'/<•_'.» i r>;»"." 
 
 ^>i^'^ 
 
 ■i^^m': 
 
 K Jk^kiLitMliit!^,iAs^uir 
 
THE GIFT OF . 
 ; B...hA..J.MA2^A±L.. 
 
 A..15L5.I3 jJa/iiie.. 
 
3 1924 031 256 484 
 olin.anx 
 
Cornell University 
 Library 
 
 The original of tliis book is in 
 tine Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924031256484 
 
Ptate I. 
 
A TEXT-BOOK 
 
 ELEMENTS OF PHYSICS 
 
 HIGH SCHOOLS AND ACADEMIES. 
 
 ALFRED P. GAGE, A.M., 
 
 IHSTBDCTOK IK PHYSIOS IN THE ENGLISH HIGH SCHOOL, BOSTON, MASS. 
 
 BOSTON: 
 
 PUBLISHED BY GINN & COMPANY. 
 
 1889. 
 
i/ H-lb- 1" "Si IT©" 
 
 Entered according to Act of Congress, in the year 1882, by 
 
 ALFRED P. GAGE, 
 iq the Office df the Librarian of CongresS} at Washington. 
 
 C:£ 
 
 Typography by J. 8. Cdshing & Co., Boston. 
 Prbsswork by Gimn & Co., Boston. 
 
AUTHOE'S PEEFACE. 
 
 IN his Report for the year 1881, Mr. E. P. Seaver, Superintendent 
 of the Public Schools of Boston, says : — 
 " It is a cardinal principle in modern pedagogy that the mind 
 gains a real and adequate knowledge of things only in the presence 
 of the things themselves. Hence the first step in all good teaching 
 is an appeal to the observing powers. The objects studied and the 
 studying mind are placed in the most direct relations with one 
 another that circumstances admit. Words and other symbols are 
 not allowed to intervene, tempting the learner to satisfy his mind 
 ~vith ideas obtained at second-hand. One application of this prin- 
 ciple is seen in the so-called object-teaching ; but the principle is 
 applicable to all teaching, and all methods of teaching based on 
 it are known as objective methods. The theory goes even further, 
 and declares, in general, that no teaching which is not objective in 
 method can properly be called teaching at all. Hence we have this 
 test : Is our teaching objective in method ? " 
 
 This unequivocal language, from the pen of one of our foremost 
 educators, faithfully and forcibly reflects the sentiment of the age, 
 and leaves nothing further that need be said in advocacy of object 
 or inductive teaching. The question for us to consider is, How shall 
 object-teaching be conducted? Shall the teacher manipulate the 
 apparatus, and the pupil act the part of an admiring spectator? 
 or. Shall the pupil be supplied with such apparatus as he cannot 
 conveniently construct, always of the simplest and least expensive 
 kind, with which he shall be required, under the guidance of his 
 teacher, to interrogate Nature with his own hands? By which 
 
IV 
 
 aitthob's preface. 
 
 method -mil he acquire the most vigorous growth, and be most 
 likely to catch something of the spirit which animates and encourages 
 the faithful investigator? Can elegantly illustrated works and lucid 
 lectures on anatomy and operative surgery take the place of the 
 dissecting room? Have lecture-room displays proved very effectual 
 in awakening thought and in kindling fires of enthusiasm in the 
 young? Or would a majority of our practical scientists date their 
 first inspiration from more humble beginnings, with such rude uten- 
 sils, for instance, as the kitchen affords? Is the efficiency of instruc- 
 tion in the natural sciences to be estimated by the amount of costly 
 apparatus kept on show in glass cases, labelled " hands off," or by 
 its rude pine tables and crude apparatus bearing the scars, scratches, 
 and other marks of use ? Why should this fundamental study, which 
 logically precedes all other experimental sciences, and ought there- 
 fore, beyond aU others, to be sound and thorough, be left in the 
 condition of " a mere cram subject " ? 
 
 Fortunately we are able to appeal to experience in a kindred 
 field for an answer to the first two questions propounded. During 
 the last twenty years there has been almost a universal change 
 from the former method of instruction in Chemistry to the latter, 
 so that to-day our best high schools and academies are provided 
 with chemical laboratories for pupils' work. The result has been 
 that this branch, which was formerly a dull and almost profitless 
 study, has become one of the most interesting and useful in the high 
 school curriculum. Is there any reason why laboratory practice should 
 not do a similar work for Physics ? In other words. Do not the same 
 arguments that have been urged for the introduction of chemical 
 laboratories apply with equal propriety and force in advocacy of 
 physical laboratories? 
 
 But it is claimed by some that " In Physics the laboratory practice 
 must necessarily be somewhat limited," and the usual, and almost 
 the only reason given, is " on account of the expense." This objec- 
 tion rests upon the flimsiest of foundations. The expense of 
 
author's preface. V 
 
 equipping and maintaining a physical laboratory which, will answer 
 the requirements of this book, ought to be considerably less than 
 a similar expense to meet the demands of Eliot and Storer's Ele- 
 mentary Manual of Chemistry. In the English High School, in the 
 city of Boston, the sum of three hundred dollars has furnished a 
 physical laboratory which answers the requirements of a large 
 school. Many and many a school has invested in showy but almost 
 useless apparatus, — for example, in trifling electric playthings, — a 
 sum of money which would go far towards the establishment of a 
 simple working laboratory. But more, much more, depends upon 
 the teacher than the cost of material. " If he has the real scientific 
 spirit, he will do a great deal with small appliances; but if his 
 work is done in a perfunctory manner, then the best equipment in 
 the world will serve him but scantily." 
 
 Although this book has been prepared with a view to laboratory 
 work, it may, in common with all text-books, be used as a mere cram- 
 book. It may be advantageously used by those teachers who prefer 
 or are compelled, by a real or a supposed want of time, to perform 
 experiments themselves with elaborate apparatus. Such apparatus, if 
 the teacher possesses it, is best explained to the pupil viva voce, and 
 pictures of the apparatus are not needed, while the book will serve an 
 additional and an important purpose of showing how the same results 
 may be obtained in a more simple way. The great central ideas 
 which are kept prominent throughout the book, and which serve to 
 connect the different departments of Physics in one coherent whole, 
 are the doctrines of the conservation of energy and the conclatii ,i 
 of forces. So far as practicable, experiments precede the statements 
 of definitions and laws, and the latter are not given until the pupil 
 is prepared, by previous observation and discussion, to frame them for 
 himself. The subjects are so arranged that, in case a year is devoted 
 to this study. Heat and Electricity may be studied in the winter 
 months, and Light in the sunny days of summer. 
 
 Many problems are given in connection with the various principles 
 
vi authok's preface. 
 
 and laws. It is not expected that all pupils will perform all the 
 problems ; but the teacher will select judiciously from them. If th* 
 minds of the pupils are quite immature, or the time devoted to this 
 study is very limited, it would be advisable to omit some of the 
 more diflSeult topics ; such, for instance, as are treated in §§ 93-97, 
 and others. Most teachers prefer the " too much " to the " too little." 
 
 Every teacher has a method of his own. But perhaps the follow- 
 ing plan, practised by the author, may be suggestive to some : He 
 divides the experiments into three classes: home, laboratory, and 
 lecture-room experiments. The first class is indicated in the assign- 
 ment of a lesson. They are such as may be performed vdth such 
 simple means as every pupil has at his home. The laboratory experi- 
 ments are conducted as follows : Suppose that the number of pupils 
 engaged at one time is fifteen, about as many as one teacher can care 
 for successfully, and that the number of experiments to be performed 
 during the hour is five, which is about an average number ; then, to 
 save a multiplicity of apparatus of the same kind, only three sets of 
 apparatus of a kind are provided for each experiment. As soon as a 
 pupU completes an experiment with one piece of apparatus, he looks 
 about for an idle piece of some other kind; or, finding none, 
 he improves the time in writing notes on his experiments until 
 apparatus is ready for him; in this way each pupU performs five 
 experiments during the hour, and devotes an average time of twelve 
 minutes to each experiment, including the time of writing notes. 
 The third class of experiments includes such as require the use of 
 apparatus that cannot safely be placed in the hands of pupils, — a 
 very limited number, — and those which have been performed by 
 the pupils, and which the teacher may wish to repeat in a more 
 elaborate way. 
 
 Laboratory practice and didactic study should go hand in hand, 
 and divide time with one another about equally. In general, let the 
 experiment precede the instruction, the pupils being guided in their 
 investigations in the proper channels by the book and by blackboard 
 
AUTHOR S PREFACE. Vll 
 
 directions. Do not teach pupils to swim before entering the water. 
 Supt. Seaver, in another part of his report, exclaims : — 
 
 " How many of our text-books begin, not with the suggestion of 
 concrete illustrations, but with abstract definitions, and still more 
 abstract 'first principles,' — blind guides to the blind teacher, and 
 sovtrces of perplexity to teachers who are not blind," etc. 
 
 Why should the pupil so frequently, to hig great discouragement, 
 be called upon to break through a wall of such diflBculties before 
 coming in contact with Nature? 
 
 The author would take this occasion to acknowledge with pro- 
 found thanks his indebtedness to many distinguished profes-sors of 
 Physics for valuable assistance. Professor C. K. Wead of Michigan 
 University has read the entire work in manuscript, and Dr. C. S. 
 Hastings of Johns Hopkins University has read the larger portion 
 in manuscript and the remainder in proof-sheets ; and their many 
 practical suggestions have largely contributed to whatever of success 
 may have been achieved. Prof. T. C. MendenhaU of the Ohio State 
 University has rendered valuable assistance in the preparation of the 
 summary of mechanical formulas and units on page 128, as well as 
 in the revision of the proofs. To Professors A. E. Dolbear, Tufts 
 College ; C. R. Cross and S. W. Holman, Mass. Inst, of Technology ; 
 C. F. Emerson, Dartmouth College; J. E. Davies, University of Wis- 
 consin ; B. C. JiUson, Western University of Pemisylvania ; A. C. 
 Perkins, Exeter Academy ; J. E. Vose, Cushing Academy, Ashburn- 
 ham; J. O. Norris, East Boston High School; G. C. Maim, Jamaica 
 Plain High School ; and others, who have kindly and patiently read 
 and criticised the proofs as they have passed through the press, our 
 hearty thanks are due. 
 
 Under the guidance and counsel of such an array of distinguished 
 instructors, we may well feel a degree of confidence that the teachings 
 of the book are not far wrong. Yet it should be distinctly under- 
 stood, that for any errors which may have crept into the book, the 
 author holds himself entirely responsible. 
 
C0I^TEIi5"TS. 
 
 FAOE 
 
 CHAPTEE I. 
 
 MATTER AND ITS PROPBETIES. 
 
 Introduction. — Molecule. — Constitution of matter. — Physical 
 and chemical changes. — Force. — Three states of matter. — 
 Phenomena of attraction, — adhesion, cohesion, etc 1 
 
 CHAPTEE II. 
 
 DYNAMICS. 
 
 Dynamics of fluids. — Pressure in fluids. — Barometer. — Compres- 
 sibility and expansibility of fluids. — Transmitted pressure. — 
 Siphon. — Apparatus for raising liquids. — Buoyant force of 
 fluids. — Specific gravity. — Motion. — Laws of motion. — 
 Composition and resolution -of forces. — Center of gravity. — 
 Curvilinear motion. — Accelerated and retarded motion. — 
 The pendulum. — Momentum. — Work and energy. — Trans- 
 formation of energy. — Machines 44 
 
 CHAPTEE III. 
 
 MOLEOUIiAB ENERGY. — HEAT. 
 
 Heat deflned. — Temperature. — Diffusion of heat. — Effects of 
 heat. — Expansion. — Thermometry. — Lavrs of gaseous 
 bodies. — Laws of fusion and boiling. — Heat convertible into 
 potential energy, and vice versa. — Specific heat. — Thermo- 
 dynamics. — Steam engine .... .... ... 138 
 
X CONTENTS. 
 
 CHAPTER IV. 
 ELECTRICITY AND MAGNETISM. 
 
 Current electricity. — Batteries. — Effects produced by electricity. 
 
 — Electrical measurements. — Magnets and magnetism. — 
 Laws of currents. — Magneto-electric and current induction. 
 — -Thermo-electricity. — Frictional electricity. — Electrical mar 
 chines. — Applications of electricity . . ... 179 
 
 CHAPTER V. 
 
 SOUND. 
 
 Vibration and waves. — Sound-waves. — Velocity of sound. — Re- 
 flection and refraction of souud. — Loudness. — Interference. 
 
 — Forced and sympathetic vibrations. — Pitch. — Vibration of 
 strings. — Overtones and harmonics. — Quality. — Composi- 
 tion of sonorous vibrations. — Sound-receiving instruments. 
 
 — Musical instruments 272 
 
 CHAPTER VI. 
 RADIANT ENERGY. — LIGHT. 
 
 Introduction. — Photometry. — Reflection. — Refraction. — Spec- 
 trum analysis. — Color. — Interference. — Refraction and 
 polarization. — Thermal effects of radiation. — Optical instru- 
 ments 325 
 
 Appendix 399 
 
ELEMENTS OF PHYSIOS. 
 
ELEMENTS OF PHYSICS. 
 
 CHAPTER I. 
 MATTER AND ITS PROPERTIES. 
 
 I. INTRODUCTION. 
 
 §1. Experimentation. — An experiment is a question put 
 to Nature. We receive the answer by means of a phenomenon, 
 — that is, a change which we observe, sometimes by the sight 
 or hearing, sometimes by other senses. In every experiment, 
 certain facts or conditions are alwaj'S known ; and the inquiry 
 consists in ascertaining the facts or conditions that follow as a 
 consequence. The following experiments and discussions wUl 
 illustrate : — 
 
 §2. Things known and things to be ascertained. — We 
 are certain that we cannot make our right hand occupy the same 
 space with our left hand at the same time. All experience 
 teaches us that no two portions of matter can occupy the same 
 space at the same time. This property which matter possesses 
 of excluding other matter from its own space, is called impene- 
 trability. It is peculiar to matter; nothing else possesses it. 
 These facts being known, let us proceed to put certain inter- 
 rogatories to Nature. Is air matter? Is a vessel full of air 
 a vessel full of nothing? Is it " empty"? Can matter exist in 
 an invisible state? 
 
 Experiment 1. Float a cork on a surface of water, cover it with a 
 tumbler or tall glass jar, and thrust the glass vessel, mouth downward, 
 
MATTBB AND ITS PKOPERTIES. 
 
 Fig. 1. 
 
 into the water. In case a tall jar (Kg. 1) is used, the experiment 
 may be made more attractive by placing on the cork 
 a lighted candle. State how the experiment answers 
 each of the above questions, and what evidence It 
 furnishes that air is matter ; or, at least, that air is 
 like matter. 
 
 Experiment 2. Hold a test-tube for a minute 
 ovet the mouth of a bottle containing ammonia 
 water. Hold another tube over a bottle containing 
 hydrochloric acid. The tubes become filled with 
 gases that rise from the bottles, yet nothing can 
 be seen in either tube. Place the mouth of the first 
 tube over the mouth of the second, and invert. 
 Straightway a white cloud appears in the tubes. 
 Sotin a white, flaky solid collects on the bottom of 
 the lower tube. Surely, out of nothing we cannot 
 create something. Which one of the above ques- 
 tions does this experiment answer ? How does the experiment an- 
 swer it? 
 
 Fig. 2. 
 
 Again, we are quite familiar with the fact that matter exerts a 
 downward pressufe on things upon which it rests ; and that 
 matter, in a liquid state at least, exerts pressure in other direc- 
 tions than downward, as, for instance, against the sides of the 
 containing vessel. Does air exert pressure ? 
 
 Experiment 3. Thrust a tumbler, mouth downward, into water, 
 and slowly invert. You see bubbles escape fl-om the 
 mouth. What is this that displaces the water, and 
 forms the bubbles? When the tumbler becomes filled 
 with water, once more invert, keeping its mouth 
 under the surface of the water, and raise it nearly out 
 of the water, as in Figure 2. The water does not 
 fall out of the tumbler, but remains in it, entirely 
 filling it. Hence, there is some pressure exerted on 
 the free surface of the water; otherwise, the level 
 would be the same in the two communicating vessels. 
 This pressure on the surface of the water can only be 
 produced by some body resting thereupon. But there 
 
 Is no body, except the air, that rests upon it. What conclusion do 
 
 you draw from this? 
 
MINUTENESS OF PARTICLES OP MATTER. 
 
 Fig. 3. 
 
 Experiment 4. Pass a glass tube through the stopper of a bottle 
 (Fig. 3). Attach a rubber tube to the glass tube. Exhaust 
 the air by '-suction" from the bottle; pinch the rubber 
 tube in the middle, insert the open end into a basin of 
 water, and then release the tube. What causes the water 
 to enter the bottle ? Why does not the water fill the bot- 
 tle? 
 
 Finally, we know that matter has weight, and noth- 
 ing else has it. Has air weight? 
 
 Experiment 5. Exhaust the air by means of an air- 
 pump ft'om a hollow globe (Fig. 4). Having turned the 
 stop-cock to prevent the entrance of air, carefully balance 
 the globe on a scale-beam, as in Figure 5. Afterwards turn 
 the stop-cock, and admit the air. The globe is no longer 
 balanced. Once more apply weights till it is balanced. 
 
 The experiments with air teach us that it is matter, 
 since, like matter, it can exclude other matter from the space it 
 occupies, it exerts pressure, and has weight, while all the above 
 experiments draw from nature one reply, matter can exist in 
 
 AN INVISIBLE STATE. 
 
 Fig. 4. 
 
 Fig. 5. 
 
 § 3. Minuteness of particles of matter. — Physiologists 
 teach us, that, in order to smell any substance, we must take 
 
 into our nostrils, as we 
 
 breathe, small particles of 
 
 that substance which are 
 
 floating in the air. The 
 
 air, for several meters 
 
 around, is sometimes filled 
 
 with fragrance from a rose. 
 
 You cannot see anything 
 
 in the air, but it is, never- 
 theless, filled with a very 
 fine dust that floats away from the rose. The odor of rosemary 
 at sea renders the shores of Spain distinguishable long before 
 they are in sight. A grain of musk will scent a room for many 
 
4 MATTER AND ITS PEOPBKTIES. 
 
 years, by constantly sending forth into the air a dust of musk. 
 Though the number of particles that escape must be countless, 
 yet they are so small that the original grain does not lose 
 perceptibly in weight. 
 
 The microscope enables us to see, in a single drop of stagnant 
 water, a world of living creatures, swimming with as much liberty 
 as whales in a sea. The larger prey upon the smaller, and the 
 smaller find their food in the still smaller, and so on, till the 
 power of the microscope fails us. The whale and the minnow 
 do not differ more in size than do some of these animalcules, the 
 largest of which are hardly visible to the naked eye. But as 
 the smallest of these perform very complex operations in col- 
 lecting and assimilating food, we must conclude that they are 
 composed not only of many particles, but of many kinds of 
 matter. These minute living forms that people the microscopic 
 world are exceedingly large, in comparison with the incon- 
 ceivably minute particles called molecules, which physicists now 
 " measure without seeing." 
 
 § 4. The molecule. — Experiment 1. Examine carefully a drop 
 of water with the naked eye, or with a microscope. So far as you are 
 Fig. 6. ^^1® to see, the space occupied by the drop is entirely 
 
 filled with water. Fill a test-tube with water (Fig. 6). 
 Insert a cork stopper, pierced with a glass tube ; heat 
 over a lamp-flame, and note the phenomena produced. 
 The water expands, and ris^s in the smaller tube; still 
 the test-tube seems to be full of 
 water. Place it in ice-water, and 
 the water contracts. 
 
 Fig. 7. 
 
 This change of volume can 
 
 be explained only on one of 
 
 two suppositions : the space 
 
 occupied by the water may, as 
 
 it appears, be full of water, 
 which the heat causes to expand, and occupy a greater space, as 
 represented graphically in Figure 7 ; or the body of water may 
 
THE MOLECULE. 5 
 
 consist of a definite number of distinct particles called molecules 
 (as represented in Figure 8), separated from one another by 
 spaces so small as not to be perceptible, 
 even with the aid of a microscope. Expan- ^^^g^l 
 
 sion, in this case, is accounted for by a simple 
 separation of molecules to greater distances. 
 Tliere is no increase in the number of mole- 
 cules, no increase in their size, only an en- 
 largement of space between them. Which 
 of these suppositions is the more probable ? 
 
 Experiment 2. Place a tumbler full of cold 
 water in a warm place, and in about an hour 
 
 examiDe it. You find many small bubbles of air clinging to all parts 
 of the interior surface of the glass. Is it probable that outside air 
 has descended into the liquid? 
 
 Experiment 3. Place a tumbler half full of water under a glass 
 receiver of an air-pump (page 54), and exhaust the air. When a very 
 good vacuum has been obtained, bubbles of air will be seen to form 
 at all points in the liquid, and to rise and burst near the surface. 
 
 Evidently the air was previously in the same space occupied 
 by the water. This seems to contradict the first of the above 
 suppositions ; for, according to that, the space occupied by the 
 water is full of water, leaving no room for other matter. But 
 according to the second supposition, the space is not filled with 
 water; there is still room for particles of other matter in the 
 spaces among the molecules of water. Now, as we cannot con- 
 ceive of two portions of matter occupying the same space at 
 the same time {e.g., where air is, water cannot be), we con- 
 clude that the glass " full of water " is not full of water. In a 
 similar manner, it may be shown that no visible body com- 
 pletely fills the space enclosed by its surface, but that there are 
 spaces in every body that may receive foreign matter. If there 
 are spaces, then the bodies of matter that our eyes are per- 
 mitted to see are not continuous, as space is continuous. But 
 every visible body is an aggregation of a countless number of 
 separate and individual bodies called molecules. 
 
6 Matter and its pkopekties. 
 
 Perfornl, *t your homes, the two following experiments : 
 
 Experiment 4. Pulverize one-half of a teaspOonftil of starch, and 
 boil it in two tablespoonfuls of water, stirring it meantime. What 
 phenomena dccur? What do they teach? What becomes of the 
 water 1 
 
 Experiitteiit B. Fill a bowl half full with peas or beans. Just cover 
 them with tepid water, and set away for the night. Examine in the 
 morning. What phenomena do yon observe ? Explain each. 
 
 Strictly Speaking, are bodies of matter impenetrable ? What 
 onlj- is impenetrable ? When you drive a nail into wood, do you 
 make the two bodies occupj' the same space at the same time ? 
 Do the wood and the iron occupy the same space ? How only 
 can you esJplain this phenomenon, consistently with the princi- 
 ples of impenetrability of matter? 
 
 § 5. Theory of the constitution of matter. — For reasons 
 which appear above, together with many others that will appear 
 as our knowledge of matter is extended, physicists have gener- 
 ally adopted the following theorj^ of the constitution of matter. 
 Every visible body of matter is composed of exceedingly small 
 particles, called molecules; in other words, every body is the sum 
 of its molecules. No two molecules of matter in tlie universe are 
 in contact with each other. Every molecule of a body is separated 
 from its neighbors, on ail sides, by inconceivably small spaces. 
 Every molecule is in quivering motion in its little space, moving 
 back and forth between its neighbors, and rebounding from them. 
 Wlien we heat a body we simply cause the molecules to move more 
 rapidly thfough their spaces; so they strike harder blows on their 
 neighbors, and usually push them away a very little; hence, the 
 size of the body increases. 
 
 This theory seems, at first, little more than an extravagant 
 guess. But if it shall be found that this theory, and this theory 
 alone, will enable us to account for most of the known phenom- 
 ena of matter, then we shall be content to adopt it till a better 
 can be produced. 
 
POROSITY. — DENSITY. 7 
 
 § 6. Porosity. — If the molecules of a body are nowhere in 
 absolute contact, it follows that there are unoccupied spaces 
 among them which may be occupied by molecules of other sub- 
 stances. These spaces are called pores. Water disappears in 
 cloth and beans. It is said to penetrate them ; but it really 
 enters the vacant spaces or pores between the molecules of these 
 substances. All matter is porous ; thus water may be forced 
 through solid cast-iron, and dense gold will absorb the liquid 
 mercury much as chalk will water. The term pore, in physics, 
 is restricted to the invisible spaces that separate molecules. The 
 cavities that may be seen in a sponge are not pores, but holes ; 
 thej' are no more entitled to be called pores, than the cells of a 
 hone^'comb, or the rooms of a house, are entitled to be called, 
 respectively, the pores of the honej'comb or of the house. 
 
 Small as animalcules are, they are coarse lumps in comparison with 
 the size of the molecule. By means of delicate calculations, the physi- 
 cist has succeeded in ascertaining approximately the probable size of 
 the molecule. If a drop of water could be magnified to the size of the 
 earth, it is thought that its molecules would appear smaller than an 
 apple. In other words, the molecule, In size, is to a drop of water 
 what an apple is to the earth. If we should attempt to count the num- 
 ber of molecules In a pin's head, counting at the rate of ten million in 
 a second, we should require 250,000 years. 
 
 § 7. Density. — Cut several blocks of wood, apple, putty, 
 lead, etc., of just the same size, and weigh them. Do they have 
 the same weight? Canyon explain the difference by a differ- 
 ence of porosity? 
 
 Again, if j'ou can try the experiment illustrated in Figs. 4 and 
 5, using various gases, you will find that the weights of the same 
 volumes of different gases are different. But the chemist has 
 reasons for believing that there is the same number of molecules 
 in the globe whatever be the gas, if the pressure and the tem- 
 perature are the same. We see then that some bodies have more 
 matter in a given volume than others, either because the molecules 
 are closer together, or because the molecules are different ; we call 
 
8 MATTER AND ITS PROPERTIES. 
 
 them more dense. By the mass oj a body we understand the 
 quamMty of matter in it; and by its density, the ma^s in the unit 
 volume of it. For example, the density of cast-iron is about 
 450 pounds per cubic foot. 
 
 § 8. Simple and compound substances. — Place a small 
 quantitj' of sugar on a hot stove. In a few minutes it changes 
 to a black mass. This black substance is found to be char- 
 coal, or carbon, as chemists call it. Evidently the sugar must 
 have contained carbon, for the carbon came from the sugar. 
 Chemists are also able to obtain water from sugar. The heat, 
 in our experiment, expels the water in the form of steam, and 
 leaves the carbon. Carbon can be extracted from sugar in 
 another way. Prepare a very thick syrup, by. dissolving sugar 
 in hot water, and pour upon the syrup two or three times its 
 bulk of sulphuric acid. You will quickly obtain a bulky, spongy 
 mass of carbon. 
 
 Bj' suitable processes, there may be obtained from marble 
 three substances, each one of which is entirely unlike marble. 
 One of the substances is carbon ; another is a metal called cal- 
 cium, which looks verj' much like silver ; the third is a gas called 
 oxj'gen, which, wlien set free from its prison-house in the solid, 
 expands to many times the size of the marble from which it was 
 liberated. 
 
 If we should grind a small piece of marble for many hours in 
 a mortar, we should reduce the marble to a very fine powder, 
 but should fall very far short of reducing it to its molecules. 
 Still, each little particle of the powder is as truly marble as the 
 original lump. If we should continue the division, in our imagi- 
 nations, till the marble were reduced to molecules, we should 
 expect to find all the molecules just alike. Now, since our 
 smallest piece, our molecule, our unit of marble, is marble, and 
 since marble is composed of the three substances, carbon, cal- 
 cium, and oxj'gen, we conclude that our molecule itself must be 
 capable of division. No one has been able to separate any one 
 
PHYSICAL AND CHEMICAL CHANGES. 9 
 
 of these substances into other substances. No one has taken 
 away from calcium anything but calcium, or extracted from 
 carbon, or from oxygen, anything but carbon and oxygen. 
 
 Those substances that have resisted all efforts to break them 
 up into other substances are called simple substances or ele- 
 ments. Those substances that may be broken up into other 
 substances are called compound substances. Of the large num- 
 ber of substances known to man, only 71 are elements. All 
 other substances are compounds of two or more of these 71 
 elements. 
 
 A molecule of any substance, simple or compound, is that\ 
 minute mass of the substance which cannot be divided without] 
 destroying its properties. 
 
 § 9. Physical and chemical changes. — When sugar is 
 ground to a powder, the particles are simplj- torn apart, but do 
 not lose their characteristics. The powder is just as sweet as the 
 lump. Such a division is called a physical division. Generally, 
 any change in a substance that does not cause it to lose its identity, 
 in other words, to cease to be that substance, is called a physical 
 change. When sufficient heat is applied to sugar, the molecules 
 themselves are divided ; and when a molecule of sugar is divided, 
 the result is not two parts of a molecule of sugar, but the two 
 substances, carbon and water. The sweetness is destroyed ; 
 sugar no longer exists ; other substances have taken its place. 
 The molecule of sugar is no more like the substances into which 
 it has been separated, than a word is like the letters that com- 
 pose it. Such a division is called a chemical division. Gener- 
 ally, any change in a substance thai causes it to lose its identity, 
 or cease to be that substance, is called a chemical change. 
 
 Ice, heated, melts to water; water, heated, becomes steam; steam, 
 cooled, condenses to water; water, cooled, becomes solid. During 
 these changes the substance, the molecule, has not changed. There 
 has been only a change among the molecules, in distance and arrange- 
 ment. What kind of change is this? But if the steam is subjected to 
 a very intense heat, the result is that it becomes converted Into a 
 
10 MATTBK AKD ITS PKOPEETIES. 
 
 mixed gas, consisting of two gases, oxygen and hydrogen. This gas 
 is not condensable at any ordinary temperature. Unlike steam, it 
 burns and even explodes. What kind of separation is this ? What 
 has been separated ? 
 
 Blackboard crayons are prepared by subjecting the dust of plaster 
 of Paris to great pressure, which causes the particles to Unite and form 
 the crayon. What kind of change is this? What kind of union? In the 
 experiment (page 2) with the ammonia and hydrochloric-acid gases, 
 the two gases disappear, and a solid is left in their place. What kind 
 of change is this : chemical or physical? Is it union or separation? 
 
 § 10. Annihilation and creation of matter impossible. 
 
 Experiment 1. Prepare a saturated solution of calcium chloride. 
 
 Mix with an equal bulk of water and weigh the solution. Prepare a 
 dilute solution of sulphuric acid (1 to 4), and pour an equal weight of 
 the last solution on the first, all at once, and shake gently. Instantly 
 the mixed liquid becomes a solid. The solid formed is commonly 
 called plaster of Paris. It is an entirely different substance from 
 either of the two liquids used. What kind of change is this ? A new 
 substance has been formed. Has matter been created? Weigh the 
 resulting solid ; its weight equals the sum of the weights of the two 
 liquids. The conclusion is, that no matter has been created, none 
 lost. 
 
 Solids may be converted into liquids or gases ; gases may be 
 converted into liquids or solids ; substances may completely lose 
 their characteristics : but man hcCs not discovered the means by 
 which a single molecule of matter can he created out of nothing, 
 or by which a single molecule of matter can be reduced to 
 nothing. Matter cannot be created, cannot be annihilated ; it 
 is a constant quantity. The discovery of this fact laid the 
 foundation of the science of Chemistry., 
 
 This statement may not seem to accord with many occurrences of 
 every-day experience. Wood, coal, and other substances burn ; matter 
 disappears, and very little is left that can be seen. But does matter 
 pass out of existence when it disappears in burning, or does it assume 
 the invisible state known by the name of gas ? 
 
 Experiment 2. Hold a cold, dry tumbler over a candle-flame. The 
 bright glass instantly becomes dimmed ; and, on close examination, you 
 find the glass bedewed with flue drops of a liquid. This liquid is water. 
 
ANNIHILATION AND CREATION OF MATTER. 11 
 
 You may think it strange that water is formed in the hot flame; 
 yet this simple experiment shows that this is really the case. If water 
 is formed during the burning, what is the reason we do not see it ? 
 Simply because it rises in the form of steam, which is an invisible gas. 
 The visible cloud, often called steam, which is formed in fi-ont of the 
 nozzle of a tea-kettle, is not steam, but flue drops of water floating in 
 the air, — a sort of water-dust. All clouds are of the same nature. A 
 cloud always stands over Niagara Falls, even on the clearest days. 
 The water of the river falls a distance of 150 feet, and, striking a bed 
 of rocks below, some of it is dashed into fragments, or dust, which 
 rises in a cloud. 
 
 Experiment 3. Introduce a candle-flame into a clean glass bottle; 
 after it has burned a few minutes the flame goes out. Why does It 
 go out ? See whether the air in the bottle is the same as it was be- 
 fore. Pour a wineglass full of lime-water into the bottle, cover tight- 
 ly, and shake. Also pour lime-water into a bottle filled with air. The 
 former becomes white and cloudy, the latter remains clear. It is 
 apparent that some new substance has been formed during the 
 burning, which, unlike air, can turn the lime-water white. This new 
 substance is likewise an invisible gas. 
 
 So that, before we can decide whether or not matter is annihilated 
 while burning, it is necessary to collect carefully, not only the ashes, 
 but all the invisible gases that are formed. This is a somewhat 
 troublesome experiment ; but it has been frequently performed, and it 
 is found that their collective weight is quite equal to the weight which 
 the candle loses. 
 
 Water does not pass out of existence when it " dries up " ; nor are 
 raindrops and dewdrops created out of nothing. Matter is every^yhere 
 undergoing great and various changes, both chemical and physical. 
 Nature is ever arraying herself in new forms. The sun warms tlio 
 tropical ocean, converting the liquid into vapor; the vapor rises iu 
 the air, is recondensed on mountain hights, and returns in rivers to 
 the ocean whence it came. Geology teaches us that continents and 
 oceans, and eveu the " everlasting hills," have a birth and decay, as 
 well as whole tribes of animals and vegetables. Although we may 
 be counted among the living ten years hence, our bodies will, ere 
 that, have crumbled into dust ; and the matter that will then compose 
 our bodies is to-day to be found mainly in the earth upon which we 
 tread. Change is stamped upon all matter ; nothing is exempt. Only 
 the quantity of matter remains unchanged. 
 
12 MATTER AND ITS PKOPEKTIBS. 
 
 § 11. Force. — Experiment 1. From a piece of cardboard sus- 
 pend, by means of silk threads, six pith-balls, so that they may be 
 
 about 2™' apart. Procure a 
 ^^1^^^^^^^^^^^ clean, dry glass tube, about 
 40™ long and 3™ in diam- 
 eter. Rub a portion of this 
 tube briskly with a silk hand- 
 kerchief, and hold it about 
 2™ below the balls. The balls 
 seem to become suddenly pos- 
 sessed of life. They gather 
 about the rod, and strive to 
 reach it. If we cut one of 
 the threads, the ball will fly 
 straight to the rod, and cling to it for a time. The means by which 
 the rod pulls the balls is invisible. Yet evidence is positive that the 
 rod has an influence on the balls, — that it pulls them. Slip a piece of 
 glass between the rod and the balls ; still the influence is felt by the 
 balls. The glass does not sever the invisible bonds that connect the 
 balls with the rod. 
 
 Now slowly bring the rod near the balls, till they touch. They at 
 first cling to the rod; but soon the rod, as if displeased with their 
 company, begins to push them away. Withdraw the rod; the balls 
 do not hang by parallel threads as before, but appear to be pushing 
 one another apart. Gradually bring the palm of the hand up beneath 
 the balls, but without touching them. The balls gradually yield to 
 the pull of the hand, and come together. Remove the hand, and 
 they again fly apart. Matter does not seem to be the dead, inert 
 thing which it is often called ; it can push and pull. 
 
 Experiment 2. Raise one of these balls with the fingers, and then 
 withdraw the fingers. Something from below seems to reach up, and 
 pull the ball down again. The same happens with each one of the 
 balls ; every ball is pulled by something below. What is it that pulls 
 the balls? Carry the balls into another room, the same thing occurs. 
 Can-y them to any part of the earth, the same thing occurs. It must 
 be that it is the earth Itself that pulls the balls. The earth pulls the 
 fruit and the leaf from the tree to itself; it pulls all objects to itself; 
 and more, — it holds them there. Attempt to raise anything from the 
 ground, and you feel the earth's pull resisting you. 
 
 Attempt to break a string, or crush a piece of chalk, and you find 
 
 > Tables of the Metric Measures may be found in the Appendix, Section A. 
 
MOLAR AND MOLECULAR FORCES. 13 
 
 that, notwithstanding the molecules of these bodies do not touch one 
 another, they possess a force which tends to keep them together, and 
 to resist your attempt to separate them. 
 
 § 12. Force defined. — This tendency to push and to 
 pull, which matter possesses, is called force. We do not 
 i<now why separate portions of mattei' tend to approach one 
 another, or to separate from one another. We do not know the 
 nature of force ; we cannot sec it or grasp it ; we simply 
 know that there must be a cause for certain effects produced. 
 The familiar effects produced are motion and rest. For exam- 
 ple, we see a body move ; we know that there is a cause: that 
 cause we attribute to force. When a body in motion comes to 
 rest, we look for a cause, and that cause we attribute to force. 
 It is difBcult to define force ; probably the most comprehensive 
 definition that has been given is the following: Force is that 
 which can produce, change, or destroy motion. 
 
 All force exhibits itself in pushes or pulls. All motion is 
 produced bj' pushes or pulls, or by a combination of both. A 
 pulling force is called an attractive force, or simply attraction. 
 A pushing force is called a repellent force, or repulsion. 
 
 § 13. Attraction and repulsion mutual. — Experiment. 
 
 Suspend a wooden lath in a sling. Eub one end of a glass rod with 
 silk, and bring that end of the rod near to one end of the lath. The 
 lath is attracted by the rod and moves toward it. Now place the rod 
 in the sling, and bring the lath near to its excited end. The lath draws 
 the rod to itself. We conclude that the pulling force belongs to both 
 — that both are concerned in the pulling. In the experiment with the 
 pith-balls (§ 11, Exp. 1), they seem to be mutually pushing each other. 
 All attraction and repulsion between different portions of matter are mutual. 
 
 §14. Molar and molecular forces. — The glass rod does 
 not seem to jjossess any attractive force, until it is rubbed with 
 the handkerchief. The pith-balls do not repel one another until 
 they have first touched the glass rod. After a time, the rod 
 and the balls lose both their attractive and repellent forces. 
 Or, if we pass the hand several times over the part of the rod 
 
14 MATTER AND ITS PEOPEETIES. 
 
 that has been rubbed, and over the balls, they quickly surrender 
 their forces. These forces are temporary. They are called 
 electnc forces, and their cause elearicity. The attractive force 
 that draws the balls to the earth existed before the experiment. 
 No manipulation can destroy it or increase it ; it is eternal and 
 unchangeable, and exists between all portions of matter. This 
 force is called the force of gravity, and the phenomenon is C9,lled 
 gravitation. 
 
 We have seen the effects of attractive and repellent forces, 
 reaching across sensible distances. Have we any evidence 
 that these forces exist among portions of matter, at insensible 
 distances, i.e., at distances too short to be perceived by our 
 senses ? Stretch a piece of rubber ; you realize that there is « 
 force resisting you. You reason that if the supposition be true, 
 that the grains or molecules that compose the piece of rubber dp 
 not touch each other, then there must be a powerful attractive 
 force reaching across the spaces between the molecules, to 
 prevent their separation. After stretching the rubber, let go 
 one end. It springs back to its original form. What is the 
 cause ? Compress the rubber ; its volume is diminished. (Does 
 this confirm our supposition respecting the granular structure 
 of matter?) Remove the pressure; the rubber springs back to 
 its original form. What is the cause ? 
 
 Every body of matter, with the possible exception of the 
 molecule, whether solid, liquid, or gaseous, maybe forced into 
 a smaller volume by pressure, — in other words, matter is com- 
 pressible. When pressure is removed, the body expands int© 
 nearlj' or quite its original volume. This shows two things: 
 first, that the matter of which a body is formed does not ret^ly 
 Jill all the space which the body appears to occupy; and, second, 
 that in the body is a force, which, acting from within outward,, 
 resists outward pressure tending to compress it, and ea^ands the 
 body to its original volume when pressure is removed. This is, 
 of course, a repellent force, and is exerted among molecules, 
 tending to push them farther apart. 
 
MATTER. 15 
 
 But it has previously been shown that there is also an attract- 
 ive force existing between the molecules. Now what is the 
 effect, when two forces act on a body in opposite directions? 
 Let two boys, at opposite ends of a table, push the table. If 
 both push with equal force, the table does not move ; it is as if 
 no one pushed it. But if one boy pushes a little harder than 
 the other, then the table moves in the direction in which the 
 greater force is applied. Now we have the key to the solution 
 of a difflculty, which always arises in the mind of a beginner iu 
 science, when he first hears the startling statement that the 
 molecules of bodies, of his own body even, do not touch one 
 another. If faith were of quick growth, he would shudder at 
 the thought of falling to pieces, or of being wafted away by 
 the winds as so much dust. 
 
 The ancients, perceiving that matter must be built up of 
 small parts, overcame this difficultj' bj' supposing that the 
 minute particles have hooks or claws by which they grasp one 
 another. Our knowledge of the operation of forces enables us to 
 dispense with hooks and claws, much to the advantage of science. 
 We see that the molecules of a bodj- are kept from falling 
 apart, or from separation, bj' a universal attractive force ; they 
 are also kept from falling together, or from permanent contact, 
 by an ever-existing repellent force. These forces act at insen- 
 sible distances between molecules, and hence are called molecular 
 fm-ees. When forces act between bodies at sensible distances 
 they are called molar forces. Give illustrations (1) of molar 
 forces ; (2) of molecular forces. 
 
 II. THREE STATES OF MATTER. 
 
 § 15. Matter presents itself in three different states : solid, 
 liquid, and gaseous, — fairly represented by earth, water, and 
 air. Because these forms are so common and abundant, some 
 ancient philosophers held that all solid matter is formed of 
 earth, all liquids of water, and all gases of air. On this account 
 
16 MATTER AND ITS PKOPEETIES. 
 
 they called them, together with Are, elements or primary matter. 
 They cannot now be so regarded from a chemical point of view, 
 because each of them has been separated into still more simple 
 substances ; nor from a physical standpoint, because, as will 
 soon be shown, most substances may exist in any one of these 
 states. 
 
 § 16. Characteristics of each of these states. 
 
 Experiment 1. Provide two vessels, a cubical dish and a goblet, 
 each having a capacity of about 200™". Also provide 200<='='" of sand, 
 200"™ of water, and a cubical block of wood containing 200''™. 
 Grasp the block, and place it in the cubical vessel. Attempt to do the 
 same thing with the water. Why can you not grasp the water ? Pour 
 a portion of the water into the cubical vessel. When you move a por- 
 tion of the block, the whole block moves. When you pour a portion 
 of the water into the cubical vessel, the whole does not necessarily go. 
 Why is this ? Why is it that we can dip a cupful of water out of a 
 pailful, without raising the whole? Pour all the water into the goblet. 
 The water adapts itself to the shape of the goblet, and the vessel is 
 filled. Attempt to place the block of wood in the goblet. What dif- 
 ference in phenomena do you observe ? Why this difference ? Pour 
 the sand from vessel to vessel. It adapts itself to the shape of each 
 vessel. Why ? Drop the block of wood on a table. Pour water on the 
 table. How does a liquid behave when there is no vessel to confine it ? 
 
 Experiment 2. Throw small particles of sawdust into the goblet of 
 water ; you can thus render perceptible any motion of the water in the 
 goblet, just as, by throwing blocks of wood on the smooth surface of 
 a river, you can discover the motion of the river. Notice the ease 
 with which the particles move about, rise, and sink. As they become 
 quiet, slightly jar the vessel, or tap it with the end of a pencU, and 
 notice the ease with which disturbance is produced throughout the 
 liquid. Now rap the side of the block with a hammer, and observe 
 how immovable are the particles of wood. 
 
 Our experiments teach us that the molecules of solids are not 
 easily moved out of their places; consequently, solid masses 
 form such a firmly connected whole that their shape is not easily 
 changed, and a movement of one part causes a movement of the 
 whole. On the other hand, the molecules of liquids have scarcely 
 any fixedness of position, but easily slip between and around one 
 
THREE STATES OF MATTER. 17 
 
 another; consequent^, liquid bodies easily mold themselves to 
 the shape of the vessel that contains them, are poured from ves- 
 sel to vessel, and are easily separated into parts. 
 
 But what shall we say of the sand, which, like water, adapts 
 itself to the shape of the containing vessel, and can be poured ? 
 Is sand a liquid? and are pdwders liquids? No, powders are a 
 collection of small lumps of solid matter. When powders arc 
 poured, lumps of matter roll around one another, as when 
 potatoes are poured from basket to basket. When liquids are 
 poured, molecules glide past one another. 
 
 It is not so easy to study the characteristics of gases, because 
 we cannot usually see them. But we may be aided by a device 
 similar to that employed to make the movement of water visible. 
 
 Experiment 3. Darken a room, and admit, through a small crack 
 or hole, a beam of direct sunlight. You see particles of dust dancing 
 in the path of the light ; the motion never ceases. See how easily the 
 motion is quickened by gently waving the hand at some distance from 
 the beam of light. 
 
 Experiment 4. Place under the receiver of an air-pump a partially 
 inflated balloon, Fig. 32, page 53 (or a Seven-in-one apparatus with thu 
 piston near the closed end of the cylinder, and stop-cock closed), and 
 exhaust the air. The tendency of gases to expand becomes evident. 
 
 In gases, fixedness of position of the molecules is entirely want- 
 ing, and freedom of motion among themselves is almost perfect. 
 They appear to be in a continual state of repulsion, and conse- 
 quently have a tendency to expand to greater and greater volumes. 
 They expand indefinitely, unless confined by pressure, while 
 liquids and solids tend to preserve a uniformity of volume. 
 
 Liquids do not rise above what is called their surface, and we 
 may have a ve.ssel half full of a liquid ; but gases have no defi- 
 nite surface, and there is no such thing as a vessel half full of 
 gas. On the other hand, if gases are subjected to pressure, their 
 volume may be indefinitely diminished ; for instance, the air that 
 now fills a quart vessel may be compressed into a pint vessel, 
 or even into less space, if sufficient force is used. The com- 
 
18 MATTER AND ITS PKOPEETIES. 
 
 pression of liquids is barely perceptible, even when the pressure 
 is very great. 
 
 § 17. Philosophy of the three states of matter. — We 
 conclude from the difficulty which we experience in separating 
 the parts of a solid body, that the molecular attractive force in 
 solids is very great. From the ease with which we usually 
 separate the parts of a body of liquid, we might conclude that 
 this force in liquids is very weak. But before arriving at any 
 conclusion, it is necessary to consider how the difficulty of sepa- 
 ration of the parts of a liquid is to be measured. It is very 
 easy to tear off a portion of a sheet of tinfoil, but we should not 
 surely regard this as an evidence that the molecules of tin have 
 but little attraction for each other, for in tearing such a body we 
 only apply the force to a comparatively few molecules at a time. 
 We can form a just estimate of the strength of molecular attrac- 
 tion only by attempting to separate the foil into two portions by 
 such means as that the separation may take place no sooner at 
 one point than at another. So, too, it is very easy to separate 
 a drop of water into two portions, but this is no measure of the 
 attractive forces unless we take precautions that we do not applj- 
 the separating force successively to different molecules. If we 
 succeed in preventing such a successive action, and there are 
 certain methods of doing this more or less perfectly, we should 
 find the process much more difficult, — more so indeed, than to 
 produce a similar change in many solids. ^ 
 
 There is, however, a difference in the molecular action in 
 solids and liquids ; such that, in the latter state, the molecular 
 forces offer no resistance to a shaping force, while in the former 
 state, change of shape can only be brought about by the appli- 
 cation of considerable force. 
 
 In a gas, on the contrary, there is little attraction between the 
 molecules ; but as they are constantly hitting one another, and 
 thereby tending to drive one another apart, it requires an external 
 force to keep them together. 
 
 ' The ceheeiTe force of water ie at least 132 lbs. per square inch. — Maxwbll. 
 
PHILOSOPHY OF THE THREE STA.TES OP MATTBB. 19 
 
 Note. In gases, the molecules are thought to be in motion like gnats 
 In the air ; in liquids, like men moving through a crowd ; in solids, the 
 motion of each molecule is like that of a man in a dense crowd where 
 it is almost or quite impossible to leave his neighbors, yet he may turn 
 around, and have some motion from side to side. 
 
 Practically, the condition of any portion of matter depends 
 upon its temperature and pressure. (See p. 160.) Just as at 
 ordinary pressures water is a solid, a liquid, or a gas, according 
 to its temperature, so any substance may be made to assume 
 any one of these forms unless a change of temperature occasions 
 a chemical change. 
 
 There are certain apparent exceptions to the laet statement ; 
 for example, charcoal, though it has been vaporized, has never 
 been obtained in a liquid state, simply because sufficient press- 
 ure has never been used. Ice will change to a vapor, but can- 
 not be melted unless the pressure exceeds six grams per square 
 centimeter. For a similar reason, iodine and camphor vaporize, 
 but do not melt. Alcohol has never been solidified, or frozen.' 
 It has been rendered thick and pasty, — a semi-solid condition, 
 — showing that it only requires a little lower temperature than 
 any to which it has been exposed, to complete the solidification. 
 
