 
 
 Adhesion, 25. 
 
 Air-pump, 41, Mercury, 42. 
 
 Amalgamating zincs, 172. 
 
 Ammeter, 187. 
 
 Ampere, 182. 
 
 Ampere's theory of magnetism, 215; 
 laws of currents, 215. 
 
 Annealing, 23. 
 
 Artificial cold, 145. 
 
 Barometer, 34 ; Aneroid, 35. 
 Batteries, Electric, 196-198; Stor- 
 age, 234. 
 Beats, 271. 
 Boyle's law, 40. 
 Buoyant force of fluids, 56. 
 
 Capillary phenomena, 27-28. 
 Center of gravity, 82. 
 Centrifugal tendency, 93. 
 Circuit, Divided, 195; Electric, 171. 
 
 Cohesion, 19. 
 
 Color by absorption, 336; Cause of, 
 329. 
 
 Color vision, Theory of, 340. 
 
 Colors, Complementary, 340; Mix- 
 ing, 338; Prismatic, 327. 
 
 Commutator, 227. 
 
 Compressibility of gases, 38. 
 
 Condenser, Air, 44. 
 
 Contrast, Effect of, 341. 
 
 Coulomb, 182. 
 
 Couple, Mechanical, 78. 
 
 Critical angle, 314. 
 
 Crystallization, 20. 
 
 Curvilinear motion, 92. 
 
 Density, 9, 59; Specific, 60. 
 Diathermancy, 139. 
 Dielectric, 161. 
 Distillation, 139. 
 Ductility, 25. 
 
 Dynamo, 223-230, 365-367. 
 Dynamometers, 13. 
 
 E 
 
 Ear, 289. 
 
 Elasticity, 24; of gases, 38. 
 Electric current, 170; Effects of, 
 175-181 ; Strength of, 182. 
 
372 
 
 INDEX. 
 
 Electric light, 236-239. 
 
 Electric motor, 230, 231, 368, 369. 
 
 Electrical induction, 161. 
 
 Electricity, Conduction of, 160; 
 What is it ? 159. 
 
 Electrification, 157, 158. 
 
 Electrodes, 170, 176. 
 
 Electrokinetics, 165, 169. 
 
 Electrolysis, 175; Reversibility of, 
 234. 
 
 Electrolyte, 169. 
 
 Electro-motive force, 182; of dif- 
 ferent cells, 194. 
 
 Electroplating, 241. 
 
 Electroscope, 159. 
 
 Electrostatics, 165. 
 
 Electrotyping, 239. 
 
 Energy, 5, 100, 102, 103; Conserv- 
 ation and correlation of, 150 ; 
 Kinetic and potential, 100; Ra- 
 diant, 292; Unit of, 101. 
 
 Equilibrium,, 13, 77, 84. 
 
 Ether, The, 292. 
 
 Evaporation, 140. 
 
 Exchanges, Prevost's theory of, 
 344. 
 
 Expansion, 130-132 ; Abnormal, 
 132. 
 
 Extra currents, 220. 
 
 Eye, 349. 
 
 Falling bodies, Laws of, 87. 
 
 Flexibility, 24. 
 
 Fluids, 9; Buoyant force of, 56; 
 Elasticity of, 38; Measurement 
 of atmospheric, 33; Pressure in, 
 29, 51. 
 
 Foci, Conjugate, 321. 
 
 Force, 14 ; Centripetal, 92 ; Graph- 
 ical representation of, 71; Gravi- 
 
 tation units of, 17; How meas- 
 ured, 12. 
 
 Forces, Composition of, 72, 75; 
 Equilibrium of, 13; Molecular, 
 18 ; Resolution of, 73. 
 
 Focus, Principal, 319. 
 
 Galvanometer, 186. 
 Galvanoscope, 179. 
 Gases, Elasticity of, 38. 
 Gravitation, 15; Law of, 16. 
 
 Hardness, 22. 
 
 Harmonics, 273. 
 
 Heat, 121; Conduction of, 125; 
 Convection of, 126-129; Latent, 
 143; Mechanical equivalent of, 
 151; of liquefaction, 142; Sources 
 of, 122; Specific, 148. 
 
 Hydrometers, 62. 
 
 Hydrostatic press, 50. 
 
 Images, Formation of, 296, 308, 
 
 321. 
 
 Impenetrability, 2. 
 Incandescence, 293. 
 Induction coils, 220; Electrical, 
 
 161; Electro-magnetic, 216-222; 
 
 Faraday's law of, 219; Lenz's 
 
 law of, 220. 
 Inertia, 70. 
 Insulators, 184. 
 Isogonic lines, 208. 
 
 Joule, 184. 
 
 Joule" 1 s equivalent, 150. 
 
INDEX. 
 
 378 
 
 Kinetic energy, 100. 
 
 L 
 
 Lenses, 317. 
 
 Lenz's law of induction, 219. 
 
