' 
 
AN 
 
 ELEMENTARY PHYSICS 
 
 FOR SECONDARY SCHOOLS 
 
 BY 
 
 CHARLES BURTON THWING, PH.D. (BONN) 
 
 PROFESSOR OF PHYSICS IN KNOX COLLEGE 
 
 FORMERLY INSTRUCTOR IN PHYSICS IN THE UNIVERSITY OF WISCONSIN 
 AUTHOR OF "EXERCISES IN PHYSICAL MEASUREMENT" 
 
 PART I: PRINCIPLES 
 
 PART II: LABORATORY EXERCISES 
 
 
 ov TrdAA* dAAa TroAv 
 
 BOSTON, U.S.A. 
 
 BENJ. H. SANBORN & CO. 
 1900 
 
^5 V, k 
 
 T^ls 
 
 COPYRIGHT, 1900, 
 BY CHARLES BURTON THWING. 
 
 Press of Samuel Usher, Boston, Mass. 
 
PREFACE. 
 
 THAT there is a demand for a new School Physics 
 recent correspondence with over fifteen hundred second- 
 ary schools abundantly shows. That there are good 
 books now before the educational public cannot be 
 denied. The good books those reasonably accurate, 
 scientific, and modern are too difficult, too diffuse, or 
 require more than the usual school equipment of appa- 
 ratus. In the so-called attempt to " enrich the grammar 
 school courses," physics has been in a few cases intro- 
 duced, and a moderate demand created for very elemen- 
 tary books. Thus the instructor has been left to a 
 choice between books too elementary and simple, and 
 those that make too great a demand upon the pupils in 
 the usual secondary school course. 
 
 The author's experience as a teacher of physics, both 
 in secondary schools and college, has given him excep- 
 tional opportunity to know the capacity of the average 
 student. His relations with a large number of teachers 
 of elementary science have been such as to make him 
 aware of the limitations under which teachers work, 
 both as to specific preparation for the work of teach- 
 ing physics and still more as to material equipment, 
 
 iii 
 
 96805 
 
IV PEE FACE. 
 
 The book has been written, therefore, with the needs 
 and limitations of the average teacher and pupil con- 
 stantly in mind. Illustrations are drawn, wherever 
 possible, from facts already known to the pupil. 
 
 The illustrative experiments described in the text are 
 few in number and require only simple apparatus. For 
 teachers who have more elaborate apparatus at command 
 the accompanying handbook gives full references to text- 
 books which are in every teacher's library. 
 
 The plan of relegating to the handbook all matter 
 useful mainly to the teacher relieves the book of much 
 fine-print lumber, and allows the text to proceed with- 
 out interruption in a connected and logical treatment of 
 the subject. 
 
 The same end is still further subserved by putting 
 certain illustrative experiments in the lists of exercises 
 for review which follow each chapter, and by putting 
 the laboratory exercises by themselves in Part II. 
 
 Flexibility in amount of work done is attained by 
 giving a large number of exercises, some of which are 
 rather difficult. Of the seventy-five laboratory exercises 
 in Part II, but forty would be required Jor entrance to 
 Harvard. Of the exercises in Part I, most classes 
 would probably perform about half. The text should 
 all be mastered by the pupil as far as he goes. 
 
 The work in Part II which contains many new and 
 practical ideas should begin the second week of the term 
 and continue parallel with work on the text. The ex- 
 periments in Part II are all quantitative and lead to 
 
PEE FACE. V 
 
 results which may be easily verified from data in the 
 teacher's hands. The tendency of the best teaching 
 practice is growing rapidly in the direction of leaving 
 qualitative experiments to the class room to be per- 
 formed by the teacher, or under his direction, and giving 
 to the pupil experiments involving the law which he 
 has already learned from the book. To calculate the 
 breaking stress of one or two particular wires from 
 measurements of the diameters of the wires and the 
 force required to break them, and to find that the value 
 obtained compares fairly well with the results obtained 
 by others as given in the book, is good proof of the 
 correctness of the law. Careful weighing with the steel- 
 yards and balance illustrates the law of moments per- 
 fectly, while giving the student a much better training 
 in accuracy than he will get by using levers supported 
 below their centres of gravity, as suggested in many 
 books. Most of the experiments in Part II have been 
 tested during the past three years in a number of 
 schools, including both the large city high school 
 and the small country school, with most gratifying re- 
 sults. 
 
 The order of arrangement of the chapters in Part I 
 demands a word of explanation. The author's observa- 
 tion has been that the student encounters so many 
 difficulties in the early part of the study of mechanics 
 that he is likely to become discouraged before his in- 
 terest is fully aroused in the subject. He is hardly 
 familiar with the idea of force before the more complex 
 
VI PREFACE. 
 
 idea of energy is thrust at him and he becomes con- 
 fused. Moreover, he is expected to comprehend the 
 law of conservation of energy when he has studied but 
 one form of energy. 
 
 By first treating all forms of energy as forms of 
 motion, or capable of being converted into motion, the 
 subject of energy is deferred until the student is in 
 possession of a large body of facts which bear directly 
 upon it. Moreover, the importance of a thorough knowl- 
 edge of mechanics is emphasized by bringing it directly 
 into relation with heat and electricity. 
 
 It is believed that the treatment of wave motion here 
 given is more connected and clear than is usually found 
 in elementary text-books. The subject of index of 
 refraction is treated with scientific accuracy without the 
 introduction, either implicitly or by name, of the trigo- 
 nometric functions (pages 204 and 351). It is the 
 author's firm conviction that treatments involving any 
 knowledge of mathematical notions beyond those gained 
 in elementary algebra and plane geometry are out of 
 place in a text-book designed for secondary schools. 
 The definition of index of refraction as a ratio of the 
 velocities of light in the two media calls attention to 
 the physical fact involved, while its definition as the 
 ratio of the sines of two angles directs attention to one 
 of the methods usually employed in its determination. 
 
 Teachers are requested in examining the book to read 
 the corresponding portions of the handbook in connec- 
 tion with the text. 
 
PREFACE. vil 
 
 Corrections or suggestions from teachers using the 
 book will be gratefully received by the author, who 
 realizes that the task of writing a book which shall be 
 at once simple and accurate is by no means an easy 
 one. 
 
 I am under obligations to Mr. Frank Wenner, In- 
 structor in Knox Academy, to Professor F. L. Bishop, 
 of Bradley Polytechnic Institute, to Mr. Allan C. 
 Rearick, Instructor in Science in Kewanee High School, 
 and to Mr. L. E. Flanegin, Superintendent of Schools, 
 Elm wood, 111., who have rendered valuable assistance 
 in the preparation of the book, either in the way of 
 suggestions or in reading the proof, and to Mr. Wenner 
 and Mr. G. A. McMaster for work upon the draw- 
 ings. C. B. T. 
 
 GALESBURG, ILL., January, 1900. 
 
CONTENTS.* 
 
 PART I. PRINCIPLES. 
 
 INTRODUCTION. 
 
 The Place of Physics (a) among the Sciences, 1; (b) in Educa- 
 tion, 3; (c) in Practical Life, 3. 
 
 CHAPTER I. 
 MATTER AND MOTION. 
 
 Definitions, 4; Kinds of Motion, 5; Force, 8; Velocity, Accel- 
 eration, 10; Mass, Momentum, 11; Newton's Laws of Motion, 13; 
 Composition and Resolution of Forces, 14; Measurement, Units, 
 20; Exercises, 23. 
 
 CHAPTER II. 
 BALANCING FORCES. 
 Kinds of Equilibrium, 25; Moment of Force, 30; Gravitation, 32. 
 
 SOME PROPERTIES OP MATTER. 
 
 Elasticity, Molecules, Cohesion, 34, 35 ; Liquids in Open Vessels, 
 38; Capillarity, 41 ; Floating Bodies, 46 ; Liquids in Closed Vessels, 
 47; Gases in Open Vessels, 48; Pumps, 51-54; Fluids in Contact, 
 Diffusion, 55; Exercises, 59. 
 
 * The references are to pages. 
 
 ix 
 
X CONTENTS. 
 
 CHAPTER III. 
 HEAT. 
 
 Nature of Heat, 61; Effects of Heat, 62; Temperature, 63; Ex- 
 pansion, 64; Thermometry, 65; Quantity of Heat, Specific Heat, 
 70; Change of State, 71; Latent Heat, 71; Conduction, Convection, 
 76-77; Heat and Human Life, Weather, Clothing, 77-79; Exer- 
 cises, 82. 
 
 CHAPTER IV. 
 
 ELECTRICITY AND MAGNETISM. 
 
 Introductory Remarks, 84; Magnets, 85; Magnetic Forces, 86; 
 The Magnetic Field, 88; Terrestrial Magnetism, 94. 
 
 Electric Charges, 94; Induction, 98; Nature of the Charge, 100; 
 Electric Discharge, 104; Electrical Machines, 107; Capacity, Con- 
 densers, 112; Electroscope, 114; Discharge in Gases, 116; Exer- 
 cises, 117. 
 
 Electric Currents, 120; Magnetic Effects of Current, 122; Bat- 
 teries, 123; Electrolysis, 126; Heat Effects, Resistance, 128; Ohm's 
 Law, Units, 130; Useful Heat Effects, 131; Motion from Current, 
 135; The Telegraph, 137; Motors and Dynamos, 140; Induction 
 Coils, 144; Exercises, 151. 
 
 CHAPTER V. 
 WORK. ENERGY. MACHINES. 
 
 Definitions, 157; Conservation of Energy, 160; Units, Equiva- 
 lents, 162; Energy and Life, 166; Machines, 169; Heat Engines, 
 180; Storage and Transmission of Energy, 186; Exercises, 189. 
 
 CHAPTER VI. 
 VIBRATIONS. WAVES. 
 
 Vibratory Motion, 192; The Pendulum, 194; Wave Motion, 197; 
 Reflection, 200; Refraction, 204; Exercises, 205. 
 
CONTENTS. Xi 
 
 CHAPTER VII. 
 SOUND. 
 
 Nature of Sound, 207; Rods, Plates, Bells, 208-209; Pitch, 210; 
 Musical Intervals, Consonance, 211; Resonance, Pipes, 214; Veloc- 
 ity of Sound, 216; Musical Scales, 220; Exercises, 224. 
 
 CHAPTER VIII. 
 LIGHT. 
 
 The Sensation of Light, 226; Shadows, 227; Images (a) by Small 
 Openings, 228; (ft) by Reflection, 229; (c) by Refraction, 235; Op- 
 tical Instruments, 239; Color by Refraction, The Spectrum, 243; 
 Color Mixture, 245; Color by Interference, 249; The Spectroscope, 
 251; Intensity of Light, 255; Light and Electricity, 256; Space 
 Telegraphy, 257; New Forms of Radiation, 258; The Role of Wave 
 Motion in Nature, 259; Exercises, 260. 
 
 PART II. LABORATORY EXERCISES. 
 
 INTRODUCTION. 
 
 Measurement as a Form of Training, 265; Sources of Error, 266; 
 Hints to the Student, 267. 
 
 CHAPTER IX. 
 LENGTH. 
 
 Units and Equivalents, 268; The Metre Stick, 269; Dividers and 
 Calipers, 273; The Vernier, 278; Eye Estimations, 282; The Mi- 
 crometer, 283; The Spherometer, 285. 
 
 CHAPTER X. 
 MASS. 
 
 Definitions and Units, 288; The Balance, 289; Weighing by 
 Swings, 297; Density (a) by Dimensions and Weight, 300; (6) by 
 Displacement, 302; (c) by Archimedes' Principle, 304; (d) with 
 the Bottle, 305; (e) by Balancing Columns, 307; Tables of Densi- 
 ties, 309. 
 
xii CONTENTS. 
 
 CHAPTER XI. 
 TIME. 
 
 Units, 310; The Pendulum, 311; Torsional Pendulum, 312; De- 
 termination of Gravity, 313; The Pulse, 313; The Respiration, 314; 
 Estimation of Time, 314. 
 
 CHAPTER XII. 
 FORCE. 
 
 Pressure of the Air, 316; Use of the Manometer, 319; Capil- 
 lary Constant, 320; Modulus of Elasticity, 322; Breaking Strength, 
 326; Friction, 327. 
 
 CHAPTER XIII. 
 HEAT. 
 
 Thermometry, 329; Expansion, 332; Specific Heat, 333; Humid- 
 ity, 336. 
 
 CHAPTER XIV. 
 ELECTRICITY. 
 
 Resistance, 339; Wheatstone's Bridge, 340; Specific Resistance, 
 342; Temperature Coefficient of Resistance, 343; Potential Differ- 
 ence, 345. 
 
 CHAPTER XV. 
 
 SOUND. 
 
 Velocity of Sound (a) in Air, 346; (6) in Solids, 347; Pitch of 
 a Fork, 3/9. 
 
 CHAPTER XVI. 
 
 LIGHT. 
 
 Photometry, 350; Index of Refraction, 351; Lenses, 354; Mag- 
 nification, 356. 
 
 INDEX OP PROPER NAMES, 357 ; GENERAL INDEX, 361. 
 
PHYSICS. 
 
 PART I. PRINCIPLES. 
 
 INTRODUCTION. 
 
 i. The Place of Physics among the Sciences. - 
 
 Natural Science has for its aim the explanation of nat- 
 ural phenomena the things which happen about us 
 every day. It was originally all comprised under Nat- 
 ural Philosophy, or Physics. Our knowledge of natural 
 phenomena has so increased during the last few cen- 
 turies that no one man could hope to master all of it. 
 Natural Science has been divided, therefore, into several 
 branches. Astronomy deals with phenomena wholly 
 beyond our control. Chemistry studies changes which 
 result in the formation of new substances. Biology 
 deals with the phenomena manifested in living things. 
 Physics is now confined to the study of those changes 
 which occur in the position, appearance, or state (solid, 
 liquid, gaseous) of bodies ; it seeks to trace each change 
 to an adequate cause and to discover the laws^ which 
 govern the phenomena observed. Physics includes the 
 subjects of mechanics, heat, electricity, sound, and light. 
 The laws enunciated in physics are assumed, and the 
 instruments described in physics are employed, in the 
 other sciences. 
 
2 INTE OD UC TION. 
 
 Physics, then, is at the foundation of all the sciences. 
 Physics itself is founded upon a body of observed facts 
 which are interpreted by reason in accordance with the 
 principles of mathematics. The exact expression of 
 the relation between a large number of similar facts is 
 called a law. Men had observed for ages that bodies 
 unsupported in the air tend to fall toward the earth. 
 It was only after many years of patient observation and 
 the making of careful measurements that the fact be- 
 came known that all bodies at the surface of the earth 
 fall, if unimpeded, with the same velocity, the velocity 
 gained being 32.16 feet (9.8 metres) for every second 
 of time the body is falling. This fact, after being tested 
 by innumerable experiments, is now known as the law of 
 falling bodies. 
 
 Among the many new facts which are constantly being 
 discovered there are always some, the relation of which 
 to the body of known facts is not yet apparent. When 
 a large number of such facts have been collected some 
 bold philosopher offers an explanation, or as scientists 
 say, a hypothesis. This hypothesis, if it seems to other 
 scientists to be worthy of consideration, is tested to see 
 if it will explain all the known facts. If it does explain 
 the known facts, and especially if it leads to the dis- 
 covery of new facts, it comes in time to be accepted as 
 a theory. The Atomic Theory, for example, attempts to 
 harmonize all the known facts of chemistry, and does so 
 to a degree that was hardly anticipated by those who 
 first proposed it. The theory seldom has so sure a f oun- 
 
INTRODUCTION. 3 
 
 elation as the separate laws or facts which it attempts to 
 explain, yet it serves a most useful purpose, even when 
 it does no more than aid us in keeping those laws and 
 facts in memory. 
 
 2. The Place of Physics in Education. The study 
 of physics involves to an exceptional degree the train- 
 ing of the senses to perceive, the hand to perform, and 
 the mind to interpret, on the one hand, what the senses 
 observe ; to direct, on the other, what the trained hand 
 shall perform. In cultivating accuracy, it discourages 
 slovenliness and untruthfulness and stimulates the mind 
 to that highest of human pursuits, the search for truth. 
 
 3. The Place of Physics in Practical Life. Me- 
 chanical inventions are not, as many thoughtless people 
 suppose, mere lucky accidents ; they are the direct result 
 of a knowledge of the laws of nature. The man who 
 discovers a new law of physics seldom sees how his dis- 
 covery is to be of any practical benefit to mankind. 
 Faraday, toiling patiently in his laboratory to discover 
 the laws of electro-magnetic induction, never dreamed 
 that liis discovery of these laws would one day make 
 possible the electric lighting of our homes and streets, 
 the electric propulsion of railway trains, and the trans- 
 mission of spoken words across a continent. Yet these 
 are but a few of the applications of Faraday's discov- 
 eries to the daily life of men. 
 
 Enough has been said, it would seem, to make it evi- 
 dent that there are excellent reasons for giving physics 
 a place in the course of study. 
 
CHAPTER I. 
 MATTER AND MOTION. 
 
 4. Matter and Motion Defined. We have seei- 
 already that physics is the study of the changes that 
 occur in the things about us. We shall see as we pro- 
 ceed that all changes in the appearance of things are 
 due to motion, either of the things themselves or of 
 their parts. 
 
 Motion may be denned as change of position, the 
 position of an object being determined by its distance 
 and direction from other objects. In geometry we deal 
 with motions of points and lines, as when a point is said 
 to move so that its path is a straight line or a circle. 
 All physical changes, however, imply the motion of 
 matter. 
 
 Matter is a term with the meaning of which we are 
 all more or less familiar, yet a term which it is not easy 
 to define. We know matter primarily by the effort 
 required to move it out of its place. If we walk in air 
 we are so accustomed to the resistance which it offers 
 to our movements that we think of our motion as un- 
 impeded ; but if we walk in water or through thick 
 underbrush we are conscious of a resistance which can 
 be overcome only by a considerable effort on our part. 
 Matter also makes itself known to us through the senses 
 
 * 
 
KINDN OF MOTION. 5 
 
 of sight, hearing, smell, and taste. It is chiefly through 
 the senses of sight and hearing, especially the former, 
 that we gain our knowledge of physical changes. 
 
 A definite portion of matter, separated from other 
 matter, is called a body. The various kinds of matter 
 of which bodies are composed are called substances. 
 Thus a pencil is a body, composed of wood and graphite. 
 Substances possess certain characteristic properties : 
 cedar wood is of a reddish color, is brittle, and will 
 float in water ; graphite is black, leaves a trace on paper, 
 and is heavier than water. The pencil possesses in its 
 different parts the properties of the substances which 
 compose it, and has besides a definite form and size. 
 
 The amount of matter in a body is called the mass of 
 the body. The amount of matter in unit volume of a 
 substance is called the density of the substance. 
 
 The various properties of bodies are made manifest 
 to us by the motions which are transmitted from these 
 bodies to our organs of sense. We shall best explain 
 the properties of matter, therefore, by examining the 
 motions of bodies. Meanwhile we must call to mind 
 frequently many facts which have already come to our 
 notice and keep ourselves ever alert to see new facts 
 which may serve to illustrate the subject in hand. 
 
 5. Kinds of Motion. I. A body may move from 
 one position to another in such a way that the direction 
 from one point in the body to another point in the body 
 remains unchanged. Such motion is called motion of 
 
6 
 
 MATTER AND MOTION. 
 
 translation, or translator^ motion. Thus the cube CDB 
 (Fig. 1) may have moved to the position O'D'B' in 
 
 / 
 / 
 
 / 
 
 / 
 
 / 
 / 
 / 
 / 
 
 / 
 
 
 / 
 
 / 
 / 
 
 
 / 
 / 
 
 A 
 
 ' , 
 
 I ' 
 ^/ 
 
 such a way that CD 
 did not depart from 
 the vertical direction. 
 The motion was then 
 translatory. If the 
 successive positions 
 of a point, as (7, lie 
 in a straight line, the motion is recti- 
 linear; if in a curved line, curvilinear. 
 B Thus, if C followed the straight line 
 CFC 1 , the motion was rectilinear ; if the 
 line CEC', curvilinear ; and if CEC' is 
 nl I a segment of a cir- ^, 
 
 FIG. l. c } e ^ ft wag c i rcu l ar . 
 
 II. A body may move in such a 
 way that the distance of every point 
 in it from a fixed point remains un- 
 changed, while the direction from one 
 point in the body to another point in 
 the body changes. Thus the cube in 
 Fig. 2 may move from the position DB to <7'2XJ5', the 
 
 o- 
 
 D 
 
 > B 
 
 Y 
 
 FIG. 2. 
 
KINDS OF MOTION. 7 
 
 point remaining at a fixed distance from 0, while the 
 direction of CD is constantly changing. Such motion is 
 rotary. A line drawn through such that all points 
 on the line remain on the line during rotation is called 
 the axis of rotation. The path of every particle in 
 the body is a circle, having its centre on the axis. 
 
 III. A body may move in such a way that after 
 moving a certain distance in one direction it stops and 
 retraces its path in the opposite direction, as the pendu- 
 lum of a clock does. Such motion is called motion of 
 vibration, or vibratory motion. Vibratory motion is often 
 so rapid that the eye cannot follow it. The prongs of 
 a tuning fork, the string of a violin, indeed, every body 
 which is producing sound vibrates thus rapidly. 
 
 IV. When a vibrating body is surrounded by a sub- 
 stance the particles of which may be set in vibration, 
 the particles nearest the vibrating body will be set in 
 vibration first. These particles will communicate their 
 motion to those next them, and the disturbance will 
 thus spread throughout the substance. Such motion 
 is called wave motion. It is usually represented by 
 
 a wavy line, 
 as in Fig. 3. 
 
 FIG. 3. * The path of 
 
 any particle is not such a wavy line, but is usually a 
 short straight line or a small ellipse. No single particle 
 moves forward, but each particle vibrates for a short 
 time, sets its neighbor in vibration, and then comes to 
 rest. The motion progresses from particle to particle, 
 
8 MATTER AND MOTION. 
 
 each particle vibrating in turn. A water wave moves 
 across the lake : a chip on the water moves up and down, 
 but not forward. It is by wave motion that sound and 
 light reach us from distant objects. The particles of the 
 bodies themselves, and of the intervening medium as 
 well, vibrate in very short paths ; the sound or light 
 that is, the wave motion travels to great distances. 
 
 6. The Cause of Motion, Force. It is the uni- 
 versal experience of mankind that bodies not endowed 
 with life have no power to put themselves in motion. 
 Newton perceived also, what is equally true, that bodies 
 once in motion have no power to stop themselves or 
 change their direction of motion. If, then, we see a 
 body which was at rest begin to move, or a body which 
 was rising in the air begin to fall, we say something 
 has acted upon it. Provisionally, while we are seeking 
 to find what that something may be, it is convenient to 
 give it a name. We call by the name force any cause 
 which tends to change the motion of bodies. If a 
 body, as a ship or a railway train, starts from the state 
 of rest (the condition in which it has no motion rela- 
 tive to bodies near it), and moves due east, we say a 
 force has acted upon it from the west. If it goes 
 faster and faster toward the east we say a force con- 
 tinues to act from the west. If it goes more slowly 
 eastward we say a force is acting from the east, 
 which, if it continues to act, will bring the body to 
 rest. If a stone is thrown horizontally it will not 
 
THE NATURE OF FORCE* '.- ^ '"' 9 
 
 continue to move in a horizontal path, but will gradually 
 approach the ground. If we saw a boy throw the stone 
 we say we know the cause of the horizontal motion. 
 We saw nothing pushing or pulling the stone toward 
 the ground, yet because it went downward we say there 
 was a force acting in the downward direction. The 
 fact that all bodies tend to move earthward has led us 
 to give to that force which causes such motion toward 
 the earth a special name, gravity.* 
 
 7. The Nature of Force. As was suggested in the 
 last paragraph, there are forces the nature of which is 
 evident, and other forces the nature of which is not 
 known. It may be said, however, that so far as we 
 know the nature of force, every force is itself the result 
 of motion. The wind is able to move the ship because 
 the air is itself in motion. The steam in the cylinders 
 of the locomotive is able to drive the train because mo- 
 tion in the form of heat was first imparted to the steam 
 in the boiler. 
 
 The manner in which the motion of an engine when 
 transmitted by belting to a dynamo-machine is so 
 changed that it may be carried along a slender wire for 
 miles to be again converted into visible motion in the 
 street car is not yet well understood, but it seems prob- 
 able that motion is present during every step of the 
 process of transferring motion from the engine to the 
 car, even though we are not able to perceive it. 
 
 * Gravity from Latin gravis, heavy, gravitas, weight. 
 
10 MATTE It AND MOTION. 
 
 So far as we know, every bird came from an egg, 
 which egg, in turn, had a bird for its mother ; so far as 
 we know, every motion is the result of some antecedent 
 motion. 
 
 8. Rate of Motion. Speed. Velocity. We have 
 all observed that bodies in motion do not all move 
 equally fast. A strong wind Avill drive a windmill faster 
 than a light breeze. A professional pitcher can throw 
 a ball swifter than a schoolboy can. When distance 
 travelled, only, and not direction of motion is considered, 
 we call the distance travelled in one second the speed of 
 a body. Velocity is rate of change of position, and in- 
 cludes both speed and direction of motion. If the dis- 
 tinction between speed and velocity is carefully made 
 much confusion will be avoided. A train which travels 
 240 miles in four hours has an average speed of 60 
 miles per hour, or one mile per minute, or 88 feet per 
 second. 
 
 length of path traversed 
 Speed = - , or 
 
 time occupied 
 
 >=4- 
 
 t 
 
 9. Change of Velocity. Acceleration. Motion 
 with constant speed and in a constant direction is con- 
 stant motion. Motion which changes either in speed or 
 direction is called accelerated motion, and the rate of 
 
QUANTITY OF MOTION. 11 
 
 change of motion of a body is called its acceleration. 
 A body which moves five centimetres in the first second, 
 ten centimetres in the second, fifteen in the third, 
 etc., has a constant acceleration of five centimetres 
 per second. A body moving in a circle with uniform 
 speed is an example of accelerated motion ; for, though 
 the speed remains constant, the direction of motion is 
 constantly changing. It takes a force constantly acting 
 to produce a constant change of speed in the first case. 
 It takes a force constantly acting to produce the con- 
 stant change of direction in the second case. If a 
 heavy body be whirled by a string held in the hand we 
 are conscious of a constant pull which we must exert 
 upon the string to keep the ball from moving off in a 
 straight line. 
 
 We may now define force as any cause capable of 
 producing acceleration. 
 
 To sum up : 
 
 change of velocity 
 
 Acceleration = - - ; ' - -, or 
 
 time in which change occurred 
 
 10. Quantity of Motion. Mass. Momentum. - 
 A given force will produce a greater change of velocity 
 in a light body than in a heavy one. The amount of 
 acceleration alone is not a measure of the magnitude 
 of a force : we must also take into account the amount 
 of matter moved. The quantity of matter composing 
 
12 MATTE 11 AND MOTION. 
 
 a body is called the mass of that body. The mass of a 
 body is measured by the acceleration a given force will 
 produce upon the body. The greater the mass the 
 smaller the acceleration produced by a given force. 
 We are accustomed to form a rough estimate of the 
 force we ourselves exert by the effort we are conscious 
 of putting forth. We are conscious of more effort when 
 we push aside a brick with the foot than when we push 
 aside a block of Avood of the same size. We say the 
 brick is harder to move than the block, and therefore 
 has more matter in it. 
 
 Quantity of motion is called momentum. It is equal 
 in amount to the product of the numbers representing 
 the mass and velocity of the body. 
 
 Momentum =. mass X velocity, or 
 
 M=mv 
 
 Since the change of momentum of a body is the meas- 
 ure of the force applied to it, and since the mass of the 
 body is not supposed, in our discussion of motion, to 
 suffer any change in amount, it follows that the force 
 expended in producing any given motion is measured 
 by the product of the number of units of mass times 
 the number of units of acceleration. 
 
 Force = mass X acceleration, or 
 CO f=vna 
 
 With these preliminary definitions in mind, we should 
 now be prepared to state and discuss the three famous 
 
NEWTON'S LAWS OF MOTION. 13 
 
 axioms of Sir Isaac Newton, which are known as New- 
 ton's Laws of Motion. 
 
 n. Newton's Laws of Motion. I. Every body 
 continues in its state of rest or uniform motion in a 
 straight line unless acted upon by some external force. 
 
 11. Amount of motion is proportional to the force 
 applied and in the direction in which the force acts. 
 
 III. Action and reaction are equal in amount and 
 opposite in direction. 
 
 12. Discussion of the First Law. We have seen 
 in Section 6 that force is required to change motion, 
 that is, to alter the speed or direction of a body. If 
 the body is at rest its speed is zero, and, since it has no 
 motion, it has no direction of motion. If no force is 
 applied the body remains at rest. 
 
 When a body is in motion a force would be required 
 to produce any acceleration of that motion, that is, to 
 change either the speed or direction of the motion. It 
 follows that the body continues in its present state un- 
 less a force is applied. The helplessness of matter is 
 called inertia, and force is sometimes said to be spent 
 in overcoming inertia. Since, however, inertia is a 
 purely negative property of matter it seems better to 
 say that force is spent in producing change of motion 
 than to say that force overcomes the tendency of bodies 
 not to move. 
 
 Illustrations of the first law will occur to every one. 
 
14 MATTER AND MOTION. 
 
 A person who jumps from a moving car keeps the mo- 
 tion of the car till his feet strike the ground. His head 
 continues to move forward even then, and unless he 
 runs forward it is quite probable that his head, too, will 
 strike the ground before it loses all its motion. Drops 
 of water fly off from a rapidly rotating grindstone. 
 Bits of niud are thrown from a carriage wheel. Kail- 
 ways have the outer rail laid higher than the inner 
 where sharp curves occur to prevent the engine from 
 leaving the track, as it would do if it kept on in a 
 straight line. The rotation of the earth causes the 
 water of the ocean to heap up at the equator until it is 
 about thirteen miles higher there than at the poles. 
 The Mississippi River, therefore, notwithstanding its 
 source is 1,575 feet above sea level, is really about two 
 miles higher at its mouth than at its source. If the 
 earth should cease to rotate the Mississippi would flow 
 rather swiftly toward the north. 
 
 13. Discussion of the Second Law. Composition 
 and Resolution of Forces. In Section 10 we have 
 defined " amount of motion," or momentum, as mass 
 times velocity. The fact that the velocity of a body 
 has changed is proof that a force has acted upon it. 
 The second law implies that no matter how many forces 
 are acting upon a given body at one time each force 
 will produce the same effect as if it alone were acting, 
 and the total effect must be found by combining the 
 effects of all the forces. This may be done in a very 
 
DISCUMICW OF THE SECOND LAW. 15 
 
 simple way when the magnitude and direction of each 
 of the forces are knoAvn. A line has both length and 
 direction. A line may be used, therefore, to represent 
 the magnitude and direction of a force. Let the mag- 
 nitude of each force be represented by the length, and 
 the direction of each force by the direction, of a line. 
 The absolute length of the lines is of no importance so 
 long as their relative lengths correspond to the relative 
 magnitude of the forces. Suppose it is required to find 
 the magnitude and direction of the force which is the 
 equivalent of two forces, one a force of magnitude, 4, 
 acting from the west, the other a force of magnitude, 3, 
 acting from the south, as ^ 
 if A should kick a foot- 
 ball from the south with 
 a force of three pounds, T 
 
 while at the same instant 
 
 iVl _^_____^_^________ 
 
 B kicks it from the west _> 
 
 with a force of four pounds. FIG. 4. 
 
 Represent the force of 3 from the south by the line 
 MN (Fig. 4) and the force of 4 from the west by the 
 line MP. Both forces are supposed to be applied at 
 M. The arrowheads indicate the direction of motion. 
 
 Now, since each force produces the same effect as if 
 it alone were acting, we may suppose the ball to move 
 long enough under the influence of the first force alone 
 to reach the point N, then under the influence of the 
 second force only to move toward the west from N for 
 a like length of time. The ball would arrive in the 
 
16 MATTER AND MOTION. 
 
 time specified at the point R, which is the same point it 
 would reach if the two motions occurred at the same 
 instant. The ball has now moved from M to R, hence 
 the line MR represents by its length and direction the 
 magnitude and direction of a force which is equivalent 
 
 ^__ to the two forces MN and 
 
 N l~" 4 ,'''^ MP acting at M. This 
 
 x x x equivalent force is called 
 
 x x the resultant of the other 
 
 x x two forces. Its numerical 
 
 value is readily found from 
 FIG. 5. 
 
 geometry : 
 
 M 
 
 When the directions of the forces make any other 
 than a right angle with each other the value of the 
 resultant may be found by constructing a good-sized 
 diagram to scale and measuring the length of the line 
 which represents the resultant. 
 If more 
 than two 
 forces are act- 
 D ing at a point 
 the lines rep- 
 resenting the 
 forces are 
 
 joined end to FIG ' 7 ' 
 
 end. The line connecting the beginning and end of 
 the chain thus formed represents the resultant. Thus 
 
DISCUSSION' OF THE SECOND LAW. 17 
 
 forces AB, AC, AD, AE, AF, act at the point A 
 (Fig. 6). 
 
 Draw AB' \\ AB 
 
 B'C ! || AC 
 C'D' || AD 
 D'E' || AE 
 E'F' || AF 
 
 Then A'F' (Fig. 7) is the resultant. 
 
 The method employed for two forces is commonly 
 called the triangle of forces. It is but one case of the 
 more general method called the polygon of forces. If 
 the two forces act in the same straight line their resultant 
 is evidently their sum or their difference, according to 
 whether they act in the same or in opposite directions. 
 
 The process of finding the resultant of two or more 
 forces is called the composition of forces. 
 
 Since the velocity produced upon a given mass is 
 proportional to the force producing it, it is evident that 
 velocities may be compounded exactly as forces are. 
 
 It is often desirable to resolve the force acting upon 
 a body into two or more forces. The process is called 
 resolution of forces. It is the converse of composition 
 of forces. A common case is that of a body moving 
 along a path which is not parallel to the direction of 
 the force acting, as when a ship sails westward by 
 means of a south wind. A somewhat simpler case is 
 the following: A car standing upon track 1 (Fig. 8) is 
 to be pushed west by a switch engine on track 2 by 
 means of a rigid iron bar AB. According to the second 
 
18 
 
 MATTER AND MOTION. 
 
 law of motion, the force which moves the car west must 
 act in that direction. Only a portion of the force AB 
 acts westward. Let us resolve AB, then, into two 
 components, one westward, CB, producing motion, one 
 northward, AC, producing pressure on the tracks. 
 
 FIG. 8. 
 
 Knowing the distance apart of the tracks and the length 
 of the bar AB we can at once determine the numerical 
 value of each of the two components. 
 
 The reason is now obvious why the resultant of sev- 
 eral forces not in the same straight line is always less 
 than the sum of the forces. It is also evident that 
 when the direction of motion is not in the direction 
 
 of a certain force there 
 
 v ^x x must be other forces acting 
 
 \ ^x x at the same time with that 
 
 \ x* x force. The direction of 
 
 X AT motion is always the direc- 
 
 M '' tion of the resultant of all 
 
 the forces acting. 
 
 In the case given on page 16 we may resolve MN 
 (Fig. 9) into two forces, MP producing motion and 
 PN not producing motion. Similarly we may resolve 
 NR into PR producing motion and NP not producing 
 motion. The sum of the forces producing motion is: 
 
DISCUSSION OF THE THIRD LAW. 19 
 
 MP -|- PR = MR. The sum of the forces not produc- 
 ing motion is : NP + PN== 0. 
 
 14. Discussion of the Third Law. The third law 
 of motion implies that there are always two bodies con- 
 cerned in every motion. If a moving bat strikes a ball 
 \vhich is moving in the opposite direction the amount of 
 motion destroyed in each is equal. If a croquet ball 
 at rest is. struck by a mallet so that the mallet conies to 
 rest the ball will move forward with a momentum equal 
 to that which the mallet had before impact. The ball 
 has exerted as much force in stopping the mallet as the 
 mallet has exerted in moving the ball. 
 
 If a man in a large boat draw a small boat toward him 
 in the water by means of a rope both boats will move, 
 but the small one will move faster, and, therefore, farther, 
 than the large one. Their relative velocities may readily 
 be found as follows : Call * m v v v M l and m v i> 2 , M 2 
 the masses, velocities-, and momenta of the two boats. 
 Then M =. mv 
 
 and since M l = 
 m i v l = 
 If we suppose m l = 5 
 w 2 =2 
 v.<= 10 
 
 2 x 10 
 
 =4 
 
 g 
 
 or the small boat will move two and one half times as 
 fast as the large one. 
 
 * Read m, " m sub one." 
 
20 MATTER AND MOTION. 
 
 MEASUREMENT. UNITS. 
 
 15. The Fundamental Units. In our discussion of 
 motions and the forces which produce them we have 
 assumed that it is possible to express in numbers the 
 mass of a body, the distance it travels, and the time 
 spent in motion. The exact determination of these 
 and similar quantities is one of the principal tasks of 
 the physicist, for upon such measurements every law 
 and theory in physics rests. 
 
 A moment's reflection will show that to measure 
 velocity we must measure distance and time, to measure 
 momentum we must measure mass, distance, and time. 
 It has been found possible to express all physical quan- 
 tities, electrical and magnetic included, in terms of the 
 three fundamentals, length, mass, and time. 
 
 For the measurement of any quantity we require a 
 unit of quantity of the same sort, the magnitude of 
 which has been determined by cojnparison with some 
 standard agreed upon by scientists, The system of 
 units based upon the metre and known as the metric 
 system is in universal use by scientists and is fast being 
 adopted by the civilized nations of the world for use in 
 commercial transactions. 
 
 A metre is the length of a certain bar preserved at 
 Paris, copies of which are in the possession of the 
 Bureau of Weights and Measures at Washington. Its 
 length is equal to 39.37 English inches, or about 1.4. 
 yards. The metre is divided into 100 centimetres, as 
 our dollar is divided into 100 cents. The centimetre is 
 
DERIVED UNITS. 21 
 
 divided into ten millimetres. For long distances the 
 kilometre is used. A kilometre equals 1,000 metres. 
 Tables of English equivalents will be found in Part II. 
 
 The unit of mass is the gram. A gram is the mass 
 of one cubic centimetre of water at a certain tempera- 
 ture (39.8 F. = 4C.). The gram is divided into 
 centigrams and milligrams, the prefixes centi and milli 
 denoting here, as always, hundredths and thousandths 
 of the unit. A mass of 1,000 grams is called a kilo- 
 gram. It is equivalent to 2.2 English pounds. A 
 new five-cent nickel weighs five grams. A litre of 
 water (1,000 cubic centimetres) weighs, of course, one 
 kilogram. 
 
 The unit of time used by physicists is that which we 
 use in daily life, the second. It is scnTRF of a mean 
 solar day. 
 
 Methods of measuring these fundamental quantities 
 are explained in Part II of this book. 
 
 The system of units based upon the centimetre, grain, 
 and second is known as the c. g. s. system. 
 
 16. Derived Units. The unit of velocity has 
 received no special name. A body has unit velocity 
 when it moves unit space in unit time, hence in the 
 c. g. s. system the unit of velocity is the centimetre-per- 
 second. The unit of momentum is the gramr-centimetre- 
 per-second. The unit of acceleration is the centimetre- 
 per-second-per-second. The unit of force is the gram- 
 centimetre-per-second-per-second. Happily it has received 
 
22 MATTER AND MOTION. 
 
 a shorter name, the dyne.* A dyne is the force which, 
 acting for one second upon a mass of one gram, will 
 accelerate its velocity one centimetre per second. For 
 example, a body is acted upon for one second by the 
 force of gravity. It is required to find the intensity of 
 the force which gravity exerts upon it. It has been 
 found that, no matter what the mass of the body may 
 be, it will gain in one second a velocity of 980 cm. 
 The force acting upon each gram of the body is there- 
 fore 980 dynes. f Forces of considerable size may be 
 conveniently measured in grams or even in kilograms. 
 The value may then be expressed in dynes, if the exact 
 value for the force of gravity per gram of mass is 
 known at the place where the measurement is made. 
 
 The exercises which follow are intended to illustrate 
 and fix in mind the principles treated in this chapter. 
 For convenience the various formuhe are collected and 
 placed at the head of the exercises. They should be 
 fully understood and thoroughly memorized. We shall 
 meet them again and again. 
 
 Formulae. 
 
 s = - whence (la) I = st (Ib) t=- 
 
 6 S 
 
 a = whence (2a) v at (2b) t = 
 
 M-=. mv whence (3 a} m = (3b^ v =. 
 
 v- ^ m 
 
 f f 
 
 f = ma whence (JicC\ m = - (4^ a=. 
 
 a m 
 
 *Dync from Greek dyn, forco. 
 
 fThis value is approximate. It varies in reality from 977 to 984 at different 
 places on the earth's surface. 
 
EXERCISES. 23 
 
 Exercises. 
 
 1. What kinds of motion are illustrated () in the sewing 
 machine ; (&) in the bicycle ? 
 
 2. When a top is set spinning (rt) what keeps it spinning ; 
 (6) what makes it finally stop ? What law of motion is illus- 
 trated ? 
 
 3. An. ice boat has sharp runners, so that it cannot slip side- 
 wise. It is directed toward the northeast. If the wind is 
 blowing ten miles an hour from the south is it possible for the 
 boat to be driven by it faster that ten miles an hour toward the 
 northeast ? Explain. 
 
 4. A horse pulls a loaded wagon exerting a force of 300 
 pounds, (a) How man}' dynes is that ? (6) Where is the 300 
 pounds of reaction required by the third law of motion ? (c) If 
 he were on smooth ice with perfectly smooth shoes, could he 
 do it? 
 
 5. The earth rotates once in twenty-four hours. Calling its 
 circumference 25,000 miles, what is the speed of a point on 
 the equator (a) in miles per hour ; (&) in kilometres per hour ; 
 (c) in feet per second ; (d) in metres per second ? (e) Why 
 does it not stop, as the top does ? 
 
 6. (a) Which law of motion is illustrated by the "kick" of 
 a gun ? (6) Why does not the gun hurt as badly as the bullet 
 does? 
 
 7. A body starts from rest and gains constantly in velocity 
 until at the end of ten seconds it has a speed of 20 metres per 
 second : (a) What was its acceleration ? (6) How far did it 
 travel ? 
 
 Solution. 
 
 (a) by equation (2) a = - = 2 metres per sec. 
 
 0-1-20 
 (6) by equation (1) I = st = - - X 10 = 100 metres. 
 
24 MATTER AND MOTION, 
 
 NOTE. The speed s must be taken as the average speed, 
 which is, of course, equal to half the sum of the initial and 
 final speeds when the acceleration is constant. 
 
 8. A ball rolls down a smooth inclined plane 10 metres long 
 and 6 metres high (see Fig. 10). We may resolve the weight 
 of the ball into two components one || and one _}_ the plane, 
 that is, one in the direction of motion and one at right angles 
 
 to it. According to the second law 
 of motion the first component only 
 produces motion. The total force of 
 gravity upon the ball would produce 
 an acceleration of 9.8 metres per sec- 
 ond per second. What acceleration 
 will the component ca produce? 
 NOTE. Since the right triangles ABC and abc have the 
 
 sides AB 1 be and ab 1 BC thev are similar, and = 
 
 ba BA 
 
 9. A body falls freely under the influence of gravity. It 
 has a constant acceleration of 9.8 metres per second per 
 second : (a) What is its velocity at the end of five seconds ? 
 (6) How far has it fallen ? 
 
 10. A man who can lift but 120 pounds wishes to lift a 200- 
 pound barrel of salt into a wagon 3 feet high. If he is to roll 
 it up a plank, how long a plank must he use ? 
 
 11. A car weighing 1,000 kilograms moves east with a 
 velocity of 20 metres per second, and strikes a car weighing 
 600 kilograms which is at rest. Both cars now move east : 
 (a) What is their joint momentum ; (6) their joint velocity 
 after impact ? 
 
 12. A Spanish ball weighing 8 kilograms and moving north 
 at the rate of 50 metres a second meets an American ball 
 weighing 20 kilograms and moving south at the rate of 20 
 metres per second : What is the velocity of the combined mass 
 after impact ? 
 
CHAPTER II. 
 BALANCING FORCES. 
 
 17. We are all of us compelled after deliberation to 
 accept the truth of Newton's first law of motion, and 
 yet our own observation is that the bodies we see moving 
 do not continue in motion long after the force which 
 sets them going ceases to act. The condition of com- 
 parative rest rather than a state of motion seems to us 
 the normal state of inanimate objects. To see a moving 
 body come to rest does not surprise us. It is when a 
 body continues long in motion without the visible appli- 
 cation of force that our wonder is aroused. 
 
 The explanation of this seeming contradiction is 
 found in the fact that moving bodies impart motion to 
 all bodies which they touch and that no body can move 
 at the surface of the earth without touching something. 
 A body moving in the air must push the air to one side, 
 it must put the air in motion. It will lose its own 
 motion, therefore, little by little till it will ultimately 
 come to rest. But the air is not the chief hindrance to 
 motion in most cases. Gravity is constantly acting. 
 The body falls to the earth. If it rolls along uneven 
 ground it will be lifted out of the hollows by its own 
 momentum until, in rubbing against the earth, it has lost 
 so much of its motion that it finally comes to rest in a 
 
 25 
 
26 BALANCING FORCES. 
 
 hollow, out of which it has not sufficient momentum 
 to lift itself (see Fig. 11). This rubbing of one body 
 against another is known as friction. It is in reality of 
 the same nature as the hindrance due to the large ine- 
 qualities of the surface of the ground just mentioned. 
 The smoothest surface, when examined under the micro- 
 scope, is seen to be covered with little hollows and 
 projections. When one body rests upon another the 
 projections of the one fit into the hollows of the other 
 
 (see Fig. 12). Before 
 
 Q y *~p- ' -* the first body can slide 
 
 FIG. 11. along the surface of 
 
 the second it must 
 be lifted enough to 
 
 " 
 J let the projections 
 
 FI0 - 12 - of the two bodies 
 
 clear each other. While the motion continues there is 
 still a tendency for the projections to drop into the 
 depressions, hence friction continues until the moving 
 body comes to rest. Polishing the surfaces reduces the 
 height of the projections and so diminishes friction. The 
 application of oil or graphite fills the depressions and has a 
 like effect. The heavier the moving body the greater the 
 friction. This indicates that the force which brings the 
 body to rest is gravity. Now, gravity does not cease to 
 act when the body comes to rest, as you may convince 
 yourself by holding a heavy weight in your hand while 
 the hand rests upon the table. In fact, the condition 
 of rest is never proof that no force is acting upon the 
 
KINDS OF EQUILIBRIUM. 
 
 27 
 
 body which is at rest; it is proof that the forces acting 
 are balanced, that is, that the resultant of all the forces 
 acting upon the body is zero. 
 
 This balanced condition has received the name 
 equilibrium. When the forces acting upon a body are 
 in equilibrium any one of the forces is equal in magni- 
 tude and opposite in direction to the resultant of the 
 remaining forces. 
 
 18. Kinds of Equilibrium. A block lying upon the 
 ground in any one of the first three positions shown 
 in Fig. 13 is in equilibrium with reference to gravity. 
 
 FIG. 13. 
 
 It is evidently more easily overturned in 1 than in 2, 
 and less easily in 3 than in 2 or 1. It might be bal- 
 anced also in position 4, but in that position it would 
 be overturned by the slightest application of force in 
 almost any direction. In 1, 2, or 3 the body must be 
 lifted to overturn it. In 4 the body is as high as it 
 can be and touch the ground. The equilibrium in the 
 first three cases is said to be stable, in the last case 
 
28 
 
 BALANCING FORCES. 
 
 unstable. The different degrees of stability in the first 
 three cases may be more clearly shown if we first intro- 
 duce the idea of centre of mass. Let a body be sup- 
 ported by a string attached to it at any point, and let 
 the body come to rest. If we imagine a plane drawn 
 from the point of support downward toward the 
 centre of the earth the body will be divided into two 
 parts, such that the force of gravity 
 acting upon the matter in one part of 
 the body exactly balances the force 
 acting upon the matter in the other 
 part of the body as far as producing 
 rotation about the point of support, 
 F (Fig. 14), is concerned. Let a 
 second plane of the same sort be 
 drawn through F. Now support the 
 body at a new point, F', and draw a vertical plane 
 through that point also. The point of intersection of 
 the three planes is the centre of mass of the body. 
 
 A force directed through the centre oj: mass has no 
 tendency to set the body in rotation. A force applied 
 to the body, not through the centre of mass, does tend 
 to produce rotation. When a body is supported at a 
 point directly under or over its centre of mass, gravity 
 does not tend to make it rotate. We say, therefore, 
 that gravity acts upon a body exactly the same as it 
 would if the mass of the body were collected at the 
 centre of mass. The centre of mass is often called the 
 centre of gravity. When a body as a whole is lowered 
 
 FIG. 14. 
 
 
KINDS OF EQUILIBRIUM. 
 
 29 
 
 or raised, that is the same as lowering or raising its 
 centre of mass. In Fig. 15 let C, O f represent in each 
 case the positions of the centre of gravity as the body is 
 overturned. It is evident that the distance the centre 
 
 -7C 
 
 B ~ -- 
 
 3 
 
 FIG. 15. 
 
 of mass is lifted is greatest in 3, which is, therefore, the 
 position of greatest stability. In 4 the least motion will 
 lower the centre of mass, and hence the equilibrium 
 is unstable. 
 
 The sphere (1, Fig. 16) is neither stable nor un- 
 stable, since its centre of mass is neither raised nor 
 lowered by overturning it. The equilibrium is, therefore, 
 said to be neutral. 
 
 o 
 
 w 
 
 111 
 
 FIG. 16. 
 
 The conditions for stability are that the centre of 
 mass should be low and that the base, that is the 
 
30 BALANCING FORCES. 
 
 figure formed by connecting the points of support, 
 should be large. The load of hay (3, Fig. 16) is less 
 stable than the load of stone (2, Fig. 16), because its cen- 
 tre of mass is higher. It would be more likely to upset, 
 therefore, on a rough road, than would the load of stone. 
 
 19. Moments. If a rigid bar be supported near 
 its centre of mass it will be in neutral equilibrium. 
 Experiment shows that two equal forces acting down- 
 ward upon the two sides or arms of the lever will not 
 
 produce equilibrium, 
 
 I except the forces be 
 
 &/TL applied at equal dis- 
 
 b tances from the cen- 
 
 ' *v x ^ / R tre of rotation, and 
 
 that a force of 1 at a 
 distance 2 will bal- 
 ance a force of 2 at a 
 
 distance 1. In general the effect of a force in produc- 
 ing rotation is measured by the product of the magnitude 
 of the force, times the distance of the line of application 
 of the force from the centre of rotation. This product 
 is called the moment of a force. 
 
 Moment of a force = force X distance from centre. 
 The distance to the line of application of the force is, 
 of course, the perpendicular distance. 
 
 The condition of equilibrium for a lever, as for any 
 body free to rotate about a fixed axis, is that the sum of 
 the moments of all the forces acting upon it shall be zero. 
 
THE LEVER BALANCE. 
 
 31 
 
 In the case illustrated in Fig. 17 the sum of the 
 moments of the forces M and R tending to rotate the 
 lever toward the right is: 4x3 + 3x6 = 30. The 
 moment of the force N is 5 X 6 = 30 toward the left. 
 Since the sum of these moments is zero the lever is in 
 equilibrium. 
 
 20. The Lever Balance. The force of gravity at 
 any place is the same for equal masses. A lever sus- 
 pended at a point 
 slightly above its 
 centre of gravity has 
 attached at equal 
 
 FIG. 19. 
 
 It will again be 
 horizontal when 
 the masses i n 
 the two pans 
 are equal (see 
 Figs. 18, 19). 
 
 FIG. 18. 
 
 distances from its 
 centre pans in which 
 the masses to be 
 compared are placed. 
 The lever, or beam 
 as it is called, should 
 be horizontal when 
 the pans are empty. 
 
 <Qs~l 
 
 6 
 
 FIG. 20. 
 
32 BALANCING FOECSS. 
 
 When large masses are to be compared with smaller 
 ones a lever with unequal arms (Fig. 20) is employed. A 
 
 FIG. 21. 
 
 familiar form is called the steelyards (Fig. 21). In the 
 large scales used for weighing grain or coal combina- 
 tions of several levers are employed, so as to reduce 
 the size of the standard weights used. 
 
 21. Universal Gravitation. With truly prophetic 
 insight, Sir Isaac Newton conceived that the force of 
 gravity, which acts between the earth and all bodies 
 upon its surface, reaches also to the moon and to all the 
 planets of our solar system indeed to the limits of our 
 visible universe. Certain it is that some force must be 
 constantly acting to keep the moon constantly changing 
 its direction as it revolves about the earth in a nearly 
 circular orbit. Certain it is, too, that gravitation (of 
 which gravity is but a special example), acting in accord- 
 ance with the laws enunciated by Newton, is fully 
 competent to keep the planets in equilibrium, each main- 
 taining its average distance from the sun constant from 
 century to century. 
 
NEWTON'S LAW OF GEAVITATION. 33 
 
 22. Newton's Law of Gravitation. Every particle 
 of matter in the universe attracts every other particle. 
 ^The force impelling any two bodies toward each other is 
 proportional to the product of the masses of the two 
 bodies and inversely proportional to the square of the 
 distance between their centres of mass. ^ 
 
 If A, B are two spheres whose masses are m v ra 2 , and 
 distance between centres, r, then : 
 
 where Kis a, number which is constant for any set of 
 units used in measuring m and r. It is the attraction 
 between two unit masses (1 g. each) whose centres of 
 mass are unit distance (1 cm.) apart. In dynes JT 
 .000000065. It is a very small quantity, as one can 
 readily see, since the force between the earth and a body 
 weighing a gram is only 980 dynes, while the mass of 
 the earth is so great as it is. 
 
 The force between two kilogram weights at a distance 
 of ten centimetres is so small that very delicate instru- 
 ments are required to detect it at all. 
 
 The force between the earth and the moon is much 
 greater. If the moon could be stopped in its revolu- 
 tion about the earth it would fall at once to the earth. 
 As it is, the force of gravitation is employed in deflect- 
 ing the moon's motion from a straight line. Gravita- 
 tion, then, tends to equilibrium. In the case of bodies 
 moving in orbits a sort of equilibrium an equilibrium 
 of motion, in which the average distance of a body from 
 
34 BALANCING FORCES. 
 
 neighboring bodies remains constant has been already 
 attained. All bodies which are actually falling toward 
 each other are tending to a condition of equilibrium. 
 At the surface of the earth bodies must first be lifted 
 before they can fall. When a body is once lifted we 
 know the law, we learned it in childhood : " All that 
 goes up must come down." 
 
 SOME PROPERTIES OF MATTER. 
 
 23. Elasticity. A body was defined in Section 4 as 
 a portion of matter having a definite size and shape. 
 Now the size and shape of a body may be changed 
 somewhat by the application of force without perma- 
 nently altering either its size or shape. As soon as the 
 force ceases to act the body returns to its original con- 
 dition. This could only be true if a force acted to 
 make it so return. We call the forces, concerned in 
 preserving constant the size and shape of bodies elastic 
 forces, and the property which different substances 
 possess in different degrees of exhibiting elastic force 
 we call elasticity. 
 
 Any force which acts upon a body so as to change its 
 form or size from that which it would assume under the 
 action of the elastic forces is called a stress. The effect 
 of a stress in deforming the body is called a strain. 
 When the stress is removed elasticity causes the body 
 to recover from the strain and return to its original 
 form and size. 
 
POBES, MOLECULES, COHESION. 35 
 
 If a metre stick, with its ends resting upon two 
 blocks or books, have a kilogram weight placed upon it 
 at its middle, it will be depressed until the elastic force 
 of the wood is equal to one kilogram, when it will 
 come to rest. If the weight be now removed the stick 
 will again become straight. 
 
 The air in a boy's pop-gun is compressed against an 
 elastic force which increases until the wad is forced out, 
 when the air returns at once to its original volume. 
 
 24. Pores, Molecules, Cohesion. In order to 
 understand how the same body can occupy a different 
 amount of space at different times we must suppose 
 that before the air in the pop-gun, for example, was 
 compressed, there were portions of space in it which 
 were not occupied, so that some of the particles could 
 be forced into these pores. There are excellent reasons 
 for thinking that all bodies are composed of very small 
 particles which have been called molecules.* The pores 
 are the spaces between the molecules. Two forces are 
 constantly acting, one to draw the molecules toward 
 each other, one to push them apart. The force which 
 draws the molecules together is cohesion (called ad- 
 hesion when it acts between two different bodies). 
 In what respects cohesion differs from gravitation 
 is not yet known. It is effective only through very 
 small distances. Very fine iron dust will remain dust 
 
 * Mol/e-cule, Latin moleculum, from moles, mass, and culum, little a little 
 mass. 
 
36 BALANCING FORCES. 
 
 though its particles are in contact. Under heavy pres- 
 sure, however, most powdered substances will cohere, 
 especially if they are first moistened or heated, but 
 the structure of the body thus formed differs from the 
 structure of the substance before it Avas ground to 
 powder. 
 
 The force which balances cohesion is called heat. It 
 is a vibratory motion of the molecules which prevents 
 their coming closer together. If a body is made hotter, 
 therefore, its molecules are driven farther apart it 
 becomes larger. If the body loses heat it grows smaller, 
 until cohesion and heat exactly balance each other. In 
 a solid body cohesion so far predominates over heat that 
 the molecules retain certain definite positions \vith ref- 
 erence to each other. If enough vibratory motion is 
 imparted to the molecules in the form of heat, cohesion 
 will be so far overcome that it Avill no longer be able to 
 keep the body in a definite shape, the substance becomes 
 liquid and under the influence of gravity takes the 
 shape of the vessel in which it is contained, its upper 
 surface being nearly horizontal. If heat be still further 
 applied the liquid will expand for a time, but if a suffi- 
 cient amount of heat is imparted to the body the par- 
 ticles will be driven so far apart that cohesion loses all 
 control and the body becomes a gas. 
 
 Most substances may exist in any one of these three 
 forms. All gases are now liquefied in the laboratory. 
 All solid bodies may now be volatilized, or turned to 
 gas. Some substances do not readily take the liquid 
 
ELASTICITY EXPLAINED. 
 
 37 
 
 FIG. 22. 
 
 form but pass at once from solid to gaseous, or from 
 gaseous to solid. This matter will be discussed more 
 fully under the subject of heat. 
 
 In Fig. 22 let the small black dots at a represent the 
 position of the molecules of a small body at a given 
 instant. The circles may represent the range of the 
 motion of the individual molecules. At b more heat 
 has been added to the body, the molecules require more 
 room in which to vibrate, 
 the body is larger. At 
 c after more heat has 
 been added the body has 
 become a liquid. To 
 represent on the same scale the gaseous condition 
 would require a diagram too large for this book. 
 
 25. Elasticity Explained. We may explain in the 
 light of the statements just made the phenomena which 
 we have ascribed to elastic forces. In short, heat and 
 
 cohesion are the elastic forces. 
 In Fig. 23 let a represent a 
 bar of steel. Let b represent 
 the same bar, which has been 
 bent by applied forces into the 
 form shown. The molecules 
 in the lower row are nearer 
 together than they normally 
 are, those in the upper row farther apart. Heat is 
 striving to drive the lower row apart> cohesion tends 
 
 PIG. 23. 
 