 As regards the temperature at which different substances 
 assume the different states, there is great diversity. Oxj'gen 
 and nitrogen gases, or air, — which is a mixture of the two, — 
 liquefy and sohdify only at extremely low temperatures ; and 
 then, only when the attractive force is aided by tremendous 
 pressure. On the other hand, certain substances, as quartz and 
 lime, are liquefied only by the most intense heat generated by an 
 electric current. The facts, summed up, are as follows : no one 
 of the three states of matter, solid, liquid, or gaseous, is peculiar 
 to any substance; the state that a substance assumes depends 
 solely on its temperature and pressure ; so that every solid may be 
 regarded as simply matter in a frozen state, every liquid as mat- 
 ter in a melted state, and every gas as matter in a state of vapor, 
 
 1 Since this statement was written alcohol has been frozen at about —130° 0. 
 
20 MATTER AND ITS PKOPEBTIES. 
 
 Every liquid has been solidified and volatilized, and every gas 
 has been liquefied and solidified. Air was one of the last of the 
 gases to surrender its reputation of being a " permanent gas." 
 Not till the year 1878 was it reduced to lumps. We may predict 
 the future of our globe. If its heat increases sufficiently, the 
 whole world will become a thin gas. If its heat diminishes indefi- 
 nitely, all earth and air will become a solid mass. 
 
 III. PHENOMENA OF ATTRACTION. 
 According to the circumstances under which attraction acts, 
 we have the various phenomena called gravitation, cohesion, ad- 
 hesion, capillarity, chemism, and magnetism. Sometimes these 
 terms are used as names of the unknown forces that cause the 
 phenomena. 
 
 § 18. Gravitation. — That attraction which is exerted on all 
 matter, at all distances, is called gravitation. Gravitation is 
 universal, that is, every molecule of matter attracts every other 
 molecule of matter in the universe. The whole force with 
 which two bodies attract one another is the sum of the attrac- 
 tions of their molecules, and depends upon the number of mole- 
 cules the two bodies collectively contain, and the mass of each 
 molecule. The whole attraction between an apple and the earth 
 is equal to the sum of the attractions between every molecule 
 in the apple and every molecule in the earth. 
 
 § 19. Weight, — It is scarcely necessary to state, that what 
 is understood by the weight of a bodj- is the mutual attraction 
 between it and the earth. The term mass is equivalent to the 
 expression quantity of matter. It follows, then, that weight is 
 proportional to mass. Why do we weigh articles of trade, such 
 as sugar and tea? 
 
 § 20. Does the apple attract the earth -with as much 
 force as the earth attracts the apple ? — Let us examine this 
 question. First assume that the molecules of the apple and the earth 
 have equal masses, i.e., are homogeneous; then the attraction of any 
 
LAW OF GKAVITATION. 21 
 
 molecule in the apple for any molecule in the earth is equal to the 
 attraction of any molecule in the earth for any molecule in the apple. 
 That is, if the earth and the apple consisted each of a single like mole- 
 cule, their attraction for each other would be equal. Now suppose 
 that the apple contains two and the earth five such molecules. Let 
 the force with which one molecule attracts another be represented by n. 
 Now, each molecule of the apple attracts the five molecules in the earth 
 with a force of 5)1; the two molecules in the apple would attract the 
 earth with a force of 10 n. On the other hand, each molecule of the 
 earth attracts the molecules of the apple with a force of 2 n, and the 
 five molecules in the earth would attract the apple with a force of 
 1071. It is obvious that the same course of reasoning will apply in 
 case the attraction is between two molecules whose masses differ, 
 and consequently between all bodies of whatever mass or substance. 
 Hence a body of small mass attracts a body of large mass as strongly 
 as the latter attracts the former. 
 
 If the apple attracts the earth as strongly as the earth attracts the 
 apple, why does not the earth rise to meet the apple ? Let us examine 
 a similar case. Suppose that a man in a boat pulls on a rope attached 
 to a ship. His pulling draws the boat to the ship, but the ship does 
 not appear to move. But if five hundred men, iu as many boats, pulled 
 together, the ship would be seen to move. Did the one man produce 
 no motion ? If so, then would the five hundred men produce no mo- 
 tion, since five hundred times nothing is nothing? Yes, the apple 
 moves the earth as surely as the earth moves the apple ; but the apple 
 has more to move, and, consequently, It moves the earth a distance as 
 many times less than it is moved by the earth, as the quantity of mat- 
 ter in the earth is times the quantity of matter in the apple. The re- 
 spective distances the two bodies move vary inversely as their masses. 
 
 § 21. The force of gravity varies with the distance 
 from the center. — Observations made in various ways show 
 that the force of gravity varies over the surface of the earth. It 
 can be proved by geometrical methods that a sphere or a spheroid 
 acts upon a molecule without it as though all its attractive force 
 were concentrated at its center. Now it is found that the nearer 
 an object without the earth's surface is to the center^of the earth 
 the greater is the force of gravity. The polar diameter of the 
 ■^arth is about 26 miles less than its equatorial diameter, and, 
 consequently, the distance from the center to the surface at the 
 
22 MATTEE AND ITS PROPERTIES. 
 
 poles is 13 miles less than to the surface at the equator. This 
 considerable difference in distance from the center occasions an 
 appreciable difference between the weight of a body (having any 
 considerable mass) at the equator and at the poles ; and, since 
 the distance of the surface from the center constantly increases 
 as we go from the poles toward the equator, the weight of all 
 objects transported from the poles toward the equator constantly 
 diminishes. 
 
 It is obvious that any object raised above the earth's surface, 
 as in a balloon, must weigh less than at the surface of the earth. 
 But the hights with which we commonly have to deal in our ex- 
 periments are so small in comparison with the earth's radius, that 
 the differences in weight due to differences in hight at a given 
 place can scarcely be detected by most delicate tests. 
 
 The statement that " weight is proportional to mass " (§19) 
 must, therefore, be restricted to a comparison of masses at the 
 same place and at the same altitude only. The propriety of 
 making a distinction between the terms mass and weight is 
 now apparent, as the former implies that which does not change 
 when a body is transferred from place to place, while the 
 latter may change. 
 
 If the earth were of uniform density, bodies carried below its 
 surface would lose in weight as the distance below the surface 
 increases. At one-fourth the distance to the center there would 
 be a loss of one-fourth the weight. At one-half the distance 
 the weight would be one-half; and at the center nothing. Is 
 weight an essential property of matter ? State certain condi- 
 tions on which a body would have no weight. 
 
 The terms up and dovm are derived from the attraction be- 
 tween the earth and terrestrial objects. Down is toward the 
 center of the earth, or it is the direction in which a body falls or 
 tends to move in consequence of gravitation. Up is the oppo- 
 site direction. It is apparent that the up and down of one 
 place cannot correspond with the up and down of any other 
 place. 
 
COHESION. 23 
 
 QUESTIONS. 
 
 1. If an iron pound-weight and a pound of sugar were balanced with 
 ordinary scales at the equator, and transported to one of the poles of 
 the earth, would they cease to balance each other ? 
 
 2. If the same quantity of sugar be suspended from a spring-balance 
 at the pole, will this instrument indicate just a pound, more or less ? 
 
 3. Imagine yourself at the center of the earth. In what direction 
 must you turn your face in order to look up ? 
 
 4. Imagine a person at one of the poles, and another at the equa- 
 tor, to be looking down upon you at the center of the earth. Would 
 they both look in the same direction ? 
 
 6. Draw a circle to represent the earth, aud two lines to represent 
 the direction in which the two persons would look. 
 
 6. What is the origin of " water-power " ? 
 
 7. What is the cause of tides ? 
 
 8. Which is more difficult, to ascend or descend a hill, and why ? 
 
 9. The earth has about 81 times as much matter in it as the moon. 
 At which body would you weigh more ? 
 
 10. Is there a place between the two bodies at which you would 
 weigh nothing ? If so, why ? 
 
 11. How far does the earth's attraction extend ? 
 
 12. Which would you prefer, a pound of gold weighed with a spring- 
 balance at the surface of the earth, or a pound weighed 3,000,000"«> 
 below the surface ? 
 
 § 22. Cohesion. — That attraction which holds the molecules 
 of the same substance together, so as to form larger bodies, is 
 called cohesion. It is the force that prevents our bodies, and 
 all bodies, from falling down into a mass of dust. It is that 
 force which resists a force tending to break or crush a bod^'. It 
 is greatest in solids, usually less in liquids, and nothing in gases. 
 It acts only at insensible distances, and is strictly a molecular 
 force. "When once the cohesion is overcome, it is difHcult to force 
 the molecules near enough to one another for this force to become 
 effective again. Broken pieces of glass and crockery cannot 
 be so nicely readjusted that they will hold together. Yet two 
 polished surfaces of glass, placed in contact, will cohere quite 
 strongly. Or if the glass is heated till it is soft, or in a semi- 
 
24 MATTER AND ITS PROPERTIES. 
 
 fluid condition, then, by pressure, the molecules at the two 
 surfaces will flow around one another, pack themselves closely' 
 together, and the two bodies will become firmly united. This 
 process is called welding. In this manner iron is welded. 
 
 Cohesive force varies greatly in different substances, according 
 to the variation in the nature, form, and arrangement of the 
 molecules of which they are composed. These modifications of 
 the force of attraction give rise to certain conditions of matter, 
 designated as crystalline, amorphous, hard, flexible, elastic, brit- 
 tle, viscous, malleable, ductile, and tenacious. 
 
 § 23. Crystalline and amorphous conditions of matter. 
 — If our vision could be rendered keen enough to enable us to 
 see and examine the molecular structure of different substances, 
 to look into their bodies, as we look into the starry heavens, and 
 observe the positions, the spaces, and the arrangement of that 
 unexplored world, there would undoubtedly be unfolded to us 
 wonders and beauties of which we have never dreamed. We 
 should probably behold an endless variety of arrangement among 
 the molecules. We might learn why it is that the molecule of 
 the diamond, of graphite, and of charcoal being the same {i.e., 
 the same substance), we get, possiblj' by different arrangement 
 and different behavior of molecular forces, the hard, transparent, 
 and brilliant diamond in the one case, the soft, opaque, metallic- 
 looking graphite in another, and finally the porous, black, and 
 shapeless charcoal. 
 
 Obtain a piece of mica, or Iceland spar, and a piece of chalk, 
 and attempt to cut them in two, by applying the knife in differ- 
 ent directions. You find that you can easily cleave the mica in 
 one direction, and obtain a smooth, shining surface. This is 
 called its plane of cleavage. Cut it in any other direction, and 
 you get rough and ragged surfaces. The spar may be cleft 
 easily and smoothly in three directions. But the chalk may be 
 cleft in one direction as well as another, and in no direction can 
 a smooth surface be obtained. We learn by these trials that 
 
CRYSTALLIZATION. 25 
 
 matter maj- have method in its arrangement, or possess definite 
 structure. 
 
 When matter exhibits structure or method in its molecular 
 arrangement, it is said to be crystalline. Examples of crj's- 
 talline arrangement are mica, Iceland spar, and carbon in the 
 form of diamond. When its molecular arrangement is method- 
 less or structureless, it is said to be amorphous. Examples of 
 amorphous matter are chalk, glue, glass, and carbon in the form 
 of charcoal. 
 
 Experiment 1. Pulverize 20e of alum, aud dissolve In 50™™ of hot 
 water ; suspend a thread in the solution, and put it away where it can 
 quietly and slowly cool. After it has become cold, you will find 
 attached to the thread beautiful transparent bodies of regular shape. 
 The process by which matter in solidifying assumes a structural con- 
 dition is called crystallization, and bodies which have acquired regular 
 shape by this process are called crystals. Obtain crystals of saltpetre, 
 blue vitriol, and potassium bichromate, by dissolving as much as pos- 
 sible of these substances in hot water, and allowing the solutions to 
 cool, always slowly and quietly. 
 
 Experiment 2. Thoroughly clean a piece of window-glass, and pour 
 upon it a hot, concentrated solution (see § 36) of ammonium chloride 
 or saltpetre. Allow the liquid to drain off, hold it up to the sunlight, 
 and you will see beautiful crystals rapidly springing into existence, 
 spreading and branching like vegetable growth. 
 
 Very interesting illustrations of crj-stallization are those deli- 
 cate lacelike figures which follow the touch of frost on the 
 window-pane. Figure 10 represents a few of more than a thou- 
 sand forms of snowflakes that have been discovered, resulting 
 from a variety of arrangement of the water molecules. 
 
 Nature teems with crj'stals. Nearly every kind of matter, in 
 passing from the liquid state (whether molten or in solution) to the 
 solid state, tends to assume symmetrical forms. Crystallization 
 is the rule ; amorphism, the exception. Break open a sugar-loaf, 
 and you will find the surface fracture composed of small, shining, 
 crystalline surfaces. You can scarcely pick up a stone and break 
 it, without finding the same crystalline fracture. Every piece 
 
26 
 
 MATTER AND ITS PBOPERTIBS. 
 
 of ice is a mass of crystals, so closely packed together that the 
 individuals are not distinguishable. 
 
 § 24, Change of volume by crystallization. — This tend- 
 ency of matter to structural arrangement is not only very inter- 
 esting, but very important in the arts. It is very natural to 
 
 Fig. 10. 
 
 suppose that the new arrangement of molecules, when passing 
 from the liquid to the solid state, should occasion either an 
 increase or diminution in volume. We are not surprised when 
 we find that water, in freezing, disregards the law of contraction 
 by cold, and that the molecules are not found so closely packed 
 
CHANGE OF VOLUME BY CEYSTALLIZATIOK. 27 
 
 together, in the new and structural state, as when under the 
 influence of cohesion alone. 
 
 The force exerted by the molecules in changing positions is 
 so enormous as to burst the strongest vessels. Hence our ser- 
 vice-pipes are burst when water is allowed to freeze in them. 
 Huge rocks are dislodged from their resting-places in the native 
 quarrj' on the mountain-side by water getting into the crevices, 
 freezing, expanding year after year, and pushing the rocks 
 from their support. Cast-iron and many alloj-s, such as tj'pe- 
 raetal, expand on solidifying. Such metals may be cast in 
 molds, since, in expanding, they fill all the minute cavities of 
 the mold. Most metals contract on solidifying. Hence gold, 
 silver, and copper coins require to be stamped. Cast-iron, 
 when broken, exhibits a crystalline fracture. Wrought-iron, 
 when subjected to long-continued jarring, — for instance, the 
 axles of car-wheels, and iron cannon, — becomes ver}' brittle, 
 and, when broken, exhibits a verj^ marked crystalline fracture 
 which it would not have shown before long use. It is probable 
 that the molecules of iron, when shaken up by the jarring, are 
 free to arrange themselves in their peculiar method, and that, in 
 this new arrangement, the cohesive force is weakened. 
 
 § 25. What is the cause of this almost universal ten- 
 dency of matter to crystallize ? — "We have no absolute 
 knowledge of the doings in the molecular world. But we have 
 very satisfactory methods of judging. Analogy is the light by 
 which we must frequently explore inaccessible space. We de- 
 termine the laws that govern large, tangible masses, and from 
 these we infer the laws that govern small, intangible bodies, or 
 molecules. Let us adopt this method in attempting to unravel 
 the mj'stery before us. 
 
 Experiment 1. Take two cambric needles, and draw each several 
 times, from the eye to the point, over the same end of a magnet. Now 
 suspend each needle by a thread, so that it will be balanced in a hori- 
 zontal position. Bring the eye of one near the point of the other. 
 When brought near enough, they attract each other. Bring the point 
 
28 MATTER AND ITS PROPBBTIES. 
 
 of one near the point of the other ; they repel one another. Bring the 
 eye of one near the eye of the other ; they repel one another. We thus 
 discover that the relation of these two needles to one another is such, 
 that if unlike ends are brought together they attract one another, but 
 if like ends are brought together they repel one another. The opposite 
 character which the ends of the needle exhibit is called polarity. 
 
 Now break one of the needles into two pieces, and experiment as 
 before. The two pieces exhibit the same polarity that the two unbroken 
 needles did. Break them into still smaller pieces, and the smallest 
 piece that you can obtain possesses polarity, as certainly as the original 
 needle. Imagine the work of division to be continued till the molecule 
 is reached. Is it too much to assume that the molecule may possess 
 polarity ? 
 
 Experiment 2. Next, place a magnet beneath a sheet of paper, and 
 sift iron flUngs over it. The instant they strike the paper they arrange 
 themselves in lines around the magnet (see Fig. 162, page 221). Gently 
 tap the paper, and they arrange themselves still more definitely. This 
 reminds us of the effect of jarring on the car-axle and cannon, where 
 molecules, once set in motion, tend to arrange themselves according to 
 some guiding principle. Next, lay the magnet on a bed of iron filings 
 (see page 214), and then raise it. We find the filings clinging most 
 abundantly to the ends, diminishing in number toward the middle. 
 
 We pass readily from these facts to conclusions respecting the mo- 
 lecular arrangement in the crystal. Only grant the supposition that the 
 molecule is endowed with something similar to polarity, and we can 
 picture to ourselves the molecules, like the iron filings, wheeling into 
 line in obedience to their polar forces. Crystals are more easily cleft in 
 some directions than in others : may not this be accounted for by 
 supposing that, like the magnet, the attraction on some sides of the 
 molecule is greater than on others ? 
 
 § 26. Hardness. — Name some metal that you can scratch 
 with a finger-nail. See if you can scratch a piece of copper 
 with a piece of lead, and vice versa. Get as many specimens as 
 possible of the following substances : talc, chalk, glass, quartz, 
 iron, silver, lead, copper, rock-salt, and marble. Ascertain 
 which of them will scratch glass, and which are scratched by 
 glass. What term do we employ in speaking of those substances 
 that are easily scratched? To those that are scratched with 
 difficulty? Which is the softest metal that you have tried? 
 
FLEXIBILITY. 29 
 
 The hardest? Which is the softer metal, iron or lead? Which 
 is the more dense metal? Does hardness depend upon density? 
 What force must be overcome in order to scratch a substance ? 
 When will one substance scratch another? 
 
 To enable us to express degrees of hardness, the following 
 table of reference is generally adopted : — 
 
 MOHK'S SCALE OF HARDNESS. 
 
 1. Talc. 6. Orthoclase (Feldspar). 
 
 2. Gypsum (or Rock-Salt). 7. Quartz. 
 
 3. Calcite. 8. Topaz. 
 
 4. Fluor-Spar. 9. Corundum. 
 
 5. Apatite. 10. Diamond. 
 
 By comparing a given substance with the substances in the 
 table, its degree of hardness can be expressed approximatelj' by 
 one of the numbers used in the table. If the hardness of a sub- 
 stance is indicated by the number 4, what would you understand 
 by it? 
 
 § 27. Flexibility. — Such substances as may be bent, or admit 
 of a hinge-like movement among their p. ^ 
 
 molecules, are called ^ea;i6te. What 
 difference have you noticed in differ- 
 ent jack-knife blades ? How can 3'ou 
 tell a soft blade from a hard blade? 
 If j'ou bend a stick, as in Figure 11, it is apparent that the 
 molecules on the upper side must be separated from each other 
 a little farther than usual, and that they must have slightly 
 rolled round one another, while those on the under side must be 
 crowded together more closely than usual. On the other hand, 
 the molecules in a glass rod have fixed relative positions which 
 will permit very little disturbance. 
 
 §28. Elasticity. — Obtain thin strips of the following sub- 
 stances : rubber, wood, ivory, whalebone, steel, brass, copper, 
 
30 
 
 MATTER AND ITS PEOPBRTIBS. 
 
 iron, zinc, and lead. Stretcli tiie piece of rubber. What change 
 in its molecular condition must occur when it is stretched? 
 What molecular force causes it to contract when the stretching 
 force is removed? Compress the rubber. What change of 
 molecular condition takes place in compression? What force 
 causes it to expand when the pressure is removed ? Bend each 
 one of the above strips. Note which completely unbends when 
 the force is removed. Arrange the names of these substances 
 in the order of the rapidity and completeness with which the}' 
 unbend. 
 
 What change takes place among the molecules on the concave 
 side of the bent strips? What, among the molecules on the 
 convex side? What two forces are concerned in the unbending? 
 Twist the cord of a window-tassel. What causes it to untwist? 
 The property which matter possesses of recovering its former 
 shape and volume, after having yielded to some force, is called 
 elasticity. To what forces is elasticity due? Does all mat- 
 ter possess this property in the same degree? Does the rub- 
 ber possess the same abilitj' to unbend, as to contract after 
 being stretched? In what four ways have j'ou 
 tested the elasticity of substances? Does a sub- 
 stance possess equal power of recovering its form 
 after yielding to each of these four methods of 
 applying force? Why are pens made of steel? 
 What moves the machinery of a watch ? What 
 is the cause of the softness of a hair mattress or 
 feather-bed ? 
 
 A common spring-ljalance used for weighing con- 
 sists of a steel spring wound into a coil. The weight 
 of the body to be weighed straightens or draws out 
 the spring. A pointer moving over a plate which is 
 divided into equal parts shows how much the spring has been drawn 
 out. But the entire virtue of this apparatus consists in the elasticity 
 of the spring, or Its power to recover its original form after being 
 drawn out. Give other illustrations of the application of elasticity 
 to practical purposes. 
 
 Fig. 12. 
 
BRITTLENESS. — VISCOSITY. 31 
 
 Any alteration in the form of a body due to the application of 
 a force is called a strain, and the force by which the strain is 
 produced is called the stress. A body which, having experienced 
 a strain due to a certain stress, completely recovers its original 
 condition when the stress is removed, is said to be perfectly 
 elastic. Liquids and gases are perfectly elastic (see § 48) . Solids 
 are perfectly elastic up to a certain limit, which varies greatly in 
 different substances. If the sti'ess exceeds a certain limit, the 
 form of the solid becomes permanently altered, and the state of 
 the body, when the permanent altei'ation is about to take place, 
 is called the limit of perfect elasticity. In soft or plastic bodies 
 this limit is soon reached. What is the result of overloading 
 caiTiage springs? 
 
 § 29. Brittleness. — Apply sharp blows with a hammer to 
 each of the substances whose hardness you have tested (§ 26), 
 and ascertain which are the most easily broken or pulverized. 
 Observe that some substances suffer a permanent change in form 
 when subjected to a stress which exceeds their limit of elasticity, 
 while others break before there is any permanent alteration in 
 form. The latter are said to be brittle. 
 
 § 30. Viscosity. — Support in a horizontal position, at one 
 of its extremities, a stick of sealing-wax, and suspend from its 
 free extremity a small weight, and let it remain in this condition 
 several daj's, or perhaps weeks. At the end of the time the 
 stick will be found permanently bent. Had an attempt been 
 made to bend the stick quickly, it would have been found quite 
 brittle. A body which, subjected to a stress for a considerable 
 time, suffers a permanent change in form, is said to be viscous. 
 Hardness is not opposed to viscosity. A lump of pitch may be 
 quite hard, and yet in the course of time it will flatten itself out 
 by its own weight, and flow down hill like a stream of syrup. 
 Liquids like molasses and honey are said to be viscous, in dis- 
 tinction from limpid liquids like water and alcohol. 
 
32 MATTER AND ITS PROPERTIES. 
 
 § 31. Malleability and ductility. — Some substances pos- 
 sess, in the solid state, a certain amount of fluidity ; that is, 
 their molecules may be displaced without overcoming their cohe- 
 sion. Place a piece of lead on an anvil, and hammer it. It 
 spreads out under the hammer into sheets, without being broken, 
 though it is evident that the molecules have moved about among 
 one another, and assumed entirely different relative positions. 
 Heat a piece of soft glass tube in a gas-flame, and, although the 
 glass does not become a liquid, it behaves very much like a 
 liquid, and can be drawn out into very fine threads. When a 
 solid possesses sufficient fluidity to admit of being drawn out 
 into threads, it is said to be ductile.^ When it will admit of 
 being hammered or rolled into sheets, it is said to be malleable. 
 
 As might be expected, those siibstances that are ductile are also mal- 
 leable. Bnt the same substance does not usually possess the two 
 properties in an equal degree. Platinum is the most ductile metal. It 
 can be drawn into wire finer than a spider's thread. It is the seventh 
 metal in the rank of malleability. Gold Is the most malleable metal. 
 It can be hammered into leaves so thin, that it would require 300,000 
 to make a book one inch thick. It ranks next to platinum in ductility. 
 Iron, at a red heat, is very malleable and ductile. What metals can 
 be drawn into wires ? What metals can be rolled or hammered into 
 sheets? 
 
 §32. Tenacity. — In order that a substance may be ductile, 
 it is evident that it must possess a strong cohesive force, so as 
 to prevent rupture. The power that matter possesses of resisting 
 rupture, by a pulling force, is called tenacity.^ A body may be 
 tenacious without being ductile, but it cannot be ductile without 
 being tenacious. It is remarkable that the tenacity of most 
 metals is increased by being drawn out into wires. It would 
 seem, that, in the new arrangement which the molecules assume, 
 the cohesive force is stronger than in the old. Hence cables 
 made of iron wire twisted together, so as to form an iron 
 
 » Ductile, draw-able. > Malleable, as it were malletMble. 
 
 ' Tenacity, property of holding. 
 
ADHESION. 33 
 
 rope, are stronger than iron chains of equal weiglit and length, 
 and are much used instead of chains, where great strength is 
 required. 
 
 §33. Adhesion. — Grasp with j'our finger a piece of gold- 
 leaf, and, honest as you may be, it will stick to your fingers ; it 
 will not drop off, it cannot be shaken off', and to attempt to pull 
 it off' is to increase the difficulty. Dust and dirt stick to clothing. 
 Thrust j'our hand into water, and it comes out wet. You can 
 climb a pole, because your hands stick to the pole ; but if the 
 pole is greased, climbing is not so easy. We could not pick 
 anything up, or hold anything in our hands, were it not that 
 these things stick to the hands. 
 
 Every minute's experience teaches us that not only is there an 
 attractive force between molecules of the same kind of matter, 
 but there is also an attractive force between molecules of unlike 
 matter. That force which causes unlike substances to cling 
 together, is called adhesion. Is adhesion a molar or a molecular 
 force? How does it differ from cohesion? Whj- do not gold 
 watches, and other articles of gold jewelry, appear to stick to 
 the fingers? What keeps nails, driven into wood, in their places? 
 What would happen if all adhesion between the diff'erent parts 
 of the building you are in should 
 be suddenly destroj'ed? When a 
 liquid sticks to a solid, what term 
 do we usually employ in desci'ib- 
 ing the phenomenon? 
 
 Experiment t. Suspend a plate 
 of glass, about 8™ square, from one 
 arm of a scale-beam, attaching the 
 threads to the plate with sealing- 
 wax. Balance it, and place a dish of water under the glass, so that its 
 under surface will just touch the surface of the water. You may 
 now add several grams' weight to the other side of the beam without 
 destroying the balance. Finally, the glass is apparently pulled away 
 from the water. But on examination you will find It wet, so that you 
 
34 MATTER AND ITS PKOPEKTIES. 
 
 have really succeeded, not in separating the glass from the water, but 
 water from water. Then the weight that you were obliged to add does 
 not measure the adhesive force between the glass and the water ; , it 
 merely measures the amount of force necessary to tear the liquid apart. 
 The same force was not sufficient to tear the liquid from the solid, 
 hence we infer that the adhesion between a solid and a liquid may he 
 greater than the cohesion in the liquid. 
 
 Glass is wet by water, but is not wet by mercury. Is there 
 no adiiesion between mercury and glass? 
 
 Experiment 2. Substitute mercury for water in the last experi- 
 ment. As soon as the glass touches the mercury a slight adhesion 
 occurs, which can be measured by the weight required to be placed in 
 the opposite scale-pan in order to separate them. 
 
 It is probable that there is some adiiesion between all substances 
 when brought in contact. If a liquid adheres to a solid more 
 firmly than the molecules of the liquid cohere, then will the solid 
 be wet by the liquid. If a solid is not wet by a liquid, it is not 
 because adhesion is wanting, but because cohesion in the liquid 
 is stronger. That gases adhere to solids is proved by the 
 phenomena of absorption described in § 37. 
 
 QUESTIONS. 
 
 1. Why will not water wet articles that have been greased ? 
 
 2. Why is it difficult to lift a board out of water ? 
 
 3. Why does water run down the side of a tumbler when it is 
 inclined, instead of falling vertically ? Suggest some method of pre- 
 venting it. 
 
 4. In what does the value of cement, glue, and mucilage consist 1 
 
 5. What enables you to leave a mark with a pencil or crayon ? 
 
 § 34. Capillarity. — Examine the surface of water in a goblet. 
 You find the surface level, as in A (Fig. 14), except around the 
 edge next the glass, where the water is curved upward so as 
 to resemble the interior surface of a watch crystal. Mercury 
 placed in a goblet (B) has its edge turned downward, resembling 
 the exterior surface of a watch crystal. This seems to indicate 
 
CAPILLARITY. 
 
 35 
 
 a repulsion between mercury and glass. But a previous experi- 
 ment (page 34) has shown that, instead of repulsion, there is a 
 slight adhesion between 
 
 Fig 14 
 
 these substances. "^ 
 
 Pour any liquid on a 
 level surface which it 
 does not wet, — e. g., 
 water on paraflBne or 
 wax, or mercury on 
 glass. It spreads itself 
 over the surface, but the 
 edges are everywhere 
 rounded or turned down 
 like the edges of mercury in a goblet. Surely these rounded 
 edges are not caused by the repulsion of the sides of a vessel. 
 The edges of all liquids will be turned down unless the adhesion 
 between them and the sides of the vessels exceeds the cohesion 
 in the liquid. The glass does not cause the turning down of 
 the surface of mercmy in the goblet, — its tendency is rather to 
 prevent it. 
 
 Thrust verticallj' two plates of glass into water, and gradu- 
 ally bring the surfaces near each other. Soon the water rises 
 between the plates, and rises higher as the plates are brought 
 nearer. Thrust a glass tube of very fine bore into water ; the 
 attraction within it, on all sides, will raise the water to twice the 
 hight it would reach when between two plates whose distance 
 apart is equal to the diameter of the bore of the tube. Thrust 
 a tube of the same bore into alcohol ; this liquid rises in the 
 tube, but not so high as water. The surfaces of both the 
 . water and the alcohol are concave. If the tube is placed 
 in mercury, the opposite phenomena occur: the mercury is 
 depressed, and its surface is convex.' Both ascension and 
 
 1 The Bcope of this book will not admit of an explanation of the phenomena of 
 capillarity. The student can iind a lucid treatment of this subject in Maxwell's "Theory 
 of Heat," pp. 260-274; also under " Capillary action," Encyclopaedia Britannica. 
 
36 MATTER AND ITS PBOPEKTIES. 
 
 depression diminish as the temperature increases, being greatest 
 at the freezing point of the given liquid, and least at its boiling 
 point. (Regarding heat as a repellent force, can you give any 
 reason why the ascension should be less at high than at low 
 temperatures?) Inasmuch as the phenomena are best shown 
 in tubes having bores of the size of hairs, they are in such 
 cases called capillary^ phenomena, and the tubes are called 
 capillary tubes. 
 The phenomena of capillary action are well shown by placing 
 Hg. 15. various liquids in U-shaped glass 
 
 tubes, having one arm reduced to a 
 capillary size, as A and B in Figure 
 1 o . Mercury poured into A assumes 
 convex surfaces in both arms, but 
 does not rise so liigh in the small 
 arm as it stands in the large arm. 
 Pour water into B, and all the phe- 
 nomena are reversed. C is a glass 
 tube containing water and mercury, 
 and showing the shapes that the surfaces of the two liquids take. 
 Generalizing the above facts, we have the four laws of capil- 
 lary action : — 
 I. Liquids rise in tubes when they wet them, and are depressed 
 when they do not. 
 II. The ascension or depression varies inversely as^ the diameter 
 of the bore. 
 
 III. The ascension and depression vary with^ the nature of the 
 
 substances employed. 
 
 IV. The ascension or depression varies inversely with the tem- 
 
 perature. 
 Illustrations of capillary action are abundant. It feeds the 
 lamp-flame with oil. It wets the whole towel, if one end is left 
 for a time in a basin of water. It draws water into wood, and 
 causes it to swell with a force sufHeient to split rocks, and to 
 raise large weights. How does a little water in a wooden tub 
 prevent its falling to pieces ? 
 
 > Capillary, hair-like. ' Observe that tbrougbout this treatise the word as expresses 
 an exact proportion. When there is not an exact proportion, the word with is used. 
 
SOLUTION OF SOLIDS. 37 
 
 §35i other molecular phenomena. — Besides the phe- 
 nomena we have just studied, there are a great many others 
 depending in part on molecular attraction, but much more on the 
 molecular motions, of which we learned in § 5, page 6. Many 
 of them are quite familiar and important ; but the explanation, 
 even when it can be given, is usually complicated and incom- 
 plete. The principal names given these phenomena are solution, 
 absoi-ption, and diffusion. 
 
 § 36. Solution of solids — depends mainly on molecular 
 attraction. Hold a lump of sugar so tliat it will just touch the 
 surface of water. Soon water is drawn up into the pores of the 
 lump by capillary action, and the whole lump, including the 
 part not submerged, becomes moist. Next you discover that 
 the lump becomes smaller, and slowly disappears in the water. 
 
 When a solid becomes diffused through a liquid, it is said to 
 be dissolved. The dissolving liquid is called a solvent, and the 
 resulting liquid is called a solution. A liquid will dissolve a 
 solid, only when the adhesion between them is greater than the 
 cohesion in the solid. A liquid always dissolves a solid more 
 rapidly at first, less rapidly as the adhesion becomes more nearly 
 satisfied ; and when it is completely satisfied, or is balanced by 
 the cohesion in the sohd, the liquid will dissolve no more of the 
 solid, and the solution is said to be saturated. When a solution 
 will take much more of a solid, it is said to be dilute; and 
 concentrated, when it will take little or no more. 
 
 If the solid be first pulverized, the liquid has more surface on 
 which to act, and the solid is dissolved much more rapidly. 
 Heat generally weakens cohesion more than it weakens adhesion; 
 hence, with few exceptions, hot liquids dissolve solids more 
 rapidly and in greater quantities than cold liquids. Boiling 
 water dissolves three times as much alum as cold water ; conse- 
 quentl}:, when a hot saturated solution of alum is allowed to 
 cool, at least two-thirds of the alum must be restored to the 
 solid state (see Exp. 1, page 25), while one-third, or the amount 
 
38 MATTJEE AND ITS PEOPEKTIBS. 
 
 that the cold liquid is capable of dissolving, remains in solution. 
 The remaining solution is called the mother-liquor. Lime, and 
 a few other substances, are dissolved better in cold water. 
 Crystals of such substances are only obtained by gradual evap- 
 oration of the solvent. 
 
 Water Is the great solvent. When we speak of the sohibility of a 
 substance, water Is always uuderstood to be the solvent, unless some 
 other liquid is specified. Why is it fortunate that water is so good a 
 solvent? Name substances that water does not dissolve. Of the 
 many substances insoluble in water, some, as phosphorus, gums, and 
 resin, find a solvent in alcohol ; sulphur, in bi-sulphide of carbon ; lead, 
 in mercury; and fats, in ether or benzine. Would you wash var- 
 uished furniture with alcohol? How are grease-spots removed from 
 clothing? 
 
 § 37. Absorption of gases by solids — depends mainly on 
 molecular attraction, and is generally superficial. Certain solids 
 possess so strong an attraction for gases that they not only draw 
 the gases into the small cavities or holes within them, but greatly 
 condense them there. It should be carefully noted that the 
 attraction in this case is generally between the gases and the 
 surfaces of cavities, and is hence called superficial, in dis- 
 tinction from intermolecudar attraction, which is the name given 
 to the phenomenon when gases are taken into the pores of a 
 body. 
 
 Freshly-burned charcoal placed in dry air, may, in a few days, 
 have its weight increased one-fiftieth in consequence of the air 
 that it absorbs. (Has air weight?) The attraction of charcoal 
 for noxious gases is especially great, making it very eflScient 
 in cleansing the air in hospitals, and in removing noxious 
 odors from putrid animal and vegetable matter by absorbing the 
 foul gases that are generated. It does not check decay, but 
 rather hastens it. A rat, which had been buried in charcoal 
 dust, was uncovered at the end of a month ; nothing visible was 
 left but the hair and bones, yet no bad odor was perceptible. 
 Why do farmers mix muck with manures? 
 
FREE DIFFUSION OF LIQUIDS. 39 
 
 §38. Absorption of gases by liquids — depends on molec- 
 ular aUraction and motion, and is intermolecular. Water, at a 
 temperature of 0° Cen., is capable of condensing in its pores 
 six hundred times its own bulk of ammonia gas. "Water thus 
 charged with this gas is called " ammonia water." The amount 
 of gas that a liquid will absorb is increased by pressure. " Soda 
 water " is simply water saturated with carbonic-acid gas under 
 great pressure ; it contains no soda. When the pressure is 
 removed, a large part of the gas escapes, causing efferves- 
 cence. 
 
 § 39. Free diSusion of liqiiids — depends mainly on mo- 
 tion. — Experiment 1. Into a test-tube containing 20"=™ of water, 
 pour about 2""'" of olive-oil, and shake. By shaking, the oil becomes 
 divided into small particles, which give the water an opaque, milky- 
 white appearance, but it Is not separated Into its molecules. After 
 standing for a few minutes, the oil almost completely separates from 
 the water, and rises to the top. 
 
 Experiment 2. Partially flU a glass jar (Fig. 16) with water. Then 
 Introduce beneath the water, by means of a long tunnel, a concentrated 
 solution of sulphate of copper. The lighter liquid j,, ,„ 
 
 rests upon the heavier, and the line of separation 
 between the two liquids is at first distinctly marked. 
 But in the course of days or weeks this line will 
 gradually become obliterated, the heavier blue liquid 
 will gradually rise, and the lighter colorless liquid will 
 descend, till they become thoroughly mixed. 
 
 Experiment 3. Take about 1=™ of bisulphide of 
 carbon, color it by dropping into it a small particle 
 of iodine, and pour this colored solution into a test- 
 tube nearly filled with water. The colored liquid, 
 being heavier than the water, sinks directly to the 
 bottom, and shows no tendency to mix with the water. But, in the 
 course of time, you discover that the colored liquid diminishes in 
 quantity, and finally disappears. The peculiar odor of this substance 
 which pervades the air in the vicinity shows that a considerable por- 
 tion has evaporated. But it must have worked its way gradually 
 through the water above it. 
 
40 
 
 MATTBB AND ITS PEOPEETIES. 
 
 If, during the operation of diffusion in the last two experi- 
 ments, 3'ou examine the liquid with a microscope, you will not 
 be able to trace any currents ; hence the motion of liquids in 
 diffusion is not in mass, but by molecules, — a kind of inter- 
 molecular motion. We learn that some liquids, even when 
 stirred together, will not remain mixed ; while others, whose 
 densities are very different, when merely placed in contact with 
 each other, slowly mix of themselves. 
 
 Fig. 17. 
 
 § 40. Diffusion of liquids through poroub partitions. 
 — Osmose. — Dialysis. — Very complex. — Experiment. Cut 
 off the bottom of a conical-shaped bottle ' (or, better, use a glass tun- 
 nel or lamp-chimney) ; fit to the neck of the 
 bottle a cork, having a glass tube passiug 
 through it (Fig. 17). Tie tightly over the bot- 
 tom a piece of gold-beater's skin or parch- 
 ment paper. Fill the bottle with a concen- 
 trated solution of sulphate of copper, and 
 press the cork into the bottle so that the liquid 
 will stand a little way up the tube, say at a. 
 Now suspend the apparatus in a vessel of 
 water, so that the bottom may be covered. 
 In less than an hour it will be found that the 
 liquid has risen in the tube, showing that 
 water must have passed through the septum,^ 
 and mixed with the solution. Examine the 
 water in the outer vessel, and you will find 
 that it is slightly tinged with the blue vitriol, 
 showing that some of the solution has also 
 passed through the septum. But the liquid 
 has risen in the tube, showing that more of 
 the water than of the solution has passed 
 through the septum. 
 
 When liquids or gases force their way 
 through porous septa, and mix with each other, the diffusion is 
 called osmose.^ To distinguish the two opposite currents, the 
 flow of the liquid or gas towards that which increases in volume 
 
 1 See Appendix, Section B, * Septum, partition. 3 OBmoae, impulse. 
 
PEBB DIPFTJSION OP GASES. 
 
 41 
 
 Fig. 18. 
 
 is called endosmose,^ and the opposite current is called exos- 
 mose.'^ 
 
 It is found that crystallizable substances are the best subjects 
 of osmose, while those which are usually amorphous, such as 
 gelatine and guiomy substances, are very little inclined to 
 osmose. Those substances that pass readily through septa 
 are called crystalloids ;^ those that do not are called colloids.'* 
 
 The principle of unequal diffusibility of liquids through septa 
 finds important application in chemical 
 and pharmaceutical laboratories. For 
 example, from a rod (Fig. 18) is sus- 
 pended a glass vessel having a bottom 
 of parchment paper. Such a vessel is 
 called a dialyzer. In the dialyzer is 
 placed, for instance, the liquid contents 
 of the stomach or intestines of a dead 
 animal, suspected of containing some 
 poison, and the vessel is floated in a 
 vessel of water. If either arsenic or 
 strychnine is present it will separate from 
 the albuminous matter in the food, and 
 pass tlii<jugh the septum into the water. The process of sep- 
 arating mixed liquids by osmose is called dialysis. 
 
 § 41. Free diffusion of gases — depends almost wholly on 
 molecular motion. — Experiment. Fill a test-tube with oxygen gas, 
 and thrust in a lighted splinter; the splinter bums much more rapidly 
 than m the ah:. Fill another tube with hydrogen gas, and keep the 
 tube inverted (for, this gas being about sixteen times lighter than air, 
 there will be no danger of its f alUng out) . Thrust in a Ughted spUnter ; 
 the gas takes fire, and burns with a pale flame at the mouth of the tube. 
 Next flU one tube with oxygen and the other with hydrogen gas, and 
 place the mouth of the latter over the mouth of the former, as in Fig- 
 ure 19. In about a muiute apply a lighted spUnter to the mouth of each 
 
 ' Endosmose, inward impulse. 
 2 Exosmose, outward impulse. 
 
 ' Crystalloid, Uke crystal. 
 * Colloid, like gvm. 
 
42 MATTER AND ITS PEOPBETIBS. 
 
 tube (let the mouth of each tube be freely open to prevent accident) ; 
 a slight explosion takes place in each instance. It is apparent that 
 although the oxygen gas is sixteen times heavier than the hydrogen, 
 some of it has risen into the upper tube, while some of the lighter 
 hydrogen has descended into the lower tube, and the two gases have 
 become difftised. 
 
 Man3' pairs of liquids do not diffuse into each other, but every 
 gas diffuses into every other gas, and it is impossible to prevent two 
 gases from mixing when placed in contact. 
 '^' (It is thought best to introduce the subject of 
 
 diffusion of liquids and gases in this place, 
 though it has little or no connection with the 
 subject of adhesion. The explanation of 
 diffusion must be deferred to its proper place 
 in the chapter on Heat, page 158.) 
 
 In consequence of this universal tendency to 
 dlflfasion, gases will not remain separated, — i.e., 
 a lighter resting upon a heavier, as oil rests upon 
 water. This is of immense importance in the 
 economy of nature. The largest portion of our 
 atmosphere consists of a mixture of oxygen and 
 nitrogen gases. There are always present also 
 small quantities of other gases, such as carbonic- 
 acid gas, ammonia gas, and various other gases, 
 which are generated by the decomposition of 
 organic matter. These gases, obedient to gravity 
 alone, would arrange themselves according to 
 their weight, — carbonic-acid gas at the bottom, 
 or next the earth, followed respectively by oxy- 
 gen, nitrogen, ammonia, and other gases. Neither animal nor vegetable 
 life could exist in this state of things. But, in consequence of their 
 diffusibility, they are found intimately mixed, and in the same relative 
 proportions, whether in the valley'or on the highest moimtain peak. 
 
 § 42. Diffusion of gases through porous partitions — 
 depends on the size of molecules, sine of pores, and on molecular 
 motion; very complex. 
 
DIFFUSION OF GASES. 
 
 43 
 
 Experiment. Take a thin, unglazed earthen cup, such as is used in 
 Bunsen's battery (page 190) , and plug up the open 
 end with a cork through which extends a glass 
 tube. Place the exposed end of the tube in a cup 
 of colored water. Lower a glass jar, filled with 
 hydrogen or coal-gas, over the porous cup, as in 
 Figure 20. Instantly air is forced down through 
 the tube, and escapes in bubbles from the colored 
 liquid. The gas in the larger vessel forces its way 
 through the pores of the cup, diffuses itself in the 
 air contained in it, and causes an unusual pressure 
 on the colored liquid, as is evinced by the air that 
 is forced out through it. In a minute remove the 
 glass jar. The hydrogen now escapes through the 
 sides of the cup, and mixes with the air on the out- 
 side ; a partial vacuum is formed in the cup, and 
 water rises in the tube. In both cases air passed 
 through the sides of the porous cup, but the influx 
 and efflux of hydrogen was much more rapid. 
 
 An interesting modification of this apparatus is the diffusion foun- 
 tain (Fig. 21). By passing the glass tube of the porous cup through 
 the cork of a tightly-stopped vessel, and hav- j,j ^i. 
 
 ing another glass tube pass through another 
 perforation in the same cork, water is forced 
 out in a jet several feet in hight, when the 
 hydrogen jar is held over the porous cup. 
 
 Children well understand that toy balloons, 
 which are made of collodion and filled with 
 coal-gas, collapse in a few hours after they are 
 inflated. This is caused by the escape of the 
 gas by osmose. Nature furnishes an illustra- 
 tion of osmose of gases in respiration. In the 
 lungs the blood is separated from the air by 
 the thin, membranous walls of the veins. 
 Carbonic-acid gas escapes from the blood through these septa, and 
 oxygen gas enters the blood through the same septa. 
 
CHAPTER IL 
 DYNAMICS. 
 
 IV. DYNAMICS OF FLUIDS. 
 
 § 43. Equilibrium, pressure, and tension. — That branch 
 of science which treats of force and the motions it produces is 
 called dynamics. It has been shown that force may act on a 
 body to produce motion or rest ; also that two or more forces 
 may so act on a body as to neutralize each other's effect. In 
 the latter case, the body continues in the same condition, either 
 of motion or rest, as if it were independent of the action of the 
 forces, and is said to be in equilibrium,^ and the forces acting 
 on it are also said to be in equilibrium. Inasmuch as no body 
 is ever free from the action of force, it must be that a body at 
 rest is in a state of equilibrium. 
 
 If any portion of a force is not effective in producing motion, 
 — i.e., if part or all of it is exerted against other forces, — there 
 may result what is called a pressure on the body ; as when we 
 push on a wall or on a heavy sled moving over the ice, or a 
 book presses the table. The same force which causes a body to 
 fall when unsupported, causes it to press on any obstacle which 
 prevents it from falling. Or, if the force is exerted on a body 
 ill which the molecular attraction is strong, — i.e., on a solid, — 
 we may have a pull or tension, as when we hang in a swing, or 
 hang a stone from a rubber band. If the body under the influ- 
 ence of a force maintains a uniform velocity, we may measure 
 the force by the pressure (or tension) exerted, or may measure 
 the pressure by the amount of the force, whichever may be more 
 convenient. The case of uniform velocity includes the case of rest. 
 
 ' EduUibriuiD, equal balance. 
 
PEESSUKE IN FLUIDS. 
 
 45 
 
 § 44. Pressure in fluids. — It will be seen that, with the 
 exception of the phenomena of capillarity and those occasioned 
 by difference in compressibility and expansibility, liquids and 
 gases are governed by the same laws. We shall, therefore, treat 
 them together, in so far as they are alike, under the common term 
 of fluid. 
 
 It should be borne in mind that we are placed on the borders 
 of two oceans. A watery ocean borders our land ; an aerial 
 ocean, which is called the atmosphere, surrounds us. Every 
 molecule, in both the gaseous and liquid oceans, is drawn to- 
 ward the earth's centre by gravity. This gives to both fluids 
 a downward pressure upon everything upon which they rest. 
 
 The gravitating power of liquids is everywhere apparent, as 
 in the fall of drops of rain, the descent of mountain streams, 
 the power of falling water to propel machinery, and the weight 
 of water in a bucket. But to prove the downward pressure of 
 air requires special experiments. If we lower a pail into a 
 well, \t fills with water, but we do not perceive that it becomes 
 heavier therebj' ; the downward pressure is not felt. But when 
 we raise a pailful out of the water, it suddenly becomes heavy. 
 If we could raise a pailful of air out 
 of the ocean of air, might not the 
 weight of the air become perceptible ? 
 If we dive to the bottom of a pond 
 of water, we do not feel the weight 
 of the pond resting upon us. We do 
 not feel the weight of the atmospheric 
 ocean resting upon us ; but we should 
 remember that our situation with ref- 
 erence to the air is like that of a 
 diver with reference to water. 
 