 Light, Prismatic analysis of, 326; 
 
 Undulatory theory of, 293.. 
 Lightning, 168. 
 Light-waves, Sources of, 293. 
 Liquefaction, 137. 
 Locomotive, 156. 
 Luminous objects, 295. 
 
 M 
 
 Machines, 108; Law of, 110. 
 
 Magnetic circuit, 205; field, 177, 
 209; lines of force, 177, 203; 
 polarity, 201; rentivity and re- 
 sistance, 202; transparency and 
 induction, 201. 
 
 Magnetism, Ampere's theory of, 
 215; Terrestrial, 206-209. 
 
 Magnets, Forms of, 202; Law of, 
 200. 
 
 Malleability, 25. 
 
 Manometric flames, 278. 
 
 Mass, 7; Unit of, 8. 
 
 Matter, 1, 6; Amorphous, 22; Mi- 
 nuteness of particles of, 6; 
 Theory of constitution of, 7; 
 Three states of, 9. 
 
 Metric system, 357, 358. 
 
 Microphone, 246. 
 
 Microscope, Compound, 346; 
 Simple, 324. 
 
 Moments of forces, 77. 
 
 Momentum, 67. 
 
 Motion, 10; Graphical representa- 
 tion of, 70; Newton's laws of, 
 69, 71, 80. 
 
 N 
 
 Nodes, 251. 
 
 Ohm, 184. 
 Ohm's law, 185. 
 Optical center, 318. 
 Overtones, 272. 
 
 Pendulums, 95, 96, 361. 
 Penumbra, 298. 
 Phenomenon, 1. 
 Phonograph, 287. 
 Phosphorescence, 293. 
 Photometry, 301. 
 Physics, 1; Celestial, 334. 
 Pigments, Mixing, 339. 
 Pitch, Musical, 269. 
 Polarization in voltaic cells, 172. 
 Porosity, 7. 
 
 Potential, Electrical, 166, 167. 
 Power, 104. 
 
 Pressure, Atmospheric, 29; Trans- 
 mission of fluid, 47. 
 Prisms, Optical, 317. 
 Pumps for liquids, 45, 46. 
 
 Quality of sound, 275. 
 
 Radiant energy, 292. 
 
 Radiation, 129, 342 ; Only one kind 
 
 of, 334. 
 
 Radiators, 345. 
 Radiometer, 291. 
 Rainbow, 327. 
 Ray, 294. 
 Reflection, Law of, 304 ; Total, 314. 
 
374 
 
 INDEX. 
 
 Refraction, Cause of, 312; Double, 
 
 316; Indices of, 312. 
 Resistance, Electrical, 184, 188-194. 
 Resonators, 264. 
 RuhmkorjTs coil, 222. 
 
 Shadows, 297. 
 
 Shunts, 195. 
 
 Siphon, 54. 
 
 Solenoid, 211. 
 
 Sonometer, 270. 
 
 Sound, 257; Analysis of, 275; In- 
 tensity of , 261; Quality of , 275; 
 Synthesis of, 276. 
 
 Sounding plates and bells, 283. 
 
 Sound-waves, 254-257; Interference 
 of, 266, 285; Measuring length 
 and velocity of, 265 ; Reenf orce- 
 inent of, 263 ; Reflection of, 259 ; 
 Speed of, 258. 
 
 Speaking tubes, 262. 
 
 Specific density and specific gravity, 
 60; heat, 148. 
 
 Spectra, 326-334. 
 
 Spectroscope, 330. 
 
 Spectrum analysis, 333. 
 
 Steam-engine, 152-156. 
 
 Stereopticon, 351. 
 
 Storage batteries, 234. 
 
 Telegraph, 241-243. 
 
 Telephone, 243-246. 
 
 Telescopes, 348. 
 
 Temperature, 124; Absolute, 136. 
 
 Tenacity, 20. 
 
 Tension, 26; Surface, 26. 
 Thermo-dynamics, 150. 
 Thermo-electric currents, 235. 
 Thermometry, 133. 
 Transformer, 232. 
 Transparency and translucency, 
 295. 
 
 Undulatory theory of light, 293. 
 Units, Absolute, 106. 
 
 Vaporization, 137. 
 
 Velocity, 88, 90. 
 
 Ventilation, 128. 
 
 Vibrations, 248-250; Composition 
 
 of sonorous, 277; Forced and 
 
 sympathetic, 267. 
 Viscosity, 24; Surface, 26. 
 Vision, Defects of, 350. 
 Visual angle, 303. 
 Vocal organs, 286. 
 Volt, 183. 
 
 Voltaic arc, 237; cell, 170, 173, 174. 
 Volume, 7. 
 
 W 
 
 Watt, 184. 
 
 Wave motion, 248-254. 
 Weight, 8, 16. 
 Wheatstone bridge, 192. 
 Wind instruments, 280. 
 Work, 98-100; Unit of, 101; 
 Wasted, 103. 
 
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