38 BALANCING FOKCE8. 
 
 to draw the upper row together. In other words, the 
 body tends to return to its original shape. Elasticity 
 of shape is thus seen to be exactly like elasticity of size. 
 In both cases it is the effect of forces tending to prevent 
 expansion or compression. In solids different parts 
 of a body may be compressed or expanded unequally. 
 In liquids and gases this is impossible, hence liquids 
 and gases (both of which are called fluids*) have no 
 form and exhibit only elasticity of size or volume. 
 Owing to the freedom of motion of the molecules in 
 fluids, all fluids are highly elastic. 
 
 26. Liquids in Open Vessels. A liquid in an open 
 
 vessel is acted upon not only 
 by the elastic forces but by 
 gravity. Every particle of 
 the liquid is pressed down- 
 ward by the weight of the 
 liquid above it and by the 
 weight of the air. Let a 
 (Fig. 24) be a molecule of 
 
 water. It is pressed downward by the weight of the air 
 and the water above it. But since it is at rest it must 
 be pressed upward by an equal amount. Moreover, if 
 it were not pressed from all sides by a like amount it 
 would slip out of its place, since the particles of a liquid 
 are free to move among themselves. The fact is that 
 the molecules <?, d, and all others which are the same 
 
 Latin fluere, to flow. 
 
LIQUIDS IN OPEN VESSELS. 39 
 
 distance below the surface are pressed downward with 
 the same force that a is. They must all press sidewise 
 by a like amount or the liquid would not be at rest. 
 The molecules at e, d, press the sides of the vessel with 
 a force equal to that exerted upon them by their 
 neighbors ,/, g. Any surface on the line de has a 
 pressure upon it which is proportional to the area of the 
 surface, but is the same for all equal surfaces for that 
 depth and is alike in every direction. 
 
 Let us now suppose that by tilting the vessel suddenly 
 the water is thrown into the position shown in Fig. 25. 
 The pressure upon c is less than that upon , conse- 
 quently a will be pushed 
 away from b with a greater 
 force than it is pushed away 
 from c. The same is true 
 of other particles, hence they 
 will move to the left till 
 equilibrium is restored, that 
 is, until all parts of the 
 liquid surface are at right angles to the direction of 
 gravity. The last statement presupposes that the body 
 of liquid is so large that gravity is the principal force 
 acting. 
 
 If other forces are acting the liquid will come to rest 
 with every point of its surface perpendicular to the 
 resultant of all the forces acting at that point. 
 
 Let us first consider the case of a liquid acted upon 
 by gravity only. It follows from the principle just 
 
 FIG. 25. 
 
40 
 
 BALANCING FORCES. 
 
 stated that in any number of communicating vessels, no 
 matter what their size or shape, a liquid will have the 
 same level (see Fig. 26). In a tea-pot the liquid rises 
 
 FIG. 26. 
 
 as high in the spout as in the pot itself and no higher. 
 
 The pressure of any particle at a (Fig. 27) due to the 
 
 liquid in (7must be exactly equal 
 to that due to the liquid in D, or 
 the liquid would not come to 
 rest. If the height of the liquid 
 above a were greater in D than 
 in (7, the pressure would not be 
 equal and there would be a 
 FIG. 27. movement from D to 0. 
 We may now sum up the facts in regard to the behavior 
 
 of liquids in open vessels in the following statements : 
 
 I. The pressure at any point in a liquid is the same 
 in all directions. 
 
CAPILLARY PHENOMENA. 
 
 41 
 
 II. The pressure at any point in a liquid of uniform 
 density, due to the weight of the liquid, is proportional to 
 the depth of the point below the surface of the liquid. 
 
 III. The surface of a liquid at rest is perpendicular at 
 any point to the resultant of all the 
 
 forces acting at that point. 
 
 If we now examine some cases in 
 which gravity is not the greatest force 
 acting upon the liquid, we shall see 
 that they are apparently, but not 
 really, exceptions to the third law. 
 
 FIG. 28. 
 
 27. Capillary Phenomena. If a 
 piece of clean glass be dipped in 
 
 water some of the water will adhere 
 to the glass when it is removed (Fig. 
 28). Here adhesion is more power- 
 ful than gravity, and the surface of 
 the water may be almost parallel to 
 the direction o f 
 gravity (Fig. 28). 
 Let us again dip 
 the plate of glass in water (Fig. 29). 
 The water will be drawn to the water 
 on the glass by cohesion, to the 
 glass by adhesion, and downward by 
 gravity. Very near the glass adhe- 
 sion is most powerful, hence the re- 
 sultant is nearly horizontal, as at P (Fig. 30) ; a little 
 
 FIG. 29. 
 
 FIG. 30. 
 
42 
 
 BALANCING FORCES. 
 
 distance from the glass gravity is much the greatest 
 force acting, while at P" the forces are nearly equal in 
 magnitude. 
 
 If two glass plates are placed very near each other in 
 water the weight of the liquid between them is small 
 as compared with the adhesion between the water and 
 the glass, hence the water rises to 
 a considerable height above the 
 level of the rest of the water in 
 the glass. In a very fine glass 
 tube the weight of water is ex- 
 ceedingly small as compared to 
 the surface of glass and water in 
 contact. In such tubes water 
 rises to a height of several centi- 
 Such tubes are called capillary 
 
 FIG. 31. 
 
 metres (a, Fig. 31). 
 tubes,* and the phenomenon of 
 elevation of a liquid in capillary 
 tubes is called capillarity. 
 
 If instead of clean glass we 
 had used oily glass, to which 
 water does not adhere, or if in- 
 stead of water we had used mer- 
 cury, cohesion in the liquid itself 
 would have caused a depression 
 of the surface where the liquid touched the glass, as 
 shown in Fig. 32. 
 
 FIG. 32. 
 
 * Latin capillus, a hair. 
 
SURFACE TENSION. 43 
 
 28. Surface Tension. Water falls through the air 
 in drops. Water on the surface of the leaves of plants 
 to which it does not adhere collects in spheroidal 
 masses. Mercury spilled upon the table collects in 
 
 spheroids, the smallest of 
 which are nearly perfect 
 FlG - 33 - spheres, the larger being flat- 
 
 tened by their greater weight (Fig. 33). A glass rod 
 or a stick of sealing wax, when broken, shows sharp 
 edges. If the broken end of the glass rod or the stick of 
 wax be held in a flame to soften it the sharp corners are 
 rounded off. How can these phenomena be explained ? 
 
 The liquids in question (for the wax and glass 
 are melted in the flame) behave as if their surfaces 
 were stretched, or, in scientific language, under ten- 
 sion. The drop of water has least surface when it 
 is a perfect sphere. The mercury in Tig. 32 is pushed 
 down by the glass plate, just as if there were a 
 skin of rubber over the surface. For 
 this reason all capillary phenomena, 
 as well as the other phenomena just 
 referred to, are usually explained as 
 results of surface tensions. It remains 
 
 to be explained why liquids are under FIG - &. 
 
 tension at their surfaces. A molecule of water at a 
 (Fig. 34) is acted upon by the cohesion of all of the 
 molecules within a certain small distance from it, 
 but it is drawn equally in all directions and is, there- 
 fore, in equilibrium. A molecule near the surface, 
 
44 
 
 BALANCING FORCES. 
 
 as b (Fig. 34), is acted upon only from one side, and so 
 there is always a force acting inward. It is transmitted, 
 of course, throughout the liquid and produces the same 
 effect as would a thin elastic rubber bag stretched over 
 the liquid. We know that if we push in a stretched 
 membrane at one point, it tends when released to come 
 back to a flat surface again. A drop of water or of any 
 liquid behaves in the same way. The surface of any 
 liquid will tend to take the shape that will make it the 
 smallest possible. The tension is along the surface, 
 hence when the surface is flat there is no tendency to 
 
 FIG. 35. 
 
 motion. If, however, the surface is curved, as when a 
 tube is pushed down into a vessel of mercury (c, Fig. 
 35), the tension of the surface tries to shorten the sur- 
 face and so pulls the mercury downward. In case of 
 a wet glass tube in water (a, Fig. 35), the surface is 
 shortened if the water rises. The force at any point in 
 the surface may be represented by a line tangent to the 
 surface. This force (if the surface is curved) has a 
 component acting toward the centre of curvature, the 
 
SURFACE TENSION. 
 
 45 
 
 magnitude of which is greater as the curvature becomes 
 greater. This fact will help us to explain why a soap 
 bubble which has been flattened by fanning it, or a 
 drop of water which has become elongated in falling, 
 tends at once to take the spherical form, that is, the 
 form in which the curvature is the same at every point. 
 This is also the form having the least surface for a 
 given volume. 
 
 In Fig. 36, if the tension at B is resolved into two 
 components, one toward the centre and one at right 
 angles to it, 
 we see that 
 the compo- 
 nent BC is 
 greater the 
 greater the 
 curvature of 
 the surface. 
 In the case 
 of the sphere 
 the curva- 
 ture is every- 
 where equal. 
 In the tubes 
 
 (Fig. 35) the liquid comes to rest when the -difference 
 in pressure due to a difference in height inside and 
 outside the tube balances the tension due to the curvature. 
 
 If a drop of water be drawn into a wet tube which 
 tapers and the tube be then held in a horizontal posi- 
 
 FlG. 3G. 
 
46 BALANCING FORCES. 
 
 tion, as in Fig. 37, the curvature at b will be greater 
 than at c (being equal to the curvature of the tube at 
 those points), hence the water will move toward b. A 
 drop of mercury in a similar tube (see Fig. 38) will 
 move in the opposite direction. The surface at b (Fig. 
 37) must be thought of as extending along the inside 
 of the tube to the end at a. When the liquid has been 
 
 drawn to a the 
 
 . 37. forces will be 
 
 equal at every point in the surface. The mercury 
 in Fig. 38 will move till the tube no longer presses it 
 out of the spher- 
 ical shape at a. 
 It will not then 
 be perfectly FIG 38 - 
 
 spherical, because of its own weight, but the curvature 
 will be equal on its two sides and its motion will cease. 
 
 29. Floating Bodies. If a body when immersed in 
 water and left to itself rises toward the surface, there 
 must be an upward force acting against gravity and that 
 force must be greater than the weight of the body. By 
 the second law stated on page 41 the pressure on the 
 bottom of the body is greater than on the top, since 
 there is a greater height of water above b (see Fig. 39) 
 than above a. 
 
 If the body is a cube 1 cm. in height the pressure on 
 
ARCHIMEDES' LAW. 47 
 
 the top at a depth of 6 cm. is 6 grams, but the pressure 
 on the bottom at a depth of 7 cm. is 7 grams. The 
 resultant upward pressure is therefore 1 gram, which is 
 the weight of the water displaced by the body. This 
 fact was discovered by Archimedes, who gave his name 
 to the law. The law may be stated as follows : 
 
 Archimedes' Law. A solid immersed in a fluid is 
 buoyed upward by a force equal to the weight of the 
 fluid which it displaces. 
 
 Since the volume of liquid displaced by a solid is 
 equal to the volume of the solid, and since the 'volume 
 of a gram of water is one cubic centi- 
 metre, it follows that the loss of weight 
 of a solid when immersed in a liquid 
 is numerically equal to the volume of 
 the solid. If the liquid weighs the 
 same per unit volume as the solid does 
 
 r 1 
 
 the solid will come to rest at any point 
 in the liquid. If the solid is lighter, volume for volume, 
 than the liquid the solid will rise above the surface of 
 the liquid far enough so that the portion immersed 
 displaces an amount of the liquid equal in weight to 
 the weight of the solid. This principle is made use of 
 for finding the volume of an irregular solid. The solid 
 is first weighed in air, then weighed again immersed in 
 water. The difference between the two weights in grams 
 is equal to the volume in cubic centimetres of the body. 
 
 30. Liquids in Closed Vessels. We have seen that 
 
48 BALANCING FORCES. 
 
 the pressure at any point in a liquid due to the weight 
 of the liquid is transmitted equally in every direction. 
 If the vessel be closed by a movable piston so that ad- 
 ditional pressure may be applied the same law holds. 
 Thus the pressure applied at the pumping station of a 
 city water system is transmitted through the water in 
 the pipes to all parts of the city, forcing the water to the 
 tops of high buildings or at lower levels delivering it 
 under pressure sufficient to run a water motor. The 
 subject will be further discussed under machines. 
 
 31. Gases in Open Vessels. Gases have some 
 properties in common with liquids. They transmit 
 pressure equally in all directions. Archimedes' law is 
 true of liquids and gases alike. A feather weighing 
 one gram is as heavy as a gram of lead, but it falls to the 
 ground much more slowly because it displaces a large 
 volume of air. Liquids and gases differ, however, in 
 some important particulars. Gases have no definite 
 surface, hence cannot have surface tension. A gas 
 seeks to diffuse itself indefinitely because its particles 
 are too far apart to be influenced by cohesion. Let 
 heat be removed from the gas so that its particles are 
 not driven apart when they chance to touch each other, 
 or let pressure be applied to bring the particles near 
 together, and cohesion takes effect at once, reducing the 
 gas to a liquid. 
 
 Liquids, again, have a very definite volume. They 
 are almost perfectly incompressible. Gases are very 
 
GASES IN OPEN VESSELS. 
 
 49 
 
 easily compressed, the volume of a gas being determined 
 by the pressure which it sustains. Every open vessel at 
 the surface of the earth is filled with air. The weight 
 of the air contained in any given vessel varies from day 
 to day, as the pressure of the air varies. The weight of 
 the air being determined by the pressure of the air 
 above will change if there are disturbances in the air 
 above such as to cause the air to 
 be heaped up at certain places 
 on the earth's surface. There 
 are such disturbances, known as 
 storms, which move across the 
 country from west to east. The 
 pressure of the air often varies 
 as much as two or three per cent 
 } in two days during the passage 
 of a storm. A diminution of 
 pressure precedes a storm, a fact 
 which is made use of to foretell 
 the approach of storms. Let us 
 see how the pressure of the air 
 may be measured. Let a U tube 
 80 cm. high (Fig. 40) be filled tfl 
 about half full with mercury. 
 The mercury will come to rest 
 FIG. 40. with its two surfaces on a level. FIG - 41 - 
 The pressure of the air on the two surfaces is equal. 
 If now we exhaust the air from the left-hand arm, a, of 
 the U tube, the pressure of the air in b will force the 
 
50 
 
 BALANCING FORCES. 
 
 mercury up in a until the weight of the air is exactly 
 balanced by the column of mercury ab' (see Fig. 41), the 
 portion of the mercury below bb f being equal in both 
 arms. If the arm a be now closed permanently and the 
 arm b be cut off to a convenient length, we have a 
 
 means of meas- 
 uring the pres- 
 sure of the air; 
 for as the pres- 
 sure of the air 
 increases or di- 
 minishes we 
 have but to 
 measure the dif- 
 ference in height 
 of the two mer- 
 cury surfaces. 
 Such an instru- 
 ment is called 
 a barometer.* 
 The air may be 
 removed from 
 the long arm by- 
 Ming the entire 
 tube with mer- 
 cury, employing a rubber tube and funnel as shown in 
 Fig. 42, a, and then inverting the tube. The same end 
 may be accomplished by using a straight tube, b (Fig. 43), 
 
 * Greek, bar and metron, weight, measure. 
 
 FIG. 42. 
 
 FIG. 43. 
 
PUMPS AND SIPHONS. 
 
 51 
 
 which is filled and then inverted 
 in a small vessel of mercury, c. 
 The mercury will fall in the tube 
 until the pressure of the air is 
 exactly balanced. 
 
 It will balance at about 73 
 cm. to 78 cm., depending on the 
 elevation of the place and the 
 condition of the weather. 
 
 32. Pumps and Siphons. 
 (#) If water were used in a 
 barometer instead of mercury, 
 it would rise 13.6 times as high 
 as mercury does, since mercury 
 is 13.6 times as heavy as water. 
 The common pump consists of 
 a long tube, , the lower end of 
 which dips in water, while the 
 upper end is provided with a 
 close-fitting piston for removing 
 the air. A device called a valve, 
 v, allows the air to escape when 
 the piston is pushed downward, 
 but closes when the piston is 
 lifted so that no air enters. . FIG * **' 
 
 The air which remains in the tube is under diminished 
 pressure, and water will rise in the tube till the pressure 
 of the air and water within the tube balance that of the 
 
52 
 
 BALANCING FORCES. 
 
 air on the outside. A second valve, v\ is placed in the 
 tube below the piston, so that another portion. of air 
 may be removed, and so on until the water comes above 
 the piston, where it flows out at the spout, s. Such a 
 pump will raise water about 30 feet. 
 
 (6) A siphon is used for transferring liquids from 
 higher to lower levels over an elevation. It consists of 
 
 FIG. 45. 
 
 a bent tube, which is first filled with the liquid and then 
 inverted with one arm under the surface of the liquid, 
 the arm outside of the vessel being lower than the one 
 within. In Fig. 45 the pressure at in the direction 
 of CA is one atmosphere less the weight of the column 
 AC-, the pressure at C in the direction CB is one 
 atmosphere less the weight of the column BC. The 
 
GASES IN CLOSED VESSELS. 53 
 
 pressure is greater in the direction CB by the weight of 
 A'B, and the liquid will flow until it is at the same level 
 in both vessels. 
 
 33. Archimedes' Principle applies to Gases. A 
 
 solid immersed in a gas, as all bodies near the surface 
 of the earth are immersed in air, is buoyed up by a 
 force equal to the weight of the air displaced by it. A 
 pound of feathers weighed out with a balance and iron 
 weights is really heavier than a pound of lead. Placed 
 on the two arms of the balance in air they would bal- 
 ance each other. In vacuum the arm carrying the lead 
 would require some additional weight to again produce 
 equilibrium. 
 
 34. Gases in Closed Vessels. A gas wholly fills 
 the vessel containing it, no matter how large the vessel 
 may be. The pressure of a given body of gas is in- 
 versely proportional to the space it occupies, or what 
 amounts to the same thing, its volume times its pressure 
 is a constant quantity : 
 
 Volume X pressure = constant 
 vp k 
 
 This statement is known as Boyle's Law. It does 
 not apply to vapors, that is, gaseous substances, which 
 by a small increase of pressure or lowering of temper- 
 ature would be liquefied, for when a vapor begins to 
 liquefy it may be subjected to pressure without much 
 
54 
 
 BALANCING FORCES. 
 
 diminishing the space occupied by the vapor. Boyle's 
 Law is said to apply, therefore, to the so-called " perfect 
 gases" at ordinary temperatures. Air, oxygen, and 
 hydrogen are good examples of perfect gases. 
 
 Boyle's Law may be veri- 
 fied experimentally by means 
 of a bent tube, having its 
 shorter end closed (see Fig. 
 46) and the bend of the tube 
 filled with mercury. When 
 the mercury is at the same 
 level in both arms of the tube 
 the pressure on the confined 
 air is the same as on the free 
 air, and is measured by read- 
 ing the barometer. If the 
 open arm be filled to any 
 height, as A, the air in the 
 closed arm will be compressed 
 to a smaller volume. The 
 height of the barometer plus 
 the height of A above B' 
 measures the pressure upon 
 the confined air. If the tube 
 is of uniform diameter the volume of the air is propor- 
 tional to the length CB. 
 
 35. Air Pumps. If part of the gas in any closed 
 vessel is removed the remaining gas immediately ex- 
 
 FIG. 46. 
 
FLUIDS I.V CONTACT. DIFFUSION. 
 
 55 
 
 pands and fills the entire space. Thus, if the piston, 
 p (Fig. 47), is drawn from near the bottom of the cylin- 
 der, (7, pushing the air before it, the air in the receiver, 
 R, will expand and occupy the cylinder. If R is twice 
 as large as C, one stroke of the piston removes one 
 third of the air in R, a second stroke removes one 
 third of the remainder, and so on, the limit of exhaus- 
 tion being determined by the degree of perfection of 
 
 the joints about the piston and valves. Compression 
 pumps, like the common bicycle pump, have the valves 
 opening inward. 
 
 36. Fluids in Contact. Diffusion. (a) If a ves- 
 sel containing a gas be opened in a room the gas will at 
 once expand till it is equally distributed throughout 
 the room. Tin's fact is evident when the gas has a 
 
56 
 
 BALANCING FORCES. 
 
 marked odor, but it is equally true in any case. It is 
 also true that the air in the room will enter the vessel, 
 and, in time, the contents of the vessel and the room 
 will be identical. If, however, gases differing Avidely 
 in density be placed in the same vessel, the heavier gas 
 will tend to go to the bottom; but, unless the vessel is 
 very large indeed, every part of the vessel will show 
 
 the presence of all the gases 
 in the vessel. The percen- 
 tage of carbon dioxide present 
 in a sleeping room is always 
 greater near the floor than 
 near the ceiling. This pene- 
 tration by a gas of a space 
 already occupied is called 
 diffusion. 
 
 The rate of diffusion for 
 heavy gases is less than that 
 for light ones. If a porous 
 battery cup (see Fig. 48) 
 be fitted with a large cork 
 through which passes a glass 
 tube, the air in the cup will 
 diffuse outward through the pores of the clay at the 
 same rate that the air on the outside diffuses inward. 
 Should we now dip the lower end of the tube in a glass 
 of colored water, the water will rise in the tube to the 
 height of the water in the glass ; but if we place over 
 the porous cup a bell glass containing a light gas like 
 
 FIG. 48. 
 
FLUIDS IN CONTACT. DIFFUSION. 57 
 
 hydrogen or illuminating gas, the hydrogen will diffuse 
 into the porous cup faster than the air diffuses out, the 
 pressure in the cup will be increased, and bubbles will 
 be forced out at the bottom of the tube. If we now 
 remove the bell glass the hydrogen will pass out through 
 the pores of the cup faster than the air passes in, the 
 pressure within the cup will be diminished, and the 
 water will rise in the tube higher than in the glass and 
 then gradually fall when equilibrium has been restored 
 between the gases in the cup ; that is, when the propor- 
 tion of hydrogen and air is the same inside the cup as 
 outside. 
 
 (>) When a gas is in contact with a liquid some of 
 the gas will penetrate the liquid. Thus water which 
 has been exposed to air contains air enough to keep 
 fishes alive. Housekeepers know, too, that milk left 
 open near onions absorbs the odor emitted by the 
 onions. 
 
 (c) Liquids which do not separate of their own 
 Accord when mixed will mix by diffusion when placed 
 in contact. The process is much slower than in the 
 case of gases, but it may be observed without difficulty 
 by introducing, by means of a thistle tube, a heavy liquid, 
 like copper sulphate solution, to the bottom of a tall jar 
 containing water. If the tube is withdrawn carefully, 
 the line of separation beween the water and the heavy 
 copper sulphate solution will be plainly marked. After 
 the jar has stood quietly for a day or two, however, the 
 copper sulphate will be seen to have diffused into the 
 
58 BALANCING FORCES. 
 
 water. In a week the blue color will have reached the 
 very top of the water, thus making evident the fact 
 which we have many other reasons for believing, namely, 
 that the particles of fluids are in incessant motion among 
 themselves, and are not, even in liquids, confined per- 
 manently to any particular part of the body of fluid of 
 which they form a part. 
 
 37. Osmose. If two solutions are separated by 
 parchment paper arid one wets the paper while the 
 other does not, the former will diffuse through the 
 paper. Solutions of crystalline substances, like sugar 
 and salt, pass readily through such porous paper, while 
 gums, albumen, and the like do not. This fact is often 
 made use of to separate substances of the first class 
 which are in solution with those of "the second class. 
 Osmose, as this property of diffusion of solutions 
 through porous partitions is called, is of especial inter- 
 est in the study of plant life. In winter the fluids of 
 a tree are allowed to diminish in amount so as to pre- 
 vent injury to the cells by freezing. In spring the roots 
 take up moisture from the soil, passing it from cell to 
 cell by the process of osmose, till the sap, often con- 
 taining a noticeable amount of sugar, reaches the tip of 
 the farthermost twig. The circulation of the sap of 
 plants is thus carried on without that complicated sys- 
 tem of arteries and pumps which is found in the 
 higher animal organisms. 
 
EXERCISES. 59 
 
 Exercises. 
 
 13. Why do steel journals run more easily in brass than in 
 steel bearings ? 
 
 14. Mention some cases where friction is an advantage. 
 
 15. (a) Do wood and other vegetable tissues shrink or swell 
 when wet ? (fr) Is a rope longer or shorter when wet ? Ex- 
 plain. 
 
 16. Is a three-legged or a four-legged stool the more stable 
 on uneven ground ? 
 
 17. (a) A steelyard has the hook which supports the weight 
 one half inch from the fulcrum. How far apart must the one 
 fourth pound notches be placed on the beam if the bob weighs 
 one half pound ? (6) Sketch a steelyard which will weigh to 
 one ounce. 
 
 18. The force of gravity on one gram at the earth's surface 
 is 980 dynes. What is the force on the same mass 100 kilo- 
 metres above the surface of the earth ? 
 
 Suggestions : (5) /= --= If is the constant of grav- 
 itation, and m l7 m 2 are constant in value, so / varies inversely 
 with r 2 , that is, /://:: -L : _L. or / : /' :: r' 2 : r\ .-./ = 
 
 In this example r 6,400 km. 
 r> = 6,500 km. 
 
 19. Two kegs of shot, weighing 100 kilograms each, lie on the 
 floor with their centres 40 cm. apart. What is the force tend- 
 ing to make them roll toward each other ? 
 
 20. (a) The mass of the moon is ^- that of the earth, and 
 its diameter 0.273 that of the earth. What is the value of / 
 (the force on one gram) at the surface of the moon ? (&) The 
 
60 
 
 BALANCING FORCES. 
 
 mass of Mars is i| that of the earth, and its diameter 0.534 
 that of the earth. What is the value of / at its surface ? 
 
 21. Why does a hydrogen balloon float in air ; wood in water 
 and not in air ; iron in mercury and not in water ; an iron ship 
 in water ? Can the floating of clouds in air be explained in the 
 same way as the foregoing ? 
 
 22. Why does a needle float if carefully placed in a horizontal 
 position on water ? 
 
 23. Why will the wood of a ship sunk in deep water no 
 longer float if set free ? 
 
 24. (a) What part of a milldam should be strongest ? (6) 
 Need it be stronger if the pond is a mile long than if it is but 
 a few rods long ? 
 
 25. Explain how a spoon may be filled heaping full of water. 
 
 26. Why does not 
 good letter paper 
 make good blotting 
 paper ? 
 
 27. How do fishes 
 rise and sink in 
 water ? 
 
 28. The capillary 
 tube in Fig. 49 is so 
 small that the water 
 
 will rise in it to a height of 10 cm. If it were bent at a height 
 of 8 cm., would the water from A flow over into B ? 
 
 29. Why does boiled water taste "flat" even after being 
 cooled ? 
 
 30. A withered apple placed under the receiver of an air 
 pump will, when the air has been exhausted, swell out and 
 look plump and smooth. Explain. 
 
 31. What well-known facts are best explained on the hypoth- 
 esis that matter is made up of very small parts (molecules) 
 which are in constant motion and have in most cases some 
 space between them ? 
 
CHAPTER III. 
 HEAT. 
 
 38. The Nature of Heat. We have seen that 
 many phenomena not easy to explain on any other hy- 
 pothesis are explained by supposing that matter consists 
 of molecules which are, so far as we know, always in 
 motion among themselves, the amount of motion pres- 
 ent in the molecules of any body being the cause which 
 determines whether the body is at any instant solid, 
 liquid, or gaseous. We have called this movement of 
 the molecules among themselves heat, and we shall now 
 proceed to study more in detail the phenomena con- 
 nected with and the laws which govern this kind of 
 motion. 
 
 It is to be observed that heat, as we shall use the term, 
 is a motion of the particles of matter among themselves 
 and is therefore confined to bodies, and may be trans- 
 mitted from one part of a body to another and from 
 one body to another body in contact with it, but cannot 
 be transmitted through empty space. The radiations 
 which come to us from the sun through empty space 
 are not heat, but a form of energy, which may be trans- 
 formed into heat or into some other form of energy 
 according to circumstances. Radiant energy will there- 
 fore be treated in another place. 
 
 61 
 
62 HEAT. 
 
 39. Effects of Heat. O) The most obvious effect 
 of heat is the sensation of warmth produced in us when 
 a hot body comes in contact with our skin, (ft) A 
 piece of iron when heat is being continually imparted 
 to it may become too hot for us comfortably or even 
 safely to touch, and finally it may glow, first red, then 
 white. Most bodies which give us light are hot, light 
 being a form of motion which in these cases results from 
 heat and accompanies it. 
 
 (c) Heat changes the size of bodies. Except in spe- 
 cial cases (when some substances pass from the liquid 
 to the solid form, for example), the effect of heat is to 
 cause bodies to expand. As has been remarked already, 
 cohesion, the unknown force which draws the molecules 
 together, is opposed by heat. If the amount of heat is 
 increased, the molecules will be driven farther apart 
 the body will occupy more space. 
 
 (d) The change of state of bodies from solid to liquid 
 and gaseous has already been referred to. 
 
 (e) Many chemical changes are conditioned upon 
 heat. The very combustion which is the source of heat 
 and light in a candle flame cannot occur unless the 
 wick of the candle is first heated much hotter than the 
 temperature of a living room. When a gust of air 
 blows the hot gases away from the burning wick the 
 flame is extinguished. While any adequate discussion 
 of chemical changes is beyond the scope of this book, 
 we may well pause here to note the difference betAveen 
 physical and chemical changes. The physicist finds it 
 
TEMPERA T UfiE. 6 3 
 
 convenient to consider matter made up of molecules, 
 all the molecules of a particular substance being exactly 
 alike and remaining identical throughout all the various 
 physical changes to which the substance may be sub- 
 jected. The chemist goes a step farther and imagines 
 the molecule to be composed of atoms which may be 
 unlike, though all the atoms of any one of the funda- 
 mental substances, or elements as they are called, are 
 identical. When a molecule is separated into its com- 
 ponent atoms, or when two or more atoms unite to form 
 a new molecule, a chemical change has occurred. 
 
 The body to which heat is imparted usually becomes 
 hotter, or, to use scientific terms, its temperature is 
 raised. 
 
 40. Temperature. The term temperature, while 
 not easy to define, is used in a very definite sense. It 
 is used to express the relative hotness (or coldness) of 
 bodies. Any two bodies are at the same temperature 
 if, when they are in contact, neither gains heat from the 
 other. If one of two bodies which are in contact im- 
 parts heat to the other, the one which imparts heat is 
 always at a higher temperature than the one receiving 
 it. Amount of heat must not be confused with temper- 
 ature. A kettle full of lukewarm water contains more 
 heat than a cupful of boiling hot water, though the 
 temperature of the latter is the higher. We are accus- 
 tomed to form judgment of the temperature of bodies 
 by our sensations. We call bodies hot, warm, cool, 
 
64 HEAT. 
 
 cold, etc., without attaching to these words any very 
 exact or definite meaning. Our sensations of heat 
 depend so much upon the condition of our body at the 
 time of making the observation that they cannot be 
 relied upon to furnish exact information. Thus, if one 
 hand be held for a few moments in ice water while the 
 other is held in water as hot as can be borne, and then 
 both hands be plunged at once into a vessel of blood- 
 warm water, the latter will feel warm to the hand 
 which has been in cold water, while it feels cold to the 
 hand which has just come out of hot Avater. A com- 
 mon method of measuring temperature with exactness 
 depends upon the expansion of bodies by heat. 
 
 41. Expansion. Coefficient of Expansion. All 
 solids expand when heated. The amount of increase 
 in volume is usually too small to be detected without 
 the use of some special device. A ball which passes 
 easily through a ring when both are cold will not pass 
 when the ball has been heated. If while the ball is hot 
 the ring be heated also, the ball will again pass through. 
 Railway rails are laid with space between the ends to 
 allow for expansion in hot weather. 
 
 Liquids expand much more than solids for the same 
 change in temperature, while gases expand still more 
 rapidly than liquids. This would seem to be explained 
 by the weakening of cohesion at the instant when the 
 change of state occurs in each case. Water, from some 
 cause not yet well understood, is peculiar in that it first 
 
THERMOMETRY. 65 
 
 contracts on being heated (starting at the temperature 
 of ice) and then begins to expand ; after passing the 
 temperature of maximum density it expands like other 
 liquids. 
 
 The perfect gases, like air, expand at a uniform rate. 
 The expansion of air by heating plays a most important 
 part in the heating and ventilation of houses and in the 
 circulation of the atmosphere. These matters will be 
 discussed more fully later. 
 
 The expansion per unit of length of a solid for one 
 degree change of temperature is called the coefficient of 
 linear expansion. The rate of increase in volume per 
 unit volume for one degree change of temperature is 
 called the coefficient of cubical expansion. It is three 
 times the coefficient of linear expansion. Before it can 
 be determined we must first have a unit of temperature. 
 
 42. Thermometry. Since most substances expand 
 uniformly with increase of temperature, expansion may 
 be used as a measure of change of temperature. Water 
 freezes at a certain definite temperature and melts at 
 the same temperature. Water boils at another very 
 definite temperature (for a given atmospheric pressure) <, 
 These temperatures serve admirably, therefore, as points 
 of reference. Two scales of temperature are in common 
 use, the Fahrenheit, 'used only by English-speaking 
 people, the Centigrade, used universally by scientists. 
 In the former the difference of temperature between the 
 temperature of melting ice and that of boiling water is 
 
66 
 
 HEAT. 
 
 divided into 180 equal parts, called degrees Fahrenheit 
 (180 F.), while in the latter the same difference in 
 temperature is divided into 100 equal 
 parts, called degrees Centigrade (100 C.). 
 Fahrenheit took as his zero the tempera- 
 ture of a freezing mixture made of ice and 
 sal ammoniac. It is said that he aimed 
 thus to avoid negative readings, as this was 
 the lowest temperature observed by him 
 at Dantzig in the year 1709, when he was 
 making his experiments. The zero Fah- 
 renheit is 32 below the freezing point of 
 water, which makes the boiling point of 
 water 180 -f 32 = 212 F. Celsius, who 
 devised the Centigrade scale, used the 
 freezing point of water as his zero, thus 
 making the boiling point of water 100 C. 
 The change covered by a Fahrenheit degree 
 is therefore ||{r == I ^hat coverec ^ ty a 
 Centigrade degree. To reduce any num- 
 ber of Fahrenheit degrees to Centigrade 
 degrees we must therefore multiply by |. 
 The reading on Fahrenheit scale is 32 at 
 the freezing point; hence to reduce Fah- 
 renheit reading to Centigrade subtract 32 
 and multiply by |. 
 
 (7) Reading C. = f (Reading F. 32). 
 
 (8) Reading F. = f Reading C. + 32. 
 Fig. 50 makes the matter plain. 
 
 j 
 
 C. 
 
 L 
 
 F. 
 
 100^ 
 
 =212 
 
 _i 
 
 L_2OO 
 
 90_| 
 
 Ll9O 
 
 80-J 
 
 L.I80 
 
 
 Ll70 
 
 704 
 
 Ll6O 
 
 
 Liso 
 
 60J 
 
 Ll40 
 
 J 
 
 Ll30 
 
 50_! 
 
 Ll20 
 
 -f 
 
 Ll 10 
 
 40_:: 
 
 LJOO 
 
 30J 
 
 L.9O 
 
 
 Lao 
 
 20 1 
 
 L70 
 
 i 
 
 Leo 
 
 IOJ 
 
 Lso 
 
 3 
 
 L.40 
 
 o_| 
 
 L32 
 
 -4 
 
 L20 
 
 lO_| 
 
 Lio 
 
 -; 
 
 L,o 
 
 J 
 
 Lio 
 
 30-j 
 
 L20 
 
 J| 
 
 Lso 
 
 4O = 
 
 LAO 
 
 1 
 
 FIG. 50. 
 
THERMOMETRY. 67 
 
 The thermometers most used consist of a glass tube 
 of very small bore, terminating in a bulb which contains 
 mercury or alcohol. The tube was sealed at a temper- 
 ature at which the liquid filled both bulb and tube. At 
 the lowest temperature for which the thermometer is 
 designed the liquid still extends a short distance into 
 the tube. A comparatively small expansion of the 
 liquid in the bulb causes a movement of the fine thread 
 in the tube of sufficient amount to be easily seen. The 
 method of marking a thermometer, or calibrating it as 
 it is called, is explained in Part II. 
 
 The glass which contains the mercury expands only 
 about one seventh as much as the mercury. Alcohol 
 expands more than five times as much as mercury, and 
 therefore makes a more sensitive thermometer than does 
 mercury. It does not freeze even at the lowest arctic 
 temperatures, while mercury solidifies at 39 C. Al- 
 cohol is not opaque, however, even when colored, so that 
 an alcohol thermometer is more difficult to read than a 
 mercurial thermometer. 
 
 Air expands four times as much as alcohol, and is, 
 therefore, very suitable for measuring small changes of 
 temperature over a small range. The air thermometer 
 has the disadvantage that its readings vary with the 
 atmospheric pressure, so that a reading of the barometer 
 must be made whenever the temperature is observed. 
 
 The difference in expansion of two metals is some- 
 times made use of in constructing thermometers. If 
 a strip of iron and a strip of zinc are riveted together 
 
HEAT. 
 
 at several points so that the compound bar is straight 
 when cold, the two metals will expand when heated and 
 the bar will be curved as shown in Fig. 51. If the end 
 at a is rigidly fastened to a support, the free end may 
 be made to transmit its movements to a pointer, which 
 will indicate the temperature upon a dial. The dial 
 
 may be calibrated by 
 comparison with a 
 good mercurial ther- 
 mometer. 
 
 The same sort of 
 compound bar may 
 be made to close alter- 
 nately two electric 
 circuits when the tem- 
 perature of the room 
 varies any given 
 amount above or be- 
 low the normal, thus 
 turning off or on the 
 steam, and so auto- 
 matically regulating the temperature of the room. 
 Such a device is called a thermostat. It is sometimes 
 used to give an alarm of fire if the temperature reaches 
 a dangerous point. 
 
 43. Law of Charles. Absolute Zero. It was 
 
 proved by Charles in 1787 that at constant pressure the 
 volume of a gas increases uniformly with its temperature. 
 
 FIG. 51. 
 
QUANTITY OF HEAT. 69 
 
 The rate of increase is the same for all gases and at 
 C. this rate is 2*3, or 0.00366. 
 
 If the volume is kept constant the pressure increases 
 at this same rate. A quantity of air which, with the 
 barometer at 760 mm., occupies 273 c.c. at C. 
 would, if the pressure were kept constant, occupy 373 
 c.c. at 100 C. and 173 c.c. at - - 100. If, then, we 
 mark an air thermometer in degrees of the same length 
 as for the Centigrade scale, but call the freezing point 
 of water 273, we shall have a scale on which the read- 
 ings are directly proportional to the volume of the gas. 
 Such a scale is called an absolute scale. Its zero is at 
 273 C., a temperature which of course can never 
 be reached in the laboratory. It is believed that the 
 spaces between the stars are at the absolute zero, how- 
 ever, since there is no evidence for the presence of 
 matter in any appreciable amount in the space between 
 us and the sun, except within a few hundred miles of 
 the earth and a few thousand miles of the sun. 
 
 To express Centigrade readings in absolute we have 
 only to add 273 to the Centigrade reading. Thus 
 50 C.= 323 absolute. 
 
 44. Quantity of Heat. The quantity of heat re- 
 quired to raise the temperature of a given body one 
 degree differs with the kind and quantity of matter 
 comprising the body. The unit of heat is the heat 
 required to raise the temperature of one gram of water 
 1 C. The unit of heat thus denned is called the 
 
70 HEAT. 
 
 calorie. It requires 200 calories to raise the temper- 
 ature of 20 grams of water 10. 
 
 45. Heat Capacity. Specific Heat. The quantity 
 of heat (measured in calories) required to raise the 
 temperature of any body 1 C. is the heat capacity of 
 that body. The quantity of heat required to raise the 
 temperature of one gram of any substance 1 C. is called 
 the specific heat of that substance. It is a quantity 
 which is very different for different substances, but is 
 constant for any given substance through a moderate 
 range of temperature. The specific heat of iron, for 
 example, is 0.113. The heat capacity of an iron kilo- 
 gram weight would be 1,000x0.113 = 113 calories, 
 while the heat capacity of one litre of water (weight 
 one kilogram) is 1,000 calories, or nine times as much. 
 If one kilogram of iron at 100 C. were plunged into 
 one kilogram of water at C., the temperature of the 
 water would rise 10 C. and that of the iron would fall 
 90 C., since the two substances in contact tend to come 
 to equilibrium. It follows that by putting together 
 known masses of two substances at different (known) 
 temperatures, we may determine the relative specific 
 heats of the substances ; and, if the specific heat of one 
 is known, the specific heat of the other may be found at 
 once. For the quantity of heat transferred is H= mst, 
 where m is the mass, s the specific heat, and t the change 
 of temperature. But the heat lost by one body exactly 
 equals the heat gained by the other.* That is: 
 
 * Proper precautions must be taken to prevent loss to the air or other bodies. 
 
FUSION. 71 
 
 '= H f , whence mst = m's't' and 
 
 ~ m't> 
 
 This method of determining specific heat is called the 
 method of mixtures. 
 
 46. Fusion. If we heat a solid like ice or wax it 
 will rise in temperature for a time and then begin to 
 melt, the temperature remaining constant after melting 
 has once begun until the whole is melted, when the 
 temperature again begins to rise. If the liquid is now 
 allowed to cool slowly it will begin to solidify at the 
 same temperature at which it melted. There are two 
 important differences to be noted in the solidification of 
 water and wax. The water solidifies in crystals, that 
 is, prism-like bodies of definite geometrical form, while 
 the wax exhibits no structure whatever. 
 
 The water, probably because the arrangement of the 
 molecules in a particular geometrical form leaves more 
 space between them, expands in solidifying, while the 
 wax contracts. Those metals, like iron and brass, which 
 expand on solidifying make excellent castings because 
 they fill out the mold. Gold or silver, 011 the other 
 hand, must be minted or stamped to give clear, sharp 
 outlines. 
 
 The fact that water expands on freezing, coupled 
 with the fact that it contracts when warmed from to 
 4 Q C., has important bearings on the life of all marine 
 animals in particular, and, in less degree, upon the life 
 
72 HEAT. 
 
 of all animals outside the Torrid Zone. If ice were 
 heavier than water the first ice formed on a lake in 
 autumn would sink to the bottom, another layer would 
 form and sink, and the process would continue till the 
 lake became a mass of ice. In spring the top layer 
 would melt, but since water transmits heat downward 
 very slowly the lower portions would probably never 
 thaw out. Let us consider what actually happens. 
 The surface water in autumn cools down to 4 C., its 
 temperature of maximum density, and sinks to the bot- 
 tom. Freezing is thus delayed till the entire body of 
 water is at 4, when the portion at the top cools to 
 and freezes, and the water next to the layer of ice is 
 slowly cooled to the freezing point and added to the 
 first layer formed, the entire layer of ice seldom extend- 
 ing more than a few feet at most downward, while the 
 great body of water never freezes. 
 
 47. Vaporization. Most liquids, if left exposed to 
 the air, gradually disappear. The molecules within the 
 liquid, while they are all in motion, have not all the 
 same velocity. Some of those which are moving fastest 
 make their way through the surface and go off as vapor ; 
 the liquid slowly evaporates. Any increase in temper- 
 ature will increase the number of particles which have 
 velocity enough to penetrate the surface film and so 
 increase the rate of evaporation. It is obvious, too, 
 that a large exposed surface is favorable to rapid evapo- 
 ration. If the air above the surface is at rest it will 
 
EBULLITION. 73 
 
 soon become saturated; that is, it will be so full of 
 vapor that the gaseous particles constantly striking the 
 surface of the liquid will make their way into the liquid 
 as fast as those within escape. When the space above 
 a liquid is saturated, evaporation and condensation are 
 going on at the same rate, which amounts to the same 
 thing as if evaporation ceased. Evaporation is hindered 
 by the pressure of the air on the surface of the liquid ; 
 it therefore goes on very rapidly in a partial vacuum, a 
 fact which is sometimes made use of in evaporating the 
 water from sugar sap. The pans are covered with a 
 tight-fitting hood, which terminates in a pipe leading to 
 an air pump. This pump removes the vapor at the 
 same time it diminishes the pressure, thus producing 
 very rapid evaporation. 
 
 Evaporation goes on from the surface of solids also, 
 but in less degree than from liquids, since the molecules 
 have less freedom of motion. A block of ice left on 
 the shady side of a building on the coldest day in 
 winter will slowly evaporate, as may be seen from the 
 fact that its corners become rounded. A lump of 
 camphor left exposed to the air will slowly evaporate, 
 though it does not melt. The evaporation of a solid is 
 called sublimation. % 
 
 48. Ebullition. Evaporation occurs only from ex- 
 posed surfaces. If a liquid be heated hotter and 
 hotter, a point will in general be reached where vapor 
 bubbles will form on the surface of the vessel where 
 
74 HEAT. 
 
 heat is applied and in the body of the liquid itselt. 
 These bubbles will at first form, rise into the cooler 
 portions of the liquid and collapse, giving forth at 
 times a note like the " singing " of a teakettle. When 
 the whole of the liquid reaches the temperature at 
 which the bubbles formed they will rise rapidly to the 
 surface. The liquid is boiling, and if heat is still 
 applied it will continue to boil without any lise in tem- 
 perature till all the liquid has been vaporized. The 
 boiling point of a liquid is definite for a given pressure 
 of the atmosphere, but falls with diminished pressure. 
 On the top of Pike's Peak water boils at 187 F., while 
 at sea level it boils at 212 F. It is not worth while, 
 therefore, to attempt to cook vegetables by boiling in 
 an open vessel at such high altitudes. 
 
 In a locomotive boiler carrying a steam pressure of 
 two hundred pounds to the square inch water boils at 
 382 F. This fact accounts for the terrible severity of 
 scalds produced by escaping steam following the burst- 
 ing of a boiler in a railway collision. 
 
 49. Distillation. The fact that different substances 
 boil at different temperatures makes it possible to sepa- 
 rate two liquids by heating the mixture to a tempera- 
 ture a little above the boiling point of the more volatile 
 liquid, which will then go off in vapor. The vapor is 
 conveyed in pipes through cold water, where it con- 
 denses. Alcohol and water are separated in this way. 
 Since evaporation occurs at temperatures below the 
 
EVAPOEATION A COOLING PROCESS. 75 
 
 boiling point, a small portion of Avater vapor goes over 
 with the alcohol. The process may be repeated, how- 
 ever, and the portion first collected from the second 
 distillation Avill be almost perfectly pure alcohol. A 
 still is shown in Fig. 52. 
 
 50. Evaporation a Cooling Process. Latent Heat. 
 
 We have seen that when a liquid is evaporating it is 
 the molecules having the highest velocities which leave 
 
 FIG. 52. 
 
 the liquid. Since the temperature of the liquid de- 
 pends upon the average velocity of its molecules, it is 
 evident that the liquid must be cooled by evaporation. 
 If we wet the bulb of a thermometer with water the 
 temperature of the bulb will fall to a point several 
 degrees below the temperature of the room, the amount 
 it falls depending in part upon the amount of moisture 
 in the air. Indeed, the difference in reading between 
 the wet and dry thermometers at any given tempera- 
 ture is an index to the humidity of the air. When 
 
76 HEAT. 
 
 water is boiling the heat supplied to keep it boiling 
 makes good the loss of heat by vaporization. Since 
 this heat produces no sensible rise in temperature, it has 
 been called latent (hidden) Jieat. When the vapor 
 liquefies, the heat which kept the molecules apart 
 against cohesion becomes again sensible heat. The 
 amount of heat required to vaporize one gram of water 
 at 100 C. is 536 calories, or 5.36 times as much as 
 would heat the same quantity of water from to 100. 
 Tins quantity, 536 calories, is called the latent heat of 
 vaporization of water at 100. It is somewhat more at 
 lower temperatures and less at higher. 
 
 A similar loss of sensible heat occurs in the change 
 of state of water from solid to liquid, though much less 
 in amount. The latent heat of fusion of water at C. 
 is 80 calories. This is equivalent to saying that the 
 amount of heat required to melt a quantity of ice at 
 would raise the temperature of the same quantity of 
 water from to 8tf. 
 
 51. Conduction. If one end of an iron bar is 
 heated in the fire the other end will, after a time, grow 
 hot also. The motion imparted to the particles by the 
 hot coals is soon passed along to adjoining particles, 
 which in turn pass it to those farther away. This 
 process is called conduction. Substances differ greatly 
 in their power of conduction, the metals being good 
 conductors, while wood, wool, cotton, water, and air 
 are poor conductors. 
 
HEAT AND HUMAN LIFE. 
 
 77 
 
 52. Convection. Fluids, like air and water, while 
 they are poor conductors, possess two properties which 
 make it possible for them to convey heat with consider- 
 able rapidity : (1) they have freedom of motion among 
 their particles, and (2) they expand a great deal when 
 heated. The result is that if a fluid comes in contact 
 with a heated surface which is below it, it begins to 
 expand as soon as heated, and, being lighter than the 
 surrounding fluid, is forced upward by the latter, which 
 takes its place, thus keeping up a constant circula- 
 tion by means of 
 
 which heat is con- 
 veyed to great dis- 
 tances. The pro- 
 cess is therefore 
 called convection. 
 The pointed shape 
 of a candle flame , 
 ,is due to the con- 
 vection currents 
 formed in the air 
 (see Fig. 53). 
 
 \ 
 
 FIG. 53. 
 
 53. Heat t id Human Life. The temperature of 
 the human body does not vary in health more than a 
 degree or two from 98.6 F. Yet we live in a climate 
 where variations of 50 occur within twenty-four hourp 
 and the extreme variation in a season may reach 150. 
 It may be profitable then, by way of review, to see how 
 
78 HEAT. 
 
 the laws of heat which we have been studying beai 
 upon some of the problems which face us every day. 
 
 54. Weather. Wind, temperature, rain, clouds, 
 change from day to day and furnish a never-failing 
 topic of conversation. Everybody is interested in the 
 weather, yet most of us do not observe weather changes 
 as carefully or understand them as fully as we might. 
 Winds may be simple convection currents flowing 
 toward the hottest region of the earth. Such are the 
 " trade winds " which flow toward the equatorial regions 
 and the sea breezes which blow toward the land in day 
 time, alternating with land breezes toward the sea at 
 night. 
 
 The winds which most affect the weather in tern 
 perate regions, particularly away from the sea, are the 
 cyclonic winds which blow toward an area of low baro- 
 metric pressure. Such low areas move across the 
 country from west to east, followed by regions of high 
 pressure, about once in five or six days on the average ; 
 and it is by following the movement of such storm 
 areas that the officials of the Weather Bureau are able 
 to predict in advance the weather changes winch are 
 likely to occur within the next thirty-six hours. To 
 the east of a low area the winds blow from the east 
 and south and are warm and laden with moisture. As 
 the low area passes we encounter west and northwest 
 winds and the temperature falls. The cooler north 
 winds condense the moisture which the south winds 
 
HEATING AND VENTILATION. 79 
 
 bring, hence we have the most clouds and rain when 
 the barometer is low, folloAved by fair and cooler 
 weather as the barometer rises. Absorption of solar 
 radiation by day and loss by radiation at night will be 
 better understood when we have studied radiant energy. 
 We protect ourselves against weather changes in two 
 ways : we wear clothing and live in houses. 
 
 55. Clothing. The heat of our bodies is maintained 
 by chemical changes which occur in the bodily tissues. 
 These changes are in the nature of a disintegration or 
 destruction of the tissues, the loss being constantly 
 made good from the food which we eat. The supply 
 of heat thus furnished is very irregular, but the body 
 is provided with an automatic regulating device in the 
 pores of the skin. Moisture is constantly exuding from 
 these pores and evaporating, thus cooling the body. 
 When the body is warm the pores open and we perspire 
 freely; when we are cold the pores close. Clothing 
 checks the circulation of air near the skin, and, being 
 made of non-conducting materials, retards the escape of 
 heat from the body. 
 
 56. Heating and Ventilation. When a house is 
 heated with a hot-air furnace taking the air from out of 
 doors the rooms do not lack for fresh air, but the heat- 
 ing of the house is not likely to be as satisfactory as 
 when the cold air is supplied to the furnace from the 
 coldest parts of the house, such as a hallway or a 
 
80 
 
 HEAT. 
 
 northwest room. With this arrangement the cold air 
 flows down to the furnace while the hot air from the 
 registers finds- its way to these colder parts of the house 
 to supply the place of the cold air. Fresh air may be 
 admitted to any part of the house through windows or 
 
 FIG. 54. 
 
 through openings provided for the purpose. The cir- 
 culation is shown in Fig. 54.. 
 
 When a large room is to be heated by a stove the end 
 may be often much more satisfactorily accomplished if, 
 instead of leaving the circulation of air in the room to 
 chance, with the chances in favor of stagnation and a 
 
HEATING AND VENTILATION. 81 
 
 wide variation of temperature, the stove be surrounded 
 by a large drum, open at top and bottom and reach- 
 ing from near the floor to a point some distance above 
 the top of the stove. The drum may be in two parts 
 hinged together for convenience in getting at the stove. 
 A little reflection will show that the drum will shield 
 that portion of the room nearest to the stove from ex- 
 cessive heat, while, by setting up convection currents, it 
 brings the cold air from the farthest parts of the room 
 to the stove, where it is heated and returned along the 
 ceiling, thus heating the room uniformly and much im- 
 proving the ventilation at the same time. In buildings 
 heated by steam or hot water the hot fluid circulates 
 through the pipes by convection, and the heat is dis- 
 tributed by placing in each room a radiator consisting 
 of a coil of pipe having an amount of surface suited to 
 the size of the room. In the matter of ventilation these 
 systems are inferior to the hot-air furnace. Pipes are 
 sometimes so placed in the ventilating flues, however, 
 as to create a draught and ventilate the room. 
 
 A combination of both systems is now being used in 
 cities where power is easily procured in which air is 
 driven over hot steam pipes (in summer over ice) by 
 means of a fan run by an electric motor or other power 
 and forced through registers to all parts of the room. 
 In this way a large church may be thoroughly ventilated 
 and heated in half an hour during the coldest weather, 
 or made comfortably cool with a few hundred pounds 
 of ice in summer. 
 
82 HEAT. 
 
 Exercises. 
 
 32. It is desired to obtain the temperature of a liquid. What 
 error might arise (a) if the thermometer were read soon aftei 
 inserting in the liquid ; (6) if the thermometer were inserted 
 only far enough for the liquid to cover the bulb ; (c) if you tool 
 the thermometer out of the liquid to read it ? Explain. 
 
 33. Why is there sometimes frost on the grass in autumr 
 when a self -registering minimum thermometer records no lowei 
 than 36 F.? 
 
 34. Explain how the height of a mountain above sea leve' 
 might be determined with a thermometer. Would it be neces 
 sary to make observations on more than one day to obtain accu 
 rate results ? 
 
 35. What is normal blood temperature (a) in Centigrad* 
 degrees ; (6) in absolute degrees Centigrade ; (c) in absolute 
 degrees Fahrenheit ? 
 
 36. Why is extreme heat harder to bear in moist climates 
 than the same temperature in dry climates ? 
 
 37. Why is extreme cold felt more in moist climates than ir 
 dry? 
 
 38. Why do boiler makers use red-hot rivets for fastening 
 the plates of a boiler together ? 
 
 39. Why do freezing water pipes burst ? 
 
 40. A certain metal, if thrown cold into a vessel of th< 
 same metal molten, floats. Will this metal make sharj 
 castings ? 
 
 41. Why do we say that when smoke falls from the chimneys 
 it is likely to rain ? 
 
 42. (a) Why does a pitcher containing cold water "sweat' 
 in summer ? (6) A kerosene lamp set away clean is often founc 
 covered with a film of kerosene. Is this fact analogous to tht 
 " sweating " of the pitcher of water ? 
 
EXEECI8E8. 83 
 
 43' An air thermometer (see Fig. 55) was filled with 
 water to the point A. When dipped in a beaker of 
 hot water it first fell to B and then rose to C ; taken 
 out and plunged in cold water it rose to D and then 
 fell. Explain. 
 
 44. In hot weather metal objects feel hotter than 
 wooden objects which are beside them in the sun. 
 
 Are they really very much hotter, and if not, why do 
 they seem so ? What is the case in cold weather ? 
 
 45. Ice houses are made with double walls having 
 sawdust between them. Would a wall of logs the 
 
 same thickness as the double rilled wall serve as well ? . 
 
 46. How would it be possible at high altitudes to 
 
 cook vegetables by boiling ? 
 
 47. Tubs of water are often placed in a cellar to 
 prevent vegetables from freezing. Explain. 
 
 48. Why are the extremes of heat and cold greater 
 in the middle of a continent than on the coast ? 
 
 49. Why do clothes dry faster on a windy day than 
 when the air is calm ? 
 
 50. A litre of air at 746 mm. pressure and 20 C. 
 has what volume under standard conditions ; namely, 
 760 mm. and C.? 
 
 51. An iron rail is 30 feet long at 20 F. What is 
 its length at 120 F.? Iron expands 0.0000064 of its 
 length for each degree. 
 
 B 
 
CHAPTER IV. 
 ELECTRICITY AND MAGNETISM. 
 
 57. Introductory Remarks. While the laws gov- 
 erning the group of related phenomena which we desig- 
 nate as electrical and magnetic are very well known, it 
 must be borne in mind that we are as yet not able to 
 give any very satisfactory answer to the question : What 
 is electricity? To be sure, we have not the slightest 
 notion what cohesion is or what gravitation is. The 
 words cohesion and gravitation are but symbols for 
 what we choose to designate the causes of two classes 
 of phenomena. Our inability to define more exactly 
 these forces need not stand in the way of our study of 
 the phenomena connected with them. Indeed, it is 
 only by frankly admitting our ignorance and seeking to 
 find out as large a body of facts as possible that we 
 may ever hope to reach a knowledge of the ultimate 
 nature of such fundamental entities as matter, electric- 
 ity, and gravitation. 
 
 The average student has not so large a fund of 
 observation and experience from which to illustrate 
 electrical phenomena as he had in the subjects treated 
 in preceding chapters. He will find it necessary, there- 
 fore, to observe closely and remember carefully every 
 new fact which comes in his way. 
 
 84 
 
MAGNETIC POLES. 85 
 
 There is every reason why all intelligent people 
 should wish to understand that wonderful agent which 
 is to play so important a part in the life of the century 
 now opening, if indeed, as we must suppose, the dis- 
 coveries of the last fifty years have but opened the way 
 to still more wonderful discoveries yet to be made. 
 
 58. Magnets. It was long ago discovered that cer- 
 tain specimens of iron ore had the power to attract bits 
 of iron to themselves. From the country where these 
 " lodestones " * were most frequently found Magne- 
 sia they were called magnets. It was very early 
 known, too, that if a bar of steel be rubbed with a lode- 
 stone or natural magnet it will itself become a magnet, 
 and that such artificial magnets will, when suspended, 
 point nearly north and south. An elongated mass of 
 lodestone will do the same thing, but the fact is much 
 more readily observed with a long and slender bar like 
 a compass needle. The mariner's compass is such a 
 bar or needle supported on a pivot so as to move freely 
 in a horizontal plane. It was in use before the time of 
 Columbus. 
 