 Fig. 22. 
 
 Ebcperlment 1. Fill two glass jars (Fig. 22) with water, A having a. 
 glass bottom, B a bottom provided by tying a piece of sheet-rubbej 
 tightly over the rim. Invert both in a larger vessel of water, C. 
 The water in A does not feel the downward pressure of the air directly 
 
46 
 
 DYNAMICS. 
 
 above it, the pressure being sustained by the rigid glass bottom. But 
 it indirectly feels the pressure of the air on the surface of the water In 
 the open vessel, and it is this pressure that sustains the water in the 
 jar. But the rubber bottom of the jar B yields somewhat to the 
 downward pressure of the air, and is forced inward, untU it is bal- 
 anced by the upward pressure of the water, plus the tension of the 
 rubber. 
 
 Take a glass tube D, 1™ long, having a bore of 1™ diameter. Cov- 
 ering one end with a finger, fill with water, and invert in C. You feel 
 the weight of the air pressing your finger against the tube. Remove 
 the finger and the water in the tube at once sinks to the level of the 
 water in the vessel C, because the downward pressure of the air on the 
 column of water, plus the weight of the column of water, is greater 
 than the upward pressure. In every instance we find that the down- 
 ward pressure of air gives rise to an upward pressure in the liquid. In 
 this respect fluids differ widely from solids, whose molecules are so 
 firmly held together that, when one part is pushed in any direction, 
 that part drags the rest with it. 
 
 We have accounted for water being sustained in the vessels A, B, 
 and D, by an upward pressure produced by the downward pressure of 
 the air. Does this downward pressure create an upward pressure in 
 the air itself, so that, if the vessels are lifted out of the water, the 
 
 Fig. 23. 
 
 water will not fall out? 
 
 Experiment 2. Keeping the finger pressed on the 
 end of D, raise it slowly and vertically out of the 
 water. The water does not fall out. Why? Slip 
 a thin glass plate, or a piece of thick pasteboard, 
 under the mouth of A, and, pressing it against the 
 mouth, raise the vessel carefully out of the water, 
 and remove the hand from the plate. The water 
 does not fall out, nor does the plate fall. Why? 
 
 Experiment 3. Force a tin pail (Fig. 23), having 
 a hole in.lts bottom, as far as possible into water, 
 without allowing water to enter at the top. A stream of water spurts 
 through the hole. Why? Why does it require so much effort to 
 force the pail down into the water? Does downward pressure cause 
 a lateral pressure? 
 
 Experiment 4. Make holes, at different depths, in the side of a ves- 
 sel (Fig. 24) containing water. Water issues in streams, with consid- 
 erable force, from the orifices. Why? 
 
 Experiment 5. Bind a piece of thin sheet-rubber tightly over a 
 
PEBSSTTRE INCEEASES WITH THE DEPTH. 
 
 47 
 
 wide-mouthed bottle, and place it in water in different positions. In 
 whatever position the 
 
 Fifir 24 
 
 bottle is placed, the rub- 
 ber is pressed inward. 
 What lesson does this 
 teach? 
 
 Experiment 6. The 
 Magdeburg hemispheres 
 (Fig. 25) are two hemis- 
 pherical cups, having 
 their edges made smooth 
 so as to be "air-tight" 
 when placed in contact. 
 Each cup is provided with a handle. One of the handles consists of 
 two parts, a stem and a ring, the two parts being connected by a screw. 
 The stem has a bore passing through it, and a stop-cock, 
 which regulates the passage of air through the bore. 
 Place the lips of the cups in contact, remove the ring, 
 screw the stem to the plate of an air-pump, and exhaust 
 the air from the sphere ; then close the stop-cock, and 
 replace the ring. Now~two boys grasping the rings, and 
 holding the sphere in any position they choose, can only 
 with great difficulty puU them apart. Why? 
 
 Boys amuse themselves by Ufting bricks (Fig. 26) with 
 a circular piece of leather, moistened and 
 pressed against the surface of the brick, so as 
 to exclude the air. The pressure of air against 
 the leather binds it to the brick in whatever 
 position placed. 
 
 We conclude that gravity causes pressure in a body 
 of fluid in all directions. 
 
 mg. 25. 
 
 Fig. 26. 
 
 § 45. Pressure increases with the depth. — In the ex- 
 periment with the vessel with apertures in its side (Fig. 24) , 
 we find that the deeper the orifice, the greater the velocity of 
 the stream. And in the experiment with the wide-mouthed 
 bottle covered with rubber, we find that, at the same depth, the 
 rubber is pressed inward equally in all directions, but, as it is 
 narried to gi-eater depths, the pressure is increased. 
 
48 
 
 DrNAMICS. 
 
 Experiment. Take a glass tube bent in the form represented by a. 
 Figure 27 ; place mercury in the lower part of the tube, so as to fill the 
 short arm, and gradually lower the tube into a 
 deep vessel, of water. The downward pressiire 
 of the water wUl force the mercury up the long 
 arm to a hight proportional to the depth of the 
 tube in the water. 
 
 § 46. Pressure at any point in a jauid 
 equal in all directions. — Experllnentl. In- 
 troduce another tube, containing mercury, of the 
 form represented by 6, Figure 27 ; lower both tubes 
 so that the orifices in the water shall be at the 
 same level, and it will be found that the downward 
 pressure in a and the lateral pressure in 6 will force the mercury to the 
 same level, cd. 
 
 Experiment 2. Cover one end of a lamp-chimney (Fig. 28) with a 
 circular piece of leather, and suspend from the hand by 
 means of a string attached to the center of the leather 
 and passing through the chimney. Hold the leather 
 firmly against the bottom of the chimney, and lower the 
 covered end a little way into a vessel of water. You 
 may now drop the string, and the upward pressure of 
 the water will keep the leather in place. Pour water 
 slowly into the chimney, and, when the water in the 
 chimney nearly reaches the level of the water outside, 
 the leather wUl fall. The upward pressure of the water 
 in the vessel against the leather is just "balanced by the 
 downward pressure of the water in the chimney and the 
 weight of the leather. Why does not a pailful of water in a well seem 
 heavy ? 
 
 The results of experiments thus far show that, at every point 
 in a body of fluid, gravity causes pressure to be exerted equally in 
 all directions, and that in liquids the pressure incredses as the 
 depth increases. 
 
 Have we any means of ascertaining the pressure at any point 
 in the atmosphere? 
 
 Experiment 3. Prepare a U-shaped glass tube closed at one end 
 (Fig. 29) , SO™ in hight from the center of the bend, and with a bore of 
 liom section. Fill the closed arm with mercury and iuvert. The mer- 
 
PRESSURE AT ANY POINT IN A FLUID. 
 
 49 
 
 cury in the closed arm will sink about 2™ to A, and will rise 2™ in tlie 
 open arm to C ; but the surface A is 76™ higher than the surface C. 
 This can be accounted for only by the atmos- j,, „ 
 
 pheric pressure. The column of mercury BA, ' — ~ 
 
 containing 76™"", is an exact counterpoise for a 
 column of air of the same diameter extending 
 from C to the upper limit of the atmospheric 
 ocean, — an unknown hight. 
 
 The weight of the 76'"^ of mercury in the 
 
 column BA is 1033. 3« exactly, but, for 
 
 convenience, may be said to be about 1*. 
 
 Hence the weight of a column of air of 
 
 jqcm section, extending from the surface of 
 
 the sea to the upper limit of the atmosphere, 
 Fig. 30. ' is about 1''. But 
 
 gravity causes 
 equal pressure 
 in all directions. 
 Hence, at the 
 level of the sea, 
 
 all bodies are pressed upon in all 
 directions by the atmosphere, with a 
 force of about I' per square centi- 
 meter, about 15 pounds {exactly 14.7 
 lbs.) per square inch, or about one- 
 ton per square foot. Fluid pressure 
 is generally expressed in atmos- 
 pheres. An atmosphere (when the. 
 term is used to denote pressure) is 
 the pressure of 1" per square centi- 
 meter. 
 
 A man of average size sustains an ex- 
 ternal pressure of about fifteen tons. If the area of the bottom of an 
 " empty " pail is one square foot, the downward pressure on its bottom 
 is a little more than one ton ; how can any person carry such a pail? 
 and why is its bottom not forced out? 
 
50 
 
 DYNAMICS. 
 
 rig. 31. 
 
 § 47. Barometer. — Figure 30 represents another form of ap- 
 paratus, which is more commonly used for ascertaining atmospheric 
 pressure. It consists of a straight tube about 85™ long, closed at 
 one end, and filled with mercury. When this tube is inverted, the 
 
 open end having 
 been covered w'th a 
 finger and plunged 
 into an open cup of 
 mercury, and the 
 finger withdrawn, 
 the mercurj' in the 
 tube will sink till 
 it balances the at- 
 mospheric press- 
 ure. This experi- 
 ment was devised 
 by Torricelli, an 
 Italian. The ap- 
 paratus is called a 
 barometerA The 
 empty space above 
 the mercury in the 
 tube is called aTor- 
 ricellian vacuum. 
 The history of this 
 experiment is very 
 interesting and im 
 portant, inasmuch 
 as it was the first 
 demonstration of 
 the pressure of the 
 atmosphere. (See 
 Whewell's History of Inductive Sciences, Vol. I., page 345.) 
 The hight of the barometric column is subject to fluctuations ; 
 1 Barometer, weight nuxuurer. 
 
BAKOMETEK. 51 
 
 this shows that the atmospheric pressure is subject to variations 
 from various causes. The barometer is always a faithful moni- 
 tor of all changes in atmospheric pressure. It is also service- 
 able as a weather indicator. Not that any particular point at 
 which mercury may stand foretells any particular kind of 
 weather, but any sudden change in the barometer indicates a 
 change in the weather. A rapid fall of mercury generally fore- 
 bodes a storm, while a rising column indicates clearing weather. 
 
 If the barometer is carried up a mountain, it is found that the 
 mercury constantly falls as the ascent increases. This shows 
 that the pressure is greater near the bottom of the aerial ocean 
 than near its top. It is found that the pressure increases very 
 rapidly near the bottom, as may be understood by studying 
 Figure 31. The shading shows the variation in density of the 
 ah'. The figures in the left margin show the hight of the atmos- 
 phere, in miles ; those on the right the corresponding hight of 
 the mercury, in inches. The average hight of the mercurial 
 column, at the level of the sea, is about 76™ (30 inches) . 
 
 It will be seen that the density at a hight of 3 miles is but 
 little more than ^ the density at the sea-I§vei ; at 6 miles, \ ; at 
 9 miles, \; at 15 miles, ^ ; at 35 miles it is calculated to be 
 only gfl^flo , so that the greatest part of the atmosphere must be 
 within that distance of the surface of the earth. On the other 
 hand, if an opening could be made in the earth, 35 miles in 
 depth below the sea-level, it is calculated that the density of the 
 air at the bottom would be 1,000 times greater than at the sea 
 level, so that water would float in it. Air has been compressed 
 to this density. 
 
 To what hight the atmosphere extends is unknown. It is 
 variously estl^ted at from 50 to 200 miles. If the aerial ocean 
 were of uniform density, and of the same density that it is at 
 the sea-level, its depth would be a little short of five miles. 
 Certain peaks of the Himalayas would rise above it. It may be 
 readily seen that hights of mountains may be measured approxi- 
 mately by the aid of a barometer. 
 
52 DYNAMICS. 
 
 QUESTIONS. 
 
 1. A person on the top of Mt. Blanc would take In what portion of 
 the air, on expanding his lungs to a certain extent, that he would at 
 the bottom ? 
 
 2. How would this affect breathing, considering that a person re- 
 quires a definite amount of air in a given time, in order to sustain 
 life? 
 
 3. A person ascending 6 miles in a baUoon leaves what proportionaV 
 part of the whole mass of air below him ? 
 
 4. When the barometric column stands at 492"™, what is the atmos- 
 pheric pressure in grams per square centimeter ? 
 
 6. A barometer carried into a mine stands at 982™""; what is the 
 atmospheric pressure in the mine 1 
 
 § 48. Compressibility and expansibility of gases. — The 
 increase of pressure attending the increase in depth, in both 
 liquids and gases, is readily explained by the fact that the lower 
 layers of fluids sustain the weight of all the layers above. Con- 
 sequently, if the body of fluid is of uniform density, as is very 
 nearly the case in liquids, the pressure will increase in nearly 
 the same ratio as the depth increases. But the aerial ocean is 
 far from being of uniform density, in consequence of the extreme 
 compressibility of gaseous matter. The contrast between water 
 and air, in this respect, may be seen in the fact that water, sub- 
 jected to a pressure of one atmosphere, contracts .0000457 of 
 its volume ; under the same circumstances, air contracts one- 
 half. For most practical purposes, we may regard the density 
 of water at all depths as uniform, while it is far otherwise in 
 large masses of gases. 
 
 The pressure at different depths in liquids may be illustrated 
 by piling several bricks one on another, when the pressures that 
 different bricks sustain vary directly with their depths below 
 the upper surface of the pile. On the other hand, pressure of 
 gases at different depths may be illustrated by piling fleeces of 
 wool one on another. Since the volume of each successive 
 fleece varies with the weight it bears, the pressures which differ- 
 ent fleeces sustain are not proportional to their respective depths 
 
COMPRESSIBILITY AND EXPANSIBILITY OF GASES. 53 
 
 below the upper surface of the pile. At twice the depth, 
 there would be much more than twice the pressure, because 
 the lower point would sustain more than twice the number of 
 fleeces. 
 
 Closely allied to compressibility is the elasticity of gases, or 
 their power to recover their former volume after compression. 
 The elasticity of all fluids is perfect. By this is meant, that the 
 force exerted in expansion is always equal to the force used in 
 compression ; and that, however much a fluid is compressed, it 
 will always completely regain its former bulk when the pressure 
 is removed. Liquids are perfectly elastic ; but, inasmuch as 
 they are perceptibly compressed only under tremendous pres- 
 sure, they are regarded as practically incompressible, and so it is 
 rarely necessary to consider their elasticity. It has already been 
 stated (page 17) that matter in a gaseous state expands indefl- 
 nitely, unless restrained by external force. The atmosphere is 
 conflned to the earth by the force of gravity. 
 
 Experiment. Partially fill an india-rubber balloon with air, and 
 tightly close it. What is the external force that prevents the air in the 
 balloon from expanding and completely in- 
 flating the balloon ? Place it under the glass 
 receiver of an air-pump (Fig. 32), and ex- 
 haust the air; the balloon becomes com- 
 pletely distended, and possibly bursts. Before 
 it is placed under the receiver, the balloon 
 sustains a pressure of 15 
 pounds on every square 
 inch. What prevents a col- 
 lapse under this pressure ? 
 Inasmuch as the balloon 
 shows no signs of disten- 
 tion, or collapse, untU 
 
 placed under the receiver, it would seem that this 
 great outward pressure is exactly balanced by the 
 tension of the air within. 
 
 Glass-blowers prepare thin glass bottles (Fig. 33) 
 for the purpose of illustrating the tension of air. Containing air of 
 ordinary density, they are sealed and placed under the receiver of an 
 
 Fig. 32. 
 
 Fig. 33. 
 
64 
 
 DYKAMIC8. 
 
 air-pump; the surrounding air (in other words, the outside pressure) is 
 removed, and the enclosed air then bursts the bottles, throwing frag- 
 ments of glass in all directions. 
 
 At every point, then, in a body of air, forces are acting out- 
 wards. Ttie air is somewhat like a spring coiled up, and ready 
 to relax itself, when opportunity is given. Since this elastic 
 force at the bottom of the column exactly balances the fofc^ of 
 gravity acting on the whole column, i.e., equals the weight of the 
 whole column, it follows that, at the sea-level, the elastic force 
 .of air is ordinarily l"" per square centimeter. 
 
 § 49. Air-pump. — The air-pump, as its name implies, is 
 used to withdraw air from a closed vessel. Figure 34 will serve 
 
 to illustrate its oper- 
 
 vig. 34^ ation. R is a glass 
 
 receiver from which 
 air is to be exhausted . 
 B is a hollow cylin- 
 der of brass, called 
 the pump-barrel. A 
 plug P, called a pis- 
 ton, is fitted to the 
 interior of the barrel, 
 and can be moved 
 up and down by the 
 handle H ; s and I 
 are valves. A valve 
 acts on the principle 
 of a door intended to open or close a passage. If you walk 
 against a door on one side, it opens and allows you to pass ; but 
 if you walk against it on the other side, it closes the passage, 
 and stops your progress. Suppose the piston to be in the act 
 of descending. The compression of the air in B closes the valve 
 t, and opens the valve s, and the enclosed air escapes. Alter 
 the piston reaches the bottom of the barrel, it begins its ascent ; 
 when the air above the piston, in attempting to rush down 
 
THE AIR-PUMP. 55 
 
 to fill the vacuum that is formed between the bottom of the 
 barrel and the piston, closes the valve s. But as soon aS a 
 vacuum is formed above t, and the downward pressure on the 
 valve removed, the air in E expands, opens the valve t, and fills 
 the space in B that would otherwise be a vacuum. But, as the 
 air in R expands, it becomes rarefied ; and, as there is less air, 
 so there is less tension. The external pressure of the air on R, 
 being no longer balanced by the tension of the air within, presses 
 the receiver firmly upon the plate L. Each repetition of a 
 double stroke of the piston removes a portion of the air remain- 
 ing in R. The air is removed from R by its own expansion, 
 However far the process of exhaustion may be carried, the 
 receiver will always be filled with air, although it may be exceed- 
 ingly rarefied. The operation of exhaustiop is practically ended 
 when the tension of the air in R becomes too feeble to lift the 
 valve t. 
 
 D is another receiver, opening into the tube T, that connects 
 the receiver with the barrel. Inside the receiver is placed a 
 barometer. It is apparent that air is exhausted from D as well 
 as from R ; and, as the pressure is removed from the surface of 
 the mercury in the cup, the barometric column falls ; so that 
 the barometer serves as a gauge to indicate the approximation 
 to a vacuum. For instance, when the mercury has fallen 380""" 
 (15 inches), one-half of the air has been removed. 
 
 QUESTIONS. 
 
 1. Why is it difficult for a person to lift the receiver from the pump 
 after the air is exhausted from it ? 
 
 2. Why is it easily raised before the air is exhausted ? 
 
 3. Suppose that the air In the pump-barrel, when the piston is raised, 
 is one-eighth of all the air in the pump, including the air In the receiv- 
 ers ; what portion of the air is removed by the first double stroke ? 
 
 4. What portion of the original amount of air is removed at the 
 second double stroke? 
 
 5. Which double stroke removes the most air ? 
 
 6. If there were no force required to lift the valve t, why could not 
 a perfect vacuum be obtained ? 
 
66 
 
 DYNAMICS. 
 
 Fig. 35. 
 
 7. It is a very good pump that reduces the hight of the mercurial 
 column to 3°™. What portion of the air has been removed in that 
 case ? 
 
 An absolute vacuum nas never been attained. The difficulty 
 may be readily understood. According to the most recent cal- 
 culations, the number of molecules 
 contained in a cubic centimeter 
 of air of ordinary density is some- 
 thing like 21,000,000,000,000,- 
 000,000 (twenty-one million tril- 
 lion) ; consequently, when it is 
 reduced to one-millionth its us- 
 ual density, 21,000,000,000,000 
 (twenty-one trillion) molecules 
 are still left. The exhaustion 
 may be carried much farther than 
 by purely mechanical means, by 
 heating a piece of charcoal in 
 the receiver while the pumping is 
 going on. Heat expels the air 
 in its pores. After the pumping 
 has ceased, the charcoal is al- 
 lowed to cool, when it condenses 
 a large portion of the remaining 
 air in its pores. (See § 37, page 
 38.) 
 A very cheap and efficient sub- 
 stitute for an air-pump for many purposes may be arranged as 
 in Figure 35, in which a is an elevated tank of water having a 
 faucet 6 by which the rapidity of the flow of water may be regu- 
 lated. The tube c should be as long as the hight of the room 
 will admit, and its lower end should dip into a cup of water d. 
 To the end of the branch-pipe e there may be connected, by 
 means of rubber tubing h, a glass tube leading to a vessel g, from 
 which air is to be exhausted. Water falling freely through a 
 
MARIOTTE S LAW. 
 
 57 
 
 vertical tube exerts no lateral pressure ; consequently there is 
 no tendencj' to enter the branch e. As the water in falling 
 increases in velocity, it tends to separate, leaving between the 
 cylinders of water vacuous spaces. The lower end of the pipe c 
 being immersed in water, air cannot enter there ; j-ig 35 
 
 but the air in the receiver g expands and rushes 
 through the tube e, to fill these vacua, and thus 
 exhaustion is effected. In Sprengel's air-pump 
 mercury- is substituted for water, and air is reduced 
 by it to less than one-millionth its usual density. 
 
 Experiment 1. Take a glass tube (Fig. 36), having 
 a bulb blown at one end. Nearly fill it with water, so 
 that when inverted there will be only a bubble of air in 
 the bulb. Insert the open end in a glass of water, place under a 
 receiver, and exhaust. Nearly all the water will leave the bulb and 
 tube. "Why? What wiU happen when air is admitted to the receiver? 
 
 Experiment 2. Through a cork of a tightly-stopped bottle pass one 
 arm of a U-shaped glass tube C (Fig. 37) . 
 
 Introduce the other arm into the empty ^'g- ^- 
 
 vessel B. Place the whole under a glass 
 receiver, and exhaust the air. What phe- 
 nomena will occur? What will happen 
 when air is admitted to the receiver? 
 
 § 50. Mariotte's Law. — The 
 experiment illustrated by Figure 32 
 showed that the volume of a given 
 body of gas depends upon the pres- 
 sure to which it is subjected. To 
 find more exactly the relation between these quantities, proceed 
 as follows : — 
 
 Experiment 1. Take a bent glass tube (Fig. 38), the short arm 
 being closed, and the long arm, which should be at least 85™ long, 
 being open at the top. Pour mercury into the tube till the surfaces in 
 the two arms stand at zero. Now the surface in the long arm supports 
 the weight of an atmosphere. Therefore the tension of the air en- 
 
58 
 
 DYNAMICS. 
 
 Fig. 38. 
 
 closed in the short arm, which exactly balances it, must be about 16 
 pounds to the square inch. Next pour mercury into the long arm till the 
 surface in the short arm reaches 5, or till the volume of air enclosed is 
 reduced one-half, when it will be found that the hight of the column A C 
 is just equal to the hight of the barometric column 
 at the time the experiment is performed. It now 
 appears that the tension of the air in AB balances 
 the atmospheric pressure,jjZ2is a column of mercury 
 AC, which is equal to another atmosphere; .•. the 
 tension of the air in A B = two atmospheres. But 
 the air has been compressed into half the space it 
 formerly occupied, and is, consequently, twice as 
 dense. If the length and strength of the tube 
 would admit of a column of mercury above the 
 surface in the short arm equal to twice A C, the 
 air would be compressed into pj gg 
 
 one-third its original bulk; and, 
 inasmuch as it would balance a 
 pressure of three atmospheres, its 
 tension would be increased three- 
 fold. 
 
 Experiment 2. Next take a 
 glass tube (Fig. 39) open at both 
 ends, and about 24 inches long. 
 Tie three strings around the tube, 
 — one 3 inches from the top, 
 another 6 inches, and the third 21 
 inches. Nearly fill a glass jar, B, 
 25 inches high with mercury. 
 Lower the tube into the mercury 
 till it reaches the string at 3. 
 Press a finger firmly over the up- 
 per end, and raise the tube till the 
 string at 21 is on a level with the surface of the mer- 
 cury in the jar. The mercury in the tube will stand at 
 6. At first the air enclosed in the tube between 3 and 
 the finger withstands an upward pressure of the mer- 
 cury sufficient to sustain a column of mercury 30 inches high, or one 
 atmosphere. When the tube is raised and the mercury stands at 6, 15 
 inches high, one-half of that upward pressure is exerted in sustaining 
 the 15 inches of mercury, and the other half is exerted on the enclosed 
 
QTTE8TI0NS. 
 
 69 
 
 air. But the pressure on the air is reduced one-half, while the volume 
 Is doubled. The results of the two sets of experiments may be tabu- 
 lated as follows : — 
 
 Pressure J, J, 1, 2, 3, 4, &c. 
 
 Volume 3, 2, 1, J, J, J, &c. 
 
 Density J, J, 1, 2, 3, 4, &c. 
 
 Elastic force i, 2> 1. 2, 3, 4, &c. 
 
 From these results we learn that,' at twice the pressure there 
 is half the volume, while the density and elastic force are 
 doubled. At half the pressure the volume is doubled, and 
 the density and elastic force are reduced one-half. Hence the 
 law : The volume of a body of gas varies inversely as the pres- 
 sure, density, or elastic force . This is, sometimes called Mariotte's, 
 and sometimes Boyle's, law, from the names of the two men 
 who discovered it at about the same time. This law is true for 
 all gases within certain limits, but under extreme pressure the 
 reduction in volume is greater than indicated by it. The greatest 
 deviation from it occurs with those gases that are most easily 
 liquefied. 
 
 QUESTIONS. 
 1. Into the neck of a bottle partly filled with water (Fig. 40), in- 
 . sert a cork very tightly, through which passes a glass 
 Pig. 40. tube nearly to the bottom of the bottle. Blow forci- 
 
 bly into the bottle. On removing the mouth, water 
 will flow through the tube in a stream. Why? 
 
 2. How can an ounce of -air, 
 in a closed fragile vessel, sus- ' ^' 
 tain the outside pressure of 
 the atmosphere, amounting to 
 several tons? 
 
 3. What drives the pellets 
 from a pop-gun ? 
 
 4. Figure 41 represents a 
 dropping-bottle, much used in 
 chemical laboratories. Why 
 do bubbles of air force their 
 way down into the liquid? 
 
 5. Stop the upper orifice, and the liquid will quickly cease to drop. 
 Why? 
 
60 
 
 DYNAMICS. 
 
 S'tg.42. 
 
 9. 
 
 6. The inconvetiience arising, in many culinary and laboratory oper- 
 ations, from water " boiling away," may be remedied as represented In 
 Figure 42. A bottle filled with water is so suspended that its mouth 
 is just below the surface of the boiling liquid. As 
 the water evaporates, and its surface falls below the 
 mouth of the bottle, an air-bubble enters the bottle, 
 expands, and pushes out enough water to cover once 
 more the mouth of the bottle. Why does not the air 
 push out all the water from the bottle? 
 
 7. Figure 43 represents a weight-lifter. Into a 
 hollow cylinder s is fitted air-tight a piston (. The 
 cylinder is connected vrith an air-pump by a rubber 
 tube u. When air is exhausted the piston rises, lift- 
 ing the heavy weight attached to it. Why? 
 
 8. If the area of the lower surface of the piston is 
 20v°', how heavy a weight ought to be lifted when 
 the air Is one-half exhausted ? 
 
 Suppose you tightly stopper a bottle at the top of Mont Blanc, car- 
 YUg ^ ry it to the sea-level, 
 
 ' — ' Insert the mouth of 
 
 the bottle In water, 
 and withdraw the 
 stopper ; what would 
 happen ? 
 
 10. Show that the 
 labor of working the 
 kind of air-pump de- 
 scribed (§ 49) increas- 
 es as the exhaustion 
 progresses. 
 
 §51. Condenser. 
 — In the experi- 
 ment witb the botUe 
 (Fig. 40), air was 
 condensed in the 
 mouth by musenlar 
 contraction, and forced into the bottle. An apparatus A (Fig. 
 44), intended to condense air in a closed vessel, is called a 
 condenser'. Its construction is like that of the barrel of the 
 
:PBESStrRE TRANSMITTED UNDIMINISHED, ETC. 61 
 
 Fig. 44. 
 
 air-pump, except that the position of the valves is reversed. 
 (Compare with Fig. 34.) What differences do you notice in 
 respect to the valves? What happens to 
 the valves when the piston in the condenser 
 is forced down? If the condenser is con- 
 nected with a closed vessel B, how much 
 air would be forced into it at one down 
 stroke? What prevents the air from es- 
 caping during an up stroke? If, after air is 
 condensed in B, the cylinder C is connected 
 with it by a screw, and the stop-cock ( is 
 suddenly turned, what would happen to the 
 bullet s ? What name would you give to such 
 an apparatus? 
 
 The Western Union Telegraph Company, in 
 New Yorlc City, employs atmospheric pressure in 
 forwarding messages to its central office from 
 the various telegraph stations in that city. Tubes of uniform size, free 
 from sudden curvatures, and laid under ground, connect the branch 
 
 1 offices with headquarters. RoUs of paper, or letters to be des- 
 g patched, are deposited in a cylindrical box c (Fig. 45), which 
 fits the interior of the tube. The box being dropped into the 
 end of the tube 
 Fig. 45. { j at a, and the air 
 
 being exhausted 
 from the tube at 
 the end 6, by 
 means of an air- 
 pump worked by 
 steam, air rushes 
 in at a and pushes 
 
 the box through the tube with a force of several pounds for every square 
 inch of the end of the box. The operation is still further facilitated 
 by the aid of a condensing-pump worked by steam at the end a. 
 
 i 
 
 § 52. Pressure transmitted undiminished in all direc- 
 tions. — Fill the globe G (Fig. 46) , and about one-fifth the cylin- 
 jdor C, with water. The water in the tubes a, b, c, and d, will rise 
 
62 
 
 DYNAMICS. 
 
 Fig. 46. 
 
 to the same level with the water in the cylinder C. Now force 
 the piston P into the cylinder, and the downward pressure will 
 cause jets of water to issue from each of the tubes. But the 
 streams from the 'tubes a, b, and c, rise to exactly the same 
 hight that the stream from the tube d does, although the liquid 
 
 in the latter tube re- 
 ceives the direct ac- 
 tion of the downward 
 force. It thus appears 
 that the pressure is not 
 felt alone by that por- 
 tion of the liquid that 
 lies in the path of the 
 force, but is felt equally 
 in all parts and in all 
 directions. 
 
 If the globe is filled 
 with air, and subjected 
 to pressure as above, 
 currents of air will is- 
 sue from the several 
 tubes with equal force. 
 This property of trans- 
 mitting pressure equal- 
 ly in all directions, 
 which is peculiar to fluids, is due to their mobility and perfect 
 elasticity. 
 
 Figure 47 represents a number of elastic hoops enclosed in 
 the vessel ABCD. A weight, placed on a, communicates to 
 it a downward pressure. It is evident, that not only is the 
 pressure communicated to the hoops below it in succession, and 
 finally to the bottom of the box, but there is also a lateral pres- 
 sure due to the elastic property of the hoops. The hoop c, 
 receiving pressure from b, above, reacts, exerting an upwajd 
 pressure ; it also presses laterally upon the side A, and the hoop 
 
PEESSTJEB TEANSMITTBD UNDIMINISHED, ETC. 63 
 
 n, and downward upon d ; d and n in turn transmit pressure to 
 their adjacent hoops, and thus every hoop receives and trans- 
 mits, upward, downward, and Fig. 47. 
 laterally, a force equal to the 
 downward pressure of the weight 
 W. Hence that portion of the 
 bottom immediately under the 
 weight receives no greater pres- 
 sure from W than an equal area 
 of any other part of the bottom, 
 or than an equal area of either 
 of the sides, A and B, or the top 
 C. This operation illustrates, 
 somewhat imperfectly, the meth- 
 od by which elastic fluids trans- 
 mit pressure undiminished in all 
 directions. 
 
 If we take a quantity of water 
 in a vessel A (Fig. 48), shut 
 in by two pistons, a and 6, whose areas are respectively 
 16*™ and 41™, and place a 10-gram weight on the platform d, 
 and an equal weight on the platform c, it will be found that 
 the latter is not suflBcient to balance the 
 former, but that it will require a 40-gram 
 weight' placed on c to preserve equilibrium. 
 But the area of the piston b is 4*™, while 
 the piston a contains four such areas ; 
 hence it follows that a pressure of 10^ is 
 transmitted to each of the 4*™ of a, and just 
 supports the 40-gram weight. Had the area 
 of the piston h been l'™, then the 10-gram 
 weight placed on it would require a 160-gram 
 weight placed on a to balance it; that is, a pressure of 10* 
 WQuld be exerted on every square centimeter of a. 
 
 Obviously this form of apparatus cannot be made to work well on 
 
 Fig. 48. 
 
64 
 
 DYNAMICS. 
 
 accouut of the friction of the pistons; but we may substitute for 
 the pistons and weights columns of liquids. For instance, let the 
 connecting tube and the lower part of the barrels be filled with mer- 
 cury; the two free surfaces will be at the same level. Now if lOs 
 of any liquid, e.g. water, is poured into b, the level of the mercury 
 will be changed; and, to bring it back to its original level, 40^ of some 
 liquid must be poured into a. 
 
 We conclude, therefore, that a pressure exerted on a given 
 area of a fluid enclosed in a vessel is transmitted to every equal 
 area of the interior of the vessel; and that the whole pressure that 
 may he exerted upon the vessel may he increased in proportion as 
 the area of the part subjected to external pressure is decreased. 
 
 § 53. Hydrostatic bellows. — This principle is well illus- 
 trated by means of the hydrostatic hellows. Two boards, h and 
 Fig_ 49 c (Fig. 49), each having an area of (say) 
 
 400'™", are so connected, by leather at- 
 tached to their edges, as to form an au*- 
 tight vessel called the bellows. A glass 
 tube a, having a bore of 1'™ secition, 
 communicates with the interior of the bel- 
 lows. Let water be poured into the tube 
 a till the board b is raised a few centime- 
 ters. The water will stand at the same 
 hight in the tube and bellows. Now, if 
 50<^ of water be poured into the tube, it 
 will require a weight of 20,000* to be 
 placed upon 6 to prevent its rising. Any 
 weight less than that will be raised by 
 the 50* of water. If, instead of water being introduced into the 
 bellows, a person stand on 6, and blow into tli^ tube, he can 
 easily raise himself by the force of his breath. 
 
 § 54. Hydrostatic press. — Closely allied to the bellows is 
 the hydrostatic press, sometimes called Bramah's press from the 
 name of the inventor. You see two pistons, t and s. Figure 50' 
 
PRESStTRE IN FLUIDS DUE TO GRAVITY. 
 
 65 
 
 The area of the lower surface of t is (say) one hundred times 
 that of the lower surface of s. As the piston s is raised and 
 depressed, water is pumped up from the cistern A, forced into 
 the cylinder x, and exerts 
 an upward pressure 
 against the piston t one 
 hundred times greater 
 than the downward pres- 
 sure exerted upon s. 
 Thus, if a pressure of one 
 hundred pounds is applied 
 at s, the cotton bales will 
 be subjected to a pressure 
 of five tons. 
 
 The pressure that may 
 be exerted by these press- 
 es is enormous. The hand 
 of a child can break a 
 strong iron bar. But observe that, although the pressure ex- 
 erted is very great, the upward movement of the piston t is 
 very slow. In order that the piston t may rise 1™, the piston s 
 must descend 100™. The disadvantage arising from slowness of 
 operation is little thought of, however, when we consider the 
 great advantage accraing from the fact that one man can pro- 
 duce as great a pressure with the press as a hundred men can 
 exert without it. 
 
 The press is used for compressing cotton, hay, etc. , into bales, 
 and for extracting oil from seeds. The modern engineer finds 
 it a most efficient machine, whenever great weights are to be 
 moved through short distances, as in launching the Great East- 
 ern steamship. 
 
 § 55. Pressure in fluids due to gravity. — Having con- 
 sidered the transmission to the walls of the containing vessel, of 
 external pressure applied to any portion of a surface of a liquid, 
 
Fig. 51. 
 
 66 DYNAMICS. 
 
 we will examine the effects of pressure due to the weight of the 
 liquids themselves. Suppose that we have three vessels filled 
 
 with water, A, B, 
 ^^^^^, and C (Fig. 51) , of 
 ^H^I^B^^^^HBBW^^^^^EBm equal depth, and 
 BmI I^^^H^^N^HtlVPnnMWlllfl having bottoms of 
 
 HN !^^|KUilil^^Hy!!lll^ii!i!jii^| 6QU^1 areas. It is 
 
 H|^^^S^^H^^^H^^H^^^H^H plain the bot- 
 
 tom of vessel A sus- 
 tains a pressure equal to the weight of the column of water 
 abed, or just the weight of the water in the vessel. The pres- 
 sure on hj, a portion of the bottom of vessel B, is equal to the 
 weight of a column of water ghji. But this pressure is trans- 
 mitted undiminished to the surface fh ; consequently, the 
 pressure on fh is equal to the weight of a column o^ water of 
 the size of efhg, and the pressure on JZ is equal to the weight of 
 a column ijlk. Hence the pressure oh the whole bottom fl is 
 fequal to the pressure of a column of water eflk, ot the same 
 as the pressure on the bottom of vessel A. But the weight of 
 the water in B is less than the weight of the water iii A. Hence, 
 (1) the pressure on the bottom of a vessel may he gredter than the 
 weight of the water in the vessel. 
 
 In vessel C, the side mq sustains the downward pressure of 
 the body of water mqn; and the side pr sustains the pressure of 
 the body orp; whUe the bottom qr sustains only the pressure 
 of the column nqro, which is equal to the pressure on the bot- 
 toms of each of the vessels, A and B. Hence, (2) the pressure \ 
 on the bottom of a vessel may be less than the weight of the water 
 in the vessel. 
 
 We conclude, therefore, that (3) the pressure on the bottom 
 of a vessel depends on the depth and area of the bottom and 
 the density of the liquid, and is independent of the shape of the 
 vessel and the quantity of liquid. — The important fact that the 
 pressure on the bottom does not depend on the shape of the 
 vessel is often called the hydrostatic paradox, because, though 
 true, it seems at first absurd. 
 
PKESSUEB IN FLUIDS DUE TO GBAVITY. 
 
 67 
 
 PiK, 52. 
 
 Bxperlment. The last conclusion may be verified with apparatus 
 like that represented in Figure 52. Vessels A, B, and C have different 
 capacities, but equal depths, and the disk d is to serve successively 
 for the bottom of 
 each. Each vessel, 
 when in use, is sup- 
 ported by the tripod 
 e. The disk is sup- 
 ported and pressed 
 up strongly against 
 the bottom of the 
 vessel by means of 
 a string passing up 
 through the vessel, 
 and attached to a 
 spring-balance. Let 
 water be poured in- 
 to vessel C, and reg- 
 ulate at pleasure the 
 amount of down- 
 ward pressure nec- 
 essary to push the 
 bottom oflf and al- 
 low the water to 
 escape. Note the 
 depth of water 
 when the bottom is 
 forced off, and mark the level of the surface with the pointer/. Also 
 note the pressure indicated by the index of the balance. Substitute 
 vessel A for vessel C. Pour the water caught in the basin g, in the 
 last experiment, into vessel A, tiU it reaches the pointer /, when the 
 bottom will be forced off at the same depth as before, as shown by the 
 pointer, and by the same pressure, as shown by the spring-balance. 
 But much less water is required than was used with the vessel C. The 
 experiment, repeated with vessel B, wUl give the same results with the 
 use of a stm less quantity of water. 
 
 (4) The pressure due to gravity on any portion of the bottom 
 of a vessel is equai to the weight of a column of that liquid whose 
 base is the area of that portion of the bottom pressed upon, and 
 whose highi is the greatest depth of the water in the vessel. Thus, 
 
68 DYNAMICS. 
 
 Suppose the area of hj, of the bottom of vessel B (Fig. 51), is 
 100'™, and the depth gh is 9™ ; then the column ghji contains 
 900"™- And, since the weight of one cubic centimeter of water 
 js one gram, the weight of the column is 900^, which is the 
 pressure on the surface hj; and the pressure on each of the 
 equal surfaces fh and jl being the same as on hj, the pressure 
 on the entire bottom is 2700''. 
 
 Evidently the lateral pressure at any point of the side of a 
 vessel depends upon the depth of that point; and, as depth 
 at different points of a side varies, hence, (5) to find the pres- 
 sure upon any portion of a side of a vessel, we find the weigM of 
 a column of water whose base is the area of that portion of the 
 side, and whose hight is the average depth of that portion. Thus, 
 tre compute the pressure on the side ab of vessel A (Fig. 51), 
 bj' multiplying the area of the side 90""" (dimensions, 9 x 10™), 
 by the depth to the middle point x, 4^™, and. this by the weight 
 of 1""" of water, ^hich gives 405* for the pressure on the side 
 db. 
 
 QUESTIONS AND PROBLEMS. 
 
 1. It is apparent that a dam (Fig. 53), to be equally capable of 
 resisting pressure in all its parts, should be made thicker towards the 
 bottom. How rapidly should its thickness 
 ^'g- ^- increase ? 
 
 2. At high tide, suppose the flood-gate of 
 a dock to be closed, leaving the surface of 
 water on the inside and outside of the gate 
 at the same level. From which does the gate 
 sustain the greater pressure, the water in 
 the dock, or the ocean of water outside ? 
 Why? 
 
 3. The interior dimensions of the rectan- 
 gular vessel (Fig. 54) are 25™ in length, 20'"" in width, and 15™ in 
 depth. The vessel is full of water. Compute the total pressure on 
 each of the six sides. 
 
 4. Suppose that the plug n (Fig. 54) , the area of whose end is 4<i™, 
 is pressed down upon the surface of the water with the force of 1008; 
 what additional pressure will each side of the vessel sustain ? 
 
THE SURFACE OF A LIQUID AT REST IS LEVEL. 69 
 
 Fig. 64. 
 
 6. How great will be the whole pressure that each side sustains, 
 due to the weight of the liquid and the external pressure? 
 
 6. Suppose mercury, which Is 13.6 times heavier 
 than water, to be employed Instead of water, what 
 would be the answers to the three preceding ques- 
 tions? 
 
 7. Into the top of a keg filled with water, a brass 
 tube 10" long is inserted, a transverse section of 
 whose bore is l?"™. The depth of the water in the 
 cask is 30™, and the area of the bottom of the cask 
 is 404>™. (o) Compute the pressure on the bottom of the keg. 
 (6) Compute the pressure on the bottom of the cask if the tube is flUed 
 with water, (c) What is the weight of the water in the tube that 
 causes this extra pressure? 
 
 8. What crushing-force on each side would an empty cubical box, 
 the area of one of whose sides is !«"•, sustain, if lowered 1*"" into the 
 sea? 
 
 9. What crushing-force on each side would this box sustain from 
 the atmospheric pressure at the searlevel, if the air were completely 
 exhausted therefrom? 
 
 10. Suppose the top of the vessel (Fig. 54) to be the weak part of 
 the vessel, not able to sustain more than 508 pressure on lO?™, what 
 pressure applied to the plug will burst the vessel? 
 
 § 56. The surface of a liquid at rest is level. — By jolt- 
 ing a vessel the surface of a liquid in it may be made to assume 
 the form seen in Figure 55. Can it retain this form ? Take 
 two molecules of the liquid at the points a 
 and b, on the same horizontal level. The 
 downward pressure upon a is the weight of 
 a column of molecules ac, and the downward 
 pressure upon 6 is the weight of the column 
 bd. Now, since the pressure at a given depth 
 is equal in all directions, bd and ac represent 
 the lateral pressures at the points b and^a respectively. But 6c? 
 is greater than ac ; hence, the molecules a and 6, and those lying 
 in a straight line between them, are acted upon by two unequal 
 forces in opposite directions. There will, therefore, be a move- 
 ment of molecules in the direction of the greater force toward 
 
 Fig. 65. 
 
70 
 
 DYITAMICS. 
 
 a, till there is equilibrium of forces, which will only occur when 
 the points a and 6 are equally distant from the surface ; or, in 
 •other words, there will be no rest till all points in the surface are 
 on the same horizontal level. ' 
 
 . This fact is commonly expressed thus: "Water always seeks its 
 lowest level." In accordance with this principle, water flows down an 
 inclined plane, and will not remain heaped up. An illustration of tho 
 application of this principle, on a large scale, is found in the method 
 of supplying cities with water. Figure 56 represents a modem aque- 
 duct, through which water is conveyed from an elevated pond or river 
 a, beneath a river 6, over a hill c, through a valley d, to a reservoirs, 
 in a city, from which water is distributed by service-pipes to the dwell- 
 
 FiT. 5(i. 
 
 lugs. The pipe is tapped at different points, and fountains rise theo- 
 retically to the level of the water in the pond, but practically not so 
 high, on account of the resistance of the air and the check which the 
 ascending stream receives from the falling drops. Where should the 
 'pipes be made stronger, on a hill or in a valley? Where will water 
 issue from faucets with greater force, in a chamber or in a basement? 
 How high may water be drawn from the pipe in the house /? 
 
 § 57. Artesian wells, etc. — In most places, the crust of the 
 earth is composed of distinct layers of earth and rock of various kinds. 
 These layers frequently assume concave shapes, so as to resemble cups 
 placed one within another. Figure 57 represents a vertical section 
 exposing a few of the. surface-layers of the earth's crust : a is a stratum 
 of loose sand or gravel; i, a clay-bed; c, a stratum of slate; d, a 
 stratum of limestone ; the whole resting on a bed of granite e. If you 
 hollow out a lump of clay, and pour water into the cavity, you will 
 find that the water will percolate through the clay very slowly. Water 
 that falls in rain passes readily through the gravel a, till it reaches the 
 clay-bed 6, where it collects. Hence a weW, sunk to the clay-bed, will 
 
PABADOX. 
 
 71 
 
 fill with water as high as the water stands above the clay. Water also 
 works its way from elevated places down between the strata of rocks. 
 If a hole is bored through the slate c, water will rise above the surface 
 of the ground in a fountain, in attempting to reach the level of its 
 source on the hill ; and if bored still lower, through the stratum d, a 
 still higher fountain may result. Such bot-ings are called Artesian 
 wells. Water frequently forces its way through Assures in tiie rocky 
 strata to the surface, as at t, and gives rise to springs. 
 
 Fig. 57. ' 
 
 § 58. "Any quantity of liquid, hoWever small, may bal- 
 ance any quantity of liquid, however large." — If joii lead 
 a pipe through a dike by the seashore, and curve it upward, the 
 water will rise no higher than the sea-level, even though the pipe 
 should end in a quill. 
 
 Notwithstanding that every-day experience teaches that 
 "liquids seek a level," it may seem strange that the large 
 quantity of water in a teapot is balanced by the small quantity 
 in the nozzle. Why, for instance, should the liquid in the small 
 arm B balance the liquid in the large arm A, of the vessel in 
 Figure 58 ? Imagine the* liquid in A to be divided into columns 
 a, b, c, and d, each equal to the column e. It is clear that the 
 downward pressure of any one of the columns a, 6, c, d, or e, 
 will balance the downward pressure of any one of the other 
 columns, and that there is no reason why e should rise above 
 any one, or all, of the others. 
 
72 DYNAMICS. 
 
 § 59. Siphon. — A siphon is an instrument used for trans- 
 ferring a liquid from one vessel to another through the agency 
 of atmospheric pressure. It consists of a tube of any material 
 (rubber is often most convenient) , bent into a shape somewhat 
 like an inverted U. To set it in ope- 
 
 ^ — ration, fill the tube with a liquid, stop 
 
 each end with a iinger or cork, insert 
 one end in the liquid to be transferred, 
 bring the other end below the level of 
 the surface of the liquid, remove the 
 stoppers, and the liquid will immedi- 
 ately flow. Why ? The force that 
 raises the liquid in the short arm of the 
 siphon A (Fig. 59) is the pressure of 
 the atmosphere less the downward pressure of a column of water 
 dc. The excess tends to carry the water over through the bend. 
 On the other hand, the upward pressure at b, tending to carry 
 the water back into the vessel, is an atmosphere less the weight 
 of a column of water ba. But the former excess is greater than 
 the latter by the weight of a column eb ; consequently the liquid 
 moves in the direction of the greater force towards 6, with a 
 velocity dependent on the distance eb. When the distance eb 
 becomes zero, as in B, the flow ceases, and the liquid stands in 
 the tube. 
 
 If one of the vessels is raised a little, as in C, the liquid will 
 flow from the raised vessel, till the surfaces in the two vessels 
 are on the same level. The remaining diagrams in this cut 
 represent some of the great variety of uses to which the siphon 
 may be put. D, E, and F are different forms of siphon fountains. 
 In D, the siphon tube is filled by blowiifg in the tube/. Explain 
 the remainder of the operation. A siphon of the form Gr is 
 always ready for use. It is only necessary to dip one end into 
 the liquid to be transferred. Why does the liquid not flow out 
 of this tube in its present condition ? H illustrates the method 
 by which a heavy liquid may be removed from beneath a lighter 
 liquid. By means of a siphon a liquid may be removed from a 
 
SrPHONS. 
 
 78 
 
 vessel in a clear state, without disturbing sediment at the bot- 
 tom. I is a Tantalus cup. A liquid will not flow from this 
 cup till the top of the bend of the tube is covered. It will then 
 continue to flow as long as the end of the tube is in the liquid. 
 The siphon J may be filled with a liquid that is not safe or 
 
 Fig. 69. 
 