 59. Magnetic Poles. If we dip a slender bar mag- 
 net, like a magnetized knitting needle, into iron filings, 
 the filings will adhere to the magnet only near the 
 ends, AD and OB (Fig. 56). If we cut off that por- 
 tion at each end to which the filings adhered and dip 
 the magnet again in filings, the filings will again adhere 
 
 * Lode, a vein of iron. 
 
86 ELECTRICITY AND MAGNETISM. 
 
 to the ends of the portion DC which remains. It 
 would appear, therefore, that while the magnetism 
 manifests itself only at the ends of the bar, it is really 
 present in other parts of the bar, or it would have 
 disappeared when the ends were cut off. Had we cut 
 
 B 
 
 D 
 
 FIG. 56. 
 
 the bar at its middle point we should have obtained 
 two magnets, each attracting filings at its ends. More- 
 over, the two pieces, AD, CB, cut from AB behave 
 exactly like the original magnet. The ends of a bar 
 magnet are called poles. If we suspend a bar magnet, 
 and, after allowing it to come to rest, mark the end 
 which points to the north, we shall find that end which 
 we have marked will always be the north-seeking end 
 
 N _ S N _ S N _ S 
 FIG. 67. 
 
 of the magnet ; that is to say, the two poles of the mag- 
 net are unlike. If A was a north-seeking pole in the 
 magnet shown in Fig. 56, the arrangement of poles in 
 the fragments would be as shown in Fig. 57, 
 
 60. Attraction and Repulsion. When the N-end 
 of a magnet is brought near the N-end of a suspended 
 
INDUCED MAGNETISM. 87 
 
 magnet, like a compass needle, the N-end of the needle 
 is repelled and the S-end attracted. In like manner, a 
 S-pole repels a S-pole and attracts a N-pole. Briefly 
 stated, like poles repel, unlike attract. 
 
 61. Law of Force. We may define unit pole as 
 follows : let two poles be of equal strength, such that 
 at a distance apart of one cm/ they repel each other 
 with a force of one dyne, they are unit poles. Coulomb 
 proved that the law of force is similar to the law of 
 gravitation: two mag- 
 netic poles of strength 
 m units and m f units 
 respectively at a dis- 
 tance r cm. apart re- 
 pel or attract each 
 other with a force 
 proportional to the 
 product of their FIG. 58. 
 
 strengths divided by the square of the distance apart. 
 
 62. Induced Magnetism. Magnets are commonly 
 made by rubbing steel bars upon a magnet. A piece 
 of soft iron needs only to be brought near a magnet to 
 become itself a magnet for the time being, j Thus the 
 nail in Fig. 58 attracts the second nail and holds it so 
 long as the former is in contact with the magnet. If 
 we remove the magnet the nails no longer cling 
 together. Hard steel is not so easily magnetized as 
 
88 
 
 ELECTRICITY AND MAGNETISM. 
 
 soft iron, but the steel retains its magnetism after 
 removal from the magnet, while the iron does not,) 
 This fact is analogous to the fact that it is less easy to 
 put an edge or a point on hard steel than on soft iron, 
 but the edge or point will be retained correspondingly 
 better by the steel. Magnetic attraction occurs only 
 between magnets in every case, for the pieces of soft 
 
 FIG. 59. 
 
 iron all become magnets by induction, as it is called, 
 and are then attracted. The induced pole nearest the 
 magnet is always of opposite kind to that which in- 
 duces it. It is evident, therefore, that a magnet cannot 
 repel soft iron, since unlike poles always attract. 
 
 63. The Magnetic Field. A magnet moves a mag- 
 netic needle without touching it. The needle may be 
 
THE MAGNETIC FIELD. 89 
 
 enclosed in a glass bottle. The magnet still acts upon 
 it. The air may be exhausted from the bottle. The 
 magnet acts exactly as before. This space surrounding 
 a magnet, witliin which a magnet cannot come without 
 being influenced to take a particular direction and 
 within which also every bit of soft iron becomes tempo- 
 rarily a magnet, is called the magnetic field. It extends 
 
 FIG. 60. 
 
 in all directions from the magnet, growing weaker as we 
 go farther from the magnet, in accordance with the law 
 of force stated in Section 61. 
 
 If we place a piece of glass or stiff cardboard on a 
 magnet, dust iron filings over the glass and gently tap 
 it, the iron filings will arrange themselves end to end, 
 the direction of each bit of iron being the direction of 
 the resultant of the two forces from the two poles of 
 
90 
 
 ELECTRICITY AND MAGNETISM. 
 
 the magnet. Fig. 59 is taken from a photograph of 
 such a chart of the magnetic field made by using a 
 photographic plate instead of the piece of glass.* Fig. 
 60 shows the field between unlike poles, while Fig. 61 
 shows the field between like poles. 
 
 64. Magnetic Induction Explained. We have 
 seen that a magnetized knitting needle may be divided 
 
 FIG. 61. 
 
 into a great many short parts, and each little piece will 
 be a magnet. This suggests that every molecule of a 
 magnet is itself a magnet nay more, that every mole- 
 cule of iron is a magnet. In a bar of soft iron the mol- 
 ecules, being magnets and more free to turn than in the 
 
 *The work was of course performed in a dark room. When the filings were 
 in position an electric light was turned on for a second. The filings were then 
 brushed off, and the plate developed. 
 
MAGNETIC SUBSTANCES. 91 
 
 steel, take the most stable position possible ; that is, 
 every N-pole will get as near a S-pole as possible. In 
 this position the force of any N-pole is neutralized by 
 the S-pole near it as far as producing any effect outside 
 the iron is concerned. If a strong magnet is brought 
 near the iron it turns the little molecular magnets all 
 one way, and the molecules at the ends will attract, 
 while those at intermediate points in the bar still neu- 
 tralize each other. Fig. 62, a, shows the arrangement 
 
 b 
 
 FIG. 62. 
 
 of the molecules before the magnet is brought near ; 
 >, while the magnet is in the neighborhood. 
 
 When a steel knitting needle has been given a single 
 stroke with a magnet it is a weak magnet, since only 
 part of the molecules have been arranged. By further 
 stroking all may be made to point in the same direction, 
 after which no magnet, however strong, could induce 
 any more magnetism in the needle than it already 
 possesses. 
 
 65. Magnetic Substances. We have hitherto 
 spoken only of iron as a substance capable of magnet- 
 
92 ELECTRICITY AND MAGNETISM. 
 
 ization. It is not, however, the only magnetic sub- 
 stance. Nickel and cobalt are magnetic to a small 
 degree as compared to iron, but to a large degree as 
 compared to air, water, and most other substances. 
 Most substances are so slightly magnetic that their 
 magnetic properties can be detected only by means of 
 very delicate instruments. 
 
 66. The Nature of the Magnetic Field. While air 
 or other substances which may happen to lie within the 
 field of force of a magnet are influenced by that field, 
 they are in no way necessary to its existence. The 
 force which is transmitted from a magnet to a compass 
 needle is not conveyed by means of the air. We can- 
 not think of a body being set in motion without con- 
 tact, direct or indirect, with the body which sets it in 
 motion. It is believed that all motions which are trans- 
 mitted from one body to another not in contact with 
 it are conveyed through a medium which pervades all 
 space, even the space occupied by matter. This medium 
 which is very elastic is called the ether. The ether in a 
 magnetic field is supposed to be in a state of strain due 
 to a stress, which the magnet, in some way, puts upon 
 it. We are familiar with the transference of stress in 
 an elastic fluid from one body to another in the fluid. 
 The bullet in an air gun has motion imparted to it in 
 this manner. The stress in a field betAveen two unlike 
 poles would drive a N-pole along the lines of force in- 
 dicated in Fig. 60 away from the N-pole toward the 
 
EFFECT OF HEAT ON A MAGNET. 93 
 
 S-pole. A N-pole placed between the two N-poles in 
 Fig. 61 halfway between them would be in unstable 
 equilibrium, but once started toward either magnet 
 would move along the lines of stress to the S-pole of 
 that magnet toward which it started. 
 
 The action between two magnetic poles could be 
 explained by supposing the lines of force to be stretched 
 elastic cords which are all the time trying to contract, 
 and which constantly repel each other. A strong field 
 of force would be one in which these lines lie very 
 close together. In a field of unit strength there is 
 assumed to be one line parsing through every square 
 centimetre of a plane drawn at right angles to the 
 lines. It will be seen that the lines may be thought of 
 in two ways, either as mere geometrical lines indicating 
 by their direction the direction of the force at every 
 point, or as physical cords which tend to shorten and 
 widen as a stretched rubber cord does. The direction 
 of the lines is always supposed to be from a north to a 
 south pole. Every line is a closed curve passing in at 
 one end of the magnet and out at the other. 
 
 67. Effect of Heat on a Magnet. A steel needle 
 which has been magnetized will lose its magnetism if 
 heated red hot. This is easily explained if we remem- 
 ber that the molecules tend to arrange themselves pro- 
 miscuously. The agitation due to heat sets them free, 
 they return to their natural positions, and the needle is 
 demagnetized. Jarring a magnet has a similar effect; 
 
94 ELECTRICITY AND MAGNETISM. 
 
 68. Magnetism of the Earth. The earth acts 
 like a great magnet, having its poles at some distance 
 from the geographical poles, the' one in the northern 
 hemisphere being in the northern part of Hudson's 
 Bay. 
 
 The magnetic needle points due north at places on a 
 line which coincides roughly with the meridian which 
 passes through that pole. At places in the Eastern 
 States the needle points west of north. At places west 
 of Central Ohio the needle points east of north. This 
 declination must be known for any place before the 
 compass can be used to tell directions accurately. In 
 cities the compass is now of little use in surveying 
 because of the presence of large masses of iron, such 
 as gas and water pipes. 
 
 The horizontal declination of the needle, that is, its 
 variation from true north in different parts of the 
 world, was known to Columbus, who recorded the decli- 
 nation for a large number of localities in the Atlantic 
 Ocean. 
 
 Compass needles are usually balanced so as to swing 
 only in a horizontal plane. ; If a needle is allowed to 
 point in the direction of the lines of force of the 
 earth's field, it will dip downward at the north end in 
 the northern hemisphere. 
 
 69. Electric Charges. Attractions and Repul- 
 sions. It was known to the ancient Greeks that 
 amber, a fossil gum, when rubbed, would attract light 
 
ELECTRIC CHABGES. 
 
 95 
 
 bodies like bits of wood or pith. The Greek word for 
 amber electron has given us our words electrify, 
 electricity, and so forth. A body which has by contact 
 with another body of different material acq'uired the 
 power to attract light bodies is said to be electrified. 
 If a glass rod be rubbed with silk the rod will attract 
 bits of pith, paper, and 
 other light materials. The 
 particles of pith cling to 
 the rod for a time, then 
 jump away as if repelled. 
 A light ball of pith or cork 
 (see Fig. 63) hung by a silk 
 thread from an insulating 
 support will be attracted to 
 the rod, and after contact 
 will be repelled. The ball 
 will be attracted to a stick 
 and will attract small par- 
 ticles of pith. The ball 
 has become electrified by 
 touching the electrified rod. 
 When the rod was rubbed with the silk, the silk was 
 electrified as well as the rod. The ball which has been 
 charged by touching the glass rod will be attracted by 
 the' silk but repelled by the rod. We say, therefore, 
 that there are two kinds of electrification, and we call 
 the kind on the glass positive or plus, that on the silk 
 negative or minus. When a vulcanite rod or a bar of 
 
 FIG. 63. 
 
96 
 
 ELECTEICITY AND MAGNETISM. 
 
 sealing wax is rubbed with flannel or fur, the rubber or 
 wax is negatively electrified, the flannel or fur posi- 
 tively. Bodies having like electrification repel, those 
 having unlike attract. Fig. 64 shows diagrammatically 
 the action between pairs of rods, one of which is elec- 
 trified and suspended in a sling of paper so that it may 
 swing, while the other is electrified and held near it. 
 The black rods are vulcanite, the light ones glass. 
 
 FIG. 64. 
 
 70. Conductors. Insulators. Dr. Gilbert, physi- 
 cian to Queen Elizabeth, examined a large number of 
 substances and found that under the same conditions 
 certain substances could be electrified, others apparently 
 could not. He called them " electrics " or " non-elec- 
 trics," according to his results. Most of his work has 
 proved correct ; but, like all men of science, he taught us 
 also by his mistakes. He tried to electrify a metal rod 
 while holding it in his hand, and failing, he concluded 
 metals were " non-electrics." If he had held the metal 
 rod in a pad of silk he would have obtained an oppo- 
 
CONDUCTORS. INSULATORS. 
 
 97 
 
 site result. His facts were correct, for the body carried 
 the charge to earth from the metal rod, but his theory 
 was wrong because he did not reckon in the effect of 
 his hand on the metal rod. We now classify bodies as 
 conductors and non-conductors or insulators. A charge 
 on one part of any body which is an insulator does not 
 spread to other parts of the body. A charge on a con- 
 ductor spreads in- 
 stantly to all parts 
 of the conductor. 
 The metals are 
 good conductors, 
 as also is water- 
 vapor, wet cotton, 
 wet wood, moist 
 air, or any wet sub- 
 stance. On the 
 ather hand, dry 
 cotton, dry wood, 
 and dry air are 
 good insulators, 
 that is, poor con- 
 ductors. The earth is a good conductor, so then any 
 charged body which is connected to the earth by another 
 conductor, such as a wire, a gas pipe, or the human body, 
 will at once lose its charge. We find it necessary, there- 
 fore, when we wish to charge a conductor, to insulate it 
 from the earth by placing it on a support of glass, 
 rubber, paraffine, varnished wood, or the like. 
 
 FIG. 65. 
 
ELECTEIC1TJ AND MAGNETISM. 
 
 71. Electrostatic Field of Force. Induction. 
 
 The charged body has about it a field of force some- 
 what similar to the field about a magnet, but with some 
 very important differences. The lines of electric force 
 do not return to the body from which they start, but 
 always end on another body having a charge of the 
 opposite kind, as shown in Fig. 65. 
 
 Any body placed in a field of force will intercept the 
 
 lines of force. Thus 
 a ball between two 
 oppositely charged 
 rods will be the stop- 
 ping place for lines 
 leaving the -f- rod 
 and the starting place 
 
 FIG. 66. 
 
 for lines going to 
 t h e - - r o d. 1 1 i s, 
 therefore, positively 
 charged on one side 
 and negative 1 y 
 charged on the other 
 (see Fig. 66). 
 If there is a single charged body in a room the lines 
 of force go to the walls of the room or to any object 
 which may be near the charged body. Since every line 
 has an end as well as a beginning, there is for every pos- 
 itive charge an equal negative charge somewhere, which 
 is equivalent to saying that the sum of all the charges 
 is zero. The force between two unit charges at 1 cm. 
 
ELECTROSTATIC FIELD OF FORCE. 
 
 99 
 
 distance is 1 dyne ; the force between charges q and q* 
 at distance r is, in air : 
 
 an) /=! 
 
 In any other medium the force is 
 
 where K is a constant which must be determined for 
 each substance. The constant is called the specific in- 
 ductive capacity. It is a striking coincidence that the 
 formulae representing the force in the cases of gravita- 
 tion, magnetism, and electrification should be identical. 
 Let us see if we can explain the law in the last case by 
 way of example. 
 
 The field of force at any point is measured by the 
 number of lines of force to the sq. cm. at that point. 
 The force at 1 cm. from unit charge is 1 dyne. At the 
 same distance from a charge of 144 there are 144 lines to 
 
 FIG. 67. 
 
 the sq. cm. (see Fig. 67). A body 1 cm. square would 
 intercept 144 lines at 1 cm., but it would intercept only 
 36 at 2 cm. and 4 at 6 cm. For the lines are twice as 
 
100 ELECTEICITT AND MAGNETISM. 
 
 far apart at 2 cm. as at 1 cm., hence there are 6 rows of 
 6 each while at 6 cm. there are but 2 rows of 2 each. 
 The stress in the field is therefore seen to diminish with 
 the square of the distance. It is obvious that to double 
 the charge at A would double the number of lines of 
 force at all points of the field, or the attraction is pro 
 portional to q. The same is true of g f 9 hence the force 
 varies directly as the product of the charges and in- 
 versely as the square of the distance between them. 
 
 72. Nature of the Electric Charge. Many, if not 
 most, chemical elements consist of molecules containing 
 two atoms which are alike except that one is electrically 
 positive, while the other is negative. When these two 
 atoms are united in a molecule they neutralize each other 
 as far as any action outside the molecule is concerned, 
 hence most bodies as we find them are not electrified. 
 Let us suppose now that bodies differ among themselves 
 in their affinities for the two kinds of atoms ; thus wax 
 has an affinity for negative atoms, while glass has an 
 affinity for positive ones. The oxygen of the air is 
 made up of such positive and negative atoms. When it 
 touches wax the wax is not able to overcome the affinity 
 of the negative oxygen atoms for the positive atoms with 
 which they are united. If, however, a piece of wax and 
 a piece of glass are brought together so close that the 
 molecules of oxygen in the thin layer of air are very 
 near to both substances at the same time, the plus atoms 
 will be drawn in one direction and the minus atoms in the 
 
NATURE OF THE ELECTRIC CHARGE. 
 
 101 
 
 opposite direction ; their bond of union is overcome and 
 the glass is coated with plus oxygen atoms, while the wax 
 is coated with the same number of minus oxygen atoms 
 (see Fig. 68). The charge of each atom being equal, 
 the two charges are equal also. In our experiments we 
 use for one of the bodies to be electrified a silk cloth 
 rather than a bit of wax, because the cloth may be 
 
 FIG. 68. 
 
 brought near to the glass at many places at once. We 
 also rub the cloth along the rod to bring it in contact at 
 as many points as possible. 
 
 The physical lines of force, according to the explana- 
 tion just given, always begin upon a negative atom and 
 end upon a positive atom. They may be thought of as 
 chemical bonds stretched out to sensible distances. 
 
102 
 
 ELECTRICITY AND MAGNETISM. 
 
 73. The Electrophorus. A metal plate filled with 
 wax is rubbed with fur and thus negatively electrified. 
 If, now, a metal plate provided with an insulating handle 
 be brought near the wax (it may touch it at a few points 
 without removing more than a small fraction of the 
 
 FIG. 
 
 charge from so poor a conductor as wax), the plate will 
 have a plus charge induced upon its lower surface (see 
 Fig. 69) and an equal minus charge, upon its upper 
 surface. The lines of force, which start at the upper 
 surface, end on the hand of the operator. If, now, the 
 finger be touched to the plate the negative charge will 
 
DISTEIBUT10N OF THE CHAEGE. 103 
 
 distribute itself over the body of the operator and thence 
 to the earth, which is so large a conductor that the 
 charge at any one place upon it is practically zero. 
 Meanwhile the plus charge on the lower side of the plate 
 is held there by the attraction of the minus charge on 
 the wax, but if we take away the finger and lift the 
 plate to a distance from the wax the plus charge will dis- 
 tribute itself over the plate and may be drawn from 
 it in the form of a spark by presenting the knuckle to 
 the edge of the plate. This operation may be repeated 
 a large number of times. If the plate is allowed to give 
 its charge to an insulated conductor, the latter may be 
 charged. 
 
 The charge on the plate of the electrophorus was pro- 
 duced by induction. 
 
 74. Distribution of the Charge on a Conductor. - 
 
 We have said that a charge distributes itself over a con- 
 ductor. It does not follow that it always distributes 
 itself uniformly, however. This is the case only when 
 the conductor is a sphere. The farther the body de- 
 parts from the spherical form, the more irregular is the 
 distribution of the charge on the body. To express it 
 differently : the charge has greatest intensity at those 
 points where the curvature is greatest. This is anal- 
 ogous to the distribution of surface tension in a soap 
 film and goes to support the theory that the charge 
 consists of a strain in the ether at the surface of the 
 conductor. It is evident that the charge on a plate 
 
104 
 
 ELECTRICITY AND MAGNETISM. 
 
 having rounded edges will be most intense at the edges, 
 for there the curvature is greatest. If a rubber bag 
 were stretched over a sphere the tension on the rubber 
 would be alike at all points. If a cube of the same area 
 were substituted for the sphere the tension would be 
 greater at the edges than on the sides and would be 
 greatest at the corners. 
 
 75. Electric Discharge. Any elastic medium, if 
 
 stretched be- 
 yond a certain 
 point, gives 
 way. The 
 air which 
 
 FIG * 70 * 
 
 K 
 
 charged body 
 is in a state 
 of strain. 
 When a cer- 
 tain limit is 
 reached the 
 air gives way 
 
 and the body is discharged : equilibrium is restored. 
 When the edge of the charged plate of the electrophorus 
 was brought near the sphere, a spark was seen and 
 heard between the plate and the sphere : the plate was 
 discharged. % The air near the sphere must have been 
 under greater strain than at other parts of the plate. 
 Let us see why, The plus charge on the plate induced 
 
ELECTRIC DISCHARGE. 105 
 
 a minus charge on the side of the sphere nearest to it 
 (Fig. 70, ) and a plus charge on the opposite side. 
 The minus charge on the sphere attracted the plus on 
 the plate, causing it to accumulate at a until the attrac- 
 tion of the free plus atoms near the plate for the minus 
 atoms of the oxygen in the air, assisted by the attrac- 
 tion of the minus atoms near the sphere for the plus 
 oxj^gen atoms, became great enough to break down 
 the bonds uniting the oxygen molecules in the space 
 between. The result was to produce equilibrium be- 
 tween the sphere and plate, but not between these con- 
 ductors and the earth/ The plus charge at c still 
 remains on the ball and a plus charge (less than the 
 original charge by the amount on the sphere) remains 
 on the plate. If the sphere had originally been con- 
 nected to earth the plus charge would not have remained 
 at b and the discharge would have resulted in perfect 
 equilibrium. The union of the atoms of oxygen liber- 
 ated heat just as the union of oxygen atoms with carbon 
 atoms does in combustion. The rapid expansion of the 
 air so suddenly heated produced a sound like that of a 
 firecracker, when powder burns suddenly in a confined 
 space. Thunder and lightning are produced by enor- 
 mous discharges from cloud to cloud in the sky. When 
 a highly charged cloud lies near the earth it may induce 
 an opposite charge in the earth, resulting in a discharge 
 between the cloud and the earth. The lightning strikes, 
 as we say. When lightning strikes it follows the best 
 conductor. The passage of a discharge through a tree 
 
106 ELECTRICITY AND MAGNETISM. 
 
 may heat the sap enough to vaporize it and rend the 
 tree in splinters. The discharge from cloud to cloud 
 evidently finds the shortest path not always the easiest. 
 Fig. 71 is reproduced from a photograph taken at Tripp, 
 South Dakota, July 22, 1898, by W. C. Gibbon. 
 
 FIG. 71. 
 
 76. Discharge from Points. The curvature at a 
 point is infinite ; the intensity at a point is therefore so 
 great that the charge escapes rapidly into the air. All 
 conductors which are designed to hold a charge must 
 have their edges rounded. The discharge from the 
 points of leaves and blades of grass is usually sum- 
 
ELECTRICAL MACHINES. 
 
 107 
 
 cient to equalize the potential between the earth and a 
 thundercloud unless the cloud approaches very rapidly. 
 This explains why lightning strokes are of such infre- 
 quent occurrence. 
 
 77. Electrical Machines. It is often convenient to 
 have at our command larger charges than can be ob- 
 tained by rubbing a glass rod or by means of the elec- 
 
 -tlB 
 
 FIG. 72. 
 
 trophorus. Machines employing the principles of friction 
 or of induction are known respectively as frictional or 
 induction machines. An old-fashioned frictional ma- 
 chine is shown in Fig. 72. A large glass plate, 6r, is 
 made to revolve between two leather pads, P. The plus 
 charge on the glass is carried past the pointed conductor, 
 where it draws off the induced negative charge, leaving 
 
108 
 
 ELECTRICITY AND MAGNETISM. 
 
 A positively charged. The negative charge passes from 
 the pads to B> whence it may be conveyed to earth by 
 a chain when only a positive charge is wanted. This 
 machine has given place to a type of induction machines 
 in which the inducing charge goes on increasing as the 
 machine is operated. Such machines produce much 
 more powerful charges than the frictional machine. The 
 
 FIG. 73. 
 
 kinds most in use are the Toepler-Holtz machine and the 
 Wimshurst machine. The Toepler-Holtz machine is 
 shown in Fig. 73 and diagrammatically in Fig. 74. It 
 consists of a revolving plate, P, which carries upon its 
 front surface six or eight metallic buttons, b. Behind 
 the revolving plate is a stationary plate, P', which serves 
 to support two paper armatures, A, A f , as they are 
 called. In front of the revolving plate are an inducing 
 
ELECTRICAL MACHINES. 
 
 109 
 
 bar, BB f , with points and brushes of wire at its ends, 
 and two conductors, (7, C", for receiving the charge. Two 
 little arms, #, a', connected with the armatures, A, A', 
 convey, by means of little metallic brushes, any charge 
 
 FIG. 74. 
 
 that is on the buttons, , to the armatures. The action 
 of the machine may be explained as follows : a small 
 minus charge is produced on one of the paper armatures, 
 say A', by rubbing it with flannel. This initial charge 
 may be exceedingly small; indeed, if the machine has 
 
110 ELECTRICITY AND MAGNETISM. 
 
 been lately in use the small charge remaining on the 
 armature will be sufficient. This small charge acts 
 inductively through the glass on BB' to attract a plus 
 charge to B' and repel a minus charge to B. These in- 
 duced charges will escape from the points at B and B', 
 electrifying the glass. Part of the charge, however, is 
 given to the little buttons, 5, which, as the plate rotates, 
 carry it to the brushes on a, a r , and thus to A, A'. The 
 charges on the armatures are thus being continually 
 augmented, and that, too, very rapidly, since the greater 
 the charge on J., the greater the induction on B. Mean- 
 while the plus charge on the upper part of the glass plate, 
 P, induces a minus charge on the points of (7, which 
 escapes, leaving C positively charged; and the minus 
 charge on the lower part of P in like manner charges 
 0' negatively. The charges C and O 1 continue to 
 increase till the air between them gives way and a dis- 
 charge occurs. The armatures, however, do not dis- 
 charge, hence a second large charge on C and 0' may 
 be obtained quickly. Indeed, if C and O' are not too 
 far apart, an almost continuous succession of sparks may 
 be made to pass between them. 
 
 78. Potential. Capacity. If a ball of 1 cm. radius 
 receive unit charge it will be more intensely electrified 
 than a ball of 10 cm. radius having the same charge, 
 exactly as a given quantity of heat applied to the small 
 ball will heat it hotter than an equal quantity applied 
 to the large one. The term in electricity which corre- 
 
POTENTIAL. CAPACITY. Ill 
 
 sponds to temperature in heat is potential. The poten- 
 tial of a ball of 1 cm. radius having a charge of plus 1 
 unit is 1 ; the potential of the ball of 10 cm. radius 
 having the same charge is 0.1. The capacity of a con- 
 ductor is the quotient of its charge by its potential. 
 The capacity of a body is known, then, if we can meas- 
 ure the charge which it receives, from a source of 
 known potential. Potential is usually denoted by V. 
 If we denote quantity of charge by Q and capacity by 
 we may write : 
 
 (13) 0= Q- 
 V 
 
 The potential of the earth is reckoned as zero. The 
 potential of all conductors in contact with each other 
 soon becomes identical, just as the temperature of two 
 bodies in contact soon becomes the same. 
 
 The potential of a conductor which is connected to 
 the earth is therefore zero. The potential of ihe space 
 surrounding a body diminishes as we leave the body. 
 A charge always " flows " from places of high to places 
 of low potential, just as heat flows from places of high 
 to places of low temperature. A discharge which takes 
 place through a good conductor, like a copper wire, is 
 usually called a current. We are not to infer from the 
 use of the term current that we are dealing with a fluid. 
 What takes place in the wire seems to be different from 
 what takes place in the air when a spark passes, but the 
 result accomplished is the same : equilibrium or equal- 
 ity of potential is restored in both cases. 
 
112 
 
 ELECTRICITY AND MAGNETISM. 
 
 FIG. 75. 
 
 79. Condensers. The potential of the space about 
 a conductor is lowered by the presence of a conductor 
 of lower potential. A plate, A (Fig. 75), connected to 
 the positive conductor of an electrical machine, (7, having 
 a potential of 100 will itself have a potential of 100. 
 
 If the capacity 
 of the plate is 
 10 the plate will 
 receive a charge 
 of 1,000 units 
 before its poten- 
 tial rises to 100. 
 If we now hang 
 near A a plate, 
 B, which is connected to the earth, the potential on the 
 side of A next to B will be lowered and an additional 
 quantity must flow from before the potential of A 
 will rise to 100. The closer B is to A the greater the 
 charge required to equalize the potential. 
 
 Such an arrangement of plates as that just described 
 is called a condenser because it allows a large charge to 
 be collected in a small space, or, in other words, it 
 increases the capacity of the conductor A. A common 
 form of condenser is the Leyden jar. It consists of a 
 glass jar coated to about two thirds its height with tin- 
 foil, both outside and inside. A rod terminating in a 
 ball passes through the insulating cover and communi 
 cates by a chain to the inner coating (see Fig. 76). The 
 glass has a specific inductive capacity six times as great 
 
113 
 
 as that of air, hence the capacity is six times as great 
 
 as a condenser having plates of the same size. The jar 
 
 is charged by connecting the ball to one 
 
 pole of the electrical machine while the 
 
 outer coating is held in the hand or 
 
 otherwise connected to earth. It may 
 
 be discharged by touching one end of a 
 
 wire having rounded ends to the outer 
 
 coating and then bringing the other end 
 
 near the knob. A very powerful charge 
 
 will sometimes pierce the jar. Franklin 
 
 devised an experiment to prove that the 
 
 charge is wholly in the dielectric and 
 
 not at all in the conductor. A jar is F I<*- 
 
 made with removable coats (see Fig. 77). After being 
 
 charged, the inner coating is removed by means of a glass 
 
 rod or its ebonite handle, and the jar is lifted out of 
 
 FIG. 77. 
 
 the outer coating. The coatings now show no signs of 
 electrification, while the jar attracts pith balls. If the 
 coatings are again put in place the jar will give a spark. 
 
114 ELECTRICITY AND MAGNETISM. 
 
 The purpose of the coatings is to distribute the charge 
 to the glass in charging and to collect it at the moment 
 of discharge. That the charge is not all given up by 
 the glass is shown by the fact that it is usually possible 
 to get a second (or residual) charge a few moments 
 after a condenser has been discharged. 
 
 Electrical machines are usually provided with two 
 Leyden jars. The positive conductor is connected with 
 the inner coating of one jar, the negative with the 
 inner coating of the other, and the two outer coatings 
 being connected by a wire which may be broken by a 
 switch when it is not desired to use the condensers 
 (see Fig. 73). 
 
 80. The Gold-leaf Electroscope. It is often desir- 
 able to make a more delicate test of electrical charges 
 than can be made with the pith ball. For this purpose 
 a gold-leaf electroscope is used. It consists of a rod 
 rounded or furnished with a ball at its upper end and 
 having attached to its lower end two strips of gold-foil. 
 The rod passes through the stopper of a bottle which 
 encloses the leaves, protecting them from draughts of 
 air (see Fig. 78). When a glass rod is brought near 
 the ball the electroscope has a positive charge induced 
 in the leaves by induction. If while the rod is near 
 the finger is touched to the knob the repelled plus charge 
 will pass to earth, leaving the electroscope negatively 
 charged. If we remove the finger and then the rod 
 the electroscope will have a permanent charge. A nega- 
 
THE GOLD-LEAF ELECTROSCOPE. 
 
 115 
 
 tively charged body brought near will cause the leaves 
 to diverge further, while a positively charged body will 
 cause the leaves to collapse. If a rubber rod had been 
 used instead of the 
 glass rod the electro- 
 scope would have 
 been positively 
 charged. A conven- 
 ient method for test- 
 ing bodies for kind 
 and amount of elec- 
 trification is to use 
 what is called a proof 
 plane. It consists of 
 a small metal button 
 
 r I (jr. Jo* 
 
 with round edges 
 
 cemented to the end of a glass rod. A metal ball or 
 button tied to a silk thread will do as well. The proof 
 plane is touched to the body to be tested and the charge 
 received by the plane is carried to the electroscope. If 
 the charge is not strong the plane may be touched to 
 the ball of the electroscope. 
 
 By means of an electroscope Faraday proved that 
 the charge on a conductor induced by a charged body 
 brought near it is equal to the charge on the inducing 
 body. He performed the experiment with an ice-pail, 
 hence it is known as Faraday's ice-pail experiment. It 
 is an excellent illustration of the laws of induced 
 charges. A small pail, P (Fig. 78), is supported on an 
 
116 ELECTRICITY AND MAGNETISM. 
 
 insulated support and a ball which has been charged by 
 contact with a rubber rod is lowered by a silk thread 
 into the pail. The leaves of the electroscope will 
 diverge a certain amount. If the ball be now touched 
 to the pail the charge on the ball will just neutralize 
 the induced charge on the pail and the divergence of 
 the leaves will not be in the least altered. This shows 
 that the charge induced on the pail was exactly equal 
 and opposite to the inducing charge on the ball. 
 
 81. The Discharge in Gases. If we draw apart the 
 knobs of an electrical machine while it is in operation a 
 point will be reached at which sparks can no longer 
 pass, but a hissing noise may be heard. If the room is 
 darkened we may see faint brushes of purplish light 
 issuing from one of the knobs. It will be found by 
 testing that this is the negative conductor. Similar 
 brush discharges may be seen on the plate and at the 
 pointed conductors on various parts of the machine. 
 The positively charged points show little dots of white 
 light instead of the brushes. If we now connect the 
 two knobs to wires which are sealed into the end of a 
 glass tube which is connected to an air pump, it will be 
 observed that when part of the air has been exhausted 
 from the tube brush discharges will pass through the 
 tube, and, if the exhaustion can be carried far enough, 
 the whole tube will glow with pink light. Tubes may 
 be obtained from which the air has been exhausted 
 until not more than the thousandth part remains. They 
 
EXEECISES. 117 
 
 are called Geissler's tubes. In such tubes the negative 
 end glows with a violet light, while the positive end is 
 pink, often arranged in layers or stratifications concave 
 toward that end and reaching nearly to the negative 
 end of the tube. A dark space separates the two dis- 
 charges. The colors are not the same if other gases 
 are in the tubes. The discharge in such exhausted 
 tubes bears a close resemblance to the aurora borealis or 
 northern lights, which are believed to consist of electri- 
 cal discharges through the rare air in the upper regions 
 of our atmosphere. 
 
 Tubes which are exhausted to a still greater degree 
 than Geissler's are known as Crookes' tubes. The slight 
 amount of gas remaining in a Crookes' tube shows no 
 color, but the tube itself glows with a phosphorescent 
 light opposite the negative end. The tubes are the 
 source of Roentgen X-rays, which will be considered in 
 another place. 
 
 Exercises. 
 
 52. (a) Place a bar magnet on a large sheet of paper. Set 
 a small compass on the paper and make a dot on the paper near 
 each end of the needle. Set the compass aside and connect 
 the dots by a line. Kepeat this operation for a large number 
 of places on the paper. (&) Support a magnetized sewing 
 needle by a thread fastened to it with wax, so that it will hang 
 horizontally when no magnet is near it. Bring it over the 
 centre of a bar magnet at a distance of say 10 cm. above the 
 magnet, and then move it slowly toward one end of the magnet 
 and afterward toward the other end. 
 
 53. A sailor was asked if he ever crossed the "line " (equa- 
 tor). He replied that he had, When asked how he knew, he 
 
118 ELECTRICITY AND MAGNETISM. 
 
 replied that he watched the compass and the instant the ship 
 crossed the line the needle turned and pointed south. Explain. 
 
 54. An artesian well made by driving a long iron pipe into 
 the ground was found to possess magnetic properties, such that 
 knife blades thrust into the water as it flowed from the pipe were 
 magnetized. Is it more probable that the water was magnetic 
 or that the iron pipe was magnetized by being jarred while in 
 the earth's field ? If the point of a knife were rubbed on the 
 upper end of this pipe, what sort of pole would the point be- 
 come? 
 
 55. "Why should care be taken never to drop or otherwise jar 
 a magnet ? 
 
 56. Why are magnets often made in a horseshoe form ? 
 
 57. A knitting needle is bent into a horseshoe form and then 
 magnetized. If the distance between its ends were measured 
 before it was magnetized and again afterwards, would it be 
 found greater before or after magnetization ? 
 
 58. Would it probably have any effect on the time-keeping 
 qualities of a watch if its hairspring should become magnetized ? 
 
 N 
 
 FIG. 79. 
 
 59. A long bar magnet has poles of strength 80. A compass 
 needle having poles of strength 2 is pointing toward the X-polo 
 of the magnet. The needle is 2 cm. long and its nearest pole 
 is 4 cm. from the N-pole of the magnet (see Fig. 79). What 
 is the force of attraction in dynes, what is the force of repul- 
 sion, and what the resultant force ? What would the resultant 
 force be if the distance were half as great ? 
 
 60. If an iron rod be tapped with a hammer while it points 
 in the direction of the dip needle it will become a mag-net with 
 the lower end a N-pole. If we now reverse it and tap it the 
 
EXEECISES. 119 
 
 magnetism will be reversed, and the end which was at first 
 down and is now up is a S-pole. In what position should 
 it be held 111 order that it may be w r holly demagnetized by 
 tapping ? 
 
 61. (a) Plot the field of a horseshoe magnet by means of 
 iron filings. (6) In a similar way plot the field between two 
 unlike poles of bar magnets at a distance of 8 cm. from each 
 other and with a piece of soft iron 1 or 2 cm. square lying mid- 
 way between them. 
 
 62. A 1-milligram weight lies on a glass plate and has a 
 charge of 10 units upon it. How large a charge at a distance 
 of 2 cm. will lift the weight from the glass ? 
 
 63. Charge an insulated pail and test it inside and out with 
 a proof plane and electroscope. 
 
 64. Put an electrical machine in motion and test the various 
 parts for positive and negative electrification. Do not let the 
 machine stop till the test is finished. Stop the machine, start 
 again and repeat the tests to see if you get any indication that 
 the machine reverses. 
 
 65. Why is it more difficult to brush lint from clothing in 
 cold, dry weather than at other times ? 
 
 66. Lay a pane of glass on the table and rub it with a silk 
 cloth. Dust a few fine iron filings on the glass. Lift the glass 
 and note the behavior of the filings. Explain. 
 
 67. Kub a sheet of paper with a dry flannel cloth and place 
 it against the wall of the room. 
 
 68. Let water from an elevated vessel flow out of a pipette 
 at the lower end of a rubber tube. Bring an electrified rod 
 near the water jet. Note and explain (a) the movements of 
 the jet ; (6) any changes in the jet itself. 
 
 69. Connect two metal handles by wires to the outside coat- 
 ings of the jars of an electrical machine ; arrange the knobs so 
 that a short spark passes. By holding the handles observe the 
 physiological effect of an electric current. 
 
120 
 
 ELECTRICITY AND MAGNETISM. 
 
 82. Electric Currents. While electric charges are 
 of great interest to us from the theoretical side, the 
 greater part of the applications of electricity employ 
 what we call electric currents. In 1786 Galvani ob- 
 served that some freshly prepared frogs' legs lying near 
 an electrical machine twitched when a discharge passed. 
 In trying to use frogs' legs as an electroscope to test 
 the electrification of the air the frogs' legs came in con- 
 tact with an iron balcony and twitched when removed. 
 
 FIGS. 80 and 81. 
 
 Galvani believed this was due to a charge generated in 
 the muscles of the specimen used, but Volta thought it 
 could be explained by the contact of dissimilar metals. 
 Volta constructed the first battery and from this time 
 dates the study of electric currents. If a strip of zinc 
 which is connected to ground be touched by a piece of 
 copper which is connected to a very sensitive electro- 
 scope, the leaves of the electroscope will diverge, show- 
 ing a difference of potential between the two plates 
 
ELECTRIC CURRENTS. 121 
 
 (see Fig. 80). This difference of potential by contact of 
 dissimilar substances has been explained in Section 72. 
 If we now connect the wire which was 
 attached to the earth to the one attached to 
 the electroscope the charge will disappear. 
 A current has flowed through the wire from 
 the copper to the zinc (see Fig. 81). The 
 current lasts but an instant, however, like 
 the discharge from a Leyden jar, only much 
 weaker. If instead of bringing the metals FlG> S2 ' 
 in contact in air we bring both metals in contact with 
 water, which has a salt or an acid dissolved in it, the 
 current will flow continuously (see Fig. 82). Let us try 
 to explain what occurs. The acid which is dissolved in 
 water consists, let us say, of a positive atom of hydro- 
 gen, the chemical symbol for which is H, united to a 
 negative atom of chlorine, the symbol for which is Cl. 
 The molecules of acid in a solution are not like the mole- 
 cules of oxygen in air, but a great many of the 'mole- 
 cules are dissociated so that they pass quickly to the 
 metals, the plus H going to the copper, while the minus 
 Cl goes to the zinc. When the plates are joined out- 
 side the solution by a wire a discharge occurs through 
 the wire, but other atoms of H rush to the copper 
 plate and other atoms of Cl to the zinc plate, so that 
 the current is kept up continuously. The H atoms 
 unite with each other and form hydrogen bubbles which 
 rise to the surface of the liquid, while the chlorine 
 combines with the zinc. 
 
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124 
 
 ELECTRICITY AND MAGNETISM. 
 
 sometimes carbon, carbon being almost the only solid 
 substance outside of the metals which is a good con- 
 ductor. We have seen that some plan must be used 
 to get rid of the products of the chemical change which 
 occurs in the battery and so avoid polarization. The 
 batteiy most commonly used is the Daniell's cell in the 
 form known as the gravity cell, because its two fluids are 
 kept apart by their difference in 
 specific gravity (see Fig. 86). 
 We may begin with a cell hav- 
 ing a copper plate at the bot- 
 tom, a zinc plate at the top, and 
 a very dilute solution of sul- 
 phuric acid. Sulphuric acid 
 consists of two radicals or com- 
 binations of atoms which are 
 treated like atoms, namely, hy- 
 drogen and sulphion, H 2 and 
 SO 4 . When the plates are connected by a wire the hy- 
 drogen collects on the copper plate and soon polarizes 
 the battery. To prevent this action the copper plate is 
 covered with copper sulphate, CuSO 4 . Now sulphion, 
 as the radical SO 4 is called, has a stronger affinity for 
 hydrogen than for copper, so it gives up its copper atom, 
 which is deposited on the copper plate, and unites with 
 the hydrogen to form sulphuric acid. The chemist ex- 
 presses this reaction by an equation thus : 
 
 FIG. 86. 
 
 H 2 + CuS0 4 = Cu + H 2 S0 4 
 
BATTEBIES. 
 
 125 
 
 But sulphion has a stronger affinity for zinc than for 
 hydrogen, so it gives up its hydrogen and takes zinc, 
 making zinc sulphate, ZnSO 4 : 
 
 Zn + H 2 S0 4 = H 2 + ZnS0 4 
 
 and so the rnerry round keeps up and the difference of 
 potential remains constant while a constant current 
 flows through the wire. The 
 battery thus consumes zinc and 
 copper sulphate, while it pro- 
 duces copper and zinc sulphate. 
 The zinc sulphate must occa- 
 sionally be siphoned off and 
 replaced by water, while cop- 
 per sulphate crystals are added 
 to make good the loss. This 
 is the only battery which works 
 best if kept in constant action. 
 A gravity or Daniell's cell 
 should be kept on closed circuit 
 when not in use ; all other bat- 
 teries should have the circuit 
 broken instantly when they are 
 not to be longer used. 
 
 While the current furnished by the gravity cell is 
 steady, it is not strong. The various carbon batteries, 
 known as Leclanche* or sal ammoniac batteries, give 
 a strong current for a short time, but soon polarize. 
 They recover quickly, however, and so are well adapted 
 
 FIG. 87. 
 
126 
 
 ELECTEICITY AND MAGNETISM. 
 
 to use for electric bells and telephones. Usually a zinc 
 rod, a large carbon plate, and a solution of ammonium 
 chloride (sal ammoniac) constitute the battery (see 
 Fig. 87). The bubbles of hydrogen soon escape from 
 the large rough surface of the carbon. This battery is 
 cheap and easily renewed. 
 
 When a strong current for a considerable time is 
 wanted the plunge battery or chromic acid battery is used. 
 In this battery a large zinc plate is hung from the lower 
 side of a piece of vulcanite between two carbon plates. 
 The plates are plunged into a solution of chromic acid. 
 The plates must be lifted whenever the battery is not 
 in use. This battery requires frequent cleaning and 
 renewal, but it is the best resort for strong currents 
 when storage batteries or dynamo currents are not to 
 be had. 
 
 86. Chemical Effects of the Current. Electrolysis. 
 
 -The direction taken 
 by the dissociated atoms 
 in a solution with two 
 unlike plates dipping in 
 it is determined by the 
 nature of the plates. If 
 two like plates dip in 
 such a solution there will 
 be nothing to determine 
 
 the direction, and consequently no effect will be ob- 
 served. Now suppose two plates of platinum, which 
 
ELECTBOPLATING. 127 
 
 dip in dilute sulphuric acid, are connected to the plates 
 of a battery, as shown in Fig. 88. Atoms of hydrogen 
 at once go to the negative ^plate, the sulphion takes hy- 
 drogen from the water molecules (H 2 O), leaving free 
 oxygen, which collects on the positive \plate. The final 
 result is to decompose the water into hydrogen and oxy- 
 gen. If the plates are held under test tubes the gases 
 may be collected, when the volume of hydrogen will be 
 found just twice that of the oxygen. 
 
 If lead plates had been used the oxygen would have 
 united with the lead, forming lead oxide. The cell, with 
 two unlike plates, lead and lead oxide, would, when dis- 
 connected from the battery, be itself a battery. This, 
 somewhat modified, is the principle of the lead storage 
 battery. 
 
 87. Electroplating. An important application of 
 electrolysis to the arts is in the deposition of metals by 
 the electric current. The object to be coated is made 
 the negative terminal (attached to the zinc plate) of a 
 battery, while the positive terminal is composed of a 
 plate of the metal to be deposited. Both plates dip in 
 a solution of a salt of the metal to be deposited. The 
 current deposits the metal on the negative terminal, 
 or electrode, as it is called, while the metal from the 
 positive electrode goes into the solution. 
 
 It is sometimes easiest to separate metals from the 
 ores which contain them by chemically producing the 
 salts of the metals. The metals may then be recovered 
 
128 ELECTRICITY AND MAGNETISM. 
 
 from the salts by electrolysis. Copper is produced on 
 a large scale in this way. 
 
 88. Electrotyping. Books are now seldom printed 
 from the movable type in which the matter was at first 
 set. A mould is made from the type in wax, which is 
 then coated with finely powdered graphite (a form of 
 carbon) to make it conduct, and is made the negative 
 electrode in a bath of copper sulphate. The current 
 deposits copper in the mould in a form which perfectly 
 reproduces the type. The thin sheet of copper is 
 backed by type metal and wood of the proper thickness 
 and the types are free to be used again without having 
 been worn in the least, while the plates, after use, may 
 be laid away till another edition of the book is wanted. 
 
 89. Heat Produced by the Current. Resistance. - 
 
 When one body moves upon another the rubbing of the 
 molecules against each other sets them in motion, or, 
 we say, friction produces heat. Something analogous 
 to friction, but of course very different, hinders the 
 transfer of an electric charge. We have seen that the 
 air is intensely heated in the path of a spark discharge. 
 A wire offers much less resistance to the passage of a 
 current than air does, but the current always heats the 
 wire and the fluid of the battery also. If the fluid is a 
 good conductor, and a bad conductor is in the circuit 
 outside the battery, the battery will be heated but little, 
 while if the battery is a poor conductor and the circuit 
 
HEAT PRODUCED BY TtiE CURRENT. 129 
 
 is a good one, the battery will become heated more than 
 the wire. The resistance of a conductor is the exact 
 opposite of conductivity. If we indicate conductivity 
 by C and resistance by R we may write : 
 
 = or R = 
 R 
 
 Ohm proved that the resistance of a conductor of uni- 
 form cross section varies directly as its length and in- 
 versely as its cross section. Two wires of the same 
 length and diameter have different resistances if they 
 are of different materials ; that is to say, substances have 
 specific resistance (or conductivity) just as they have 
 specific density and specific heat. The resistance of a 
 conductor whose uniform cross section is a, whose length 
 is , and whose specific resistance is r, is : 
 
 If the cross section is a circle the area of the cross sec- 
 tion is 3.1416 times the square of the radius. The 
 cross section of two wires of equal diameter is evidently 
 twice as great as that of a single wire. Two wires side 
 by side have, therefore, but half as much resistance as 
 one wire. The resistance of a pure metal varies greatly 
 with its temperature, increasing as the temperature in- 
 creases. There is good reason to believe that at abso- 
 lute zero all pure metals would conduct perfectly. 
 Certain alloys have nearly the same resistance for a 
 considerable range of temperature. 'German silver is 
 
130 ELECTRICITY AND MAGNETISM. 
 
 an alloy of this sort, which is much used in making 
 standards of resistance. 
 
 90. Ohm's Law. Units. We have learned that 
 a current flows because of a difference of potential, and 
 that the intensity of the current is proportional to that 
 difference of potential. We have further seen that the 
 intensity of the current is diminished as the resistance 
 of the conductor increases. Ohm wrote : 
 
 *=f 
 
 where i denotes intensity of current (or current simply), 
 E denotes difference of potential (sometimes called 
 electro-motive force), and R denotes the total resistance 
 of the circuit. It follows that : 
 
 (15a) E Ri and (756) R = 
 
 * i 
 
 The units in everyday use for measuring these quan- 
 tities are named for three men, who laid the foundation 
 for our knowledge of electric currents. Intensity of 
 current, i, is measured in amperes, difference of poten- 
 tial, E, is measured in volts, while resistance, R, is 
 measured in ohms : 
 
 volts 
 
 amperes = 
 
 ohms 
 
 An ohm is the resistance of a thread of mercury 1 mm. 
 in cross section and 106 cm. long. A volt is the differ- 
 ence of potential between the terminals of a gravity cell. 
 An ampere is the current which would flow through a 
 
USEFUL HEAT EFFECTS. 131 
 
 resistance of one ohm with a difference of potential of 
 one volt. More exact definitions than these may be 
 given, but these will answer all practical purposes. 
 
 We shall get some notion of the magnitude of the 
 units by employing them in various ways. 
 
 91. Useful Heat Effects. By using good conduct- 
 ors in a circuit, except at particular points which have 
 a high resistance, we may obtain intense heat at those 
 points. In the two forms of electric lighting in com- 
 mon use this is done. The arc light consists of two 
 rods of carbon the ends of which are allowed to touch, 
 closing the circuit. The resistance at the point of con- 
 tact (the contact being poor) is high, the carbons be- 
 come heated, and are then drawn a short distance apart. 
 The current continues to pass the gap, following the 
 heated carbon vapor ; a small hollow or crater is formed 
 in the positive carbon, which is heated white hot and 
 furnishes most of the light. The positive carbon is 
 usually placed uppermost, so that the light from the 
 crater may be thrown downward (see Fig. 89). The 
 temperature of the arc is estimated at 4,000 C. It is 
 the highest temperature which can be obtained artifi- 
 cially, and is sufficient to volatilize all substances. The 
 light is by far the most intense of any artificial light 
 known. The arc lamp requires about 6 or 8 amperes 
 at 50 volts and gives 1,000 candle power. Various 
 mechanical and electrical devices are used to open the 
 arc after the current has started and to feed the carbons 
 
132 
 
 ELECTRICITY AND MAGNETISM. 
 
 together as they waste away. Arc lamps are usually 
 connected in series, so that the total resistance of the 
 line is the sum of the resistances of all 
 the lamps (see Fig. 90). A line of 
 twenty lamps would have a resistance of 
 some tiling like 125 ohms and would re- 
 quire a difference of potential of 1,000 
 volts. As the negative terminal of the 
 dynamo and the farther end of the line 
 are usually connected to ground, it is not 
 safe for a person standing 011 the ground 
 or on a wet floor to touch such a circuit. 
 For lighting houses the incandescent 
 lamp is used. It consists of a thread or 
 filament of carbon, often a carbonized 
 silk thread, sealed within a glass bulb and 
 connected with the circuit by platinum 
 wires, which are sealed into the glass. 
 The air is exhausted from the bulb so that the carbon, 
 when heated white hot by the current, is not burned. 
 
 FIG. 89. 
 
 FIG. 90. 
 
 The common size of incandescent lamp gives 16 candle 
 power and uses 0.5 ampdre at 100 volts, or 1 ampdre 
 
USEFUL HEAT EFFECTS. 133 
 
 at 50 volts. Incandescent lamps are connected parallel, 
 the two line wires being kept at a constant difference 
 of potential (see Fig. 91). The more lamps there are 
 connected at any one time, the more current flows, 
 or, in other words, the less the resistance of the circuit. 
 A lamp is turned on by closing a gap in the circuit by 
 means of a key. Electric lamps give off no smoke and 
 consume no oxygen from the air. They must, however, 
 be used full power or not at all, as commonly made, and 
 are more expensive than the so-called incandescent gas 
 lamp invented by 
 
 Welsbach for the j> <j> 
 
 same illuminating 
 power. The ability 
 
 to turn the lamp on o 
 
 or off at a moment's 
 
 notice and to control 
 
 a number of lamps 
 
 in a ceiling or other 
 
 inaccessible place from a single convenient point is a 
 
 great convenience. Moreover, the incandescent lamp is 
 
 perfectly cleanly and requires no attention whatever. 
 
 The electric heating of houses and cooking by the 
 heat from the current, while perfectly possible and very 
 convenient, have not become common because too ex- 
 pensive. 
 
 The welding of metals by the electric current is 
 accomplished by connecting the metals in the circuit 
 as the carbons of an arc lamp are connected. The heat 
 
134 ELECTRICITY AND MAGNETISM. 
 
 generated at the point of contact increases the resistance 
 at that point, which still further heats the metal until 
 it is soft enough to unite, when the ends are pushed to- 
 gether and the current is cut off. A very large current 
 of low potential is required for this work. 
 
 92. The Current Produced by Heat. The contact 
 difference between two metals in air is different for dif- 
 ferent temperatures. If two strips of unlike metals are 
 connected to form a closed circuit, there will be no cur- 
 rent flowing in the circuit as long as the two places of 
 
 FIG. 92. 
 
 union (^A, B, Fig. 92) are at the same temperature, since 
 the differences of potential at A and B are the same : 
 but if A be placed near a flame while B is kept cool, the 
 differences of potential at A and B will not be the same, 
 and a current will flow through the circuit so long as 
 the points A and B are kept at different temperatures. 
 A series of such elements is shown in Fig. 93. A series 
 of 50 or 100 such elements made of antimony and 
 bismuth and joined in series with a delicate galvanom- 
 eter make an exceedingly sensitive thermometer. 
 
 Thermo-electric generators are now made which take 
 
MOT10X PRODUCED BY THE CURRENT. 135 
 
 the place of batteries, the heat from a single Bunsen 
 burner furnishing a difference of potential of 5 volts 
 and a current on short circuit of 4 ampdres. Such a 
 generator serves admirably for charging storage batteries 
 and for electroplating 
 and the running of small 
 motors. The difference 
 of potential is very 
 constant. 
 
 FIG. 
 
 93. Motion Produced 
 by the Current. We 
 have seen that a mag- 
 netic needle is deflected 
 by the passage of a cur- 
 rent in its neighborhood because the conductor is sur- 
 rounded by a field of magnetic force. Two parallel 
 currents will attract or repel each other, depending on 
 
 FIG. 94. 
 
 their direction with reference to each other. If going 
 in the same direction they will attract, if going in 
 opposite directions they will repel. The lines of force 
 always tend to neutralize each other just as electric 
 charges do, or as the two opposite stresses at the two 
 
136 
 
 ELECTRICITY AND MAGNETISM. 
 
 ends of a stretched cord do. At A (Fig. 94), where the 
 currents are both flowing into the paper, the magnetic 
 lines are seen to be opposite and the currents attract ; 
 at B, where the currents flow in opposite directions, the 
 magnetic lines between the wires, being alike, repel. 
 
 94. Solenoids. Electro-magnets. A long wire 
 wound spirally about a cylinder has, when carrying a 
 .current, a field of magnetic force about it which is iden- 
 tical with the field of a bar magnet (see Fig. 95). 
 
 FIG. 95. 
 
 Two such solenoids behave toward each other like two 
 bar magnets. If a core of soft iron is placed in the 
 solenoid the field of force becomes very much stronger ; 
 indeed", such an electro-magnet, when carrying even a 
 moderately strong current, is more powerful than a good 
 bar magnet. Its chief usefulness depends upon the 
 fact that its strength may be increased or diminished at 
 will by increasing or diminishing the current, the mag- 
 netism disappearing almost wholly the instant the 
 circuit is broken. Electro-magnets are oftenest made in 
 the horseshoe form to give them great lifting power or 
 
THE ELECTEO-MAGNETIC TELEGEAPH. 137 
 
 to make the path of the lines of force as much in the 
 iron as possible, rather than in air, where they are less 
 intense. 
 
 95. The Electro-magnetic Telegraph. An electro- 
 magnet having a piece of soft iron which is supported 
 by a hinged bar and held away from the magnet by a 
 spring constitutes what is known as a sounder. The 
 movable piece of iron is called the armature. The 
 sounder is the instrument used for receiving messages, 
 the sending being done with a simple switch called a 
 
 FIG. 96. 
 
 key. Let the key, K, be open, the spring holds the 
 armature up against the stop, s. Closing the key 
 allows the battery current to flow through the electro- 
 magnet, the armature is drawn down, strikes the stop, V, 
 and makes a sound. When the key is opened the 
 magnet no longer acts and the spring draws the arma- 
 ture back against s. In Morse's printing telegraph, 
 which is now but little used, a point on the stop made a 
 dot on a moving paper if the circuit was kept closed 
 a very short time, or a dash if the key was kept closed 
 a longer time. Although the messages are now read 
 
138 
 
 ELECTRICITY AND MAGNETISM. 
 
 almost universally by ear, the signals are called dots and 
 dashes, and various combinations of dots and dashes 
 constitute the alphabet. The code of signals is as 
 follows : 
 
 a 
 
 1} 
 
 c - - - 
 
 d 
 
 e - 
 
 f 
 
 9- 
 
 h 
 
 -- - 
 
 j 
 
 k 
 
 u 
 
 1 
 
 V 
 
 2 
 
 w 
 
 3 
 
 X 
 
 4 
 
 y-- -- 
 
 5 
 
 iy _ 
 
 
 
 6 
 
 &- --- 
 
 7- 
 
 i 
 
 8 
 
 f 
 
 9 
 
 
 n 
 
 It is evident that by closing K a signal will be made 
 at the sounder, no matter how far away K is placed, 
 provided that the battery is strong enough to send a 
 current of sufficient strength through the line. The 
 resistance of a long telegraph line is several thousand 
 ohms, and the currents are weak even when the return 
 circuit is made through the earth. 
 