 (i 
 
 J-^^^ 
 
 
 -^~ 
 
 r 
 
 
 
 B 
 
 =S^ 
 
 -- 
 
 f 1 
 
 fli 
 
 .AWEf/ 
 
 
 1 ' ^ 
 
 
 1^ 
 
 rjii 
 
 
 
 If 
 
 y 
 
 1- 
 
 Lj 
 1 ^ 
 
 mm. 
 
 1" 
 
 I 
 
 1 jj 
 
 I 
 
 n 
 
 ! 
 
 _ 
 
 h 
 
 , i 
 
 III 
 
 
 H 
 
 1 
 
 1 lUOIUoU 
 
 4^ 
 
 A / 
 
 /_• _ ( / 
 
 
 f*f 
 
 11 f 
 
 ^'1, 
 
 
 — Sw 
 
 
 J 
 
 - 
 
 
 /_■■ 
 
 
 
 
 " " f 
 
 
 
 
 I 
 
 » 
 
 l» 
 
 pleasant to handle, by placing the end j in the liquid, stopping 
 the end Ti, and sucking the air out at the end I till the lower end 
 is filled with the liquid. 
 
 Gases heavier than air may be siphoned like liquids. Vessel o 
 
74 DYNAMICS. 
 
 contains carbonic-acid gas. As the gas is siphoned into the 
 vessel p, it extinguishes a candle-flame. Gases lighter than 
 air are siphoned by inverting both the vessels and the siphon. 
 
 QUESTIONS. 
 
 1. What is the greatest hight to which the bend r (in A, Fig. 69) 
 can be carried, and allow water to flow ? 
 
 2. What would be the greatest hight if mercury were used ? 
 
 3. Suppose the bend r is 15"> above the liquid ; what theoretically 
 ought to happen when the end 6 is unstopped ? 
 
 4. What would happen if the long arm were cut off at e ? 
 
 5. What would happen if it were cut off between e and a ? 
 
 6. What would happen if the siphon were lifted out of the liquid ? 
 
 7. What would be the effect of lengthening the long arm ? 
 
 8. Must the two arms of a siphon be of Unequal length? 
 
 9. How far can a liquid be carried by a siphon ? 
 
 10. Will a siphon work in a vacuum ? 
 
 11. Imagine that some such condition of things as is represented by 
 the apparatus K (Fig. 59) exists in the earth, and that the siphon a 
 has a smaller bore than the siphon c ; can you account for intermittent 
 springs which flow and cease to flow at nearly equal intervals of time? 
 
 § 60. Apparatus for raising liquids. — The siphon can 
 
 only be used for transferring liquids over bights to a lower 
 
 ^ ^„ level. Liquids cannot be transferred to a 
 
 ivlg. 60. 
 
 higher level bj' atmospheric pressure alone. In 
 fact, atmospheric pressure is only a conven- 
 ience, and never does work. If the piston- a 
 of a syringe (Fig. 60) is raised, the air is rare- 
 fled below it, and the atmospheric pressure will 
 force water up into the syringe ; but to raise 
 the piston, against the atmospheric pressure 
 tending to force it downward, requires as much 
 muscular energy as would be required to raise 
 
 the same quantity of water to the same hight as that to which 
 
 it is raised in the syringe. 
 
 The common lifting-pump is constructed like the barrel of 
 
 an air-pump. Figure 61 represents the piston in the act of 
 
APPARATUS POE RAISING LIQUIDS. 
 
 7$ 
 
 Fig. 61. 
 
 rising. As ttie air is rarefied below it, water rises by atmos- 
 pheric pressure, and opens the lower valve. The weight of the 
 water above the piston closes the upper valve, and 
 the water is discharged from the spout. When the 
 piston is pressed down, the lower valve closes, 
 the upper valve opens, and the water between the 
 bottom of the barrel and the piston passes through 
 the upper valve above the piston. How high 
 can the bottom of the barrel be above the surface 
 of the liquid, if the liquid to be pumped is water ? 
 How high if it is mercury? 
 
 The liquid is sometimes said to be 
 raised in a lifting-pump by the " force 
 of suction." Is there such a force ? 
 
 Fig. 62. 
 
 Experiment. Bend a glass tube into 
 a U shape, with unequal arms, as in Figure 62. Fill the 
 tube with a liquid to the level cb. Close the end 6 with 
 a finger, and try to suck the 
 
 liquid out of the tube. You Hgjs^ 
 
 find it impossible. Remove 
 
 the finger from 6, and you can suck the 
 
 liquid out with ease. Why? 
 
 The piston of a force-pump (Fig. 
 63) has no valve, but a branch pipe 
 leads from the lower part of the bar- 
 rel to an air-condensing chamber a, 
 at the bottom of which is a valve c, 
 opening upward. As the piston is 
 raised, water is forced up through the 
 valve d, while water in a is prevented 
 from returning by the valve c. When the piston is forced 
 down, the valve d closes, the valve c opens, and water is 
 forced into the chaniber a, condensing the air above the water. 
 The elasticity of the condensed air forces the water out of the 
 hose 6 in a continuous stream. 
 
76 
 
 DYNAMICS. 
 
 V. BUOYANT FORCE OF FLUIDS. 
 
 Experiment 1. Gradually lower a large stone, by a string tied to 
 It, into a bucket of water, and notice that its weight gradually becomes 
 less till it is completely submerged. Slowly raise it out of the water, 
 and note the change in weight as it emerges from the water. Suspend 
 the stone from a spring balance, weigh it in air and then in water, and 
 ascertain its loss of weight in the latter. Repeat the experiment with 
 pieces of iron, wood, and other substances. Inflate a bladder, and 
 force it beneath a .surface of water. Fill a thin rubber balloon with 
 coal-gas, and it will rise to the top of the room. 
 
 In all these experiments it seems as if something in the fluid, 
 underneath the articles submerged, were pressing up against 
 them. This lifting-force is caUed the buoyant force of fluids. 
 Every body immersed appears to lose part of its weight; 
 some bodies appear to lose all their weight. Do bodies really 
 lose any portion of their weight when immersed in a liquid? 
 
 Experiment 2. Place a beaker of water on a scale-pan of a balance- 
 beam, and weigh. Weigh a stone first in the air, then In water, and 
 ascertain the apparent loss of weight. 
 Then suspend the stone from a support 
 (Fig. 64) , and weigh the beaker of water 
 with the stone immersed, and it will be 
 found that the beaker and its contents gain 
 in weight precisely as much as the sttfne 
 loses. That is, the water supports what is 
 not supported by the string, and no weighf 
 is really lost. Repeat the experiment with 
 a block of wood. 
 
 Experiment 3. Make a saturated solu- 
 tion of salt in water. Weigh the same 
 stone in air, fresh water, and salt water. 
 The apparent loss of weight is greater in salt than in fresh water. 
 Throw a piece of iron into mercury. It floats on the mercury li^e 
 cork on water. Fill a vessel with carbonic-acid gas; blow a soap- 
 bubble, and drop it into the vessel. It will not sink in the vessel, but 
 rolls over the side and falls to the floor. It appears that some fluids 
 have greater buoyant force than others. The water of the Dead Sea, 
 in Palestine, is so salt (i.e., so heavy) that a person could not possibly 
 sink in it. 
 
 Fig. u. 
 
WHY A SOLID IS BUOYED UP BY A FLUID, ETC. 77 
 
 Flg.ffi. 
 
 § 61. Why a solid is buoyed up by a fluid, and with 
 how great a force it is buoyed up. — Suppose dc6a (Fig. 
 65) to be a cubical block of marble immersed in a liquid. It is 
 obvious that the downward pressure upon 
 the surface da is equal to the weight of the 
 column of liquid edao. The upward pres- 
 sure on the surface cb is equal to the 
 weight of a column of liquid echo. The dif- 
 ference between the upward pressure against 
 cb and the downward pressure on da, is the 
 weight of a column of liquid ecbo less the 
 weight of a column of liquid edao, which is 
 a column of liquid dcba {ecbo — edao = dcba) . 
 But a column of liquid dcba has precisely 
 the volume of the solid submerged. Therefore, a solid is buoyed 
 up by a fluid in consequence of the unequal pressures upon its top 
 and bottom at their different depths, and the amount of the buoyancy 
 is the weight of a body of 
 that fluid equal in volume 
 to the solid immersed. The 
 last proposition is gener- 
 ally stated as follows : A 
 solid loses in weight as 
 much as the weight of the 
 fluid it displaces. 
 
 Flff. 66. 
 
 Experiment 4. The last 
 statement may be verified 
 with apparatus like that 
 shown in Figure 66. Fill the 
 vessel A till the liquid over- 
 flows at E. After the over- 
 flow ceases, place a vessel c 
 under the nozzle. Suspend 
 a stone from the balance-beam B, and weigh it in air, and then 
 carefully lower it into the liquid, when some of the liquid will flow 
 into the vessel c. The vessel c having been weighed when empty, 
 
78 
 
 DYNAMICS. 
 
 weigh it again with Its liquid contents, and it will be found that Its 
 increase in weight is just equal to the loss of weight of the stone. 
 
 Experiment 5. Next suspend a block of wood that will float in 
 the liquid, and weigh it in air. Then float it upon the liquid, and 
 weigh the liquid displaced as before, and it will be found that the 
 weight of the liquid displaced is just equal to the weight of the block 
 
 Hence, a floating mass displaces its own weight of liquid; in 
 •p. g, other words, a floating mass will 
 
 sink till it displaces an equal 
 weight of the liquid, or till it 
 reaches a depth where the buoyant, 
 force is equal to its own weight. 
 
 Experiment 6. Next, partially 
 fill with water a glass (Fig. 67), 
 graduated in cuhic centimeters and 
 fractions of the same. Note the 
 level of the water. Drop one of the solids into the water, and note 
 again the level of the water. The difference between the two levels 
 is the number of cubic centimeters of water that the solid displaces. 
 But one cubic centimeter of water weighs one gram. Hence, the 
 number of cubic centimeters displaced is equal to the weight in grams 
 of the water displaced, and this is the loss in weight the solid sustains 
 in water. 
 
 There is an adage that '''a pound of feathers weighs more 
 than a pound of gold." Is there truth in the statement? 
 
 Experiment 7. Instead of feathers, we will employ a hollow glob? 
 a (Fig. 68) ; in place of the " pound of gold," we will pj gg 
 
 use a counterpoise b, of any metal whose weight is 
 just equal to the weight of the globe. Then, when 
 the globe and counterpoise are suspended from the 
 opposite arms of the balance-beam c, the beam will 
 be horizontal. Now place the whole on the plate 
 of an air-pump, cover with a receiver, and exhaust the 
 air. As soon as the exhaustion commences, the globe 
 begins to descend, and at the end of the operation the beam is com- 
 pletely tilted. Although the globe and counterpoise were both buoyed 
 up by the air. It becomes evident, when this support is removed, that 
 
DENSITY AND SPBCIFIO GRAVITY. 79 
 
 the globe was buoyed up more than the counterpoise, as we might 
 expect from the fact that it displaces more air. 
 
 A pound of feathers displaces more air than a pound of gold, 
 and is therefore buoyed up more by the air ; consequent!}- the 
 pound of gold, which balances a pound of feathers in the air, 
 does not balance them in a vacuum. We learn from this experi- 
 ment that bodies weigh less in air than in a vacuum, and that 
 loe never learn the true weight of a body, except when weighed 
 in a vacuum. 
 
 It has been stated (page 51) that the density of the atmosphere Is 
 greatest at the surface of the earth. A body free to move cannot dis- 
 place more than its own weight of a fluid ; therefore a balloon, which is 
 a large bag filled with a gas about fourteen times lighter than air at the 
 sea-level, will rise till the balloon, plus the weight of the car and cargo, 
 equals the weight of thfr air displaced. The aeronaut, wishing to 
 ascend still higher, throws out a portion of his cargo; wishing to 
 descend, he allows some of the gas to escape at the top of the bailoon 
 by means of a valve, which he controls by means of a cord passing 
 through the balloon to the car. 
 
 QUESTIONS. 
 
 1. Why is it difficult to stand in water reaching the neck ? 
 
 2. Why can a person raise a stone under water, which he cannot 
 lift when out of water ? 
 
 3. A piece of cork weighs 50B; what weight of water does it dis- 
 place when floating ? 
 
 4. What weight of mercury will a piece of iron weighing 500? dis- 
 place ? 
 
 VI. DENSITY AND SPECIFIC GRAVITY. 
 
 § 62. Density. — We speak of a piece of cork as being 
 heavier than a nail, at the same time that we speak of cork as 
 light and iron as heavy. This seeming contradiction is ac- 
 counted for by the different meanings which we attach to the 
 terms light and heavy. In both cases, light and heavy are used 
 as terms of comparison. In the former instance, we compare 
 
80 DYNA^^cs. 
 
 the weights of the two particular bodies, without reference to 
 volume ; in the latter, we call cork light and iron heavy, having 
 no particular bodies in view, but because we know by experience 
 that cork is not so dense as iron ; i.e., a given volume of cork 
 contains less matter than an equal volume of iron. The term 
 weigM refers simply to the number of grams, kilograms, etc., 
 that a particular body weighs without reference to the material 
 or the volume. The density of a body can be stated only by 
 expressing (or understanding) two quantities, viz., mass and 
 volume. For example, suppose that a block of wood measures 
 2 X 10 X 20™ and has a mass of {i.e., weighs) 300^ ; its density is 
 then — ^^^ — = IM = 0.75 gram per cubic centimeter. When 
 
 """^ 2X10X20 400 " *^ 
 
 we speak of cork as lighter than iron, it is evident that we are 
 comparing the densities of these two substances. 
 
 § 63. Speoiflc gravity. — Tlie specific gravity of a siibstance 
 is the ratio of the density of that substance to the density of another 
 substance assumed as a standard; in other words, it is the num- 
 ber which expresses how many times heavier a certain volume of 
 a given substance is than an equal volume of another substance. 
 
 To facilitate comparison of densities, uniform standards are 
 adopted. Distilled water at its maximum density, at 4° C, is 
 the standard of specific gravity for all solids and liquids. In- 
 asmuch as one cubic centimeter of water weighs one gram, 
 when the weigh* of one cubic centimeter of any substance is given 
 in grams, i.e., when its density is given in its usual metric 
 units, the same number also expresses its specific gravity. 
 Thus one cubic centimeter of water weighs one gram ; hence 1 
 is the specific gravity of water. The density of silver is 10.53* 
 per cubic centimeter; hence the specific gravity of silver is 
 10.53. The standard for gases is air at the average sea- 
 level density, and at a temperature of 0° C. The weight of one 
 cubic centimeter of air, under these conditions, is 0.0012932*, 
 or about -j^ of the weight of one cubic centimeter of water. 
 
 Let G = the specific gravity of a substance ; D = its density 
 
SPECIFIC GEAVITY. 
 
 81 
 
 in grams per cubic centimetei| ; V = the volume of a given body 
 of it in cubic centimeters ; W = the weight of the given body 
 in grams ; W = the weight in grams of an equal volume of the 
 
 standard. Then, as shown above, D = — , and, by definition, 
 
 "W" ^ 
 
 Gr = — , • G is numerically equal to D, and W to V. 
 
 Since the loss of weight of a solid immersed in a liquid is 
 just the weight of an equal volume of that liquid, it is evident 
 that, if we divide the weight of a solid in air by its loss in weight 
 when immersed in water, the quotient will he its specific gravity. 
 
 Experiment 1. Obtain small lumps of glass, iron, lead, marble, 
 granite, etc., and weigh each in air. Partly fill with water a measur- 
 ing-beaker graduated in cubic centimeters, and note the level of the 
 water. Drop a lump into the water, and note the level again. The 
 rise of water, as indicated by the graduated scale, gives the volume 
 (V) of the specimen. With these data find the density (D) , employing 
 
 W 
 the formula D = — -. Next weigh each of these lumps submerged in 
 
 Wftter, and find its loss in weight ; and, from the data obtained, ascer- 
 
 tain G from the formula G = 
 
 W 
 
 Prepare blanks, and tabulate yoar 
 
 regPhlts thus 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 Kame of 
 Substance. 
 
 w 
 
 V 
 
 ccm 
 
 D 
 
 or G 
 
 e 
 
 W 
 
 g 
 
 Win 
 water. 
 
 g 
 
 
 G 
 or D 
 
 e 
 
 Av. 
 
 e 
 
 :E'Iint glass. 
 
 435 
 
 134 
 
 3.24 
 
 .09- 
 
 435 
 
 305 
 
 130 
 
 3.34 
 
 .01-1- 
 
 8.29 
 
 .04- 
 
82 DYNAMICS. 
 
 When the result obtained differs from tliat given in the table of spe- 
 cific gravities (see Appendix, page 402), the difference is recorded in 
 the column of errors (e). When the former is greater than the latter, it 
 is indicated by a plus sign affixed to the number ; when less, by the 
 minus sign. The results recorded in the column of errors are not nec- 
 essarily real errors ; they may indicate the degree of impurity, or some 
 peculiar physical condition, of the specimen tested. 
 
 Experiment 2. Obtain good specimeus of cork, oak, elm, and poplai- 
 woods, all of which float on water. Tie to a specimen a piece of lead 
 heavy enough to sink it; immerse the two, thus attached, in a measur- 
 ing-glass, and find the number of cubic centimeters of water displaced by 
 them. In the same way find the amount displaced by the lead alone. 
 Subtract the amount displaced by the lead from the amount displaced by 
 the two, and the remainder will be the amount displaced by the specimen . 
 Then, regarding the number of centimeters of water displaced as so 
 
 W 
 many grams, apply the formula G = rrry. 
 
 Example. Find the specific gravity of a piece of elm wood. At- 
 tach to it a piece of lead weighing (say) 408. 
 
 The combined solids displace 28.S8 of water. 
 
 The lead displaces 3.58 " 
 
 The elm displaces 25.0s " 
 
 The elm weighs in air 20.0? " 
 
 The specific gravity of elm wood is . . . 20.0-h25 = .8. 
 
 Experiment 3. Find the specific gravity of alcohol, a saturated so- 
 lution of common salt, sea-water, naphtha, olive-oil, pure milk, and 
 mercury in the following manner : ascertain the loss in weight of a 
 sinker in each one of these liquids, also in water, and then apply the 
 
 W 
 formula G = ==-, . Here W and W' represent the loss of weight of the 
 
 sinker in the liquid and Tvater respectively. 
 
 Example. Compute the specific gravity of alcohol from the follow- 
 ing data : — 
 
 A piece of marble weighs in air .... 56.808 
 
 The same weighs in water 36.808 
 
 Loss in water 20.008 
 
 56.808 
 
 The marble weighs in alcohol 40.968 
 
 Loss in alcohol 15.848 
 
HYDEOMETERS. 83 
 
 Since 20^ and 15.84b are the weights respectively of equal volumes of 
 ater and alcohol, 
 gravity of alcohol. 
 
 W 15 84 
 
 water and alcohol, and since G=— , , then = .792, the specific 
 
 § 64. Hydrometers. — Experiment. Take a uniform rod of 
 light wood about a foot long, and marlc oflF on it a scale of equal parts. 
 .\ convenient size is ^ inch square, and a suitable scale is j^ig. 69. 
 inches and half inches. Coat the rod with paraffine to pre- 
 vent its absorbing water and swelling. Bore into the end 
 marked zero a hole about 2 inches deep, and drive in bullets 
 tiU the rod will sink in water (Fig. 69) just to some inch- 
 mark, and stop the end with parafflne. If it sinks too deep, 
 cut off the upper end of the rod. 
 
 Suppose the rod sinks 8 inches in water ; then, if it is ^ inch 
 square, it displaces 2 cu. in. of water. The weight of the 
 water displaced must just equal the weight of the rod (see 
 page 78). Now immerse it in alcohol; it sinks deeper, say to 
 the 10-inch mark ; that is, y^ cu. in. of alcohol weigh the same 
 
 V 8 
 as f cu. in. of water; therefore, G = r-:y=— = .800. If in 
 
 brine it sinks only 6f in., G = ;^ = 1.20. || ||j| 
 
 Apparatus like that described is called a hydrometer. In- 
 stead of a rod of wood, a glass tube is generally used, ter- 
 minating in a bulb containing shot or mercury. The tube 
 contains a scale with numbers corresponding, which express the specific 
 gravity, so that no computation is necessary. Make solutions of 
 various substances, and test their specific gravity with your hydrome- 
 ter, and test the accuracy of the results so obtained by other processes. 
 
 The most direct way of finding tiie specific gravity of liquids 
 and gases is by employing vessels that hold definite weights of 
 the two standards, water or air, and then weighing these vessels 
 when filled with other liquids or gases ; and, after deducting the 
 
 W 
 
 weight of the vessel, applying the formula, G = — • 
 
 The specific gravity of a solid that is dissolved by water may 
 be found by weighing it in a liquid that will not dissolve it 
 (e.g., rock-salt in naphtha); and, having found its specific 
 
84 DYNAMICS. 
 
 gravity as compared with the liquid used, multiply this result by 
 the specific gravity of the liquid. 
 
 W W 
 
 From the formula D = — , we have V = 77 i hence, the volume 
 
 of an irregular-shaped body may be found in cubic centimeters by 
 dividing its weight in grams by its density. 
 
 W 
 
 Again, from the formula D = — , we have W= V x D. Hence, 
 
 when the volume and density of a body are known, its weight in 
 grams may be found by multiplying its volume in cubic centime- 
 ters by its density. 
 
 QUESTIONS AND PROBLEMS.' 
 
 1. How high can sulphuric acid be raised by a lifting-pump? 
 
 2. What is the weight of 50k of water in water? 
 
 3. Find the specific gravity of wax from the following data : weight 
 of a given mass of wax in air is 808; wax and sinlier displace 102.88™"" 
 of water ; sinker alone displaces 14™™. 
 
 4. Why does a light liquid (e.g., oil), introduced under a heavier 
 liquid (e.g., water), rise? 
 
 5. Glass is about three times heavier than water; how, then, can a 
 glass tumbler float in water? 
 
 6. How can Iron vessels float in water? 
 
 7. A block of ice containing 500°™ is floating on water ; how many 
 cubic centimeters are out of water? 
 
 8. Will ice float or sink in alcohol? 
 
 9. How much more matter is there in SOO""™ of sea-water than in 
 the same volume of fresh water? 
 
 10. In 50* of gold how many cubic centimeters? 
 
 11. What is the density of gold? 
 
 12. What is the density of cork? 
 
 18. What is the density of air at ordinary pressure, and at a tempera- 
 ture of 0° C? 
 
 14. An irregular piece of marble loses 538 when weighed in water. 
 How many cubic centimeters does it contain? 
 
 16. When will a body sink, and when float? 
 
 16. How many cubic centimeters of air at the sea-level does it take 
 to weigh as much as 1"="> of water? 
 
 1 Consult the Tables of Specific Gravities, in ttie Appendix, Section C. 
 
QUESTIONS AND PROBLEMS. 85 
 
 17. How much will I'' of copper weigh in water? 
 
 18. What does a piece of lead 20 x 10 x 5™ weigh? 
 
 19. What will it weigh in water? 
 
 20. What will it weigh in mercury? 
 
 21. What becomes of the weight that is lost? 
 
 22. If 158 of salt be dissolved in li of water, without Increasing the 
 volume of the liquid, what will be the specific gravity of the solu- 
 tion? 
 
 23. A mass of lead weighs 1* in air. What will it weigh in a 
 vacuum? 
 
 24. A mass whose weight in air is 30e, weighs in water 36b, and in 
 another liquid 278. What is the specific gravity of the other 
 liquid? 
 
 25. A silver spoon, weighing 1508, is supported by a string in water. 
 What part of the weight is sustained by the string, and what part is 
 supported by the water? 
 
 26. A boat displaces 25"=i'"> of water. How much does it weigh? 
 
 27. If 50'' of stone were placed in the boat, how much water would 
 It displace? 
 
 28. If the boat is capable of displacing lOO*" of water, what weight 
 must be placed in it to sink it? 
 
 29. An empty glass globe weighs 1008; full of air it weighs 102.18; 
 full of chlorine gas, it weighs 105.9288. What is the specific gravity 
 of chlorine gas? 
 
 30. What weight of alcohol can be put into a vessel whose capacity 
 is 11. 
 
 31. You wish to measure out 508 of sulphuric acid. To what num- 
 ber on a beaker graduated in cubic centimeters will that corre- 
 spond? 
 
 32. State how you would measure out 808 of nitric acid in a measur- 
 ing-beaker. 
 
 33. A measuring-beaker contains 35™™ of naphtha. What is the 
 weight of the naphtha? 
 
 34. A lead pipe is carried 20™ below the surface of water in a reser- 
 voir. What bursting-force per square centimeter must it be capable of 
 sustaining? 
 
 35. A cubical vessel, each of whose sides contains 2500'""", is filled 
 with water. What pressure does its bottom sustain? One of its sides? 
 
 36. A solid floats at a certain depth in a liquid when the vessel 
 which contains it is in the air; if the vessel is placed in a vacuum, will 
 the solid sink, rise, or remain stationary? 
 
86 DYNAMICS. 
 
 VII. MOTION. 
 
 § 65. Motion and rest relative terms. — To a person 
 riding in a railway car, and confining his attention to objects 
 in the car, everything appeal's to be at rest ; but let him direct 
 his attention to objects by the wayside, and at once he discovers 
 that all in the car are in motion. Matter may be at rest with 
 reference to certain objects, and in motion in regard to others. 
 Motion and rest are wholly relative terms, and inapplicable to an 
 object considered apart from all others. We cannot locate an 
 object except with reference to another object, nor can we con- 
 ceive of change or permanence of position of an object, except 
 in relation to some other object. The aeronaut, moving at the 
 rate of. sixty miles an hour, knows not that he is moving at all, 
 till he looks away from his balloon, and sees cities and towns 
 passing in panorama beneath him. 
 
 § 66. All matter is in motion. — Tliere is no such thing as 
 absolute rest in the universe. There is no use for the word rest, ex- 
 cept to indicate, with reference to each other, the condition of 
 objects that are moving in the same direction and with the 
 same velocity. For example, a span of horses drawing a car- 
 riage, at the rate of ten miles an hour, are at rest with reference 
 to each other and the carriage. The stars, that compose the 
 heavenly constellations, maintain punctiliously theu* relative 
 positions, while they sweep with prodigious velocities through 
 space. The phrase " at rest" can only be used in an extremely 
 limited sense, and in common language refers only to the condi- 
 tion of an object with reference to that on which it stands, as a 
 car, deck of a ship, or surface of the eai-th. It is only by putting 
 totirely out of mind the niotions of the earth that we can speak 
 of any terrestrial object as being at rest. *" 
 
 Not only is there motion of mass as a whole, or visible me- 
 chanical motion, but there is a motion of the molecules within 
 the mass, — ■ a^ invisible molecular motion called heai. We 
 cannot see the movements of the molecules of steam, but we 
 
VELOCITY. 87 
 
 know that they exist by their great power, manifested in moving 
 macliinery. 
 
 § 67. Velocity. — Uniform and varied motion. — All 
 motion takes time ; hence the term velocity, which refers to the 
 space traversed in a unit of time. Motion may be uniform or 
 varied : uniform, when an object traverses successively equal 
 spaces in all equal intervals of time ; varied, when unequal 
 spaces are traversed in any equal intervals of time. Varied 
 motion may be accelerated or retarded : accelerated, when the 
 spaces traversed increase at each successive interval of time ; 
 retarded, when thej' diminish. The motion of a train of cars, in 
 starting from a station is at first accelerated, afterwards tolerably 
 uniform, and when the brakes are applied, it becomes retarded. 
 Strictly speaking, all motions are varied ; there is no illustration of 
 absolutely uniform motion in Nature nor in art, though we may 
 conceive of its possibility and have very closely approximated to it. 
 
 The velocity of a body having accelerated or retarded motion can 
 be given only at some definite point by an estimate of the distance it 
 would traverse In a unit of time, were it to continue In uniform motion 
 at the speed It has at that point. For Instance, a railway train passes 
 us, and we estimate that Its velocity Is 30 miles an hour, although In a 
 few minutes Its speed may be reduced to 10 miles an hour, and a little 
 later It may come to rest. When we assign a velocity of 30 miles an 
 hour, we have no thought of whether it will run 30 miles during the 
 next hour, or whether It will run an hour; we mean that, should it 
 retain Its present speed, It will be 30 miles away from us at the end of an 
 hour. 
 
 VIII. FIRST LAW OF MOTION. — INERTIA. 
 
 Now, what is it that sets in motion that which was previously 
 at rest? We may call it force; but what idea does this term 
 convey? Let us question our own experience. We leave an 
 apple lying upon a table ; have we not entire confidence that it 
 will continue to lie there, unless disturbed by some other body ? 
 If on returning we find it gone, are we not sure that it has been 
 removed by the action of some body other than itself? An 
 
88 DYNAMICS. 
 
 apple falls to the ground, and although the action is one of the 
 most mysterious in all nature, yet do we not almost instinctively 
 trace the cause to some action between the apple and the earth? 
 The ball at rest is put in motion by a bat ; but must not the bat 
 first be put in motion ? And when we find the cause of its mo- 
 tion, is itnot an antecedent motion in some other object? We 
 conclude, then (1), that motion cannot originate in an object 
 isolated from all others, hut it always arises from mutual action 
 between at least tv^io bodies. 
 
 Again, the bat, having received motion, is capable of impart- 
 ing motion to the ball ; but, having set in motion one ball, is it 
 equally capable of putting in motion another ball? Can a mass 
 impart motion and retain all its motion ? Is it not like a com- 
 mercial transaction, a trade, to which there are two parties, one 
 a buyer and the other a seller ? that is, are not all transactions 
 between the parties (i.e., the mover and the moved) of the na- 
 ture of a transfer, which should be entered on the debit side of 
 one's account, and the credit side of the other's? We conclude 
 (2) that motion in one body is caused only by another body's 
 parting with some of its power of producing motion. 
 
 If a sled, on which a child is sitting, is suddenly put in mo- 
 tion, the child is left in the place from which the sled started. 
 If the child and sled are both in motion, and the sled is sud- 
 denly stopped, the child lands some distance ahead. If the 
 sled is started slowly, the child partakes of the motion of the 
 sled, and is carried along with, it; and if the sled gradually 
 stops, the child's motion is gradually checked, and it retains its 
 place on the sled. This shows (3) that masses of matter receive 
 motion gradually and surrender it gradually. 
 
 Even very small bodies require time to start and to stop. The sand- 
 blast, employed for engraving figures on glass, furnishes a fine illus- 
 tration of this fact. A box of fine quartz-sand is placed in an elevated 
 position. A long tube extends vertically down from the bottom of this 
 box. The plate of glass to be engraved is covered with a thin layer of 
 melted wax. When cool, the design Is sketched with a sharp-pointed 
 
FIRST LAW OF MOTION. 89 
 
 Instrument, in the wax, leaving the glass exposed only where the lines 
 are traced. The plate is then placed beneath the oriiice of the tube, 
 and exposed to a shower of sand. The velocity of the sand-grains is 
 not at its maximum at the start, but is constantly accelerated tUl they 
 reach the plate, where their velocity in turn is gradually given up. 
 The wax, on account of its yielding nature, gradually brings them to 
 rest; but the glass, notwithstanding its hardness, cannot stop them 
 quite at its surface ; and, therefore, it suffers a chipping action from 
 the sand. Thus the soft wax affords a protection from the action of 
 the faUiug sand of all parts except those Intended to be cut. A still 
 greater force is generally given to the sand by steam blown through 
 the tube. For this reason the apparatus is called a sand-blast. Hard 
 metals like steel are engraved in the same manner. Yet the hand 
 may be held in the blast several seconds without injury. (What is the 
 difference in the effects of catching a base-ball with hands held rigidly 
 extended, and allowing the hands to yield somewhat to the motion of 
 the ball?) 
 
 Roll a marble on a carpet, — it soon stops ; roll it on a smooth 
 marble floor, — it rolls much farther. On a perfectly smooth sur- 
 face it might roU for hours. If we could provide such a surface, 
 and dispense with the resistance of the air, how long would it 
 roll? These conditions are impracticable? True. But have 
 not the heavenly bodies rolled for millions of years through fric- 
 tionless space, unchecked because unimpeded ? 
 
 Motion unobstructed is perpetual. Motion undisturbed is in a 
 straight line. Along which will a marble roll more nearly in a 
 straight line, a smooth or a rough floor? What if the floor were 
 perfectly smooth? 
 
 The relations between matter and force are admirably and 
 concisely expressed in what are known as Newton's TJiree Laws 
 of Motion. 
 
 § 68. First Law of Motion. — A body at rest remains at 
 rest, and a body in motion moves with uniform velocity in a 
 straight line, unless acted upon by some external force to change 
 its condition. 
 
 That part of the law which pertains to motion is briefly summarized in 
 the familiar expression, ' ' perpetual motion." ' ' Is perpetual motion pos- 
 
90 DYNAMICS. 
 
 sible?" has been often asked. The answer is simple, — Yes, more than 
 possible, necessary, if no force interferes to prevent. What has a person 
 to do who would establish perpetual motion? Isolate a moving body 
 from interference of all external forces, such as gravity, friction, and 
 resistance of the air. Can the condition be fulfilled? 
 
 In consequence of its utter inability to put itself in motion or 
 to stop itself, every body of matter tends to remain in the state 
 that it is in with reference to motion or rest ; this inability is 
 called inertia. Evidently the term ought never to be employed 
 to denote a hindrance to motion or rest. The First Law of 
 Motion is often appropriately called the Law of Inertia. 
 
 IX. SECOND LAW OF MOTION, AND APPLICATIONS. 
 
 If a person wished to describe to j-ou the motion of a ball 
 
 struck by a bat, he would be obliged to tell you three things : 
 
 (1) where it started, (2) in what direction it moved, and (3) hoiv 
 
 ^. , far it went. These three essential 
 
 Tip:. 70. •' 
 
 elements may be represented graphi- 
 cally by lines. Thus, suppose balls 
 at A and D (Fig. 70) to be struck 
 by bats, and that they move respec- 
 tively to B and E in one second. Then the points A and D are 
 their startiug-points ; the lines AB and DE represent the direc- 
 tion of their motions, and the lengths of the lines represent both 
 the distances traversed and the relative intensities of the forces 
 applied. In reading, the direction should be indicated by the 
 order of the letters, as AB and DE. 
 
 Let a force whose intensity may be represented numerically 
 by 8 (e.^., S^), acting in the direction AB (Fig. 71), be applied 
 continuously to a ball starting at A, and suppose this force capa- 
 ble of moving it to B in one second ; now, at the end of the second 
 let a force of the intensity 4, directed at right angles to the direc- 
 tion of the former force, act during a second, — it would move 
 the ball to C. If, however, when the ball is at A, both of these 
 forces should be applied at the same time, then at the end of a 
 
COMPOSITION OF FORCES. 91 
 
 Fig. 71. 
 
 second the ball will be found at C. Its path will not be AB nor 
 
 AD, but an intermediate one, 
 
 AC. Still, each force produces in 
 
 effect its own separate result, 
 
 for neither alone would carry it to 
 
 C, but both are required. Hence, 
 
 the 
 
 § 69. Second law of motion. 
 
 — A given force has the same effect 
 
 ill producing motion, whether the 
 
 body on which it acts is in motion or at rest; lohetlier it is acted 
 
 upon by that force alone, or by others at the same time. 
 
 § 70. Composition of forces. — It is evident that a single 
 force, applied in the direction AC (Fig. 71), might produce the 
 same result that is produced by the two forces AB and AD. 
 Such a force is called it resultant. A resultant is a single force, 
 that may be substituted for tiuo or more forces, and produce the 
 same result that the combined forces produce. The several forces 
 that contribute to produce the resultant are called its components. 
 When the components are given, and the resultant required, the 
 problem is called composition of forces. The resultant of two 
 forces acting at an angle to each other is always a diagonal of a 
 parallelogram, of which the components form two adjacent sides. 
 Thus, the lines AD and AB represent respectively the direction 
 and relative intensity of each component, and AC represents 
 the direction and intensity of the resultant. 
 
 The numerical value of the resultant may be found by com- 
 paring the length of the line A C with the length of either A B 
 or AD, whose numerical values are known. Thus, AC is 2.23 
 times AD; hence, the numerical value of the resultant AC is 
 4 X 2.23 = 8.92. 
 
 When the components act at right angles to each other, as in 
 Figure 71, the resultant divides the parallelogram into two equal 
 right-angled triangles ; and the intensity of the resultant may be 
 
92 DYNAMICS. 
 
 found hy calculating the hypothenuse, having two sides of either 
 triangle given. Thus, V4^ + 8^= 8.9+ the numerical value of 
 the resultant AC. 
 
 Copy upon paper and find the resultant of the components 
 AB and AC, in each of the four diagram? in Figure 72. Also 
 
 Fig. 72. 
 
 assign appropriate numerical values to each component, and find 
 the corresponding numerical value of each resultant. 
 
 When more than two components are given, find the resultant 
 
 of any two of them, then of this resultant and a third, and so on 
 
 till every component has been used. Thus, in Figure 73, AC is 
 
 „ ,„ the resultant of AB and AD, 
 
 Fig. 73. ' 
 
 and AF is the resultant of AC 
 and AE, i.e., of the three forces 
 AB, AD, and AE. (Invent 
 several problems similar to this, 
 in which three, four, or more 
 forces are to be combined, and 
 work out the results.) 
 
 Generally speaking, a motion 
 may be tlie result of any number 
 of forces. When we see a body in motion, we cannot determine 
 by its behavior how many forces have concurred to produce its 
 motion. 
 
 § 71. Resolution of forces. — Assume that a ball moves a 
 certain distance in a certain direction, A C (Fig. 74) , and that 
 one of the forces that produces this motion is represented, in 
 intensity and direction, by the line AB; what must be the 
 
RESOLUTION OF FORCES. 
 
 93 
 
 intensity and direction of the other force? Since AC is the 
 resultant of two forces acting at an angle to each other (§ 70) , 
 it is the diagonal of a paral- 
 lelogram of which AB is one ^" ^*" 
 
 of the sides. From C, draw 
 CD parallel and equal to 
 BA, and complete the par- 
 allelogram by connecting 
 the points B and C, and A 
 and D. Then, according to the principle- of composition of 
 forces, AD represents the intensity and direction of the force 
 which, combined with the force AB, would move the ball from 
 A to C. The component AB being given, no other single force 
 than AD will satisfy the question. 
 
 Had the question been, What forces can produce the motion 
 AC? an infinite number of answers might be given. In a like 
 manner, if the question were, "What numbers added together 
 will produce 50? the answer might be 20 + 30, 40+10, 20 + 
 20+10, and so on, ad infinitum; but if the question were, 
 What number added to 30 will produce 50? only one answer 
 could be given. 
 
 Experiment. Verify the preceding propositions in the following 
 manner : From pegs A and B 
 (Fig. 75), in the frame of a 
 blackboard, suspend a known 
 weight W, (say) 10 pounds, by 
 means of two strings con- 
 nected at C. In each of these 
 strings insert dynamometers' 
 X and y. Trace upon the black- 
 board short lines along the 
 strings from the point C, to 
 indicate the direction of the 
 two component forces ; also 
 trace the line CD, in continuation of the line WC, to indicate the 
 direction and intensity of the resultant. Remove the dynamometers, 
 
 ' Dynamometer, force-metisurer. The most common form is a spring balance. 
 
94 DYNAMICS. 
 
 extend the lines (as Ca and C6), and on these construct a parallelogram, 
 from the extremities of the line C D regarded as a diagonal. It will 
 be found that 10: number of pounds indicated by the dynamometer 
 a; : : C D : Ca ; also that 10 : number of pounds indicated by the dyna- 
 mometer y :: CD: C6. Again, it is plain that a single force of 10 
 pounds must act in the direction C D to produce the same result that is 
 produced by the two components. Hence, when two sides of a parallelo- 
 gram represent the intensity and direction of two component forces, the 
 diagonal represents the resultant. Vary the problem by suspending the 
 strings from different points, as E and P, A and F, etc. 
 
 § 72. Composition of parallel forces. — If the strings C A 
 and CB (Fig. 75) are brought near to each other, as when sus- 
 pended from B and E, so that the angle formed by them is 
 diminished, the component forces, as indicated b3' the dyna- 
 mometers, will decrease, till the two forces become parallel, 
 when the sum of the components just equals the weight W. 
 Hence, (1) two or more forces applied to a body act to the greatest 
 advantage when they are parallel, and in the same direction, in 
 which case their resultant equals their sum. 
 
 On the other hand, if the strings are separated from each 
 other, so as to increase the angle formed by them, the forces 
 necessary to support the weight increase until they become ex- 
 actly opposite each other, when the two forces neutralize each 
 other, and none is exerted in an upward direction to support the 
 weight. If the two strings are attached to opposite sides of the 
 weight (the weight being supported by a third string), and 
 pulled with equal force, the weight does not move. But if one 
 is pulled with a force of 15 pounds, and the other with a force 
 of 10 pounds, the weight moves in the direction of the greater 
 force ; and if a third dynamometer is attached to the weight, on 
 the side of the "weaker force, it is found that an additional force 
 of 5 pounds must be applied to prevent motion. Hence, (2) 
 when two or more forces are applied to a body, they act to greater 
 disadvantage the farther their directions are removed from one 
 another; and the result of parallel forces acting in opposite dWec- 
 tions is motion in the direction of the greater force, proportionate 
 to their difference. 
 
COUPLE. 
 
 96 
 
 Fig. 76. 
 
 When parallel forces are not applied at the same point, the 
 question arises, What will be the point of application of their 
 resultant? To the opposite extremities of a bar AB apply two 
 sets of weights, which 
 shall be to each other as 
 3:1. The resultant is a 
 single force, applied at 
 Some point between A 
 and B. To find this 
 point it is only necessary 
 to find a point where a single force, applied in an opposite 
 direction, will prevent motion resulting from the parallel forces ; 
 in other words, to find a point where a support may be applied 
 so that the whole will be balanced. That point is found by trial 
 to be at the point C, which divides the bar into two parts so 
 that AC : CB : : 1 : 3. Hence, (8) when two parallel forces act 
 upon a body in the same direction, the distances of their points of 
 application from the point of application of their resultant are 
 inversely as their intensities. 
 
 The dynamometer E indicates that a force equal to the sum 
 of the two sets of weights is necessary to balance the two forces. 
 A force whose effect is to balance the effects of several compo- 
 nents is called an equilibrant. The resultant of the two com- 
 ponents is a single force, equal 
 
 to their sum, applied at C in the '- 
 
 direction CD. 
 
 § 73. Couple. — If two equal, 
 parallel, and opposite forces are 
 applied to opposite extremities of 
 a stick AB (Fig. 77), no single 
 force can be applied so as to keep the stick from moving ; there 
 will be no motion of translation, but simply a rotation around 
 its middle point C. Such a pair of forces, equal, parallel, and 
 opposite, is called a couple. 
 
96 DYNAMICS. 
 
 PROBLEMS, ETC. 
 
 1. A man and a boy, grasping opposite ends of a pole S" long, sup- 
 port thereon a weight of 50^ between them. Where should the weight 
 be placed that the boy may support 20''? 
 
 2. If the weight were placed 40™ from the man, how much would 
 each support? 
 
 3. Suppose that a boat is headed directly across a river half a mile 
 wide, and is rowed with a velocity that would land it upon the opposite 
 shore in half an hour, if there were no current ; but the current carries 
 the boat down the stream at the rate of one mile an hour. Where will 
 the boat land? 
 
 4. How far will it travel? 
 
 6. How long will it be in crossing the river? 
 
 6. A ship is sailing due south-east at the rate of 10 miles per hour; 
 what is its southerly velocity ? 
 
 7. Find, both by construction and calculation, the intensity of two 
 forces, acting at right angles to each other, that will support a weight 
 of 15 pounds. 
 
 8. Verify the results with dynamometers. 
 
 X. OTHER APPLICATIONS OP THE SECOND LAW OF MO- 
 TION. —CENTER OF GRAVITY. 
 
 Let Figure 78 represent any body of matter ; for instance, a 
 
 stone. Every molecule of the body is acted upon by the force 
 
 Fig. 78. ^^ gravity ; the intensity of this force is 
 
 ^^«^k measured by the weight of the molecule. 
 
 ^nf^W ^ ^Ik '^^^ forces of gravity of all the molecules 
 
 ^^ p/4^rt(M form a set of parallel forces acting verti- 
 
 y^4^^^^/f0fr\ cally downward, the resultant of which 
 
 equals their sum, and has the same direction 
 
 as its components. The resultant has a 
 
 definite point of application in whatever 
 
 position the body may be, and this point 
 
 is called its center of gravity. The center 
 
 of gravity {e.g.) of a body is, therefore, the point of application 
 
 of the resultant of all these forces; and for many purposes the 
 
 whole weight of the body may be supposed to be concentrated at 
 
 its center of gravity. Hence mathematicians, by the pla^e of a 
 
 body, usually mean that point where the c. g. is situated. 
 
CENTEB OF GRAVITY. 97 
 
 Let Gr in the figure represent this point. For many practical 
 purposes, then, we may consider that gravity acts only upon this 
 point, and in the direction GF. If the stone falls freely, this 
 point cannot, in obedience to the first law of motion, deviate 
 from a vertical path, however much the body may rotate during 
 its fall. Inasmuch, then, as the e.g. of a falling body always 
 describes a definite path, a line G- F that represents this path, 
 or the path in which a body supported tends to move, is called 
 the line of direction. 
 
 It is evident that if a force equal to its own weight and 
 opposite in direction is applied to a body anywhere in the line 
 of direction (or its continuation), this force will be the equi- 
 librant of the forces of gravity ; in other words, the body sub- 
 jected to such a force is in equilibrium, and is said to be sup- 
 ported, and the equilibrant is called its supporting force. To 
 support any body, then, it is only necessary to provide a support 
 for its center of gravity. The supporting force must be applied 
 somewhere in the line of direction, otherwise the body will fail. 
 
 Experiment. — Place a stick of wood, two meters long, horizontally 
 across the tip end of a finger. When you succeed in getting the finger 
 directly under its e.g., it will rest, but not- till then. The difficulty of 
 poising a book, or any other object, on the end of a finger, consists 
 wholly in keeping the support under the center of gravity. 
 
 Figure 79 represents a toy called a "witch," consisting of a 
 cylinder of pith terminating in a Pig 79 
 
 hemisphere of lead. The toy will not 
 lie in the position shown in the figure 
 on a horizontal surface ab, because 
 the support is not applied immediately 
 under its e.g. at G ; but, when placed horizontally, it immedi- 
 ately assumes a vertical position. It appears to the observer 
 to rise ; but, regarded in a mechanical sense, it really falls, be- 
 cause its e.g. , where all the weight is supposed to be concen- 
 trated, takes a lower position. 
 
98 DYNAMICS. 
 
 Whether a body mil stand or fall depends upon whether or not 
 its line of direction falls within its base. The base of a body is 
 not necessarily limited to that part of the under surface of a body 
 that touches its support. For example, place a string around 
 the four legs of a table close to the floor : the rectangular figure 
 bounded by the string is the base of the table. (What is the 
 base of a man when standing on one foot? on two feet?) 
 
 § 74. How to find the center of gravity of a body. — 
 Experiment. Attach a string to a potato by meaus of a tack, as in 
 Figure 80, and suspend from the hand. When the potato comes to rest 
 yig_ 80. there will be an equilibrium of forces, and 
 
 the e.g. must be in the same line with the 
 equilibrant of gravity ; hence, if a knitting- 
 needle is thrust vertically through the po- 
 tato from a, so as to represent a continua- 
 tion of the vertical line oa, the e.g. must 
 lie somewhere in the path an made by the 
 needle. Suspend the potato from some 
 other point, as 6, and a needle thrust verti- 
 cally through the potato from 6 will also 
 pass through the e.g. Since the e.g. lies 
 in both the lines aii and 6s, it must be at c, 
 their point of intersection. It will be found that, from whatever point 
 the potato is supported, the point c wiU always be vertically under the 
 point of support. On the same principle the e.g. of any body is found. 
 But the eg; of a body may not be coincident with any particle of the 
 body; for example, the e.g. of a ring, a hollow sphere, etc. 
 
 § 75. Three states of equilibrium. — The weight of a 
 body is a force tending downward ; hence, a body tends to as- 
 sume a position such that its e.g. will be as low as possible. 
 
 Experiment 1. Try to support a ring on the end of a stick, as at 
 6 (Fig. 81). If you can keep the support exactly under the e.g. of the 
 ring, there will be an equilibrium of forces, and the ring will remain at 
 rest. But if it is slightly disturbed, the equilibrium will be destroyed, 
 and the ring will fall. Support it at o ; in this position its e.g. is as 
 low as possible, and any disturbance will raise its e.g. ; but, in conse- 
 
STABILITY OP BODIES. 
 
 99 
 
 Fig. 81. 
 
 quence of the tendency of the e.g. to get as low as possible, it will 
 quickly fall back into its original position. 
 