 For operating on long lines a device called a relay is 
 used. It consists of an electro-magnet having a large 
 number of turns, small wire being used so as to bring the 
 current close to the iron core. The armature of a relay 
 is hinged to move with a small force so that a weak cur- 
 rent can actuate it. This armature when drawn toward 
 the magnet acts as a key to close a local circuit, having 
 a battery and sounder. The local circuit has a low re- 
 sistance, and is readily operated by a few cells with force 
 
ELECTRIC BELLS. 
 
 139 
 
 enough to give as loud a sound as is desired. A line 
 containing a relay and local circuit is shown in Fig. 97. 
 
 FIG. 97. 
 
 All of the instruments are duplicated at every office on 
 the line. Every key has a switch, which is kept closed 
 except when the operator is sending a mes- 
 sage. Each office has a particular letter by 
 which it is called. Every office on the line 
 may read any message which goes over the 
 line. When a particular office is wanted 
 its call is repeated till the operator answers 
 by opening his switch, after which he closes 
 the switch and receives the message. 
 
 96. Electric Bells. The electric bell 
 is arranged to break its own circuit as fast 
 as it is closed, thus keeping up a succession 
 of taps as long as the key or push button 
 is kept closed. Its connections are shown 
 in Fig. 98. When the circuit is closed by FlG * 98> 
 pushing the button at j9, the armature, , is drawn toward 
 the magnet and the hammer strikes the bell. By mov- 
 
140 
 
 ELECTRICITY AND MAGNETISM. 
 
 ing away from the stop, , the armature breaks the cir- 
 cuit, the spring draws the armature back, and the cycle 
 of operations is repeated. 
 
 97. Electric Motors. An electric motor consists of 
 an electro-magnet in the field of which, another electro 
 magnet is made to revolve continuously by making and 
 
 FIG. 99. 
 
 breaking the circuit through it. The stationary magnet 
 is called the field magnet, the movable one the arma- 
 ture. It is evident that if a current is made to flow 
 through ns (see Fig. 99) when it is in the vertical 
 position, it will rotate in the direction of the arrow. 
 Now if, when ns has reached the horizontal position, the 
 current in it be reversed, thus reversing the poles in 
 
ELECTRIC MOTORS. 
 
 141 
 
 the armature, the latter will continue to rotate in the 
 same direction. The armature is mounted on a shaft 
 which rotates between the poles of the field magnet 
 and the reversal of the current is accomplished by 
 means of a device called a commutator (see Fig. 100). 
 The commutator consists of a divided ring fastened to 
 the shaft and insulated 
 from it. The ends of 
 the wire which form the 
 coils of the armature are 
 connected to the two 
 halves or segments of 
 the commutator. Two " FIG. 100. 
 
 strips of copper or carbon called brushes are supported 
 in a fixed position so as to rub upon the rotating com- 
 mutator. The wires carrying the circuit are attached 
 to these brushes. It is evident that as the armature 
 rotates, the direction of the current in the armature 
 
 changes once during 
 each revolution. The 
 motion will be more 
 steady if the armature 
 have two coils at right 
 angles to each other. 
 The commutator must 
 then have four segments and each coil will be idle half 
 the time (see Fig. 101). In large motors the commu- 
 tator often has 120 or more segments. A typical motor 
 is shown in Fig. 102. 
 
 FIG>101 - 
 
142 
 
 ELECTRICITY AND MAGNETISM. 
 
 98. Currents Produced by Motion. We have seen 
 that currents may be the result of chemical action and 
 that chemical action may be produced by a current, 
 likewise that currents may be produced by heat and 
 that heat is an effect easily produced by the current. 
 It is perhaps to be expected, then, that since motion may 
 be produced by a current, a current might be produced 
 by motion. Such is, indeed, the case whenever a con- 
 ductor is moved 
 across the lines of 
 magnetic force. 
 This fact, which 
 was discovered by 
 Faraday in 1837, 
 is of the greatest 
 importance. Such 
 currents are known 
 as induced cur- 
 rents. The laws 
 which govern their 
 production may easily be illustrated by means of a coil 
 of wire attached to a galvanoscope, a bar magnet, and 
 an electro-magnet having a removable core. The coil 
 attached to the galvanoscope is usually referred to as the 
 secondary circuit (see Fig. 103). The electro-magnet 
 is called the primary circuit. The galvanoscope should 
 be far enough removed so that its needle will not be 
 much disturbed by the movements of the magnet. If 
 we thrust a bar magnet into the coil the needle of 
 
 FIG. 102. 
 
CURRENTS PEODUCED BY MOTION. 
 
 143 
 
 the galvanoscope will be deflected, but when the mag- 
 net comes to rest the needle will return to zero. Now 
 if we quickly pull the magnet out, the needle will be 
 deflected in the opposite direction. If the other pole 
 of the magnet be used 
 the deflection will be 
 opposite in direction. 
 The primary coil, which 
 is a magnet when a 
 current flows through 
 it, will produce exactly 
 the same effects, the 
 deflections being great- 
 er when the core is in 
 the coil. If the pri- 
 mary coil be placed 
 in the secondary coil 
 while connected with 
 the battery and a vari- 
 able resistance, cur- 
 rents will be induced 
 if we suddenly increase or diminish the resistance. 
 Similarly, if we break or make the primary circuit, cur- 
 rents will be induced in the secondary. 
 
 The quickness with which the change is made in all 
 the cases mentioned determines the difference of poten- 
 tial produced. It will thus appear that we are not 
 limited as we are in the case of batteries and thermo- 
 piles, but may produce very high potentials without 
 
 FIG. 103. 
 
144 
 
 ELECTRICITY AND MAGNETISM. 
 
 very high resistances. All that is required is that there 
 shall be a conductor moving rapidly in a field of mag- 
 netic force, or, better, a field of force rapidly changing 
 in intensity in the neighborhood of the conductor. 
 
 99. Spark Coils. A primary circuit having an 
 interrupter like that of an electric bell will, if it con- 
 sist of a large number of coils, induce at the instant 
 the circuit is broken a difference of potential in itself 
 which opposes the breaking of the circuit and produces 
 
 a spark. In 
 this case each 
 coil of the cir- 
 cuit acts upon 
 its neighbors 
 PI ^ u and the pro- 
 
 cess is called 
 s e 1 f -indue tion. 
 Such simple spark coils are used for lighting gas and to 
 a limited extent for medical purposes. The common 
 form of induction coil (Ruhmkorff's, Fig. 104) has but 
 few turns in the primary coil, while the secondary, 
 which is around it, has a very large number of coils oi 
 fine wire. Such coils are used to illuminate vacuum 
 tubes and for medical purposes. The terminals of the 
 primary are usually connected to a condenser which 
 reduces the self-induced spark in the primary. This 
 primary spark is a disadvantage in two ways : it burns 
 the contacts and it diminishes the spark in the secondary 
 
 . 104. 
 
THE DYNAMO. 
 
 145 
 
 by retarding the break in the primary. The spark pro- 
 duced by an induction coil is identical in its effect 
 with that produced by the Toepler-Holtz machine. 
 
 100. The Dynamo. Any electric motor if connected 
 to a galvanometer and turned by hand will show a current 
 through the galvanometer. Indeed, the conditions for 
 generating a strong continuous current are exactly met 
 in the motor. 
 
 Suchama- i () 
 
 chine when A * 
 
 used for pro- 
 ducing a cur- 
 rent is called 
 a dynamo-^ 
 electric ma- 
 chine or, more 
 briefly, a dy- 
 namo. The 
 construction 
 of the m a- 
 
 chine we need not describe again. It is identical with 
 the motor. The field magnets have a small amount of 
 permanent magnetism sufficient to start a small cur- 
 rent in the armature coil as soon as it begins to rotate. 
 This current, or part of it, flows through the coils of 
 the field magnet and the potential soon rises to a maxi- 
 mum and remains steady for a constant speed and load. 
 In order to explain the induced current in terms of the 
 
 FIG. 105. 
 
146 
 
 ELEOTEICITY AND MAGNETISM. 
 
 magnetic field we must now recall that a magnetic field 
 is thought of as filled with elastic lines of force which 
 tend to contract lengthwise and mutually repel. A 
 wire carrying a current has lines of force about it. If 
 these lines of force about the wire are more numerous 
 in one part of a circuit than in another their mutual 
 
 repulsion causes 
 them to spread 
 out and equalize 
 the potential. 
 How does a wire 
 which moves 
 across lines of 
 force get the 
 lines wrapped 
 about it that 
 is, get a current 
 flowing through 
 it ? Let the row 
 of black dots in 
 Fig. 105 repre- 
 sent the succes- 
 sive positions of 
 a wire which is cutting through a line of force as it 
 moves downward through the field. The line stretches 
 more and more till it finally breaks, reuniting above 
 and leaving a line of force about the wire in the direc- 
 tion corresponding to the lines about a current which is 
 flowing into the paper. At B a wire moving upward 
 
 OCOOOOG 
 
 D 
 FIG. 106. 
 
VERSITY 
 
 
 THE DYNAMO. 
 
 147 
 
 would have lines about it corresponding to a current 
 out of the paper. If A and B are the upper and lower 
 sides of a coil then the current flows round the coil. 
 The lines (rings) of force which are constantly forming 
 at A and B are as constantly spreading out along the 
 wire to equalize the potential. See a top view in Fig. 
 106, where it may be seen that the lines of force which 
 
 X^^'\'^^^\y*\/^^ v ^^''\^*r/ l ^'>''C'^ 
 
 / / V v v y \. x < y y\ y X * * X X / X X < \ 
 
 I / XX KM A X XX XX ^ XX XX XX X^ 
 
 FIG. 107. 
 
 reach and D from the two points A and B are going 
 in the same direction and hence the current flows in 
 one direction in all parts of the wire. When A is at 
 the top and B is at the bottom they are moving parallel 
 to the lines of force and cut none of them. They 
 therefore generate no current at this part of the revolu- 
 tion, while a maximum current is generated when the 
 coil is cutting squarely across the lines. When A be- 
 
148 
 
 ELECTRICITY AND MAGNETISM. 
 
 gins to ascend and B to descend the current will be 
 reversed in the coil, but owing to the commutator it 
 will always flow in one direction through the external 
 circuit at D. It will be seen that a dynamo having but 
 one coil and but one pair of segments in its commuta- 
 tor would give a very unsteady current. Increasing 
 the number of coils increases the steadiness of the 
 
 current. In Fig. 
 107 the current 
 strength for suc- 
 cessive short inter- 
 vals during three 
 revolutions of the 
 
 FIG. 108. 
 
 dynamo is shown 
 by the curves. At 
 A the current falls 
 to zero twice dur- 
 ing each revolu- 
 tion. At B with 
 two coils it falls but .7 as low, at with 4 coils but 
 .9 as low, and at Z>, where 24 coils are used, the current 
 does not vary to any perceptible extent. A modern 
 dynamo is shown in Fig. 108. 
 
 101. Alternators. For certain purposes an alternat- 
 ing current has advantages over a direct current. If we 
 solder the ends of our armature coil to a pair of rings 
 which are not split, but placed side by side on the shaft 
 and insulated from the shaft and from each other, the 
 
AL TERN A TORS. 149 
 
 brushes which rest on these rings will convey to the 
 circuit the identical current which flows in the arma- 
 ture coil, that is, an alternating current. It is desirable 
 that the alternations occur very frequently. The field 
 magnet is therefore usually made with a number of 
 poles wound so that alternate poles are north poles. 
 The coil then passes from a north to a south pole sev- 
 
 FlG. 109. 
 
 eral times during each revolution. The field magnets 
 cannot be maintained by the alternating current, as they 
 would be continually changing polarity. It is usual to 
 employ the current from a small direct current dynamo 
 for the purpose. Fig. 109 shows an alternating current 
 dynamo with the accompanying direct current exciter 
 driven by a belt from the shaft of the alternator. 
 
150 
 
 ELECTRICITY AND MAGNETISM. 
 
 102. The Transformer. If the current from an 
 alternator is sent through the primary coil of an induc- 
 tion coil while the hammer is wedged shut fast, an 
 induced alternating current of much higher potential 
 but smaller in amount will flow through the secondary. 
 If the current from the alternator is sent through the 
 long secondary coil a large current of low potential 
 will flow in the short coil of the primary. It is very 
 
 desirable i n 
 the distribu- 
 tion of elec- 
 tric currents 
 over large 
 towns to use 
 high poten- 
 tials, since 
 this makes 
 possible the 
 use of small 
 wires for con- 
 veying the 
 
 currents. These high potential currents are not safe for 
 common people to handle, but by sending them through 
 a transformer they may be changed to any desired poten- 
 tial. The transformer consists of an iron core around 
 one part of which are wound a large number of turns of 
 fine wire, which carries the high potential current, P, 
 from the dynamo (Fig. 110). Around the other part are 
 wound a few turns of large wire, $, which carry a low 
 
EXEECISES. 151 
 
 potential current to the house. Such currents are 
 exactly as good for use in incandescent lamps as direct 
 currents ; for, although the current falls to zero at every 
 alternation, the alternations occur so often (more than 
 a hundred times per second) that the filament of the 
 lamp has no time to fall in temperature between times. 
 
 Exercises. 
 
 70. Connect the zinc and copper plates of a gravity cell to a 
 galvanoscope, but use water with a few c.c. of sulphuric acid 
 instead of the regular copper sulphate solution. The instru- 
 ment must be sensitive enough to deflect at least twenty degrees. 
 Note the changes in deflection for half an hour. Now remove 
 about half of the acidulated water and replace it with copper 
 sulphate solution and add a small handful of copper sulphate 
 crystals. Note the deflections for half an hour. Test the 
 same battery with the same instrument every day for a week, 
 keeping the circuit closed between times through some resist- 
 ance like a telegraph sounder. 
 
 71. (a) Connect through a galvanoscope or an ammeter each 
 of two gravity cells separately, then the two in series, then the 
 two parallel. (6) Compute what current you ought to get in 
 each case if the cells had each a potential difference of 1 volt 
 and a resistance of 5 ohms. What is the sum of the potential 
 differences in each case? of the resistances ? 
 
 72. What is the effect on the potential difference of a cell 
 of : (a) doubling the size of the plates, (6) moving the plates 
 nearer together, (c) effect on resistance of doubling the size, 
 (d) effect on resistance of bringing the plates nearer together ? 
 
 73. Six gravity cells, each having a potential difference of 
 1 volt and a resistance of 5 ohms, may be connected in four 
 different ways as shown in Fig. 111. Which is the best way 
 to connect them when the largest obtainable current is desired : 
 
152 
 
 ELECTRICITY AND MAGNETISM. 
 
 (a) through a low resistance, say 1 ohm, (6) through 7 ohms, 
 (c) through 40 ohms ? 
 
 74. What sort of battery would best be selected (a) for 
 electric bell work, (6) for an induction coil, (c) for telegraphy ? 
 
 75. Two metals, bismuth and antimony, have a contact dif- 
 ference of potential which is changed .000117 volt for 1 C. 
 How many bismuth-antimony pairs must be connected in 
 series to give a potential difference of 1 volt if the tempera- 
 ture difference is 
 100 C. ? 
 
 76. A dynamo 
 giving a constant 
 difference of 
 potential of 55 
 volts is con- 
 nected to a cir- 
 cuit wired for 20 
 lamps, any one 
 of which may be 
 turned on or off 
 at pleasure. 
 Each lamp has 
 a resistance, 
 when hot, of 50 
 ohms. An am- 
 meter is connected in the circuit. What current will the 
 ammeter record when one lamp is turned on ? 10 lamps ? 
 
 77. A dynamo intended to be used with 55 volt lamps is 
 found to give but 48 volts when run at 1,600 revolutions per 
 minute. How many revolutions should it make to give 55 
 volts ? 
 
 78. Beneath a large shallow flat dish (see Fig. 112) place a 
 sheet of cross-section paper having a number in each square. 
 
 FIG. in. 
 
EXEECISES. 
 
 153 
 
 Put enough acidulated water in the dish to fill it to a depth of 
 about 1 cm., and dip the wires from a battery into the liquid, 
 one near each end of the dish. Now place one wire from a 
 galvanometer at any point, a, near one side of the dish and 
 find a point, &, on the other side, such that when the other 
 wire from the galvanometer is dipped in the liquid at the point 
 no current will flow. Points a and & are at the same potential. 
 Keeping a at the same place find three or four other points 
 
 FIG. 112. 
 
 between a and 6 which are also at the same potential. Indi- 
 cate all these points on a sheet exactly like the one under the 
 dish and connect them by a line. Plot a number of such equi- 
 potential lines and then draw lines from Z to 0, crossing the 
 equipotential lines at right angles. These latter are lines of 
 force. 
 
 79. The fall of potential in any part of a circuit is propor- 
 tional to the resistance of that part of the circuit. The differ- 
 ence of potential at the terminals of a dynamo is found by the 
 voltmeter to be 110 volts. The line is of copper wire, No. 
 
154 ELECTBICITY AND MAGNETISM. 
 
 12, which has a resistance of 0.005 ohm per metre. At the 
 end of the line 1 km. from the station, what is the difference 
 of potential between the wires ? If you have lamps designed 
 for 110, 105, and 100 volts which should you use at the end of 
 the line? Which at a point halfway? Would it make a dif- 
 ference whether 2, 10, or 20 lamps were used ? Note that if 
 the potential is too high for the lamps they will be quickly 
 " burned out," while if too low they will not be bright, but red. 
 
 80. (a) Connect a long wire to a gravity cell and determine 
 the direction of the current in the wire by means of a compass 
 needle. (6) Determine in the same way the direction of a 
 current from a storage cell or two cells of plung.e battery, then 
 cut the wire, bare the ends, and dip them into acidulated water. 
 The positive wire should be coated with copper oxide formed 
 by the union of the oxygen, which collects there, with the 
 copper. 
 
 81. A current of 1 ampere deposits 0.003277 gram of copper 
 per second from a solution of copper sulphate. What is the 
 strength of a current which deposited 1.26 grams of copper in 
 one hour ? 
 
 82. With a current of 10 amperes how long would it take to 
 deposit a layer of copper .2 mm. thick over an electrotype hav- 
 ing a surface of 20 sq. cm. ? 
 
 83. Measure the length and diameter of a long piece of iron 
 wire such as is used for supporting stove pipes and compute its 
 resistance, taking the specific resistance of iron wire at 20 C. 
 as 0.000014. Connect a battery through the iron wire and an 
 ammeter and jcompute the resistance of the battery and am- 
 meter combined. The resistance of the ammeter is usually so 
 small as to be negligible. Cut the wire in halves and try the 
 experiment with each half separately. Compare the three 
 values obtained for the resistance of the battery. It is not to 
 be expected that they will agree very closely, especially if the 
 temperature of the room changes much. 
 
EXERCISES. 155 
 
 84. Connect a galvanometer to a Daniell cell and hold a bar 
 magnet in different positions above the needle to find what 
 positions will increase 
 the deflection and what 
 positions will diminish 
 it. It is usually possible 
 so to adjust the field that 
 the needle may be made 
 to deflect between 30 
 and 60, which is the 
 best amount for all pur- 
 
 poses. It is useless to ^ 
 
 try to measure the cur- 
 
 i a * FlG - 113 - 
 
 rent by the deflection of 
 
 a galvanometer when the deflection is nearly 90 or when the 
 deflection is exceedingly small. 
 
 85. Suppose two small needles fastened together parallel on 
 one support with their north poles opposite, as shown in Fig. 
 113. Would they be more or less sensitive to the effects of a 
 current through the coil of wire than one of them alone would 
 be? Such an arrangement is called an astatic pair. What 
 does astatic mean? 
 
 86. Why should the coils of a galvanometer always be placed 
 north and south when the galvanometer is to be used ? 
 
 87. Connect by wires two metal handles to the terminals of 
 the secondary of a small induction coil and test the physiologi- 
 cal effects of the current. Connect the same handles to points 
 on opposite sides of the break of a vibrating electric bell in such 
 a way as to include the magnet in the circuit and test the bell 
 for physiological effects. Has the bell a secondary circuit? 
 Whence the effect ? Test in the same way the strongest bat- 
 tery in the laboratory. 
 
 88. A common telephone consists of a bar magnet in front 
 of which is supported, in the rubber enclosing case, a sheet of 
 
156 
 
 ELECTRICITY AND MAGNETISM. 
 
 soft iron. A coil of wire surrounds the magnet near the iron 
 disk. When the coils of two such telephones are connected in 
 series by wires as in Fig. 114, words spoken at T may be heard 
 at T', a mile or more away. 
 
 (a) Explain how the motion of the iron diaphragm at T pro- 
 
 FIG. 114. 
 
 duced by the vibrations of the air causes induced currents in 
 the coil, which, when conducted along the wire to T', set the 
 diaphragm of that telephone yibrating. (6) Which telephone 
 acts like a dynamo and which like a motor? Explain. 
 
CHAPTER V. 
 WORK. ENERGY. MACHINES. 
 
 103. Work. Energy. In our study of motions 
 hitherto we have seen that motion of any sort could 
 produce motions of other sorts, but we have not given 
 much attention to the quantity of the effect which any 
 given cause produces. We have studied the how of 
 the phenomena rather than the how much. We propose 
 now to review what we have learned and see if the 
 separate topics cannot all be brought into closer rela- 
 tions than we have yet perceived to subsist between 
 them. 
 
 We shall use the words work and energy in a some- 
 what technical sense and we must bear in mind 
 that they are so used. We must be especially careful 
 to note the distinction between force and work. A force 
 is measured by the velocity which it imparts to unit 
 mass in unit time. Unit force, when no other force is 
 acting, gives unit velocity to unit mass in unit time. A 
 dyne of force gives to one gram a velocity of one cen- 
 timetre per second in a second of time. If this unit 
 force moved the unit mass through unit distance it did 
 unit work upon it. Work is measured by the product 
 of the force acting times the distance through which it 
 moved the body. 
 
 157 
 
158 WORK. ENERGY. MACHINES. 
 
 Work = force X distance 
 
 s-in^ ^7 VV 
 
 (16) wfl 
 
 If two forces balance each other so that no motion 
 results no work is done. 
 
 Any units of force and distance may be used for 
 measuring work. The foot-pound is the work done in 
 moving a pound one foot against gravity. The erg * is 
 the work done when the force of a dyne produces 
 motion through a distance of J. cm. The work done 
 in lifting a gram 1 cm. is 980 4\$K{m. The foot-pound 
 is equal to 980 X 453.6 X 30.48 = 13,548,703 ergs. 
 The erg is well adapted to the measurement of small 
 amounts of work, the foot-pound, kilogram-metre, and 
 so forth, for measuring large amounts. 
 
 Any body which has motion imparted to it gains 
 thereby the ability to put other bodies in motion, or, in 
 other words, the ability to do work. A ball fired from 
 a gun in empty space would do no work until it should 
 strike some body which offered resistance to its motion. 
 When it had done an amount of work equal to that 
 which was imparted to it, it would come to rest. Our 
 earth is rushing through space at the rate of 18.5 
 miles per second. If it should strike another planet 
 it would do work on a magnificent scale, but it meets 
 with no perceptible resistance, and therefore does no 
 work. It takes work to lift the hammer of a pile- 
 driver high in air. So long as the hammer hangs there 
 
 * Erg from Greek ergon, work. The same root is found In en-erg-y, from 
 Greek energia. 
 
WORK. ENERGY. 
 
 159 
 
 (see Fig. 115) it possesses the ability to do work 
 loose it and let it fall, it does work. The ability to do 
 work we call energy. The energy of a body is the 
 measure of the work which has been done upon it, less 
 what it has since done, or it is the measure of the work 
 the body must do before it can come to rest, if it is in 
 
 FIG. 115. 
 
 motion, or the work it must do to reach a condition of 
 perfectly stable equilibrium, if it is at rest. The mov- 
 ing bullet and the lifted hammer both possess energy. 
 Though they are not at the instant doing work, it took 
 work to put them in their present relations to other 
 objects, The energy of the bullet is energy of motion, 
 
160 WORK. ENEEGT. MACHINES. 
 
 usually called kinetic * energy ; the energy of the lifted 
 hammer is energy of position or potential energy. 
 Kinetic energy always implies that the body has been 
 acted upon by a force, but if its quantity of kinetic 
 energy is not changing there are no forces now acting. 
 Potential energy implies that the body is in equilibrium 
 under a balance of forces, the cessation of any one of 
 which would result in motion. A bent bow is held in 
 place by two hands pulling apart, the hand holding the 
 string lets go and the arrow speeds away with energy, 
 now kinetic, which was a moment ago potential in the 
 strained bow and string. The sum of the energy of 
 the system of bodies (bow and arrow) is unchanged. 
 We say the energy has been transformed in kind, but 
 unchanged in amount. 
 
 104. Conservation of Energy. No physical change 
 can occur without a transfer of energy, and conversely, 
 every transfer of energy involves some sort of change 
 in the motions of at least two bodies. We shall call 
 all the bodies concerned in any particular transfer of 
 energy a system. In all experiments where careful 
 measurements are possible, it is found that similar 
 measured quantities of energy will always produce 
 equal effects of any particular kind. A moving ball 
 which has a certain mass and volocity will generate a 
 perfectly definite amount of heat when it strikes. A 
 certain strength of electric current will produce in a 
 
 * Greek, kineo, move. 
 
CONSERVATION OF ENERGY. 161 
 
 given time a perfectly definite amount of heat, or chem- 
 ical action, or mechanical motion. The amount of 
 chemical action, or heat, or mechanical motion, which 
 was produced by the current mentioned, would, if 
 spent entirely in producing current, produce exactly 
 the quantity of electrical energy with which we started. 
 
 The most serious practical difficulty met with in 
 carrying out such experiments is the tendency of energy 
 to distribute itself to neighboring bodies in the form of 
 heat. All careful experiments, however, lead to the 
 one conclusion, that energy is never gained or lost in 
 any transfer, or, in other words, the quantity of energy 
 of a system of bodies concerned in a transfer of energy is 
 absolutely constant. This law, which is the product of no 
 one man's labor, but represents the sum of the results 
 of thousands of students of natural phenomena, is the 
 great fundamental law of physics. It is known as 
 the Law of Conservation of Energy. 
 
 If w be the quantity of energy lost by any one of 
 a system of bodies and w', w", etc., be the quantities 
 gamed by the other bodies in the transfer, then : 
 (17) w = w f + w" + etc. 
 
 If e, d , e", etc., represent the energy of each body of 
 the system at any instant, then: 
 
 (18) e + e'+e" + etc. = constant 
 so long as the system is kept from contact with bodies 
 outside the system. In practice such perfect isolation 
 of a system of bodies is exceedingly difficult to secure. 
 
162 
 
 WOEK. ENERGY. MACHINES. 
 
 The more nearly perfect the isolation, however, and the 
 more careful the measurements, the more nearly the re- 
 sults will be found to agree with the law. It is evident 
 that we require for a systematic study of energy a 
 system of units which shall comprise a separate unit 
 for each sort of energy and a system of equivalents 
 by which energy measured in one form may be com- 
 pared with that measured in other forms. 
 
 105. Units of Energy. Equivalents. The poten- 
 tial energy of a stretched spiral spring, as a spring 
 balance, is measured directly in ergs 
 if we know what force was used 
 in stretching the spring and how 
 much its length was increased, or, 
 more exactly, how much the tlis* 
 ^ E> ,CO tance between the points of appli- 
 6 cation, A, B (Fig. 116), of the 
 
 B two opposing forces was changed 
 under the influence of the force. 
 The potential energy of a ball 
 which has been lifted to a height 
 I is measured in ergs when we 
 know the height I in centimetres 
 and the force in dynes, which is 980 times the mass in 
 grams. If the body should now fall towards the earth 
 a distance of I centimetres it would possess an amount 
 of kinetic energy equal to the potential energy which 
 it has lost in falling the distance I, The body has a 
 
 FIG. 116. 
 
UNITS OF ENERGY. EQUIVALENTS. 163 
 
 definite velocity at any instant, as every moving body 
 has. Let us try to find an expression for the energy 
 in terms of mass and velocity. The velocity of a body 
 which has fallen for t seconds under a constant accel- 
 
 eration, a, is 
 
 v = at 
 
 If it started from a position of rest its initial velocity 
 was zero. Its average velocity, v', is therefore, 
 
 But the distance, Z, traversed in time t is 
 (1) I v't = i at - 1 = i a 2 
 
 The force acting upon the body was 
 
 (4) / ma 
 and the work done in lifting it was 
 
 (16) w = /Z 
 which represents the energy it 'has gained in falling. 
 
 w = /J = mal = 
 
 Since at =. v, a?t 2 = v 2 , and 
 w = fl = \ mv 2 
 
 That is to say, the kinetic energy of a body of mass w, 
 moving with a velocity v, is measured by half the prod- 
 uct of its mass times the square of its velocity. 
 
 A problem which engaged the attention of several 
 physicists during the first half of the century just 
 
164 
 
 WOEK. ENERGY. MACHINES. 
 
 closing was the determination of the mechanical equiva- 
 lent of heat, or, as we may now express it, the measure- 
 ment of the quantity of energy represented by a defi- 
 nite quantity of heat. Dr. Joule, of England, made the 
 determination by means of a calorimeter in which a 
 known mass of water was heated by the motion of a 
 
 paddle wheel actuated 
 by falling weights (see 
 Fig. 117). The rise in 
 temperature times the 
 mass of the water meas- 
 ured the heat. He found 
 the work represented 
 by one calorie of heat 
 to be 41,590,000 ergs. 
 The factor 4.159 XlO 7 
 is known as Joule's 
 equivalent and is represented by J. The value of J 
 from the most recent determinations is 4.19 X 10 7 . We 
 may express calories in ergs by multiplying by J. 
 
 (21) w=JH 
 
 The energy liberated or consumed during any chemi- 
 cal change may be measured by allowing the change to 
 take place in a calorimeter and measuring the quantity 
 of heat evolved or absorbed. In like manner, the 
 energy of the electric current may be measured and 
 compared with the energy supplied in the form of me- 
 chanical motion to the dynamo which generates the 
 current. 
 
 FIG - m - 
 
UNITS OF ENEEGY. EQUIVALENTS. 165 
 
 Radiant energy, from the sun or any hot body, may 
 be measured by allowing the radiations to fall upon a 
 surface wliicli absorbs the radiations and converts them 
 into heat. Radiant energy consists of a wave motion 
 which is transmitted through the ether. It becomes 
 known to us only after it is converted into some other 
 form of energy, as when in the form of light it affects 
 our eyes (probably a chemical effect), or the sensitive 
 photographic plate (certainly a chemical effect), or 
 when it takes the form of heat, as all forms of energy 
 are prone to do. 
 
 We shall discuss the nature of radiant energy more 
 fully in a later chapter. For our present purposes it is 
 enough to know that it is a form of energy which is 
 transmitted at enormous velocities through what we 
 call empty space as well as through matter, and that 
 it may be transformed directly into heat or chemical 
 energy and thus indirectly into other forms. 
 
 To recapitulate, we are accustomed to distinguish 
 five forms of energy: (a) Mechanical energy, which is 
 kinetic in a moving body, potential in a body which 
 has been moved out of a position of stable to a posi- 
 tion of unstable equilibrium ; (6) thermal energy, 
 which is kinetic when it raises the temperature of 
 bodies, potential when it changes the state from solid 
 to liquid or liquid to gaseous ; (c) chemical energy, 
 which is kinetic in the form of heat or the electric 
 current at the instant the chemical change takes place, 
 but is potential in all compounds which are not, like 
 
166 WORK. ENERGY. MACHINES. 
 
 the oxides, in the most stable state possible ; (c?) elec- 
 trical energy, which is potential in the form of the static 
 charge and in the magnet, but kinetic in the current ; 
 (e) radiant energy, which is always kinetic and is 
 therefore the form which all energy tends to take, for 
 this is the law of all change. Bodies which are in an 
 unstable condition tend to lose the potential energy 
 which they possess by virtue of their instability. For 
 example, all masses which are lifted tend to fall; all 
 springs which are bent tend to straighten ; all gases tend 
 to liquefy and all liquids tend to condense ; all ele- 
 ments tend to oxidize or to undergo a change similar 
 to oxidation ; all electric charges tend to discharge. 
 All of the changes mentioned generate heat which radi- 
 ates off into space, and if the loss were not supplied 
 by the radiant energy which comes to us from the sun 
 our earth would soon become cold, motionless, and life- 
 less. 
 
 1 06. Energy and Life. Why do living beings 
 work, why must we work to live at all, and work much 
 to live as we want to live ? Our food, at once the ma- 
 terial of which our bodies are built and the source of 
 the energy of all our bodily movements, does not lie 
 within our grasp. It must be sought, often pursued ; 
 when got it must be prepared. Our clothing, houses, 
 implements, furniture, must be gathered in crude form 
 and shaped to meet our uses, must be converted from 
 its present condition to a less stable one, must have 
 
SOURCES OF USEFUL ENERGY. 167 
 
 work clone upon it to fit it for our use. The earth 
 which covers the stone in the quarry must be thrown 
 aside, the stone must be broken in pieces, lifted out 
 and carried to a new location, shaped Avith the chisel, 
 set in place, before it is a part of the foundation of a 
 house. Every one of these operations was resisted by 
 a force, gravitation or cohesion, which opposed the 
 change and necessitated the doing of work. 
 
 The man who shapes a tool of wood or iron must 
 pull apart with knife or file the molecules, or bend and 
 shape them into new forms. All these changes are 
 opposed by forces to overcome which requires the doing 
 of work. 
 
 As man's wants and desires increase he finds that 
 more and more work is required if he is to satisfy them. 
 The amount of energy which his own body can supply 
 is limited. The civilized man can assimilate no more 
 food than the savage. If he is to do the things he 
 desires to do, he must find other sources of energy 
 which he may utilize. They lie ready to his hand if 
 only his brain can devise ways to use them. 
 
 107. Sources of Useful Energy. Among the 
 sources of energy available for man's use are (a) the 
 bodily energy of animals; (5) the energy of flowing 
 water and the tides and waves of the sea; (<?) the 
 energy of the winds ; (c?) chemical energy, particularly 
 of combustion and of electric batteries. 
 
 Let us trace these secondary sources of energy back 
 
168 WORK. ENEEGY. MACHINES. 
 
 as far as possible to see if any of them have a common 
 source. The bodily energy of animals is derived from 
 the food they eat, which consists of other animals and 
 of plants. The animals eaten lived on plants, so that 
 ultimately the source of food supply is almost wholly 
 the plant kingdom. Now plants are able to use the 
 stable compounds of the soil and air and convert them 
 into unstable compounds useful for animal food only 
 under the influence of sunlight. The sun is then the 
 ultimate source of animal energy. The water which 
 drives our mills does so because it is in a position to 
 flow down hill. It possesses potential energy because 
 it has been lifted to the clouds in the form of vapor by 
 heat derived from solar radiation, and it delivers its 
 energy to any one who can use it on its way back to 
 the sea. The winds, too, are, as we saw when studying 
 heat, convection currents in the air set up by heat 
 received from solar radiation. The waves of the sea 
 are due chiefly to the winds, hence windmills and wave 
 mills are driven indirectly by solar radiation. 
 
 The energy of expanding steam which we utilize in 
 the steam engine we derive from the chemical combina- 
 tion of the carbon of wood and coal with the oxygen 
 of the air. Combustion is in fact a rapid oxidation of 
 carbon or hydrogen. The coal was once living trees 
 into whose composition the carbon was wrought after 
 -being torn from its stable union with oxygen by the 
 energy supplied to the leaves of the plants by solar 
 radiation. 
 
MACHINES. 169 
 
 Chemical batteries employ substances, like zinc and 
 acid, which are not found in their present condition in 
 nature but have had work done upon them by man. 
 Batteries ought not to be reckoned therefore as primary 
 sources of energy. The tides are due to the interac- 
 tion of the earth and the moon, and do not therefore 
 derive their energy from a distance. We see, however, 
 that the sources of energy upon which we depend 
 chiefly, and indeed almost wholly, are all traceable to 
 one source the sun. When we have used this energy 
 or let it pass us by unused, as by far the greater part 
 does and always will, it passes out again into that 
 boundless ocean of ether whence it came. 
 
 1 08. Machines. Man alone, of all animals, uses 
 tools, implements, machines. In a broad sense a 
 machine may be defined as a device by means of which 
 energy is transformed so as to be advantageously 
 applied. A man could dig a well (in some localities) 
 with his hands alone, but give him a shovel with which 
 he can pry the dirt apart and throw it out twenty hand- 
 fuls at a time and he will work to better advantage 
 than without the simple machine. If the well is deep 
 he will gain an additional advantage if he use a rope 
 and bucket to lift the clods to the top. He may even 
 find it profitable to attach a windlass to his rope and 
 use a much larger bucket than he could lift without it. 
 A horse can carry a man or a small load on his back ; 
 hitched to a wagon on good roads he can draw ten 
 
170 
 
 WORK. ENERGY. MACHINES. 
 
 times the load. Sewing by hand goes slowly because 
 the limit of speed is reached far sooner than the limit 
 of strength. The sewing machine transforms strength 
 into speed and multiplies the power of the seamstress 
 sevenfold. 
 
 In our study of machines we shall perhaps proceed 
 in the order of simplicity if we follow the historical 
 order and take up first the traditional simple machines. 
 
 109. The Lever. A rigid bar arranged to turn 
 about a fixed point is called a lever. The fixed point 
 is called the fulcrum (see Fig. 118). The two forces are 
 
 applied at different 
 
 P' O P points on the bar, P, 
 
 P r . By the law of 
 moments there will 
 be equilibrium when 
 the force f which 
 acts at P times the 
 distance P is equal 
 to f times P' Q, and 
 the moments are op- 
 posite in direction. 
 Both forces may act 
 on the same side of 
 the fulcrum, only so that their moments are opposite. 
 Let us now suppose the moment of the force / to be a 
 little greater than/ 7 , so that 
 / X PO /' X P'O + the friction of the bearing 
 
 FIG. 118. 
 
THE LEVER. 171 
 
 There will then be motion in the direction PQ. Then 
 the work done by the force f in moving the distance 
 PQ = I is fl and the work done at P 1 is f'l'. Since I 
 and V are arcs of circles whose radii are PO and P 1 
 respectively, it follows from geometry that 
 
 PO I 
 (fl) 1*0 = T 
 
 But from the law of moments 
 
 (i) f X PO=fxP'0 or jr = 
 Whence it follows from (#) and (6) that 
 
 fl=fl f 
 
 when the forces are in equilibrium. When motion is 
 produced, / = f'l' -\- work done in overcoming friction, 
 
 w", whence 
 
 (17) w = w' + w" 
 
 which is the law of work. 
 
 In the older treatises on mechanics the force applied, 
 /, was called the power and the force obtained, f, was 
 called the iveight. The words power and weight have 
 very definite meanings in physics and meanings not 
 at all alike. It seems best not to retain these words, 
 therefore, in our discussion of machines. 
 
 The distances PO and P 1 being straight lines are 
 easier to measure than the arcs PQ and P'Q. Their 
 ratio may be used therefore for the ratio of I to I', to 
 which it is always equal. 
 
172 WORK. ENERGY. MACHINES. 
 
 The lever has numerous applications. The spade, 
 the handspike or crowbar, the pump handle, all serve 
 to enable a man to overcome forces greater than he is 
 able to exert, but always at the expense of distance. 
 In every case the hand moves a greater distance than 
 the object at the other end of the lever. 
 f 
 
 The ratio ^- is called the mechanical advantage of the 
 
 machine. It is to be borne constantly in mind that the 
 real advantage consists in obtaining the energy in a 
 form better suited to our needs. The traveller who gets 
 four marks for a dollar in Germany or five francs for a 
 dollar in France is pleased " because he gets what he 
 needs, and he is even willing to pay the broker a small 
 percentage for making the exchange. In mechanical 
 transfers we must always pay exchange too. It is in 
 the form of heat and is always delivered on the spot. 
 We make it as small as possible by avoiding friction 
 and other sources of heat waste, but no rational me- 
 chanic expects to get back all he puts in, much less win 
 any energy by means of a machine. 
 
 A machine which transfers energy with but little loss 
 is said to be an efficient machine, and the ratio of w' 
 to w is called the efficiency of the machine. Since 
 w =. w r -\- w" and since w ff is never zero, it follows that 
 w' /w is always less than unity, or, as usually expressed, 
 less than 100 per cent. 
 
 EYK _ wor k obtained 
 
 work expended 
 
THE LEVEE. 173 
 
 W W 
 
 where w" represents the total work not obtained in use- 
 ful form but lost usually in overcoming resistance in 
 the machine itself. The useful work obtained, w', is 
 spent in overcoming resistance on objects other than the 
 machine, and may take any of the well-known forms of 
 kinetic or potential energy. 
 
 The efficiency of a lever depends very much on the 
 amount of friction at the fulcrum, but very much more 
 upon the direction of application of the force. When 
 a lever rests upon a knife edge, as in the balance, fric- 
 tion for small loads may be made exceedingly small in 
 amount, but when a similar arrangement is used with 
 the crowbar there must be friction enough to keep the 
 bar from slipping. The use of the crowbar is limited 
 by the fact that as soon as the 
 object has been lifted a short 
 distance, it must be supported 
 while the fulcrum is raised 
 so that the operation may be 
 repeated. 
 
 Where pressure is applied 
 from a single direction while 
 the lever is allowed to make FIG - 
 
 a full revolution, as in the crank of a bicycle, there is 
 only a small part of the revolution, near P (Fig. 119), 
 where the whole of the force applied produces rotation. 
 At Q the component be producing rotation is smaller 
 
174 
 
 WORK. ENERGY. MACHINES. 
 
 than the component 06, which is wasted in producing 
 pressure on. the bearing. At P the efficiency is nearly 
 100 per cent, \vhile at Q it is less than 50 per cent, and 
 at the top and bottom the force applied is almost all 
 wasted. We overcome this defect in a large measure 
 by applying our force mainly during that part of the 
 revolution where it will accomplish most. 
 
 1 10. The Pulley. If the force were applied to a 
 lever by means of a rope acting downward at the end 
 - - of the lever we should encounter the 
 same disadvantages as in the bicycle 
 crank, but if instead of a lever we use 
 a grooved wheel over which a rope 
 passes, the force may always be applied 
 at the proper point, while the fulcrum 
 may be placed once for all higher than 
 the point to which the load is to be 
 lifted. If the wheel be thought of as 
 having spokes (see Fig. 120) it is evident 
 that the horizontal pair of spokes may be 
 considered the two equal arms of a lever 
 
 CD 
 
 FIG. 120. 
 
 I at the instant when the wheel is in the 
 position shown. Since the wheel is prac- 
 tically solid any diameter may be such a lever. Friction 
 keeps the rope in position on the wheel without greatly 
 retarding the motion. The pulley is free from the 
 defects of the lever, but it offers in its simple form no 
 mechanical advantage whatever. Since 1=1', f must 
 
THE PULLEY. 
 
 175 
 
 equal f and more. The pulley even in tins simple 
 form is useful, however, since it changes the direction 
 
 of the application of the force. A man , Q ~ 
 
 can lift a large bucket of water from a 
 well more easily by pulling downward 
 on the rope than by 
 leaning over the well 
 and pulling upward, 
 while a horse cannot 
 conveniently pull in 
 any direction but the 
 horizontal. The two 
 fixed pulleys used in 
 the pile driver (Fig. 
 115) enable us to em- 
 ploy a horse for lift- 
 ing the weight. 
 
 f 
 
 f 
 
 FIG. 121. 
 
 By the arrangement 
 of pulleys shoAvn in Fig. 121 the load 
 which is attached to a movable. pulley 
 moves but half as far as the point of 
 application of the force moves, and 
 we have a mechanical advantage of 2, 
 while the use of a third pulley as in 
 Fig. 122 gives us a mechanical advan- 
 tage of 3. 
 FIG. 122. 
 
 in. The Wheel and Axle. The winch or wind- 
 lass, the capstan, the wheel and axle combine the prin- 
 ciples of the lever and the pulley. They all consist of 
 
176 
 
 WORK. ENEEGY. MACHINES. 
 
 FIG. 123. 
 
 an axle about which a rope is wound drawing the load. 
 
 The load is moved by force applied at the circumfer- 
 ence of a larger 
 wheel or at the 
 end of a crank. 
 Fig. 123 shows 
 a common winch 
 or windlass. In 
 machine shops 
 combinations of 
 pulleys of vari- 
 ous sizes on the 
 
 same shaft, connected by belts with pulleys on various 
 
 other machines in use, make it possible to run any 
 
 machine in a shop 
 
 at any desired 
 
 speed from an en- 
 gine whose speed is 
 
 constant. When it 
 
 is desirable to run 
 
 the same machine 
 
 at different speeds, 
 
 as is the case with 
 
 the lathe, a pair 
 
 of cone pulleys 
 
 is used. See (7, O r 
 
 (Fig. 124), where 
 
 D is the driving pulley of the engine, SS 1 a line of 
 
 shafting from which attachments are made either directly 
 
 FIG. 124. 
 
THE WHEEL AND AXLE. 177 
 
 to other machines or to countershafts from which the 
 energy is conveyed to the machines as wanted. With 
 the belt on the cone pulleys as shown, the lathe has its 
 lowest speed. The cones are of such dimensions that 
 the same length of belt will fit in all cases. 
 
 When two shafts are connected by pulley and belt 
 the one carrying the larger pulley must go the more 
 slowly, since all parts of the belt travel at the same 
 speed, and a point in the circumference of either pulley 
 travels with the speed of the belt. In Fig. 124, for 
 example, the driving wheel, D, has a speed of 2,000 
 revolutions per minute, and a diameter of 120 inches; 
 P has a diameter of 12, Q of 24, R of 24, T of. 5, and 
 T' of 20. To find the speed of 0' we have only to 
 multiply 2,000, the speed of the driving pulley D, by the 
 ratios of the sizes of the successive pairs of pulleys, thus : 
 
 120 A 5 
 Speed of C" =2,000 X ~ X g X ^ =5,000 
 
 Where great compactness is desired the two wheels 
 are brought into direct contact by cogs. A series of 
 such cogwheels is called a train of wheels. By a 
 proper combination of sizes the train of wheels in a 
 clock is made to drive the hour, minute, and second 
 hands at the proper relative speeds. In cases like the 
 bicycle, where a belt would slip and the wheels cannot 
 conveniently be placed in contact, sprocket wheels and 
 chain accomplish the purpose. The rear wheel may be 
 given any desired speed by suitably choosing the rela- 
 tive size of the two sprocket wheels. 
 
178 
 
 WORK. ENERGY. MACHINES. 
 
 ii2. The Inclined Plane. When a body is rest- 
 ing on an inclined plane its weight is supported partly 
 by the plane, partly by some force acting parallel to the 
 plane. The ratio of the two forces is the ratio of the 
 two components, be, ac (Fig. 125). 
 The ratio of the force overcome 
 to the force applied is 
 
 ba 
 A 
 
 ac 
 
 FIG. 125. . J 
 
 But since the angles B and b have their sides mutually 
 perpendicular, triangles ABO and abc are similar and 
 ba BA [ 
 
 Whence it follows that 
 
 <-> = 
 
 that is to say, the advantage of 
 an inclined plane is the ratio 
 of the length to the height of 
 the plane, provided that the 
 force acts along the plane. 
 
 The wedge may be treated as 
 a pair of inclined planes placed 
 base to base (see Fig. 126). The force is applied in the 
 direction OB to overcome the force of cohesion which 
 is in a direction at right angles to OB. It follows that 
 ' f> _ GB 
 
 '~ 
 
 FIG. 126. 
 
THE SCREW. 
 
 179 
 
 When wedges are used to split large stones a row of 
 holes is drilled along the line on which the stone is to 
 be divided and several wedges are driven at the same 
 time. If the only object aimed at is to shatter the 
 stone a charge of powder or dynamite is often used. 
 
 113. The Screw. When a wagon road or a rail- 
 way is to he carried up a very steep mountain it does 
 not go straight 
 up, but winds 
 in a spiral, 
 making the 
 ascent by go- 
 ing several 
 times the dis- 
 tance. The 
 length of the 
 incline is thus 
 increased with- 
 out increasing 
 its height, thus 
 greatly increasing the mechanical advantage. The same 
 principle is employed in the screw, where the advantage 
 is usually still further increased by the use of a wheel 
 or a lever at the head of the screw (see Fig. 127). 
 The distance which the screw advances in one revolution 
 is the distance, d, between the adjoining threads of the 
 screw measured parallel to the axis of the screw, while 
 the distance moved by the applied force is the circum- 
 
 FlG. 12 
 
180 WORK. ENERGY. MACHINES. 
 
 ference, <?, described by the point of application of the 
 force. The advantage of the screw is therefore 
 
 Thus a force of 2 pounds applied to the handle of a 
 screw-driver 2.1 inches in diameter (= 6.6 inches in cir- 
 cumference) w^ould exert upon a screw having 12 
 threads to the inch a force of 158.4 pounds. 
 
 The simple machines just described the lever, the 
 wheel, the incline (including the screw) have been 
 known and used for thousands of years. The innu- 
 merable mechanical contrivances in use to-day, from the 
 wheelbarrow to the typesetting machine, are all but 
 combinations of the simple machines. It is when we 
 seek to employ other forms of energy than those 
 known to the ancients (animals, wind, waterfalls) that 
 we meet machines involving principles not found in 
 the simple machines, but always associated in practice 
 with them. 
 
 114. Heat Engines. As long ago as B.C. 200, 
 machines employing the expansive force of heated air 
 and steam were described, by Hero, or Heron, of Alex- 
 andria. He arranged the device shown in Fig. 128, 
 by which a fire kindled on the hollow altar causes the 
 air within to expand, forcing the water out through the 
 siphon into a bucket, where its weight served to open 
 the temple doors. When the fire was allowed to die out 
 the doors closed as miraculously as they had opened. 
 

 
 HEAT ENGINES. 
 
 181 
 
 Hero's steam engine is shown in Fig. 129. It is 
 easily constructed. Steam from the basin enters by 
 one of the hollow columns supporting the ball, which 
 is made to revolve by 
 the reaction of the 
 air upon the escaping 
 steam. 
 
 The steam engine 
 invented by Watt in 
 1765 was the out- 
 grow t h of various 
 forms of the " atmos- 
 pheric " engines which 
 were the fruit of 
 Guericke's invention 
 of the air pump a 
 hundred years before. 
 In these engines a vacuum was produced in a cylinder 
 
 by the condensation of steam 
 within it, and a piston was 
 ?/; V' pushed into the cylinder by 
 the pressure of the atmos- 
 phere. Such engines were 
 used for pumping water from 
 mines, but were very waste- 
 ful of steam. 
 
 Watt not only invented the 
 steam engine, which with 
 Fl(; 129 _ slight modifications is used 
 
 FIG. 128. 
 
182 
 
 WOEK. ENERGY. MACHINES. 
 
 to-day, but he also invented most of the devices by 
 which it is controlled and rendered efficient, such as 
 the automatic governor and .throttle valve. The slide 
 valve was invented by his assistant, Murdoch. 
 
 The principle of the steam engine may be under- 
 stood from Fig. 130. The steam from the boiler enters 
 the steam chest at $ whence it is admitted to the 
 cylinder through the ports, P, P', by means of the 
 
 FIG. iso. 
 
 slide valve, V, which opens port P while the piston is 
 near the end J., at the same time closing the passage 
 from P' to the steam chest and opening it to the ex- 
 haust, thus allowing the condensed steam to escape 
 at atmospheric pressure. By the time the shaft has 
 made half a revolution the piston is in suitable position 
 at the other end of the cylinder, the valve has moved 
 so as to open P', arid live steam is now admitted to the 
 right-hand side of the piston head, while condensed 
 steam escapes through P to the air. 
 
HEAT ENGINES. 
 
 183 
 
 The oscillating motion of the piston is converted 
 into rotary motion by a crank attached to a shaft which 
 carries a large driving pulley. Attached to the same 
 shaft is a smaller crank or eccentric which operates the 
 slide valve. 
 
 In the best steam engines not more than twenty per 
 cent of the energy liberated in the combustion of coal is 
 utilized, yet coal is so cheap that it continues to furnish 
 most of the energy used for manufacturing purposes. 
 
 115. A form of engine which is coming quite gen- 
 erally into use where but a small amount of power is 
 required is the so-called gas engine (Fig. 131). The 
 propulsive force is 
 furnished by the ex- 
 plosion produced by 
 igniting a mixture of 
 air and coal gas or gas- 
 oline vapor within the 
 cylinder. The gas 
 mixture is admitted 
 only at every other rev- 
 olution, since the prod- 
 ucts of combustion must first be expelled by the 
 piston on its first return stroke. During the second 
 stroke the mixed gases are admitted through a valve, 
 which closes like a pump valve when the piston starts 
 back. When the piston is at the end of its stroke and 
 has compressed the gases it closes an electric circuit, 
 
 PIG. i3i. 
 
184 WORK. ENERGY. MACHINES. 
 
 which is broken when the piston starts on its second 
 outward stroke, producing a spark which ignites the 
 gases, and the cycle of operations is then repeated. 
 
 The fact that the force is exerted on but one side of 
 the piston and but once in two revolutions makes the 
 engine less steady than the steam engine, with its two 
 impulses for each revolution. This fault is overcome 
 to some extent by the use of heavy fly wheels. 
 
 Regulation is accomplished by a governor, which 
 entirely closes the supply valve when the speed exceeds 
 a certain amount. When the load is light the explo- 
 sions occur only at rare intervals, so that but little gas 
 is wasted. Gas engines are now used to drive self- 
 propelling carriages, a fact which is likely to lead to a 
 very light and compact form of machine. At the 
 present time it is more expensive than the horse as 
 regards first cost, if not as regards maintenance. 
 
 The gas engine has a higher efficiency than the steam 
 engine, yet it has not nearly reached the highest effi- 
 ciency of which it is theoretically capable. 
 
 116. Rate of Doing Work. Power. Activity. 
 The amount of energy which any machine transforms 
 in unit time is its rate of doing work, or, briefly, its 
 power or activity. Watt introduced the term horse- 
 power as the unit of activity, and defined it as 33,000 
 foot pounds per minute. The metric unit is the watt. 
 It is defined as 10,000,000 ergs per second = 1 joule 
 per second = 1 volt X 1 ampere. 
 
OTHEE ENGINES. 185 
 
 (29) 1 h.p.= 746 watts 
 
 The horse-power of a dynamo is usually expressed 
 in kilowatts. Thus a 50 k.w. dynamo would furnish 
 50 amperes at 1,000 volts and would require a 67 h.p. 
 engine to run it. If we now recall that a calorie is 
 4.19 joules, we see how easy it is to measure both 
 energy and power in any one of its forms, and then to 
 compare the quantity measured with the same quantity 
 measured in another form. This enables us to find the 
 efficiency of a machine like the heat engine, which 
 transforms energy from one form to another. 
 
 117. Other Engines. The applications of the laws 
 of energy and the principles of machines to water 
 wheels, tide wheels, and windmills may be left as ari 
 exercise for the ingenuity of the student as he may have 
 opportunity to study them. He has only to remember 
 that no exception has ever been found to the law of 
 the conservation of energy, and he may feel very sure 
 that the man who claims to have invented a machine 
 which will run and do work, even enough to overcome 
 friction, after the energy supplied to it has been ex- 
 pended, is either deceived himself or is trying to 
 deceive others for his own profit. The man who is 
 pursuing the phantoms of perpetual motion should 
 devote himself to solving some of the many problems 
 which offer sure reward to the successful inventor. 
 
 No man can hope to create energy. No man need 
 wish to do so, for energy by the millions of horse-power 
 
186 WOEK. ENERGY. MACHINES. 
 
 is going to waste constantly at our very doors. The 
 energy contained in the water which falls on the roof 
 of a large hotel in a year would, if utilized, run the 
 elevator twelve hours a day the year round. The 
 energy of the sun which falls on a large factory and is 
 radiated again into space would, if all utilized, run all 
 the machines in the factory. A small fraction of the 
 energy of -the wind which blows across every farm 
 would, if harnessed, do all the work of the farm. 
 
 The men who are to profit themselves and their gen- 
 eration by their inventions must first master the known 
 laws of nature and then apply them to existing 
 problems. 
 
 118. The Storage of Energy. If the energy from 
 so intermittent a source as the wind, for example, is to 
 be utilized to any large extent by people who must 
 work every day, means must be found to store the 
 excess of one day against the needs of another day. 
 On the other hand, some forms of energy, like light, are 
 consumed principally at certain hours of the day, and 
 the engine must have power enough to supply the 
 greatest demand, though an engine a third as large 
 could do the work if it were distributed uniformly 
 throughout the day. Many large lighting stations now 
 have large storage batteries which are charged during 
 the middle of the day and help carry the load in the 
 evening. Indeed, the storage battery is as yet the only 
 successful device for storing energy on a large scale. 
 
THE TRANSFERENCE OF ENERGY. 187 
 
 Plants, as we know, store the energy of the sun's 
 rays, but the supply thus stored could not meet our 
 demands if the treasures stored in the coal fields dur- 
 ino- the ages rich in carbon were exhausted. Ere the 
 
 o o 
 
 coal fields are all used ways will perhaps be found to 
 collect and store the solar energy by artificial means 
 which will make us independent of coal, as iron and 
 paper are making us independent of wood, and as 
 aluminum might easily make us independent of copper 
 and tin. 
 
 119. The Transference of Energy from Place to 
 Place. It often happens that large waterfalls are 
 located at some distance from a mine, where it 
 would be very desirable to use the energy of the fall- 
 ing water. The desired end may be accomplished by 
 converting the energy into the form of an electric cur- 
 rent, when it may easily be carried by wires to a con- 
 siderable distance, to be again converted by means of 
 motors into mechanical motion. 
 
 In large towns there are usually a number of small 
 shops, printing oifices, etc., which need a small amount 
 of power at somewhat irregular intervals. The total 
 amount of power needed can be supplied from one 
 large engine, with one or two men to care for it, much 
 more economically than by a number of small engines. 
 
 Several plans have been used for distributing the 
 power. The pressure applied to water by a large 
 pump at a central station may be used by water motors 
 
188 WORK. ENEBGY. MACHINES. 
 
 at any place on the line of pipes. The friction of 
 moving water on the pipes is, however, so great that 
 very large pipes are required both for the inflow and 
 the escape of the water, so that the ordinary service 
 pipes are not sufficient to furnish any considerable 
 power at the pressures usually employed. Compressed 
 air furnishes a simple means of conveying power, but 
 one which has not come into general use because of the 
 expense of laying pipes of sufficient strength and size. 
 
 Here again the electric current is found to be admi- 
 rably adapted to the distribution of power. Electric 
 conductors may be carried anywhere and tapped at any 
 point ; indeed, the point of contact may be continuously 
 changing, as in the trolley car, without any serious loss 
 }yj leakage. The ease with which the current may be 
 turned on or off or varied in amount at pleasure, and 
 the variety of uses to which it may be put heat, light, 
 mechanical work, electroplating make the electric cur- 
 rent the ideal form of energy for transference to a dis- 
 tance and for distribution in small quantities. 
 
 When the energy is to be carried long distances high 
 potentials are used, because the heat lost in the wire is 
 proportional to the square of the current strength. 
 Thus if 100 kilowatts are to be carried at 100 volts, we 
 have 
 
 100 k.w. = 100 volts X 100 amperes 
 
 but at 1,000 volts we have 
 
 100 k.w. = 1,000 volts X 10 amperes 
 
EXERCISES. 189 
 
 In the first case the current strength is ten times that 
 in the second, and the heat lost in the wire is 10 2 or 
 100 times as much for a wire of a given size. 
 
 Exercises. 
 
 89. (a) Two men lift a 200 pound barrel of salt upon a 
 wagon 3 feet high. How much work do they do ? (6) One 
 man rolls the same barrel of salt upon the same wagon, using 
 an inclined plane 9 feet long. How much force does he exert ? 
 How much work does he do ? (See Fig. 132.). 
 
 FIG. 132. 
 
 90. A man weighing 150 pounds carries 50 pounds of brick 
 up a ladder 20 feet high, (a) How much work has he done ? 
 (6) How much useful work? (c) What is the efficiency of 
 this method of working ? If he can draw up 100 pounds to 
 the same height and in the same time by means of a single 
 pulley and a box weighing 20 pounds, friction being equivalent 
 to 30 pounds, (d) how much work does he do ? (e) How much 
 useful work ? (/) What is the efficiency of the method used ? 
 
 91. A horse which can exert continuously a force of 500 
 pounds is used to lift the material for a building. A number 
 of iron girders, each weighing 600 pounds, are to be lifted. 
 What combination of pulleys will just use the full strength of 
 the horse if 20 per cent of the work he does is spent in over- 
 coming friction ? 
 
 92. A certain class of freight engines can pull a load of 100 
 tons up a grade of 2 feet in 100. Suppose all grades on the 
 line reduced to 1 foot in 100, what load can these engines pull 
 
190 
 
 WORK. ENERGY. MACHINES. 
 
 if we suppose the work done in overcoming friction equal to 
 i the work done by the engines ? 
 
 $3. A crane (Fig. 133) employs a system of 5 fixed and 5 
 movable pulleys and a windlass having an axle 8 inches in 
 diameter, to which is attached a wheel having 40 cogs driven 
 by a wheel having 8 cogs, to which is attached a crank 16 
 inches long. How large a stone can a man lift if he applies a 
 force of 25 pounds to the end of the 
 crank ? K"o allowance is to be made for 
 friction. 
 
 94. (a) How much work is required 
 to lift a ton (2,000 pounds) of coal from 
 a mine 500 feet deep ? (&) What must, 
 be the power of an engine to lift 20 
 tons per day from this mine ? 
 
 95. How much coal would the engine 
 in the last exercise consume per day if 
 it converts 15 per cent of the energy 
 of combustion of coal into mechanical 
 work ? The heat of combustion of coal 
 is 7,800 calories per gram. 
 
 96. A man lifts his own weight, say 
 150 pounds, 2 inches every step he 
 takes. What is his rate of working if 
 
 FIG. 133. ne ta kes s t e p s 2 feet in length and 
 
 walks on a level at the rate of 3 miles per hour ? 
 
 97. A man weighing 145 pounds propels himself at the rate 
 of 10 miles an hour on a bicycle weighing 25 pounds over level 
 pavement. If he should remove his feet from the pedals at 
 any instant, the wheel would run 528 feet before being brought 
 to rest by friction. What is the man's rate of working ? 
 
 98. A storage battery is charged at the rate of 20 amperes 
 
EXEBCI8ES. 191 
 
 
 
 for 12 hours. It will give a current of 10 amperes for 20 
 hours. What is its efficiency? 
 
 99. The battery mentioned in the preceding exercise has a 
 difference of potential of 50 volts, (a) When discharging at 
 16 amperes, what is its power in watts ? (&) If a motor when 
 connected to this battery consumes 8 amperes at 60 volts and 
 does work at the rate of Jiorse-power, what is the efficiency 
 of the motor ? 
 
 100. A freight train weighing 100 tons is moving at the rate 
 of 20 miles an hour, (a) How much kinetic energy has it ? 
 (&) How much energy would there be lost if the train were 
 brought to rest by applying the brakes ? (c) Suppose that a 
 dynamo were connected to the axle of one of the cars and 
 made to store energy in a battery, or that a pump similarly 
 attached were used to compress air in a reservoir, could a part 
 of this waste energy be utilized ? 
 
 101. Explain why more coal must be burnt to run a local 
 train a given distance than to run a through train of the same 
 size the same distance. 
 
CHAPTER VI. 
 
 VIBRATIONS. WAVES. 
 
 120. Vibratory Motion. Most bodies which have 
 not been recently disturbed are at rest in that position 
 in which they have the least possible potential energy : 
 
 a ball hung from the end of 
 a string hangs with the string 
 in a vertical position, the ball 
 being as near the earth as it 
 can get ; a vessel of water has 
 its surface horizontal ; a dew- 
 drop is spherical. If we draw 
 the ball to one side (P, Fig. 
 134) and let it go, the poten- 
 tial energy we have thus im- 
 parted to it will be converted 
 into motion, but the ball will 
 not stop in its former position 
 of rest, since its momentum 
 will carry it past to P', a 
 point almost as far from as P is. After coming to 
 rest at P' it will return through almost to P, repeat- 
 ing the operation until the work done by it in pushing 
 aside the air has consumed the energy given it when it 
 was pulled aside. 
 
 19? 
 
VIBEATOEY MOTION. 193 
 
 If a vessel partly filled with water be tilted as in 
 Fig. 135, and then quickly restored to its original posi- 
 tion, the water at will alternately rise and fall between 
 P and P' and finally come to rest at 0. 
 
 Such motion is called vibratory motion. The dis- 
 tance PO is called the amplitude of vibration. The 
 time occupied by the particle in going from P through 
 
 FIG. 135. 
 
 to P 1 and back again to P is called its period of 
 vibration, and the number of vibrations made in one 
 second is called the rate of vibration. All vibratory 
 bodies which have a definite and constant period of 
 vibration are said to have harmonic motion. It is called 
 harmonic motion because all musical sounds are due to 
 motion of that sort. Such motion is indeed very com- 
 mon because most bodies are in a state of comparative 
 rest in stable equilibrium, but are frequently disturbed 
 by small forces which are able to set them in vibration, 
 though not great enough to move them from their 
 places. Thus the boughs of a tree sway to and fro in 
 every breeze, yet stay in one place for scores of years. 
 Whenever the force of displacement, as likewise the 
 force of restitution, increases directly with the displace- 
 ment, the motion will be harmonic and the period of 
 
194 VIBE A TIONS. WA VES. 
 
 vibration constant. We can easily prove that the force 
 required to stretch a spiral spring is proportional to the 
 elongation produced in the spring, for the scale of a 
 spring balance is a scale of equal parts. 
 If we hang a small weight from a light 
 spiral spring, pull it downward and re- 
 lease it, it will vibrate with a slowly di- 
 minishing amplitude, but with a constant 
 period. The hairspring of a watch (Fig. 
 136) vibrates in the same way. Vibrating 
 pendulums and vibrating springs furnish us, therefore, 
 with the means of measuring time. 
 
 121. The Pendulum. The pendulum furnishes a 
 good example of harmonic motion. The force of resti- 
 tution, that is, the force tending to make the ball 
 return to its position of equilibrium, is gravity. It is 
 obvious that when the ball (see Fig. 137) is anywhere 
 except at 0, gravity may be resolved into two compo- 
 nents, one of which acts to restore the ball to its posi- 
 tion of equilibrium. This component is greater at P 
 than at Q. The force of restitution is greater the greater 
 the amplitude. Since there is always a force acting 
 toward 0, the motion is accelerated toward 0, that is to 
 say, the ball will go faster and faster as it approaches 
 0, but slower and slower as it leaves 0. The energy 
 of the pendulum at P and at P f is all potential, while 
 at it is all kinetic. At intermediate points it is 
 partly potential and partly kinetic. 
 
THE PENDULUM. 
 
 195 
 
 Galileo noticed that the great chandelier in the 
 cathedral at Pisa seemed to swing in equal times. He 
 placed his finger 
 on his pulse and 
 verified the truth 
 of his first impres- 
 sion. Further ex- 
 periment showed 
 that the time of 
 a pendulum de- 
 pends upon its 
 length, which 
 must be measured 
 from its centre of 
 mass to the point 
 of support, and 
 with the force of 
 gravity at the 
 place. It may be proved mathematically that the period, 
 T, of a pendulum of length Z, is 
 
 FIG. 137. 
 
 (30) T=2*\/ 
 9 
 
 where * = 3.1416 and g is the force of gravity. The 
 time of oscillation, , which is the time between two 
 passages of the ball through 0, is just half as great : 
 
 (81) t = 8.1416 \J 
 A pendulum whose time of oscillation, , is one 
 
196 VIBRATIONS. WAVES. 
 
 second is called a seconds pendulum. Its length may 
 be easily found from the equation (31) 
 
 t = 3.1416 
 
 \/JL 
 
 = (3.1416? - 
 
 I = 
 
 The same formula will give us the value of g when 
 we have measured t and Z. 
 
 It will be seen that the only variable quantities in 
 this formula (31) are I and g. It follows that the 
 mass, size, and material of the pendulum have no effect 
 on its time of oscillation. It is to be remarked that 
 formula (31) is true only on the supposition that the 
 amplitude of vibration is small as compared to the 
 length of the pendulum. 
 
 A simple pendulum is one in which the weight of the 
 string is so small that the centre of mass of the pen- 
 dulum can be thought of as identical with the centre 
 of mass of the bob, which must be small. If the bob 
 is a ball or disc we measure I from the centre of the 
 bob to the point of support. 
 
 The length of a pendulum is changed by tempera- 
 ture, and various plans have been devised for correcting 
 the error thus caused. Descriptions of compensating 
 
WAVE MOTION. 197 
 
 pendulums may be found in the larger treatises on 
 physics or in any good cyclopaedia. 
 
 122. Wave Motion. The particles of solid bodies 
 are so related to each other that if any particle be set 
 in vibration it will impart its motion to the particles 
 nearest to it, these particles in turn passing the motion 
 to their neighbors. Thus the slamming of a heavy 
 door in a large building will send tremors to every part 
 of the building. The explosion of a powder magazine 
 will shake buildings miles away. 
 
 Fluids also transmit disturbances, not by being dis- 
 torted as solids are, for they have no form, but by 
 being compressed. 
 
 A disturbance which is transmitted from particle to 
 particle through a medium is called a wave. 
 
 There are but two ways known to us in which energy 
 may be transmitted from body to body: (1) by the 
 motion of bodies themselves, as when a bullet is fired 
 or a stream of water flows; (2) by waves, as when 
 pressure is imparted to the water in closed pipes or to 
 the ether surrounding the sun, and the pressure is 
 transmitted to all points in any way connected with the 
 source of energy. 
 
 Every vibrating body sends waves through the bodies 
 it touches. Wave motion is therefore present every- 
 where. As heat and sound and light it assails us on 
 every hand. The study of wave motion is, therefore, 
 of the highest interest to us. 
 
198 VIBBA TIONS. WA VES. 
 
 We have all noticed that a pebble dropped in still 
 water will send a wave to every part of the pool. The 
 reason is obvious: the water displaced by the pebble 
 heaped upon the water near it presses upon it, falls, and 
 is carried as far below the level surface as it was above 
 it first, as the water did in the dish shown in Fig. 135. 
 
 The pressure is transmitted to all points of the water 
 until in time the wave has reached every point. 
 
 When the water at any point as P (Fig. 138) has 
 
 FIG. 13. 
 
 made a vibration and a fourth, and is starting up for 
 the second time, there are a number of particles at 
 equal distances from P which are just starting up for 
 the first time (R, R). The distance PR is called a 
 wave length, and all particles which are any whole num- 
 ber of wave lengths distant from P are said to be in 
 the same phase. The distance PR we shall call I. It 
 is evident that if every vibrating particle in the medium 
 makes n vibrations per second, the rate of propagation 
 of the disturbance, or, as we say, the velocity, v, of the 
 
 wave, is 
 
 (33) v = nl 
 
 This expression is true for all kinds of wave motion. 
 The velocity of waves of any sort in a particular 
 medium is constant, but when the waves pass into a 
 different medium the velocity will, in general, change. 
 
DIRECTION OF WAVES. 
 
 199 
 
 123. Direction of Waves. A wave which travels 
 along the bounding surface between two fluids, like air 
 and water, travels outward in concentric circles. A 
 wave in a string travels along the string. A wave in a 
 large body of any homogeneous medium travels out- 
 ward from the centre of disturbance in concentric 
 spheres. The direction of vibration of the particle 
 may be the same as the direction of propagation of the 
 
 2.OO O O OOOOOOOOOOO O O OO 
 P O P O f T* 
 
 FIG. 139. 
 
 wave: the wave motion is then said to consist of 
 longitudinal vibrations ; or the particles may vibrate in a 
 direction at right angles to the direction of propagation 
 of the wave : the vibrations are then said to be trans- 
 verse? The waves on the surface of water and the 
 waves which are sent along a clothesline when it is 
 struck with a stick are transverse. The waves of pres- 
 
200 VIBE A TIONS. WA VE8. 
 
 sure which are imparted to water in pipes by means of 
 a force pump are longitudinal. 
 
 The two sorts of waves may be represented diagram- 
 ma tically as in Fig. 139, where the circles represent 
 particles of the medium in various phases of vibration. 
 At 1 a transverse wave is shown, at 2 a longitudinal 
 wave. To save time in drawing the figure it is cus- 
 tomary to represent both sorts of waves as at 3, leaving 
 the sort of wave to be stated in the discussion. The 
 distance PR = I is a wave length, and P and R are in 
 the same phase, while P and P 1 or and 0' a-re in 
 opposite phases. 
 
 124. Reflection. It was remarked above that waves 
 change their velocity on entering a different medium. 
 
 It is to be 
 obs erved 
 
 FI0140 further that 
 
 the- energy 
 O f a train of 
 FIG - 141 - waves in 
 
 any medium is never all transmitted to the second 
 medium; a part of it is always reflected or turned 
 back at the bounding surface. If the velocity of the 
 waves is less in the second medium than in the first, 
 the reflected wave will be opposite in phase to the orig- 
 inal wave (see Fig. 140). If the velocity is greater in 
 the second medium the wave will be reflected without 
 change of phase (see Fig. 141). 
 
ADDITION OF WAVES. 201 
 
 Except in the cases of large bodies of water and the 
 atmosphere we have to deal with waves in a body of 
 limited size, and must therefore have to do with waves 
 at bounding surfaces. It will be well for us, therefore, 
 to examine the subject somewhat more in detail. 
 
 125. Addition of Waves. Stationary Waves. - 
 When two waves pass any portion of a medium at the 
 same time, each wave produces the same effect on every 
 particle of the medium as if it alone were 
 passing. This is in accordance with Newton's 
 second law of motion. The resultant motion 
 is, therefore, the geometrical sum of the two 
 motions, and the resultant wave may be quite 
 different from either of the two components. 
 
 If one end of a rubber tube be attached to 
 
 \ 
 
 a hook in the ceiling while the other end is 
 fastened to a hook in the floor or table, waves 
 may be sent up toV tube by striking a quick 
 blow near the lower end of the tube. When 
 a wave reaches the top it will be reflected 
 V s with a change of phase. If at the instant 
 FJG the reflected wave starts downward a second 
 142 - one is sent up from 8 (Fig. 142), the two 143 ' 
 waves will meet midway and interfere. It is easy to 
 see that a particle halfway up (Fig. 143) is pulled in 
 opposite directions by almost equal forces and will there- 
 fore remain at rest. If a continuous series of waves be 
 sent from S at equal intervals they will all interfere 
 
202 
 
 VIBRA TION8. WA VES. 
 
 so as to produce rest at the middle but motion in the 
 other parts of the tube, which will appear as in Fig. 
 144. The point at rest is called a node, while the points 
 
 of greatest activity are called 
 
 antinodes. We shall indicate 
 
 nodes by N, antinodes by A 
 
 hereafter. By timing the 
 
 waves suitably we may pro- 
 duce two nodes besides those 
 
 at the end, as in Fig. 145, or 
 
 three or four or more at 
 
 pleasure. In every case the 
 
 distance between two nodes 
 
 is half a wave length. 
 
 (34) NN=AA=L 
 
 The case just cited is an 
 FIG. FIG. 
 144. 145. illustration of the general 
 
 case shown in Fig. 140, where v l > v 2 . 
 The case where v l < v 2 may be illustrated if we fasten 
 the upper end of our tube to a string which is fastened 
 to the hook as shown in Fig. 146. The reflected and 
 incident waves (as waves sent from S are called) will 
 evidently interfere in such a way as to reenforce each 
 other as they pass ; the middle portion will not be a 
 node, neither will the upper end, but the nodes will be 
 situated as shown in Figs. 147 and 148. 
 
 FIG. Fio. FIG. 
 146. 147. 148. 
 
 126. Law of Reflection. The wave in a rope or 
 
LAW OF REFLECTION. 
 
 203 
 
 rubber tube is reflected back along the tube as a matter 
 of course, but when a water wave, for example, strikes 
 a pier the direction of the reflected wave is not exactly 
 opposite to that of the incident wave unless the latter 
 was moving at right angles (normal) to the pier. Let 
 fit f'i (Fig- 149) be the Avave fronts of a train of waves 
 incident upon the bounding surface BB', f r , f f r the 
 front of the same wave after reflection. The waves are 
 supposed to have come from a point so distant that the 
 
 FIG. 149. 
 
 wave fronts may be treated as straight lines. When a 
 certain point C on f { has reached the bounding surface 
 BB', there is a point C 1 on f\ which has also just 
 reached BB'. If we draw CD _L f t and C'I>' J_ / r , 
 it is evident that D will reach C in the same time 
 that C' requires to reach D 1 , whence D C = D' C' = I. 
 In the right-angled triangles C'DO and CD'C' the sides 
 C'D* and CD are equal and C'C is common. They are 
 therefore equal and angle DC'C = angle D'OO' ; that is 
 
204 
 
 vis MA r/o.v/y. WA VES. 
 
 to say : the angles made by the incident and reflected 
 waves with the bounding surface are equal. 
 
 127. Refraction. In Fig. 150 /,, /', are the fronts 
 of waves incident on BB' and f R , f' R the fronts of that 
 portion of the waves which enter the second medium. 
 When f { has just touched BB' at (7, /',. has also just 
 touched BB' at (7 ; , while other portions of these waves, 
 
 FIG. 150. 
 
 /j, f'x, have advanced at a different velocity in the sec- 
 ond medium. Draw CD' J_ /', and C'D _L f R . The 
 distance D' C was traversed hy the wave in the first 
 medium in the same time that the distance C'D was 
 traversed in the second medium, or 
 D'C 
 
 C'D 
 
 - = n, a constant 
 
 The velocity of any particular waves in any given 
 medium is constant and the ratio v 1 /v 2 is therefore con- 
 stant. It is known as the index of refraction and is 
 
EXERCISES. 205 
 
 denoted by n. Refraction may be defined as the 
 change of direction which a wave undergoes in passing 
 from one medium to another. It is evident from the 
 figure that the direction of the wave front will be 
 changed except when the wave front is parallel to the 
 bounding surface, that is, when the angle between the 
 incident wave and the bounding surface is zero. In 
 general, the greater the angle, the more the wave will 
 be refracted. 
 
 It should be remarked that reflection and refraction 
 take place in the manner just described only when the 
 bounding surfaces are plane over an area which is large 
 compared with the length of a wave. 
 
 The subject of diffraction may well be deferred until 
 light waves are studied. 
 
 Exercises. 
 
 102. () What is the length of the seconds pendulum at a 
 place where #=979? () What would be the rate of this 
 pendulum at a place where ^\= 981 ? 
 
 103. At a certain place a, pendulum was found to make 21 
 oscillations in 20 seconds. Its length was 90.2 cm. What is 
 the value of g at that place ? 
 
 104. Two pendulums have lengths in the ratio of 3 to 4. 
 What is the ratio of their periods ? 
 
 105. Place a rectangular dish of mercury or water on the table 
 and strike a series of blows on the table with the fist. Strike 
 simultaneously with both fists at points at right angles to two 
 adjacent sides of the dish and note the waves on the surface of 
 the liquid. A whirling table or an electric motor in motion 
 will often set up such waves, 
 
206 
 
 VIBE A TIONS. WA VE8. 
 
 106. A rope along which impulses are being sent at the rate 
 of 5 per second vibrates in 4 segments. The rope is 6 metres 
 long, (a) What is the wave length ? (6) What is the velocity 
 of the wave ? 
 
 107. Plot on cross-section paper a train of waves having a 
 wave length of 4 cm. and an amplitude of 1 cm., and a second 
 
 FIG. 161. 
 
 train having a wave length of 3 cm. and an amplitude of 1 cm. 
 Plot the sum of the two waves by taking the sum or difference 
 of the distances from the axis of points 2 mm. apart along the 
 axis as illustrated in Fig. 151, where the lengths are respec- 
 tively 1 and 2. 
 
CHAPTER VII. 
 SOUND. 
 
 128. Nature of Sound. Sound is a sensation re- 
 ceived by the auditory nerve. It has its origin in some 
 vibrating body, as we may easily convince ourselves by 
 observation. If we touch a sounding string or bell we 
 perceive that it is in a state of vibration. Not only so, 
 but when we stop its vibrations by touching it the sound 
 ceases. The vibrations of the sounding body are con- 
 veyed to the -ear by waves in an elastic medium, usually 
 the air, which sets in vibration the drum of the ear. 
 The way in which the vibrations of the ear drum, after 
 being transmitted by the chain of bones in the middle 
 ear to the fluids of the inner ear, are analyzed and per- 
 ceived as separate impressions is not well understood. 
 In physics we are more directly concerned with the con- 
 ditions requisite for producing and transmitting to the 
 ear the vibrations. These are pouring in upon us from 
 every side even in our hours of sleep, and we cannot 
 shut them out as we shut out light. Indeed, the pre- 
 vention of the vibrations which produce sound must 
 one day become a very important factor in the comfort 
 and health of people who live in cities. 
 
 129. Noises and Musical Notes. The ear delights 
 
 207 
 
208 SOUND. 
 
 in order. A rapid succession of waves of the same sort 
 produces a pleasant impression upon the ear, while a 
 confused mingling of many sorts of waves produces 
 a sound which is disagreeable. The confused rattle of 
 a moving railway train, the squeaking of the wheels 
 against the track as a curve is rounded, and the flapping 
 of the brake shoes against the wheels are not pleasing 
 to the ear of the passenger, but when the train stops at 
 the end of a division and the wheel tester strikes each 
 wheel in turn with his hammer we notice that each 
 wheel gives a clear musical note. We shall find, if we 
 test various bodies like sticks, tables, dishes, stones, 
 iron bolts, indeed any hard body which is free from 
 loose parts, that each body has a definite note of its 
 own. 
 
 130. Vibrating Rods. If we select two wooden 
 rods of equal dimensions we shall find that they give 
 notes nearly alike. By sawing one into two unequal 
 
 FIG. 152. 
 
 parts we shall get two rods which will give notes which 
 are not like either the long rod or each other. Let us 
 see why there should be a difference between them. 
 Let Fig. 152 represent three wooden rods resting on 
 
BELLS AND PLATES. 209 
 
 bits of rubber tubing. They are alike in all respects 
 save length. If a blow be struck at S a wave will 
 travel to FJ where it will be reflected and return to S to 
 be again reflected. A series of waves will be 
 sent out into the air at intervals, which depend 
 upon the time taken for the wave to traverse 
 the stick. The ends of the stick are free and 
 are consequently antinodes. There will be 
 another antinode at the centre, with nodes at 
 points one fourth of the length of the stick 
 from each end. 
 
 The wave length of the stationary wave is 
 the same as the length of the rod. Each part 
 of the rod vibrates like a pendulum, and for rods 
 which are alike in all other respects the period 
 of vibration, like that of the pendulum, varies 
 with the square of the length. A thick rod 
 vibrates more slowly than a thin one of the 
 same length. Metal rods emit notes which 
 are purer and louder than those given by 
 wooden rods. The tuning fork (Fig. 153) 
 is a steel rod bent double and provided with 
 a handle at its middle point. The bending FlG - 154> 
 of the fork brings the nodes nearer together than they 
 would otherwise be, and the fork vibrates as indicated 
 in Fig. 154. 
 
 131. Bells and Plates. The vibrations of plates 
 are analogous to those of rods, while the vibrations of 
 
 T 
 
210 
 
 SOUND. 
 
 bells are somewhat similar to those of forks. When 
 a bell is struck as at A (Fig. 155), its form is altered 
 
 from the circular 
 a slightly elliptical 
 shape. Its elasticity 
 draws it back and 
 carries it past, as in 
 other vibrating bod- 
 ies. The result is to 
 set the bell vibrating 
 in four segments. 
 This may be beauti- 
 fully shown by filling 
 a jar or glass half full 
 of water and striking 
 the rim. The parts 
 next the antinodes will be thrown into ripples, while the 
 parts next the nodes remain comparatively quiet. If 
 the bell is struck at a point which is slightly heavier 
 than some point near it, this point will tend to become 
 a node 'and there will be a curious changing effect 
 known- as beats. This will be explained in Section 134. 
 
 132. Pitch. When two forks of different dimen- 
 sions are struck in succession we have no difficulty in i 
 deciding that the tones they give are different. If one 
 is much larger than the other we shall all agree that the 
 larger gives a tone which differs from that of the small 
 one, just as the tones of a man differ from those of a 
 
 FIG. 155. 
 
 
 
MUSICAL INTEEVALS. 211 
 
 child ; the long fork has a lower pitch, as we say. The 
 pitch of a note is determined by its vibration frequency, 
 n. The pitch of women's voices is, on the average, 
 twice as high as that of men. The pitch of a rod 20 
 cm. long is four times as high as that of a rod of the 
 same thickness but 40 cm. long. A tuning fork which 
 is not exactly of the proper pitch may be tuned by fil- 
 ing off the ends if it is too low or by filing it thinner 
 if it is too higlv The variation of pitch with frequency 
 may be easily shown by holding a card against a toothed 
 wheel which is made to revolve at different speeds, or 
 by directing a blast of air from a tube which has a small 
 nozzle toward a row of holes in a revolving disc of 
 cardboard or metal. Such a disc, called a siren, is usu- 
 ally provided with several rows of holes, so that the 
 pitch may be changed by passing the nozzle from one 
 row of holes to another without changing the speed of 
 the disc. If we let the speed of the toothed wheel or 
 siren fall till the frequency is less than about sixteen 
 vibrations per second, we shall begin to hear the separate 
 impulses. When the number of vibrations exceeds 
 40,000 per second we cease to be able to hear them at 
 all. It is quite probable that certain insects hear notes 
 which our ears are quite unable to perceive because of 
 their high pitch. 
 
 133. Musical Intervals. Consonance. Dissonance. 
 
 -When two musical notes are sounded at once the 
 effect upon the ear is sometimes pleasant and sometimes 
 
212 SOUND. 
 
 very disagreeable. It has been found that this difference 
 depends on the relative vibration frequency of the two 
 notes. The ratio of the frequency of two notes is 
 called the musical interval between them. If this inter- 
 val can be expressed by small numbers the combined 
 effect is pleasant to the ear, and the notes are said to be 
 consonant. Intervals which can be expressed only by 
 large numbers are dissonant. Primitive music concerned 
 itself mainly with the order of succession of the differ- 
 ent notes, the same tune being followed by all voices ; 
 modern music combines several tunes or parts in one 
 harmony, the variety and richness of which is still fur- 
 ther enhanced in the orchestra by employing instru- 
 ments which give tones of different quality. We shall 
 recur to the matter of quality in a later section, but it 
 will be found to be, after all, dependent upon frequency. 
 Vibrations differ only in two particulars frequency and 
 amplitude^ The amplitude of vibration determines the 
 loudness of the sound. The remaining characteristics 
 of a musical note, namely, pitch and quality, are depend- 
 ent upon the rate of vibration. 
 
 134. Beats. If two tuning jforks have the same 
 pitch they will, when sounded together, produce the 
 most perfect consonance. The interval is i. If now 
 we attach a bit of wax to a prong of one of the forks 
 its rate will be slightly diminished ; the waves from the 
 two forks when sounded together will interfere, first re- 
 enforcing, then destroying each other. The effect pro- 
 
OVERTONES OB PARTIAL S. 213 
 
 duced is called a beat. It is disagreeable, producing 
 much the same effect upon the ear that a flickering 
 light does upon the eye. The number of beats per sec- 
 ond is equal to the difference between the vibration 
 numbers of the two notes. Tuners of musical instru- 
 ments make use of beats in tuning the instrument. 
 They have only to seek to diminish the number of 
 beats until beats are no longer heard ; when the string 
 or pipe is known to be in unison with the standard fork. 
 Beats in bells are overcome to some extent by chipping 
 away with a chisel the parts which are too heavy. 
 
 135. Overtones or Partials. We saw in Section 
 125 that a body of limited dimensions, like a string 
 with its ends fastened, may vibrate as a whole or in any 
 whole number of equal parts. It has been found that 
 most vibrating bodies when vibrating as a whole also 
 vibrate in segments at the same tii^e. When a body 
 vibrates as a whole it gives the lowest note which it is 
 capable of giving. This is called its fundamental tone: " 
 The highest tones which it gives when vibrating in 
 parts are called partiah or overtones. When it vibrates 
 in two parts it gives its first overtone, in three parts its 
 second overtone, and so on. The first five partial tones 
 are perfectly consonant with the fundamental and each 
 other, for their intervals are all expressed in small num- 
 bers : f, f , f , |, A 4, etc . 
 
 The overtones given by any particular sounding body 
 will depend much upon the shape and material of the 
 
214 SOUND. 
 
 body itself. Since the overtones present in one voice or 
 instrument are different from those in another, the tone 
 produced by their combination with the fundamental will 
 be different. The pitch of the note we judge from the 
 pitch of the fundamental, which, if present at all, is usu- 
 ally the prevailing note. The minor differences produced 
 by the peculiarities of the instrument we call the quality 
 of the note. Strings break very readily into segments 
 and are therefore rich in overtones. A board can vi- 
 brate in almost any number of parts, yet has no marked 
 preference for its fundamental. Boards are therefore 
 well adapted to take up the vibrations of strings and 
 forks which are in contact with them, thus reenforcing 
 the note of the string or fork. 
 
 136. Resonance. Pipes. If one lifts the dampers 
 from all the strings of a piano and sings a single note, 
 the strings corresponding to the fundamental and the 
 principal overtones of the note sung will be set in vi- 
 bration and may be distinctly heard. A window in a 
 church will often be set rattling when a particular note 
 of the organ is sounded. This phenomenon is called 
 resonance. It is due to the fact that the resounding 
 body has the same natural period of vibration as the 
 sounding body, so that the impulses given by the sound- 
 ing body are timed just right to reenforce each other. 
 The reenforcement of a tuning fork by a column of air 
 is easily shown by holding a fork which has just been 
 struck over a tall jar and slowly pouring water into the 
 
RESONANCE. PIPES. 
 
 215 
 
 A 
 
 jar to shorten the air column. When the air column is 
 exactly the right length the fork will speak loudly 
 enough to be heard distinctly all over the room (see 
 Fig. 156). The bottom of the pipe will be a node and^ 
 the top will be an antinode, so that the length of the 
 column would be exactly 1 1 if. it were not for the fact 
 f, that the size and shape 
 
 of the opening at the 
 
 top changes slightly the 
 
 position of the antinode, 
 
 throwing it a little dis- 
 tance above the top of 
 
 the. jar. If a jar three 
 
 times as tall as the short- 
 est column of air which 
 
 will reenforce the fork 
 
 is used resonance will 
 
 again occur, for the air 
 
 column will break into 
 
 segments, as shown in 
 FIG. 156. Fig. 15T. The reso- 
 nance of air columns is employed in organ pipes, the 
 pipes being made of the proper length to reenforce the 
 different notes. The air is set into irregular vibrations 
 by being blown against the mouthpiece in Fig. 158. 
 Those vibrations which are of the right period to be 
 reenf orced by*the pipe are the ones which we hear. The 
 closed pipe, like the resonance jar, is one fourth the 
 length of a wave in air.- The open pipe (Fig. 159) has 
 
 FIG. 157. 
 
216 SOUND. 
 
 an antinode at each end. Its length, therefore, is half 
 a wave length, hence it must be twice as long as a closed 
 pipe which is to give the same 
 note. 
 
 Organ pipes are often pro- 
 vided with reeds like the reeds 
 of an accordion or harmonica 
 (mouth organ). Organ pipes 
 are often lacking in some of the 
 higher overtones. The lack is 
 made good by smaller pipes 
 which are so connected to the 
 keys as always to speak when 
 the fundamental does. 
 
 Such wind instruments as the 
 
 flute and cornet have means of FIG * 159> 
 FIG. 158. 
 
 varying the length of the air column to pro- 
 duce a number of different notes. Each of the funda- 
 mental lengths can be made to serve for a number of 
 notes by varying the tension of the lips and the pressure 
 of the breath, as is done in the bugle. The fundamental 
 note of such instruments is not used. 
 
 137. Velocity of Sound Waves. The resonance 
 jar furnishes a convenient method of measuring the 
 velocity of sound in air. Thus in Fig. 160 
 
 (34) NN= I I 
 v = nl 
 
 whence : (36) v = 2n NN 
 
VELOCITY OF SOUND WAVES. 
 
 217 
 
 where the vibration number of the fork is supposed to 
 be known. The velocity of sound varies inversely with 
 the square root of the density of the 
 medium. Since, therefore, air expands 
 by heating, sound travels faster in 
 warm air than in cold. The velocity of 
 sound in air at C. is 332 metres per 
 second. At any temperature, t, it is 
 
 FIG. 160. 
 
 (37) v = 332 t/ 1 + .004 t 
 
 since air expands ^-^ = .004 for each 
 degree Centigrade above C. 
 
 The velocity of sound in solids may 
 be found by a beautiful method due to 
 Professor Kundt. He clamps a rod at 
 its middle point and attaches a cork 
 to one end, which is allowed to project 
 into a long glass tube (see Fig. 161). The bottom of 
 the tube as it lies in a horizontal position is covered with 
 fine cork filings, and the other end of the tube is closed 
 with a movable cork which fits snugly and is used to 
 
 
 FIG. lei. 
 
 vary the length of the tube. The rod is stroked with 
 a rosined cloth and thus set into rapid longitudinal vibra- 
 tions. The cork, which fits loosely in the tube, sets the 
 air in the tube in vibrations, which by reflection from 
 the farther end produce stationary waves in the tube. 
 
218 SOUND. 
 
 The dust at the antinodes is violently agitated and falls 
 into little ridges when the sound ceases. The distance 
 between the antinodes is easily measured. The middle 
 of the rod is a node and the ends antinodes. The length 
 of the rod is, therefore, half the length of a wave in the 
 solid. If v a is the velocity of sound waves in air at 
 the given temperature, then v s , the velocity in the solid 
 used, is 
 
 where l s , l a are the lengths of a wave in the solid and 
 in air respectively. 
 
 It should be borne in mind that all stationary waves 
 are caused by the interference of waves reflected from 
 
 FIG. 162. 
 
 opposite bounding surfaces. The length of a wave 
 may be measured, also, by the interference of two waves 
 from the same point, which travel by different paths to 
 a second point, as shown in Fig. 162. If one branch 
 of the rubber tube is half a wave length longer than 
 the other for waves of the frequency of the fork 
 which is vibrating at S, the waves will meet at E in 
 
VIBRATING STRINGS. 219 
 
 opposite phase and produce silence. An interesting 
 example of the production of silence by the interfer- 
 ence of two sound waves is the case of a tuning fork. 
 If a vibrating tuning fork be slowly rotated near the 
 ear or over a resonance jar, four positions may be found 
 where no sound is heard. 
 If while the fork is in 
 one of these positions a 
 paper tube be slipped 
 over one prong of the R */i\ 
 
 fork so as not to touch 
 it, the sound will again 
 be heard. This is read- , 
 
 rIG. loo. 
 
 ily understood by refer- 
 ring to Fig. 163. When the prongs approach each other 
 condensations are sent toward (7, rarefactions toward R. 
 At all points on the diagonal lines, which are equally 
 distant from and R, the waves will meet in opposite 
 phases and destroy each other. 
 
 138. Vibrating Strings. We have referred so 
 often to the vibrations of stretched strings that the 
 nature of these vibrations should now be pretty well 
 understood. The mathematical laws governing the 
 vibration frequency of strings are easily demonstrated 
 by experiment. They may be stated as follows : 
 
 The number of vibrations per second of a tightly 
 stretched string which is giving its fundamental note 
 is : 
 
220 SOUND. 
 
 1. Inversely proportional to its length. 
 
 2. Directly proportional to the square root of the 
 tension. Vy 
 
 3. Inversely proportional to its linear density. 
 These three laws may be summed up in one formula : 
 
 where L is the length of the string, / is the tension in 
 dynes, and m the mass per unit length of the strings. 
 
 These laws are all exemplified by such stringed in- 
 struments as the guitar and the violin. The player 
 raises the pitch of any string by touching it so as to 
 shorten the vibrating portion. He raises the pitch in 
 tuning by increasing the tension. The heavy strings 
 are the ones which give the lower notes. 
 
 The point at which a string is struck or bowed affects 
 its quality by determining to some extent what over- 
 tones shall be present. The hammers of a piano are so 
 placed as to prevent the occurrence of a certain higher 
 overtone which is not consonant with the others. Over- 
 tones are often spoken of as harmonics. This term 
 should be applied only to such overtones or partials as 
 are consonant with the fundamental tone. 
 
 139. Musical Scales. The foundation of all our 
 music is the scale of eight notes, the eighth or octave of 
 which has just double the frequency of the first. The 
 relative frequencies of the major scale are variously 
 
MUSICAL SCALES. 221 
 
 represented in lines 1, 2, and 3, the absolute frequencies 
 in lines 4, 5, and 6. 
 
 1. % % % % % % 15 /8 % 
 
 2. First Second Third Fourth Fifth Sixth Seventh Octave 
 
 3. Do Ke Mi Fa Sol La Si Do 
 
 F5? 
 
 
 
 
 
 
 
 /<3 
 
 EBE:: 
 
 
 
 
 ^-. 
 
 2 
 
 <S> 
 
 
 
 r ^. 
 
 P 
 
 
 
 
 
 
 
 c' 
 
 d' 
 
 e' 
 
 f 
 
 o-' 
 
 o 
 
 a' 
 
 b' 
 
 c" 
 
 264 
 
 297 
 
 330 
 
 352 
 
 396 
 
 440 
 
 495 
 
 528 
 
 5. 
 
 6. 
 
 This scale is made up by combining three major triads, 
 and is therefore known as the major scale. The major 
 triad is so called because it is composed of three notes 
 which, when sounded together, give the most perfect 
 harmony, namely, the first, third, and fifth, or, Do, Mi, 
 Sol. If we add the octave it gives us the major chord. 
 Helmholtz pointed out that the reason for the perfect 
 consonance of the major triad lies in the fact that no 
 beats occur between any of the overtones of any tone 
 either with the fundamentals or overtones of any other 
 of the triad. This may be illustrated by an example. 
 
 FIRST THIRD FIFTH 
 
 Fundamental 200 250 300 
 
 First partial 400 500 600 
 
 Second 600 750 900 
 
 Third 800 1,000 1,200 
 
 Fourth 1,000 1,250 1,500 
 
 Fifth 1,200 1,500 1,800 
 
222 SOUND. 
 
 It will be seen that there is unison between the second 
 partial of the first and the first partial of the fifth, as 
 also between the fourth partial of the first and the third 
 partial of the third. Indeed, there are four pairs in 
 unison. But in no case is the difference between the 
 number of vibrations of any pair less than the difference 
 between the fundamentals of the first and fifth. By 
 way of contrast let us compare the second, fourth, and 
 sixth. 
 
 SECOND FOURTH SIXTH 
 
 Fundamental 225 267 333 
 
 First partial 450 534 666 
 
 Second 675 801 999 
 
 Third 900 1,168 1,332 
 
 Fourth 1,125 1,335 1,665 
 
 Fifth 1,350 1,582 1,998 
 
 The combination 666 and 675 is bad, but when we 
 combine 1,350, 1,335, and 1,332 the effect is wholly 
 unpleasant. 
 
 The relative frequencies of the major triad, as will be 
 seen from the table, are : 
 
 Vl : % : % 
 c' : e' : g' 
 
 or, expressed in whole numbers : 
 
 4:5:6 
 c' : e' : g' 
 
 If we form a second triad taking c" as 6, and still an- 
 other taking g' as 4, we have : 
 
' MUSICAL UCALES. 223 
 
 4:5:6 
 c' : e' : g' 
 
 f : a' : c" 
 g' : V : d" 
 
 From which we obtain : 
 
 f : c" = f : 2c = 4 : 6 whence f = % c' 
 a' : c" = a' : 2c = 5 : 6 whence a' = % c 
 g' : b' =4:5 and g' : c' = 6 : 4 .-. b' = 1% c ' 
 
 The major scale is thus seen to be composed of three 
 major triads. 
 
 It is readily seen on inspecting the table of intervals 
 below that there are five intervals of nearly equal mag- 
 nitude and two which are only about half as large. 
 The former are called full tones, the latter semitones. 
 Note, c' d' e' f g' a' b' c" 
 
 iveiative -, , ^ , ~/ */ o / K / - K / r> / 
 
 frequency, % % % % % % '% % 
 
 Intervals, % 10 /9 16 /15 % 10 /9 % 16 /15 
 
 To make possible the writing of music in scales 
 higher than the one just shown (which is known from 
 its keynote as c major) semitones have been inserted 
 between c' and d' and in the other intervals, which are 
 full tones, by sharping or flatting the notes that is, by 
 raising them ^ or by lowering them ^V Thus: c# 
 (c sharp) is equal to || c, while d!7 (d flat) is |-| d. 
 The semitone added is not halfway between c and d, 
 and ctf and d'p are not identical, for c# = JJ c = 
 | . 264 = 275, while dfr = d = 297 = 285. 
 
224 SOUND. 
 
 In ascending the scale sharps are used, in descending 
 flats are used. The scale of eighteen notes thus formed 
 is called the chromatic scale. 
 
 The tempered scale was devised for use with instru- 
 ments like the piano and organ, which, unlike the violin 
 and the voice, must have a separate string or pipe of 
 fixed length for each note. To avoid the excessive 
 number of notes required the octave is divided into 
 twelve equal intervals, each of which has a frequency 
 
 12 / 
 
 equal to y 2 =1.059 times the note below. This 
 arrangement necessitates throwing all intervals except 
 the octave slightly out of tune. Long use makes us 
 accustomed to the lack of perfect harmony, so that we 
 give little heed to it. The human voice can hardly be 
 at its best, though, when accompanied by the piano. 
 
 The progress of music as an art side by side with the 
 science of music is a good example of the interdepend- 
 ence of all human efforts. 
 
 Exercises. 
 
 108. (a) What length of closed organ pipe will give c'? 
 (6) What note will an open pipe of the same length give ? 
 
 109. (a) Compute the linear density of a string of a mono- 
 chord (Fig. 164) after measuring its diameter. Make the 
 other measurements necessary for computing n in formula (39). 
 (6) Calculate n by means of a resonance tube made of a large 
 glass tube with a piston for varying its length, and see how the 
 two values agree. 
 
 no. What is the velocity of sound waves in a brass rod 120 
 cm. long which excites waves 24 cm. long in a Kundt's tube? 
 The temperature of the air was 20 C- 
 
EXERCISES. 225 
 
 in. (a) Will a tuning fork vibrate longer in tne hand or 
 resting on a table? (6) In which place will it give the louder 
 sound ? Explain. 
 
 112. An echo is sent back (by reflection) from a barn. The 
 last of a series of words requiring five seconds to utter can be 
 spoken just before 
 
 the first word is 9 ^ 
 
 returned. The HSj 
 
 air is at the tem- 
 perature of freez- 
 ing water. How 
 far away is the 
 barn? FlG ' 164 ' 
 
 113. Two telegraph sounders are on the same circuit, which 
 is closed twice a second by a pendulum. One sounder is by 
 the observer's side, the other is 550 feet away. What is the 
 velocity of sound if the two sounders seem to tick in unison ? 
 
 114. A stone is dropped down a well. After two seconds 
 the splash of the stone in the water is heard. How far is the 
 surface of the water below the top of the well ? 
 
 115. (a) An organ pipe gives a note of frequency 264 at 
 16 C. What will it give at 28 C.? (6) Would a piano string 
 which is in tune with the pipe at 15 be in tune at 28 C.? 
 
 116. A tuning fork placed at S (Fig. 162) gives the mini- 
 mum sound at E when the long arm of the tube is 65 cm. 
 longer than the short arm. The temperature is 20 C. What 
 is the pitch of the fork ? 
 
CHAPTER VIII. 
 LIGHT. 
 
 140. The Sensation of Light. Light is a sensation 
 which is peculiar to the optic nerve. It may be pro- 
 duced in various ways, but is usually the result of dis- 
 turbances in external objects which are transmitted to 
 the eye as waves. What we have learned of Avaves in 
 general and of sound waves will be of use to us in the 
 study of light. It is common to call by the name light 
 the cause of the sensation of light as well as the sensa- 
 tion itself, and no serious confusion need result from 
 our using the term in both senses. 
 
 141. Definitions. Every body which is at any in- 
 stant visible to us is said to emit light at that instant. 
 A small class of bodies emit light regardless of the 
 presence or absence of other luminous bodies. Such., 
 bodies are said to be self-luminous. They are usually, 
 though not always, very hot, like the sun or a gas 
 flame. Bodies through which objects are clearly visible 
 are transparent, as water and glass. Bodies which are 
 not transparent but yet alloAV much light to pass through 
 are translucent. Such are milk, ground glass, opal. 
 Bodies which allow no light to pass are opaque. Most 
 solid bodies (not crystals) are of this class. 
 
LIGHT FROM A POINT. SHADOWS. 
 
 227 
 
 142. Light from a Point. Shadows. Every lu- 
 minous body may be thought of as made up of a large 
 number of luminous points. If light is a disturbance 
 which spreads from a 
 luminous point in a uni- 
 form medium it will 
 advance with equal ve- 
 locities in all directions 
 until it meets a differ- 
 ent medium. Let tS 
 (Fig. 165) be such a FIG. 165. 
 
 luminous point. The wave fronts are concentric spheres 
 and are always perpendicular to radii drawn from S as a 
 centre. An opaque object as 0' cuts off all that portion 
 of the waves which strikes it, leaving a space POOP 1 
 
 which is not illumi- 
 nated by /SI This 
 agrees with what we 
 have all observed. 
 It is commonly ex- 
 pressed by saying 
 that light travels in 
 straight lines. The 
 normal to a wave front is often called a "ray." We 
 shall hereafter understand the word ray in that sense. 
 The shadow cast by a luminous surface has not sharp 
 outlines, since there are portions which lie in the shad- 
 ows of some points and yet are illuminated by other 
 points. Fig. 166 shows the shadow cast by a luminous 
 
228 
 
 LIGHT. 
 
 surface. There are supposed to be an unlimited num- 
 ber of points between S and /S\. The space between 
 P and Q receives light from an increasing number of 
 these points as we proceed from P to Q. The space 
 between P and Q' receives no light from >S>S r It is 
 called the umbra, or full shadow. The rest of the space 
 between Q and P' is called the penumbra, or partial 
 shadow. During a partial eclipse of the sun that part 
 of the earth where the eclipse is seen passes into the 
 penumbra of the shadow cast by the moon. During a 
 total eclipse the observer is in the umbra. 
 
 143. Pictures by Small Openings. A beautiful 
 illustration of the rectilinear propagation of light is 
 
 furnished by 
 making a single 
 small opening 
 thro u g h the 
 side of a box 
 FIG. 167. ' and fastening 
 
 a sheet of paper against the side opposite the opening. 
 If we follow the light from two points of an object, as 
 SS l (Fig. 167), till it strikes the paper, we see that for 
 every point of the object there is a corresponding spot 
 on the paper. The result is to give us, on the paper, an 
 inverted picture, or image as it is- called, of the object. 
 The image is, however, faint if the hole is very small, 
 and blurred if the hole is larger, for the spots S'SJ are 
 not points, but circles larger than the opening. 
 
PICTUEES BY REFLECTION. 
 
 229 
 
 All our perception of the forms of objects is condi* 
 tioned upon the formation of images upon the sensitive 
 wall (retina) of the eye. We shall now explain the 
 ways in which images may be formed which are much 
 more perfect in detail as well as more brilliantly illumi- 
 nated than the pinhole images just described. 
 
 144. Pictures by Reflection. We learned in our 
 study of waves that a wave after reflection from a 
 
 FIG. 168. 
 
 plane surface makes an angle equal to the angle of 
 incidence, but in the opposite direction. Every reflect- 
 ing surface is plane for a very small area at any point on 
 the surface. The angle made by a wave at any point 
 on a curved surface with the surface at that point is the 
 angle which it makes with a plane tangent to the surface 
 at the point. Let us bear in mind that the difficulty with 
 our pinhole image is that the light from AS' which falls 
 exactly at 8' (Fig. 167) is only that which travels along 
 
230 
 
 LIGHT. 
 
 the radius SS' 9 and if we attempt to get more light by 
 making the hole larger, none of the additional light 
 admitted falls exactly upon S', but only near it, making 
 a confused image. The problem is, then, to make a 
 large portion of the waves winch diverge from S meet 
 at S'. This can only be done by changing the direction 
 of the waves in some regular manner, such that those 
 which diverge most from the radius SS 1 shall be bent 
 
 M' 
 
 more than those which diverge less. This is accom- 
 plished if the waves are reflected from a spherical sur- 
 face MM', as in Fig. 168, where all the waves from S 
 which strike the mirror meet at $', which is called the 
 image of 8. The light after reflection seems to an eye 
 at E to diverge from S'. A series of such images 
 arranged symmetrically with corresponding points in 
 the object 'bofistitute a real image of the object. When 
 the mirror is of such a form that the waves do not 
 
PICTUEE8 BY REFLECTION. 
 
 231 
 
 really diverge from centres, but only seeni to do so, the 
 image is said to be virtual. ' Thus the convex mirror in 
 Fig. 169 makes the waves from 8 diverge still more 
 than they did before striking the mirror, but they seem 
 to diverge from a point S' behind the mirror where 
 there are really no waves from S, and 3' is said to be a 
 virtual image of S. 
 
 A plane mirror also gives a virtual image, but the 
 
 amount of divergence of the waves is unchanged 
 (see Fig. 170). It is easily shown that the image of a 
 point in a plane mirror lies in a line drawn from the 
 point perpendicular to the mirror and as far beliind the 
 mirror as the point is in front. Let $' { T7 ig. 171) be 
 the image of S in a plane mirror, and $J^a ^perpendic- 
 ular to the mirror. S' must lie on the line SP pro- 
 
232 
 
 LIGHT. 
 
 duced, since SP is at once perpendicular to the mirror 
 and the wave front, making the angle of incidence zero. 
 Let SQ be the direction of another portion of the wave 
 which strikes the mirror at Q and draw RQ perpendicu- 
 
 FIG. 171. 
 
 lar to the mirror at Q. Let QS n be the direction of 
 propagation of the wave after reflection from Q. 
 Angle PSQ = Angle SQR 
 SQR = RQS" 
 EQS= PS'Q 
 whence: PSQ = PS'Q 
 
 In the right triangles SPQ and S'PQ the sides PQ are 
 identical, and angles PSQ and PS'Q are $qual. The 
 triangles, therefore, are equal and PS 1 = PS. 
 
 145. Position of the Image of an Object. To de- 
 termine the position of the image of an object we may 
 
POSITION OF THE IMAGE OF AN OBJECT. 233 
 
 locate the image of two or more prominent points. In 
 the case of plane mirrors this is easily done by drawing 
 perpendiculars through the mirror to points as far be- 
 hind the mirror as the luminous points are in front 
 of it. In the case of spherical mirrors it might be 
 done by drawing any two radii till they meet after 
 reflection. The measurement of angles is, however, less 
 easy than the measurement of lines, and it happens that 
 there are two radii (or rays as they are commonly called) 
 which can always be drawn without measuring the 
 angles. Let MM' 
 (Figs. 172 and 
 173) be a spherical 
 mirror drawn from 
 C as a centre. A 
 line through 
 perpendicular t o 
 the centre of the 
 mirror is called the FIG - 172 - 
 
 principal axis of the mirror. All waves passing along 
 a ray drawn through C are reflected back along the same 
 ray. It can be proved that all waves moving along 
 rays drawn parallel to the principal axis, CX, will be 
 reflected along rays which pass through a point jP, half- 
 way between O and the mirror. This point is called 
 the principal focus.* It is the place where plane waves, 
 like those from the sun or any distant object, meet after 
 reflection. Let it be required to find the image of an 
 
 * Latin focus, fireplace. 
 
234 
 
 LIGHT. 
 
 object SS r Draw SPF, making SP parallel to OX. 
 Draw SCQ. Their point of intersection S' is the image 
 of 8. Find the image of ^ in the same manner. Join 
 them and we have the image of the object. For differ- 
 ent positions of the object the position of the image 
 will be different, but the method of finding the position 
 of the image is always the same. 
 
 The statement that all rays parallel to the principal 
 axis pass through the principal focus is only true if the 
 mirror is a small segment of a sphere. Large mirrors 
 
 FIG. 173. 
 
 must have a correspondingly large radius of curvature. 
 Spherical mirrors are but little used in optical instru- 
 ments, the reflecting telescope being almost the only 
 example of their use. They are much employed for 
 collecting and directing the light of signal lamps, loco- 
 motive headlights, and the. like, where no accurate 
 image is required. If the lamp is placed at the focus 
 of a concave mirror the reflected rays will be parallel. 
 By moving it toward the mirror any desired amount 01 
 divergence may be produced. By moving it away from 
 
PICTURES BY REFRACTION. 
 
 235 
 
 the mirror the light may be made to converge at any 
 desired point. 
 
 146. Pictures by Refraction. We have seen in 
 Section 127 that, in general, waves suffer a change of 
 direction in passing from one medium to another. . 
 Let LL (Fig. 174) be a segment of a sphere, of 
 glass say, made by a plane passing at some distance 
 from the centre, so that it shall be but a small seg- 
 ment of a sphere, or by the intersection of two 
 spheres. It is a lens. When convex on both sides, 
 it is called a double-convex lens. Light waves from 
 S which fall upon LL (Fig. 175) will be in part re- -L 
 fleeted, but we are at present concerned with the 174.' 
 part that passes through the lens. The waves strike the 
 central part of the lens first, and are retarded, since 
 
 the velocity in glass is less than in air. In the case 
 
 shown in Fig. 175 the waves in the glass are nearly 
 
 ' plane. The portions of the wave farthest from the axis, 
 
 (7(7, emerge first and gain upon the part that has not 
 
236 
 
 LIGHT. 
 
 yet emerged, so that when the wave is again in air its 
 curvature has been reversed, and it converges at S'. 
 
 All lenses which are thicker at the centre than at the 
 edge converge the waves and are called converging 
 
 lenses. Three kinds of con- 
 verging lenses are shown in 
 Fig. 176, namely: (1) double- 
 convex, (2) plano-convex, 
 (3) concavo-convex. 
 
 The principal focus of a 
 converging lens is easily found 
 by experiment. It is the place 
 of convergence of plane 
 waves which have passed through the lens. In a double- 
 convex lens of flint glass with equal curvatures on its 
 
 FIG. 177. 
 
 two sides, the focus is not far from the centre of cur- 
 vature. The distance OF (Fig. 177) is called the focal 
 length of the lens. 
 
 An object placed at a distance 2 OF from the lens 
 will be focused at an equal distance on the opposite 
 
IMAGES FORMED BY LENSES. 
 
 237 
 
 FIG. 178. 
 
 side at F', which is sometimes called the secondary 
 focus. 
 
 Objects outside F' will be focused between F and F', 
 and objects between F and the lens will be focused out- 
 side F'. 
 
 Lenses 
 which are 
 thicker at the 
 edges than in 
 the centre in- 
 crease the di- 
 vergence of 
 
 waves and are called diverging lenses. Since they can- 
 not cause divergent waves to converge, they never form 
 real images, but only virtual ones (see Fig. 178). 
 
 Three forms of diverging lenses are shown in Fig. 179, 
 
 namely: (1) convexo- 
 concave, (2) plano-con- 
 cave, (3) double-concave. 
 Diverging lenses are 
 used by draughtsmen to 
 enable them to judge 
 how a drawing will ap- 
 pear when reduced in 
 size. They are used also 
 in spectacles for near-sighted persons. Most lenses used 
 in optical instruments are converging. 
 
 147. Position of Images Formed by Lenses. As 
 in mirrors, so in lenses, if we find where two rays from 
 
238 
 
 LIGHT. 
 
 a point meet again we have found the image of that 
 
 point. 
 
 Rays parallel to the 
 principal axis are re- 
 fracted so as to converge 
 at the focus. Waves 
 which pass through 0, 
 the optical centre of the 
 lens, suffer no perma- 
 nent change of direction, 
 but only a slight dis- 
 placement to one side, 
 like light which has 
 
 FJG 18() passed through a plate 
 
 with parallel sides (see 
 
 FIG. 181. 
 
 Fig. 180), for the 
 faces -at points 
 intersected by a 
 line through the 
 centre are par- 
 allel. - 
 
 To find the 
 
 FIG. 182. 
 
SOME OPTICAL INSTRUMENTS. 
 
 239 
 
 image of an object, SS^ (Figs. 181 and 182), we first 
 find the image of S by drawing rays 8PF and SQ and 
 producing them till they meet at S'. The image of S 1 
 is found in a similar manner. The image is found to be 
 real and inverted in one case, virtual and upright in the 
 other. 
 
 The two cases shown are typical and all other cases 
 may be treated in the same manner. 
 
 148. Some Optical Instruments. The simplest 
 optical instrument is the magnifying glass, or simple 
 
 microscope. 1 1 
 
 consists of a con- 
 
 verging lens. 
 
 The object is 
 
 placed between 
 
 F and the lens, 
 
 and the image is FlG - 183 - 
 
 virtual, upright and enlarged, as shown in 
 
 Fig. 183. 
 
 The compound microscope (Fig. 184) con- 
 sists of a small 
 
 converging lens 
 
 of short focus, 
 FIG. 184. called the ob- 
 jective, which is placed near 
 the object and forms an in- 
 verted real image at the 
 upper end of the tube, and FlGt 
 
240 
 
 LIGHT. 
 
 FIG. 186. 
 
 a second converging lens called the eyepiece, which is a 
 
 single or double magnifying lens used to view the image 
 
 formed by the objective. 
 
 The camera consists of a dark box having a lens, L 
 (see Fig. 185), at the front which forms a 
 real inverted image on a screen at the back. 
 The distance between lens and screen, ss, 
 may be varied to bring objects at different 
 distances into focus. The screen may be 
 removed also, and replaced by a sensitive 
 plate. A diaphragm, d, often of the form 
 
 shown in Fig. 186, may be turned so as to control the 
 
 amount of light admitted through the lens. 
 
 The eye is very like a camera. It has a lens called 
 
 the crystalline lens, 
 
 L (Fig. 187), a sen- 
 sitive membrane, the 
 
 retina, r, at the back 
 
 to receive the image, 
 
 a diaphragm, the iris, 
 
 i, for varying the 
 
 amount of light, and 
 
 an arrangement for 
 
 adjusting the focus 
 
 for near or distant 
 
 objects. 
 
 This adjustment is 
 
 called accommodation, and is accomplished by changing 
 
 the curvature of the lens by means of certain muscles 
 
 at its circumference. 
 