 A body is said to be in stable equilibrium, if its position is 
 such that a disturbance would raise its 
 e.g., since in that event it would tend to 
 return to its original position. On the 
 other hand, a body is said to be in un- 
 stable equUibrium when a disturbance 
 would lower its e.g., since it would not 
 return to its original position. 
 
 A body is said to be in neutral or in- 
 different equilibrium when it rests equally 
 well in any position in which it may be 
 placed. A sphere of imiform density, 
 resting on a horizontal plane, is in neutral equilibrium, because 
 its e.g. is neither raised nor lowered by a change of base. Like- 
 wise, when the support is applied at the e.g., as when a wheel 
 is supported by an axle, the body is in neutral equilibrium. 
 
 It is evident that, if the e.g. is below the support, as in the last 
 experiment with the ring, the equilibrium must be stable; but, as 
 in Figure 79, a body may be in stable equilibrium, though its 
 e.g. is above the point of support. (When is this possible ?) 
 
 It is difficult to balance a lead-pencil on the end of a finger ; 
 but by attaching two knives to it, as in Figure 82, 
 the e.g. may be brought below the support, and it 
 may then be rocked to and fro without falling. 
 
 Fig. 82. 
 
 § 76. Stability of bodies. — The ease or diffi- 
 culty with which bodies supported at their bases are 
 overturned depends upon the bight to which their 
 e.g. must be raised in overturning them. The let- 
 ter c (Fig. 83) marks the position of the e.g. of each of the four 
 bodies A, B, C, and D. To turn any one of these bodies over, 
 its e.g. must pass through the arc ci, and be raised through the 
 hight ai. By comparing A with B, and supposing them to be 
 
100 DYNAMICS. 
 
 of equal weight, we leam that of two bodies of equal MgM and 
 weight, the e.g. of that body which has the larger base must be 
 raised higher, and is, therefore, overturned with greater difficulty. 
 A comparison of A and C, supposing them to be of equal 
 weight, shows that when two bodies have equal bases and weights, 
 the higher body is more easily overturned. D and C have equal 
 bases and bights, but D is made heavy at the bottom, and this 
 lowers its c;g. and gives it greaier stability. 
 
 Fig. 83. 
 
 QUESTIONS. 
 
 1. Where is the e.g. of a box? 
 
 2. Why is a pyramid a very stable structure ? 
 
 3. What is the object of ballast in a vessel ? 
 
 4. State several ways of giving stability to an inkstand? 
 
 6. (a) In what position would you place a cone on a horizontal 
 plane, that it may be in stable equilibrium ? (6) That it may be in neu- 
 tral equilibrium ? (c) That it may be in unstable equilibrium ? 
 
 6. In loading a wagon, where should the heavy luggage be placed ? 
 Why? 
 
 7. Why are bipeds slower in learning to walk than quadrupeds ? 
 
 8. Why is mercury placed in the bulb of a hydrometer ? 
 
 9. How will a man rising in a boat affect its stability ? 
 
 10. Which is more liable to be overturned, a load of hay or a load of 
 stone of equal weight ? 
 
 11. (a) How would you place a book upon a table, that it may be in 
 stable equilibrium ? (6) That it may be in unstable equilibrium? 
 
CUBVILINEAB MOTION. 101 
 
 XI. OTHER APPLICATIONS OF THE SECOND LAW OF 
 MOTION. — CURVILINEAR MOTION. 
 
 According to the first law of motion, everj' moving body pro- 
 ceeds in a straight line, unless compelled to depart from it by 
 some external force. If the external force is continuous, i.e., 
 acts at every point, the direction is changed at every point, and 
 the result is a curvilinear motion; and if the force is constant, 
 and acts at right angles to the path, the curve becomes a circle. 
 
 Thus, suppose a ball at A (Fig. 84) , suspended by a string from a 
 point d, to be struck by a bat, In a manner that would cause it to move 
 in the direction Ao. At the same time it is restrained from taking that 
 path by the tension of the string, which 
 
 operates like a force drawing It toward Fig. 84. 
 
 d. It therefore takes, In obedience to 
 the two forces, an intermediate course 
 toward c. At c its motion is in the di- 
 rection en, in which path it would move, 
 but for the string, in accordance with 
 the first law of motion. Here, again, it 
 is compelled to take an intermediate 
 path toward e. Thus, at every point, 
 the tendency of the moving body is to 
 preserve the direction it has at that 
 point, and consequently to move in a 
 straight line. The only reason it does 
 
 not so move, is that it is at every point forced from its natural path 
 by the pull of the string. But if, when the ball reaches the point i, 
 the string is cut, the ball, having no force operating to change its mo- 
 tion, continues in the direction in which it is moving at that point; 
 i.e., in the direction ih, which is a tangent to Its former circular path. 
 
 This tendency of a body moving in a curvilinear path to fly 
 off in a straight line has been en-oneously attributed to a sup- 
 posed "centrifugal force," which is constantly urging it away 
 from the center, its escape being prevented only by a force 
 pulling it toward the center. 
 
 Centrifugal force has in reality no existence ; the results that 
 
102 DYNAMICS. 
 
 are commonly attributed to it are due entirely to the tendencj' 
 of moving bodies to move in straight lines in consequence of 
 tlieir inertia. If a moving body is to describe a curvilinear 
 path, a force called a centri23etal force must be constantly applied 
 to it at an angle to its otherwise straight path. [We shall make 
 use of the expression centrifugal force for want of a better one, 
 and because it has obtained universal currencj'.] 
 
 The greater the velocitj' of the moving body, the greater must 
 be the force applied to produce a given departure from a straight 
 line. This may be shown by suspending a weight to a dyna- 
 mometer, and swinging them about the hand. If, when 30 
 revolutions are made in a minute, the force, as indicated by the 
 d3-namometer, is 4 pounds, then, on doubling its velocity, the 
 force will be increased to 16 pounds. If the weight is doubled 
 and the velocity remains the same, this force will be doubled. 
 Hence, to produce circular motion, the centripetal force must he 
 increased as the square of the velocity increases, and as the mass 
 increases. 
 
 The farther a point is from the axis of motion,' the farther it 
 has to move during a rotation, consequently the greater its 
 velocity. , Hence, bodies situated at the earth's equator liave 
 the greatest velocity, due to the earth's rotation, and consequenth- 
 the greatest tendency to fly off from the surface, the effect of 
 which is to neutralize, in some measure, the force of gravity. It 
 is calculated that a body weighs about -j^-g- less at the equator than 
 ;at either pole, in consequence of the greater centrifugal force at 
 the former place. But 289 is the square of 17 ; hence, if the 
 earth's velocity were increased seventeen-fold, objects at the 
 equator would weigh nothing. 
 
 We have also learned (page 22) that a body weighs more at 
 the poles in consequence of the oblateness of the earth. This 
 is estimated to make a difference of about ^^. Hence, a body 
 will weigh at the equator about ^ + ^^ = y^^ less than at the 
 poles. 
 
 ' A.rh, 1111 imaginary straight line passing through a body about which It rotates. 
 
QUESTIONS. 
 
 103 
 
 Experiment. Arrange some kind of rotating apparatus, e..g., A, 
 Figure 85. Suspend a skein of tliread a by a string, aud rotate ; it 
 assumes the shape of the oblate spheroid a'. This illustrates the 
 probable method by which the earth, on the supposition that it was 
 once in a fluid state, assumed its present spheroidal state. (Explain.) 
 Suspend a glass fish aquarium e, about one-teuth fuU.of colored water, 
 and rotate. The liquid gradually leaves the bottom, rises, and forms an 
 
 equatorial ring within the glass. Pass a string tlirougli the longest 
 diameter of an onion c, and rotate; the onion gradually changes its 
 position so as to rotate on its shortest axis. (Explain.) A chain 6 as- 
 sumes on rotation a similar position. 
 
 QUESTIONS. 
 
 1. Why does not the sphere d (Fig. 85) change its position when 
 rotated? 
 
 2. Why does the earth rotate on its shortest axis? 
 
 3. State the various facts illustrated in the act of slinging a stone. 
 
 4. (a) When will water and mud fly oflf from the surface of a re^ 
 volving wheel? (6) Why do they fly off? (c) In what direction do 
 they fly ? 
 
 6. What is the force that keeps the earth and the other planets in 
 their orbits? 
 
 6. How do you account for their curvilinear motion? 
 
104 DYNAMICS. 
 
 XII. OTHER APPLICATIONS OF THE SECOND LAW OF 
 MOTION.— ACCELERATED AND RETARDED MOTION. 
 
 § 77. Accelerated motion or velocity. — So far the only 
 ease of motion under the action of a continuous force that we 
 have studied is that of curvilinear motion, in which the force 
 acts at an angle to the direction of the motion at every point, 
 and so the direction of the force is constantly changing ; but if 
 the motion takes place in the same straight line as that in which 
 the force acts, we shall have one of the cases of varied motion 
 referred to on page 87. 
 
 Even if several men push against a heavy car we may be un- 
 able to recognize any motion for two or three seconds ; but, if 
 they continue to exert force upon the car, it will move with 
 greater and greater velocity until the resisting force (which in- 
 creases with the velocity) becomes equal to that applied b}' the 
 men. This continually increasing velocity is termed acceler- 
 ated velocity. 
 
 The most familiar illustration is that of falling bodies. We 
 are sufficiently aware of the difference in the results that would 
 follow a jump from a fifth-story window and a jump from a 
 first-story window. Inasmuch as the velocity of falling bodies 
 is so great that there is not time for accurate observation during 
 their fall, we must resort to some method of checking their 
 velocity, without otherwise changing the character of the fall. 
 
 Experiment. Take a smooth board (Fig. 86), about 4™ long, and 
 place it so that one end shall be about 4='" higher than the other. Sus- 
 
 . pend within easy view 
 
 Vis 86 
 
 ^^m^^^^^^^^^^^^^^^^^^^^^^^m ^ string (about 1«> long) 
 
 ^^^^^^SSSSSS^^^^^^^^^^^^mM ^^^ ^ ^ pendu- 
 
 ^^^^^^^^^^^^^^^^^^^^^^^^Hl lum. Set it in vibra- 
 ^^^^^^^^^^^^^^^^^^^^^^^^"^ tlon, and, at the instant 
 the ball reaches one extremity of its arc, let a marble begin to roll 
 down the inclined plane. Let another person mark tlie point on the 
 board that the ball reaches at the end of one swing of the pendulum. 
 Repeat the operation several times, and mark the points that it reaches 
 
ACCELERATED MOTION OR VELOCITY. 
 
 105 
 
 at the end of the second and thii'(f swings ; also verify the preceding 
 points by several trials; if there is a difference, take the mean dis- 
 tance between the points obtained at the end of a given swing for an 
 approximate result. If the experiment is conducted with care, it will 
 be found that during the first swing, which we call a unit of time (T), 
 the marble moves through a certain space, which we represent by the 
 expression J k ; during the second unit of time it moves through | k, 
 three times the space that it did in the first unit of time ; and during 
 the third unit of time it moves through | k. 
 
 Arrange the results of your observations in a tabulated form as fol- 
 lows : — 
 
 No. of units of 
 time. 
 
 Total distance 
 passed over. 
 
 Distance passed 
 over in each 
 unit; also av- 
 erageveloalty. 
 
 Increase of ve- 
 locity in each 
 unit, i.e., ac- 
 celeration. 
 
 Velocity at the 
 end of each 
 unit. 
 
 1 
 2 
 
 1 (P) 
 4 " 
 
 3 " 
 
 2 " 
 
 2 a*) 
 
 4 " 
 
 3 
 
 9 " 
 
 5 " 
 
 2 " 
 
 6 " 
 
 4 
 
 16 " 
 
 7 " 
 
 2 " 
 
 8 " 
 
 etc. 
 
 etc. 
 
 etc. 
 
 etc. 
 
 etc. 
 
 The marble, under the influence of gravity, starts from a 
 state of rest, and moves through one space in a unit of time. 
 Gravity, continuing to act, accomplishes no more nor less dur- 
 ing any subsequent unit of time. But the marble moves through 
 three spaces during the second unit ; hence, two of the spaces 
 must be due to the motion it had acquired during the first unit. 
 In other words, if the action of gravity were suspended at the 
 end of the first unit, the marble would still move on, and would 
 pass through two spaces during the second unit. It therefore 
 has at the end of the first unit a velocity (V) of two spaces (k) . 
 But it started from a state of rest ; hence the constant action of 
 gravity causes, during the first unit, an acceleration of velocity 
 equal to two spaces {h) ; and it causes the same acceleration 
 during every subsequent unit. The distance k is called the ac- 
 celeration due to the constant force. A body impelled by a single 
 constant force, and encountering no resistances, always Jias a 
 uniformly accelerated motion. 
 
106 DYNAMICS. 
 
 § 78. Formulas for uniformly accelerated motion. — 
 If we represent the distance traversed during a given unit of 
 time by s, and the total distance the body has accomplished 
 from the outset to the end of a given unit of time by S, we have 
 the following formulas for solving problems of uiuformly accel- 
 erated motion • — 
 
 (1) V=(Jix2T) = A:T. 
 
 (2) s = ik (2T-1). 
 
 (3) S = jfeTS or S = ij/T'. (See §79.) 
 
 § 79. Velocity of a falling body independent of its 
 mass and kind of matter. — If we grasp a coin and a feather 
 between the thumb and finger, and release both at the same in- 
 stant, the coin will reach the floor first. It would seem as 
 though a heavy body falls faster than a light bodJ^ Galileo was 
 the first to show the falsity of this assumption. He let drop 
 from an eminence iron balls of different weights : they all 
 reached the ground at the same instant. Hence he concluded, 
 that the velocity of a falling body is independent of its mass. (This 
 celebrated experiment should be repeated by every student.) 
 
 He also dropped balls of wax with the iron balls. The iron 
 balls reached the ground first. Are some kinds of matter affected 
 p. g^ more strongly by gravitation than others ? If a coin and a 
 feather are placed in a long glass tube (Fig. 87), and the 
 air exhausted, and the tube turned end for end, it will 
 be found that the coin and the feather will fall with equal 
 velocities. Hence, gravity attracts all matter alike; but, 
 inasmuch as a wax ball presents, according to the amount 
 of matter in each, more surface for resistance of the arir 
 than an iron ball, it falls more slowly. We conclude, 
 therefore, that all bodies fall with equal velocities in a 
 vacuum. 
 
 When the body falls freely, and the unit of time is one 
 second, we use the letter g instead of k to represent the 
 acceleration. Experiments show that in the latitude of 
 all the Northern States the value of g is 9.8", or about 
 32| ft. ; that is, the velocity gained if the force of gravity acts 
 
RBTAKDBD MOTION. 107 
 
 one second is 9.8"" per second, and the body would fall in the 
 first second 4.9- or 16^ ft. 
 
 § 80. Retarded Motion. — If we reverse the order of the 
 figures in Figure 86, the same diagram will represent the motion 
 of a body rolling upward, or the motion of a body under the influ- 
 ence of a retarding force. The formulas given (§ 78) for find- 
 ing velocities, etc., of bodies having uniformly accelerated 
 motion, may be used for finding velocities, etc. , of bodies having 
 uniformly retarded motion ; but the questions should be so 
 framed as to be an exact converse of the questions to be solved. 
 Thus, if we would find the velocity of a body at the end of the 
 first second, or at the beginning of the second second, thrown 
 upward by a force that would cause it to rise six seconds, we 
 should calculate the velocity that a falling body has at the end 
 of the fifth second, or at the beginning of the sixth second. 
 
 PROBLEMS. 
 
 (Solve these problems in both the metric and the English measures.) 
 
 1. Disregarding tlie resistance of tlie air, what distance will a body 
 fall from a state of rest in five seconds? 
 
 2. What distance will it fall during the fifth second? 
 
 3. What is its velocity at the end of the fifth second? 
 
 4. A stone, dropped from a balloon, strikes the ground in seven 
 seconds. How high is the balloon? 
 
 6. Under the influence of a constant force, a body moves 500"" in a 
 minute. How far will it go in an hour? 
 
 6. What will be its velocity at the end of the first half -hour? 
 
 7. How far will it move during the fifty-ninth minute? 
 
 8. A body falls four seconds ; meantime it is acted on by a constant 
 force which causes it to move in a horizontal direction 2™ in the 
 first second. Where will it strike the ground? 
 
 9. What is its horizontal velocity at the end of the fourth second? 
 
 10. What is its vertical velocity at the end of the fourth second? 
 
 11. With what vertical velocity must a body start that it may ascend 
 three seconds? 
 
 13. How far does it rise during the first second? 
 13. At what point does a ball shot horizontally from a gun begin to i 
 faU? 
 
108 
 
 DYNAMICS. 
 
 § 81. Projectiles. — Experiment. Take a bottomless tin can 
 A (Fig. 88), and connect a rubber tube C, 2"" long, with a glass tube 
 passing through a stopper at B, and insert a short glass tube at D. 
 Keep the can filled with water, bend the lower part of the rubber tube 
 at D, so as to direct the stream at different angles of elevation, and 
 observe the peculiarities of the curves formed by the streams, and the 
 different vertical and horizontal distances reached by each. 
 
 In this experiment j'ou have a miniature representation of the 
 paths of all projectiles,' such as cannon-balls, stones thrown 
 from the hand, etc. The horizontal distance that the projectile 
 attains is called its range or random. Theoretically, the great- 
 est range is obtained at an angle of 45° ; but practically, on 
 account of the resistance of the air, it is at a little less than 40°. 
 
 Fig. 88. 
 
 Every projectile is acted upon by two forces : (1) the force of 
 gravity, and (2) the resistance of the air. It also has a certain 
 velocity and direction at the instant of projection. If this 
 velocity and direction are known, and the resistance of the air is 
 disregarded, the path of a projectile can be determined. Thus, 
 suppose that a projectile is thrown from A (Fig. 89) at an 
 
 » Projectile, a body thrown. 
 
PROJECTILES. 109 
 
 angle of 45°, that it is in the air six units of time, and that the 
 vertical hights reached at the end of the first three units succes- 
 sively, are B, C, and D. Its horizontal motion, if unimpeded, 
 is uniform, and the corresponding points reached in that direc- 
 tion at the same moments are (say) B', C, and D'. Combining 
 these two motions, we obtain the points B", C", and D", reached 
 by the projectile successively, at the end of each of the first three 
 units of time. The force of gravity constantly acting to change 
 its direction, it must describe, during the first three units, the 
 curved line AB"C"D". Since the time of ascent and descent 
 are equal, it must reach its greatest vertical hight at the end of 
 the third unit, when it begins its descent. The path of descent 
 D"E"F"G" is found in a similar manner. The path thus de- 
 scribed is known as a parabolic curve; but, inasmuch as this is 
 practically modified by the resistance of the air, it in reality 
 describes a peculiar path called a ballistic curve. The curve 
 
 Fig. 89. 
 
 D"E"F"G" represents also the path of a projectile thrown from 
 D", in the direction of the line D"G', with a horizontal velocity 
 that it would cause it to reach G' at the end of the third unit of 
 time. 
 
 An excellent verification of the second law of motion is found 
 in the fact that a ball, projected horizontally, will reach the 
 ground in precisely the same time that it would if dropped from 
 a state of i-est from the same hight. That is, any previous 
 motion a body has in any direction does not affect the action 
 of gravity upon the body. 
 
no 
 
 DYNAMICS. 
 
 Experiment 2. Support two iron bars, a and 6 (Fig. 90), bent into 
 the form of a curve, about 3=™ apart, and so situated that a ball n, roll- 
 ing down them, will be discharged from them in a horizontal direction. 
 So connect the wires of an electric battery c with these bars, thatwhile 
 the iron ball n rests upon them the circuit is closed, and the iron ball 
 m is supported by the attraction of the electro-magnet e. Now allow 
 n to roll down the curved path. When it leaves the bars, the circuit is 
 broken, e instantly loses its power to hold m, and m drops. But both 
 balls reach the floor at the same instant. If the horizontal velocity of 
 n is varied, by allowing it to start at different points on the bars, so as 
 to cause it to describe different paths, the two balls will, in every case- 
 acquire exactly equal vertical velocities. 
 
 Fig. 90. 
 
 XIII. OTHER APPLICATIONS OF THE SECOND LAW OF 
 MOTION. — THE PENDULUM. 
 
 Experiment 1. From a bracket fiuspend by strings leaden balls, as 
 in Figure 91. Draw B and C one side, and to different hights, so that 
 B may swing through a short arc, and let both drop at the same instant. 
 C moves much faster than B, and completes a longer journey at each 
 swing, but both complete their swing, or vibration, in the same time. 
 
 Hence, (1) the time occupied by the vibration of a pendulum 
 is independent of the length of the arc. Of only very small arcs 
 
CBKTBR OF OSCILLATION. 
 
 Ill 
 
 may this law be regarded as practically true. The pendulum 
 requires a somewhat longer time for a long arc of vibration than 
 for a short one, but the difference becomes perceptible only when 
 the difference between the arcs is great, and then only after many 
 vibrations. 
 
 Experiment 2. Set all the balls swinginj 
 gether ; the shorter the pendulum, the 
 faster It swings. Make B 1™ long, and 
 F J™ long. Watch in hand, count the 
 vibrations made by B. It' completes 
 just 60 vibrations in a minute ; in other 
 words, it " beats seconds." A pendu- 
 lum, therefore, to beat seconds must 
 be 1™ long (more accurately, .993"", or 
 39.09 in.). Count the vibrations of 
 F ; it makes 120 vibrations in the same 
 time that B makes 60 vibrations. Make 
 G one-ninth the length of B; the for- 
 mer makes three vibrations while the 
 latter makes one, consequently the 
 time of vibration of the former is one- 
 third that of the latter. 
 
 Hence, (2) the time of one vibra- 
 tion of a pendulum varies as the 
 square root of its length. 
 
 only B and C swing to- 
 Fig. 91. 
 
 QUESTIONS AND PROBLEMS. 
 
 1. What would be the effect if B were made twice as heavy as C? 
 Why? 
 
 2. What Is the length of a pendulum that beats half-seconds? Quar- 
 ter-seconds? That makes one vibration in two seconds? That makes 
 two vibrations per minute? 
 
 3. State the proportion that will give the number of vibrations per 
 minute made by a pendulum iO""" long. 
 
 § 82. Center of oscillation. — Experiment l. Connect six 
 balls, at intervals of 15°", by passing a wire through them, after the 
 manner of pendulum A. This forms a campound pendulum composed 
 
112 DYNAMICS. 
 
 of six simple pendulums. Set A and B vibrating; A vibrates faster 
 than B, although their lengths are the same. Why is this? If A were 
 actuated only by the ball /, it would vibrate in unison with B. If the 
 ball a were free, it would move much faster than /; but, as they are 
 constrained to move together, the tendency of a is to quicken the 
 motion of /, and the tendency of / is to check the motion of a. But e 
 is quickened less than /, and d less than e; on the other hand, & is 
 checked by / less than a, and c less than &. It is apparent that there 
 must be some point between a and /, whose velocity is neither quick- 
 ened nor checked by the combined action of the balls above and below 
 it, and where, if a single ball were placed, it would make the same 
 number of vibrations in a given time that the compound pendulum 
 does. Shorten pendulum B, and find the required point. This point 
 is called the center of oscillation. 
 
 Every compound pendulum is equivalent to a simple pendulum, 
 whose length is equal to the distance between the center of oscilla- 
 tion and the point of suspension of the compound pendulum. In- 
 asmuch as the distance between the point of suspension and the 
 center of oscillation determines the rate of vibration, whenever 
 the expression lervgth of pendulum is used, it must be undetstood 
 to mean this distance. Strictly speaking, a simple pendulum is 
 a heavy material point suspended by a weightless thread. Of 
 course such a pendulum cannot actually exist ; but the leaden 
 FiK 92 ^*'^' suspended by a thread, is a near approximation 
 
 I to it. 
 Experiment 2. Suspend on the frame of Figure 91 a lath 
 AB (Fig. 92), l" long, and shorten the pendulum B till 
 it swings in the same period as the lath ; the ball of B 
 marks the center of oscillation of the lath, which is found 
 to be two-thirds the length of the lath below the point 
 of suspension. Attach a pound-weight to the lower end of 
 AB ; its vibrations are now slower, and the simple pendulum 
 B must be lengthened to vibrate in the same time as the lath 
 and weight; hence the center of oscillation of the lath is 
 lowered by the addition of the weight. Move the weight 
 up the lath; the vibrations are quickened. (What is the office of a 
 pendulum bob?) 
 
 Ebcperlmcnt 3. Remove the weight, bore a hole through the lath at 
 
CENTER OF PERCUSSION. 113 
 
 its center of oscillation 0, and, passing a knitting-needle through the 
 hole, invert the lath and suspend it by the needle. The pendulum is 
 now apparently shortened, and we naturally expect that its vibrations 
 will be quicker than when suspended from A. But the part B C now 
 vibrates in opposition to the part C A, rising as it sinks, and sinking as 
 it rises. This tends to check the rapidity of the vibrations of C A, 
 and it is found that the pendulum vibrates in the same time when sus- 
 pended from C as when suspended ftom A. 
 
 TJie point of suspension and the center of oscillation are inter- 
 changeable; in other words, there are always two points in a com- 
 pound pendulum about which it will oscillate in the same time. 
 
 This suggests a practical way of finding the center of oscilla- 
 tion, and the equivalent length of a compound pendulum. For 
 we have only to find another point of suspension from which the 
 pendulum makes the 
 same number of vibra- 
 tions, in a given time, 
 as from its usual point 
 of suspension : that 
 point is its center of 
 oscillation ; and the 
 distance between it and 
 the usual point of sus- 
 pension is, technically 
 speaking, the length of 
 the pendulum. It will 
 be seen that these two points are unequally distant from the 
 center of gravity. 
 
 § 83. Center of percussion. — Experiment. Suspend the 
 lath by a string attached to one of its extremities, and with a club 
 strike it horizontally near its upper extremity. This end of the lath 
 moves in the direction of the stroke (A, Fig. 93), at the same time 
 causing a sudden jerk on the string, which is felt by the hand. Strike 
 the lath in the same direction, near its lower extremity ; the upper end 
 of the lath now moves in a direction opposite to the stroke (B), at the 
 same time causing a similar jerk of the string. Next strike the lath 
 
114 DYNAMICS. 
 
 successively at points higher and higher above its lower extremity ; it 
 is found that the jerk on the string becomes less till the center of oscil- 
 lation is reached, when no pull on the string is felt, and neither end 
 of the lath tends to precede the other, but both move on together (C). 
 The full force of the blow is spent in moving the stick, and none is 
 expended in pulling the string. This point is called the center of per- 
 cussion. 
 
 The center of percussion is coincident with the center of oscilla- 
 tion. It is the point where a blow, given or received, is most 
 effective, and produces the least strain upon the support or axis 
 of motion. The base-ball player soon learns at what point on 
 his bat he can deal the most effective blow to the ball, and at 
 the same time feel the least tingle in his hands. 
 
 § 84. Some useful applications of the pendnlum. — 
 The force that keeps a pendulum vibrating is gravity. Were 
 it not for friction and resistance of the air, a pendulum, once 
 set in motion, would never cease vibrating. Since the force 
 of gravity keeps the pendulum in motion, it follows thkt the rate 
 of vibration of a given pendulum must be determiiled by the 
 intensity of this force. Hence it is apparent, that if the rate 
 of vibration is known, the intensity of the force of gl-avity may 
 be calculated. It is found by experiment that the time of vi- 
 bration vaiHes inversely as the square root of the force of gravity. 
 
 So the pendulum becomes a most serviceable instrument for 
 measuring the intensity of gravity at various altitudes and at 
 different latitudes on the earth's surface. (Compare § 21). It 
 is also the most accurate instrument for measuring time that has 
 been invented. Its value, as a time-measurer, depends upon 
 the absolute uniformity of the rate of vibration as long as its 
 length is constant, and the length of its arc very small. But as 
 heat is ever modifying the dimensions of all visible bodies, 
 various devices have been called into existence by which heat 
 may be made to correct automatically" its own mischief. Clocks 
 that do not have self -regulating pendulums are fast in winter 
 and slow in summer. (How would j'^ou regulate them?) 
 
MOMENTUM. 115 
 
 QUESTIONS. 
 
 1. Where is the center of percussion in a hammer or axe ? Why ? 
 
 2. At what point (disregarding the length and weight of the arm 
 that swings it) should a blow be dealt with a bat of uniform dimen- 
 sions when held in the hand at one extremity ? 
 
 3. What change in the location of the center of percussion is pro- 
 duced by making one end of a bat heavier than the other ? 
 
 4. Which end of a bat, the heavier or lighter, should be held in the 
 hands ? Why ? 
 
 XIV. MOMENTUM.— THIRD LAW OF MOTION. 
 
 § 85. MomentTim. — A small stone dropped upon a cake of 
 ice produces little effect ; a large stone dropped upon the ice 
 crushes it. An empty car in motion is much more easily stopped 
 than a loaded car. We dread the approach of large masses 
 because we instinctively associate with them a large amount of 
 motion or force. It is evident that if two bodies move with the 
 same speed, there is a greater quantity of motion in that which 
 contains the greater quantity of matter, just as there is more 
 heat in a gallon of water than in a pint of water, when both have 
 the same temperature. 
 
 Again, we have a similar dread of masses moving with great 
 velocities. A ball tossed is a different affair from a ball thrown. 
 Our experience, then, teaches us that the quantity of motion^ or, 
 in a word, the momentum a body may have, depends upon its 
 mass and velocity. For example, a large mass, moving slowly, 
 has great momentum, but the same mass will have twice the 
 momentum if its velocity is doubled ; again, a small mass, mov- 
 ing swiftly, has great momentum, but its momentum is increased 
 in proportion as its mass is increased. 
 
 If the motion of a mass weighing 1'', having a velocity of 1"" 
 per second, is taken as a unit of momentum, then a mass weigh- 
 ing 5'', moving with the same velocity, would have a momentum 
 of 5 ; and if the latter mass should have a velocity of 10"" per 
 second, its momentum would be 5x10 = 50. Hence, the nu- 
 merical value of momentum is found by multiplying units of mass 
 
116 DYNAMICS. 
 
 hy units of velocity. There is no name for the unit of momen' 
 turn. We return to this subject on page 123. 
 
 QUESTIONS AND PROBLEMS. 
 
 1. Compare the momenta of a car weighing 60 tons, moving 10 ft 
 per minute, and a lump of ice weighing 5 cwt., at the end of the third 
 second of its fall. 
 
 2. Why are pile-drivers made heavy? Why raised to great hights? 
 
 3. A boy weighing 25^ must move with what velocity to have tiie 
 same momentum that a man has weighing 80^ running at the rate of 
 lO*™ per hour? 
 
 4. A body has a certain momentum after falling through, a certain 
 space. How many times this space must it fall to double its mo- 
 mentum? 
 
 § 86. Third law of motion. — It has been shown (page 88) 
 that motion cannot originate in a single body, but arises from 
 mutual action between two bodies. For example, a man can lift 
 himself by pulling on a rope attached to some other object, but 
 not by his boot-straps, or a rope attached to his feet. When- 
 ever one body receives motion, another body always parts with 
 motion, or is set in motion in an opposite direction ; that is, in 
 every change in regard to motion there are always at least two 
 bodies oppositely affected. 
 
 Experiment. Moat two blocks of wood of unequal masses on 
 water, connecting them by a stretched rubber band. Let go the blocks, 
 and the band will set both in motion, but the smaller block will have 
 the greater velocity. 
 
 A man in a boat weighing one ton pulls at one end of a rope, the 
 other end of which is held by another man, who weighs twice as much 
 as the first man, in a boat weighing two tons : both boats will move 
 towards each other, but in opposite directions ; the lighter boat will 
 move twice as fast as the heavier, but with the same momentum. 
 
 If the boats are near each other, and the men push each other's boats 
 with oars, the boats will move in opposite directions, though with dif- 
 ferent velocities, yet with equal momenta. 
 
 The opposite impulses received by the bodies concerned are' 
 usually distinguished by the terms action and reaction. We 
 
THIRD LAW OF MOTION. 117 
 
 measure these by their momenta. As every force is either a 
 push or a pull (§ 12), and produces equal momenta in two 
 bodies in opposite directions, hence, the 
 
 Third Law of Motion: To every action there is an equal 
 and opposite reaction. 
 
 The application of this law is not always obvious. Thus, the 
 apple falls to the ground in consequence of the mutual attrac- 
 tion between the apple and the earth. The earth does not 
 appear to fall toward the apple. But, allowing that their mo- 
 menta are equal, we are not surprised that the motion of the 
 earth is imperceptible, when we reflect that the velocity of the 
 earth must be as many times less than that of the apple as 
 the mass of the apple is less than that of the earth. (Compare 
 §20.) 
 
 QUESTIONS. 
 
 1. The velocity of the rebound or " kick " of a gun is slight when 
 compared with the velocity of the ball. Why? 
 
 2. In rowing a boat, what are the opposite results of the stress 
 between the oar and the water? 
 
 3. Point out the results of the action and reaction that occur when 
 a person leaps from the ground. 
 
 Fig. 91 
 
 4. If there were no ground or other object beneath him, and he 
 were motionless in space, could he put himself in motion? Why? 
 
 5. A boy, running, strikes his head against another boy's head. 
 Which is hurt? Why? 
 
 6. Suspend two balls of soft putty of equal weight, A and B (Fig. 
 94). Draw A one side, and let it fall so as to strike B. Both tails 
 
118 DTKAMICS. 
 
 will then move on together; with what momentum compared with A's 
 momentum when it strikes B? 
 
 7. What will be the momentum of each ball after A strikes B, com- 
 pared with A's momentum when it strikes B? 
 
 8. How will their velocity compare with A's velocity when it 
 strikes B? 
 
 9. Raise A and B equal distances in opposite directions, and let fall 
 so as to collide. Both balls will instantly come to rest after collision. 
 Show that this result is consistent with the third law of motion. 
 
 10. Substitute, for the inelastic putty balls, ivory billiard balls, which 
 are highly elastic. Let A strike B. Then B goes on with A's origiaal 
 velocity, while A is brought to rest. Show that this result is consis- 
 tent with the third law of motion. 
 
 11. Suspend four ivory balls, C, D, B, and F. Let C strike D. D 
 eventually receives all of C's momentum, and instantly communicates it 
 to E, E to F, and F, having nothing to which to communicate It, moves 
 with C's original velocity. Trace the actions and reactions throughout. 
 
 12. What would happen if the four balls were inelastic? 
 
 § 87. Law of reflection. — Experiment l. Hold D (Fig. 94) 
 firmly in Its place, and allow C to strike it. D being immovable, C's 
 entire momentum is spent in compressing the balls, and, on recovering 
 their shape, C is thrown back to its starting-point at C But in this 
 case the hand exerts as much force to prevent the motion of D as 
 _,. g. would be necessary to project C to C. When 
 
 an elastic body strikes another fixed elastic 
 
 body, it rebounds with its original force. 
 
 Experiment 2. Lay a marble slab A (Fig. 
 95) upon a table, and roll an ivory ball in the 
 line DC, perpendicular to the surface of the 
 slab ; the ball rebounds in the same line to D. 
 Roll the ball in the line B C ; it rebounds in 
 the line C B. The angle BCD, which its for- 
 ward path makes with D C, a perpendicular to the surface struck, is 
 called the angle of incidence. The angle BCD, which its retreating 
 path makes with the same perpendicular, is called the angle of reflection. 
 
 It is found by measurement that these angles are equal when 
 the two bodies are perfectly elastic. This equality is expressed 
 by the Law of Reflection : When the striking body and the body 
 struck are perfectly elastic, tlie angle of reflection is equal to the 
 angle of incidence. 
 
WORK. 119 
 
 XV. WORK AND ENERGY. 
 
 § 88. "Work. — We have learned (page 44) that a force may 
 produce either motion or pressure (or tension), or it may produce 
 both effects at the same time and in the same body. But a force does 
 work, in the sense in wliich this term is used in science, only when it 
 produces motion. A person may support a weight for a time and 
 become weary from the continuous application of force to prevent the 
 weight from falling, or, in other words, to prevent the force of gravity 
 from doing work, but he accomplishes no work, because he effects no 
 change, i.e., causes no motion. The body that is moved is said to have 
 work done upon it; and the body that moves another body is said to do 
 work upon the latter. When the heavy weight of a pile-driver is 
 raised, work is done upon it ; when it descends and drives the pile 
 into the earth, work is done upon the pile, and the pile in turn does 
 work upon the matter In its path. 
 
 Whenever a force causes motion, it does work. A force may act for an 
 indefinite time without doing any work; but whenever a force acts 
 through space, work is done. Force and space (or distance) are essen- 
 tial elements of work, and are naturally the quantities employed in 
 estimating work. A given force acting through a space of one meter 
 will do a certain amount of work ; it is evident that the same force 
 acting through a space of two meters will do twice as much work. 
 Hence the general formula, 
 
 W = FS, (1) 
 
 in which W represents the work done, P the force employed, and S 
 
 the space through which the force acts. 
 
 In case a force encounters resistance, the magnitude of the force 
 
 necessary to produce motion depends upon the amount of resistance. 
 
 Indeed, in cases in which the body having been moved through a 
 
 given space comes to rest in consequence of resistance, the entire 
 
 work done upon the body is often more conveniently determined by 
 
 multiplying the resistance by the space through which it is overcome, and 
 
 our formula becomes by substitution of resistance, R, for the force 
 
 which overcomes it, 
 
 W = RS. (2) 
 
 For example, a ball is shot vertically upward from a rifle in a vacuum ; 
 the work done upon the ball may be estimated by multiplying the 
 average force (diflicult to ascertain) exerted upon it by the space 
 through which the force acts (a little greater than the length of the 
 barrel), or by multiplying the resistance offered by gravity, i.e., its 
 weight (easily ascertained) by the distance the ball ascends. Also, in 
 
120 DYliTAMICS. 
 
 case the motion produced is uniform, the resistance and the force are 
 equal, and it is immaterial which formula is used. When there is no 
 resistance and the only effect is acceleration, as when a body falls 
 freely In a vacuum, we must estimate the work done (in this case by 
 gravity) by the first formula. When it is required to estimate only 
 that part of the work done in producing acceleration, the formulas 
 given on page 124 will be found convenient, work being substituted 
 for energy, inasmuch as both are measured by the same units. 
 
 § 89. Unit of work. — We shall first consider the unit em- 
 ployed when resistance is taken as oue of the elements of work. (In 
 § 96 will be defined the unit usually employed when the force Is 
 employed as a factor of work.) The unit of work adopted by the 
 French is the work done in raising I'' through a vertical hight of 1™. 
 It is called a kilogrammeter (abbreviated ^s^). The English unit of 
 work is that done in raising one pound one foot, and is called a foot- 
 pound. The kilogrammeter is about 7^ (more accurately, 7.233) times 
 greater than the foot-pound. Now, since the work done in raising l"^ 
 1™ high is l''e™, the work of raising it lO" high is IQi'sm, which is the 
 same as the work done in raising 10'' 1™ high; and the same, again, as 
 raising 2^ 5™ high. 
 
 There are many other kinds of work besides that of raising weights. 
 But since, with the same resistance, the work of producing motion in 
 any other direction is. just the same as in a vertical direction, it is 
 easy, in all cases in which the two elements of work (viz., resistance 
 and space) are known, to find the equivalent In work done in raising a 
 weight vertically. By thus securing a common standard for measure- 
 ment of work, we are able to compare any species of work with any 
 other. Por instance, let us compare the work done by a man in sawing 
 through a stick of wood, whose saw must move 10' ' "against an average 
 resistance of 12*, with that done by a bullet in penetrating a plank to a 
 depth of 2'=™ against an average resistance of 200''. Moving a saw 
 10™ against 12'' resistance is equivalent to raising 12'' 10™ high, or 
 doing 120''e™ of work ; a bullet moving 2™ against 200'' resistance does 
 as much work as is required to raise 200'' 2™ high, or 200 x .02 = 4''b™ 
 of work. 120 -H 4 = 30 times as much work done by the sawyer as by 
 the bullet. 
 
 § 90. Rate of doing work. — In estimating tlie total 
 amount of work done, the time consumed is not taken into con- 
 sideration. The work done by a hod-carrier, in carrying 1,000 
 bricks to the top of a building, is the same whether he does it in 
 
POTENTIAL AND KINETIC ENERGY. 121 
 
 a day or a week. But in estimating the power of any agent to 
 do work, as of a man, a horse, or a steam-engine, in other words, 
 the rate at which it is capable of doing work, it is evident that 
 time is an important element. The work done by a horse, in 
 raising a barrel of flour 20 feet high, is about 4000 ft.-lbs. ; 
 but even a mouse could do the same amount of work in time. 
 The unit in which rate of doing work is usually expressed is a 
 horse-power. Early tests showed that a very strong horse may 
 perform 33,000 ft.-lbs. of work in one minute. So 1 horse- 
 power = 33,000 ft.-lbs. per minute = 550 ft.-lbs. per second = 
 about 4570^8" per minute = about 7Q^«^ per second. 
 
 § 91. Energy. — The energy of a body is its capacity of 
 doing work, and is measured by the work it can do. Doing 
 work usually consists in a transfer of motion, or energy, from 
 the body doing work to the body on which work is done. Wher- 
 ever we find matter in motion, whether in the solid, liquid, or 
 gaseous state, we have a certain amount of energy which may 
 often be made to do useful work. 
 
 § 92. Potential and kinetic energy. — Place a stone, 
 weighing (say) 10'', on the floor before you ; it is devoid of 
 energy, powerless to do work. Now raise it, and place it on a 
 shelf (say) 2" high ; in so doing you perform 20''^'" of work on 
 it. As you look at it, lying motionless on the shelf, it appears 
 as devoid of energy as when lying on the floor. Attach one end 
 of a cord 3" long to it, and, passing it over a pulley, wind 2"" 
 of the string around the shaft connected with a sewing-machine, 
 coflfee-mill, lathe, or other convenient machine. Suddenly with- 
 draw the shelf from beneath the stone. It moves, it sets in 
 motion the machine, and you may sew, grind coffee, turn wood, 
 etc., with the power given to the machine by the stone. 
 
 Surely, the work done on the stone in raising it was not lost ; 
 the stone pays it back while descending. There is a very im- 
 portant difference between the stone lying on the floor, and the 
 
122 DYNAMICS. 
 
 stone lying on the shelf : the former is powerless to do work ; 
 the latter can do work. Both are alike motionless, and you can 
 see no difference, except an advantage that the latter has over 
 ih& fovvoBV in position. What gave it this advantage? Work. 
 A tody, then, may possess energy due merely to advantage op 
 POSITION, derived always from work bestowed upon it. So a body 
 at rest is not necessarily devoid of energy. In the stone lying 
 passively on the shelf there exists a power to do work as real as 
 that possessed by the stone which, falling freely, has acquired 
 great velocity. 
 
 We see, then, that energy may exist in either of two widely 
 different states, and yet be as real in one case as in the other. 
 It may exist as actual motion, either visible, as in mechanical 
 motion, or invisible, as in the molecular motions called heat ; or 
 it may exist in a stored-up condition, as in the stone lying on the 
 shelf. In the former case it is called kinetic (moving) or actual 
 energy ; in the latter, it is called potential energy, or energy of 
 
 We are as much accustomed to store up energy for tuture use 
 as provisions for the winter's consumption. We store it when 
 we wind up the spring or weight of a clock, to be doled out 
 gradually in the movements of the machinery. We store it 
 when we bend the bow, raise the hammer, condense air, and 
 raise any body above the earth's surface. 
 
 How, then, is energy stored in a body ? Only at the expense 
 of work done upon it. The force of gravitation is employed to 
 do work, as when mills are driven by the power of falling 
 water ; but the water is first deposited on the hillside by the 
 energy of the sun's heat. Elasticity of springs is employed as 
 a motive power ; but elasticity is due to an advantage of position 
 which the molecules of springs have acquired in consequence of 
 force applied to them. 
 
 We conclude, then, that a body possesses potential energy 
 when, in virtue of work done upon it, it occupies a position of 
 advantage, or its molecules occupy positions of advantage, so that 
 
FORMULA FOR ENERGY. 123 
 
 the energy expended can be at any time recovered by the return 
 of the body to its original position, or by the return of its mole- 
 cules to their original positions. 
 
 §93. Energy contrasted with momentum. — Problem. 
 
 A bullet weighing 308 is shot with a velocity of 98™ per second from a 
 
 gun weighing 4'' ; required the momentum and the energy of both the 
 
 bullet and the gun, and the velocity of the gun. Solution : Using the 
 
 kilogram, the meter, and the second as units, the momentum of the 
 
 ball is .03 X 98 = 2.94 units. If the ball were shot vertically upward, 
 
 98 
 its velocity would diminish 9.8™ per second ; so it would rise -— = 10 
 
 9.8 
 
 seconds, and, therefore, before its energy is expended, to a hight 
 of (§ 78) 4.9"" X 10' = 490'>'. Hence, its energy at the outset is 
 .03x490= 14.7*8™. Similarly for the gun, by the third law of mo- 
 tion its momentum must be just the same as that of the ball, 2.94 
 units; its velocity is therefore 2.94 -^ 4 = .735™ per second. Then 
 
 735 
 T=: ^ — = .075 second ; the hight (supposing the gun to be raised verti- 
 9.8 
 
 cally by the impulse received) = 4.9 X .075' = .02766" ; and its energy 
 
 = 4 X .02766 = .1102*8". 
 
 While, therefore, the momenta generated in the two bodies by the 
 
 14 7 
 burning of the powder are equal, the energy of the bullet is — '— = 133| 
 
 times that of the gun. (Why are the effects produced by the bullet 
 more disastrous than those produced by the recoil of the gun?) 
 
 § 94. Formula for energy. — We can find, as in the above 
 
 example, to what vertical hight a body having a given velocity 
 
 would rise, and thus in all cases determine its energy ; but a 
 
 formula may be obtained which will give the same result with 
 
 less trouble: thus, substituting g for Je in Formula 1 (§78), 
 
 V = gT; hence, y y2 
 
 T = -,orT2=^- 
 9 9" 
 
 Again, S = ^gT' ; substituting the value of T^ in this equation, 
 
 we have v^ v^ 
 
 I 9 ^9 
 
124 DYNAMICS. 
 
 But energy = WS (weight into hight) ; substituting for S in 
 this equation its value, we have, 
 
 (1) Energy = ■^—• 
 
 Farther on, we shall see thatW = Mg'; substituting for "W in 
 the last equation its value, we have, also, 
 
 (2) Energy = ^. 
 
 It is evident that, wlien the weight (W) or mass (M) of a body 
 remains the same, its energy is proportional to the square of its 
 velocity, while its momentum, as we have learned, is proportional 
 to its velocity. In other words, the effect of increasing the velocity 
 of a moving body would seem to be to increase its working power 
 much more rapidly than its momentum-. Is this practically true? 
 
 Experiment. Fill an ordinary water-pail with moist clay. Let a 
 leaden bullet drop upon the clay from a hight of .S". Then drop the 
 same bullet from a hight of 2°", or four times the former hight, in order 
 that it may acquire twice the velocity. In the latter case it penetrates 
 to four times the depth that it did in the former. 
 
 So it appears that the energy of a moving body varies, not as 
 its velocity, but as the square of its velocity. Doubling the 
 velocity multiplies the energy fourfold ; trebling the velocity 
 multiplies it ninefold, and so on ; but the corresponding mo- 
 mentum is multiplied only twofold, threefold, etc. A bullet 
 moving with a velocity of 400 feet per second, will penetrate, 
 not twice, taut four times, as far into a plank as one having a 
 velocity of 200 feet per second. A railway train, having a 
 velocity of 20 miles an hour, will, if the steam is shut off, con- 
 tinue to run four times as far as it would if its velocity were 10 
 miles an hour. The reason is now apparent why light sub- 
 stances, even so light as air, exhibit great energy when tfieir 
 velocity is great. 
 
 § 95. Measure of a force. — Commonly we measure forces 
 by a spring balance, and say that the force, for instance, with 
 
MBASUKE OF A FORCE. 125 
 
 which a horse draws a wagon is 50'' ; that is, a spring interposed 
 between the horse and the wagon is stretched just as much as it 
 would be by the force of gravity acting on a mass of 50'' hung 
 from the spring. But often it is impossible to measure the 
 force except by the motion it produces. Experience has shown 
 that a useful and accurate measure of a force is the momentum it 
 produces or destroys in a second; if the body is already in mo- 
 tion, we must say the change of momentum produced in a second. 
 
 For example, gravity we know will impart in three seconds, 
 to a body having a mass of (say) 5^, and free to fall, a velocity 
 of 3 X 980°"" per second ; that is, the momentum generated is 
 5 X 3 X 980. Then, by definition above, the measure of the 
 force of gravity on the body is ^"^^ ^^° = 5 x 980. When the 
 centimeter, gram, and second are taken as the units of length, 
 mass, and time respectively, the sj'stem of units of measurement 
 based on them is called the C.G.S. system, and in it the unit 
 of force is called a dyne. 
 
 A dyne is that force which, acting for a second, will give to a 
 gram of matter a velocity of one centimeter per second. In the 
 example above we have a force of 5 X 980 = 4900 dynes. 
 
 We can almost as easily graduate a spring balance to indi- 
 cate forces in dynes as in pounds ; and then we have a unit 
 which is constant wherever we go on the earth or above it. 
 (Compare § 21.) 
 
 The gravity unit of force is the weight of any unit of mass, 
 e.g., a gi'am, kilogi'am, pound, or ton. In distinction from 
 gravity units, the C.G.S. units are called absolute units. Gravity 
 units are easily changed to absolute units ; thus in the Northern 
 States the force of gravity acting upon 1» of matter free to fall 
 will give it an acceleration of velocity of 980™ per second ; hence 
 in these latitudes the gravity unit is equal to 980 absolute units. 
 
 Returning to our example, represent 5«, the mass of the body 
 moved by M ; by g, 980™ per second, the acceleration produced 
 by gravity ; and by W, the weight, or F, the force : then 
 W = F = Mgr. 
 
126 DYNAMICS. 
 
 The equation is a general one ; that is, whenever any two of the 
 three quantities specified are known, the third maj- be computed 
 
 If the force acts, not against gravity, but against resistances 
 considered as constant, such as the forces shown in cohesion, 
 elasticity, etc., the equation will still be true, only g should be 
 replaced by some other letter, as a. 
 
 Now let us learn what is the 
 
 § 96. Measure of the eflfeot of a force. — One measure we 
 know already, — the product of the force into the distance 
 through which it acts ; that is, the work done, or the energy 
 imparted to the body moved, is a measure of the effect of a force. 
 If the force is measured in dynes, and the distance is centi- 
 meters, the work done will be expressed in a C.G.S. unit called 
 an erg. An erg is the worlc done or energy imparted by a force 
 of one dyne working through a distance of one centimeter. Be- 
 sides the erg we have the common gravitation units, the kilo- 
 grammeter, and foot-pound ; that is, we have another measure just 
 as we ma ' have various kinds of measures for common things ; 
 just as, for instance, we may express lengths in inches, meters, 
 or miles ; masses, in grains or pounds, etc. 
 
 Experiment 1. Suspend by a long cord a heavy body, — lO^ or more, 
 — and with a string attached to the body draw it to one side, pulling 
 for two, four, and six seconds, and let go. The longer you pull the 
 greater is the velocity given to the body, provided it is not moved far 
 from its place of rest. 
 
 Experiment 2. Suspend by a string 1™ long a stone whose mass is 
 (say) hK Attach to the stone a No. 36 cotton thread ; this will sup- 
 port about 1"^. Pull the ball slowly to one side; when it has been 
 drawn about 20™ from its place of rest, the thread will break, and the 
 ball will swing back to the other side like a pendulum, and so when it 
 passes through its lowest point it has a definite momentum. 
 
 Attach new pieces of thread, and pull more and more quickly, break- 
 ing the thread each time ; the motion produced is less and less. As 
 the string is straightened the pull on it increases from zero to I'' ; so 
 the average force each time is about the same ; in gravitation units, 
 nearly or exactly ^. Here, as before, with the same force, the momen- 
 tum produced varies as the time during which the force axU. 
 
MEASUEE OF THE EFFECT OP A EOEOE. 127 
 
 But if we use stronger and stronger threads, we may pull more and 
 more quickly than at first, and yet give to the ball just the same mo- 
 mentum as at first; that is, the effect of a greater force acting for a 
 shorter time is to produce the same momentum. 
 
 So far then as our experiments go, they teach that the product 
 of a force into the time it acts, or the momentum produced, is a 
 measure of the effect of a force. We may draw the same conclu- 
 sion from our last equation, F = M.g : multiply both sides by T, 
 the time during which the force acts, and we have FT = Mg'T 
 = MV = Momentum (§ 85). If T equals one second, we see 
 that the momentum of a moving body is the measure of the force 
 that would in one second give it this motion. It is evident 
 that if motion is to be produced by a force acting for a very 
 short time, the force must be enormous. 
 
 We have, then, two measures of the effect of a force, — mo- 
 mentum and energy. The iirst is found by multiplying the force 
 by the time it acts ; the second, by multiplying the force by the 
 space through which it acts. The latter can also be found by 
 multiplying the momentum by one-half the velocity. One is 
 MV ; the other is ^MV^. Which is the correct measure? Both 
 are correct ; so the question now is. Which is the more useful .'' 
 Experience shows that momentum is a useful measure only in 
 cases where the force acts all the time in the line of motion, as 
 in falling bodies, or where it acts for so short a time that the 
 body does not sensibly change its position during the action, as 
 in the cases of a blow, a jerk, collision between balls, etc. 
 Klxperience further shows that energy in all cases gives a useful 
 measure. 
 
 § 97. Summary of mechanical units, and formulas for 
 their determination.' — The following tables show the quanti- 
 ties measured, the unit of each in the C.G.S. system, and the 
 formulas for the determination of the derived quantities : — 
 
 > It la not expected that pupils of the ordinary high school will master this sec- 
 tion; yet they may frequently find It convenient for reference, while the more 
 advanced student cannot fall to be greatly profited by Its careful study. 
 
128 DYNAMICS. 
 
 FUNDAMENTAL QUANTITIES AND UNITS. 
 
 Length (L or S) 1™. 
 
 Mass (M) IK. 
 
 Time (T) 1 sec. 
 
 DERIVED QUANTITIES, UNITS, AND FORMULAS. 
 Velocity (V) = rate of motion ; unit, 1<™ per sec. ; in uniform motion, 
 
 V = |- (1) 
 
 Acceleration (A) = rate of change in velocity ; unit, an increase of 
 velocity in 1 sec. of 1=™ per sec. ; body starting from rest under 
 
 V 
 constant force, A = — • (2) 
 
 Force (F) ; unit, 1 dyne = a force that in 1 sec. imparts to 18 a velocity 
 of 1™ per sec. ; .-. F = MA. (3) 
 
 Work or Energy (E) ; unit, 1 erg = the work done by 1 dyne working 
 through 1™; .-. B = MAS = FS. (4) 
 
 Rate of doing work, or Work Power (P) ; unit, 1 erg per sec. ; 
 P = M§. (5) 
 
 Momentum; unit, is moving with a velocity of 1™ per sec, or that 
 produced by 1 dyne in 1 sec. ; Momentum = M V. 
 
 MV 
 From (2) and (3) we have the very useful equations, F = -=7- and 
 
 FT 
 V=^- (6) and (7) 
 
 A body, mass M, acted upon by the force F, starting ftom rest will 
 
 FT 
 acquire in time T a velocity "V = -^ • The acceleration, which 
 
 from (3) is = TT , is a constant quantity, and the whole space 
 
 passed over will be equal to the time T multiplied by the mean 
 velocity. The latter is one-half the final velocity; hence, mean 
 
 FT F T"* 
 
 V = rr-j:, and S = -T-TTj. (an equation of great importance). (8) 
 To find an expression for the energy of a moving body combine (4) and 
 
 (8): W = yj|-; butFT = MV, .-. E = -^- (9) 
 
 Anywhere in the Northern States, the weight of in = 980 dynes. 
 Ikgm = 98,000,000 ergs ; 1 foot-pound = 13,660,000 ergs. 
 1 horse-power = 447,000,000,000 ergs per min. 
 
 § 98. Transformation of energy. — In the operation of 
 raising the stone (§ 92) , kinetic energy is transformed into poten- 
 
PHYSICS DEFINED. 129 
 
 tial energy. During its descent it is re-transformed into kinetic 
 energy. If, instead of being attached to machinery, and thereby 
 made to do work, the stone is allowed to fall freely, it acquires 
 great velocity. On striking the ground, its motion as a body 
 suddenly ceases, but its molecules have their quivering motions 
 accelerated. Mechanical motion is, thereby, transformed into 
 heat. We shall often have occasion to examine the transforma- 
 tions of energy, as into electric energy, heat, etc. , but never of 
 momentum. We shall study Joule's equivalent (page 174), 
 expressing the relation between the unit of energy, or work, 
 and the unit of heat ; but it is certain that there is no relation 
 between the latter and the unit of momentum. 
 
 § 99. Physics defined. — All physical phenomena consist 
 either alone in transferences of energy from one portion of 
 matter to another, or in both transferences and transformations 
 of energy. Transformations may be from one condition of 
 energy to another, as from kinetic to potential ; or from one 
 phase of kinetic energy to another, as from mechanical motion 
 to heat ; or both may occur, as when the falling stone does 
 work, a part of its energy being expended in producing mechan- 
 ical motion, and a part being transformed into heat, occasioned 
 by friction of the moving parts. 
 
 Physics is that branch of natural science which treats of trans- 
 ferences and transformations of energy. It does not, however, 
 in its usual limitation, include a group of phenomena which occur 
 outside the earth, and also a group whose essential character- 
 istic is an alteration in the nature of the material considered. 
 The study of the former group is the object of Astronomy; of 
 the latter, that of Chemistry. 
 
 QUESTIONS AND PROBLEMS. 
 
 1. Does the energy expended in raising the stones to their places in 
 the Egyptian pyramids still survive? 
 
 2. What kind of energy is that contained in gunpowder? 
 
 3. What transformation of energy takes place in burning coal? 
 
 4. When steam works by expansion, its temperatiu-e is reduced. Why? 
 
130 DYNAMICS. 
 
 5. How much work Is done per hour if 80'' are raised 4™ per minute? 
 
 6. (a) What energy must be Imparted to a body weighing 50e that it 
 may rise i seconds? (6) How many times as much energy must be 
 imparted to the same body that it may ascend 5 seconds? (c) Why? 
 
 7. Compare the momenta, in the two cases given in the last question, 
 at the instants the body is thrown. 
 
 8. How much energy is stored in a body which weighs 50'', at a 
 hight of 80™ above the earth's surface? 
 
 9. How much energy would the same body have if it had a velocity 
 of lOO™ per second? 
 
 10. Suppose it to fall in a vacuum, how much kinetic energy would 
 it have at the end of the fourth second? 
 
 11. If it should fall through the air, what would become of a part of 
 the energy? 
 
 12. A projectile weighing 25'' is thrown vertically upward with an 
 initial velocity of 29.4™ per second. How much energy has it? 
 
 13. What becomes of its energy during its ascent? 
 
 14. (a) Compare the momentum of a body weighing 50*, and having 
 a velocity of 2" per second, with the momentum of a body weighing 
 50B, having a velocity of 100™ per second. (6) Compare their ener- 
 gies. 
 
 15. Which, momentum or energy, will enable one to determine the 
 amount of resistance that a moving body may overcome? 
 
 16. Explain how a child who cannot lift SO'' can draw a carriage 
 weighing 150''. 
 
 17. A car weighing 6000'' is drawn by a horse with a speed of 100™ per 
 minute. The index of the dynamometer to which the horse is attached 
 stands at 40''. (a) At what rate is the horse working? (6) Express 
 the rate in horse-powers. (See § 90.) 
 
 18. A dynamometer shows that a span of horses pull a plow with 
 a constant force of 70''. What power is required to work the plow if 
 they travel at the rate of 3''™ per hour? 
 
 19. What horse-power in an engine will raise 1,350,000'' 5™ in an 
 hour? 
 
 20. How long will it take a 3 horse-power engine to raise 10 tons 50 
 feet? 
 
 21. How far will a 2 horse-power engine raise lOOO*: in 10 seconds? 
 
 22. How much work can a 5 horse-power engine do in an hour? 
 
 23. How long would it take a man to do the same work, the amount 
 of work a man can do in a day being about 90,000'*"? 
 
 24. If you would increase the energy of a moving body fourfold, 
 how much must yon increase its velocity? 
 
USES OF MACHINES. 
 
 131 
 
 Kg. 96. 
 
 XVI. MACHINES. 
 
 § 100. Uses of machines. — Kxperiment l. Obtain from a 
 hardware store two or three pulleys, and arrange apparatus as in Figure 
 96. The dynamometers a and 6 read 4 lbs. each, showing that the 
 power (P) employed to support each weight (W) of 8 lbs. is just 
 one-half of the weight.' If the power applied in each instance is 
 slightly increased, the weights wiU rise. Eaise each of the weights 
 and measure the distances traversed respectively by W and P in each 
 instance. It will be found that the distance that W moves is just one- 
 half the distance that P moves; i.e., if "W rises 2 ft., P must move 4 
 ft. Now, 8 (lbs.) X 2 (ft.) = 16 foot-pounds of work done on W. 
 Again, 4 (lbs.) X 4 (ft.) = 16 foot-pounds of wort performed by P. 
 It thus seems that the work applied by the power is just equal to the 
 
 work done upon the weight. 
 What advantage is derived 
 from the use of the apparatus? 
 It has been proved that no ad- 
 vantage is gained, so far as the 
 amount of work is concerned. 
 But suppose that W Is 400 lbs., 
 and that the utmost power (P) 
 that one man can exert is 200 
 lbs. Then, without this ap- 
 paratus, the services of two 
 men would be required ; where- 
 as one man could raise the 
 weight with the apparatus. 
 The advantage gained in this 
 case would seem to be one of 
 conwnienae. 
 
 Experiment 2. Let P and 
 W of A exchange places. The 
 index of the dynamometer a 
 now reaches 16 lbs. There 
 seems to be in this case a loss 
 of power, for a power of 16 
 lbs. is only able to sustain a weight of 8 lbs. But so far no work 
 has been done. (Why?) Kaise W, and measure the distance trav- 
 ersed respectively by P and W. P moves only 2 ft. for every 4 ft. 
 that W moves. Now, 2 (ft.) X 16 (lbs.) = 32 foot-pounds of work 
 I A small allowance must be made for the weight of the movable puUe^s. 
 
i32 
 
 DYNAMICS. 
 
 done by P. And i (ft.) x 8 (lbs.) = 32 footpounds of work done 
 fipon W. We thus learn that, when the power is employed in doing 
 work, there is really no loss of power in this method of applying the 
 Apparatus. Is there any advantage gained in this case by the use of 
 Apparatus? We found that W moved twice as far, and consequently 
 With twice the velocity, that P moved. 
 
 It thus appears that, if it should be desirable to move a weight with 
 greater velocity than it is possible or convenient for the power to 
 move, it may be accomplished through the mediation of a machine, by 
 applying to it a power proportionately greater than the weight. This 
 apparatus is one of many contrivances called machines, through the medi- 
 ation of which power can be applied to resistance more advantageously 
 flan when it is applied directly to the resistance. Some of the*many 
 advantages derived from the use of machines are : — 
 
 (1) They may enable us to overcome a large resistance with a compara 
 tiilely small power by causing the power to move through a proportionately 
 greater distance, (i.e. with greater velocity) ; or, conversely, they may enable 
 its to secure great velocity (i.e. to do work with great speed) by employing 
 d power proportionately greater than the resistance. 
 
 (2) They may enable us to employ a force in a direction that is more 
 ionvenient than the direction in which the resistance is to be moved. 
 
 Fig. 97. (3) They may enable us to employ other forces 
 
 than our own in doing work; e.g., the strength 
 of animals, the forces of wind, water, steam, 
 etc. (How are the last two uses illustrated in 
 Figure 97 ?) 
 
 § 101. Law of machines. — Let P 
 be the power applied to a machine, p 
 the distance through which it moves in 
 a given time, W the weight moved or 
 external resistance overcome, and w the 
 distance through which it is moved in 
 the same time ; then the mechanical work 
 applied to the machine is Pp {e.g., 
 in kilogrammeters or foot-pounds), 
 and the mechanical work done by 
 the machine is Ww. Now we have 
 learned from the above experiments that (1) Vp ='Ww. 
 
LAW OF MACHINES. 133 
 
 Hence we have for all machines, without exception, the follow- 
 ing general law : The work applied to a machine is equal to the 
 work done by the machine. 
 
 No machine, therefore, creates or increases energy. No ma- 
 chine gives back more energy than is spent upon it. P can be 
 made as small as we please by taking p great enough : in this 
 ease we see that in proportion as power is gained, time, distance, 
 or velocity is lost. On the other hand, W remaining the same, 
 w (the distance traversed by W in a given time, i.e., its velocity) 
 may be increased indefinitely by taking P large enough : in this 
 case, as velocity, time, or ^ace is gained, power is lost. A ma- 
 chine, then, is much like a bank : it pays out no more than it 
 receives. A bank will give you in exchange for a fifty-dollar 
 note fifty one-dollar notes ; or, for fifty one-dollar notes, de- 
 posited successively, it will return to j'ou a fifty-dollar note. In 
 a similar manner, if you apply to a machine a power suflScient 
 to move 50 lbs. 1 ft., you may get from it the ability to move 
 1 lb. 50 ft. ; or, if you apply to a machine a force of 1 lb. suc- 
 cessively through 50 ft. of space, you may get from it the ability 
 to move 50 lbs. through 1 ft. of space. 
 
 In our discussion hitherto we have ignored the internal resist- 
 ances, chiefly due to friction, which exist in every machine. The 
 whole work done by a machine is practically divided into two 
 parts, — the useful part and the wasted part ; the former, ex- 
 pressed as a fraction of the whole, is usually called the efficiency 
 or modulus of the machine. But energy is indestructible. That 
 portion of the visible energy that is apparently destroyed by 
 friction is transformed into heat, which is wasted, so far as the 
 work to be done by the machine is concerned. Let I represent 
 internal work performed in the machine, i.e., the wasted work, 
 and "W w the external work ; then our general formula for 
 machines, as modified in its practical applications, becomes. 
 
 (2) Pp=Ww + I; 
 that is, the work allied to a machine is equal to the effective 
 work, plus the internal work done by the nmchine. So that, so 
 
134 
 
 DTNAJIIICS. 
 
 far from any machine being a source of power, as is sometimes 
 erroneously supposed, no machine practically returns as much 
 power as is applied to it. 
 By division, Formula (1) Pp = Ww becomes 
 
 ^^■> p-«' 
 i.e., weight : power : : the distance through which the power 
 m.oves : the distance through which tJie weight is moved in the 
 „. ^ same time. Prob- 
 
 Flr. 98. 
 
 lems pertaining to 
 machines may gen- 
 erally be solved by 
 Formula (3), and 
 afterwards suitable 
 allowances may be 
 made for the in- 
 ternal work done. 
 Thus, suppose that 
 P (Fig. 99) is 10 
 lbs., and it is re- 
 quired to find what 
 weight (W) it will 
 raise. By experi- 
 ment we find that P 
 travels 8 ft. while 
 W travels 4 ft. 
 Then, x (W) : 10 
 (P) : : 8(p) : 4(w) ; whence a; = 20 lbs. The 20 lbs. in W is just 
 sufficient to balance the 10 lbs. in P ; anything less than 20 lbs. 
 will be raised. 
 
 It is to be observed that, as we saw on page 119, work is not 
 always, or even usually, expended in raising a weight, but in 
 overcoming resistance of any kind ; so we may interpret Formula 
 (3) thus ; resistance : power : : the distance through which the 
 power moves : the distance through which the resistance is over- 
 come. 
 
QTJESTIONS AND PKOBLEMS. 135 
 
 QUESTIONS AND PROBLEMS. 
 
 1. If the power applied, to any machine is 2'', and it moves with a 
 velocity of 10" per second, wif* what velocity can It move a resistance 
 of 10^? To how great a load could it give a velocity of SO" per second? 
 
 2. A power of 50'', moving through a space of 100™, is capable of 
 moving how many kilograms through a space of 2"? What advantage 
 would be gained by the use of the machine ? 
 
 3. Watch the movements of the foot in working the treadle of a 
 sewing-machine, also the movements of the needle in sewing, and 
 determine what mechanical advantage is gained by the machine. 
 
 4. Arrange three levers, as in Figure 98 ; and, calling the distance 
 (o&) of the power from the prop the power-arm of the lever, and the 
 distance (6c) of the weight from the prop the weight-arm, verify by 
 experiment the following special formula for levers -. — 
 
 W_£ _ power -arm 
 P w weight-ftrm 
 
 N.B. — EquIHbrinm must first be established between the two arms of the flrst 
 lever, by placing weights on the short arm. 
 
 5. Ascertain the advantage that may be gained by each lever. 
 
 6. A lever is tS™ long ; where must the prop be placed in order that 
 a power of 2'' at one jig 99 
 
 end may move 4* at 
 the other end? What 
 wiU be the pressure 
 on the prop? 
 
 7. Show that the 
 results obtained in 
 the last problem are 
 consistent with the 
 third law of parallel 
 forces (page 95). 
 
 8. What advantage 
 Is gained by a lever, 
 when its power-arm 
 Is longer than its weight-arm? What, when its weight-arm is longer? 
 
 9. Two weights, of 5'« and 20*, are suspended from the ends of a 
 lever 70™ long. Where must the prop be placed that they may balance ? 
 
 10. What mechanical advantage is gained by a lemou-squeezer? 
 
 11. If P (Fig. 99), weighing 1 lb., is suspended 15 spaces ft-om the 
 fulcrum of the steelyard, what weight (W) suspended 3 similar spaces 
 the other side of the fulcrum will balance it? 
 
136 
 
 DYNAMICS. 
 
 12. How would you weigh out 6 lbs. of tea with the same steelyard? 
 
 13. If the circumference of the axle, Figure 100, is 60™, and the 
 power applied to the crank travels 240™ during each revolution, what 
 power will be necessary to raise the bucket of coal weighing (say) iff^? 
 
 14. How many meters must the power travel (Fig. 100) to raise the 
 bucket from a cavity 10" deep? 
 
 15. (a) In the train of wheels (Fig. 101), If the circumference of 
 
 Fig. xoo. tlie wheel a is 36 in., and that 
 
 of the pinion 6 is 4 in., a power 
 of 1 lb. at P will exert what 
 force on the circumference of 
 the wheel d 1 (6) If the cir- 
 cumference of the wheel d be 
 30 in., and that of the pinion c 
 6 in., the power of 1 lb. at P 
 will exert What force on the 
 circumference of the wheel/? 
 (c) If the circumference of the 
 Wheel /be 40 in., and that of the axle e 8 in., how many pounds in W 
 will be necessary to prevent motion of the train of wheels, when P 
 J^ 101. weighs 1 lb.? (<2) If W has a 
 
 velocity of 5 ft. per second, 
 what will be Fs velocity? 
 
 16. Prepare a special for- 
 mula for the solution of prob- 
 lems pertaining to the wheel 
 and axle. 
 
 17. The weight W (Fig. 
 102), In traversing the in- 
 clined plane AB, only rises 
 through the vertical hight CB, 
 while P must move through a 
 distance equal to AB. Let 
 Ii represent the length of an 
 inclined plane, and H its hight, 
 and prepare a special formula 
 
 for the solution of problems pertaining to the inclined plane. 
 
 18. A skid 12 ft. long rests one end on a cart 3 ft. high, and the 
 other end on the ground. What force must a boy exert while rolling a 
 barrel of flour weighing 200 lbs. over the skid into the cart? 
 
 19. During one revolution a screw advances a distance equal to the 
 
QUESTIONS ANB PROBLEMS. 
 
 137 
 
 distance between two turns of the thread, measured in the direction of 
 the axis of the screw. Suppose the screw in the letter-press, Figure 
 103, to advance J in. at each revolution, and a power of 25 lbs. to bf 
 applied to the circumference of the wheel 6, whose diameter is 14 in. 
 What pressure would be ex- 
 erted on articles placed be- ^" 
 neath the screw. [The cir- 
 cumference of a circle is 
 3.1416 times its diameter.] 
 20. The toggle-joint (Fig. 
 104) is a machine employed 
 where great pressure has to 
 be exerted through a small 
 space, as iu punching and 
 shearing iron, and in print- 
 ing-presses, in pressing the types forcibly against the paper. An 
 
 illustration may be found in th^ 
 joints used to raise carriage-tops. 
 Force applied to the ng. 104. 
 joint c will cause 
 the two linlis ac and 
 be to be straight- 
 ened, or carried for- 
 ward to d, while the 
 guides move through 
 a, distance equal to 
 (ac -I- 6c) — ab. If 
 da = lO™, ab = 98"^, 
 and ac -I- 6c = 100™, 
 then a force of 80s applied at c would exert what average pressure 
 on obstacles in the path of the guides? 
 
 21. Show that the hydrostatic press, page 65, conforms in its oper 
 ation to the general law of machines. 
 
CHAPTER III. 
 MOLECULAR ENERGY. - HEAT. 
 
 XVII. WHAT HEAT IS.— SOME SOURCES OF HEAT. 
 
 In the preceding pages the theory of heat has been several 
 times anticipated ; we are now better qualified to judge of its 
 truth or falsity. 
 
 § 102. Mechanical motion convertible into heat. — Ex- 
 periments. Hold some small steel tool upon a rapidly revolving dry- 
 grindstone; a shower of sparks flies from the stone. Place a ten- 
 penny nail upon a stone and hammer it briskly ; it soon becomes too 
 hot to be handled with comfort, and we may conceive that if the 
 blows were rapid and heavy enough, it might soon become red hot. 
 Rub a desk with your fist, and your coat-sleeve with a metallic but- 
 ton ; both the rubbers and the things rubbed become heated. 
 
 You observe that in every case heat is generated at the ex- 
 pense of work or mechanical motion, i.e., mechanical motion 
 checked becomes heat. "When the brakes are applied to the 
 wheels of a rapidly moving railroad train, its motion is all con- 
 verted into heat, much of which may be found in the wheels, 
 brake-blocks, and rails. The meteorites, or "shooting-stars," 
 which are seen at night passing through the upper air, some- 
 times strike the earth, and are found to be stones heated to a 
 light-giving state. They become heated when they reach our 
 atmosphere, in consequence of their motion being checked by 
 the resistance of the air. 
 
 § 103. Heat convertible into mechanical motion. — 
 Experiment. Take a thin glass flask A, Figure 105, and half fill it 
 with water; fit a cork air-tight' in its neck. Perforate the cork, 
 I A good way to nuike .1 cork air-tight is to soalt it la melted parafline. 
 
HEAT DEFINED. 
 
 139 
 
 Fis. 105. 
 
 Insert a glass tube bent as indicated in the figure, and extend it into 
 the water. Apply heat to the flask ; soon the liquid rises in the tube, 
 and flows from its upper end. 
 
 Here heat produces mechanical motion, and does work in rais- 
 ing a weight in opposition to gravity. Every steam engine is a 
 heat engine. All the power of steam consists 
 in its heat. The steam which leaves the cylin- 
 der of an engine (see page 176), after it has 
 set the piston in motion, is cooler than when 
 it entered, and cooler in proportion to the work 
 done. Furthermore, it will be shown (page 174) 
 that heat and work are so related to each other 
 that a definite quantity of the one is always equal 
 to a definite quantity of the other. 
 
 Now, when the appearance of one thing is so 
 connected with the disappearance of another, 
 that the quantity of the thing produced can be 
 calculated from the quantity of that which dis- 
 appears, we conclude that the one has been 
 foraied at the expense of the other, and that 
 they are only diferent forms of the same thing. 
 We have, therefore, reason to believe that heat is of the same 
 nature as mechanical energy, i.e., it is only another form of 
 kinetic energy. 
 
 § 104. Heat defined. — A body loses motion in communi- 
 cating it (page 88) . The hammer descends and strikes the an- 
 vil ; its motion ceases, but the anvil is not sensibly moved ; 
 the only observable effect produced is heat. Instead of the pro- 
 gressive motion of the hammer as a whole, there is now, accord- 
 ing to the modern view, an increased vibratory motion of the 
 molecules that compose the hammer, — a mere change of motion 
 in kind and locality. Of course, this latter motion is invisible. 
 The conclusion is that heat is molecular motion. A body is heated 
 by having the motion of its molecules quickened, and cooled by 
 
140 MOLECULAR ENERGY. HEAT. 
 
 parting with some of its molecular motion. One body is hotter 
 than another when the average energy of each molecule in it is 
 greater than in the other. 
 
 § 105. Heat generated by chemical action. — Experi- 
 ment. Take a glass test-tube half full of cold water, and pour intp it 
 one-fourth its volume of sulphuric acid. The liquid almost instantly 
 becomes so hot that the tube cannot be held in the hand. 
 
 When water is poured upon quicklime heat is rapidly devel- 
 oped. The invisible oxj-gen of the air combines with the vari- 
 ous fuels, such as wood, coal, oils, and illuminating gas, and 
 gives rise to what we call burning or combustion, by whicli a 
 large amount of heat is generated. In all such cases the heat 
 is generated by the combination or clashing together of mole- 
 cules of substances that have an affinity {i.e., an attraction) 
 for each other. Before their union they are in the condition 
 of a weight drawn up ; while approaching each other, they are 
 like the falling weight ; and when they collide, their motion, 
 like that of the weight when it strikes the earth, is converted 
 into heat. The chemical potential energy of the molecules is 
 converted, in the act of combination, into kinetic energy, — into 
 molecular motion. 
 
 § 106. Origin of animal heat and muscular motion. — 
 
 The plant finds its food in the air (principally the carbonic acid 
 in the air) and in the earth in the condition of a fallen weight ; 
 but, by the agency of the sun's radiation, work is pei-formed upon 
 this matter during the growth of the plant ; potential energy is 
 stored in the plant, — the weight is drawn up. The animal now 
 finds its food in the plant, appropriates the energy stored in 
 the plant, and converts it into energy of motion in the form of 
 heat and muscular motion. The plant, then, may be regarded 
 as a machine for converting energy of motion received from the 
 sun into potential energy ; the animal, as a machine for trans- 
 forming it again into the energy of motion. 
 
TEMPERATURE DEFINED. 141 
 
 § 107. The sun as a source of energy. — Not onlj- is the 
 sun the source of the energy exhibited in the growth of plants, 
 as well as of the muscular and heat energy of the animal, but it 
 is the source, directly or indirectly, of very nearly all the energy 
 employed by man in doing work. Our coal-beds, the results of 
 the deposit of vegetable matter, are vast storehouses of the sun's 
 energy, rendered potential during the growth of the plants many 
 ages ago. Every drop of water that falls to the earth, and rolls 
 its way to the sea, contributing its mite to the unbounded water- 
 power of the earth, and every wind that blows, derives its power 
 directly from the sun. 
 
 XVIII. TEMPERATURE. 
 § 108. Temperature defined. — If body A is brought in 
 contact with body B, and A loses and B gains in heat, then A is 
 said to have had originallj^ a higher temperature than B. If 
 neither body gains or loses, then both had the same tempera- 
 ture. Temperaiure is the state of a body with reference to its 
 power of communicating heat to or receiving heat from other 
 bodies. The direction of the flow of heat determines which of 
 two bodies has the higher temperature. 
 
 § 109. Temperature distinguished from quantity of 
 heat. — The term temperature has no reference to quantity of 
 heat. If we mix together two equal quantities of a substance at 
 the same temperature, the temperature of the mixture is not the 
 sum of the temperatures, — it is not greater or less than either 
 before they were mixed ; but evidently the mixture contains 
 twice as much heat as either alone. If we dip from a gallon of 
 boiling water a cupful, the cup of water is just as hot, i.e., 
 has the same temperature, as the larger quantity, although of 
 course there is a great difference in the quantities of heat the 
 two bodies of water contain. Temperature depends upon the 
 average kinetic energy of the individual molecule, while quantity 
 of heat depends upon the average kinetic energy of the individual 
 molecule multiplied by the number of molecules. 
 
142 MOLECULAR ENEEGy. — HEAT. 
 
 XIX. DIFFUSION OF HEAT. 
 
 There is always a tendency to equalization of temperature; 
 that Is, heat has a tendency to pass from a wanner body to a 
 colder, or from a warmer to a colder part of the same bod}', 
 until there is an equilibrium of temperature. 
 
 § HO. Conduction. — Experiment 1. Place one end of a wire 
 about IS"" long, in a lamp-flame, and hold the other end In the hand. 
 Heat gradually travels from the end in the flame toward the hand. 
 Apply your fingers successively at dififereut points nearer and nearer 
 the flame ; you find that the nearer you approach the flame the hotter 
 the wire is. 
 
 The flow of heat through an unequally-heated body, from 
 places of higher to places of lower temperature, is called con- 
 duction; the body through which it travels is called a conductor. 
 The molecules of the wire in the flame have their motion quick- 
 ened ; they strike their neighbors and quicken their motion ; the 
 latter in turn quicken the motion of the next ; and so on, until 
 some of the motion may be finally communicated to the hand, 
 and creates in it the sensation of heat. 
 
 Experiment 2. Hold wires of diflerent metals of the same length, 
 also a glass tube, a pipe-stem, etc., in the flame, and notice the differ- 
 ence in time that elapses before the sensation of heat is felt in the 
 different bodies. 
 
 Experiment 3. Go into a cold room, and place the bulb of a ther- 
 mometer in contact with various substances in the room ; you will 
 probably find that they have the same, or very nearly the same, tem- 
 perature. Place your hand on the same substances ; they appear to 
 have very different temperatures. This is due to the fact that some 
 substances conduct heat away from the hand faster than others. Those 
 substances that appear coldest are the best conductors. If you go into 
 a room warmer than your body, all this is reversed ; those substances 
 which feel warmest are the best conductor,?, because they conduct their 
 own heat to your hand fastest. 
 
 Experiment 4. Twist together at one end similar wires or strips 
 of iron, copper, brass, etc., 10 or 15™ long, and introduce them into a 
 
CONVECTION. 143 
 
 small flame. After a few minutes you can tell approximately the order 
 of their conducting powers, by moving a match along each wire, and 
 seeing how far from the flame it will light. 
 
 You learn that some substances conduct heat much more 
 rapidly than others. The former are called good conductors, 
 the latter poor conductors. Metals are the best conductors, 
 though they differ widely among themselves. 
 
 Experiment 5. Fill a test-tube nearly full of water, and hold it 
 somewhat inclined (Fig. 106), so that a flame may heat the part of the 
 tube near the surface of the water. The j,. ^^ 
 
 water may be made to boil near its surface 
 for several minutes before any change of 
 the temperature at the bottom will be per- 
 ceived. 
 
 Liquids, as a class, are poorer con- 
 ductors than solids. Gases are much 
 .poorer conductors than liquids. It is 
 difficult to discover that pure, dry ah* 
 possesses any conducting power. The 
 poor conducting power of our clothing is due to the poor con- 
 ducting power of the fibres of the cloth in part, but chiefly to 
 the air which is confined by it. (Why is loose clothing warmer 
 than that closely fitting ?) 
 
 Bodies are surrounded with bad conductors, to retain heat 
 when their temperature is above that of surrounding objects, 
 and to exclude it when their temperature is below that of sur- 
 rounding objects. 
 
 § 111. Convection. —When a hot brick, or a bottle of hot 
 water, is placed at one's feet, heat is also conveyed to the feet. 
 When heat is transferred from one place to another by the 
 bodily moving of heated substances, the operation is called 
 convection; but this term is rarely applied to solids. Solids 
 require some external force to effect the conveyance ; fluids do 
 not necessarily, as may be seen by the following experiments : — 
 
144 
 
 MOLECULAR BKEKGY. — HEAT. 
 
 Fig. 107. 
 
 Experiment 1. Arrange apparatus as in Fig. 107. Fill the large 
 bealier nearly full of water, and elevate it so that the tip of a Bunsen 
 flame may just touch the middle of the bottom. _Fill a glass tube B 
 with a deeply-colored aniline solution, stop one end 
 with a finger, and thrust the other end into the water 
 to the bottom of the beaker ; remove the finger, and 
 allow the solution to flow out and color the water at 
 the bottom for a little depth. Soon the colored 
 liquid immediately over the flame becomes heated, 
 expands, and thereby becomes less dense than the 
 liquid above ; consequently it rises and forms an up- 
 ward current through the colorless liquid. At the 
 same time the cooler liquid on the sides descends to 
 take the place of that which rises, and soon the 
 descending currents become visible by the coloration 
 of the water. By this means heat is conveyed to all 
 parts of the liquid, which would otherwise become 
 much hotter at the bottom than at the top in conse- 
 quence of the poor conducting power of water. 
 
 If a glass tube C, bent as shown in the flgure, is 
 flUed with water, and introduced into the beaker so 
 that the orifice of the short arm shall be 
 just beneath the surface of the colored 
 water, the colored liquid will be seen slowly 
 to ascend the short arm, while the colder 
 water will descend the longer arm. 
 
 Experiment 2. Provide a tightly-cov- 
 ered tin vessel (Fig. 108) and two lamp- 
 chimneys A and B. Near one side of the 
 top of the cover cut a hole a little smaller 
 than the large aperture of chimney B. Near 
 the opposite side of the cover cut a series of 
 holes of about 7""" diameter, arranged in a 
 circle, the circle being large enough to ad- 
 mit a candle without covering the holes. 
 Light the candle, and cover it with chim- 
 ney A, which should be outside the circle 
 of holes. Fasten both chimneys to the 
 cover with wax. Hold smoking touch-paper C (see page 278) near the 
 top of chimney B. The smoke, instead of rising, as it usually does, 
 rapidly descends the chimney, and in a few seconds will be found 
 
 Fig. 108, 
 
VENTILATION. 145 
 
 ascending chimney A. The air around the flame becomes heated, ex- 
 pands, and rises, while air from the outside rushes down the other 
 chimney to supply the deficiency in the rarefied space. Thus heat 
 from the flame is conveyed away to distant places. Cover the orifice 
 of chimney B with the hand, and the flame will quickly go out. 
 
 The last experiment furnishes an explanation of many 
 familiar phenomena. It explains the cause of chimney drafts, 
 and shows the necessity of providing a means of ingress as well 
 as egress of air to and from a confined fire. It explains the 
 method by which air is put in motion in winds. It illustrates a 
 method often adopted to ventilate mines. Let the interior of the 
 tin vessel represent a mine deep in the earth, and the chimneys 
 two shafts sunk to opposite extremities of the mine. A fire 
 kept burning at the bottom of one shaft will cause a current of 
 an- to sweep down the other shaft, and through the mine, and 
 thus keep up a circulation of pure air through the mine. 
 
 Liquids and gases are heated by convection. (Why not solids ?) 
 The heat must be applied at the bottom of the body of liquid or 
 gas. (Why not at the top?) There is a still more important 
 method by which heat is diffused, called radiation, which will be 
 treated of in its proper place, under the head of radiant energy. 
 
 § 112. Ventilation. — Intimately connected with the topic 
 Convection, is the subject (of vital importance) Ventilation, inas- 
 much as our chief means of securing the latter is through the 
 agencj' of the former. The chief constituents of our atmosphere 
 are nitrogen and oxygen, with varying quantities of water vapor, 
 carbonic acid gas, ammonia gas, nitric acid vapor, and other 
 gases. The atmosphere also contains in a state of suspension 
 varying quantities of small particles of free carbon in the form of 
 smoke, microscopic organisms, and dust of innumerable sub- 
 stances. All of these constituents except the first three are 
 called impurities. Carbonic acid is the impurity that is usually 
 the most abundant and most easily detected ; so it has come to 
 be taken as the measure of the purity of the atmosphere, though 
 
146 
 
 MOLECULAR ENERGY. HEAT. 
 
 not itself the most deleterious constituent. Pure out-door air 
 contains about 4 parts of it by volume in 10,000. If the quan- 
 tity rises to 10 parts, the air becomes unwholesome. 
 
 Experiment 1. Place a teaspoonful of unslacked lime in a tumbler 
 of water ; a part of it will be dissolved. Filter the solution through 
 unsized paper, and into the clear liquid blow breath from the lungs 
 through a glass tube. The liquid turns milky-white in appearauce, 
 because the carbonic acid in the breath unites with the lime dissolved 
 in the water, and forms the insoluble carbonate of lime, which remains 
 suspended for a time in the liquid, but finally settles as a white powder 
 at the bottom. 
 
 Experiment 2. Take a fresh quantity of lime water in each of two 
 
 Fig. 109. 
 
 glasses, and in any poorly-ventilated room which has 
 been occupied by several persons for a short time 
 (unfortunately almost any school-room will answer 
 the purpose), place one glass near the floor, and with 
 a bellows blow into the liquid a few puffs of the lower 
 stratum of air. Then place the other glass near the 
 top of the room, and blow with the bellows some of 
 the upper stratum of air into the lime water. In both 
 cases carbonic acid will be found to be present, but 
 it will be much more abundant in the upper stratum, 
 as shown by the greater rapidity with which the 
 cloudiness is produced in the upper stratum. 
 
 Experiment 3. In the center of a small circular 
 plank (Fig. 109) insert an iron wire 60™ long and 
 7ram in diameter. At intervals of 9™ solder to the 
 wire short pieces of small wire, so as to project 
 horizontally from the large wire ; and to the free ex- 
 tremities of these short wires solder small circular 
 pieces of tin 3™ in diameter. Arrange these little 
 
 Sl iasaj^^ platforms spirally around the vertical wire. Fix 
 ^^^g y \^ stumps of candles upon these platforms by means of 
 iiiilli^^ a little melted tallow. Light the candles, and carefully 
 
 llllllllliliillll cover the whole with a tall glass jar. Heated air, 
 from which the life-sustaining oxygen has been largely extracted 
 and replaced by carbonic acid, rises from each flame and accumulates 
 at the top of the jar. This air will neither support life nor combus 
 tion, consequently the highest candle flame is quickly extinguished. 
 The colder and purer air descends and feeds the lower flames, while 
 
VENTILATION. 147 
 
 flame after flame, from the top downward, is successively extinguished, 
 the lowest flame being the last to go out. 
 
 Carbonic acid gas is about one and one-half times heavier 
 than air at the same temperature ; consequently, when both have 
 the same temperature, and the former is very abundant, it tends 
 to settle to the bottom, as in the vicinity of lime-kilns, in which 
 large quantities of this gas are generated. 
 
 The knowledge of this fact has led many to suppose that a 
 means for the escape of impure air need only be provided near 
 the floor of a room. But it should be remembered (1) that the 
 tendency of carbonic acid gas, unless present in excessive quan- 
 tities, is to diffuse itself equally through a body of air ; but (2) 
 when it is heated to a temperature above that of the surrounding 
 air, as when generated by flames, or when it escapes in the warm 
 breath of animals, it is lighter than the air, and consequently rises. 
 If this impure air could escape at the ceiling while fresh air en- 
 tered at the floor, the ventilation would be good. But usually this 
 fresh au" must be warmed ; and in passing over a stove, furnace, 
 or steam radiator, its temperature will generally become higher 
 than that of the impure air, so that it will rise above the latter, 
 and pass out at a ventilator in the ceiling, leaving the floor cold ; 
 hence, the most impure air is often found in high school-rooms 
 half-way up. 
 
 Experience shows that, with the ordinary means of heating, it 
 is usually best, in cold weather, to provide for the escape of the 
 foul air at the floor into a flue, in which a draft is maintained 
 by a neighboring hot chimney-flue, or a gas-burner, while the 
 warm, fresh air is introduced at the floor, on the opposite side 
 of the room, or sometimes at the ceiling. 
 
 The quantity of fresh air introduced must be great enough to 
 dilute the impurities till they are harmless. An adult makes 
 about 18 respirations per minute, expelling from his lungs at 
 each inspiration about 500°™ of air, over 4 per cent of which is 
 carbonic acid. At this rate, about 9,000°™ of air per minute 
 become unfit for respiration ; and to dilute this sufficiently, good 
 
148 MOLBCTJLAR ENERGY. — HEAT. 
 
 authorities say that about 100 times as much fresh air is needed ; 
 or, for proper ventilation, about a cubic meter of fresh air per 
 minute is needed for each person, or, in English measures, 2,000 
 cubic feet per hour. 
 
 If the heating could be so arranged as to keep the floor prop- 
 erly warmed, the vitiated air might pass out at the ceiling, and 
 the quantity of fresh air entering at the floor, might be much 
 less than that just stated. In mild weather, when the fresh air 
 does not require warming, the inlet may be at the floor and the 
 outlet at the ceiling. 
 
 QUESTIONS AND PROBLEMS. 
 
 1. How would you ventilate the tall jar In Experiment 3 ? 
 
 2. At evening assemblies iu lighted halls, what two fruitful sources 
 of carbonic acid are ever present ? 
 
 3. Why are gas burners frequently placed under the orifices of ven- 
 tilators ? 
 
 4. A bed room is S"" square and 2.5'" high; how long would the en- 
 closed air supply two persons on the supposition that none was to be 
 re-breathed ? 
 
 5. A hall contains a thousand persons, and its dimensions are 35 X 
 18 X 7"". How often should a complete change of air be effected that it 
 may not become vitiated ? 
 
 XX. EFFECTS OF HEAT. — EXPANSION. 
 
 Having learned something of the nature of heat, and how it 
 passes from point to point, let us examine the effects it pro- 
 duces on bodies : these are expansion and change of state. 
 The first gives a means of measuring temperature, and leads- to 
 a fuller study of gases than we have yet made. Under the 
 second effect of heat we study liquefaction and vaporization., A 
 third eflfect that is very obvious, the change of temperature, will be 
 found to depend in part on what is called ^ecific heat, to be 
 studied on page 170. 
 
 § 113. Expansion of solids, liquids, and gases. — Ex- 
 periment 1. Obtain two short brass tubes, — one of a size that will 
 
COEFFICIENTS OP EXPANSION. 
 
 149 
 
 Fig. 110. 
 
 permit It just to enter the bore of the other. Heat the smaller tube ; 
 it will no longer enter the larger. 
 
 Experiment 2. Fit stoppers tightly in the necks of two similar thin 
 glass flasks (or test-tubes), and through each stopper pass a glass tube 
 about eO""" long. The flasks must be as nearly alike as possible. Fill one 
 flask with alcohol and the other with water, and crowd in the stoppers 
 so as to force the liquids in the tubes a little way above the corks. 
 Set the two flasks into a basin of hot water, and note that, at the 
 instant the flasks enter the hot water, the liquids sink a little in the 
 tubes, but quickly begin to rise, until perhaps they reach the top of the 
 tubes and run over. 
 
 When the flasks first enter the hot water they expand, and thereby 
 their capacities are increased ; meantime the heat has not reached the 
 liquids to cause them to expand, consequently the liquids sink momen- 
 tarily to accommodate themselves to the enlarged vessel. Soon the 
 heat reaches the liquids, and they begin to expand, as shown by their 
 rise in the tubes. The alcohol rises faster than 
 the water. Diflferent substances, both'in the solid 
 and liquid states, expand unequally on experi- 
 encing equal changes of temperature. 
 
 Experiment 3. Take one of the flasks used 
 in the last experiment, dry it well inside and out- 
 side, invert the flask, insert the end of the tube 
 in a bottle of colored water (Fig. 110), and apply 
 heat to the flask ; the enclosed air expands and 
 comes out through the colored liquid in bubbles. 
 After a few minutes, withdraw the heat, keeping 
 the end of the tube in the liquid ; as the air left 
 in the flask coots, it contracts, and the water is 
 forced by atmospheric pressure up the tube into 
 the flask, and partially fllls it. 
 
 § 114. Coeffloients of expansion.— There 
 
 being generally greater cohesive force between the molecules of 
 solids than between the molecules of liquids, the former expand 
 less than the latter on receiving the same amount of heat, and 
 for the same reason liquids expand less than gases. (See page 
 18.) All gases expand alike for equal differences of tempera- 
 ture, and the expansion is uniform at all temperatures. Under 
 uniform pressure the volume of any body of gas is increased by 
 
150 MOLECULAR ENERGY. — HEAT. 
 
 j4-^ its volume at the freezing point of water for every degree cen- 
 tigrade, or -j^y for every degree Fahrenlieit, its temperature is 
 raised. These fractions are called the coefficients of expansion. 
 Not only do the coefficients of expansion of liquids and solids 
 vary with the substance, but the coefficient for the same sub- 
 stance varies at diiferent temperatures, being greater at high 
 than at low temperatures. 
 
 In the expansion of fluids we have only to do with increase of 
 volume, called cubical expansion. In the expansion of solids, 
 we have frequent occasion to speak of expansion in one direc- 
 tion only, and this is called linear expansion. 
 
 § 115. Power of expansion and contraction. —The force 
 which may be exerted by bodies in expanding or contracting may be 
 very great, as shown by the following rough calculation : If an iron 
 bar, 1 sq.in. in section, is raised from 0" C. (freezing point of water) to 
 600° C. (a dull, red heat), its length, if allowed to expand freely, will be in- 
 creased from 1 to 1.006, its coefficient of expansion being about .000012. 
 Now, a force capable of stretching a bar of iron of 1 sq. in. section 
 this amount, is about 90 tons, which represents very nearly the force 
 that would be necessary to prevent the expansion caused by heat. It 
 would require an equal force to prevent the same amount of contrac- 
 tion (caused by what?) if the bar is cooled from 500° to 0° C. 
 
 Boiler plates are riveted with red-hot rivets, which, on cooling, 
 draw the plates together so as to form very tight joints. Tires are 
 fitted on carriage-wheels when red hot, and, on cooling, grip them with 
 very great force. 
 