 FIG. 187. 
 
SOME OPTICAL INSTRUMENTS. 241 
 
 Many eyes are faulty in having the retina too near to 
 or too far from the lens. When the retina is too far 
 back the object must be brought near in order to be dis- 
 tinctly seen. The person is near-sighted and should 
 wear concave glasses. When it is too near the person 
 is far-sighted and should wear convex glasses. 
 
 When the normal eye is at rest it is in focus for dis- 
 tant objects. Near objects are seen only by bringing 
 into use the muscles of accommodation. At about forty 
 years of age we begin to lose the power of accommoda- 
 tion and must wear glasses for reading, though distant 
 objects are still seen distinctly. 
 
 There are other errors of vision which the skilled 
 oculist can correct. One who has any difficulty with 
 
 c P 
 
 FIG. 188. 
 
 his eyesight should consult an oculist without delay. 
 Errors of vision cause headache and may, if uncorrected, 
 lead to inflammation of the eye and serious impairment 
 of vision. 
 
 The magic lantern, or stereopticon, consists of a pair 
 of lenses called the condenser, (Fig. 188), the pur- 
 pose of which is to collect the light from a bright 
 
242 LIGHT. 
 
 source, S, like an arc lamp, and make it converge upon 
 a projection lens, L. Between C and L and very close 
 to the former is placed, inverted, the transparent pic- 
 ture, jt?, an image of which is thus projected upon a 
 large screen at ss. 
 
 COLOR. 
 
 Up to this point we have considered only the forms 
 of images. We all know, however, that the color of an 
 object has often as much to do with its appearance as 
 the form. The image formed in the camera is a col- 
 ored image, though the ordinary photograph reproduces 
 only the lights and shades of the picture and not its 
 color. 
 
 The eye, unlike the photographic plate, distinguishes 
 differences in the appearance of objects which have 
 exactly the same shape, as when ripening fruit or 
 autumn leaves change from green to red. 
 
 According to Helmholtz, the eye is sensitive to three 
 fundamental impressions, namely, red, green, and violet. 
 The hundreds of colors which we are able to distinguish 
 result from the blending of these three fundamental 
 sensations in varying proportions. What we call white 
 light is the mixture of equal parts of the three. 
 
 149. Color by Refraction. The Spectrum. The 
 
 compound nature of white light was shown by Newton 
 in a beautiful experiment which may easily be repeated 
 by any one. Sunlight is admitted to a darkened room 
 
COLOR BY REFRACTION. THE SPECTRUM. 243 
 
 through a small hole in a shutter and allowed to fall 
 upon a prism of glass, as shown in Fig. 189. The light 
 will be refracted, as we know already, but it will not 
 all be refracted to the same extent. The result is to 
 give us a row of images of the opening, forming a beau- 
 tiful band of colors called a spectrum. 
 
 If the opening is circular the images will overlap 
 and the colors will be mixed, but if a narrow slit is used 
 the colors are pure. 
 
 The rainboiv is a great spectrum produced by the 
 
 FIG. 189. 
 
 refraction of light in drops of water. Close observation 
 Avill show that the arrangement of the colors is the same 
 as in Newton's spectrum. 
 
 It is now known that the difference in light waves 
 which causes a difference in refrangibility and also in 
 color is one of wave length. The unit of wave length 
 is the millionth of a millimetre. The shortest visible 
 waves are the violet, 380 units long, and the longest 
 are the red, reaching to 688. Between these limits are 
 waves of every possible length. 
 
244 
 
 LIGHT. 
 
 The violet sensation is excited most by waves in the 
 neighborhood of 450, but as far as 380 on the one side 
 and 560 on the other. The relative effect of the differ- 
 ent wave lengths in producing the violet sensation is 
 shown by the height of curve F(Fig. 190). 
 
 The green sensation is excited most strongly by 550, 
 but responds to Avaves from 440 to 640 (see 6r). 
 
 The maximum effect of the red is at 570, but it ex- 
 tends as far as 480 and 688 (see 7T). 
 
 It will be seen that the waves between 480 and 560 
 
 excite to some 
 extent all 
 three of the 
 primary s e n- 
 sations in the 
 retina of the 
 eye. The ef- 
 fect of excit- 
 ing the violet 
 and the green 
 
 at the same time is to give us the sensation of blue, 
 which may be a deep indigo if but little green is present, 
 or an emerald if but little violet is present. 
 
 In the same way yellow and orange result from mix- 
 ing the sensations of green and red. 
 
 The mixture of red and violet gives purple, a color 
 
 which does not appear in the spectrum, since there are 
 
 no waves which excite both red and violet, and not green. 
 
 Any pure hue mixed with white gives tints; mixed 
 
 700 
 
 650 
 
 550 
 
 500 
 
 150 
 
 350 
 
 Draw Trtlot Green Blu Indigo Vlolii 
 
 FIG. 190. 
 
COLOR MIXTURE. 245 
 
 with black, shades. Thus the browns are shades of 
 orange and sky blue is a tint of blue. 
 
 150. Color Mixture. If a circular disc be divided 
 into three equal sectors, each of which is painted one of 
 the primary colors, red, green, violet, as in Fig. 191, the 
 disc will show, when rapidly rotated about its centre, no 
 one of these colors, but will appear gray. If the colors 
 were perfectly pure it would appear white, but the black 
 in them gives the mixture a gray appearance. A smaller 
 disc having white and black segments may be placed 
 over the colored disc, and, if the black and white are in 
 the right proportions, the two grays will match. 
 
 The reason that the separate colors are not seen when 
 the disc is in motion is that any impression produced 
 upon the retina persists for a fraction of a second, so 
 that each of the colors in the rotating disc affects the 
 retina the same as if the others were not present. The 
 result is that three colored images fall upon the same 
 spot of the retina, and, since these colors excite all the 
 sensations that white light is able to excite, and in the 
 same proportions, the effect produced is that of white 
 light. If the colors were as bright as those of the spec- 
 trum the mixture would be white. Since the colors are 
 all more or less mixed with black, it is in reality gray. 
 
 A convenient plan for mixing the colors in any de- 
 sired proportions is to make a number of discs like the 
 one shown in Fig. 192, and paint each a different color. 
 The discs have each a radial slit so that they may be 
 
246 LIGHT. 
 
 slipped one upon the other, as shown in Fig. 193. They 
 may then be turned so as to expose to view any desired 
 proportions of the different colors. 
 
 Another method of mixing the sensations is to rule 
 alternate lines of the colors very close together, as in 
 Fig. 194. The images are not kept distinct by the eye, 
 but blend together and give the composite color, orange 
 or blue. 
 
 Experiment shows that a mixture of red and green- 
 ish blue produces gray. This should be so, since blue 
 is composed of green and violet. Similarly, yellow and 
 indigo blue produce gray, since together they contain all 
 the primary colors. 
 
 Such pairs of colors are called complementary colors. 
 A number of such pairs are shown in the following 
 table : - 
 
 COLOR COMPLEMENTARY 
 
 Red Greenish blue 
 
 Orange Blue 
 
 Yellow Indigo 
 
 Green Purple 
 
 Bluish green Red 
 
 Blue Orange 
 
 Indigo Yellow 
 
 Violet Greenish yellow 
 
 The colors made by mixing pairs of spectrum colors 
 are shown in the following table, where the mixture of 
 any color named in the top row with any color in the 
 left-hand column will be found at the intersection of 
 the corresponding row and column: 
 
FIG. 191. 
 
 FIG. 192. 
 
 FIG. 193. 
 
 FIG. 194. 
 
COLORS BY ABSORPTION. 
 
 247 
 
 
 Violet 
 
 Indigo 
 
 Blue 
 
 Blue 
 Green 
 
 Green 
 
 Yellow 
 
 Red 
 
 Purple 
 
 Dark 
 Rose 
 
 Light 
 Rose 
 
 White 
 
 Light 
 Yellow 
 
 Orange 
 
 Orange 
 
 Dark 
 Rose 
 
 Light 
 Rose 
 
 White 
 
 Light 
 Yellow 
 
 Yellow 
 
 
 Yellow 
 
 Green 
 Yellow 
 
 Light 
 Rose 
 
 White 
 
 Light 
 Green 
 
 Light 
 Green 
 
 Green 
 Yellow 
 
 
 White 
 
 Light 
 Green 
 
 Light 
 Green 
 
 Green 
 
 
 
 Green 
 
 Light 
 Blue 
 
 Green 
 Blue 
 
 Blue 
 Green 
 
 
 
 
 Blue 
 Green 
 
 Green 
 Blue 
 
 Green 
 Blue 
 
 
 
 
 
 
 Blue 
 
 Indigo 
 
 
 
 
 
 151. Colors by Absorption. Pigments. What we 
 call the color of an object is the color which it shows 
 when illuminated by white light. The reason that dif- 
 ferent objects have different colors is that they do not 
 reflect all colors in the same proportion. 
 
 When white light falls upon a red brick wall the 
 waves which produce green and violet sensations are 
 absorbed by the brick and converted into heat, while 
 the waves which produce the red sensation reach the 
 eye. In like manner an orange absorbs the violet and 
 reflects green and red in about equal proportions, while 
 a lemon absorbs 'Some of the red as well as the violet, 
 giving us a greenish yellow. 
 
 A black object is one which absorbs all the waves, 
 
248 LIGHT. 
 
 while a gray object is one which absorbs about the same 
 part of each of the primary colors. 
 
 We may now understand why the colored discs pro- 
 duce gray and not white. It is because the red disc 
 absorbs not only the green and violet, but a considerable 
 portion of the red as well. The same being true of the 
 other colors, the mixture must contain a large amount 
 of black. 
 
 When two paints are mixed the result is very differ- 
 ent from that obtained by mixing the sensations pro- 
 duced by the separate paints. The reason for this is 
 that the color which would be transmitted by one pig- 
 ment is absorbed in part by the other, and only that is 
 transmitted which neither pigment absorbs. 
 
 A yellow disc and a blue one will give gray when 
 blended by rotation, but yellow paint and blue paint 
 mixed give green, for the blue absorbs red and trans- 
 mits violet and green, while the yellow absorbs violet 
 and transmits red and green. The two, therefore, ab- 
 sorb all but the green. The process may be expressed 
 by an equation thus : 
 
 (a) Yellow = Bed + Green 
 (6) Blue == Violet -f Green 
 
 (a) -f (6) Yellow + Blue = Bed + Green + Violet + Green 
 = White -f Green 
 
 The fact that green paint may be made by mixing 
 blue and yellow paints led artists to reckon blue and 
 yellow as primary colors, and green as a mixed color. 
 
COLORS BY INTERFERENCE. 249 
 
 The classification suits the convenience of the artists, 
 who continue to employ it. 
 
 Most of the greens employed by artists are, however, 
 not 'made by mixing blue and yellow, but are simple 
 pigments like the oxide of chromium, and many com- 
 pounds of copper. 
 
 152. Colors by Interference. Light waves, like 
 water waves, sound waves, and all other waves, may 
 interfere so as alternately to reenforce or destroy each 
 other. 
 
 When light from any source reaches a given point by 
 two paths which differ in length, it will in general in- 
 terfere. If the light is of a single color, as red, the 
 waves which have come by the two paths will destroy 
 each other if the difference in length of the paths is a 
 half wave length or any whole number of half wave 
 lengths of red light. They will reenfore each other if 
 the difference of path is a whole wave length or any 
 whole number of wave lengths. 
 
 Suppose plane waves of wave length, I, to enter a 
 dark box by two small openings, 0, 0' (Fig. 195), which 
 are very close together, and fall upon a screen at N. 
 The openings 0, 0' will act like sources of light, send- 
 ing waves in every direction in the box. 
 
 If P be a point on the screen at such a distance from 
 that O'P OP= J Z, there will be a dark band at 
 P where the waves meet in opposite phase and destroy 
 each other. 
 
250 
 
 LIGHT. 
 
 If Q be a point such that O'Q OQ = 7, the waves 
 will reenforce each other, and a bright band will be 
 seen. 
 
 Had the light been white instead of being light of a 
 single color, Q would have had a different position for 
 each different wave length, and the band would have 
 been spread out into a spectrum. The violet end would 
 
 FIG. 195. 
 
 lie nearest the point N, the point where the normal to 
 the wave before it entered the box meets the screen. 
 This bending of a wave when passing through small 
 openings is called diffraction. A spectrum produced by 
 diffraction is called a diffraction spectrum. In the dif- 
 fraction spectrum the dispersion is proportional to the 
 wave length, and the colors are arranged as indicated 
 in Fig. 190, where the green is seen to occupy the 
 
THE SPECTEOSCOPE. 251 
 
 middle of the spectrum. In the refraction spectrum 
 the violet end is dispersed much more than the red 
 end (see Fig. 198). 
 
 A candle viewed through a slit in a card will show 
 diffraction spectra. The candle should be several me- 
 tres distant in a dark room and the card should be held 
 near the eye. The slit may be made with the point of 
 a sharp knife in the middle of a visiting card. 
 
 An umbrella held toward an arc lamp will show dif- 
 fraction colors. The moon viewed through a window % 
 screen appears drawn out in the form of a cross. 
 
 153. Colors of Thin Plates. When white light is 
 reflected from two plane surfaces which are very near 
 together the waves from one of the surfaces may inter- 
 fere with those from the other surface, so as to destroy 
 light of a certain wave length. The reflected light will 
 show the color which is complementary to the one 
 destroyed. 
 
 The colors seen on a soap bubble are produced in this 
 way, as are also the gay colors of many insects and birds. 
 The feathers of a peacock's tail would lose their brilliant 
 colors if they were pressed flat enough to destroy the 
 uniform arrangement of the little barbs of which they 
 are composed. Mother-of-pearl ground to powder loses 
 all its bright tints and appears like chalk dust. 
 
 154. The Spectroscope. For a careful study of 
 spectra an instrument called a spectroscope is used. It 
 
252 
 
 LIGHT. 
 
 consists of a stand carrying a circular plate, on which is 
 mounted a tube called the collimator, C (Figs. 196 and 
 197), which has an adjustable slit at the end nearest the 
 source of light, and a lens at the other end to make 
 parallel the rays of light before they fall upon the 
 prism, P (Fig. 196), or the grating, G- (Fig. 197), which 
 
 FIG. 196. 
 
 FIG. 197. 
 
 is to produce the spectrum. The spectrum is viewed 
 by the telescope, T, which is mounted to point toward 
 the centre of the circle. 
 
 Outside light may be cut off by a black cloth laid 
 over the central part of the instrument. The instru- 
 ment is usually graduated to degrees, so that the 
 amount of deviation may be measured. 
 
SPECTEUM ANALYSIS. 253 
 
 155. Spectrum Analysis. The spectra shown by 
 different bodies differ very much. They may, however, 
 be divided into three classes : 
 
 I. Band Spectrum. This is the spectrum shown 
 by any white-hot solid or liquid. A gas flame shows 
 such a spectrum, since the luminous part of the flame is 
 composed of solid carbon particles. It is these parti- 
 cles of solid carbon that collect, as lampblack, upon any 
 cold object held for an instant in the flame. The band 
 spectrum shows all the colors of the rainbow, that is to 
 say, it is produced by light of all wave lengths. 
 
 II. Bright Line Spectrum. This is the spectrum 
 of a glowing gas, like that obtained by burning salt in 
 the flame of an alcohol lamp or Bunsen burner. It 
 consists of one or more narrow lines which are always 
 in the same relative position for a given substance, be- 
 cause in a gas the particles are free to vibrate as they 
 please, and the atoms of each substance seem to have a 
 definite period of vibration which gives rise to light of 
 corresponding wave length, just as a given rod or string 
 gives rise to sound waves of a particular pitch. 
 
 In solids the particles jostle against one another and 
 so vibrate in all possible periods (Class I). 
 
 The bright line ' spectrum of a substance gives the 
 chemist a means of detecting the presence in a com- 
 pound of very minute portions of a substance. The 
 process is called spectrum analysis. 
 
 III. Dark Line or Band Spectrum. When white 
 light is passed through a colored glass or solution or 
 
254 
 
 LIGHT. 
 
 vapor, some of the vibrations are absorbed, leaving the 
 transmitted light wanting in certain wave lengths. The 
 spectrum will appear crossed with black lines or bands. 
 Y Sunlight and the light from many stars give spectra of 
 this class. 
 
 156. The Solar Spectrum. Fraunhofer was the 
 first to explain the dark lines of the solar spectrum, 
 which are now known as Fraunhofer s lines. He 
 showed that a vapor will absorb waves of the same 
 length as those which it emits. Thus sodium vapor 
 placed between an arc light and a spectroscope will 
 
 A a B C 
 
 Eb 
 
 Red Orange Yellow Green 
 
 Blue Indigo 
 
 FIG. 198. 
 
 produce a dark line in the yellow in exactly the posi- 
 tion where the yellow bright line appears when we 
 view burning sodium. 
 
 The dark lines of the solar spectrum are, then, due to 
 the presence of substances like sodium, iron and many 
 others, in vapor form, in the atmosphere of the sun. 
 
 The principal Fraunhofer lines, designated by Fraun- 
 hofer with the letters of the alphabet, are indicated in 
 Fig. 198. 
 
 157. Velocity of Light. The speed with which 
 light waves travel through space is so enormously great 
 
INTENSITY OF LIGHT. 255 
 
 that it is difficult for us to form any conception of it. 
 For all ordinary purposes we treat it as being infinitely 
 great. It was first measured by Roemer, a Danish as- 
 tronomer, in 1675, by means of the difference in the 
 apparent times of revolution of Jupiter's moons, depend- 
 ing upon whether the earth is moving toward or away 
 from Jupiter. He found it took light about 1,000 sec- 
 onds to cross the earth's orbit (186,000,000 miles), 
 which gives for the velocity of light 186,000 miles per 
 second. 
 
 A light wave would travel a distance equal to two or 
 three times around the earth in the time it takes to wink. 
 The light of the moon reaches us in a second and a half. 
 
 158. Intensity of Light. If three square cards, 
 (7, Z>, .# (Fig. 199), having heights of 10, 20, and 30 cen- 
 timetres respec- 
 tively, be placed 
 at distances of 
 30, 60, and 90 
 
 centimetres from ^fV "^" 
 
 a source of light, 
 
 S, it will be S~~ ~~c " D 
 
 found that the FIG. 199. 
 
 shadow of will exactly cover D or K This is equiv- 
 alent to saying that the light which fell on 100 square 
 centimetres at a distance of 30 is distributed over 400 
 square^ centimetres at twice the distance and 900 square 
 centimetres at three times the distance. 
 
256 LIGHT. 
 
 Light is thus seen to follow the same law of inverse 
 squares that gravitation, magnetic attraction, and elec- 
 tric attraction follow. 
 
 The intensity of light is reckoned in candle power. 
 To compare the intensity of two sources of light it is 
 necessary to find a point at such a distance from both 
 sources that the light received from both shall be 
 equally intense. The distance of this point from each 
 source is then measured and the intensity computed 
 by the law of inverse squares. 
 
 Some methods of measuring candle power are ex- 
 plained in Part II. 
 
 159. Light and Electricity . That the electric 
 spark, the electric arc, and the electric current are 
 sources of light is familiar to us all. There is a sense, 
 however, in which a gas jet, a candle flame, nay, even 
 the sun itself, is an electric light, for light waves are 
 now known to be merely a particular class of electric 
 waves of suitable wave length to impress the nerves of 
 the retina. 
 
 The sun emits some waves which are much too long 
 and others which are too short to affect the eye. Some 
 of the long waves may be detected by means of the 
 thermometer, some of the short ones affect the photo- 
 graphic plate. 
 
 The discovery of the identity of light waves and 
 electrical waves grew out of the mathematical study by 
 Maxwell of Faraday's researches in electricity. 
 
SPACE TELEGRAPHY. 257 
 
 More than twenty years after Maxwell published his 
 electro-magnetic theory of light, Hertz, a young Ger- 
 man physicist, undertook to find experimental proof of 
 Maxwell's theory. After about eight years of patient 
 research he found that the waves sent forth by the 
 spark from an induction coil set up sympathetic vibra- 
 tions in a coil of wire of suitable dimensions at some 
 distance from the spark, and that the waves in his little 
 secondary coil would produce a spark which gave a 
 means of detecting and measuring the intensity of the 
 waves at various distances from their source. 
 
 Hertz found that these long electrical waves (several 
 metres in length) could be reflected, refracted, and 
 diffracted exactly like light waves. In short, he de- 
 monstrated that Maxwell's theory is correct : that light 
 is but one way in which the radiant energy of a lumi- 
 nous body may manifest itself. 
 
 We speak of solar light and solar heat, because hav- 
 ing organs of sense to perceive light and heat we are 
 made daily conscious of these particular manifestations 
 of solar energy. We should rather think of solar radia- 
 tion which may manifest itself to our senses as light 
 or heat, which may produce chemical changes in the 
 photographic plate or in tanning our skins brown or 
 bleaching the color from fabrics, but which really con- 
 sists of electrical waves different in wave length, but in 
 all other respects alike. 
 
 1 60. Space Telegraphy. Electrical waves have 
 
258 LIGHT. 
 
 found an important application in telegraphy at sea. 
 Marconi has succeeded in telegraphing to considerable 
 distances to and from vessels without the aid of wires. 
 The messages are sent with as little .difficulty during 
 foggy weather as at any other time, a fact of great im- 
 portance to sailors who are on a dangerous coast in bad 
 weather. 
 
 There seems, at present, little likelihood that the sys- 
 tem will replace wires on land ^ or cables for long 
 tances across the ocean. 
 
 161. New Forms of Radiation. Lenard and Roent- 
 gen, following some lines of research suggested by 
 Hertz, found that the radiations from the negative 
 terminal of a vacuum tube (Crookes' tube) have the 
 power of penetrating objects which are opaque to light 
 waves and of causing a screen coated with fluorescent 
 chemicals to glow brightly wherever the rays strike. 
 These rays, both the Lenard rays and the X-rays of 
 Roentgen, act upon a photographic plate when it is 
 enclosed in a light-tight envelope. 
 
 The fact that the bones of our bodies are less trans- 
 parent to the waves than is the flesh makes it possible to 
 see a shadow picture of the bones of the hand when 
 the hand is held between a luminous Crookes' tube and 
 the fluorescent screen. 
 
 If a photographic plate take the place of the screen, 
 we obtain a photograph of the bones of the hand, and 
 of any foreign body which may be imbedded in the 
 
THE ROLE OF WAVE MOTION. 
 
 259 
 
 flesh. Fig. 200 is reproduced from such a photograph, 
 Bequerel has found that certain salts of uranium emit 
 rays which have the same power of impressing the plate 
 that the X-rays 
 have. 
 
 The subject of 
 electrical radia- 
 tions has aroused 
 great interest 
 among physicists, 
 and has already 
 been made the sub- 
 ject of many inves- 
 tigations. Its 
 chief applications 
 'hitherto have been 
 in surgery, where 
 it enables the sur- 
 geon to locate for- 
 eign bodies in the 
 flesh without prob- 
 ing, and to know the 
 exact nature and FIG - 20 - 
 
 extent of fractures and abnormal growths of the bones. 
 
 Physicians are now able to examine the lungs and 
 other internal organs with great ease, and without dis- 
 comfort to the patient. 
 
 162. The Role of Wave Motion. We are now 
 
260 LIGHT. 
 
 prepared to appreciate the important role which wave 
 motion plays in our lives. By it we gain most of our 
 knowledge of the world outside us, which conies to us 
 through the eye and ear. Practically all of the energy 
 which keeps our world alive and warm, the seat of 
 ceaseless change, the home of myriad living plants and 
 animals and men, instead of a dark, cold clod, conies to 
 us from the sun, across the silent spaces, in waves of 
 the intangible ether. 
 
 Exercises. 
 
 117. Why are the shadows cast by an arc lamp much sharper 
 in outline than those cast by the sun ? 
 
 118. What is the height of a tree which at a distance of 40 
 feet from the opening of a pinhole camera, gives an image 4 
 inches high on the ground glass of the camera 8 inches back 
 of the opening? 
 
 119. When the sun is 45 above the horizon, how long is 
 the shadow cast by a pole 90 feet high ? 
 
 120. (a) Construct for the image of an object placed 8 cm. 
 in front of a concave mirror of 24 cm. radius. (6) Is the 
 image real or virtual, (c) upright or inverted, ((7) enlarged or 
 diminished ? 
 
 121. Construct for the image of an object 8 cm. high placed 
 18 cm. in front of the mirror used in Ex. 120, and answer 
 questions 6, c, cZ, in regard to it. 
 
 122. Construct for the image of an object 8 cm. high placed 
 32 cm. in front of the same mirror, and answer the same ques- 
 tions in regard to it. 
 
 123. (a) Construct for the image of an object 12 cm. high 
 placed 10 cm. in front of a convex mirror having a radius of 
 
EXERCISES. 261 
 
 30 cm, (6) Is the image real or virtual, (c) upright or in- 
 verted, (cZ) enlarged or diminished ? 
 
 124. Observe the image of your face in the convex side of a 
 bright tablespoon, and explain the difference in the images de- 
 pending upon whether the spoon is held vertically or horizon- 
 tally: 
 
 125. What must be the 'height of a plane mirror in order 
 that a person may see his whole length in it at orfce ? 
 
 126. (a) Does an Indian spearing fish have to apply some 
 knowledge of the laws of refraction ? (6) Does he aim above 
 or below the apparent position of the fish ? 
 
 127. Where must the object be placed with reference to a 
 convex lens if the image is to be (a) enlarged and real, (6) 
 enlarged and virtual, (c) inverted and enlarged, (d) upright 
 and enlarged, (e) real and of the same size as the object? 
 
 128. (a) In what respects do all images formed by concave 
 (diverging) lenses agree? (6) In what respects may they 
 differ ? 
 
 129. To what are the colors due in (a) ice which has been 
 shattered by a blow, (6) deep sea water, (c) shoal sea water, 
 (d) rings about the moon, (e) the sunset sky? 
 
 130. Consult the index under " radiant energy," look up all 
 the references and write a summary of all you have learned on 
 that subject. 
 
PART II. 
 
 LABORATORY EXERCISES, 
 
PART II. LABORATORY EXERCISES. 
 
 INTRODUCTION. 
 
 Physics is to-day the most exact of the sciences for 
 the reason that the phenomena with which it deals are 
 capahle of accurate measurement. No one can form a 
 just conception of the methods by which the great 
 laws of physics have been developed who has not him- 
 self learned to make at least some simple measure- 
 ments with a fair degree of accuracy. On the other 
 hand, the student who has patiently and conscientiously 
 performed a series of measurements with the highest 
 degree of accuracy attainable by him with the instru- 
 ments at his command has gained, not only manual and 
 mental training, but moral training besides, for he has 
 learned to prefer truth to falsehood and that exact 
 statement of facts which leads ever to the discovery of 
 truth, to the loose and ambiguous statement which 
 tends to conceal the truth. 
 
 Measurement consists in obtaining an expression for 
 the magnitude of the quantity to be measured in terms 
 of some standard quantity called a unit. 
 
 The Fundamental Units. All physical quantities 
 may be expressed directly or indirectly in terms of 
 some one or more of the fundamental quantities, 
 length, mass, time, the units of which are, respectively, 
 the centimetre, the gram, and the second. 
 
266 INTRODUCTION. 
 
 While the instruments by means of which the differ- 
 ent quantities are measured may seem at first sight 
 quite unlike each other, it is yet true that the actual 
 observations made in measuring these quantities are 
 very much alike. When the instrument has been ad- 
 justed for the observation, the observation itself Avill 
 usually consist in reading or counting a number of 
 linear divisions on a scale of equal parts and the esti- 
 mation of a fraction of a division by means of the 
 eye. 
 
 The student is urged, therefore, to observe in the 
 performance of each exercise, not only the precautions 
 there mentioned for securing accuracy, but, as far as 
 they apply, the precautions observed in the preceding 
 exercises. A little time spent in considering before- 
 hand the probable sources of error in any problem may 
 save time in the end. 
 
 The various sources of error to which observers are 
 liable will be mentioned in the exercises. Accidental 
 errors may be eliminated by making a number of inde- 
 pendent observations and taking their mean, since it is 
 probable that as many observations will give a result 
 above the true value as below it. It is to be borne in 
 mind that the mean of ten observations is, as a rule, 
 entitled to ten times as much weight as is any one of 
 the ten, even though that one be exactly the same as 
 the mean. The student will understand without spe- 
 cific directions that every measurement which he is 
 asked to make is to be repeated at least twice, often 
 
IN TE OD UC TIOX. 267 
 
 ten or more times, and that all the observations are to 
 be recorded, even if they should happen to be exactly 
 alike. 
 
 If some observations differ much more from the 
 mean than most of those taken, try to find a cause for 
 the difference in the conditions surrounding the experi- 
 ment, and, if possible, remove the cause of error. 
 
 The form in which the record of work is to be kept 
 may be left to the taste of the instructor. All instruc- 
 tors will probably agree that the substance of the 
 report should include (1) a statement of the object 
 and the method of the exercise; (2) a description of 
 the apparatus used, with such sketches as are needed 
 to make the description clear; (3) an orderly record of 
 the observations made; (4) a discussion of the results 
 and method. 
 
 A Personal Hint. Not the least of the advantages 
 to be derived from a course in laboratory work is the 
 habit of order and neatness. We owe it not only to 
 the people who are our laboratory mates, but to the 
 people who are to be near us in after life, to see to it 
 that the place which we have occupied is at least as 
 clean and tidy when we leave it as when we came to it. 
 If the teacher's directions in regard to the care of ap- 
 paratus are explicitly followed by all the members of a 
 class, the added pleasure derived from the work will 
 alone more than repay the effort. 
 
CHAPTER IX. 
 LENGTH. 
 
 163. Units of Length. The metre is divided into 
 100 centimetres exactly as the dollar is divided into 
 100 cents. The centimetre is divided into 10 milli- 
 metres as the cent is divided into 10 mills. All lengths 
 may be expressed in centimetres and decimals of a 
 centimetre, and are understood to be so expressed in all 
 computations unless the contrary is stated. 
 
 Small dimensions when expressed accurately are 
 often mentioned in millimetres. Thus an inch is said 
 to be equal to about two and a half centimetres, or more 
 exactly 25.4 millimetres. 
 
 1. TABLE OF EQUIVALENTS. 
 
 Length. 
 
 1 centimetre = .3937 in. 
 1 metre = 39.37 in. 3.28 ft. = 1.0936 yd. 
 1 kilometre = 0.6214 mile. 
 
 1 inch = 2. 54 cm. 
 1 foot =0.3048 m. 
 1 yard = 0.9144m. 
 1 mile = 1.0094 km. 
 
 Area. 
 
 1 sq. cm. = 0.155 sq. in. 
 1 sq. m. = 10.714 sq. ft. = 1.196' sq. yd. 
 
ESTIMATION OF TENTHS. 
 
 9 
 
 2 <; 
 
 1 hectare = 2. 471 acres. 
 1 sq. km. = 0.386 sq. mile. 
 
 1 sq. in. = 6.452 sq. cm. 
 1 sq. ft. 929.034 sq. cm. 
 1 sq. yd. 0.83613 sq. m. 
 1 acre = 0.4047 hectare. 
 1 sq. m. = 2.59 sq. km. 
 
 Volume. 
 
 1 cu. cm. = 0.061 cu. in. 
 1 cu. m., or stere = 35.315 cu. ft. 
 1 litre = 1. 0567 qt. (U. S.). 
 
 1 cu. in. = 16.387 cu. cm. 
 1 cu. ft. = 0.028 cu. m. 
 1 cu. yd. = 0.765 cu. m. 
 
 164. Estimation of Tenths. Since the smallest 
 division of the common metre stick is the millimetre, 
 we can measure with it directly to millimetres. We 
 should always try, however, to estimate fractions of a 
 millimetre. We may at first find it more natural to 
 estimate fourths ; but since it is frequently possible to 
 estimate closer than fourths, it is better to form the 
 habit at once of estimating tenths. If the length is a 
 certain number of millimetres plus a little more than 
 i call the fraction .6, if a little less than f we may call 
 it .7, and so forth. 
 
 EXERCISE 131. To measure the length and breadth of a 
 laboratory table. 
 
 Apparatus. Metre stick, a square block of wood or iron, 
 try-square . 
 
 Directions. To measure the width of the table, 
 
270 
 
 LENGTH. 
 
 place the square as shown in Fig. 201, at the left, with 
 the ruler resting firmly against it. The ruler is then at 
 right angles to the side of 
 the table, and the end of 
 the ruler is exactly over 
 
 FIG. 201. 
 
 FIG. 202. 
 
 the edge of the table. Let 
 your assistant hold the 
 ruler in place while you remove the square, place it as 
 shown at the right-hand side of Fig. 201, and read on 
 the metre scale the centimetres, millimetres, and tenths of 
 
 a millimetre 
 at the point 
 exactly oppo- 
 site the edge 
 of the square. 
 Make s u c h 
 
 measurements at intervals along the length of the table. 
 To measure the length, place^ the metre stick against 
 the square as in Fig. 202. Since the table is probably 
 more than a metre long, place the square against the other 
 end of 
 the stick. 
 Hold the 
 square 
 in place 
 while you 
 
 remove the stick, and put in its place against the square, 
 a square block. Now hold the block in place, remove 
 the square, and measure from the block (see Fig. 203). 
 
 FIG. 203. 
 
EXERCISES. 271 
 
 Do not mark the table, as this will not only disfigure the 
 table, but prejudice the next person who measures it. 
 This remark holds good in general : no marks are to be 
 made upon apparatus except under the teacher's directions. 
 
 Record your results without reporting them to your 
 assistant, then let him make a similar series of measure- 
 ments while you assist. After you are both through 
 compare results. If either has made a serious blunder, 
 the comparison will show it. 
 
 It is well to record both your own results and those 
 of your assistant, keeping them apart, however, and 
 designating them by name. 
 
 Note the suggestions in regard to the record of results 
 on page 267. The measurements may be tabulated in 
 some such form as the following : 
 
 DIMENSIONS OF TABLE No. 4. 
 First breadth at East end. First length at North side. 
 
 Breadth in Cm. 
 
 Averages. Observer. 
 
 Self. 
 
 8G.28G 
 
 Stephens. 
 
 10 86.31 86.292 86.289 
 
 Obs. No. 
 
 Breadth. 
 
 1 
 
 86.27 
 
 2 
 
 86.28 
 
 3 
 
 86.29 
 
 4 
 
 86.29 
 
 
 
 86.30 
 
 6 
 
 86.26 
 
 7 
 
 86.28 
 
 8 
 
 86.30 
 
 9 
 
 86.31 
 
272 
 
 LENGTH. 
 
 The differences in your own results will indicate differ- 
 ences in the dimensions of the table at different points, 
 provided that your assistant's results show corresponding 
 
 differences. 
 
 Length in Cm. 
 
 Observer. 
 Self. 
 
 Obs. No. 
 
 Length. 
 
 1 
 
 186.26 
 
 2 
 
 186.27 
 
 3 
 
 186.26 
 
 4 
 
 1.86.25 
 
 5 
 
 186.26 
 
 6 
 
 186.26 
 
 186.263 
 
 Stephens. 
 
 186.257 186.260 
 
 EXERCISE 132. To measure the height of a column of liquid 
 in a glass tube. 
 
 Apparatus. Metre stick, two blocks, flat stick or strip of 
 plate glass. 
 
 Directions. Place a flat stick 
 
 in the horizontal position across 
 two blocks as near the tube as 
 possible, and measure from the 
 top of the stick (Fig. 204) to the 
 upper liquid surface, and then 
 from the same level to the lower 
 liquid surface. The sum (or 
 difference) of these two meas- 
 ures is the height required. 
 
 Care must be taken in making 
 measurements (a) to define the 
 surface : that is considered to be 
 the lowest part of the surface of 
 FIG. 204. a % u id which, like water, wets 
 
EXEBCISES. 273 
 
 the glass, the highest part of a mercury surface ; (b) to see 
 that the metre stick is held in the vertical position ; (c) to 
 make sure that the eye is in the same horizontal plane with 
 the surface to be measured. A good way to do this is to 
 hold a bit of mirror or a piece of bright tin against the 
 back side of the metre stick and slide a try-square along 
 the front of the metre stick till the edge of the square, its 
 reflection in the mirror, and the surface are all in line. 
 
 The error due to the eye's being held in any position 
 not in a perpendicular line to the scale at the point of 
 observation is called parallax. It will be necessary to 
 guard against parallax in almost every measurement 
 you will ever make. Parallax is greater the farther the 
 object is away from the scale. 
 
 After making two careful measurements change the 
 height of your base line, by turning the blocks or using 
 a stick of different thickness, and make two more. 
 
 To measure downward from the block to the lower 
 surface a piece of metric ruler having a point projecting 
 from the end should be used. For acids the point should 
 be of glass. If the ruler is sawed off an amount equal 
 to the length of the point, the reading on the ruler will 
 be the length measured. Otherwise the distance from 
 the point to some point on the ruler must be measured 
 by holding the piece of ruler beside the metre stick while 
 the point and the end of the metre stick rest upon a 
 piece of glass or other hard smooth surface. 
 
 EXERCISE 133. To measure the distance between two points 
 with the diagonal scale. 
 
274 
 
 LENGTH. 
 
 Apparatus. Dividers, diagonal scale, For the dividers, 
 any dividers or compasses with sharp points will answer. 
 
 The diagonal scale is shown in Fig. 205. It is designed 
 to aid in measuring short distances more accurately than can 
 be done with the simple scale by means of a device for read- 
 ing tenths. The scale is ruled in centimetres toward the left 
 from zero. To the right of zero is a single centimetre space 
 divided into tenths by diagonal lines, the bottom of each line 
 
 FIG. 205. 
 
 being just 1 millimetre to the right of the top end of the line. 
 The space between the top and bottom of the scale is divided 
 by horizontal lines into ten equal parts. 
 
EXEECISES. 27 ~) 
 
 t 
 
 The first horizontal line must intersect the first, or zero, 
 diagonal line .1 millimetre to the right of the nearest straight 
 line, which is the zero of the scale. The intersection of hori- 
 zontal 5 with diagonal 4 is 4.5 mm. to the right of zero of the 
 scale. 
 
 Directions. Adjust the dividers so that the hinge 
 does not work too easily and spread the points so that 
 when one is placed upon the centre of one of the given 
 points the other will exactly reach to the centre of the 
 second point. Now place the dividers upon the scale 
 with the left leg upon that centimetre division which 
 will bring the right leg within the diagonal square. 
 Starting with the dividers at the top of the scale move 
 downward, keeping the left leg on the vertical line and 
 both legs always in the same horizontal line till the 
 right leg meets the intersection of a diagonal line with 
 a horizontal. The number of the centimetre line will 
 give the centimetres, the number of the diagonal line 
 the millimetres, and the number of the horizontal line 
 the tenths of a millimetre. The reading in Fig. 205 is 
 3.26 cm. 
 
 CAUTIOX. Do not press upon the scale with the divid- 
 ers, else it will soon become blurred and useless. 
 
 After making a measurement, close the dividers and 
 repeat the measurement. 
 
 EXERCISE 134. To test your ability to estimate tenths of 
 a scale division. 
 
 Apparatus. Dividers, diagonal scale, metre stick. 
 
 Directions. Make three measurements of the dis- 
 tance between two points not before measured, using 
 
276 LENGTH. 
 
 the dividers and metre stick, and estimating tenths of a 
 millimetre as Avell as you can with the eye, then make 
 three measurements, using the diagonal scale, and com- 
 pare your results. Try not to let any of your measure- 
 ments be influenced by those already made. If any of 
 a set of measurements is better than the rest it ought 
 to be the last one rather than any of the others. 
 
 EXERCISE 135. To measure the diameter of a sphere (a) 
 with the calipers, (b) with the metre stick. 
 
 Apparatus. Outside calipers, two rectangular blocks, flat 
 stick, metre stick, heavy hammer handle. 
 
 The calipers shown in Fig. 206 are called outside calipers, and 
 are used in measuring the diameters of spheres and cylinders. 
 Directions. (a) Indicate different diameters on the 
 sphere with chalk. Open the calipers a little wider 
 
 than what you judge to be the 
 diameter of the ball and make a 
 trial. If they are open a little 
 too wide take the calipers loosely 
 in the hand with the hinge be- 
 tween the thumb and forefinger, 
 and tap gently with one leg of 
 the calipers upon the hammer 
 handle or any block that will 
 neither mar the calipers nor be 
 FIG - 206 - damaged by them. A little 
 
 practice will enable you to judge how hard a blow to 
 strike. If the legs are a little too close together slip the 
 hammer handle between them and give a slight blow 
 upon it with the inside of the caliper leg. 
 
EXERCISES. 
 
 277 
 
 When the sphere will exactly slip between the point's, 
 measure the distance the two points are apart with the 
 metre stick or diagonal scale, open the calipers and 
 then measure another diameter. Measure six diameters. 
 
 FIG. 207. 
 
 Place the blocks upon the table against the 
 straight stick and notice whether they fit squarely 
 against each other (see Fig. 207). If all sides are not 
 equally square choose the best sides, place the sphere 
 
 between the blocks and 
 press the blocks against 
 it. See that the blocks 
 are pressed firmly 
 against the stick. 
 Now measure the distance between the blocks on both 
 sides, near the top and near the bottom. Repeat the meas- 
 urement for three diameters at right angles to each other. 
 
 EXERCISE 136. To measure the inside and outside diameters 
 of a tube with the calipers. 
 
 Apparatus. Outside calipers, inside calipers (Fig. 208), 
 diagonal scale. 
 
 FIG. 208. 
 
278 LENGTH. 
 
 Directions. Proceed as in Exercise 135 (a), making 
 four measurements at each end for the inside diameter, 
 two near the end at right angles to each other, two as 
 far in as the calipers will go. 
 
 Make eight measurements of the outside diameter 
 along one element and eight more along the element at 
 right angles to the first. Record the first eight results 
 in one column and the second eight in another, and 
 compare the values to see if there is any indication that 
 the tube is flattened. Glass tubes are not unlikely to 
 be thus slightly elliptical in cross section. 
 
 With the outside calipers measure the thickness of 
 the walls of the tube, and see how it compares with the 
 thickness obtained by taking half the difference between 
 the outer and inner diameters of the tube. 
 
 165. The Vernier. The vernier is a device for 
 estimating tenths of a scale division so simple in prin- 
 ciple and construction that it may be applied to a great 
 variety of instruments. 
 
 The vernier consists of a movable scale arranged to 
 slide along a fixed scale. For simplicity let us describe 
 a vernier which reads tenths. When the zero of the 
 vernier (Fig. 209) is opposite the zero of the scale 
 the tenth division of the vernier will be found to be 
 opposite the ninth division of the scale. Each division 
 of the vernier is just .9 of a scale division in length. 
 If then the vernier be set so that 1 of the vernier is 
 opposite 1 of the scale, of the vernier is .9 to the 
 
THE VEENIEE. 
 
 279 
 
 left of 1 or .1 to the right of 0. But since the zero of 
 the vernier is the point to be read, the reading is .1 
 scale division. The reading on the scale shown in 
 Fig. 209 is 12.3. 
 
 For the of the vernier is past 12 of the scale and 
 3 of the vernier is opposite 15 of the scale, so that the 
 of the vernier is 3 X .9 = 2.7 to the left of 15, or 
 the reading is 15 2.7. 
 
 In practice we need not notice what division of the 
 scale the vernier is opposite. We do observe what 
 division of the scale the zero of the vernier is past and 
 
 1 1 1 I 1 .... 
 
 / \ 
 
 1 1 1 1 1 1 1 1 
 
 r 1 1 1 1 1 1 II 
 
 -*. I I I I 
 
 | 1 i I 1 
 
 \ 
 
 FIG. 209. 
 
 what division of the vernier coincides with a division 
 of the scale. 
 
 Verniers are often made to read twentieths of a 
 millimetre, fiftieths of an inch, sixtieths of a degree, etc. 
 
 Before using a vernier set it so that its zero coincides 
 with a division of the scale, follow along the vernier 
 till the next division of the vernier which coincides 
 
280 
 
 LENGTH. 
 
 with a division of the scale is found, and count the 
 divisions on the vernier from the first coincident line to 
 the second. If the number is n divisions the vernier 
 reads nths of a scale division. 
 
 EXERCISE 137. To measure the length of an object with the 
 simple vernier. 
 
 Apparatus. Metre stick and vernier, block. 
 
 Directions. Place the object and metre stick side by 
 side against the block and slide the vernier along till it 
 touches the end of the object (see Fig. 209). Now 
 read the vernier as already directed. 
 
 EXERCISE 138. To measure the diameter and length of a 
 small cylinder with the vernier gauge. 
 
 Apparatus. Vernier gauge. 
 
 The vernier gauge (see Fig. 210) consists of a steel scale 
 provided with two jaws at right angles to its length. One of 
 
 r 
 
 FIG. 210. 
 
 the jaws is fixed to the scale; the other, to which a vernier is 
 attached, slides along the scale. When the jaws are shut the 
 zero of the vernier should coincide with the zero of the scale, 
 for the distance apart of the jaws is then zero. The movable 
 jaw is usually provided with a screw which holds the jaw in 
 place while the reading is being taken. 
 
THE VEEN IE ft. 281 
 
 Directions. Place the object between the jaws of the 
 gauge, press the movable jaw gently but firmly against it, 
 set the screw, and read the scale and vernier. Make ten 
 measurements of the diameter and four of the length. 
 
 Correction. As remarked above, the reading should 
 be zero when the jaws are closed, but it may happen 
 that the jaws have been slightly bent, so that the read- 
 ing will vary one or two tenths from zero. Close the 
 jaws and read the vernier. The error, if any, should be 
 recorded as the error of zero. It is evident that if the 
 instrument reads 0.1 at it will read too high by .1 at 
 other points as well, and .1 must be deducted from all 
 readings, or what amounts to the same, from the average 
 of the readings taken. Bear in mind that the correction 
 is .1 when the error is -f- .1, or in general the correc- 
 tion is the error with the sign changed, or the correction 
 is the amount to be added to make the result correct. 
 
 EXERCISE 139. To measure the internal diameter of a ring 
 or hollow cylinder with the vernier gauge. 
 Apparatus. Two vernier gauges. 
 
 Directions. Close the jaws of the first gauge and 
 measure with the second gauge the distance across the 
 jaws. This amount must be added to all inside readings 
 taken with this particular instrument, since it is a nega- 
 tive error. 
 
 Record it thus : 
 
 Correction for width of jaws of vernier gauge No. 4, 1.60 cm. 
 
 Correction for error of zero, 0.01 
 
 Total correction for inside measurement, 1.59 cm. 
 
282 LENGTH. 
 
 The gauge used for inside measurements of tubes 
 or rings must have its jaws rounded on the outside. 
 The measurements are to be taken as in Exercise 138. 
 
 166. Eye Estimation of Lengths. It is often use- 
 ful to be able to form a rough estimation of distances 
 by means of the eye alone, as, for instance, if we are 
 selecting a block to support an object at a certain height. 
 One who is much accustomed to such eye estimation 
 will detect any gross error of measurement by its 
 means. Now that the student has become familiar with 
 the unit of length he will find it useful exercise to esti- 
 mate distances habitually before measuring them. 
 
 EXERCISE 140. To estimate and measure the length of 
 several objects. 
 
 Apparatus. Metre stick. 
 
 Directions. (a) Bend the forefinger and estimate 
 the length from the tip of the nail to the first joint. 
 Record your estimate and then measure the length. 
 (5) Spread the hand and estimate the distance you can 
 span with the thumb and middle finger. Record and 
 measure. (<?) Estimate and measure the length of 
 your foot, allowing, as well as you can, for the distance 
 the shoe projects at each end. (c?) Estimate and meas- 
 ure the distance from the tip of your middle finger to 
 your elbow, (e) Estimate and measure the length of 
 your steps by taking one fifth of the distance covered 
 in five steps. (/) Estimate and measure the height of 
 another student. 
 
THE MICROMETER SCREW. 283 
 
 In olden times these lengths, when referred to the 
 person of the king, served as units of length and cor- 
 responded to (a) the inch, (5) the span, (<?) the foot, 
 (d) the cubit, (e) the yard, (/) the fathom. 
 
 The form of an object and its position influence our 
 judgment of its dimensions. 
 
 EXERCISE 141. Estimation in different positions. 
 
 Directions. (a) Estimate and measure the width and 
 height of the two parts of the eight shown in Fig. 211. 
 
 (5) Estimate and measure the length of a cylinder 
 lying on its side, and of another cylin- 
 der standing on its end. A barrel is a 
 good object for the purpose. 
 
 The objects you have measured will, 
 if their dimensions are borne in mind, 
 aid you in making other estimates of 
 length. 
 
 167. The Micrometer Screw. A 
 
 still more accurate instrument than the 
 
 vernier for measuring small dimensions FIG 
 
 is the micrometer screw. It consists 
 
 of an accurately cut screw, the head of which is divided 
 
 into a number of equal parts. Its simplest forms are the 
 
 micrometer gauge and the spherometer.* 
 
 EXERCISE 142. To measure the diameter of a wire with the 
 micrometer gauge. 
 
 Apparatus. Micrometer gauge. 
 
 *Moro complicated forms are the filar micrometer, used in microscopes and 
 telescopes, and the dividing engine, used in ruling accurate scales. 
 
284 LENGTH. 
 
 The micrometer gauge (see Fig. 212) consists of a bent 
 arm, one end of which is threaded to receive a screw, the 
 other end containing an adjustable stop, 8. The linear scale 
 on the shank shows how many millimetres the screw is from 
 the stop. If the distance between the threads of the screw 
 be h mm. the screw will advance 1 mm. for every two turns. 
 The head is divided into equal parts. If the threads are h mm. 
 apart the head will be divided into 50 parts. If the threads 
 are 1 mm. apart the head will be divided into 100 equal parts. 
 In either case one division on the head corresponds to a 
 forward movement of .01 mm. by 
 the screw. By estimating tenths of 
 a division we may read .001, but we 
 are to understand that our result 
 cannot be relied upon as correct to 
 .001, since the error in setting the 
 screw is usually .002 or more. 
 
 Directions. Bring the screw and stop in contact 
 with a gentle pressure. A uniform pressure may be 
 secured by grasping the head of the screw loosely in 
 the fingers and turning till the fingers slip. Note and 
 record the zero error. Place the wire against the stop 
 and bring the screw up to it with about the same pres- 
 sure used in determining zero. 
 
 If the threads are mm. be careful to notice whether 
 the reading on the scale is a whole number of millimetres 
 or a whole number plus a half. The reading on the instru- 
 ment shown in Fig. 212 is 2.068 mm. If the screw were 
 turned one revolution backward it would be 2.568 mm. 
 Take ten readings of the diameter of the wire, average 
 the results, and determine the gauge number from 
 Table 2. Determine the gauge number also by means of 
 an American wire gauge such as is shown in Fig. 213. 
 
THE 8PHEEOMETEE. 
 
 285 
 
 2. VALUE IN MILLIMETRES OF BROWN & SHARP WIRE 
 
 GAUGE No.'s. 
 
 No. 
 
 mm. 
 
 No. 
 
 mm. 
 
 No. 
 
 mm. 
 
 No. 
 
 mm. 
 
 1 
 
 7.348 
 
 9 
 
 2.906 
 
 17 
 
 1.150 
 
 25 
 
 0.455 
 
 2 
 
 6.544 
 
 10 
 
 2.582 
 
 18 
 
 1.024 
 
 26 
 
 0.405 
 
 3 
 
 5.827 
 
 11 
 
 2.305 
 
 19 
 
 0.912 
 
 27 
 
 0.361 
 
 4 
 
 5.189 
 
 12 
 
 2.053 
 
 20 
 
 0.812 
 
 28 
 
 0.321 
 
 5 
 
 4.621 
 
 13 
 
 1.828 
 
 21 
 
 0.723 
 
 29 
 
 0.286 
 
 6 
 
 4.115 
 
 14 
 
 1.628 
 
 22 
 
 0.644 
 
 30 
 
 0.255 
 
 7 
 
 3.656 
 
 15 
 
 1.459 
 
 23 
 
 0.573 
 
 31 
 
 0.227 
 
 8 
 
 3.264 
 
 16 
 
 1.291 
 
 24 
 
 0.511 
 
 32 
 
 0.202 
 
 168. The Spherometer. -- The spherometer is a mi- 
 crometer screw of a form especially adapted to the meas- 
 urement of the curvature of 
 spherical surfaces. It may also 
 be used for measuring the thick- 
 ness of small glass plates. It 
 consists of a tripod, the three 
 pointed legs of which form an 
 equilateral triangle (Fig. 214). 
 Through the centre of the 
 tripod passes the pointed 
 screw, at the top of which the 
 head is enlarged to form a disk which is graduated on its 
 edge. The whole turns of the screw are read from the 
 vertical scale, /S', the fractions of a turn from the disk. 
 
 EXERCISE 143. To measure the thickness of a small glass 
 or mica plate with the spherometer. 
 
 Apparatus. Spherometer, glass plate. 
 
 FIG. 213. 
 
286 
 
 LENGTH. 
 
 Directions. Place the instrument upon a piece of 
 plate glass and turn the screw till it touches the glass. If 
 it is turned a little too far the tripod will be lifted so as to 
 
 wobble on its points. Turn 
 the screw back till the wob- 
 bling motion ceases. All four 
 points are now in one plane 
 and the reading is the zero 
 reading. If the scale reads 
 from the bottom up, the zero 
 Avill be near the middle of the 
 scale to permit of readings 
 being made upon concave sur- 
 faces. Take five readings of the 
 zero in different positions upon 
 the large plate glass. Having 
 determined the zero, raise the 
 screw till the plate to be measured will slip under it, 
 bring the screw to contact and read the instrument. 
 Repeat four times on different parts of the plate. The 
 average of these five readings less the average zero read- 
 ing is the thickness of the plate. 
 
 EXERCISE 144. To measure the radius of a large lens or 
 other spherical surface. 
 
 Apparatus. Spherometer and glass plate, dividers and 
 diagonal scale. 
 
 Directions. Determine the zero reading as in Exer- 
 cise 143. Raise the screw, place the spherometer upon 
 the lens, bring the screw to contact and take a reading. 
 
 FIG. 2H. 
 
THE SPHEROMETER. 
 
 Repeat at five different places as far apart as possible upon 
 
 the surface of the lens. The difference between the aver- 
 
 age of these readings and zero is the height (A, Fig. 215) 
 
 of the point p above the plane which passes through 
 
 the points of the 
 
 tripod. It re- 
 
 mains to meas- 
 
 ure d, the dis- 
 
 tance of p from 
 
 each of the three 
 
 points of the tri- 
 
 pod when all the 
 
 points are in the 
 
 same plane. To 
 
 measure d place 
 
 the instrument 
 
 upon a flat page of your notebook and press the points 
 
 down until they make dents in the paper. Bring the 
 
 screw down till it also makes a mark. Measure the dis- 
 
 tance of the central dot from each of the others with the 
 
 dividers and scale. 
 
 If R be the radius of the sphere of which our lens is 
 a segment it is evident from geometry that 
 
 whence: 
 
 from which equation, by substituting the values of d 
 and h obtained by measurement, we obtain R. 
 
CHAPTER X. 
 MASS. 
 
 169. Mass Defined. Units of Mass. By the 
 mass of a body we mean the amount of matter which 
 composes it. Since gravity at any place on the earth 
 acts with equal force upon equal masses, we require for 
 the measurement of an unknown mass (1) a standard 
 mass, (2) an instrument for comparing the force ex- 
 erted by gravity on the standard mass and the unknown 
 mass. The standard mass in the metric system is the 
 gram, which is defined as the mass of a cubic centimetre 
 of water at its temperature of greatest density (4 de- 
 grees Centigrade). For the measurement of small 
 masses sets of weights are made, usually of brass, con- 
 taining masses of 1 gram, 2 grams (two), 5 grams, 10 
 grams, 20 grams (two), 50 grams, 100 grams, 200 
 grams (two), 500 grams. For coarse weighing weights 
 of 1,000 grams, called kilograms, are made. For frac- 
 tions of a gram sets of centigram weights, usually 
 made of sheet platinum, and for very delicate weighing 
 milligram weights, often made of sheet aluminum, are 
 used. 
 
 3. EQUIVALENTS IN WEIGHT. 
 
 1 gram = 15.4324 grains. 
 
 1 kilogram = 2.2046 pounds. 
 
THE BALANCE. 
 
 289 
 
 4 ~ 
 
 6 - 
 
 8 ~ 
 
 FIG. 216. 
 
 1 grain = .0648 grams, 
 
 1 ounce (av.) = 28.35 grams. 
 
 1 (tr.) = 31.1 grams. 
 
 170. The Spring Balance. If a force be exerted 
 to elongate a spiral spring the elongation will be pro- 
 portional to the force. This principle is made use of 
 in the spring balance. 
 
 The spring balance in common use for coarse weighing 
 has been graduated by the maker 
 so that we have only to suspend 
 it by the ring at the top, hang 
 an unknown mass from the hook 
 attached to the bottom of the 
 spring, and read off the weight 
 directly from the scale (see Fig. 
 216). The difference in the 
 force of gravity at different 
 places is too small to be detected 
 by such a balance and may there- 
 fore be disregarded. 
 
 A very delicate form of spring 
 balance is that known as Jolly's 
 balance, shown in Fig. 217. It 
 consists of a long spiral spring 
 made of fine wire, suspended in 
 front of a scale. The elongation 
 produced by suspending a known 
 weight from the wire is read from the scale. 
 
 FIG. 217. 
 
 From a 
 
 series of such determinations the average elongation for 
 one gram is determined. 
 
290 MASS. 
 
 EXERCISE 145, To weigh a small object with Jolly's balance. 
 Apparatus. Jolly's balance and some small weights. 
 
 Directions. Choose a well-defined point near the 
 bottom of the spring and read its position on the scale 
 (an index is usually attached). To avoid parallax the 
 scale is usually ruled on a mirror. When the index 
 covers its image in the mirror read the position of the 
 index on the scale. If a piece of metre stick is used 
 for a scale, as in the home-made form of balance shown 
 in Fig. 217, the reading is taken from the top of a 
 try square which just touches the pan. Record the 
 zero reading, place the object to be weighed in the pan 
 and read again. Repeat both observations after shifting 
 the zero by adding a small additional weight to the pan. 
 Now find the value of one gram in scale divisions by 
 placing in the pan that one of the small weights which 
 will give a reading nearest that given by the unknown 
 weight. If five grams extended the spring 12.5 cm., 
 one gram would extend it 2.5 cm. An object which 
 extends the spring 16.3 cm. would weigh 6.52 grams. 
 
 I7 1 - The Lever Balance. The principle of mo- 
 ments furnishes 
 a convenient 
 method of com- 
 paring masses. 
 If a rigid bar 
 (Fig. 218) is 
 supported from 
 a triangular fulcrum a little higher than its centre of 
 
 <^i 
 
 6 
 
THE BALANCE. 
 
 291 
 
 gravity, it will come to rest in a horizontal position when 
 the sum of the moments of the forces on the left-hand 
 side is equal to the sum of the moments on the right- 
 hand side. If the right arm is made much longer than 
 the left arm, while the left arm is made enough heavier 
 so that the lever balances, it is evident that a single 
 
 o 
 
 FIG. 219. 
 
 weight may be made to balance different masses by 
 varying the position of the weight on the right arm. 
 
 Such balances, now known as steelyards, were in use 
 by the ancient Romans. The long arm was graduated 
 to equal parts by notches into which a link supporting 
 
 FIG. 220. 
 
 the weight could be dropped. From the short arm was 
 suspended a hook for supporting the object to be 
 weighed (see Fig. 219). A form adapted to delicate 
 weighing is shown in Fig. 220, 
 
292 MASS. 
 
 It is obvious that when the two weights are at equal 
 distances from the fulcrum the weights are equal when 
 the beam comes to rest in a horizontal position. When 
 the long arm is n times as long as the short arm the 
 weight on the short arm is n times as great as the weight 
 on the long arm. 
 
 EXERCISE 146. To weigh an object with a steelyard. 
 Apparatus. Common steelyard. 
 
 Directions. Support the steelyard in the left hand 
 by the hook farthest from the heavy end if there are 
 but two hooks, from the second if there are three. 
 Hang the body to be weighed from the hook near the 
 heavy end and move the bob till a notch is found in 
 which the lever will be horizontal. If the object is too 
 heavy turn the steelyard over and use the other scale. 
 After reading the scale and recording the weight, 
 weigh a known weight and then measure the distances 
 between the knife edges and the length of a scale divi- 
 sion, and compute, by the law of moments, the weight 
 of the bob. 
 
 EXERCISE 147. To weigh an object with a rider balance. 
 
 Apparatus. Balance with unequal arms, set of rider 
 weights. 
 
 Directions. Test the zero of the instrument and if 
 necessary adjust it by means of the screw. Place the 
 object in the pan and adjust one of the larger riders till 
 it will a little less than balance the object and add 
 smaller riders till the beam is in equilibrium. The sum 
 of the weights balanced by the different riders is the 
 
TEE BALANCE. 293 
 
 weight of the object. If in doubt about the weight of 
 the different riders weigh a known weight, as a five- 
 cent nickel, which, when new, weighs five grams. 
 
 172. The Lever Balance with Equal Arms. The 
 
 hand balance (Fig. 221) with equal arms is probably the 
 oldest balance known. 
 It was in universal 
 use for weighing 
 money before the 
 practice of govern- 
 ment coinage became 
 common. The trian- 
 g u 1 a r pin passes 
 through the centre of FIG - 221 - 
 
 the beam and rests in a double link which is held in the 
 hand or fastened by a cord to some convenient support. 
 Near the ends of the beam and at equal distances from 
 the centre are suspended from small pins the pans of 
 horn or metal which hold the weights. Such balances 
 are in common use to-day by university students in the 
 German chemical laboratories and are the best cheap 
 balances to be had. 
 
 A more convenient form of the lever balance is the 
 prescription balance or beam balance shown in Fig. 222. 
 It is identical in principle with the hand balance, but 
 the beam is supported on the top of a pillar and a long 
 and light pointer indicates on the scale small variations 
 of the beam from the horizontal position. The pillar 
 
294 
 
 MASS. 
 
 may be made in two parts, the upper being arranged to 
 slide within the lower. In the lowest position of the 
 beam the pans rest upon the base. By pressing a lever 
 the beam is lifted and the pans are set free. 
 
 EXERCISE 148. To weigh an object with the common bal- 
 ance. 
 
 Apparatus. Hand or beam balance, set of weights. 
 
 Directions. Allow the beam to swing and find 
 where the pointer comes to rest. If this point is near 
 
 FIG. 222. 
 
 the centre of the scale, note the exact point ; if it is not 
 near the centre, add enough fine shot, grains of sand, or 
 bits of paper to the proper pan to bring it near the 
 centre. Arrest the beam by means of the lever, ?, or 
 in the hand balance by holding the beam with the left 
 
THE BALANCE. 295 
 
 hand. Place the object in the left pan and put such 
 weights in the right pan as you judge will about balance 
 the object. Release the beam a little to see which side 
 is heavier. Never allow one end of the beam to go 
 very much lower than the other, especially when a load 
 is on the balance, as the knife edge of the fulcrum is 
 likely to be injured thereby. A good rule is : Never let 
 the pointer swing off the scale. 
 
 When the weights are found which will bring the 
 pointer nearly to zero let the beam come to rest and 
 note the point of rest. Suppose that there are in the 
 pan 4.64 grams and that the point of rest is 4 divisions 
 to the right of zero. You now add 1 eg. and find the 
 point of rest 2 divisions to the left. One eg. has moved 
 the pointer 6 divisions. It would have taken 4/6 eg. 
 to move it 4 divisions, that is, to bring it to zero. The 
 exact weight is therefore 4.647 grams. Support the 
 beam and remove the objects and weights, counting the 
 weights again to make sure you have made no mistake. 
 
 EXERCISE 149. To test a balance by double weighing. 
 
 Apparatus. Balance, weights. 
 
 Directions. We have assumed in Exercise 218 that 
 the arms of the balance are exactly equal in length. 
 This is by no means certain to be the case, especially in 
 a cheap balance, nor is it necessary that the arms be 
 exactly equal in order that we may weigh correctly, 
 provided we know the ratio of the lengths. 
 
 Weigh an object as accurately as possible in the left- 
 hand pan. Then weigh the object in the right-hand 
 
296 MASS. 
 
 pan. If we call the weight required to balance the 
 object when it is in the left pan W and the weight 
 required to balance it when in the right W f , while its 
 true weight is M, it is evident from the principle of 
 moments that if R and L be the length of the right 
 and left arms of the balance (see Fig. 223), 
 
 OM wQ Qw' MQ 
 
 FIG. 223. 
 
 (a) LM=EW 
 
 (b) RM = LW> 
 
 Dividing (b) by (a) 
 
 (c) E/L = LW'/BW 
 Multiplying both sides by R/L 
 
 (d) R 2 /L*=W'/W 
 
 ' whence (43) B/L = \/W'/W 
 But from (a), by dividing by .L, 
 
 (45) M = ~W 
 
 x/ 
 
 It follows that to find the true weight with a balance 
 whose arms are not equal we have only to determine 
 RjL by double weighing once for all and afterward 
 multiply the apparent weight of the object in the left- 
 hand pan by RjL. 
 
 It is further true that for nearly equal arms 
 
 W+W 
 (46) M= - 
 
THE BALANCE. 297 
 
 Having found the true weight by double weighing, check 
 your result by the method of counterpoising described 
 in the following exercise. 
 
 EXERCISE 150. To weigh by the method of counterpoising. 
 
 Apparatus. Balance and weights, dish of sand. 
 
 Directions. With the object in the left pan put 
 enough sand or shot in the right pan to exactly balance 
 it. Now remove the object and put weights enough in 
 its place to balance the sand. 
 
 EXERCISE 151. To weigh an object by the method of swings. 
 Apparatus. Balance and weights. 
 
 Directions. Find the zero of the balance. In a deli- 
 cate balance the beam does not come to rest for some 
 time, but the point of rest may be determined by ob- 
 serving the extreme position of the pointer for three 
 successive swings. Since the am- 
 plitude of swing is gradually grow- 
 ing less, owing to the resistance of 
 the air, the average of the first and '"/""(< "M"' 
 
 second swings would give us a I 
 
 point a little to the right of zero, 2 I 
 
 if the first swing was toward the /'//<, /iM M ,,m'l 
 right, while the average of the 
 second and third would give us a | 
 
 point a little to the left of zero. 
 Thus in the example illustrated '""/unj.lniiHM 
 in Fig. 224 the swings were * FIG - 224 - 
 
 * To avoid negative readings the scale is numbered from left to right usually 
 in twenty divisions, thus bringing the zero position at the 10th division. 
 
298 MASS. 
 
 14+7 
 
 = 10.5 
 
 >=10 
 
 Hence to find the zero, average the right-hand read- 
 ings and the left-hand readings separately and take the 
 mean of the two averages. 
 
 Thus: - - - = 10 
 2 
 
 After finding the point of rest arrest the beam, re- 
 lease it again and take a new set of readings. If the 
 two sets give results agreeing to a tenth of a division 
 they may be averaged and the mean taken as the zero. 
 Otherwise a number of trials must be made. If the 
 balance is in a strong draft currents of air may pene- 
 trate the case. One object of repeating observations 
 several times is to find out whether our results really 
 possess the degree of accuracy of which the instru- 
 ments and -methods used are capable. 
 
 For simplicity the readings given in the example were 
 all whole numbers. In practice tenths of a division 
 should always be estimated. If the zero falls more 
 than one scale division from the centre the instructor 
 should be asked to adjust the balance. 
 
 Having determined the zero, which we will call p^ 
 place the object in the left pan and balance it with 
 
DENSITY. 299 
 
 weights, IF, as in Exercise 220. When the adjustment 
 has been made by means of the rider to within 1 mg. 
 find the point of rest p v by swings, add 1 mg. by means 
 of the rider, and find another point of rest p 2 . The 
 weight of the object is then 
 
 (47) M = W+ Pl ~^ Po 
 
 173. Density. By the density of a substance is 
 meant the mass of unit volume of that substance. For 
 purposes of comparison it is common to speak of relative 
 densities, taking as our standard of comparison the 
 weight of unit volume of water at its temperature of 
 greatest density (4 degrees C.). 
 
 If a certain volume of a given substance is found to 
 weigh 7.7 times as much as an equal volume of water, 
 the relative density or specific gravity of the substance 
 is 7.7. 
 
 One cubic centimetre of water at 4 degrees C. weighs 
 one gram, hence the number expressing the weight of 1 
 cu. cm. of a substance expresses also its relative density 
 or specific gravity.* 
 
 If the body has a volume of v cu. cm. we must 
 divide its mass m by v to find the mass of 1 cu. cm. ; 
 hence, in general, to find the density of a body we 
 divide its mass by its volume, and our fundamental 
 formula for density is 
 
 (48) d = m/v 
 
 * For the sake of brevity we shall use the word density to denote relative 
 density. 
 
300 MASS. 
 
 The mass m we usually find by weighing the body. 
 The method of finding the volume must be adapted to 
 the case in hand. Density as just defined should, 
 strictly speaking, be distinguished as volume density. 
 The mass of unit length of a string or wire, for ex- 
 ample, is called its linear density, while the mass of 
 unit surface of a sheet of uniform thickness is called 
 its surface density. When nothing is specified to the 
 contrary, volume density is always understood. 
 
 EXERCISE 152. To find (a) the linear density and (b) the 
 volume density of a wire. 
 
 Apparatus. Metre stick, micrometer gauge, balance and 
 weights. 
 
 Directions. (a) Measure the length of the wire 
 with the metre stick and its weight with the balance. 
 
 mass 
 
 (49) Linear density = = r 
 
 length 
 
 (6) Measure the diameter of the wire and compute its 
 volume from the formula v = 3.1416 r 2 /, where v is the 
 volume, r the radius, and I the length of the cylindrical 
 wire. Compute the volume density from the formula 
 (48) d = m/v 
 
 EXERCISE 153. To determine (a) the surface density, (b) the 
 volume density of a sheet of metal bounded only by straight lines. 
 
 Apparatus. Metre stick, balance and weights, micrometer 
 gauge. 
 
 Directions. (#) Divide the given surface into tri- 
 angles by drawing diagonals. Measure the base and 
 altitude of each triangle. The sum of the areas of the 
 
DENSITY. 301 
 
 triangles is the area of the surface. On the other side 
 of the surface draw different diagonals and make an 
 independent determination of the surface. Average 
 the two values. The surface density is easily found : 
 
 (50} Surface density -^ 
 
 surface 
 
 (#) Measure the thickness and compute the volume, 
 which is the thickness times the surface. Then the vol- 
 ume density is : 
 
 (48} d m/v 
 
 EXERCISE 154. To make a set of weights. 
 
 Apparatus. Balance, weights, sheet lead, aluminum wire, 
 shears, cutting pliers. 
 
 Directions. For the larger weights, one gram and 
 larger, use heavy sheet lead. First find the surface 
 density of a rectangular piece of the lead and calculate 
 the size needed for a 5 gram weight. Cut it too large 
 and then pare it down gradually till the exact weight is 
 obtained. Be very careful at the last not to take off 
 too much. If you should get one too light use it for 
 making 2 gram weights. A strip 4 times as long as the 
 5 gram weight may be used for a 20 gram and folded 
 in 4 parts. The weights may be marked with steel dies 
 or scratched with an awl. 
 
 For fractions of a gram use two sizes of aluminum 
 wire, one for tenths, one for hundredths. Bend the 2 
 eg. piece at right angles near its middle, and the 5 to a 
 pentagon to distinguish them. 
 
 For a set of rider weights smaller wire should be 
 chosen. 
 
302 MASS. 
 
 EXERCISE 155. To find the density of a regular solid as a 
 sphere * or cylinder. 
 
 Apparatus. Micrometer gauge or vernier gauge, balance 
 and weights. 
 
 Directions. Weigh the body as accurately as pos- 
 sible. Measure the dimensions of the body carefully 
 and compute its volume. The volume of a sphere is 
 3.1416 D3/6 = .5236 D 3 , where D is the diameter of 
 the sphere. The volume of a .cylinder is 3.1416 r 2 , 
 where r is the radius and I is the length of the cylinder. 
 
 Having found the mass, m, in grams and the volume, 
 v, in cubic centimetres, compute the density by the 
 
 formula : 
 
 (48) d = m/v 
 
 EXERCISE 156. To find the density of a liquid with the 
 graduate. 
 
 Apparatus. Balance and weights, beaker, graduate. 
 
 The cylindrical graduate is a cylindrical glass jar of nearly 
 uniform diameter, graduated to cubic centimetres (see Fig. 
 225). 
 
 Directions. Weigh in a beaker a convenient quantity 
 of the liquid, pour the liquid into the graduate, and 
 weigh the beaker with what remains in it. This is a 
 better plan than to weigh the beaker first, since some of 
 the liquid will adhere to the beaker. 
 
 Read on the graduate the volume of the liquid, re- 
 membering that while the liquid rises on the sides of 
 the jar, the main body of the liquid is only as high as 
 the central part. The jar should be placed on a level 
 
 * The balls used in bicycle bearings are almost perfectly spherical. 
 
DENSITY. 
 
 303 
 
 table and the eye should be on a level with the top of 
 the liquid to avoid parallax. As before, 
 (48) d = m/v 
 
 EXERCISE 157. To find the volume and density of an irreg- 
 ular solid, using the graduate. 
 
 Apparatus. Balance and weights, graduate. 
 
 Directions. 
 
 - The solid 
 must be of 
 a size to go 
 into the grad- 
 uate easily. 
 Weigh the 
 solid. Fill 
 the graduate 
 half "" full of 
 water and 
 note the vol- 
 ume. Drop 
 the solid into 
 the water and 
 again note the 
 volume. The 
 increase in 
 volume is of 
 course the 
 volume of 
 the solid FIG. 225. 
 
 (see Fig. 225). If the solid is lighter than water it 
 may be held below the surface by means of a needle in 
 
304 
 
 MASS. 
 
 the end of a stick. The volume of the' needle point 
 may be neglected. If the solid is a crystal soluble in 
 water it may be immersed in a saturated solution of the 
 same substance, or it may be immersed in a liquid in 
 which it is not soluble. 
 
 EXERCISE 158. To find the volume and density of an 
 irregular solid by Archimedes' principle. 
 
 Apparatus. Balance and weights, tumbler, bridge, fine 
 thread. 
 
 Directions. By Archimedes' principle a solid when 
 immersed in a liquid has its apparent weight dimin- 
 ished by an amount equal to 
 the weight of the liquid dis- 
 placed. If the liquid be water 
 the number expressing its weight 
 in grams expresses also its vol- 
 ume in cubic centimetres. But 
 the volume of water displaced 
 is evidently equal to the volume 
 of the solid which displaces it, 
 whence the loss of weight of a 
 solid when immersed in water is 
 the volume of the solid. 
 
 Place the bridge over the left- 
 hand pan of the balance, taking 
 care that it does not touch the 
 pan (see Fig. 226). Set the 
 tumbler upon the bridge and susperid the solid by a 
 thread from the hook supporting the balance pan. The 
 
 FIG. 226. 
 
DENSITY. 305 
 
 body should hang free in the middle of the glass. 
 Weigh the body and then pour water, which has been 
 previously boiled to free it from air, into the glass till 
 the body is completely covered and weigh again. The 
 difference in weight will not give exactly the volume 
 of water displaced, since a gram of water at any higher 
 temperature than 4 degrees has expanded to a volume 
 greater than 1 cu. cm. Note the temperature, therefore, 
 and look up in Table 4 the volume of one gram of water 
 at the given temperature. Multiply the loss of weight 
 in water by the factor found in the table. This will give 
 you v. As usual, 
 
 (48) d = m/v 
 
 EXERCISE 159. To find the density of a liquid by Archi- 
 medes' principle. 
 
 Apparatus. As in Exercise 158. 
 
 Directions. Suspend a glass stopper as directed in 
 Exercise 157. Weigh the stopper in air and in water 
 and so find its volume. Now remove the water and fill 
 the glass with the given liquid. A saturated solution 
 of salt or of copper sulphate may be used. Find the 
 loss of weight of the stopper in the given liquid. This 
 is equal to the weight of a volume of the liquid equal 
 to the volume of the stopper. Again, 
 
 (48) d = m/v 
 
 EXERCISE 160. To find the density of a liquid with the 
 bottle. 
 
 Apparatus. Balance and weights, glass-stoppered bottle. 
 
S06 MASS. 
 
 The specific gravity bottle (Fig. 227) furnished by dealers is 
 usually a small Florence flask with a mark on its neck or, much 
 better, a light bottle with a perforated ground-glass stopper, to 
 facilitate filling the bottle without leaving air near the top. 
 Any light glass-stoppered bottle holding from 20 to 50 c.c. 
 will answer the purpose nearly as well. 
 
 Directions. Wash the bottle and dry it by putting 
 a little alcohol in it. After shaking well so that the 
 water will be taken up by the alcohol, 
 pour the alcohol into the flask kept for 
 impure alcohol. To remove what re- 
 mains in the bottle rinse it with a little 
 ether. The ether which remains will 
 soon evaporate, leaving the bottle dry. 
 Weigh the bottle, fill it with boiled 
 water, note the temperature and weigh. 
 The weight of the bottle and water less 
 ^^^^ the weight of the bottle is equal to the 
 
 FIG. 227. volume, v, contained by the bottle. 
 
 Empty and dry the bottle, fill it with the given liquid, 
 and weigh as before. The weight is m and 
 
 (48) d m/v 
 
 EXERCISE 161. To find the density of a solid with the bottle. 
 Apparatus. Balance and weights, bottle. 
 
 Directions. Find the mass, w 15 of the bottle when 
 filled with water. Weigh the solid m, and put it into the 
 bottle, allowing the water to overflow, wipe the bottle 
 
DENSITY. 
 
 307 
 
 and weigh again, w 2 . The volume of the solid is then 
 equal to the mass of water that overflowed, or: 
 
 v =. m l -j- m m 2 
 and 
 
 (48) d = m/v 
 
 EXERCISE 162. To find the density of a liquid which does 
 not mix with water, using the U tube. 
 
 Apparatus. Glass tube one metre long, bent to the shape 
 shown in Fig. 228. 
 
 Directions. Support the tube in a vertical position 
 and pour enough water into it to fill it about halfway 
 to the top. Pour into one arm enough of 
 the given liquid to fill one arm nearly to 
 the top, taking care that there is enough 
 water to fill the bend of the tube. Meas- 
 ure the height of the liquid in each arm 
 above the level of the surface of contact 
 of the two liquids. It is evident that the 
 pressure of the liquid in both tubes at the 
 level A is equal. If the tube is of uniform 
 diameter the masses of the columns AB 
 and A are equal, and if the cross section 
 of the tube were 1 sq. cm. the volume of 
 the given liquid would be AB cu. cm. and 
 its weight would be AC grams. Since 
 the ratio of the heights of the two col- 
 umns is the same whatever the size of the 
 tube may be, we may call AB = v and A C = m, and 
 we have 
 
 (48) d = 
 
 FIG. 228. 
 
308 
 
 JL 
 
 EXERCISE 163. To measure the density of a liquid by the 
 principle of the barometer. 
 
 Apparatus. Two tumblers, two glass tubes united at the 
 top by a T joint, to the stem of which is attached a piece of 
 rubber tubing (Fig. 229). 
 
 Directions. Fill one tumbler with 
 the liquid, the other with water. 
 Let one of the tubes dip in each 
 tumbler. If all of the air were now 
 removed from the tubes, the water 
 B would rise, if possible, to a height of 
 about 10 metres, due to the pressure 
 of the atmosphere. Exhaust enough 
 of the air, by applying the mouth to 
 the rubber tube, so that the water 
 will rise nearly to the top of the tube 
 and close the rubber tube with a 
 pinch cock. If the other liquid is 
 heavier than water it will rise to a 
 less height. Measure carefully the 
 height of the liquid column AB above 
 the surface of the liquid in the tum- 
 FIG. 2-29. bier and of A'O above the surface 
 
 Then, as in Exercise 162, A'C=m, 
 
 of the water. 
 AB = v, and 
 
 (48) d = 
 
 EXERCISE 164. To find the density of a substance lighter 
 than water by Archimedes' principle. 
 
 Directions. Let the student devise a method. 
 
DENSITY. 
 
 309 
 
 EXERCISE 165. To find the length of a coiled wire. 
 
 Apparatus. Same as for Exercise 158, also micrometer gauge. 
 
 Directions. Find the volume of the wire and its 
 diameter and compute its length. 
 
 4. DENSITIES. 
 
 
 
 Solids. 
 
 
 Aluminum 
 
 2.58 
 
 Pine . 
 
 0.5 
 
 Brass 
 
 8.4 
 
 Faraffine 
 
 ."- .89 
 
 Copper . 
 
 8.92 
 
 Platinum 
 
 . 21.5 
 
 Cork 
 
 0.24 
 
 Porcelain 
 
 2.2 
 
 Glass (common) 
 
 2.6 
 
 Quartz . 
 
 2.65 
 
 (flint) 
 
 3.5 
 
 Sand . t *. 
 
 2.8 
 
 Gold 
 
 19.3 
 
 Silver . 
 
 . 10.53 
 
 Ice 
 
 J).91 
 
 Steel . 
 
 7.87 
 
 Iron (wrought) 
 
 7.84 
 
 Tin . 
 
 7.29 
 
 Lead 
 
 "11.33 
 
 Wax . 
 
 . 1 .96 
 
 Oak 
 
 0.8, 
 
 Zinc . 
 
 . : 7.16 
 
 Liquids (20). 
 
 Alcohol 
 
 .789 
 
 Glycerine 
 
 ^ 1.26 
 
 Carbon bisulphide 
 
 1.29 
 
 Mercury 
 
 . 13.6 
 
 Ether . * , . 
 
 74 
 
 Sulphuric acid 
 
 1.85 
 
 
 
 Water. 
 
 
 t D 
 
 t 
 
 D t 
 
 D 
 
 0.99988 
 
 10 
 
 0.99974 20 
 
 0.99827 
 
 1 , 0.99993 
 
 11 
 
 0.99965 21 
 
 0.99806 
 
 2 0.99997 
 
 12 
 
 0.99955 22 
 
 0.9978$ 
 
 3 0.99999 
 
 13 
 
 0.99943 23 
 
 0.99762 
 
 4 1.00000 
 
 14 
 
 0.99930 24 
 
 0.99738 
 
 5 0.99999 
 
 15 
 
 0.99915 25 
 
 0.99714 
 
 6 0.99997 
 
 16 
 
 0.99900 26 
 
 0.99689 
 
 7 0.99994 
 
 17 
 
 0.99884 27 
 
 0.99662 
 
 8 0.99988 
 
 18 
 
 0.99866 28 - 
 
 0.99635 
 
 r 9 0.99982 
 
 19 
 
 0.99847 29 
 
 0.99007 
 
CHAPTER XI. 
 TIME. 
 
 174. Measurement of Time. In measuring time, 
 as in measuring length, we must be able to divide the 
 object to be measured into equal parts. The natural 
 divisions of time, the year, the lunar month, the day, 
 have been subdivided into smaller units for convenience 
 in measuring small intervals of time. Our smallest unit 
 of time, the second, is ^-RTFO of a mean solar day. The 
 period of a complete revolution of the earth upon its 
 axis is absolutely the same from day to day and from 
 year to year. If we are to make accurate time meas- 
 urements we must employ an instrument that returns 
 to a given starting point after equal intervals of time, 
 or, as we say, vibrates isochronously. This condition is 
 met if a body is held in a position of equilibrium by 
 some force and, if, when it is displaced from that posi- 
 tion, the force causing it to return is proportional to 
 the displacement. This is the sort of motion which 
 produces musical sounds, and it is known as simple 
 harmonic motion. The vibration of a tuning fork when 
 struck, a guitar string when picked and released, a ver- 
 tical spiral spring with a weight at its lower end when 
 pulled down and released, a vertical wire with a weight 
 
 310 
 
MEASUREMENT OF TIME. 311 
 
 attached when twisted and released, a common swing 
 pendulum when the bob is drawn to one side and re- 
 leased, the spiral hairspring of a watch when distorted 
 all these are examples of simple harmonic motion. 
 
 EXERCISE 166. To find the time of oscillation of a simple 
 pendulum. 
 
 Apparatus. Clock or watch, metre stick, small thread, ball. 
 
 Directions. By time of oscillation we mean one half 
 the time required for a complete vibration. The time 
 of vibration of the seconds pendulum is two seconds. 
 The pendulum should be so supported that the length 
 of the string is the same in all parts 
 of its swing. Fig. 230 shows a good 
 
 way and a bad way of supporting the _ -_-.. 
 
 string. Adjust the pendulum to a -"^-^--^ 
 convenient length, sit with your eye 
 in line with the string and a mark 
 behind it, such as the edge of the 
 support. Set the pendulum swing- 
 ing through a small arc and practise 
 counting the swings as it passes the 
 mark till you can look off for an instant at the watch 
 without losing the count. Note the hour, minute, and 
 second of the passage of the pendulum, count fifty 
 swings, and again take the time. The difference be- 
 tween these two times divided by fifty will be the period 
 of oscillation. Repeat till your observations do not 
 vary more than one or two seconds in fifty beats. Now 
 measure the length of the pendulum to the middle of 
 
 
312 TIME. 
 
 the ball with the metre stick, taking the average of the 
 lengths to the top and bottom of the ball and compute 
 the time of oscillation by the law of the pendulum 
 
 (31} t = 8.1416 ^_ 
 
 where I is the length of the pendulum and g = 980 
 
 Make the same measurements with the pendulum a 
 little longer and again with it a few centimetres shorter. 
 
 EXERCISE 167. To find the time of oscillation of a spiral 
 spring. 
 
 Apparatus. Jolly's balance, watch. 
 
 Directions. Put a small weight in the pan and mark 
 the position of the index on the scale -by fastening a 
 little paper pointer to the scale with a bit of wax. 
 Draw the spring downward two or three centimetres 
 and release it. Count the number of times, n, that the 
 index passes the mark, both up and down, in one min- 
 ute. The time of oscillation is then t = 60 / n. Count 
 for five minutes and the time is t = 300 / n', a result 
 which is more probably correct than the former. 
 
 EXERCISE 168. To find the time of oscillation of a torsional 
 pendulum. 
 
 Apparatus. Torsional pendulum, watch or clock, tele- 
 scope." 
 
 Directions. Fasten a bit of paper with a vertical 
 mark upon it on the side of the weight facing you and 
 set the telescope so that the cross hair in the eyepiece 
 will coincide with the mark when the pendulum is at 
 
MEASUREMENT OF TIME. 313 
 
 rest (see Fig. 231). If the clock beats seconds audibly 
 watch until the mark crosses the hair exactly on a sec- 
 ond, then count the seconds till it passes 
 again on an even second, while another 
 student counts the number of beats of the 
 pendulum. Time should be given for at 
 least ten beats to occur. Exchange places 
 with your assistant ] and repeat. Make 
 at least five determinations apiece. Add 
 weights to the pendulum and again deter- 
 mine the time. 
 
 EXERCISE 169. To determine the acceleration 
 due to gravity with the simple pendulum. 
 
 Apparatus. Metre stick with vernier, simple pendulum. 
 
 Directions. Measure , the length of the pendulum, 
 in centimetres, and t, its time of oscillation, in seconds, 
 with all possible care as directed in Exercise 166. If 
 the pendulum is long, the error in measuring I and t 
 will be less than with a short one. The thread must be 
 light and the bob should not be much more than 2 cm. 
 in diameter. A metal ball is better than a wooden one. 
 Why ? The oscillations of a simple pendulum are not 
 strictly isochronous except for a small arc. With a 
 pendulum one metre long the ball may swing 5 or 6 
 cm. to each side of the centre without introducing a 
 perceptible error. Having determined the value of t 
 and Z, substitute them in the formula 
 (33} g = (3.1416)* I ft* 
 
 EXERCISE 170, To count your pulse, 
 
314 TIME. 
 
 Directions. Lay your watch on the table before you. 
 Place the forefinger of the right hand on the left wrist, 
 
 as shown in Fig. 232. 
 When the location of the 
 artery is found press 
 slightly with the forefinger 
 and, with your eye on the 
 watch, count the beats 
 FIG - 232 - that occur in one minute. 
 
 Repeat three times. Ask other students for the results 
 obtained by them. 
 
 EXERCISE 171. To count the respiration. 
 Directions. Breathe quietly for a minute while you 
 count the number of respirations. Try four times. 
 Watch a student who is writing or otherwise quietly 
 employed and count his respiration. Do the results 
 obtained agree as closely as the time found for the pulse 
 beat? 
 
 175. Estimation of Time. It is frequently of use 
 to be able to estimate intervals of a few seconds with- 
 out the watch, as in making a photographic exposure. 
 
 EXERCISE 172. To estimate a short interval of time. 
 Apparatus. Watch. 
 
 Directions. Sit, watch in hand, and count with the 
 watch for three minutes or till you can count at about 
 the right rate, then note the time and looking off from 
 the watch count for fifteen seconds-and again look at the 
 watch. Record the result and repeat five times. Is 
 
MEASUREMENT OF TIME. 315 
 
 your error always on the same side ? It is sometimes 
 helpful to utter a phrase of about the right length to fill 
 the interval between counts. The words, a thousand 
 and one, a thousand and two, etc., may be made to serve 
 as a rough measure of time. 
 
 EXERCISE 173. To find your rate of walking. 
 Apparatus. Watch. 
 
 Directions. Count the steps you take in walking 
 some distance you cover daily. Repeat ten times and 
 estimate the distance from your length of step. Note 
 the time required to walk the distance at your usual 
 rate and also at the fastest rate which you are able to 
 keep up. Record any difference in the direction of the 
 wind or the like that might affect your rate. 
 
CHAPTER XII. 
 
 FORCE. 
 
 PRESSURE OF FLUIDS. 
 
 EXERCISE 174. To measure the pressure of the atmosphere 
 with the barometer. 
 
 Apparatus. The best form of instrument is Fortin's ba- 
 rometer, shown in Fig. 233. The height of the barometer is 
 the difference in level of the two mercury surfaces 
 s and s*. The zero of the scale is the tip of 
 the ivory point, which projects into the cistern. 
 Hence, that the scale may measure the height of 
 the column, the surface s must be adjusted, by 
 means of the adjusting screw at the bottom, until 
 the ivory point touches the surface of the mercury. 
 The reading is taken with the vernier, which 
 is moved by means of the milled head, m, till the 
 light reflected from the white background barely 
 disappears at the middle point of the surface, s ! . 
 To prevent parallax the vernier is graduated 
 upon a movable tube. The eye is in the proper 
 position to take a reading when the front lower 
 edge of this tube appears to coincide with the 
 back lower edge. The vernier sometimes differs 
 from the one already used only in being divided 
 to twentieths instead of tenths. 
 
 Directions. Adjust the mercury in the 
 cistern till the ivory point touches the sur- 
 face. One adjustment is sufficient for the 
 FIG. 233. ti me f the exercise. Take three readings 
 
 816 
 
THE BAROMETER. 
 
 317 
 
 3:00 
 
 742.25 
 
 3:10 
 
 742.30 
 
 3:20 
 
 742.35 
 
 3:30 
 
 742.40 
 
 3:40 
 
 742.40 
 
 3:50 
 
 742.50 
 
 4:00 
 
 742.40 
 
 rs 
 
 AVERAGE 
 
 742.25 
 
 742.27 
 
 742.30 
 
 742.30 
 
 742.30 
 
 742.33 
 
 742.40 
 
 742.40 
 
 742.45 
 
 742.43 
 
 742.55 
 
 742.52 
 
 742.60 
 
 742.55 
 
 every ten minutes for an hour. Record the time (day, 
 hour, and minute) of each observation. Tabulate the 
 results and plot a curve showing graphically the varia- 
 tions of the barometer during the hour.* Suppose your 
 observations were as follows : 
 
 READING OF BAROMETER, OCTOBER 8. 
 TIME OBSERVATIONS 
 
 742.30 
 742.30 
 742.35 
 742.40 
 742.45 
 742.50 
 742.52 
 
 To plot these results in the form of a curve we let 
 equal horizontal spaces represent equal periods of time 
 and equal vertical spaces represent equal heights of the 
 barometer. We divide the distance across a page of 
 cross-section paper or any 
 paper ruled in squares into 
 six equal parts, as shown in 
 Fig. 234. Then if the base 
 line represent a height of 
 742.25 mm. and the top line 
 a height of 742.55 mm., the various heights given in 
 our table of results will fall at the corresponding heights 
 on the paper. If we divide each vertical space into ten 
 parts the reading for 3 : 00 will fall at 2.7 divisions 
 
 *If the barometer is not provided with a vernier follow the directions given 
 in Exercise 132, using the metre stick and square. 
 
 FIG. 234. 
 
318 FORCE. 
 
 Vabove the bottom line, etc. Make a small circle at the 
 point where the vertical line which represents by its 
 distance to the right the time, meets the horizontal line 
 which represents by its height the height of the barom- 
 eter. Connect all these circles by a smooth curve and 
 we have a graphic or pictorial representation of the vari- 
 ations of the barometer between 3 P.M. and 4 P.M. of 
 October 8. 
 
 EXERCISE 175. To determine the altitude of your labora- 
 tory above the level of the sea. 
 
 Apparatus. Barometer, daily weather maps. 
 
 The weather maps may be seen at the post office, or on an 
 application of the instructor through the postmaster they will 
 be sent regularly to the laboratory, where if daily posted they 
 may be made a source of much valuable information in the 
 application of the principles of physics to the solution of the 
 problems of our atmosphere. A good aneroid barometer will 
 answer for this experiment if it has been compared with a 
 mercurial barometer and is known to be correct. 
 
 Directions. Read the barometer daily as nearly as 
 possible at the hour for which the map is drawn. 
 Locate your town as well as you can on the map and 
 note the position of the two isobars that pass nearest to 
 it. This will give you the reading of the barometer 
 reduced to sea level, since all the observations of pres- 
 sure made at the different stations are reduced to the 
 pressure that would be found down a mine whose bot- 
 tom was on a level with the ocean. The difference in 
 pressure is about 1 inch for 930 feet. The difference 
 between your reading of the barometer and the reading 
 
THE MANOMETER. 
 
 319 
 
 FIG. 235. 
 
 obtained from the map, if both are expressed in inches/" 
 will, when multiplied by 930, give the elevation above 
 sea level of your laboratory. 
 
 EXERCISE 176. To measure the pressure 
 of the gas in the laboratory. 
 
 Apparatus. Open manometer and metre 
 stick with vernier. The open manometer or 
 pressure gauge may be made of a glass tube, 
 bent as shown in Fig. 235. The bend of the 
 tube is filled with water and the horizontal 
 ann is attached by a rubber tube to the gas 
 cock. 
 
 Directions. Turn on the gas and 
 measure the difference in level of the 
 two surfaces A, B. If this distance be I centimetres 
 the volume of water supported by the gas for a surface 
 of 1 sq. cm. is I cubic centimetres and 
 its weight is I grams. The pressure is 
 therefore I grams or 980 X I dynes per 
 sq. cm. 
 
 EXERCISE 177. To measure the pressure 
 of the water at the hydrant and to compute the 
 head required to produce it. 
 
 Apparatus. Closed manometer, metre 
 stick, and vernier. The closed manometer 
 consists of a bent tube with one arm closed. 
 It has a mercury index in the bend of the tube 
 (see Fig. 236). The open end of the tube must 
 be fastened firmly by means of wire to the rubber tube. Both 
 the glass tube and the rubber tube should be very strong to 
 withstand the pressure upon them. 
 
 -D 
 
 -B 
 
 --C 
 
 -A 
 
 FIG. 236. 
 
320 FORCE. 
 
 Directions. Bring the mercury to the same level in 
 both arms of the manometer by tilting it till a little 
 mercury flows from one side to the other. Measure the 
 length, CD, of the enclosed air column and read the 
 barometer pressure, p. 
 
 Now turn on the water gradually till you have the 
 full pressure and measure the length, ED. 
 
 Call CD == v, BD = v< and AB = I. 
 
 Then from Boyle's law : vp v'p f , whence the pres- 
 sure, jt/, of the enclosed air is 
 
 (48} p' = vp/V 
 
 But p' is not the only pressure acting against the 
 pressure of the water. The weight of a mercury 
 column I cm. long is also supported by the water. The 
 
 pressure of the water is therefore 
 
 * 
 
 P =p r -)- I cm. of mercury 
 P (p' -[- 1} x 13.55 grams per sq. cm. 
 (49} P = (p' -j- I) X 13.55 X 980 dynes per sq. cm. 
 
 CAPILLARITY. 
 
 176. The Capillary Constant or coefficient of sur- 
 face tension of a liquid is defined as the weight of 
 liquid raised above its natural level per unit of length 
 of the line bounding the surface of the liquid raised. 
 In a capillary tube of radius r the length of the line 
 bounding the surface is 2 X 3.1416 r. If the liquid 
 whose density is d rises to a height h the volume of the 
 liquid raised is 3.1416 hr 2 and its weight is 3.1416 hr 2 d. 
 
THE CAPILLARY CONSTANT. 
 
 321 
 
 The capillary constant is, then, 
 
 a = 8.1416 hr*d / 2 X 3.1416 r = h hrd 
 
 or in dynes 
 
 (50) a = h hrd X 980 
 
 EXERCISE 178. To find (a) the radius of a capillary tube, 
 (b) the capillary constant of a liquid. 
 
 Apparatus. Clean mercury, balance, watch glass, crystal- 
 lizing dish, pipette, metre stick, block (Fig. 237). This block 
 consists of a little board with a 
 scale, made of a piece of metre 
 stick, attached to it. Two brass 
 nails are driven through the board 
 and project about 2 cm. 'below the 
 top of the board. , 
 
 Directions. (#) To measure 
 the radius of the capillary tube. 
 
 See that the tube is perfectly 
 dry, then draw into it a thread 
 of mercury about 3 or 4 cm. 
 long. This may be done by attaching a small rubber 
 tube to one end of the glass tube and exhausting the 
 air. Be careful not to draw the mercury into your 
 mouth. Pinch the rubber tube to keep the mercury in 
 place while you lay the glass tube upon a metre stick and 
 measure the length, ?, of the mercury column. Pour 
 the mercury out into a watch glass and weigh it. The 
 density of mercury at 20 degrees is 13.55. The volume 
 of the mercury thread is 3.1416 lr z and its weight is 
 m 13.55 X 3.1416 Zr 2 , whence 
 
 FIG. 237. 
 
322 FORCE. 
 
 (51) r 2 = m / 13.55 X 8.1416 1 
 
 from which, by extracting the square root, we obtain r. 
 
 (6) To measure A, first clean the tube, by pouring 
 nitric acid through it and rinsing with water. Set the 
 block (Fig. 237) upon the crystallizing dish and fill 
 the dish with water till the surface of the water just 
 touches the points of the nails. Make the final adjust- 
 ment with the pipette. Set the tube in front of the 
 scale and read the height of the liquid on the scale. 
 Raise and lower the tube. If the tube is clean the 
 height will not be altered. Remove the tube, set the 
 block upon the table and measure the distance from 
 the points to the bottom of the scale. Measure at both 
 ends and take the average. This distance added .to 
 the reading of the scale is equal to h. Substitute your 
 values of r and h and the value for rf, obtained from 
 Table 4, in the formula, a = */ 2 hrd X 980. 
 
 Note the temperature of the liquid and compare your 
 result with that given in Table 5. 
 
 5. CAPILLAEY CONSTANT. 
 
 TEMPERATURE WATER ALCOHOL 
 
 10 77.5 24.97 
 
 15 76.6 24.53 
 
 20 75.7 24.09 
 
 25 74.8 23.60 
 
 ELASTICITY. 
 
 177. Young 's Modulus of Elasticity is defined as 
 the force which would double the length of a rod 
 
YOUNG 9 S MODULUS OF ELASTICITY. 323 
 
 or wire of unit cross section of the substance under 
 consideration. It may also be defined as the ratio of 
 the stress to the strain. If a wire of length L and 
 cross section a is elongated an amount I by a weight W 
 
 W 
 
 the stress per unit area is , while the strain per unit 
 
 I 
 
 length is -^. The modulus, E, is the stress divided 
 j 
 
 W I 
 by the strain, or =r -. ^-, or 
 
 (6*) E = ^L 
 
 The measurements are to be taken in kilograms and 
 millimetres. 
 
 Another method of finding the modulus is by hang- 
 ing weights from the middle of a rectangular bar which 
 is supported near its ends upon knife edges, as in Fig. 
 239. If the vertical thickness of the bar be A, its 
 breadth, ft, and its length, L, between the triangular 
 supports, and if a weight, W, lowers the middle of the 
 bar a distance I it may be shown by higher mathematics 
 that the modulus, E, is 
 
 The measurements are to be taken in kilograms and 
 millimetres. 
 
 EXERCISE 179. To find the modulus of elasticity of a wire 
 by stretching. 
 
 Apparatus. As shown in Fig. 238. The wire is supported 
 by looping it over a strong hook in the ceiling. The ends are 
 
324 FORCE. 
 
 twisted together at the bottom so as to support the pan for 
 weights. To measure the elongation a lever is used consisting 
 of a metre stick having a nail through it, around which the 
 wires are wound two or 
 three times, the two wires 
 being wound in opposite 
 directions. The nail is 
 placed so that its centre is 
 just on the 1 cm. division. 
 Through the centre of the 
 6 cm. division a larger nail 
 passes and rests in two sup- 
 ports which are attached to FlG ' 238 ' 
 a block clamped to the table. A darning needle projects 6 
 cm. from the long end of the lever, making the long arm just 
 twenty times as long as the short one. 
 
 Directions. Measure the height of the pointer 
 above the table when enough weight is in the pan to 
 make the wire straight. Add one kilogram and meas- 
 ure the height again. Add a second and third weight 
 and measure the height of the pointer each time. Re- 
 move the weights and see if the zero reading remains 
 unchanged. Subtract each reading from the next 
 larger and see how they agree. If the first is much 
 larger than the rest it should be discarded, as the wire 
 was not yet straight. Repeat the operation twice and 
 average all your differences. Divide the average by 
 the ratio of the arms of the lever, and you have Z, the 
 elongation in millimetres for a force of one kilogram. 
 Measure the length of the wire from the hook to the 
 point of attachment. Measure the diameter of the wire 
 
YOUNGS MODULUS OF ELASTICITY. 325 
 
 and multiply the square of the diameter by .7854 to get 
 the area of one wire, which must, in this case, be multi- 
 plied by 2 to get a. Compute the modulus by the 
 formula 
 
 EXERCISE 180. To find the modulus of elasticity of a bar. 
 
 Apparatus. A long rectangular bar of uniform dimensions, 
 resting on two parallel knife edges ; spherometer and sup- 
 port, S (see Fig. 239). 
 
 FIG. 239. 
 
 Directions. Place the spherometer in position, with 
 its legs passing through the small holes in support, S, 
 winch is screwed fast to the table. Take a zero reading 
 before adding any weights. Add a kilogram weight 
 and again take a reading with the spherometer. Add 
 successively three weights and take a reading each 
 time. Remove the weights one at a time and take an- 
 other set of readings. The second set should agree 
 fairly well with the first if the limit of elasticity has 
 not been exceeded. Call the total weight added W, and 
 the amount tne bar is depressed I. Measure the verti- 
 cal thickness, h, of the bar, and its breadth, b. Meas- 
 ure the length of the bar, L, between the knife edges. 
 
326 FORCE. 
 
 Substitute the values obtained in the formula 
 
 SUBSTANCE 
 
 Brass 
 
 Copper 
 
 Iron 
 
 Wood 
 
 Maple 
 
 Oak 
 
 Pine 
 
 EXERCISE 181. 
 
 BREAKING STRESS 
 
 6. ELASTICITY. 
 MODULUS 
 
 kg. 
 sq. mm. 
 
 9930 
 1244!) 
 19000 
 
 1021 2.7 
 
 921 5.7 
 
 1113 4.2 
 
 To measure the breaking stress of a wire. 
 
 to 
 
 Apparatus. Pail, sand, large balance, hammer, clamp, fine 
 wire. 
 
 Directions. Clamp a hammer to the table so that 
 the handle will project as shown 
 in Fig. 240. Wind one end of 
 a fine wire several times about 
 the hammer handle and then 
 twist it securely fast, to the 
 clamp. Fasten the other end 
 of the wire to the handle of the 
 pail. The wire should be of 
 such length that the pail will 
 hang about an inch above the 
 
 FIG. 240. fl oor> 
 
 Pour sand into the pail a cupful at a time until the 
 wire breaks. Weigh the sand and pail and take out a 
 
COEFFICIENT OF FRICTION. 327 
 
 single cupful and repeat, pouring the sand in slowly so 
 as not to put in more than enough to break the wire. 
 If it breaks where it is fastened at either end the ob- 
 servation must be rejected, since any bend in the wire 
 weakens it. 
 
 Measure the diameter of the wire with the microm- 
 eter gauge and compute its cross section. The area 
 of a circle is 3.1416 r 2 . Calling the weight in kilo- 
 grams W and the area in square millimetres of a cross 
 section a, the breaking stress, $, is 
 
 FRICTION. 
 
 178. Coefficient of Friction. The coefficient of 
 friction is the ratio of the force required to overcome 
 friction to the pressure on the surfaces. 
 
 EXERCISE 182. To find the coefficient of sliding friction. 
 Apparatus. Planed board and planed rectangular block, 
 spring balance. 
 
 Directions. (a) Lay the board upon a level table, 
 fasten a spring balance to the middle of one end of the 
 block by means of a string and screw eye, and lay the 
 block on the board. 
 
 Measure the force required to keep the block sliding 
 along the board. Weigh the block. Put a weight on 
 the block and repeat. Care must be taken to keep 
 the string level. 
 
 (6) Support one end of the board at such a height 
 (to be found by trial) that the block, when once 
 
328 
 
 FORCE. 
 
 started, will continue to slide down the inclined plane. 
 If the height of the plane is AC and its base CB, the 
 
 AC 
 
 force required to overcome friction, F, is times the 
 
 C-O 
 
 weight producing pressure, IF, of the block (see Fig. 
 241). 
 
 It follows that 
 F AC 
 
 w = VB and the 
 
 coefficient of fric- 
 tion, /, is 
 
 (55) /=*L 
 FIG. 241. W 
 
 EXERCISE 183. To determine the efficiency of a pulley. 
 Apparatus. Large pulley and weights, spring balance. 
 
 Directions. Weigh the weight, IF, with the balance, 
 hang the weight to one end of the rope which passes over 
 the pulley and attach the balance to the other end. 
 Measure the force required to keep the weight rising 
 after it starts. Call it W. Then the work done 
 against friction is W - - W = F and the coefficient of 
 friction is 
 
 (55) f=*L 
 The efficiency of the pulley is 
 
 if the pulley is single, since the distance through which 
 both forces act is the same. 
 
CHAPTER XIII. 
 
 HEAT. 
 TEMPERATURE. 
 
 EXERCISE 184. To test the zero point of a thermometer. 
 Apparatus. Thermometer, funnel, and jar. 
 
 Directions. The zero point of a Centigrade thermom- 
 eter is the temperature of melting ice. Set the funnel 
 over the jar and fill it with bits of broken ice. When 
 the ice has been long enough in the room so that water 
 is dripping from the funnel, bury the thermometer in the 
 ice as far as the zero, and leave it till it has gone as low 
 as it will (say three minutes) and note the reading. If 
 it should read .3 the error is .3 and the correc- 
 tion is .3; that is, .3 must be added to the reading 
 of this thermometer at or near to give the true tem- 
 perature. 
 
 EXERCISE 185. To test the 100 point of a thermometer. 
 
 Apparatus. Thermometer, flask, Bunsen burner, jacket, 
 sheet of asbestos, support. The jacket is a large glass tube 
 passing through a thin cork, and fitting loosely in the flask. 
 
 Directions. The 100 point of a Centigrade ther- 
 mometer is the boiling temperature of pure water. 
 Water which contains impurities will have a boiling 
 point slightly higher, but as the steam will be pure 
 water it is customary to take the temperature of the 
 steam. Fill a flask half full of water, hang the ther- 
 
 329 
 
330 
 
 HEAT. 
 
 mometer, protected from the air by the jacket, from a 
 support so that it will hang about 1 cm. above the liquid 
 (see Fig. 242). Apply heat till the water boils. After 
 
 it has boiled two or three 
 minutes note the reading of 
 the thermometer* and read 
 the barometer. The ther- 
 mometer should not project 
 far above the top of the 
 jacket. The cork should fit 
 loosely upon the neck of the 
 flask, so as not to confine the 
 steam. 
 
 The boiling point is lower 
 than 100 when the pressure 
 of the air is less than 76 cm. 
 Hence a correction must be 
 made for the reading of the 
 barometer. The boiling point 
 is lowered 0.0375 C. for each millimetre decrease in the 
 pressure of the air. The true boiling point for a pres- 
 sure of b millimetres is therefore 
 
 (57) t' = 100 0.0375 (760 6) 
 
 Compute t r and compare it with your observed value. 
 The difference is the error of your thermometer near 
 100. 
 
 * Should the thermometer be several degrees too low examine It carefully 
 to see if some of the mercury is not in the little enlargement at the top. If so, 
 it mny be brought back to place by taking the thermometer in the hand and 
 swinging it downward at arm's length. 
 
 FIG. 242. 
 
TEMPERATURE. 331 
 
 EXERCISE 186. To find the temperature of your blood. 
 Apparatus. Thermometer. 
 
 Directions. Let your assistant hold the thermometer 
 in his mouth, keeping the lips closed, for about two or 
 three minutes. Read the thermometer to tenths of a 
 degree. Let your assistant take your temperature in 
 the sanle way. Compare the results obtained. Com- 
 pare the amount of difference in the results with the 
 difference obtained in the pulse rate and in the 
 respiration found in Exercises 170 and 171. 
 
 EXERCISE 187. To find the melting point of a solid 
 like paraffine. 
 
 Apparatus. Thermometer, glass tube, beaker, 
 Btinsen burner. 
 
 Directions. Draw the glass tube out at one end 
 to a capillary tube with thin walls, melt some of 
 the solid in a tin cup and draw a portion of it 
 into the tube. Close the tip of the tube in the 
 flame. Make two little rubber bands by cutting 
 bits from the end of a rubber tube, and by means 
 of the bands attach the tube to the thermometer, 
 
 as shown in Fig. 243. Heat some water in a beaker 
 
 FIG. 
 
 while you stir it with the thermometer, and watch 243. 
 carefully for the instant that the solid begins to melt, 
 as shown by its becoming transparent. Read the ther- 
 mometer, remove the flame, and watch for the liquid to 
 solidify. The thermometer may heat and cool a little 
 more slowly than the substance, hence the average of 
 the two readings should be taken as the melting point 
 
 
332 
 
 HEAT. 
 
 of the solid. Repeat four times, always observing the 
 change in the smallest part of the tube. 
 
 EXPANSION. 
 
 179. Coefficient of Expansion. 'The ratio of the 
 increase in length per unit length of a substance for 
 one degree increase of temperature is called the coeffi- 
 cient of linear expansion. 
 
 EXERCISE 188. To find the coefficient of linear expansion of 
 
 a metal. 
 
 Apparatus. Box, spherometer, cans of thin metal about 
 
 30 cm. high and 8 cm. in diameter, thermometer, piece of plate 
 glass. The bqx has holes in one end to fit the 
 legs of th^e spherometer, and a large hole for 
 th0- screw" (see Fig. 244). Two blocks at right 
 angles define the position of the can in the box. 
 The can should be wrapped in several layers of 
 flannel cloth to prevent loss of heat by radia- 
 tion. It may be sewed fast and left on the can, 
 but must not be allowed to get wet. 
 
 Directions. Set the spherometer in 
 place, measure the length, L, of the can, 
 and fill the can to within about 5 mm. of 
 the top with cold water. Take the tem- 
 perature of the water, set the can in place, 
 seeing that the seam is exactly over a mark 
 
 of the box and that the can is back 
 Put the plate glass on top of the 
 
 
 i3 
 
 
 FIG. 244. 
 
 on the bottom 
 
 against the blocks. 
 
 can, bring the spherometer screw down upon it, and read 
 
 the spherometer. Raise the screw, remove the glass and 
 
 can, take the temperature again, empty the can and fill 
 
SPECIFIC HEAT. 333 
 
 it with boiling water from a teakettle or pail, take 
 its temperature and replace it in its former position. 
 Again read the spherometer, remove the can, and take 
 the temperature. The average of the temperature just 
 before putting the can in place and just after removing 
 it may be taken as the temperature of the metal at the 
 time the spherometer reading was made. The difference 
 in the two spherometer readings is the expansion, Z, of 
 the can and the difference between the temperatures of 
 the hot and cold water is the change, t, in temperature 
 of the metal. The coefficient of linear expansion, e, is : 
 
 (58) e = 
 Lt 
 
 We assume in this experiment that the temperature 
 of the metal is the same as that of the water. If the 
 metal is thin and well protected by flannel this will be 
 very nearly the case. 
 
 Care must be taken not to spill the water in the box, 
 as the wood will expand when wet and spoil the results. 
 
 7. COEFFICIENTS OF EXPANSION. 
 
 SUBSTANCE COEFFICIENT SUBSTANCE COEFFICIENT 
 Aluminum 0.000023 Glass 0.000009 
 
 Brass 0.000018 Iron 0.000012 
 
 Copper 0.000017 Platinum 0.000009 
 
 SPECIFIC HEAT. 
 
 180. Heat Capacity. Bodies differ in their capac- 
 ity for heat, that is, in the amount of heat required to 
 raise their temperature one degree. 
 
334 HEAT. 
 
 The capacity of one gram of a substance divided by 
 the capacity of one gram of water (one calorie) is called 
 the specific heat of the substance. Water has the high- 
 est specific heat of any known substance. Hence, if we 
 take the specific heat of water as unity the specific heats 
 of other substances are expressed by fractions differing 
 considerably in value for different substances. 
 
 The principle of the method of mixtures is as follows : 
 If two substances at different temperatures be mixed 
 together the cool body will take heat from the warmer 
 till they are of the same temperature. The quantity of 
 heat lost by the hot body must equal that given the cold 
 body. Account must also be taken of the heat radiated 
 to the surrounding air and of that conducted to the 
 vessel in which the two substances are mixed and to the 
 thermometer. 
 
 EXERCISE 189. To determine the specific heat of a metal by 
 the method of mixtures. 
 
 Apparatus. Calorimeter, thermometer, shot or bits of 
 wire, test tube, beaker. 
 
 Directions. Weigh out M grams of the substances 
 whose specific heat is sought. Weigh in the calorim- 
 eter, which may be a copper beaker or a tin cup, a 
 mass, m, of water. If the temperature of the water is 
 a little less than that of the room, about as much heat 
 will be gained from the air of the room as is lost during 
 the operation. 
 
 Put the shot or bits of metal in a test tube and set 
 the tube in a beaker of boiling water till the metal has 
 
SPECIFIC HEAT. 335 
 
 had time to take the temperature of the water. Read 
 the barometer and compute the temperature. Have 
 ready the cup of cool water with a thermometer in it. 
 Note the temperature of the water. Pour the metal 
 from the test tube into the water, being careful not to 
 let any water from the outside of the test tube fall into 
 the cup. Now stir the shot and water with the ther- 
 mometer and note the highest temperature which the 
 mixture reaches before it begins to cool by radiation. 
 Call the temperature of the shot T, that of the water , 
 and that of the mixture t'. Call the specific heat of 
 water s. It is by definition equal to 1. 
 
 In any transfer of heat the amount of heat transferred 
 is equal to the mass times the specific heat times the 
 change in temperature of the substance. In this case 
 the w r ater has received ms (t 1 f) calories and the cal- 
 orimeter and thermometer have received an amount 
 which we call e (t 1 f), where e is the amount of water 
 which is equivalent in heat capacity to the calorimeter 
 and thermometer. The metal has lost MS (T t 1 ) cal- 
 ories. But the two quantities of heat are equal, hence : 
 
 MS (T t') = (ms + e) (t' t) 
 (59) S = (ms + e) (f t) / M (T V} 
 
 To find e, let the calorimeter and thermometer take 
 the temperature, t v of the room. Pour into the calorim- 
 eter m 1 grams of water at a temperature 2\ (say 30), 
 stir with the thermometer, and note the temperature 
 attained, . Then 
 
336 HEAT, 
 
 (60} e = w 1 (r i - 
 
 Substitute your values in the formula (59) and com- 
 pare the result with the value given in Table 8. 
 
 8. SPECIFIC HEATS. 
 
 SUBSTANCE SPECIFIC HEAT SUBSTANCE SPECIFIC HEAT 
 Aluminum 0.212 Iron 0.113 
 
 Brass 0.0891 Lead 0.032 
 
 Copper 0.0931 Mercury 0.033 
 
 Glass 0.02 Paraffine 0.589 
 
 HYGKOMETRY. 
 
 181. Hygrometry has to do with the amount of 
 water present at any time in the atmosphere. By the 
 absolute humidity is meant the number of grams of 
 water present in one cubic metre of air. By the relar 
 tive humidity is meant the ratio of the amount of vapor 
 in the air to the amount required to saturate the air at 
 the given temperature. The deiv point is the tempera- 
 ture at which the vapor now in the air would saturate 
 the air and be deposited as dew or frost, according to 
 whether the dew point falls above or below zero. 
 
 EXERCISE 190. To find the humidity and dew point with 
 wet and dry thermometers. 
 
 Apparatus. Wet and dry bulb thermometers. Two ther- 
 mometers of about the same size are hung a few centimetres 
 apart. To one of them is attached a wick of cotton cloth which 
 dips in a dish of water. 
 
 The evaporation of the water cools the bulb of the thermom- 
 eter, making it read lower than the dry thermometer. The 
 
HYGEOMETRT. 337 
 
 more water there is in the air, the less evaporation there will 
 be. When the air is saturated (relative humidity = 1) the two 
 thermometers will read alike. 
 