 § 116. Abnormal expansion and contraction of water. 
 — Water presents a partial exception to the general rule that 
 matter expands on receiving heat and contracts on losing it. 
 If a quantity of water at 0° C, or 32° F., is heated, it 
 contracts as its temperature rises, until it reaches 4° C, or 
 about 39° F. , when its volume is least, and therefore it has its 
 maximum density. If heated be3-ond this temperature it ex- 
 pands, and at about 8° C. its volume is the same as at G°. On 
 cooling, water reaches its maximum density at 4° C, and ex- 
 pands as the temperature falls below that point. It is probable 
 
THEKMOMBTRY. 151 
 
 tnat cr3'stallization, and consequently expansion (see page 26) , 
 begins at 4° C. (Wlaat is the temperature at the bottom of a 
 pond when water begins to freeze at the surface ?) 
 
 XXI. THERMOMETRY. 
 
 § 117. Temperature measured by expansion. — The ef- 
 fects of expansion by heat are well illustrated in the common 
 thermometer. As its temperature rises, both the glass and the 
 mercury expand ; but, as liquids are more expansible than 
 solids, the mercury expands much more rapidly than the glass, 
 and the apparent expansion of the mercury, shown by its rise in 
 tlie tube, is the difference between the actual increase of volume 
 of the mercury and that of the part of the glass vessel containing 
 it. The thermometer, then, primaril}' indicates changes in vol- 
 ume ; but as changes of volume in this case are caused bj' 
 changes of temperature, it is commonly used for the more 
 important purpose of measuring temperature. (Will a ther- 
 mometer measure quantity of heat ?) 
 
 § 118. Construction of a thermometer. — A thermometer 
 generally consists of a glass tube of capillary bore, terminating 
 at one end in a bulb. The bulb and part of the tube are filled 
 with mercury, and the space in the tube above the mercury is 
 usually, but not necessarily, a vacuum. On the tube, or on a 
 plate of metal behind the tube, is a scale to show the hight of 
 the mercurial column. 
 
 § 119. Standard temperatures. — That a thermometer 
 may indicate any definite temperature, it is necessary that its 
 scale should relate to some definite and unchangeable points 
 of temperature. Fortunately Nature furnishes us with two 
 convenient standards. It is found that under ordinary at- 
 mospheric pressure ice always melts at the same temperature, 
 called the melting point, or, more commonly, the freezing point 
 (inasmuch as water freezes and ice melts at the same tempera- 
 
152 
 
 MOLECULAR ENERGY. — HEAT. 
 
 ture). Again, the temperature of steam rising from boiling 
 water under the same pressure is always the same. 
 
 Fig. 111. 
 
 F. 
 
 Water boils.. 
 
 Blood he-It.. 
 
 Max. den. of water 
 Water freezes 
 
 Mercury freezes.... 
 
 .2°.... 
 32°..., 
 
 —37.8°. 
 
 No beat., 
 
 100°. 
 
 37°.. 
 
 4°.... 
 0° 
 
 —38.8° 
 
 —460°.. 
 
 Abs. 
 temp. 
 
 373°... 1 
 
 277° 
 273°, 
 
 § 120. Graduation of thermometers. — The bulb of a 
 thermometer is first placed in melting ice, and allowed to stand 
 until the surface of the mercury becomes stationary, and a mark 
 is made upon the stem at that point, and indicates the freezing 
 point. Then the instrument is suspended in steam rising from 
 boiling water, so that all but the very top of the column is in the 
 steam. The mercury rises in the stem until its temperature be- 
 comes the same as that of 
 the steam, when it again 
 becomes stationary, and 
 another mark is placed 
 upon the stem to indicate " 
 the boiling point. Then 
 the space between the two 
 points found is divided into 
 a convenient number of 
 equal parts called degrees., 
 and the scale is extended 
 above and below these 
 points as far as desirable. 
 Two methods of division 
 are adopted in this coun- 
 try: by one, the space is 
 divided into 180 equal 
 parts, and the result is 
 called the Fahrenheit 
 scale, from the name of its author ; by the other, the space is 
 divided into 100 equal parts, and the resulting scale is called 
 centigrade, which means one hundred steps. In the Fahrenheit 
 scale, which is generally employed for ordinary household pur- 
 poses, the freezing and boiling points are marked respectively 
 32° and 212°. The of this scale (32° below freezing point). 
 
CONVEESION PROM ONE SCALE TO THE OTHEK. 153 
 
 which is about tlie lowest temperature that can be obtained by a 
 mixture of snow and salt, was incorrectly supposed to be the 
 lowest temperature attainable. The centigrade scale, which is 
 generally employed by scientists, has its freezing and boiling 
 points more conveniently marked, respectively 0° and 100°. A 
 temperature below 0° in either scale is indicated by a minus sign 
 before the number. Thus, — 12°F. indicates 12° below 0° (or 
 44° below freezing point), according to the Fahrenheit scale. 
 Under F. and C, Figure 111, the two scales are placed side by 
 side, so as to exhibit at intervals a comparative view. 
 
 § 121. Conversion from one scale to the other. — Since 
 100° C, = 180° F., 5° C. = 9° F., or 1° C. = f of 1° F. Hence, 
 to convert centigrade degrees into Fahrenheit degrees, we mul- 
 tiply the number by f ; and to convert Fahrenheit degrees into 
 centigrade degrees we multiply by -f . In finding the temperature 
 on one scale that corresponds to a given temperature on the other 
 scale, it must be remembered that the number that expresses 
 the temperature on a Fahrenheit scale does not, as it does on a 
 centigrade scale, express the number of degrees above freezing 
 point. For example, 52° on a Fahrenheit scale is not 52° above 
 freezing point, but 52° — 32° = 20° above it. 
 
 Hence, to reduce a Fahrenheit reading to a centigrade read- 
 ing, first subtract 32 from the given number, and then multiply 
 by^. Thus, 5(F_32) = C. 
 
 To change a centigrade reading to a Fahrenheit reading, first 
 multiply the given number by f , and then add 32. Thus, 
 |C-|-32 = F. 
 
 PROBLEMS. 
 
 1. The difference between two temperatures is 80 centigrade de- 
 grees. What is the difference in Fahrenheit degrees? 
 
 2. When the temperature of a room falls 30 Fahrenheit degrees, 
 liow many centigrade degrees is its temperature lowered? 
 
 3. Suppose the temperature of the above room before the fall was 
 68° i\, (a) what was its temperature after the fall? (6) What were the 
 
154 
 
 MOLECULAR ENERGY. — HEAT. 
 
 temperatures of the room before and after the fall, according to a 
 centigrade thermometer? 
 
 4. Express the following temperatures of the centigrade scale in the 
 Fahrenheit scale : 100°; 40°; 56°; 60°; 0°; -20°; -40°; 80°; 150°. 
 
 Note. — In adding or subtracting 32°, it should be done algebraically. 
 Thus, to change — 14° C. to its equivalent on the Fahrenheit scale : | X 
 (— 14) = — 25.2 ; — 25.2° + 32° = 6.8°, the required temperature on the 
 Fahrenheit scale. Again, to find the equivalent of 24° F. in the centi- 
 grade scale : 24 — 32 = — 8; — 8X|= — 4f; hence, 24° F. is equiva- 
 lent to — 4.4° -I- C. 
 
 6. Express the following temperatures of the Fahrenheit scale in 
 the centigrade scale: 212°; 32°; 90°; 77°; 20°; 10°; -10°; -20°; 
 -40°; 40°; 59°; 329°- 
 
 § 122. Air thermometer. — Prepare apparatus as shown in 
 Figure 112. A is a glass flask of about one-fourth liter capacity, tightly 
 Fig. 112. stopped. Through the stopper extends a glass tube about 60"° 
 long, which also passes through the stopper of a bottle B, 
 partly filled with colored water. The latter stopper is pierced 
 by a hole a to allow air to pass in and out freely. A strip of 
 paper C, containing a scale of equal parts, is attached to the 
 tube by means of slits cut in the paper. 
 
 Grasp the flaslc with the palms of both hands, and thereby 
 heat the air in the flask and cause it to expand and escape 
 through the liquid in bubbles. When several bubbles have 
 escaped, remove the hands, and the air, on cooling, will con- 
 tract, and the liquid will rise and partly flll the tube. 
 
 The apparatus described is usually called an air ther- 
 mometer; but it is, more correctly speaking, a thermo- 
 scope. It renders slight changes of temperature much 
 more perceptible than a mercury thermometer, and 
 therefore is said to be more sensitive. For instance, if 
 an air thermometer and a mercury thermometer, whose 
 bulbs are of the same size, are carried from a cold 
 room into a warm room, or vice versa, the changes in 
 JB the hight of the liquid column in the air thermometer 
 will be much greater and more rapid than in the mer- 
 cury theraiometer. In the former, the temperature is measured 
 by the expansion of air ; in the latter, by the expansion of mer- 
 
ABSOLUTE TBMPEEATirBB. 155 
 
 cury. (Why is the former more sensitive than the latter?) 
 This simple air thermometer cannot have a fixed scale showing 
 the temperature in Fahrenheit or centigrade degrees as a mercury 
 thermometer does, inasmucli as the hight of the liquid column is 
 affected by atmospheric pressure as well as by temperature, so 
 that when the temperature remains the same, variations occur 
 corresponding to the changes of the barometric column. But 
 in many scientific investigations a good air thermometer is better 
 than one containing mercury. The thermopile and galvanome- 
 ter (see page 236) constitute a still more sensitive apparatus 
 for showing changes in temperature. 
 
 § 123. Measurement of extreme temperatures. — Mer- 
 cury boils at 350° C. (662° F.) and freezes at about —39" 
 C, and therefore cannot be used for indicating tempera- 
 tures above or below these points. Extremely high tempera- 
 tures are measured by the expansion of solids, usually a rod of 
 platinum, and the instrument used for this purpose is called a 
 pyrometer. Alcohol is used in thermometers employed to meas- 
 ure extremely low temperatures. The air thermometer maj' be 
 used at any temperature that will not soften the bulb and tube. 
 
 § 124. Absolute temperature. — If a body of air at 0° C. 
 is heated, its volume is increased -^f^ of the original volume for 
 every degree its temperature is raised. At 273° C. its volume 
 is consequently doubled. If a bodj' of air is cooled below 0° C. , 
 its volume is diminished for every degree its temperature is low- 
 ered ^-fiT of its volume at 0° ; and so, if its volume were to con- 
 tinue to decrease at that rate until it should reach — 273°C., 
 mathematically speaking its volume would become nothing ; but, 
 practically, the air would cease to be a gas, and would become a 
 compact, motionless mass ; that is, all molecular motion would 
 cease at that point, and so the point of no heat would be reached. 
 This point is called the absolute zero, and temperature reckoned 
 from this point is called absolute temperature. On this scale all 
 temperatures would be positive. 
 
156 MOLECULAR EKEKGY. — HEAT. 
 
 Note. — Air and all other gases we loiow (see page 20) are con- 
 verted into liquids and solids long before they reach the temperature 
 of —273° C. ; so, of course, they cease to obey the law of Mariotte 
 (page 59). Though a body has never been cooled to the absolute zero, 
 there are reasons, far more conclusive than the one given, which justify 
 us in believing that all molecular motion would cease at a point very 
 near — 273° C. In the further study of heat, the use of the scale of 
 absolute temperature is a great convenience. 
 
 The absolute temperature (based on the above theorj-) may 
 be found by adding 273 to its reading on a centigrade thermome- 
 ter, or 459 to its reading on a Fahrenheit thermometer. (See 
 Figure 111.) 
 
 § 125. Laws of gaseous bodies. — It follows, from the 
 above discussion, that the volume of a given mass of gas at con- 
 stant pressure is proportional to its absolute temperature. This 
 is called the Law of Charles. 
 
 If, however, a body of gas at 0° C. is enclosed in a vessel of 
 rigid sides, its volume must remain constant at all tempera- 
 tures. In this case the pressure on the sides is increased by 
 ^\-g of the pressure at 0° for every degree its temperature rises, 
 and is diminished 2-7-j for every degree its temperature falls ; and 
 if it were to continue to decrease at this rate, at — 273°C., it 
 would become nothing. Hence, the pressure of a given body 
 of gas, whose volume is kept constant, is proportional to its abso- 
 lute temperature. 
 
 Mariotte's law states that at a constant temperature the vol- 
 ume of a given body of gas is inversely proportional to the 
 pressure to which it is subjected; i.e., the product of the pressure 
 and the volume is constant. Now, when both the pressure and 
 the volume vary at the same time, it is evident that the prod- 
 uct of the pressure and the volume of a given body of gas is 
 proportional to its absolute temperature. 
 
 PROBLEMS. 
 
 1. Find in both centigrade and Fahrenheit degrees the absolute tem- 
 peratures at which mercury boils and freezes. 
 
 2. At 0° C. the volume of a certain body of gas is 500™"" under a 
 constant pressure ; (a) what will be its volume if its temperature is raised 
 
KINETIC THEORY OF GASES. 157 
 
 to75°C.? (6) What will be its volume if its temperature becomes 
 -20° C? 
 
 3. If the volume of a body of gas at 20° C. is 200=="', what will be its 
 volume at 30° C. ? Solution : 20° C. is equivalent to (20 + 273) 293 abs. 
 temp. ; then 293 : 303 : : 200 : 206.8='='". Ans. 
 
 4. To what volume will a liter of gas contract if cooled from 30° C, 
 to-]5°C.? 
 
 5. One liter of gas under a pressure of one atmosphere will have 
 what volume if, at a constant temperature, the pressure is reduced to 
 900S per square centimeter? 
 
 6. The volume of a certain body of air at a temperature of 17° C, 
 and under a pressure of 8008 per square centimeter, is SOO"'"" ; what will 
 be its volume at a temperature of 27° C. under a pressure of 1200S per 
 square centimeter? Solution : 17° C. is equivalent to 290° abs. temp. ; 
 27° C. is equivalent to 300° abs. temp. Then 290 : 300 : : 500 x 800 : x x 
 1200. Whence a; = 344.8==. Ans. 
 
 7. If the volume of a body of gas under a pressure of l^ per square 
 centimeter, and at a temperature of 0° C, is 1 liter, at what temperature 
 will its volume be reduced to 1=="' under a pressure of 2001^ per square 
 centimeter? Ans.: 54.6° abs. temp., or —218.4° C. 
 
 8. Find the temperatures on the absolute scale at which bodies 
 named on page 161 melt or boil. 
 
 9. If a cubic foot of coal-gas at 32° F., when the barometer is at 
 30 in., weighs ^j'ih., how much wUl an equal volume weigh at 68° F. 
 when the barometer is at 29 in.? 
 
 § 126. Kinetic theory of gases. — This theory claims that 
 in gases the molecules are so far separated from each other that 
 their motions are not generally influenced by molecular attrac- 
 tions. Hence, in accordance with the first law of motion, the 
 molecules of gases move in straight lines and with uniform ve- 
 locitj', until they collide with each other or strike against the 
 walls of the containing vessel, when, in consequence of their 
 elasticity, they at once rebound and start on a new path. We 
 may picture to ourselves what is going on in a body of calm 
 air, for instance, by observing a swarm of bees, when every 
 individual bee is flying with great velocity, first in one direction 
 and then in another, while the swarm either remains at rest or 
 sails slowly through the air. 
 
158 MOLECULAR ENERGY. — SEAT. 
 
 § 127. Pressure of a gas due to the kinetic energy of its 
 molecules. — Consider, then, what a molecular storm must be 
 raging about us, and how it must beat against us and against 
 every exposed surface. According to the kinetic theory, the 
 pressure of a gas (or its expansive power as it is sometimes 
 called) , is entirelj' due to the striking of the molecules against the 
 surfaces on which the gas is said to press, the impulses following 
 each other in such rapid succession that the effect produced can- 
 not be distinguished from constant pressure. Upon the kinetic 
 energy of these blows, and upon the number of blows per 
 second, must depend the amount of pressure. But we saw on 
 page 141, that on the energy of the individual molecules depends 
 that condition of a gas called its temperature; so, it is apparent, 
 as stated above, that the pressure of a given quantity of gas varies 
 as its temperature. Again, as at the same temperature the num- 
 ber of blows per second must depend upon the number of mole- 
 cules in the unit of space, it is apparent that the pressure varies 
 as the density. 
 
 The following estimates' made for hydrogen molecules atO°C., and 
 under a pressure of one atmosphere, may prove interesting : — 
 
 Mean velocity, 6100 feet per second. 
 
 Mean path without collision, 38 ten-millionths of an inch. 
 
 Collisions, 17,750 millions per second. 
 
 Mass, 216,000 million million million weigh 1 gram. 
 
 Number, 19 million million million fill 1 cubic centimeter. 
 
 § 128. Difflision of gases and liquids. — The kinetic the- 
 ory of gases explains why gases penetrate into any spaces open 
 to them, and likewise the phenomenon known as the diffusion 
 of gases (see page 41). The presence of a gas in a given 
 space only delays the spread of another gas in the same space 
 by collision between the molecules of the inter-diffusing gases. 
 The diffusion between liquids, though not so well understood, 
 is undoubtedly due in part to similar molecular motions. 
 
 , 1 Maxwell, 
 
LIQUEFACTION AND VAPORIZATION. 159 
 
 XXII. EFFECTS OF HEAT CONTINUED. — LIQUEFACTION 
 AND VAPOKIZATION. 
 
 Experiment 1. Melt separately tallow, lard, and beeswax. When 
 partially melted, stir well with a thermometer, and ascertain the melting 
 points of each of these substances. 
 
 Experiment 2. Place a test tube (Fig. 113), half filled with ether, 
 in a beaker containing water at a temperature of 60° C. Although the 
 temperature of the water is 40° below its boiling point, 
 it very quickly raises the temperature of the ether sufB ^'S' n^. 
 ciently to cause it to boil violently. Introduce a chemi- 
 cal thermometer' into the test tube, and ascertain the 
 boiling point of ether. 
 
 Experiment 3. Half fill a glass beaker of a liter 
 capacity with fragments of ice or snow, and set the 
 beaker into a basin of boiling-hot water. Stir the con- 
 tents of the beaker with a thermometer until the ice is 
 all melted, observing from time to time the temperature of the contents. 
 The temperature remains constant at 0° C. until the ice is all melted. 
 
 Experiment 4. As soon as the last piece of ice disappears, remove 
 the flask from the warm water, wipe the outside, and place it over a 
 Bunsen burner and heat. Observe that the temperature rises con- 
 stantly until the water begins to boil ; but after it begins to boil, the 
 temperature remains constant as long as it boils. Place more burners 
 under the beaker ; the water bolls more violently, but the temperature 
 is not raised. 
 
 Experiment 5. Place in contact the smooth, dry surfaces of two 
 pieces of ice; press them together for a few seconds; remove the 
 pressure, and they will be found firmly frozen together. The ice at the 
 surfaces of contact melts under the pressure, but when the pressure is 
 removed the liquid instantly freezes and cements the pieces together. 
 It is in this manner that snow-balls are formed. 
 
 Note. — If a thermometer is placed in a mixture of Ice and water, 
 and the mixture is subjected to great pressure, some of the ice will 
 melt and the -tiMnperature will fall; but when the pressure is removed, 
 a portion of the water freezes and the temperature rises. From this 
 we learn that the melting (or freezing) point of water is very slightly low- 
 ered by pressure. The depression is about ^if of 1° C for each atmos- 
 phere. On the other hand, it is found that substances which, unlike ice, 
 expand in melting, have their melting points raised by pressure. 
 
 1 A chemical thermometer has its scale on the glass stem, instead of a metal plate, 
 and is otherwise adapted to experimental use. 
 
160 
 
 MOLECTTLAK ENERGY. — HEAT. 
 
 Fig. lU. 
 
 Experiment 6. Half fill a thin glass flasK witn water. Boil the 
 water over a Bimsen burner ; the steam will drive the air from the 
 
 flask. Withdraw the burner, quickly- 
 cork the flask very tightly, and plunge 
 the flask into cold water, or invert the 
 flask and pour cold water upon the part 
 containing steam, as in Figure 114 ; the 
 water in the flask, though cooled several 
 degrees below the usual boiling point, 
 boils again violently. The applicatiob 
 of cold water to the flask condenses 
 some of the steam, and diminishes the 
 tension of the rest, so that the pressure 
 upon the water is diminished, and the 
 water boils at a reduced temperature. 
 
 If hot water is poured upon 
 the flask, the water ceases to boil. 
 (Why ?) Under the receiver of an 
 air-pump, water may be made to 
 boil at any temperature between 
 0° and 100° C. ; indeed, if exhaustion is carried far enough, 
 boiling and freezing may be going on at the same time. When 
 high temperature is objectionable, apparatus is contrived for 
 boiling and evaporating in a vacuum ; as, for instance, in the 
 vacuum pans used in sugar refineries. As water boils more 
 easily under diminished pressure, so it boils with more difficulty 
 when the pressure is increased ; and the temperature to which 
 water may be raised under the pressure of its own steam is 
 only limited by the strength of the vessel containing it. Ves- 
 sels of this kind are often employed to effect a complete pene- 
 tration of water into solid and hard substances. By this means 
 gelatine is extracted from the interior of bones. In the boiler 
 of a locomotive, where the pressure is sometimes 150 lbs. above 
 the atmosphere, the boiling point rises to about 180° C. (360° F.). 
 
 Experiment 7. Dissolve table-salt in ■^ater, and you may raise 
 its boiling point till it reaches 108° C. With saltpetre it may reach 
 115° C. 
 
IiAWS OF FUSION AND BOILING. 
 
 161 
 
 On the other hand, it is well known that sea-water, which con- 
 tains saline matter in solution, freezes at a lower temperature 
 than 0° C. From the above experiments, and others of a similar 
 nature, we derive the following 
 
 LAWS OF FUSION AND BOILING. 
 
 1. The temperature at which 
 solids melt differs for different sub- 
 stances, hut is invariable for the 
 same substance, if the pressure is 
 constant. Substances solidify usu- 
 ally at the same temperatures as 
 those at which they melt. 
 
 2. After a solid begins to melt, 
 the temperature remains constant 
 until the whole is melted. 
 
 3. Pressure lowers the melting (or 
 solidifying) point of substances that 
 expand on solidifying, and raises the 
 melting point of those that contract. 
 
 4. The freezing point of water is 
 lowered by the presence of salts in 
 solution. 
 
 1. The temperature at which 
 liquids boil differs for different sub- 
 stances, but is invariable for the 
 same substance if the pressure is 
 constant. Vapors liquefy at the 
 same temperatures as those at which 
 they boil. 
 
 2. After a liquid begins to boil 
 the temperature remains constant 
 until the whole is vaporized. 
 
 3. Pressure raises the boiling 
 point of all substances. 
 
 4. The boiling point of water is 
 raised by the presence of salts in 
 
 KBFEEENCE TABLES. 
 Melting Points. 
 
 Alcohol Never frozen. 
 
 Mercury -38.8° C. 
 
 Sulphuric acid — 34.4° 
 
 Ice 0° 
 
 Phospliorus 44° 
 
 Sulphur 115° 
 
 Tin about 233° 
 
 Lead " 334° 
 
 Zinc about.... 425°C. 
 
 Silver " 1000° 
 
 Gold " 1200° 
 
 Cast-iron " 1050-1250° 
 
 Wronght-iron " 1500-1600° 
 
 Iridium (the most 
 
 infusible metal) 
 
 about 1950° 
 
 Boiling Points under a Pressure of one Atmosphere. 
 
 Carbonic acid — 78° C. 
 
 Ammonia TT— 40° 
 
 Sulphurous acid — 10° 
 
 Ether 35° 
 
 Carbon bisulphide 48° C. 
 
 Alcohol 78° 
 
 Water 100° 
 
 Mercury 35 ° 
 
162 
 
 MOLECTJLAE ENERGY. — HEAT. 
 
 Boiling Points of Water at Different Pressures. 
 
 Atmespheres. 
 
 212° r 1 
 
 249.5" 2 
 
 273.3° 3 
 
 306° 5 
 
 356.6° 10 
 
 Barometer. 
 
 184°E 16.68 inches. 
 
 190° 18.99 " 
 
 200° 23.45 " 
 
 210° 28.74 " 
 
 212° 29.92 " 
 
 The temperature of the boiling point of water varies with the alti- 
 tude of places, in consequence of the different atmospheric pressure. 
 A difference of altitude of 533 ft. causes a variation of 1° T. In the 
 boiling point. 
 
 Boiling Points of Water at Different Altitudes. 
 
 Quito jf ;• -I- 9,500 ft. 
 
 Mont Blanc 
 
 Mt. Washington 
 
 Boston 
 
 Dead Sea (below) 
 
 Above the 
 
 sea-level. 
 -9,500 ft... 
 15,650 " .. 
 
 6,290 " .. 
 
 " .. 
 
 - 1,316 " . . 
 
 Mean hight of 
 Barometer. 
 
 21.53 in.. . 
 
 Temperature. 
 . . 195.8° F. 
 
 ....16.90 " .. 
 ..,.22.90 " .. 
 ,...30. " ,, 
 .,,.31.50 " .. 
 
 ...186° 
 ...200° 
 ...212° 
 ...214° 
 
 §129. Distillation. — Apparatus like that represented in 
 
 Figure 115 maybe 
 
 Fig. 115. ^ 
 
 easily constructed. 
 The following ex- 
 periment will be 
 f o u n d interesting 
 and instructive. 
 
 Experiment. Half 
 fill the flaslc A with 
 water colored with a 
 few drops of ink. 
 Boil the water, and 
 the steam arising will 
 escape through the 
 glass delivery tube 
 BB. This tube is surrounded in part by a larger tube C, called a con- 
 denser, which is kept filled with cold water flowing from a vessel D 
 through a siphon S, the water finally escaping through the tube B. 
 
EVAPOEATION. 163 
 
 The steam is condensed in its passage through the delivery tube, and 
 the resulting liquid is caught in the vessel F. The liquid caught is 
 colorless. A complete separation of the watery portion of the colored 
 liquid from the other ingredients of the ink is effected, the latter being 
 left in the flask A. 
 
 The separation is accomplished on the principle that the tem- 
 perature of the boiling points of different substances differ. The 
 water is raised to its vaporizing point, but the other substances 
 are not. The apparatus is called a still, and the operation 
 distillation. 
 
 If a volatile liquid, such as alcohol, is to be separated from 
 water, the mixture is heated to the temperature at which the 
 volatile liquid boils, but not to the boiling point of water, when 
 the alcohol will pass into the vessel F, and th^^ater, for the 
 most part, will remain in the flask. 
 
 § 130. Evaporation. — In ' boiling, the heat, usually ap- 
 plied at the bottom, rapidly converts the liquid into vapor, 
 which, rising in bubbles and breaking at or near the surface, 
 produces a violent agitation in the liquid, sometimes called 
 ebullition. Evaporation is that form of vaporization which takes 
 place quietly and slowly at the surface. The phenomena and 
 laws of vaporization of all liquids are similar, but we will study 
 only the important case of water. Although hastened by heat, 
 the evaporation of water occurs at anj' temperature, however 
 low ; even ice and snow evaporate. 
 
 TJie rapidity of evaporation varies directly loith the tempera- 
 ture, amount of surface exposed, and dryness of the atmosphere, 
 and inversely with the pressure upon the liquid. This vapor of 
 water mixes freely with the air, and diffuses readily through it, 
 acting like another gas (compare pages 42 and 158). The air 
 does not take up water like a sponge, as is commonly imagined ; 
 for, if the air could be removed from a room, where there is a 
 large vessel of water, every cubic foot of the space in the room 
 would be found to contain just as much water-vapor as it does 
 
164 MOLECULAR ENERGY. — HEAT. 
 
 when the air is present, — probably a very little more. In either 
 case, only a definite quantity would be found in each cubic foot, 
 a quantity depending on the temperature of the space. Thus, at 
 0°C., each cubic foot cau contain 0.14S; at 10°, 0.268; at 20°, 
 0.498; and at 30°, 0.858. Evidently the capacity is nearly 
 doubled by a rise of 10° in temperature. 
 
 § 131. Dew point. — When a space contains such an 
 amount of water-vapor, whether it contains other gases or not, 
 that its temperature cannot be lowered without some of the water 
 being precipitated in the form of a liquid, the space is said to be 
 saturated, and the temperature is called the dew point. The form 
 in which the condensed vapor appears is, according to its loca- 
 tion, dew, fog, or cloud.. The atmosphere is said to be dry or 
 humid, accordmg as the difference between the dew point and 
 the temperature of the atmosphere is great or little. 
 
 QUESTIONS. 
 
 1. Why does our breath produce a cloud in winter and not in sum- 
 mer? 
 
 2. (a) If air at 0° is warmed to 20° C, how will its dryness be 
 affected? (6) What effect would such warmed air have on wet clothes? 
 
 3. If saturated air at 20° is blown into a cellar where the temperar 
 ture Is 10°, what will happen? 
 
 4. What is the cause of the general complaint of dryness of air in 
 rooms heated by stoves or furnaces? 
 
 5. Does a given mass of air in such a room contain less water-vapor 
 than an equal mass of cold out-door air at the same time? 
 
HEAT TTNITS. 165 
 
 XXIII. HEAT CONVERTIBLE INTO POTENTIAL ENERGY, AND 
 VICE VERSA. 
 
 § 132. Heat units. — It is frequently necessary to measure 
 quantity of heat, and for this purpose a standard unit of measure- 
 ment is required. The heat unit generally adopted is the amount 
 of heat required to raise the temperature of one diag ram of water 
 from 0° to 1° C. This unit is called a calorie. 
 
 Let it be required to find the ^mount of heat that disappears 
 (Exp. 3, p. 159) during the melting of one kilogram of ice. 
 
 Experiment 1. Place I'' of ice at 0° C. in a beaker, and the beaker 
 in a large basin of boiling water (Fig. 116), and at the same instant 
 place in the hot water another beaker containing I'' of water at O'^ C. 
 Place in each beaker a thermometer, and at the instant that the ice 
 disappears note the temperature 
 of the water in each; It wiU be '^' 
 
 found that while the temperature 
 of the former has not changed, 
 the latter has risen to about 80° C. 
 
 It is evident that the contents 
 of both beakers must have re- 
 ceived the same amount of heat ; 
 hence, the amount of heat re- 
 ceived by the water being 80 
 calories, the amount of heat that disappears or is lost during the 
 melting of one kilogram of ice Is 80 calories. 
 
 Next, let it be required to find the amount of heat that dis- 
 appears (Exp. 4, p. 159) during the conversion of 1'' of water 
 into steam. 
 
 Experiment 2. Place l^ of water at (P C. in a beaker, and heat the 
 same with a Bunsen burner. Note the time that it takes to raise the 
 water from 0° C. to 100° C, also the lime during which the temperature 
 of the water remains stationary while the water is boiling away. The 
 latter time will be found to be about five times the former. 
 
 Now, as the water receives 100 calories during the time it is 
 
166 MOLECULAR ENERGY. — HEAT. 
 
 rising from the freezing to the boiling point, it must receive about 
 500 calories during the time it is converted into steam : but the 
 temperature of the water is not changed during the latter oper- 
 ation. More accurate methods have the number 537 ; so it fol- 
 lows that 537 calories disappear, or are lost during the conversion 
 of 1 kilogram of water into stearth. 
 
 § 133. Two questions answered. — Inasmuch as none of 
 the heat applied during the melting of ice and the conversion 
 of water into steam raises the temperature of the body to 
 which it is applied, the question arises, What does the heat do? 
 Again, Why is not ice instantly converted into water on reach- 
 ing the melting point, and water instantly converted into steam on 
 teaching the boiling point ? 
 
 The answer to the first question is, All of the heat applied in 
 melting ice is consumed in doing interior work, as it is called, 
 rhe molecules that were firmly held in their places by molecular 
 forces are now moved from their places, and so work is done 
 against these forces, just as work is done against gravity when 
 a weight is lifted. In the conversion of water into steam, a 
 similar action goes on ; the heat is expended in separating 
 the molecules so far that the molecular attractive forces are no 
 longer sensible, all except the small fraction used in overcoming 
 atmospheric pressure. ^ Heat, the energy of motion, in both 
 instances does important work, and is thereby converted into 
 the energy of position, or potential energy, — energy of the 
 same kind as that of a raised weight. 
 
 The answer to the second question is, The amount of work 
 done in both instances is great, as shown by the amount of heat 
 Consumed in doing the work ; 80 calories per kilogram of ice 
 being required in the first instance, and 537 calories per kilo- 
 gram of water in the second ; hence it requires a long time to 
 acquire the requisite amount of heat. It is fortunate that it 
 takes a large quantity of heat to melt ice ; otherwise, on a single 
 
 • This fraction is about JL. 
 
COLD BY SOLUTION. 167 
 
 warm day in winter, all the ice and snow would melt, creating 
 most destructive freshets. The heat which disappears in melting 
 and boiling is generally, but with our present knowledge of the 
 subject, rather objectionably, called latent (hidden) heat. The 
 error consists in calling that heat which has ceased to be heat, 
 i.e., has ceased to be molecular motion. 
 
 § 134. Methods of producing artificial cold. — The fact 
 that heat must be consumed because work is done, in the con- 
 version of solids into liquids and liquids into vapors, and in the 
 simple expansion of gases, is turned to practical use in many 
 ways for the purpose of producing artificial cold. They are 
 embraced under ttoee heads; viz.. Cold produced by solution, 
 by evaporation, and by ea^ansion of gases. The following ex- 
 periments will illustrate. 
 
 § 135. Cold by solution. — Freezing mixtures. —Experi- 
 ment. Prepare a mixture of 2 parts by weight of pulverized ammo- 
 nium nitrate and 1 part of ammonium chloride, and dissolve in 3 
 parts of water (not warmer than 10° C), stirring the same whUe 
 dissolving with a test-tube containing a little water. The water in the 
 test tube will be quickly frozen. A finger pj^ 
 
 placed in the solution will feel a painful 
 sensation of cold, and a thermometer wiU 
 indicate a temperature of about — 10° 0. 
 
 One of the most common freezing 
 mixtures consists of 3 parts of snow or 
 broken ice and 1 part of common salt. 
 The affinity of salt for water causes a 
 liquefaction of the ice, and the result- 
 ing liquid dissolves the salt, both oper- 
 ations requiring heat. 
 
 §136. Cold by evaporation. — Experiment l. Fill the palm 
 of the hand with ether ; the ether quickly evaporates and produces a 
 painful sensation of cold. 
 
 Experiment 2. Place water at about 10° C. in a thin porous cup, 
 such as is used in the Grove's battery (see page 190) , and introduce 
 
168 MOLECULAR ENERGY. — HEAT. 
 
 the bulb of a thermometer; although the experiment be conducted In a 
 warm room, the large surface exposed by means of the porous vessel 
 will so hasten evaporation that in the course of fifteen minutes there 
 will be a very sensible fall in temperature. 
 
 Experiment 3. Cover closely the bulb of an air thermometer (Fig. 
 117) with thin muslin, and partly fill the stem with water. Let one 
 person slowly drop ether on the bulb while another briskly blows the 
 air charged with vapor away from the bulb with a bellows. (Why ?) 
 The water iu the stem will quickly fteeze even in a warm room. 
 
 QUESTIONS. 
 
 1. Why do we bathe the fevered forehead with alcohol and water ? 
 
 2. How does perspiration contribute to our comfort ? 
 
 3. Why do we fan ourselves ? 
 
 4. Why does a windy day seem colder to us than a stiU day, although 
 the temperature is the same on both days ? 
 
 6. Why do we blow our hot tea, and why pour it Into a saucer? 
 6. How does sprinkling a floor cool the air of a room 1 
 
 § 137. Cold by expansion of gases. — "When a beer bottle 
 is opened, a fog is suddenly produced in the neck of the bottle 
 due to the chill of an expanding gas. 
 
 The work done in the expansion of a gas consists only in 
 forcing back the surrounding air. If confined air is allowed to 
 expand into a vacuum, no work is done, and the temperature is 
 not changed. By allowing condensed air containing, as it 
 usually does, watery vapor, to escape suddenly from the vessel 
 in which it is confined, icicles have been formed around the 
 orifice whence it escapes. 
 
 § 138. Potential energy converted into heat by the 
 solidifloation of liquids and the liquefaction of vapors.— 
 Experiment 1. Boil about \ liter of water in a glass flask, and add, 
 slowly, pulverized sodium sulphate until the boiling water refuses to 
 dissolve more (hot water will dissolve about twice its weight of this 
 substance). Then set the hot solution in a place where it will not be 
 disturbed, and let it stand for about 24 hours, that it may acquire the 
 temperature of the room. Thrust the bulb of a thermometer into the 
 solutiou,! and at the same time drop in a lump of sodium sulphate; 
 1 The solution is now said to be supersaturated. 
 
POTENTIAL ENEKGY, ETC. 
 
 169 
 
 solidification instantly sets in, and in a few seconds the liquid mass 
 will be almost wholly replaced by crystals. At the same time the 
 temperature, as indicated by the thermometer, rapidly rises. 
 
 The heat which is consumed in dissolving a solid, and in giv- 
 ing the molecules an advantage of position, is restored when the 
 molecules are allowed to resume their original positions, as a 
 falling weight restores the kinetic energy consumed in raising it. 
 
 Experiment 2. Place wateral; about 10° C. in a bottle, and intro- 
 duce a thermometer. Surround the bottle with a snow and salt freez- 
 ing mixture ; the temperature of the water rapidly falls until it reaches 
 0°C. 
 
 The heat which the water loses is consumed in melting the ice 
 and dissolving the salt. AtO°C. the water begins to freeze, 
 and the temperature remains stationary until all the water is 
 frozen, when its temperature again falls. The temperature of 
 the freezing mixture is much lower than that of the water while 
 freezing ; the latter, then, must give heat to the former. That 
 the mixture receives heat 
 is shown by the continua- 
 tion of the melting and 
 dissolving. But as the 
 temperature of the water 
 while freezing does not 
 fall, it must be that the 
 heat which it surrenders 
 during solidification arises 
 from the conversion into 
 heat of the potential "en- 
 ergy possessed by the molecules of the liquid. 
 
 Experiment 3. Arrange apparatus as in Figure 118. When water 
 in the flask A begins to boil, introduce the end of the delivery tube B 
 into a vessel C of water at 0° C. The steam that passes through the 
 tube is condensed on entering the cold water and heats the water. 
 When a considerable portion of the water has boiled away, weigh the 
 water remaining in A, and ascertain the quantity that has been con- 
 
170 MOLEOULAB ENERGY. — HEAT. 
 
 verted into steam ; also ascertain tlie temperature of the water in C, 
 and the number of calories which it has received. 
 
 For every kilogram of water that is converted into steam, 
 5.37'' of water (practically, considerably less than this quantity, 
 in consequence of loss of heat by radiation and evaporation 
 from C) will be raised from 0° to 100°. As 1'^ requires 100 
 units of heat to raise it to 100°, the 5.37'^ must require 637 units 
 of heat. But the steam raises the water to its own temperature 
 without having its own temperature lowered. (Whence come 
 the 537 units of heat that raise the temperature of the water?) 
 
 Heat that is consumed in liquefying solids, and in vaporizing 
 liquids, is alwxys restored when the reverse change takes place. 
 Farmers well understand that water, in freezing, gives out a 
 great deal of heat, — at a low temperature, it is true, but still 
 high enough to protect vegetables which freeze only when con- 
 siderably colder than melting ice. The fact that steam, in 
 condensing, generates a large amount of heat, is turned to 
 practical use in heating buildings by steam. 
 
 / 
 XXIV. SPECIFIC HEAT. 
 
 § 139. Temperatures of diflterent substances raised 
 unequally by equal quantities of heat. — Will equal quanti- 
 ties of heat applied to equal weights of different substances 
 raise their temperatures equally? 
 
 Experiment 1. Mix l* of water at 0° with 1^ at 20° ; the tempera- 
 ture of the mixture becomes 10°. The heat that leaves I'' of water 
 when it falls from 20° to 10° is just capable of raising 1^ of water from 
 0° to 109. 
 
 Experiment 2. Talce (say) 3008 of sheet lead, and make a loose 
 roll of it, and suspend it by a thread in boiling water for about five 
 minutes, that it may acquire the same temperature (100° C.) as the 
 water. Remove the roll from the hot water, and immerse it as quickly 
 as possible in 3008 of water at 0°, and introduce the bulb of a ther- 
 mometer. Note the temperature of the water when it ceases to rise, 
 which will be found to be about 3° (a'ccurntely 3.8°-i-V The lead cools 
 
SPECIFIC HEAT DEFINED. 171 
 
 very much more than the water warms. Lead falls about 33° for every 
 degree an equal weight of water is wai'med. 
 
 From the first experiment we Infer that a body, in cooling a 
 certain number of degrees, gives to surrounding bodies as much 
 heat as it takes to raise its temperature the same number of 
 degrees. From the second experiment we learn that the quan- 
 tity of heat that raises 1'' of lead from 3.3°+ to 100°, when 
 transferred to water, can raise 1'' of water only from 0° to 3.3°. 
 Hence we conclude that equal quantities of heat, applied to equal 
 weights of different substances, raise tJieir temperatures unequally. 
 
 § 140. Capacity for heat. — If equal weights of mercury, 
 alcohol, and water are exposed to the same heat, the mercury 
 wiU rise 30°, and the alcohol nearly 2°, while the water is rising 
 1°. From this we infer that to raise a kilogram of each of 
 these substances from 0° to 1° requires 30 times as much heat 
 for the water as for the mercury, and twice as much as for the 
 alcohol. Since heat affects the temperature of water less than 
 mercury and alcohol, the first is said to have a greater capacity 
 for heat. Tlie number of units of heat required to raise the tem- 
 perature of a body 1°C., is called its capacity for heat. 
 
 § 141. Specific heat defined. — It is a great convenience 
 to be able to compare the capacities of different substances for 
 heat. The standard employed is water, and the ratio which 
 expresses the comparison is called specific heat. 
 
 The specific heat of a body is the ratio of its capacity for heat 
 to that of an equal weight of water. 
 
 From the data obtained in the last experiment we may calcu- 
 late the specific heat of lead as follows : The same quantity of 
 heat that raises the water 3.3° (from 0° to 3.3°) raises the leail 
 96.70° (from 3.3° to 100°) ; hence, to raise the lead 1° requires 
 
 Q Q 
 
 -^-—=.034+ as much heat as to raise the water 1°. 
 96.7 
 
 The specific heat of all solids and liquids, and most gases, 
 
 increases slightly with the temperature. Thus water at 0° C. har, 
 
172 MOLECULAR ENERGY. — HEAT. 
 
 a specific heat of 1 ; at 40°, 1.0013 ; at 80°, 1.0035. Substances 
 in the liquid state usually have a higher specific heat than in the 
 solid or gaseous state. Thus water has nearly double the 
 specific heat of ice, and a little more than double the specific 
 heat of steam. 
 
 KEFERENCE TABLES. 
 
 Table of mean specific heat between 0° C. and 100° C. 
 
 Iron 1138 
 
 Hydrogen 3.4090 
 
 Air .2375 
 
 Sulphur 202G 
 
 Glass 1770 
 
 Copper 0952 
 
 Mercury 0333 
 
 Lead 0314 
 
 Specifiji heat of the same substance in different states. 
 
 Solid. Liquid. U.iseous. 
 
 Water 5040 1.0000 4805 
 
 Bromine 0833 1060 0555 
 
 Lead 0314 0402 
 
 Alcohol 55-77 45 
 
 § 142. One cause of diflference in capacity for heat. — 
 Of the whole quantity of heat applied to a solid or liquid body, 
 only a part goes to increase the heat of the body, and thereby 
 to raise its temperature ; the remainder performs interior work, 
 in overcoming cohesion between the molecules of the body, and 
 in forcing them to take up new positions. (Since, then, some 
 of the heat is converted into potential energy, we may properly 
 introduce the subject of specific heat at this place.) The 
 greater the portion of heat consumed in interior work upon a 
 body, the less there is left to raise its temperature, and conse- 
 quently the greater its capacity for heat. Thus, when equal 
 quantities of heat are applied to equal masses of water and lead, 
 more is consumed {i.e., converted in potential energy) in interior 
 work upon the water than upon the lead ; consequently the tem- 
 perature of the former is not raised as much as that of the 
 latter.. The limits of this work forbid the discussion of the 
 causes of the difference of capacity for heat of different gases. 
 
QUESTIONS AND PROBLEMS. 173 
 
 § 143. Greatoapacityof water for heat. — Water requires 
 more heat to warm it, and gives out more in cooling through a 
 given range of temperature, than any substance except hydrogen. 
 The quantity of heat that raises a kilogram of water from 0° 
 to 100° C. would raise a kilogram of iron from 0° to 800° or 
 900° C, or above a red heat : Conversely, a kilogram of water 
 in cooling from 100° to 0° C. gives out as much heat as a kilo- 
 gram of iron in cooling from about 900° to 0° C. 
 
 QUESTIONS AND PROBLEMS. 
 
 1. How much heat Is required to change 100'' of ice at 0° iuto steam 
 at 100° C? 
 
 2. (a) 1000'' of steam at 100° C. is conveyed by pipes through a 
 building, and the water resulting from its condensation returns to the 
 boiler at a temperature of 80°; how mucli heat is given out in the build- 
 ing. (6) The same quantity of heat would raise how many kilograms 
 of water from 0° to 100° ? 
 
 3. 50^ of water at 100° will melt how many pounds of ice at 0° C? 
 
 4. How much heat is required to raise I'' of ice from — 10° to 10° C? 
 
 5. (a) Apply the same quantity of heat to equal weights of ice and 
 water, each at a temperature of 0° C. ; when the latter reaches the 
 boiling point what will be the temperature of the former ? (6) Why 
 will not both have the same temperature ? 
 
 6. What eflfect on the temperature of the air has the freezing of the 
 water of lakes and other bodies of water ? 
 
 7. If 1^ of iron at 100° is immersed in I'' of water at 0° C, what will 
 be the resulting temperature ? 
 
 8. What is the specific heat of a substance, 1^ of which at 100°, when 
 put into I'' of water, at 0° raises its temperature to 5° C. ? 
 
 9. 50'' of mercury at 80° will melt what weight of ice at 0° C. ? 
 
 10. Why is hot loater in bottles often used to warm beds in prefer- 
 ence to other substances ? 
 
 11. If there were no water on the earth, why would the difference 
 in temperature between day and night, and between summer and win- 
 ter, far exceed what it is now ? 
 
 12. "Why are places in vicinity of water less subject to extremes of 
 heat and cold than places inland ? 
 
174 MOLECtTLAE ENERGY. — HEAT. 
 
 XXV. THEBMO-DYNAMICS. 
 
 § 144. Thermo-Dynamics defined. — Thermo-dynamics is 
 that branch of science that treats of the relation between heat and 
 mechanical work. One of the most important discoveries in 
 science is that of the equivalence of heat and worJc;, that is, that 
 a definite quantity of mechanical work can always produce a 
 definite quantity of heat; and conversely, this heat, if the conver- 
 sion were complete, can perform the original quantity of work. 
 
 § 145. Correlation and conservation of energy. — The 
 proof of the facts just stated was one of the most importajit 
 steps in the establishment of the grand twin conceptions of 
 modern science. (1) That all kinds of energy are so related to 
 one another that energy of any kind can be changed into energy of 
 any other kind, — known as the doctrine of correlation of 
 ENERGY ; (2) That when one form of energy disappears, an 
 exact equivalent of another form always takes its place, so that 
 the sum total of energy is unchanged, — known as the doctriije 
 of CONSERVATION OF ENERGY. Thcse two principles constitute 
 the corner-stone of physical science. 
 
 § 146. Joule's experiment. — The experiment to ascertain 
 the "mechanical value of heat," as performed by Dr. Joule of 
 England, was conducted about as follows. He caused a paddle- 
 wheel to revolve in water by means of a falling weight attached 
 to a cord wound around the axle of a wheel. The resistance 
 offered by the water to the motion of the paddles was the means 
 by which the mechanical motion of the weight was converted 
 into heat, which raised the temperature of the water. Taking 
 a body of a known weight, e.g., 80'', he raised it a measured 
 distance, e.g., 53"" high; by so doing 4240''8"' of work were 
 performed upon it, and consequently an equivalent .amount of 
 energy was stored up in it ready to be converted, first, into 
 mechanical motion, then into heat. He took a definite weight 
 
THE STEAM ENGINE. 175 
 
 of water to be agitated, e.g., 2^, at a temperature of 0°C. 
 4-fter the descent of the weight, the water was found to have 
 a temperature of 5° C. ; consequently the 2^ of water must have 
 received 10 units of heat (careful allowance being made for 
 all losses of heat) , which is the amount of heat-energy that is 
 equivalent to 4240''*^ of work, or 1 unit of heat is equivalent 
 to 424'^ of work (more accurately 423.985''8'"). 
 
 § 147. Mechanical equivalent of heat. — As a converse 
 of the above it may be demonstrated by actual experiment that 
 the quantity of heat required to raise I'' of water from 0° to 
 1° C. will, if converted into work, raise a 424'' weight 1"' high, 
 or 1'^ weight 424" high. According to the English system, the 
 same fact is stated as follows : The quantity of heat that will 
 raise 1 lb. of water TF. will raise 772 lbs. 1 ft. high. The 
 quantity, 424''*^"', or 772 ft. lbs. , is called the mechanical equiva- 
 lent of heat, or Joule's equivalent (abbreviated, simply J.). 
 