 Directions. See that the wick is moist. Read both 
 thermometers, record, wait three minutes, read again, 
 and take a third reading three minutes after the second. 
 Currents of air may affect the readings, but the differ- 
 ence should be nearly constant. Call the reading of 
 the dry thermometer , of the wet one t'. (a) Look up 
 in Table 9 the absolute humidity, A', for the tempera- 
 ture t'. It has been found that the absolute humidity, 
 H, of the air, which is at temperature , is, in a closed 
 room, 
 
 (61) H=h' 0.96 (t t') 
 
 (6) If h be the humidity of saturated air for temper- 
 ature , as given in Table 9, then the relative humidity 
 is 
 
 (62) HI = H/ h 
 
 (e) The dew point, T, for any absolute humidity, If, 
 may be found from Table 9. 
 
 Compare your results (<?) and (a) with the results 
 obtained at the same hour by some other student who 
 has used the method described in the following exercise. 
 
 EXERCISE 191. To find the dew point and absolute humid- 
 ity of the air by cooling the air. 
 
 Apparatus. Beaker, water, ice water, thermometer. 
 
 Directions. Fill the beaker one third full of water 
 at the temperature of the room. Add ice water, a little 
 
338 HEAT. 
 
 at a time, stirring with the thermometer. Watch care- 
 fully for the first deposit of dew on the outside of the 
 beaker, read the thermometer, and watch for the dew 
 to disappear and again read the thermometer. The 
 average reading, T, is the dew point. The absolute 
 humidity, H, corresponding to the dew point, T, may 
 be found in Table 9. 
 
 9. HUMIDITY. 
 
 t 
 
 A 
 
 t 
 
 h 
 
 t 
 
 h 
 
 t 
 
 h 
 
 10 
 
 9.4 
 
 15 
 
 12.8 
 
 20 
 
 17.2 
 
 25 
 
 22.9 
 
 11 
 
 10.0 
 
 16 
 
 13.6 
 
 21 
 
 18.2 
 
 26 
 
 24.2 
 
 12 
 
 10.6 
 
 17 
 
 14.5 
 
 22 
 
 19.3 
 
 27 
 
 25.6 
 
 13 
 
 11.3 
 
 18 
 
 15.1 
 
 23 
 
 20.4 
 
 28 
 
 27.0 
 
 14 
 
 12.0 
 
 19 
 
 16.2 
 
 24 
 
 21.4 
 
 29 
 
 28.6 
 
CHAPTER XIV. 
 ELECTRICITY. 
 
 EXERCISE 192. To measure the resistance of a conductor by 
 substitution. 
 
 Apparatus. Galvanometer, resistance box, switch, gravity 
 battery. 
 
 The resistance box (Fig. 245) is a wooden case containing a 
 set of coils of German-silver wire, _R, J?', 
 etc., of known resistance, which are con- 
 nected to blocks of brass, B. 
 
 The blocks may be connected by means of 
 the brass plugs P 1? P 2 , etc. The blocks and 
 plugs are so large that their resistance may be 
 neglected in comparison with the resistance 
 of the coils. When all the plugs are in- FIG. 245. 
 
 serted the resistance of the box is reckoned as 0. When P 1 is 
 removed the resistance is R. The resistance of the several 
 coils is marked upon the top of the box. 
 
 Directions. Connect 
 the battery, B, galvanom. 
 eter, 6r, resistance box, R v 
 unknown resistance, J? 2 , 
 switch, >S r , and, if needed, 
 additional resistance, R, as 
 shown in Fig. 246. When the arm of the switch, 8, is 
 on O the current flows through R r When it is on A it 
 flows through R 2 . The galvanometer should be placed 
 
 339 
 
340 
 
 ELECTEICITY. 
 
 with its coils north and south, the needle also north and 
 south and reading zero. Sometimes readings are taken 
 from a pointer at right angles to the needle. Send the 
 current through ~R 2 and read the deflection on the gal- 
 vanometer. If it is more than 60, additional resistance, 
 R, should be put in the circuit. Read both ends of 
 the needle and take the average. Having determined 
 the deflection produced when R^ is in circuit, throw M l 
 in circuit and vary it by changing the resistance in the 
 box till the deflection is exactly the same as before. 
 It is then obvious that M 2 = R r 
 
 EXERCISE 193. To measure the resistance of a conductor 
 with the Wheatstone's bridge. 
 
 Apparatus. Galvanometer, resistance box, Wheatstone's 
 bridge, gravity battery. 
 
 The principle of the bridge is illustrated in the typical dia- 
 
 gram, Fig. 247. A cur- 
 rent from the battery 
 divides at A, part going 
 
 to B throuh 
 
 J? 
 
 another part through jR 3 , 
 J? 4 . It can be proved 
 that if R l :E 2 = R 3 : R 4 
 no current will flow 
 through the galvanom- 
 eter between C and _D. 
 The converse is also true 
 that if, when a current is flowing from A to B, no current flows 
 through the galvanometer the four resistances are in the ratio 
 named. If, then, we know H l and the ratio of _B 4 to J2 3 we can 
 at once compute _R 2 - It * s 
 
 (63) B Z = B 1 XEJH Z 
 
 FIG. 
 
RESISTANCE. 341 
 
 The bridge shown in Fig. 248 is essential in principle with 
 the ideal bridge, Fig. 247. For convenience in adjusting the 
 ratio of J2 4 : E z these re- 
 sistances are composed 
 of a platinum or Ger- 
 man-silver wire of uni- 
 form diameter, one me- 
 tre in length, stretched 
 between the heavy cop- 
 per washers, A and B. 
 A metre stick fastened FlG 
 
 beside the wire enables 
 
 us to read at once the ratio of the parts into which the wire is 
 divided by the contact _D. 
 
 Directions. Connect the battery to points A, B, and 
 the galvanometer to points (7, D. The coils of the 
 galvanometer should stand north and south and the 
 needle should read zero. The key, K, may .be left 
 closed when a gravity cell is in circuit. With any 
 other battery the circuit should never be kept closed 
 except when the readings are being taken. Connect 
 the resistance box as ^ and the unknown resistance as 
 jR 2 . See that the contacts are clean and firm. Old 
 wires should be scraped with a knife. If the wires are 
 not smaller than No. 16 their resistance may be neg- 
 lected. Put some resistance in the box, close K, and 
 make contact with D at the middle of the wire. 
 Notice which way the galvanometer deflects and move 
 the contact first one way and then the other till you 
 find a position such that the galvanometer deflects the 
 other way. If you have moved far to the left of 50 
 
342 ELECTRICITY. 
 
 the resistance R l is too ' small ; if to the right, it is too 
 large. Compute roughly what 7? 2 is and put about that 
 amount in R r The contact will then fall near the 
 middle. Near 50 an error in setting the contact of 
 1 cm. will be an error of about 2 in 50, or 4 per cent, 
 while a like error at 90 will be an error of 2 in 10, or 
 20 per cent. Find the position for D where the galva- 
 nometer seems to come to zero, move it a little to the 
 right till the needle deflects, then move it a like 
 amount to the left and see if it deflects about the same 
 amount in the opposite direction. When satisfied that 
 you have the position for zero deflection read the posi- 
 tion of D on the metre stick. If it reads from left to 
 right the reading may be considered 7? 3 , while 100 
 minus the reading is J? 4 , since we are concerned only 
 with the ratio of R to R y not with their absolute 
 values. 
 
 If R l was less than R 2 take another observation, 
 making ' E l greater than E^. If possible make an 
 observation with R l nearly equal to R y 
 
 182. Specific Resistance. Two wires of the same 
 length and diameter will have the same resistance if 
 they are of the same substance, different resistances if 
 of different substances. The resistance of unit length 
 and unit cross section of a wire of any substance is the 
 specific resistance of that substance. The specific 
 resistance, r, of a wire having length .L, cross section 
 (?, and resistance R is 
 
RESISTANCE. 343 
 
 (64) r = 
 
 J 
 
 EXERCISE 194. To find the specific resistance of a metal. 
 Apparatus. Wheatstone's bridge, resistance box, galva- 
 nometer, fine wire, micrometer, metre stick. 
 
 Directions. Measure the resistance, R, length, L, 
 and diameter of the wire. From its diameter compute 
 its cross section, a. Compute the specific resistance 
 from the formula 
 
 183. Temperature Coefficient of Resistance. The 
 
 resistance of a metal increases with its temperature. In 
 the case of some alloys, like German silver, the change 
 is slight, making them suitable for standards of resist- 
 ance. In the case of carbon the resistance decreases as 
 the temperature rises. 
 
 The temperature coefficient of resistance is the rate 
 of increase in resistance per ohm of resistance for one 
 degree rise in temperature. If a conductor has a resists 
 ance R at temperature , and R' at temperature t r , its 
 coefficient between those two temperatures is 
 
 (65) c= *'-* 
 R (f 
 
 EXERCISE 195. To find the temperature coefficient of resist- 
 ance of a metal. 
 
 Apparatus. Coil of fine wire, beaker, hot water, bridge, 
 galvanometer and resistance coils, thermometer. 
 
 Directions. Support the coil, with the thermometer 
 
344 
 
 ELECTRICITY. 
 
 in it, in the beaker. Measure the resistance, R, of the 
 coil and note the temperature, t. Pour enough hot 
 water into the beaker to cover the coil. Note the tem- 
 perature, t', and measure the resistance, R'. The point 
 of greatest difficulty will be to determine the exact tem- 
 perature at the instant the reading is taken. If the coil 
 be lifted out and the water stirred and its temperature 
 taken at the instant the bridge is adjusted, the temper- 
 ature should not be far from right. 
 
 10. KESISTANCES. 
 
 SPECIFIC 
 
 TEMPERATURE 
 
 RESISTANCE 
 
 COEFFICIENT 
 
 0.0000029 
 
 0.38 
 
 0.0000016 
 
 0.39 
 
 0.0000209 
 
 0.04 
 
 0.0000097 
 
 0.53 
 
 SUBSTANCE 
 
 Aluminum 
 Copper 
 German silver 
 Iron 
 
 EXERCISE 196. To measure the resistance of a battery with 
 the Wheatstone's bridge. 
 
 Apparatus. Bridge, small induction coil, telephone. 
 
 Directions. If we should connect a battery as R^ in 
 
 the bridge, the current 
 from the battery itself 
 would flow through 
 the galvanometer 
 even if the bridge 
 were balanced. To 
 avoid this difficulty 
 substitute for the 
 battery in the bridge a small induction coil, I (Fig. 
 
 FIG. 249. 
 
POTENTIAL DIFFERENCE. 345 
 
 249), giving an alternating current and for the galva- 
 nometer a telephone, T. The telephone will be affected 
 by the alternating current from the induction coil, but 
 not by the direct current from the battery at R 2 . The 
 induction coil should be a small one of low resistance. 
 It may be run by a storage battery or, for a little while, 
 by two Leclanche batteries. 
 
 Adjust the contact for silence in the telephone. In 
 all other respects the directions given for Exercise 193 
 apply for this. 
 
 EXERCISE 197. To measure the potential difference of a 
 battery. 
 
 Apparatus. Battery, ammeter, resistance box. The re- 
 sistance of the ammeter, -B', and battery, JK", must have been 
 determined previously. 
 
 Directions. Connect the battery in series with the 
 ammeter and resistance box. With a resistance, R, in 
 the box read from the ammeter the current, i, in am- 
 peres. By Qhm's law 
 
CHAPTER XV. 
 SOUND. 
 
 184. Velocity of Sound. Sound emitted by a body 
 making n vibrations per second travels nl metres per 
 second in a medium where the length of a wave is I 
 metres. 
 
 EXERCISE 198. To find the velocity of sound in air. 
 
 Apparatus. Tuning fork making a known number of vi- 
 brations, long glass tube fitted with an outlet tube and pinch 
 cock, thermometer. 
 
 Directions. Fill the tube nearly full of water, strike 
 
 the fork against the end of a heavy block of wood and 
 
 hold it over the mouth of the tube. Let out 
 
 tfS* 
 
 a little of the water and again try the fork. 
 When the tube sounds with a considerable volume 
 of tone, measure the length for each trial. When 
 the volume of sound begins to diminish try to 
 judge which trial gave the loudest sound, fill the 
 JN' tube to a little above the point where the sound 
 seemed loudest, and repeat till you are sure you 
 have a maximum. Mark the spot, JV^Fig. 250), 
 on the tube where the sound was loudest with a 
 FIG. rubber band or a paper label. 
 
 At a point, N f , a little more than three times 
 as far from the top as the first point, should be found 
 a second point where resonance occurs. 
 
 346 
 
VELOCITY OF SOUND. 347 
 
 (34} NN> = A I 
 (33) v = nl 
 
 from which formula we may easily compute the velocity 
 of sound for the given temperature, since we know the 
 number of vibrations, n, of the fork. 
 
 Note the temperature, , of the room. Compare 
 your result with the value given in Table 11 for that 
 temperature. 
 
 11. VELOCITY OF SOUND 
 
 in centimetres per second. 
 
 SUBSTANCE 
 
 VELOCITY 
 
 SUBSTANCE 
 
 VELOCITY 
 
 Air 
 
 33,220 
 
 Hydrogen, 
 
 126,600 
 
 16 
 
 34,179 
 
 Water, 4 
 
 140,000 
 
 18 
 
 34,267 
 
 Brass 
 
 350,000 
 
 20 
 
 34,415 
 
 Aluminum 
 
 510,400 
 
 22 
 
 34,532 
 
 Copper 
 
 356,000 
 
 24 
 
 34,649 
 
 Glass 
 
 506,000 
 
 28 
 
 34,881 
 
 Iron 
 
 509,300 
 
 EXERCISE 199. To determine the velocity of sound in a 
 solid. 
 
 Apparatus. Large glass tube, long rod of wood or metal, 
 fine cork filings, cloth and rosin, metre stick. The glass tube 
 (see Fig. 251) is fitted at one end with a piston for varying the 
 length of the enclosed air column. Cork filings are distrib- 
 uted evenly along the length of the tube. The rod is firmly 
 clamped exactly at its middle point. To one end of the rod is 
 cemented a disk of cardboard or cork of a size to fit loosely in 
 the glass tube. If a hole is made in the disk to fit the rod it 
 will be held more firmly to the rod. 
 
 Directions. Support the tube so that the end of the 
 rod carrying the disk projects a few centimetres within 
 
348 SOUND. 
 
 it. "With the cloth, on which has been placed some 
 powdered rosin, rub the rod lengthwise so that a sharp 
 note will be produced by the longitudinal vibrations. 
 The disk will set the air in the tube in vibration, the 
 waves will be reflected from the piston, forming station- 
 ary waves with nodes half a wave length apart. The 
 cork filings will be disturbed at the points of greatest 
 activity and remain at rest at the nodes. The difference 
 will be made more evident if the tube is turned about 
 30, so that the filings lie to one side of the bottom of 
 the tube ready to slip down at the slightest disturbance. 
 After the note has been sounded they will present the 
 
 FIG. 251. 
 
 appearance shown in Fig. 251. Adjust the piston till 
 the proper length has been found to produce an exact 
 number of waves and consequently a sharp indication 
 with the cork dust. The antinodes are, like the nodes, 
 half a wave length apart. The rod has a node at the 
 centre and an antinode at each end ; it is therefore half 
 a wave length long. Measure l a , the distance between 
 two antinodes, by measuring the distance between two 
 sharply defined antinodes near the ends of the tube and 
 dividing the distance between by the number of spaces 
 included. Measure Z s , the length of the rod, and note 
 the temperature, , of the room. 
 
 Look up v a , the velocity of sound, for temperature, t, 
 in Table 11. 
 
PITCH OF A FOEK. 349 
 
 Then since the velocity in any medium is propor- 
 tional to the wave length in that medium, the velocity 
 of sound in the rod, v a , is 
 
 (38) v s = ^-v a 
 
 la 
 
 EXERCISE 200. To find the vibration number of a tuning 
 fork. 
 
 Apparatus. Two tuning forks, the vibration number of one 
 of which is known, resonance jar, bit of soft wax. 
 
 Directions. Pour water into the jar till it is in res- 
 onance with the standard fork. The fork to be tested 
 must have nearly the same frequency as the standard. 
 The jar will then be in resonance for both forks. Strike 
 both forks at once and hold them over the jar. If they 
 are not in perfect unison beats will be heard. Count 
 the beats in a second by the clock. 
 
 If the standard fork has a frequency, n', and there are 
 m beats per second, the frequency, n, of the other fork 
 is 
 
 (66) n n 1 m 
 
 To -find whether the plus or the minus sign is to be 
 used in this formula, reduce the time of vibration of 
 the fork you are testing by fastening a bit of wax to 
 one prong. If the effect is to diminish the number of 
 beats the fork is lower than the standard, if to increase 
 it, higher. Check this result by removing the wax from 
 that fork and putting it on the standard fork. 
 
CHAPTER XVI. 
 LIGHT. 
 
 PHOTOMETRY. 
 
 185. The Intensity of Illumination at any point 
 varies directly with the intensity of the source of light 
 and inversely as the square of the distance of the point 
 from the source of light. If two surfaces, s v 2 , at 
 distance d v d^ from two sources of light, S v $ 2 , are 
 equally illuminated, s l receiving light only from S 1 and 
 s 2 only from $ 2 , then 
 
 If S 1 be a standard candle burning 7.78 grams per 
 
 hour the candle power 
 of # 2 is 
 
 (67) S 2 = d^ / dj 
 
 EXERCISE 201. To 
 measure the candle power 
 of a lamp with Rumford's 
 FIG. 252. photometer. 
 
 Apparatus. Paper screen, wooden rod, paraffine candle of 
 size sixes. 
 
 Directions. Place the rod a few centimetres in front 
 of the screen (see Fig. 252) and set the candle about a 
 metre from the screen. Move the lamp till the two 
 
 350 
 
INDEX OF REFBACT10N. 351 
 
 shadows are side by side and of equal density. Shadow 
 s l (if the room be dark) is illuminated only by S v 
 shadow s 2 only by S 2 . Measure d v the distance from 
 S 1 to s v and d^ the distance from S z to 2 , and substi- 
 tute in the formula 2 = df / c? 2 2 . Change d l and find 
 a corresponding value for d y Find thus four values for 
 $ 2 and take their average. 
 
 EXERCISE 202. To measure the candle power of a lamp 
 with Joly's photometer. 
 
 Apparatus. Candle, metre stick, paraffine blocks. Two 
 rectangular blocks of par- 
 affine, S . (Fig. 253), 2 
 
 cm. high and 1 cm. square H 
 
 stand side by side on a FlG - 253 - 
 
 support, and are separated by a card which reaches to the 
 
 front edge of the paraffine blocks. 
 
 Directions. Set the lamp and candle at opposite 
 ends of the table and move the support till the paraffine 
 blocks Sp 9 , are equally illuminated. Measure d v d 2 
 and substitute in the formula 
 
 (67) S 2 = tV/<V 
 
 Change the distance of the lamp from the candle and 
 make another determination. 
 
 EEFRACTION. 
 
 186. Index of Refraction. The index of refrac- 
 tion of a substance referred to air is the ratio of the 
 velocity of light in air to its velocity in the given 
 substance. 
 
352 LIGHT. 
 
 (35) n = 
 
 V 2 
 
 EXERCISE 203. To find the index of refraction of glass. 
 
 Apparatus. Piece of heavy plate glass with true edges, 
 sheet of paper, board, three pins, compass. 
 
 Directions. Draw on the paper two lines at right 
 angles to each other through S (Fig. 254). Place one 
 edge of the plate glass against one of the lines. Stick 
 a pin vertically on the other line against the glass as at 
 & With the eye near the paper at E the pin may be 
 
 seen on the line through the 
 glass. Place a second pin 
 at R and move the eye 
 toward E 1 till the image of 
 8 appears in line with R 
 and the eye and set a third 
 pin at Q exactly in line with 
 FIG. 254. .RandiS". Remove the glass 
 
 and draw SR\ the direction of the light in glass, and 
 RQ, its direction in air. Produce QR to meet SO at 
 jS 1 , the image of S. With a radius SO and S as a 
 centre draw the arc 00', which is the front of a wave 
 from S, lying wholly in glass. With S' as a centre and 
 a radius S'R draw RR', which is the front of a wave 
 lying wholly in air. 
 
 It is evident that while the wave was travelling from 
 0' to R in glass it travelled from to R in air. It 
 
 follows that 
 
 v, OH' 
 
INDEX OF REFRACTION. 
 
 353 
 
 and we have only to measure OR' and O'R with the 
 dividers and scale. 
 
 EXERCISE 204. To find the index of refraction of water. 
 Apparatus. Tin cup, metre stick, try-square, clamp, shal- 
 low box, large sheet of paper, compasses, needle and block. 
 
 Directions. Place the tin cup in one corner of the 
 box (see Fig. 255), and clamp the metre stick in a 
 vertical position at the other end. Stick the needle 
 in the block, set the 
 block over the cup 
 with the needle pro- 
 jecting downward. 
 Fill the cup with 
 water till the surface 
 just touches the nee- 
 dle. Remove the 
 block and place the 
 eye near the metre 
 stick in such a posi- 
 tion that the corner, 
 at the bottom of the cup, at S, is just visible over the top 
 of the cup. Place the try-square against the metre stick, 
 and when it is in line with the top of the cup and S f , 
 the image of S, read the scale. Measure the needle to 
 find the distance of the water from the top of the cup. 
 Measure also the depth of the cup on the inside. 
 
 Lay off all of these dimensions on the sheet of paper 
 as accurately as possible and draw the lines shown in 
 Fig. 255. It is evident that 
 
 FIG. 255. 
 
354 LIGHT. 
 
 When the apparatus is in position the index of refrac- 
 tion of some other liquid, as alcohol, may be found by 
 making but one measurement, TE, constructing the 
 diagram and measuring OR' and O'H. 
 
 12. INDICES or KEFRACTION. 
 
 SUBSTANCE INDEX SUBSTANCE INDEX 
 
 Alcohol 1.36 Glass 1.66 
 
 Carbon bisulphide 1.65 Water 1.34 
 
 LENSES. 
 
 EXERCISE 205. To find the focal distance of a convex lens. 
 Apparatus. Metre stick, paper or ground glass screen, 
 candle, mirror. 
 
 Directions. (a) First method. Hold the lens be- 
 fore an open window and move the screen toward or 
 
 from it till a 
 clear image of 
 s~~ if s 1 a distant spire, 
 
 FIG. 256. tree, or cloud is 
 
 obtained on the screen (see Fig. 256). The distance / 
 from the screen to the optical centre of the lens is the 
 focal distance of the lens. The optical centre of a 
 double-convex or double-concave lens is at the centre 
 of the lens if both sides are of equal curvature. In 
 a plano-convex or plano-concave lens the optical centre 
 is at the centre of the curved surface. 
 
 (6) Second method. Place a candle or other bright 
 
LENSES. 
 
 355 
 
 FIG. 257. 
 
 object, S (Fig. 257), near a screen, s, and at one edge 
 of it. Hold a plane mirror behind the lens and move 
 lens and mirror together till a clear image of the candle 
 appears on the screen. The distance of the image or 
 object from the centre of 
 the lens is the focal dis- 
 tance of the lens, for in 
 passing once through the 
 lens the rays are made 
 parallel, and in passing 
 again through the lens these parallel rays are brought 
 together at the principal focus. If the screen were not 
 at the principal focus the distances SO and AS" could 
 not be equal. 
 
 (e) Third method. Place the lens upon the table 
 between the candle and the screen and move candle and 
 
 screen toward or from 
 it at the same rate till 
 a sharp image of the 
 candle is seen upon the 
 screen (see Fig. 258). 
 The candle and screen are now at the secondary foci 
 and the distance SS 1 is four times the focal distance of 
 the lens. This method does not require that we should 
 know the optical centre of a lens if instead of making 
 SO and AS" equal we make the length of object and 
 image equal. It will thus serve for measuring the focal 
 distance of a system of lenses, like compound photo- 
 graphic lenses whose optical centre is not easily found. 
 
 FIG - 
 
356 LIGHT. 
 
 MAGNIFICATION. 
 
 EXERCISE 206. To measure the magnifying power (a) of a 
 telescope, (b) of a microscope. 
 
 Apparatus. Cardboard scale, ruled to decimetres and 
 centimetres, fastened to the wall about two metres from the 
 floor so as to be above the heads of passers-by, millimetre 
 scale, telescope, microscope. 
 
 Directions. \a) Place the telescope at about the 
 level of the eye, and at some distance from the scale. 
 Focus the telescope on the scale by moving the eyepiece 
 
 in and out. Open the left 
 eye and try to see the scale 
 with the left eye at the same 
 time that you see the magni- 
 FlG - 259 - fied image of the scale with 
 
 the right eye. The two should overlap (see Fig. 259). 
 Count on the scale the number of divisions covered by 
 the magnified scale. Try five times and take the aver- 
 age of your observations. 
 
 (6) To find the magnifying power of a microscope 
 focus the instrument upon a millimetre scale and hold 
 a metre stick 35 cm. from the eyepiece on or below 
 the table of the microscope. Compare the overlapping 
 images as in (a). If the instrument has a micrometer 
 eyepiece the value of a division of the scale in the 
 eyepiece may be determined by counting the number 
 of divisions of the eyepiece required to cover one 
 millimetre on the millimetre scale upon which the mi- 
 croscope is focused, 
 
 ^ OF T H 
 
 UNIVERSITY 
 
INDEX OF PROPER NAMES. 
 
 [The numbers refer to pages. The names are pronounced as English people 
 pronounce them who do not know the foreign languages.] 
 
 Ampere (am'pare), Andre Marie; 
 1755-1836. French physicist. 
 lie was the first to investigate 
 carefully the relations be- 
 tween electricity and mag- 
 netism, 130. 
 
 Archimedes ( a r-k y-m e e'd e e s } ; 
 201-212 B.C. Greek mathe- 
 matician and physicist. He 
 invented numerous contriv- 
 ances to assist his country- 
 men in the defence of Syra- 
 cuse against the Komans, 47, 
 53, 304. 
 
 Becquerel ( beck-rel' ) , Henri; 
 French chemist, 260. 
 
 Boyle, Robert; 1627-1691. An 
 English physicist whose life 
 was devoted to patient inves- 
 tigation . in physical science. 
 He was particularly inter- 
 ested in the study of the air, 
 53. 
 
 Crookes, William; 1832 - . 
 English physicist and chem- 
 ist. His principal researches 
 
 in physics are connected with 
 the molecular properties of 
 gases. He gave the name 
 " radiant matter' 1 to gas in 
 an extreme state of rarefac- 
 tion, 117, 259. 
 
 Daniell (dan-yel'), John Freder- 
 ick; 1790-1845. Author of 
 a work on meteorology. In- 
 ventor of the constant bat- 
 tery, 124. 
 
 Fahrenheit (far'en-hite), Gabriel 
 Daniel. Physician and phys- 
 icist of Dantzig, 65, 66. 
 
 Faraday ( f air'a-day ) , Michael; 
 1791-1867. Renowned Eng 
 lish chemist and physicist. 
 He made the first electric mo- 
 tor and discovered the laws of 
 the induction of currents, the 
 laws of electrolytic action, 
 the identity of different sorts 
 of electrification, the different 
 inductive capacity of differ- 
 ent substances, the equality 
 of positive and negative 
 
 357 
 
358 
 
 INDEX OF PROPER NAMES. 
 
 charges. He established all 
 of these laws by numerous 
 accurate experiments and laid 
 the foundation for the work 
 of Maxwell, Hertz, and many 
 others, 3, 115, 257. 
 
 Franklin, Benjamin; 1706-1790. 
 American journalist, diplo- 
 mat, and philosopher. He 
 demonstrated the identity of 
 lightning and the electric dis- 
 charge, 113. 
 
 Fraunhofer, Joseph von; 1787- 
 1826. Bavarian optician. In- 
 ventor of the spectroscope 
 and first to explain the dark 
 lines of the solar spectrum. 
 First to make and study dif- 
 fraction gratings, by means 
 of which he measured the 
 wave lengths of light, 225. 
 
 Galileo (gal-i-lee'o); 1564-1642. 
 One of the earliest and great- 
 est experimental p h i 1 o s o- 
 phers. He was professor at 
 Pisa, where he performed his 
 famous experiments upon 
 falling bodies from the leaning 
 tower, and later at Florence 
 and Padua. He constructed 
 the first thermometer. On 
 hearing that a German oculist 
 had made a telescope he at 
 once constructed one on a 
 plan of his own and turned 
 it on the planets. He discov- 
 
 ered the satellites of Jupiter 
 and ushered in a new era 
 in astronomy as well as in 
 physics. The laws of motion 
 afterwards formally stated by 
 Newton were first discovered 
 and taught by Galileo, 195. 
 
 Galvani (gal-vah'nee), Luigi; 
 1703-1785. Italian physician 
 and physiologist. His discov- 
 ery of the physiological ef- 
 fects of electricity led to the 
 invention of the battery by 
 Volta and stimulated research 
 in this hitherto neglected 
 field, 120. 
 
 Geissler, H e i n r i c h ; 1814-1879. 
 German glass-blower. Inven- 
 tor of a mercurial air pump 
 and maker of vacuum tubes, 
 117. 
 
 Gilbert, William; 1540-1603. 
 English physician and physi- 
 cist. He made the first care- 
 ful study of static electricity 
 and of magnets, 96. 
 
 Guericke (ger'ik-e), Otto von; 
 1602-1686. German natural 
 philosopher. He invented 
 the air pump and constructed 
 the "Magdeburg hemi- 
 spheres," 181. 
 
 Helmholtz, Herman Ludwig Fer- 
 dinand; 1848-1894. Eminent 
 German physiologist and 
 physicist. His work in all 
 
INDEX OF PKOPEB NAMES. 
 
 359 
 
 matters connected with the 
 sensations of sound and light 
 is of the highest authority, 
 243. 
 
 Heron or Hero; 3d century B.C. 
 Celebrated Alexandrian math- 
 ematician and philosopher, 
 181. 
 
 Hertz (e as in very), Heinrich; 
 1857-1894. German physicist 
 famous for his experiments 
 with electrical waves. lie 
 had won world-wide, recogni- 
 tion when lie died at the early 
 age of 37. The lines of in- 
 vestigation opened up by him 
 are being followed o u t b y 
 many investigators to-day 
 with most interesting results, 
 258. 
 
 Jolly, . German physicist, 
 
 289, 312. 
 
 Joly, John; 1857. Irish scien- 
 tist, 351. 
 
 Joule (jool), James Prescott; 
 1818-1889. English physicist 
 noted for his researches in 
 heat, 164. 
 
 Kundt (koont); August; 1839 
 . German physicist, 217. 
 
 Lenard, Philipp; 1860 . 
 
 Formerly assistant to Hertz 
 at Bonn, Germany, where he 
 made his remarkable series of 
 researches on the electric 
 
 discharge in gases. Now 
 Professor of Physics at Kiel, 
 259. 
 
 Marconi (mar-co'ni), Guglielmo; 
 
 1875 . Italian inventor, 
 
 258. 
 
 Maxwell, James Clerk; 1831- 
 1879. Celebrated Scotch 
 physicist. His mathematical 
 treatises on heat and elec- 
 tricity are classic, 257, 258. 
 
 Morse, Samuel Finley Breese; 
 1791-1872. American artist 
 and inventor, 137. 
 
 Newton, Sir Isaac; 1642-1727. 
 The greatest of natural phi- 
 losophers. His law of univer- 
 sal gravitation is a notable 
 example of the application 
 of mathematics to the study 
 of physical problems. The 
 law of refraction grew out of 
 his attempts to perfect the 
 telescope, 13, 32, 33, 243, 244. 
 
 Oersted (erst'ed), Hans Chris- 
 tian; 1777-1851. Professor of 
 Physics in the University of 
 Copenhagen. His discovery 
 of the magnetic effect of elec- 
 tric currents marked a new 
 era in electrical studies, 122. 
 
 Ohm (ome), Georg Simon; 1781- 
 1854. Born at Erlangen, 
 Germany, and educated at 
 the university there. He be- 
 
360 
 
 INDEX OF FBOPER NAMES. 
 
 came Professor of Experimen- 
 tal Physics at Munich. His 
 most important contribution 
 to science, the value of which 
 can hardly be overestimated, 
 is his paper on the "Gal- 
 vanic Cell Mathematically 
 Treated, 1 ' 129. 
 
 Roemer (ray'mer), Ole; 1644- 
 1710. Danish astronomer, 
 256. 
 
 Roentgen (rent'gen, g as in get), 
 William Konrad. B o r n in 
 Holland, 1845; now Professor 
 of Physics at Wtirtzburg, 
 Germany. He has made nu- 
 merous contributions in heat 
 and optics, 117, 259. 
 
 Ruhmkorff (room'korf), Hein- 
 rich Daniel; 1803-1877. Ger- 
 man-French mechanician, 144. 
 
 Rumf ord, Count (Benjamin 
 Thomson); 1753-1814. Born 
 in America, served in the 
 British and Bavarian armies. 
 Noted for his work in heat, 
 350. 
 
 Toepler (tep'ler), 108. 
 
 Volta(vol'ta), Allesandro; 1745- 
 1827. Professor of Physics 
 at Pavia, Italy. He invented 
 the electrophorus, the con- 
 
 denser, and the absolute elec- 
 trometer, but is best known 
 by his invention of the bat- 
 tery. He made careful exper- 
 iments in gas analysis and 
 discovered independently the 
 law of Charles, 102, 120. 
 
 Watt, James; 1736-1819. The 
 inventor of the steam engine. 
 He was instrument maker in 
 Glasgow College, where Pro- 
 fessor Black, the discoverer 
 of latent heat, directed his 
 attention to the study of the 
 steam engine. He measured 
 the work done by his engine 
 and denned the horse-power, 
 181. 
 
 Welsbach (wels'bock), 133. 
 
 Wheatstone (wheet'stone), Sir 
 Charles; 1802-1875. English 
 physicist and inventor, best 
 known for his study of elec- 
 tric currents and his inven- 
 tions in telegraphy, 343. 
 
 Young, Thomas; 1773-1829. 
 Discovered the law of inter- 
 ference of light, which went 
 far to establish the undtila- 
 tory theory, and suggested 
 the theory of color sensa- 
 tion afterwards developed 
 by Helmholtz, 322. 
 
GENERAL INDEX; 
 
 Absolute, scale of temperature, 
 69; zero, 68. 
 
 Absorption, colors due to, 247. 
 Acceleration, 10; of gravity, 313. 
 Adhesion, 35, 41. 
 
 Advantage, mechanical, 172; of 
 inclined plane, 178; of pulley, 
 174; of screw, 179; of wedge, 
 178. 
 
 Air, elasticity of, 35; com- 
 pressed, for transmission of 
 power, 188; pressure of, 49; 
 resistance of, 25. 
 
 Air pump, 54. 
 
 Air thermometer, 67. 
 
 Alternating, current, 148; dy- 
 namo, 148. 
 
 Altitude, measured with barom- 
 eter, 318. 
 
 Ampere, unit of current, 130. 
 
 Amplitude, of vibration, 193; re- 
 lated to loudness, 212. 
 
 Antinodes, in vibrating bodies, 
 202. 
 
 Arc lamp, 132. 
 * The references are to pages. 
 
 Archimedes' principle, 47. 
 Atoms, 63. 
 
 Attraction, of cohesion, 35, 41; 
 of electric charges, 94; of 
 electric currents, 135 ; of grav- 
 itation, 33 ; of magnets, 86, 94. 
 
 Aurora borealis, 117. 
 
 Balance, spring, 289; lever, 31, 
 290, 292. 
 
 Barometer, 50, 316; altitude 
 measured with, 318; storms 
 indicated by, 49. 
 
 Battery, electric, 120, 123. 
 Beats, in music, 210, 212. 
 
 Bells, electric, 139 ; vibration of, 
 209. 
 
 Boiling point, of liquids, 74; of 
 water, 329. 
 
 Boyle's law, 53, 320. 
 Breaking stress, 326. 
 Bridge, Wheatstone's, 340. 
 Bubbles, form of, 45. 
 Buoyant force, of fluids, 47. 
 Calipers, 276, 277. 
 
 361 
 
362 
 
 GENERAL INDEX. 
 
 Calorie, unit of heat, 70. 
 Calorimetry, 69, 333. 
 Camera, 239, 240. 
 
 Candle power, 256 ; measurement 
 of, 350. 
 
 Capacity, electrostatic, 110; for 
 heat, 70, 333; specific induc- 
 tive, 99. 
 
 Capillarity, 42, 320. 
 
 Capillary phenomena, 41; con- 
 stant table of, 322. 
 
 Cathode rays, 116, 258. 
 Cell, voltaic, 120. 
 
 Centigrade scale of temperature, 
 65. 
 
 Centre, of mass, 28 ; of gravity, 
 28; optical, of a lens, 238. 
 
 Centrifugal force, 14. 
 
 Changes, physical, 62; chemical, 
 62. 
 
 Clothing, 79. 
 
 Coefficient, of expansion, 332; 
 table of, 333; of friction, 328; 
 temperature of resistance, 343. 
 
 Cohesion, 35, 41. 
 Cold, artificial, 66. 
 
 Color, by absorption, 247; by 
 diffraction, 251; by refraction, 
 242 ; sensation of, 242 ; mixture 
 of sensations of, 244-246. 
 
 Colors, by thin plates, 251 ; com- 
 plementary, 246 ; interference, 
 249, 251 ; mixture of, 244-246. 
 
 Combustion, a source of energy, 
 168, 183. 
 
 Commutator, of dynamo, 141. 
 Compass, magnetic, 94. 
 
 Composition, of force, 14, 17; of 
 velocities, 17. 
 
 Compressed air, for transmission 
 of power, 188. 
 
 Condenser, electric, 112. 
 
 Conduction, of heat, 76 ; of elec- 
 tricity, 96, 129. 
 
 Conductors, electric, 96, 129. 
 Conservation, of energy, 161. 
 Consonance, 212. 
 
 Constant, capillary, 320; of grav- 
 itation, 33. 
 
 Contact, electric charge by, 120. 
 Convection, of heat, 77. 
 Crookes' tube, 258. 
 Crystals, 71. 
 
 Current, electric, 111, 120, 129, 
 130; alternating, 148; attrac- 
 tions and repulsions of, 135; 
 distribution of power by, 188; 
 mechanical effect of, 126; 
 Ohm's law for, 130; produced 
 by batteries, 120; by heat, 134; 
 by motion, 142; steady, 147; 
 
GENERAL INDEX. 
 
 363 
 
 producing chemical effects, 
 126; producing heat, 128; pro- 
 ducing magnetic effects, 122. 
 
 Curvature, of lenses, 287. 
 Declination, magnetic, 94. 
 
 Degree, Centigrade, 66; Fahren- 
 heit, 66. 
 
 Density, by Archimedes' prin- 
 ciple, 304, 305, 308; linear, 300; 
 maximum of water, 71; of 
 . liquids, 302-308; of regular 
 solids, 301; surface, 300; 
 tables of, 3$9. 
 
 Dew point, 336. 
 Diagonal scale, 274. 
 Diffraction spectrum, 250. 
 
 Diffusion, of fluids, 55 ; of gases, 
 56; of liquids, 58. 
 
 Discharge, electric, from points, 
 106; in a vacuum, 116, 258. 
 
 Dissonance, 212. 
 Distillation, 74. 
 Dynamo, electric, 145. 
 Dyne, 22. 
 
 Earth, a magnet, 94. 
 Ebullition, 73. 
 
 Efficiency, of machines, 172; of 
 pulley, 328. 
 
 Elastic forces, 37. 
 
 Elasticity, 34, 322; explained, 37; 
 modulus of, 322 ; of air, 35. 
 
 Electric attractions, 94. 
 Electric battery, 120, 123. 
 Electric bell, 139. 
 
 Electric charge, 94; by contact, 
 120; nature of, 100; distribu- 
 tion of, 103. 
 
 Electric current, 111, 120, 129, 
 130; alternating, 148; attrac- 
 tions and repulsions of, 135; 
 chemical effect of, 126; effect 
 in producing heat, 128; for 
 distribution of energy, 188; 
 magnetic effect of, 126; me- 
 chanical effect of, 126; Ohm's 
 law for intensity, 130; pro- 
 duced, by batteries, 120; by 
 heat, 134; by motion, 142; 
 unit of, 130. 
 
 Electric discharge, in air, 104; in 
 rarefied gases, 117; in tubes 
 (Geissler's and Crookes'), 117. 
 
 Electric, heating, 133; lighting, 
 131; motor, 140; potential, 
 130, 345; repulsions, 94; resist- 
 ance, 128, 130, 339, 342, 344; 
 units, 130; welding, 133. 
 
 Electrical machines, 107-110. 
 
 Electricity, 84; and light, 256; 
 galvanic, 120 ; measurement 
 of, 339-345. 
 
 Electrolysis, 126. 
 Electro-magnetic telegraph, 137. 
 Electro-magnets, 136. 
 
364 
 
 GENERAL INDEX. 
 
 Electrophorus, 102. 
 Electroplating, 127. 
 
 Electroscope, pith-ball, 95; gold- 
 leaf, 114. 
 
 Electrotyping, 128. 
 
 Energy, 157, 159; and life, 166; 
 conservation of, 160, 161; dis- 
 tribution of, 187; equivalents 
 of different forms, 162 ; forms 
 of, 165; kinetic, 160, 162; illus- 
 trated in pendulum, 194; of 
 falling bodies, 163; potential, 
 160, 162; illustrated in pendu- 
 lum, 194; radiant, see radiant 
 energy ; sources of useful, 167 ; 
 storage of, 186; sun a source 
 of, 167, 260; transference of, 
 187; units of, 162. 
 
 Engine, gas, 183, 184; steam, 
 Hero's, 181; Watts', 181, 182. 
 
 Equilibrium, 27-29; kinds of, 27. 
 
 Equivalent, Joule's, of work and 
 heat, 164. 
 
 Equivalents, metric and English, 
 
 20, 268, 288. 
 
 Erg, unit of work, 158. 
 Errors, of measurement, 266. 
 
 Estimation, of tenths, 275, 279; 
 of time, 314. 
 
 Ether, 92, 260; waves in, see ra- 
 diant energy. 
 
 Evaporation, 73; a cooling proc- 
 ess, 75. 
 
 Exercises, 1-12, in matter and 
 motion, 23, 24; 13-31, in bal- 
 ancing forces, 59, 60; 32-51, 
 in beat, 82, 83; 52-69, in mag- 
 netism and static electricity, 
 117-119; 70-88, in electric cur- 
 rents, 151-156; 89-101, in 
 work and machines, 189-191 ; 
 102-107, in vibrations and 
 waves, 205, 206; 108-116, in 
 sound, 224, 225; 117-130, in 
 light, 260. 
 
 Exercises, laboratory, 131-144, 
 in length, 269-287; 145-165, 
 in mass and density, 288-309 ; 
 166-173, in time, 311-315; 174- 
 183, in force, 316-328; 184- 
 191, in heat, 329-338; 192-197, 
 in electricity, 339-345; 198- 
 200, in sound, 346-349; 201- 
 206, in light, 350-356. 
 
 Expansion, at solidification, 71; 
 by heat, 64; coefficient of, 64, 
 332; table of, 333; of gases, 
 64; of liquids, 64; of mer- 
 cury, 67; of water, 64; un- 
 equal, of metals, 68. 
 
 Eye, 240; estimation of length, 
 
 282. 
 
 Fahrenheit scale of temperature, 
 65. 
 
 Faraday's ice-pail experiment, 
 115. 
 
GENERAL INDEX. 
 
 365 
 
 Falling bodies, 2, 10, 11; energy 
 of, 163. 
 
 Field, magnetic, 88; nature of, 
 92; of force, electrostatic, 98; 
 magnetic, about a current, 
 123. 
 
 Floating bodies, 46 ; Archimedes' 
 law of, 46. 
 
 Fluids, 38; in contact, 55. 
 Fluoroscope, 258. 
 
 Focus, of mirror, 234; of lens, 
 236. 
 
 Foot-pound, J58. 
 
 Force, centrifugal, 14; denned, 
 8; lines of, 93, 98, 123; meas- . 
 urement of, 316-328; moment 
 of, 30; nature of, 9. 
 
 Forces, 25; composition of, 14; 
 elastic, 37; resolution of, 14; 
 triangle of, 16. 
 
 Fraunhofer's lines, 254. 
 
 Freezing mixture, 66. 
 
 Friction, 26; coefficient of, 327. 
 
 Fundamental, tone, 213; units, 
 
 20, 265. 
 
 Fusion, 71; latent heat of, 76. 
 Galvanometer, 123. 
 Galvanoscope, 123. 
 
 Gases and liquids, how different, 
 48; Archimedes' law applies 
 to, 53; expansion of, 69; in 
 
 closed vessels, 53; in open 
 vessels, 48; pressure of, 53. 
 
 Gaseous state, 36. 
 Gram, denned, 21, 288. 
 Grating, diffraction, 250, 252. 
 
 Gravitation, 32; constant of, 33; 
 Newton's law of, 33. 
 
 Gravity, 9 ; acceleration of, meas- 
 ured by pendulum, 313; cen- 
 tre of, 28; force of, in dynes, 
 22, 313; opposing motion, 25. 
 
 Harmonic motion, 193. 
 Harmonics, overtones, 220 
 Harmony, 212. 
 
 Heat, 36; amount of, 69; capac- 
 ity, 70, 333; conduction, 76; 
 convection, 77; effect of, 62; 
 on a magnet, 93; engines, 
 180-184; expansion due to, 
 62; tables of, 333; latent, of 
 evaporation, 75 ; of fusion, 76 ; 
 measurement of, 329 ; mechan- 
 ical equivalent, 164; nature 
 of, 61; produced by electric 
 current, 128; quantity of, 69; 
 radiant, see radiant energy; 
 sensation of, 64; specific, 70, 
 333; table of, 336; units of, 
 69. 
 
 Heating, electric, 133; of houses, 
 
 79. 
 
 Horse power, unit of work, 184. 
 
366 
 
 GENERAL INDEX. 
 
 Hue, 244. 
 
 Humidity, absolute, 336; rela- 
 tive, 336; table of relative, 
 
 Hygrometry, 336. 
 Hypothesis, 2. 
 
 Ice-pail experiment, Faraday's, 
 115. 
 
 Images, by reflection, 229-232; 
 by refraction, 235; by small 
 openings, 228; real, 230; vir- 
 tual, 241. 
 
 Incandescent lamp, 132. 
 Inclined plane, 24, 178. 
 
 Index of refraction, 204, 351; 
 table, 354. 
 
 Induction, coil, 144; electric, of 
 currents, 143; electrostatic, 
 98; magnetic, explained, 90. 
 
 Inductive capacity, 99. 
 Inertia, 13. 
 
 Instruments, optical, 239-242. 
 Insulators, electric, 96. 
 
 Intensity, of light, 255; of elec- 
 tric current, 130; of field of 
 , force, 99 ; of sound, 212. 
 
 Interference, of light waves, 249 ; 
 of sound waves, 215, 217, 218, 
 219; of waves, 201, 218, 219; 
 spectrum, 250. 
 
 Intervals, musical, 211. 
 
 Jolly's balance, 289. 
 Joule, unit of work, 184. 
 
 Joule's equivalent of heat and 
 work, 164/ 
 
 Kinetic energy, 160, 162, 194. 
 Kundt's tube, 217, 347. 
 
 Lamp, arc, 132; incandescent, 
 132. 
 
 Latent heat, of fusion, 76 ; of 
 vaporization, 75. 
 
 Law, Archimedes 1 , 47; Boyle's, 
 of gases, 53; defined, 2; of 
 Boyle, 320; of Charles, 68; of 
 conservation of energy, 161; 
 of electrostatic attraction, 98; 
 of falling bodies, 2 ; of inten- 
 sity of light, 256, 350; of mag- 
 netic force, 86; of motion, 
 13-19. 
 
 Length, eye estimation of, 282; 
 measurement of, 268-287; 
 units of, 20, 268. 
 
 Lenses, 235-239; curvature of, 
 286 ; focal length of, 354. 
 
 Lever, 170; balance, 31; princi- 
 ple of, 30. 
 
 Leyden jar, 113. 
 
 Light, and elasticity, 256; defini- 
 tions, 226; diffraction of, 251; 
 intensity of, 350; interference 
 of, 251, 252; measurement, 
 350-356; photometry, 350; 
 
HE VIRAL INDEX. 
 
 367 
 
 rectilinear propagation of, 
 227, 228; reflection of, 229- 
 234; refraction of, 234, 241, 
 351. 
 
 Lighting, electric, 131. 
 Lightning, 105, 106. 
 
 Lines of force, electrostatic, 99, 
 101; in the dynamo, 146; mag- 
 netic, 93, 135. 
 
 Liquid state, 36. 
 
 Liquids, boiling point of, 73; 
 density of, 302-308; equilib- 
 rium of, 39; evaporation of, 
 73; expansion of, 64; in closed 
 vessels, 47; in communicating 
 vessels, 40; in open vessels, 
 39-47; laws of pressure, 40. 
 
 Litre, 21, 269. 
 
 Lodestone, 85. 
 
 Loops, in wave motion, see an- 
 tinodes. 
 
 Machines, 157, 169 ; efficiency of, 
 172. 
 
 Magic lantern, 241. 
 
 Magnetic, attraction and repul- 
 sion, 86, 94; compass, 94; ef- 
 fects of electric current, 126; 
 field, 88; force, law of, 87; 
 induction, 90; lines of force, 
 88, 93, 99; needle, 94; poles, 
 85; substances, 91. 
 
 Magnetism, 84; destroyed by 
 heat, 93; induced, 87; molec- 
 ular, 91; of earth, 94. 
 
 Magnets, 85. 
 Magnification, 356. 
 
 Major, scale, 221; triad, 221, 
 222. 
 
 Manometer, 319. 
 
 Mass, 11, 12; centre of, 28; 
 measurement of, 288-309; 
 units of, 20, 288. 
 
 Matter, defined, 4; some prop- 
 erties of, 34. 
 
 Measurement, errors of, 266; ex- 
 ercises in, see exercises; phys- 
 ical, 265; units of, 20. 
 
 Mechanical advantage, 172 ; equiv- 
 alent, 164. 
 
 Melting point, of a solid, 71, 331. 
 
 Mercury, in capillary tubes, 42. 
 
 Metre, 20, 268. 
 
 Micrometer, 283. 
 
 Microscope, 239. 
 
 Mirrors, 229-234. 
 
 Modulus of elasticity, 322. 
 
 Molecules, 35; motion of, in 
 heat, 62. 
 
 Moment, of force, 30; applied 
 to lever, 171. 
 
 Momentum, 11, 12. 
 
 Motion, defined, 4; harmonic, 
 193; Newton's laws of, 13- 
 19; rate of, 10; rotary, 7; 
 
368 
 
 GENERAL INDEX. 
 
 translatory, 5; vibratory, 7, 
 192; wave, 7, 197. 
 
 Motor, electric, 140. 
 Musical scales, 213, 220, 221. 
 
 Nodes, in bells, 210; in organ 
 pipes, 216 ; in vibrating bodies, 
 202, 217, 347. 
 
 Note-book, for exercises, 267. 
 Ohm, unit of resistance, 130. 
 Ohm's law, 129 
 
 Optical, centre of a lens, 238 ; in- 
 struments, 239-242. 
 
 Organ pipes, 216. 
 Oscillation of pendulum, 311. 
 Osmose, 58. 
 Overtones, 213, 220. 
 
 Parallelogram of forces, see com- 
 position of forces. 
 
 Pendulum, 194; compensating 
 period of, 195; simple, 196; 
 time of oscillation, 311. 
 
 Penumbra, 228. 
 
 Period, of vibration, 193; of pen- 
 dulum, 195. 
 
 Perpetual motion, 185. 
 Photometry, 256, 350. 
 
 Physical, changes, 62; measure- 
 ment, 265. 
 
 Physics, founded on measure- 
 ment, 265; place among sci- 
 
 ences, 1; place in practical 
 life, 3. 
 
 Pigments, mixture of, 248. 
 Pile driver, 159, 195. 
 Pitch, in sound, 211. 
 Plates, vibration of, 209. 
 
 Polarization, of electric batter- 
 ies, 122. 
 
 Poles, of a magnet, 85. 
 Polygon, of forces, 17. 
 Pores, 35. 
 
 Potential, measurement of, 345; 
 electrostatic, 110; unit of, 130. 
 
 Power, and weight, old terms 
 for force, 171; rate of doing 
 work, 184; transmission of, 
 187; Boyle's law of, 53,320. 
 
 Pressure, of air, 316; of fluids, 
 319. 
 
 Properties, of matter, 34. 
 
 Pulley, 174-177; efficiency of, 
 328. 
 
 Pulse, to count, 314. 
 
 Pump, for air, 54; for liquids, 
 51. 
 
 Quality, of musical tones, 212. 
 Quantity, of heat, 69. 
 
 Radiant energy, 61, 165, 256, 257, 
 259; absorption of producing 
 color, 247; cause of sensation 
 
GENERAL INDEX. 
 
 369 
 
 of light, 226; law of intensity 
 of, 255; of sun, 168, 169; stor- 
 age of, by plants, 187; trans- 
 formed into heat, 61; velocity 
 of, 254; wasted, 186. 
 
 Radiation, new forms of, 258. 
 
 Rainbow, 243. 
 
 Ray, 227. 
 
 Reaction, 19. 
 
 Record of experiments, 267. 
 
 Reflection, law of, 202 ; of light, 
 229-234; of waves, 200-203. 
 
 Refraction, color produced by, 
 243; index of, 204, 351; of 
 waves, 204. 
 
 Relay, telegraphic, 138. 
 
 Resistance, box, 339; by substi- 
 tution, 33D; electric, 128; 
 measurement of, 339; specific, 
 342; table of, 344; unit of, 
 130. 
 
 Resolution, of forces, 14, 17; of 
 velocities, 17. 
 
 Resonance, 214; of air columns, 
 215, 346; of organ pipes, 216. 
 
 Respiration, to count, 314. 
 Rods, vibration of, 208. 
 
 Rotary motion, 7; of the earth, 
 14. 
 
 Ruhmkorff' s coil, 144. 
 
 Scale, absolute, of temperature, 
 69; chromatic, 224; diagonal, 
 274; major, 221; tempered, 
 224. 
 
 Scales, musical, 213, 219, 220. 
 Screw, 179; micrometer, 283. 
 Shades, of color, 245. 
 Shadows, 227. ./""" 
 Siphon, 52. 
 Siren, 211. 
 Solenoid, 136. 
 Solid state, 36. 
 
 Sound, and noise, 207; loudness 
 of, 212; measurement of, 346- 
 349; nature of, 207; pitch of, 
 211; quality of, 212; velocity 
 in air, 216, 346; velocity in 
 solids, 217, 347. 
 
 Sounder, telegraphic, 138. 
 Space telegraphy, 257. 
 Spark coil, Ruhmkorff s, 144. 
 
 Specific, gravity, see density; 
 heat, 70, 333; inductive ca- 
 pacity, 99; resistance, 342. 
 
 Spectra, classes of, 253. 
 Spectroscope, 251, 252. 
 Spectrum analysis, 253. 
 
 Spectrum, by diffraction, 250; 
 by refraction, 242; of sun, 
 254. 
 
370 
 
 GENERAL INDEX. 
 
 Speed, 10. 
 Spherometer, 285. 
 Stability, conditions of, 29. 
 
 State of bodies, change of, due to 
 heat, 62; gaseous, 48; liquid, 
 36; solid, 36. 
 
 Steelyards, 32, 292. 
 
 Stereopticon, 241. 
 
 Still, 75. 
 
 Storms, indicated by barometer, 
 
 49. 
 
 Strain, 34; electrical, 104. 
 Strength of a wire, 326. 
 
 Stress, 34; electrical, 101; break- 
 ing, 326. 
 
 Strings, vibrations of, 219. 
 
 Sun, a source of energy, 167, 
 260; see also radiant energy. 
 
 Surface tension, 43-46; see also 
 capillarity. 
 
 Tables, of breaking stress, 326; 
 of capillary constant, 322; of 
 coefficient of expansion, 333; \ 
 of specific heat, 336; of diam- 
 eters of wires, 285; of densi- 
 ties, 309; of elasticity, 326; of 
 index of refraction, 354; of 
 lengths, 270; of resistance, 
 344; of velocity of sound, 347; 
 of weights, 288. 
 
 Telegraph, electro-magnetic, 137 ; 
 Morse's printing, 137. 
 
 Telegraphy, without wires, 257. 
 
 Telephone, 156; used in measur- 
 ing resistance, 344. 
 
 Telescope, magnification of, 356. 
 
 Temperature, 63; measurement 
 of, 329; of the body, 77, 82, 
 331 ; scales of, 65 ; unit of, 65. 
 
 Tension, surface, 43-46. 
 Tenths, estimation of, 269, 275. 
 Theory, 2; atomic, 2. 
 Thermo-electric current, 134. 
 Thermo-electric generators, 134. 
 
 Thermometer, 65; air, 67; cali- 
 bration of, 329. 
 
 Thermometry, 65. 
 Thermostat, 68. 
 
 Time, measurement, 310-314; 
 units of, 20, 310. 
 
 Tint, 244. 
 
 Tones, fundamental, 213; par- 
 tial, 213. 
 
 Transformer, for alternating cur- 
 rents, 150. 
 
 Translation, motion of, 5. 
 Triangle of forces, 16. 
 
 Tuning fork, 209; vibration 
 number of, 349. 
 
 Units, C. G. S. system, 21; de- 
 rived, 21; electric, 130; fun- 
 
GENERAL INDEX. 
 
 371 
 
 dameiital, 20, 265; of accelera- 
 tion, 21; of force, 21; of heat, 
 69; of length, 20; of magnetic 
 force, 87; of momentum, 21; 
 of time, 20; of velocity, 21; 
 of wave lengths, 243; of work, 
 158, 184. 
 
 Unit pole, 87. 
 
 Vaporization, 72; latent heat of, 
 75. 
 
 Velocity, 10; of light, 254, 351; 
 of sound, 216, 217, 346; table 
 of, 347. 
 
 Velocities, composition of, 17; 
 resolution of, 17. 
 
 Ventilation, 65; of houses, 79. 
 Vernier, 278; gauge, 280. 
 
 Vibration, number of tuning 
 fork, 349; of bells, 209; of 
 pendulum, 311; of plates, 209; 
 of rods, 208; of strings, 219. 
 
 Vibratory motion, 7, 192. 
 Vision, errors of, 241. 
 Volt, unit of potential, 130. 
 
 Volume, by Archimedes' princi- 
 ple, 47, 304; by displacement, 
 303; of irregular solids, 47; 
 tables of, 309. 
 
 Water wheels, 185. 
 
 Watt, unit of power, 184. 
 
 Wave, length, unit of, 243; mo- 
 tion, 7. 
 
 Waves, 197; direction of, 199; 
 electrical, 257; longitudinal, 
 200; reflection of, 200-203; in 
 rods, 208; stationary, 202. 
 
 Weather, 78. 
 Wedge, 178. 
 
 Weighing, by swings, 296; 
 double, 295; with balance, 
 
 289. 
 
 Weight, in vacuum, 53. 
 
 Weights, directions for making, 
 301; table of, 288. 
 
 Welding, electric, 133. 
 Wheatstone's bridge, 340. 
 
 Winds, 78; a source of energy, 
 168. 
 
 Work, 157; rate of doing, 184; 
 units of, 158; why we do, 166; 
 see also energy and radiant 
 energy. 
 
 X-rays, 258. 
 
 Zero, absolute, 68; Centigrade, 
 66, 329; error of, 265; Fahren- 
 heit, 66; of thermometer, 
 329. 
 
LOAN DEPT. 
 
 -50m-8,'61