 XXVI. STEAM ENGINE. 
 
 § 148. Description of a steam engine. — A steam engine 
 is a machine in which the elastic force of steam is the motive 
 power. Inasmuch as the elastic force of steam is entirely due 
 to heat, the steam engine is properly one form of a heat engine; 
 that is, it is a machine by means of which heat is continuously 
 transformed into work or mechanical motion. 
 
 The modern steam engine consists essentially of an arrange- 
 ment by which steam from a boiler is conducted to both sides 
 of a piston alternately ; and then, having done its work in driv- 
 ing the piston to or fro, is discharged from both sides alter- 
 nately, either into the air or into a condenser. The diagram in 
 Figure 119 wiU serve to illustrate the general features and the 
 operation of a steam engine. The details of the various 
 mechanical contrivances are purposely omitted, so as to present 
 the engine as nearly as possible in its simplicity. 
 
176 
 
 MOLECTJLAB ENERGY. — HEAT. 
 
 In the diagram, B represents the boiler, F the furnace, S the steam 
 pipe through which steam passes from the boiler to a small chamber 
 VC, called the valve chest. In this chamber is a slide valve V, which, as 
 it is moved to and fro, opens and closes alternately the passages M 
 and N leading from the valve chest to the cylinder C, and thus admits 
 the steam alternately each side of the piston P. When one of these 
 passages is open the other is always closed. Though the passage 
 between the valve chest and the space in the cylinder on one side of 
 
 Fig. U9. 
 
 the piston is closed, thereby preventing the entrance of steam into this 
 space, the passage leading from the same space is open through the 
 interior of the valve so that steam can escape from this space through 
 the exhaust pipe E. Thus, in the position of the valve represented in 
 the diagram, the passage K is open, and steam entering the cylinder 
 at the top drives the piston in the direction indicated by the arrow. At 
 the same time the steam on the other side of the piston escapes through 
 the passage M and the exhaust pipe E. While the piston moves to the 
 left, the valve moves to the right, and eventually closes the passage 
 
THE STEAM EKGINE. 177 
 
 N leading from the valve chest, and opens the passage M into the same, 
 ivnd thus the order of things is reversed. 
 
 Motion is communicated by the piston through the piston rod R to 
 the crank G, and by this means the shaft A is rotated. Connected with 
 the shaft by means of the crank H, is a rod R' which connects with the 
 valve V, so that as the shaft rotates, the valve is made to slide to and 
 fro, and always in the opposite direction to that of the motion of the 
 piston. 
 
 The shaft carries a, fly-wheel W. This is a large, heavy wheel, having 
 the larger portion of its weight located near its circumference; it 
 serves as a reservoir of energy which is needed to carry the shaft past 
 two points (called the dead points) in each revolution of the shaft, where 
 the power communicated directly by the steam is ineffectual in moving 
 the shaft. It also assists to make the rotation of the shaft and all other 
 machinery connected with it uniform, so that sudden changes of velo- 
 city resulting from sudden changes of the driving power or resistances 
 are avoided. (Why should the wheel be heavy? Why should it be large? 
 Why should the rim be heavy? See p. 102.) By means of a belt pass- 
 ing over the wheel W motion may be communicated from the shaft 
 to any machinery desirable. 
 
 § 149. Condensing and non-oondensing engines.' — 
 
 Sometimes steam, after it has done its work in the cylinder, is 
 conducted through the exhaust pipe to a chamber Q called a 
 condenser, where, by means of a spray of cold water introduced 
 through a pipe T, it is suddenly condensed. This water and the 
 condensed steam must be pumped out of the condenser by a 
 special pump called technically the air-pump; thus a partial 
 vacuum is maintained. Such an engine is called a condensing 
 engine. The advantage of such an engine is obvious, for, if the 
 exhaust pipe, instead of opening into a condenser, communicates 
 with the outside air as in the non-condensing engine, the steam 
 is obliged to move the piston constantly against a resistance 
 arising from atmospheric pressure of 15 pounds for every square 
 inch of the surface of the piston. But in the condensing engine no 
 resistance arises from atmospheric pressure, and so with a given 
 
 1 The terms, low pressure and Mghpreasvre engines, are not distinctive as applied 
 to engines of tlie present day. 
 
178 MOLECULAR ENERGY. — HEAT. 
 
 steam pressure in the boiler the effective pressure on the piston 
 is considerably increased ; hence, condensing engines are usually 
 more economical in their working. 
 
 § 150. The locomotive. •— The distinctive feature of the loco- 
 motive engine is its great steam-generating capacity, consideriug its 
 size and weight, which are necessarily limited. To do the work ordi- 
 narily required of it, from three to six tons of water must be converted 
 into steam per hour. This is accomplished in two ways : viz., first, by 
 a rapid combustion of fuel (from a quarter of a ton to a ton of coal 
 per hour); second, by bringing the water in contact with a large 
 extent (about 800 sq. ft.) of heated surface. The fire in the " fire-box " 
 A (see cut on the opposite page) is made to burn briskly by means of a 
 powerful draft which is created in the following manner : The exhaust 
 steam, after it has done its work in the cylinders B, is conducted by the 
 exhaust pipe C to the smoke box D, just beneath the smoke stack B. 
 The steam as it escapes from the blast pipe F pushes the air above it, 
 and drags by friction the air around it, and thus produces a partial 
 vacuum in the smoke box. The external pressure of the atmosphere 
 then forces the air through the furnace grate and hot-air tubes G, and 
 thus causes a constant draft. The large extent of heated surface is 
 secured as follows : The water of the boiler is brought not only in con- 
 tact with the heated surface of the fire box, but it surrounds the pipes 
 G (a boiler usually contains about 150). These pipes are kept.hot by 
 the heated gases and smoke, all of which must pass through them to 
 the smoke box and smoke stack. 
 
 Study the cat carefully, trace the course of the steam from the boiler 
 H through the throttle valve I (under the control of the engineer), 
 steam pipe J, etc., to its exit from the smoke stack. Ask some engi- 
 neer to explain fi-om the object the offices of such parts as you do not 
 understand. 
 
 The steam engine, with all its merits and with all the improve- 
 ments which modern mechanical art has devised, is totday an 
 exceedingly wasteful machine. The best engine that has been 
 constructed utilizes only twenty per cent of the heat-powei 
 used. 
 
CHAPTER IV. 
 
 ELEOTRICITY AND MAGNETISM. 
 
 There is a large and important class of phenomena depending 
 on new principles that we have now to study ; among these are 
 lightning, the actions of telegraph instruments, the electric light, 
 magnetic attraction and repulsion, etc. We shall inquire whether 
 energy is involved in these actions as in all those we have so far 
 studied ; and, if so, where it comes from, and under what laws it 
 acts, and what finally becomes of it. 
 
 If we chose to begin with those experiments easiest to per- 
 form, we should take those with magnets, and some of those to 
 be studied under the head of Frictional Electricity; but we 
 should find it difiicult to see clearly how the subject of energy 
 was to be introduced. So let us take first some experiments 
 that will lead us more easily to this great central idea. 
 
 XXVII. CURRENT ELECTRICITY. 
 
 § 151. Introductory experiments. — Experiment i. Take 
 a strip of sheet copper and a strip of sheet zinc, each about lO^"" long 
 and 4™ wide. Take also a tumbler two-thirds fuU of „. ,„„ 
 
 Fig. 120. 
 
 water, and to it add about two tablespoonfuls of sul- 
 phuric acid. Place the zinc strip in the liquid; in- 
 stantly bubbles of gas collect on the surface of the 
 zinc, break away from it, rise to the surface of the 
 liquid, and are rapidly replaced by others. These are 
 bubbles of hydrogen gas, and may be collected and 
 burned. It is soon found that the zinc wastes away, 
 or is dissolved In the liquid. 
 
 Experiment 2. Place the copper strip in the liquid 
 a little way from the zinc, but nowhere touching it; no bubbles are 
 formed. Now bring the extremities of the two strips that project from 
 the liquid Into contact, as in Figure 120; quickly a change takes place; 
 
180 ELECTRICITY AND MAGNETISM. 
 
 torrents of bubbles now rise from the copper, and only a veiy few 
 from the zinc ; still it is found, after a lapse of time, that the copper 
 has undergone no change, while the zinc has wasted away. 
 
 Experiment 3. Withdraw the zinc from the liquid, and while it is 
 yet wet rub a little mercury over its surface, so that it may become 
 completely wet with the liquid metal. Now repeat the above experi- 
 ments In order. First, it is found that the zinc, when alone in the 
 liquid, is not affected by it, and no bubbles of gas are formed. But 
 when the two metals are immersed in the liquid, and are brought into 
 contact, bubbles of gas quickly appear on the copper as before, but 
 none appear on the zinc, although the zinc is still the metal that wastes 
 away, while the copper remains unchanged. 
 
 Experiment 4. Instead of placing the metals in contact, connect 
 them by means of a wire of any metal, the points of contact being 
 clean ; the bubbles are given off at the copper as before. Cut the con- 
 necting wire at any point, or separate it ftom the zinc or copper ; all 
 evolution of bubbles ceases, but begins again the instant the contact is 
 made. 
 
 Experiment S. Interpose between the connecting wire and the 
 plates, or between the cut ends of the wire, a piece of paper, wood, or 
 rubber, or use some one of these, instead of a wire, to connect the two 
 plates ; no action appears in the cell. 
 
 Thus it appears that there must be a connection, and that too 
 of a particular kind, between the two metals, in order that 
 action may occm-. The connecting wire, then, is an important 
 factor in the changes that occur, and it seems altogether prob- 
 able that some influence is exerted by the metals upon one 
 another through the wire ; in other words, that something 
 unusual is going on in the wire when so used. 
 
 Does the connecting wire possess any unusual properties dur- 
 ing this use ? 
 
 Experiment 6. Take an ordinary compass, or poise a magnetic 
 needle at its center, either by a pivot, as in Figure 121, or by a fine, 
 untwisted sUk thread, and arrange the connecting wires as in the figure. 
 The needle, when at rest, points north and south. The connecting 
 wire being over the needle, and parallel with it, bring the two extremi- 
 ties of the wire into contact; instantly the needle turns on its axis, 
 tending to place itself at right angles to the wire, and, after a few 
 
INTEODUCTORY EXPERIMENTS. 
 
 181 
 
 Fig. 121. 
 
 vibrations, takes up a permanent position, forming an angle with tlie 
 wire. Tliis deviation from its normal position is called a deflection of 
 the needle. Separate the two extremities of the wires ; the needle 
 swings back to its normal position. 
 
 Experiment 7. Bring the ends of the wires together as before, 
 interposing a piece of paper be- 
 tween them; the needle is not 
 moved. This is another illus- 
 tration of the necessity of em- 
 ploying a suitable substance for 
 a connector in order that any 
 action may take place. 
 
 Experiment 8. Take a large 
 iron nail, and plunge one end of 
 it into iron filings, and then re- 
 move it ; no filings cling to the 
 nail. Next, wrap a piece of pa- 
 per around the nail, leaving the 
 
 ends exposed, and wind around it 20 or more turns of copper wire, 
 taking pains that the coils do not touch each other. Now connect the 
 wire with the zinc and copper just used, so that there will be a con- 
 tinuous connection from one strip to the other through the coil, and 
 dip one end of the nail again into the filings; raise the nail, and a 
 considerable quantity of filings cling to the nail. 
 
 From these experiments, and others which will be performed 
 later, it appears that when the zinc and copper are thus placed 
 in acid and connected by a wire, the wire exhibits unusual prop- 
 erties. The cause of these and many other allied phenomena 
 is called electricity, and these properties in the wire are attributed 
 to the passage of an electric current through it. 
 
 Almost from the dawn of the science of electricity there have 
 been many who have believed in the existence of an " electric 
 fluid " ; but it is not yet claimed that there is any •positive proof 
 of its existence, and therefore we cannot affirm that a current 
 passes through the wire. Yet the theory upon which these 
 terms are based is at least a convenient one by which to explain 
 the various phenomena, and the terms are therefore universally 
 used. 
 
182 
 
 BLBCTEICITY AND MAGNETISM. 
 
 § 152. Some definitions. — Experiments (not easily per- 
 formed by the pupil) show that the current traverses the liquid 
 between the metallic plates in the battery at the same time that 
 it traverses the connecting wire, so that the current makes a 
 complete circuit. The term circuit is applied to the entire path 
 along which electricity is supposed to flow, and the wire along 
 which it flows is called the conductor. Bringing the two extremi- 
 ties of the wires in contact, and separating them, is called, tech- 
 nically, tndking and breaking, or closing and opening, the circuit. 
 
 Our arrangement of acidulated water and two metals is called 
 a voltaic^ cell, element, ov pair. A series of cells, properly con- 
 nected, is called a battery, though this term is sometimes applied 
 to a single cell. 
 
 § 153. Direction of the current. — It is evidently neces- 
 sary, in defining a current, to know its direction ; but as5 no 
 
 Fig. 122. 
 
 Fig. 123. 
 
 phenomena known serve to indicate the du-ection, electricians 
 have universally agreed to assume that in such a cell as described 
 the electricity flows from the copper to the zinc in the wire. 
 
 Experiment. Place the conducting wire over and parallel with a 
 magnetic needle, in the manner represented in Figure 122 ; the north 
 end of the needle is deflected toward the west. Turn the cell half-way 
 siround so as to have the position in Figure 123 ; a deflection of the 
 needle toward the east shows that the current Is reversed. 
 
 1 Voltaic, ./V-om Volta, an ItaliaD, who devised the voltaic pile, vfhioh is the parent 
 of all hiitteries. 
 
POTENTIAL. 183 
 
 §154. Poles or electrodes. — The copper strip is fre- 
 quently called the negative plate, and the zinc strip the positive 
 plate, and the end of any conductor connected with the copper 
 or negative plate is called the positive pole, or electrode, while 
 the end connected with the zinc or positive plate is called the 
 negative pole, or electrode. Then, by our assumption, if we bring 
 together the + and — electrodes, the current passes from the 
 former to the latter, across the junction ; and generally that plate 
 and that electrode is + from which the current goes, and that 
 plate and that electrode is — to which the current goes. 
 
 § 155. Potential. — If a current of water is to flow from 
 one vessel A to another B through a pipe, we know that there 
 must be a greater pressure at the end of the pipe next A than 
 at the other end ; i.e., in ordinary language, the head of water 
 in A is higher than in B. So in the study of electricity we find 
 two bodies in different conditions such that a current of elec- 
 tricity flows from one (A) to the other (B) , and we say that A has 
 a higher potential than B. In the experiments already tried the 
 +electrode, or the wire connected with the copper, has a higher 
 potential (according to our assumption for the direction of the 
 ciurent) than the —electrode or the wire connected with the 
 zinc. 
 
 It is not necessary that we know the hight from the center of 
 the earth, or above the level of the sea, of a reservoir, and the 
 tank it is to fill ; what we want to know is the difference in 
 hight between the two. Just so it is difference of potential 
 tJiat determines the direction of the flow, and the quantity of 
 electricity that is to flow through a given condrictor in a given 
 time. Sometimes the potential of a body is expressed as so 
 many units above or below that of the earth, assumed as 
 zero. 
 
 § 156. Ampere's rule for determining deflection, etc. — 
 If the magnetic needle is placed over the current, its deflection 
 
184 
 
 ELECTRICITY AND MAGNETISM. 
 
 Fig. ]24. 
 
 is the reverse of that produced when placed beneath it. This 
 tends to confuse ; but an artifice, proposed by Ampfere, will 
 readily enable us to determine the deflection, when the direction 
 of the current is known, and to deter- 
 mine the direction of the current when 
 that of the deflection is known. He 
 suggests that we imagine ourselves to be 
 swimming in the current, and with the 
 current, and facing the needle; in which 
 case the north end of the needle will 
 always he deflected towards our left. 
 (The pupil should test this rule experi- 
 mentally in various ways and many times, till he is familiar with 
 its application.) 
 
 § 157. Galvanosoope. — The magnetic needle serves the 
 double purpose of determining both the presence and direction of 
 a current in a wire. A needle used for these purposes is called 
 a galvanoscope.^ Electricity set in motion by a voltaic battery 
 is called galvanic or voltaic and sometimes current electricity. 
 
 EXERCISES. 
 
 1. Let the current be above the needle, and go from N to S ; what 
 will be its deflection? 
 
 2. Let the current be below the needle, and go from S to N ; what 
 deflection will it cause? 
 
 3. Let the needle be above the current ; what must be the direction 
 of the cm-rent when the north end is deflected to the east? 
 
 4. Let the needle be below the current, and the deflection toward the 
 east; what is the direction of the current? 
 
 5. What is the effect when the current is at the side of the needle? 
 
 § 158. How electric energy originates. — If you take the 
 liquid from a battery after considerable zinc has disappeared in it, 
 and evaporate it, there will crystallize out of it a white, transparent 
 
 > Oalvanoscope, named for Oalvani, one of the early discoverers in electricity. 
 
WHY THE HYDROGEN APPEARS, ETC. 186 
 
 solid in needle-like crystals. This substance is a compouncl of 
 zinc and sulphuric acid, and is called zinc sulphate. The solu- 
 tion of the zinc is the result of a chemical action between the 
 zinc and the acid. Hydrogen is another product of the action. 
 The water serves as a solvent of the zinc sulphate. The chemist 
 symbolizes sulphuric acid thus, Hj SO4 ; zinc, Zn. He describes 
 the change that occurs by saying that the zinc replaces the 
 hydrogen Hj in the acid (in other words, the hydrogen is set 
 free from the combination) , while the SO4 part of the acid unites 
 with the zinc, and forms zinc sulphate, ZnSOi. But we have 
 also discovered another important result of the operation ; 
 namely, that electric energy is developed by the chemical action 
 between the liquid and the zinc. 
 
 Is the electric energy created out of nothing ? "We have already 
 become familiar with the fact (§ 10.5, page 140) that chemical 
 potential energy in a lump of coal may be converted into kinetic 
 energy, as is constantly done in the steam engine. Similarly, 
 we might burn zinc to make steam. Coal and zinc, then, possess 
 a power to enter into new combinations ; this power is usually 
 called chemical energy, or chemism. It exists in a potential 
 condition, until it is aroused from this dormant state by bring- 
 uig together suitable substances. When chemical energy be- 
 comes kinetic, it may be transformed into mechanical energy, 
 as when a cannon-ball is set in motion by the burning of gun- 
 powder; or it may be changed into heat, as in the ordinal^ 
 burning of fuel ; or into both heat and electric energy, as in the 
 burning of zinc in the battery. 
 
 § 159. Why the hydrogen appears at the copper plate. 
 
 — Wlien zinc dissolves in sulphuric acid, hydrogen is liberated, 
 and ordinarily rises at once in bubbles ; but in the voltaic cell it 
 rises from the copper, yet no bubbles are seen to move through 
 the liquid between the plates. As a plausible but imperfect ex- 
 planation of these phenomena, the well-known hypothesis of 
 Grotthuss was offered. It assumes what many chemists believe. 
 
186 ELECTRICITY AND MAGNETISM. 
 
 that at the instant that a substance is liberated from a com- 
 pound it possesses unusual readiness to enter into combination 
 with other molecules. 
 
 Let the circles 1, 2, 3, etc. (Fig. 125), represent a series of 
 molecules of H2SO4 connecting the two plates. At the instant 
 Pig. 135. the circuit is closed 
 
 the SO4 of molecule 1 
 unites with a molecule 
 of zinc, setting free 
 its H2 ; this instantlj' 
 unites with the SO4 of 
 molecule 2, forming a 
 new molecule, 1', of 
 H2SO4, and setting 
 free the H2 of molecule 
 2 . This H2 unites with 
 the SO4 of molecule 3, 
 forming molecule 2'. This decomposition and recomposition 
 continues tUl the Hj of molecule 6 is set free. This Hj unites 
 with other molecules of hydrogen, and finally rises in a bubble 
 to the surface ; so the molecule of hydrogen that escapes is 
 not the molecule that was first set free at the zinc plate. 
 
 § 160. Electro-chemical series. — K two plates of zinc 
 were used in a cell, instead of a zinc and a copper, we should 
 have a tendency to opposite currents, which would neutralize 
 each other ; or, stated differently, there would be no difference 
 of potential between the two plates, and so no current. It is, 
 therefore, important that only one of the metals should be acted 
 upon. The greater the disparity between the two solid elements, 
 with reference to the action of the liquid on them, the greater the 
 difference in potential ; hence, the greater the current. In the fol- 
 lowing electro-chemical series the substances are so arranged 
 that the most electro-positive, or those most affected by dUute 
 sulphuric acid, are at the beginning, while those most electro- 
 
IMPORTANCK OF AMALGAMATING THE ZINC. 187 
 
 negative, or those least affecfed by the acid, are at the end. The 
 arrow indicates the direction of the current through the liquid. 
 
 ^ . a a 
 S ^> n o 
 
 + g § .s I I I 1 f- 
 
 -> 
 
 It will be seen that zinc and platinum are the two metals best 
 adapted to give a strong current. 
 
 The essential parts of any galvanic cell in the ordinary' form 
 are a liquid and two different solids, one of which is more 
 readily acted upon chemically b}' the liquid than the other. 
 
 § 161. Importance of amalgamating the zinc. — All 
 commercial zinc contains impurities, such as carbon, iron, etc. 
 Figure 126 represents a zinc element having on its surface a 
 particle of iron a, purposely magnified. If such a 
 plate is immersed in dilute sulphuric acid, the par- 
 ticles of iron jrith the zinc will form numerous voltaic 
 circuits, and a transfer of electricity along the surface 
 will take place. This coasting trade, as it were, be- 
 tween the zinc and the impurities on its surface, 
 diverts so much from the regular battery current, and 
 thereby weakens it. In addition to this, it occasions 
 a great waste of chemicals, because, when the regular 
 circuit is broken, this local action, as it is called, still 
 continues. If pure zinc were available, no local action would 
 occur at any time, and there would be no consumption of 
 chemicals, except at times when the circuit is closed. If 
 mercury is rubbed over the surface of the zinc, after the latter 
 has been dipped in acid to clean its surface, the mercury dis- 
 solves a portion of the zinc, forming with it a semi-liquid 
 amalgam which covers up its impurities, and the amalgamated 
 zinc then comports itself like pure zinc. 
 
188 
 
 ELECTRICITY AND MAGNETISM. 
 
 XXVIII. VARIOUS BATTERIES. 
 
 § 162. Polarization of plates. — When the zinc and cop- 
 per elements are first placed in the dilute acid, a very good 
 current of electricity is produced ; but the current soon becomes 
 feeble. The cause is easily discovered. The liberated hydro- 
 gen adheres very strongly to the copper, as there is nothing for 
 it to unite with chemically ; and therefore the plate is verj- soon 
 visibly covered with bubbles, which may be scraped off with a 
 feather or swab, but only to have the same thing repeated.' This 
 coating of bubbles impedes, to a considerable extent, the flow 
 of electricity, and diminishes the current. Besides, a plate 
 coated with hydrogen is more strongly electro-positive than usual, 
 and so, as the coating slowly forms, the difference of potential 
 between the two plates becomes less and less ; the current, 
 therefore, must become weaker and weaker as the coating thick- 
 Fig. 127. ^^^- '^^^s action is usually called polariza- 
 tion of the plates. Very many methods have 
 iix been devised for remedying these evils. They 
 are all included in two classes : mechanical 
 and chemical methods. 
 
 § 163. Smee battery. — The Smee bat- 
 tery (Fig. 127) is an example of the former 
 class. A silver plate, or sometimes a lead 
 plate, is coated with a fine, powdery deposit 
 of platinum, which gives the surface a rough 
 character, so that the hydrogen will not 
 readily adhere to it. Dilute sulphuric acid is used in this bat- 
 tery. This plate is suspended between two zinc plates, but not 
 allowed to touch them. 
 
 A very effective battery may be constructed by arranging that 
 the copper plate may revolve in the liquid, so that the hydrogen 
 may be removed by friction between the plate and liquid. But 
 this necessitates a constant force to keep the plate in motion. 
 
GRENET BATTERY. 
 
 189 
 
 No mechanical method can wholly prevent the collection of 
 hydrogen on the electro-negative plate. This can only be com- 
 pletely accomplished by furnishing some chemical with which the 
 hydrogen, as soon as liberated, may go into combination. 
 
 § 164. Grenet battery. —In the 
 Grenet or bottle battery the hydrogen 
 is disposed of by chemical action. 
 The chemical action is quite complex, 
 and will therefore be omitted. The 
 liquid used is a mixture of potassium 
 bichromate and sulphuric acid dis- 
 solved in water. The zinc plate Z 
 (Fig. 128) is suspended between two 
 carbon plates, C, C. The carbons 
 remain in the liquid all the time. 
 (Carbon is now largely used in 
 batteries for the electro - negative 
 plate.) 
 
 This battery gives a very energetic 
 current for a short time, but the liquid soon becomes exhausted. 
 It is a very convenient battery, as, when not in use, we have 
 only to draw the zinc out of the liquid by the brass stem a, 
 and, on pushing the zinc back into the liquid, action commences 
 immediatelj'. It is well to allow the battery to "rest" occa- 
 sionally by withdrawing the zinc from the liquid for a short time. 
 With one Grenet cell nearly every experiment described in this 
 book can be performed. 
 
 § 165. Bunsen's and Grove's batteries. — There is, 
 also, besides the single-fluid batteries, a large number of two- 
 fluid batteries. The zinc is immersed in the liquid to be de- 
 composed, which most frequently is dilute sulphuric acid, and 
 the conducting plate is surrounded with a liquid which can be 
 decomposed by hydrogen. The two liquids are usually sep- 
 
190 
 
 ELECTRICITY AND MAGNETISM. 
 
 arated by a porous partition of unglazed earthenware, which 
 prevents the liquids from mingling, except very slowly, but does 
 not prevent the passage of hydrogen or electricity. Bunsen's 
 battery (Fig. 129) has a bar of carbon immersed in strong nitric 
 acid contained in a porous cup. This cup is then placed in 
 another vessel containing the dilute sulphuric acid ; and im- 
 mersed in the same liquid is a hollow, cylindrical plate of zinc, 
 which nearly surrounds the porous cup. The hydrogen trav- 
 erses, by composition and recomposition, the sulphuric acid, 
 passes through the porous partition, and immediately enters into 
 chemical action with the nitric acid, so that none reaches the 
 
 carbon. There are produced by 
 this action, water — which in time di- 
 lutes the acid — and orange-colored 
 fumes of nitric oxide, which rise from 
 the battery. These fumes are very 
 offensive, corrosive, and poisonous. 
 If the nitric acid is first saturated 
 with nitrate of ammonium, the acid 
 will last longer without dilution, and 
 the fumes are almost entirely pre- 
 vented. Strong sulphuric acid will 
 not answer in anj^ battery. Usually, 
 to one part of sulphuric acid about 12 
 parts by weight or 20 by volume of water are added to dissolve 
 the sulphate of zinc formed. 
 
 Grove used a strip of platinum instead of the carbon rod in 
 his battery. When carbon is used for the negative plate, a so- 
 lution of bichromate of potassium is frequently substituted for 
 nitric acid, and thereby the disagreeable fumes are avoided. 
 Bunsen's and Grove's batteries are unequalled for powerful 
 and constant cuirents, and are the best for ordinary lecture- 
 room experiments ; but they require frequent attention, and 
 are expensive, so that they are little used for work of long 
 duration. 
 
GRAVITY BATTERY. 
 
 191 
 
 Fig. 130. 
 
 § 166. Gravity battery. — The battery principally used in 
 this counti-y for telegraphing is called the gravity battery. A 
 copper plate C, Figure 130, is 
 placed on the bottom of a vessel 
 and covered with crystals of cop- 
 per sulphate (blue vitriol), and 
 the whole covered with water. 
 As the vitriol dissolves, its spe- 
 cific gravity causes it to remain 
 at the bottom, in contact witli the 
 copper plate. The zinc plate Z 
 is suspended in the clear liquid 
 above. To start the action quickly, 
 a teaspoonful of common salt or 
 zinc sulphate is dissolved in the 
 water. As the chemical action 
 proceeds, the vitriol is decom- 
 posed, its sulphuric acid constitu- 
 ent unites with the zmc, forming soluble zinc sulphate, and the 
 copper constituent is deposited in a metallic state on the copper 
 plate. The zinc does not require amalgamation. 
 
 XXIX. EFFECTS PRODUCED BY ELECTRICITY. 
 
 § 167. Heating eflteot. — Experiment 1. Introduce between 
 the electrodes of a Bunsen or Grenet cell a piece of platinum wire A, 
 Figure 131, about e"™ long and in size about No. 30. The platinum wire 
 becomes white hot. 
 
 Experiment 2. Stretch the platinum wire over a gas-burner, turn 
 on the gas, and light it by the heat of the wire. 
 
 Experiment 3. Strew lycopodium powder over a tuft of cotton-wool, 
 and ignite it with the heated wire. 
 
 Experiment 4. Connect the battery wires (Fig. 131) with a gal- 
 vanometer (see page 198) G, as in the figure ; the needle is deflected. 
 Remove the platinum wire, and close the circuit ; the needle is deflected 
 more than before. 
 
 What transformations of energy took place in the above ex- 
 periments? 
 
192 
 
 ELECTRICITY AND MAGNETISM. 
 
 168. Luminous eflPeot. — We have already seen one illus- 
 
 j,[ jgj tration of this effect 
 
 in the glowing of the 
 
 white-hot platinum 
 
 •^■T wire. 
 
 Experiment. Attach 
 one pole of the battery 
 to a nie (Fig. 132), and 
 pass the other pole over 
 its rough surface. The 
 file forms part of the 
 circuit ; and as the wire 
 passes over it, the cir- 
 cuit is rapidly made and 
 broken, and each break 
 causes a spark at the point where the circuit is broken. The shower 
 of sparks that flies from the file is due to red-hot 
 _. „. particles of iron that 
 
 are projected into the 
 
 § 169. Chemical 
 effect. — Experi- 
 ment 1. Steep some 
 leaves of purple cab- 
 bage; the infusion has a deep purple color. Dis- 
 solve a little caustic soda, and pour a few drops 
 of the solution into a portion of the infusion, and the purple will be 
 changed to a green. Caustic soda is an alkali, and cabbage infusion is 
 turned green only by alkalies. Pour a few drops of dilute sulphuric acid 
 into another portion of the infusion, and the purple will be changed to a 
 red. Only acids turn purple cabbage infusions red. Now prepare a con- 
 centrated solution of sodium sulphate. Color the solution with a por- 
 tion of the purple cabbage infusion, and partly fill a V-shaped glass tube 
 (Fig. 133) with this liquid. Employ a battery of two Grove or Grenet 
 cells connected in series. (See p. 208.) Attach to the poles of the 
 battery-wires two narrow strips of platinum, and place one of these 
 strips in each branch of the tube, a little way apart, so that the current 
 will be obliged to traverse a part of the liquid. Close the circuit; 
 bubbles of gas are immediately disengaged from the platinum strips ; 
 
CHEMICAIi EFFECT. 193 
 
 soon the liquid around the —pole is turned green, while that around 
 the +pole is turned red. Evidently decomposition of the sodium 
 sulphate has taken place ; an acid and an alkali are the results. 
 
 The current which is maintained by chemical action in the bat- 
 tery is capable of doing chemical work outside the battery. A 
 substance that maj' be decomposed by electricity is called an 
 electrolyte, and the process electrolysis.^ The electrolyte must be 
 a compound substance, and in a liquid state, either by solution 
 or fusion. A large number of substances are composed, like 
 sodium sulphate, of an acid, and either an alkali or some other 
 substance that will neutralize an acid. Any substance that will 
 neutralize an acid is called a base, and a compound of an acid 
 and a base is called a salt. When a salt is electrolyzed, the 
 base always appears at the —pole, and the acid at the +pole. 
 
 Experiment 2. Prepare a solution of the salt copper sulphate, 
 and subject it to electrolysis, as in the last experiment ; copper collects 
 on the —platinum, and sulphuric acid and oxygen at the +platinum. 
 Kemove the platinum strips, and introduce the copper terminals ; cop- 
 per is now deposited on the —pole as before, but the -|-pole wastes 
 away. 
 
 The chemical symbol for copper sulphate is CUSO4. By 
 electrolysis it is separated into Cu and SO4. "When a copper 
 4-pole is used, the SO4 immediately unites with a molecule of 
 the copper (Cu) of this pole, and forms a new molecule of cop- 
 per sulphate (CUSO4), which is dissolved by the water. This 
 accounts for the wasting away of the +pole. The solution 
 does not lose its strength, for as fast as a molecule of copper 
 sulphate is decomposed, another is formed. But when platinum 
 poles are used, the SO4 does not combine with the platinum, but 
 enters into chemical action with the water. The SO4 combines 
 with the h3-drogen of the water, forming sulphuric acid, and the 
 oxygen of the water is set free. (SO4 + H2O =H2S04 -)-0.) 
 
 • Electrolysis, a loosening by electricity. 
 
194 
 
 BLECTBICITY AND MAGKETISM. 
 
 Fig. 134. 
 
 The liberation of the oxygen is the result of a secondarj- chemi- 
 cal action, subsequent to the electrolytic action. 
 
 Experiment 3. Prepare a solution of tin chloride, by dissolving 
 scraps of granulated tin in hot hydrochloric acid. Add a little water. 
 Electrolyze this salt in solution, using platinum poles. A beautiful 
 growth of tin crystals will shoot out from the —pole and spread 
 towards the + pole, bearing a strong resemblance to vegetable growth ; 
 hence it is called the " tin tree." 
 
 In a similar manner, silver and lead trees may be prepared 
 
 from their salts, silver nitrate and 
 lead acetate. Each metal has its 
 own peculiar form of growth ; and 
 sometimes the same metal, par- 
 ticularly silver, exhibits different 
 forms, according to the strength 
 of the solution and the power of 
 the current. In Figure 134, A 
 represents a silver tree deposited 
 from a weak solution of silver 
 nitrate, and B a tree formed from 
 a still weaker solution of the 
 same. 
 
 Experiment 4. Remove the bot- 
 tom of a glass bottle having a wide 
 mouth, fit a cork to the mouth, and 
 pass two insulated wires through the 
 cork, terminating in platinum strips (Fig. 135). Fill two test-tubes an^ 
 part of the inverted bottle with dilute sulphuric acid, and invert the 
 tubes over the platinum poles. The circuit is thus closed through the 
 liquid. Bubbles of gas immediately rise from the poles and displace 
 the liquid in the tubes. About twice as much gas collects over the 
 — pole as over the -|-pole. Thrust a lighted splinter into each of the 
 gases : the former burns ; the latter causes the splinter to burn much 
 more rapidly than it burned in the air. This indicates that the former 
 is hydrogen gas and the latter oxygen gas. 
 
 Since pure water is an almost perfect non-conductor of elec- 
 
PHYSIOLOGICAL EFFECT. 
 
 195 
 
 Fig. 135. 
 
 tricity (page 203), the probable explanation of this action is 
 very closely like that already given (page 185) 
 for the action in the simple cell. The sulphuric 
 acid is decomposed ; H2SO4 becomes Hj + SO4 ; 
 then SO4 + HjO becomes H2SO4 + O. It is cer- 
 tain that water is ultimately decomposed, for no 
 sulphuric acid is lost. This electrolysis shows 
 that water is composed of two parts by volume 
 of hydrogen to one part of oxygen. (Why 
 ought not copper poles to be used in this experi- 
 ment? Ascertain, by inserting a galvanometer 
 in the circuit, whether the current is weakened 
 by performing the work of electrolysis.) 
 
 "When the poles of a strong battery are applied 
 for some time to a person's skin, blisters appear under the poles. 
 The serous fluid that comes from the vesicles under the positive 
 pole is acid ; the fluid in the vesicles under the negative pole is 
 alkaline. 
 
 § 170. Physiological effect. — Experiment. Place the tip 
 of the tongue between the two poles of a single cell, so that the 
 tongue may form part of the circuit; 
 a stinging sensation is felt, accom- 
 panied by a peculiar acrid taste. 
 
 When a battery is known not 
 to be very powerful, the tongue 
 serves as a very convenient gal- 
 vanoscope, to detennine whether 
 the circuit is in working condition, 
 and approximately the strength of 
 the current. If the cniral nerve 
 (a white cord next the backbone) 
 of a frog, recently killed, is laid 
 bare, and one of the poles of a battery is applied to it, on touch- 
 ing a naked muscle of a leg with the other pole, the muscles are 
 instantly convulsed and the leg drawn up, as represented by the 
 
 Fig. 136. 
 
196 
 
 BLBCTBIOITY AND MAGNETISM. 
 
 dotted lines in Figure 136. The same convulsion occurs at the 
 instant the cii-cuit is broken. By touching the nerve with a 
 piece of zinc, and the muscle with a copper wire, as represented 
 in Figure 136, similar convulsions occur, on bringing the free 
 ends of the metals in contact, and on their separation. The 
 cause is obvious ; for the two metals and the moisture of the 
 flesh furnish all the essentials of a voltaic element. 
 
 The irritability of nerves and muscles begins to diminish after 
 death, and sooner or later disappears. It disappears much 
 sooner in warm than in cold-blooded animals. In the limb of 
 a frog that is properly protected, and kept at a cool temperature, 
 it may remain for two, three, or even four weeks. If one pole 
 is armed with a soft sponge, wet with salt water, and pressed 
 firmly on the closed eyelid, while the other is applied at the 
 back of the neck, or held in the hand, making and breaking the 
 circuit will cause a sensation of light of various colors. 
 
 riff. 137 
 
 I 171. Magnetic eflfeot. — Experiment. Obtain an insulated' 
 copper wire, wind twenty or more turns around a rod of well-annealed 
 iron, lO"" long and about 1""" in diameter, and close 
 the circuit. Bring a nail (Fig. 137), or other piece 
 of iron, near the rod. The rod attracts the nail 
 with much force, and this nail will attract other 
 nails. The rod has acquired all the properties of a 
 magnet, as will be seen hereafter. But the instant 
 the circuit is broken, the iron loses its magnetic 
 force, and the nails drop. 
 
 The more times the wire is wouud around 
 the rod, within a certain limit, the more power- 
 fully is it magnetized. This arrangement is 
 called an electro-magnet, because it is a mag- 
 net produced by electricity- The rod of iron 
 is called its core, and the coil of wire the Tielix. 
 
 I InBulated, covered with cotton or silk, to prevent electricity from passing from 
 one eection of wire to another in contact with it, without passing through .he whole 
 length of the wire. 
 
STRENGTH OF CUKRENT. 197 
 
 In order to take advantage of the attraction of both ends or 
 poles of the magnet, the rod is most frequently bent in a U-shape 
 (A, Fig. 138), and then it is rig. 138 
 
 called a horse-shoe magnet. 
 Sometimes two iron rods are 
 used, connected by a rectan- 
 
 gular piece of iron, as a, in 
 
 B of Figure 138. The method -'=--' ^£ 
 
 of winding is such that if the iron core of the horse-shoe were 
 
 straightened, or the two spools were placed together, end to 
 
 end, one would appear as a continuation of the other. A 
 
 piece of soft iron, b, placed across the ends, and attracted by 
 
 them, is called an armature. The piece of iron a is called a 
 
 back armature. 
 
 XXX. ELECTRICAL MEASUREMENTS. 
 
 The wonderful developments of electrical science in recent 
 years are ahnost wholly due to a better understanding of what 
 electrical measurements can and ought to be made, and how to 
 make them. Blost of this increased knowledge has been gained 
 since the first Atlantic cable failed in 1858. Let us learn how 
 to make some of them. 
 
 § 172. Strength of current. — It is evident that the ther- 
 mal and luminous effects of electrical discharges, electro-chemi- 
 cal decomposition, the deflection of the magnetic needle, the 
 magnetization of iron, and even physiological effects, or any- 
 external manifestation, may be employed to detect the presence 
 of an electric current, in a circuit however extended. It is also 
 obvious that the magnitude of these effects may serve to measure 
 the strength of the current. Now, as the quantity of water that 
 passes through a given pipe in a minute or an hour indicates 
 the strength of the current, so by the strength of an electric cur- 
 rent is meant the quantity of electricity that passes through an 
 electrical conductor in a unit of time. 
 
198 
 
 ELECTRICITY AND MAGNETISM. 
 
 § 173. Voltameter. — The quantity of electricity that passes 
 any cross section of any conductor in the same circuit, however 
 long, is, unless there is a leakage at some point, necessarily the 
 same. We may, therefore, introduce a platinum wire into anj- 
 part of the circuit, and measure the strength of a current by the 
 temperature to which the wire is raised ; or we maj- decompose 
 water and collect the gases resulting therefrom ; the strength oj 
 current is measured by the quantity of gas liberated in a unit 
 of time. The latter arrangement, called a voltameter, is easily 
 Fig. 139. constructed sufficiently accurate for many pur- 
 
 poses, and should be constructed and used by 
 I a everj' pupil. 
 
 In Figure 139, a is a glass tube 50™ long and S™" in 
 diameter (a much sliorter tube will answer ; for ex- 
 ample, a large sized test-tube), closed at one end, 
 and graduated in cubic centimeters (this may be 
 done by means of a paper scale pasted on one side 
 of the tube) ; 6 is a bottomless glass bottle of about 
 1 liter capacity. Through the stopper of the bottle 
 pass two insulated wires, terminating in platinum 
 strips, which are introduced a little way into the 
 tube. The tube is filled with water slightly acidu- 
 lated with sulphuric acid, and its orifice is im- 
 mersed in the same kind of liquid, which partly fills 
 the bottle. When the wires are connected with a 
 battery of two or more cells in series (see page 208), 
 
 the gas arising from the decomposition of the water will collect in 
 
 the top of the tube and displace the liquid. 
 
 § 174. Galvanometer. — The instrument in most common 
 use for measuring current strength is the magnetic needle, which, 
 besides its ordinary use as a galvanoscope, performs the still 
 more important office of a galvanometer. The simple magnetic 
 needle, used as already described, answers tolerably well when 
 the currents are strong, but it is not sensitive enough to be 
 sensibly moved by very weak currents. If two equal currents, 
 flowing in the same direction, are placed one above and the 
 
TANGENT GALVANOMBTEE. 199 
 
 other below a magnetic needle, they tend to produce opposite de- 
 flections, and to neutralize one another's effect, so that no deflec- 
 tion occurs. Evidently, if they flow in opposite directions, they 
 tend to produce a deflection in the same direction, and the result 
 is a deflection twice as great as that produced by a single cur- 
 rent. The same result is accomplished if the same current is 
 made to pass both above and below a needle, as in A, Figure 
 140. If the wire were carried four times around the needle, as 
 
 Fig. 140. 
 
 in B, the influence of the current on the needle would be about 
 four times that of a single turn. Very sensitive galvanometers, 
 constructed on this principle, often with thousands of turns 
 of wire, are sometimes called long-coil galvanometers, in dis- 
 tinction from those having few turns, which are called short-coil 
 galvanometers. 
 
 § 175. Tangent galvanometer. — The arrangement de- 
 scribed above is more commonly used as a galvanoscope than a 
 galvanometer, though it maj' be so calibrated as to answer the 
 latter purpose. The law connecting the current strength with 
 the deflection of the needle of this galvanometer is not known ; 
 but in another form, called the tangent galvanometer, the rela- 
 tion is expressed in a simple tangent of the angle of deflection. 
 This apparatus is coustructed on the principle that the strength 
 of currents are proportional to the tangents of the angles of 
 deflection, when the needle is verj^ short in comparison with the 
 diameter of a circle described by a current circulating around 
 it. 
 
200 
 
 ELECTEICITY AND MAGNETISM. 
 
 A magnetic needle, about S.S"™ long, is suspended freely by an un- 
 twisted thread n, Figure 141, in the center of a copper hoop a, about 
 30cra in diameter, which terminates in the wires ww' ; and these are con- 
 nected with the battery whose current is to be measured. A circular 
 card-board cc, containing a circle divided to degrees to indicate the 
 extent of deflection, is placed beneath the needle. The ring being 
 placed so that it is parallel with the needle, the needle points to 0° on 
 the scale. When a current passes through the ring a, the needle is 
 deflected. iTie tangents of the angles of deflection may be found by 
 
 Fig. 141. 
 
 reference to a Table of Natural Tangents in Section D of the Appendix, 
 and the relative strengths of currents may be determined by the law 
 given above. The construction of a very simple galvanometer that 
 may be used as a tangent galvanometer, and which will answer all 
 requirements of this book, may be found in Section E of the Appendix. 
 
 § 176. Experiments in measurements. — Inasmuch as 
 the magnitude of the effects that can be produced by an elec- 
 tric current, or the amount of work that can be done by it, 
 depends upon the strength of the current, it is of the utmost 
 importance to understand the principles by which it is regu- 
 lated. A few experiments will make this apparent. Provide 
 four coils or spools of insulated wire. Mark the coils A, B,.C, 
 and D. Let A contain 100 ft. (about 1 lb.) of No. 16 copper 
 
ON WHAT STRENGTH OF CUKBENT DEPENDS. 201 
 
 wire ; B and C respectively 100 ft. and 50 ft. of No. 30 copper 
 wire ; and D 50 ft. of No. 30 German silver wire. 
 
 Experiment 1. Place a galvanometer G and coil A in the same 
 voltaic circuit, connected as shown in Figure 143. Note the number 
 of degrees the needle is deflected. Next substitute coil B for A, and 
 note the deflection. The deflection is less than before, showing that 
 of two wires of the same material and equal length, the larger transmits, 
 from the same source, the stronger current. 
 
 Fig. li2. 
 
 Experiment 2. Place coil C in the circuit with B, and compare th? 
 deflection with that produced when B alone was in the circuit. The 
 deflection is less than before. (Why?) Take B out, and leave C in 
 the circuit. The deflection is greater than when B alone was in the 
 circuit. Other things being the same, the shorter wire transmits, from 
 the same source, the stronger current. 
 
 Experiment 3. Introduce T> in the place of C, and compare the 
 strengths of the currents in these two wires. The copper wire trans- 
 mits, from the same source, a stronger current than the German silver wire 
 of the same length and size. 
 
 Experiment 4. Compare the currents furnished by a Grove or 
 Bunsen, and a Smee or a gravity cell, when the same coil, for in- 
 stance B, is in the circuit. The Grove or Bunsen cell gives the stronger 
 current. 
 
 § 177. On what strength of current depends. — It ap- 
 pears that the strength of the current varies not onlj- with the 
 
202 ELECTRICITY AND KAGNBTISM. 
 
 size, length, and kind of condiictor, but also with the kind of 
 battery used. These will be considered consecutively. It is 
 evident that all conductors do not allow the current to pass with 
 equal facility ; in other words, some conductors offer more re- 
 sistance to the passage of a current than others. The larger 
 conductor offers less resistance than the smaller. It is found 
 by experiment that (1) the strength of currents varies directly 
 (1.1 the areas of the cross sections of the conductors, or the squares 
 of the diameters of cylindrical conductors, inasmuch as areas 
 vary as the squares of their diameters. (2) It varies in- 
 versely as the length of the conductor, i.e., if a wire one mile 
 long offers a certain amount of resistance, a wire two miles 
 long will offer twice as much resistance. (3) It varies in- 
 versely as the specific resistances of the substances used for con- 
 ductors. The conducting power of a substance is the reciprocal 
 of its resistance. Hence, if we know the conducting power of 
 
 any wire, we know that the resistance = :— ; or the 
 
 J conductivity 
 
 conductivity = 
 
 resistance 
 
 Resistance is expressed in units called ohms^ (see § 181). 
 
 The student can easily provide himself with a standard having 
 
 approximately a resistance of one ohm, by obtaining 40 feet of 
 
 No. 24 ordinarj' copper wire 0.5"" in diameter. 
 
 § 178. Formula for resistance. — HaAdng found that re- 
 sistance varies directly as the length, and inversely as the squares 
 of the diameters of conductors, we may include all its laws in the 
 formula „ jr I 
 
 in which R = the resistance, I — the length, and d the diameter 
 of a cylindrical conductor. K is a constant, such that when the 
 material of the wire is known and the denomination in which 
 I and d are expressed, a value of K taken from a table may be 
 
 ' Ohm, from the nafme of a German savant. Dr. O. S. Ohm, who first enunciated 
 the laws which determine the strength of currents. 
 
FORMULA FOE INTERNAL RESISTANCE. 203 
 
 substituted in the equation, and thus enable us to find the value 
 of R in ohms. Thus let it be required to find E of 1000 ft. of 
 copper wire 0.1 inch in diameter. The table gives the value of 
 K as 9.72 when the length of the wire is measured in feet, and 
 its diameter in thousandths of an inch ; since 0.1 inch equals 100 
 
 thousandths, R = 9.72 x ^^ = 0.972 ohm. 
 100^ 
 
 In the following table are given the relative resistances of 
 several substances, and the values of K in the above equation 
 when I is expressed in feet and d in thousandths of an inch. 
 
 REFERENCE TABLE OF RELATIVB RESISTANCES, ETC. 
 
 Rel. Resist. K. 
 
 Silver @0°C 1.00 9.15 
 
 Copper " 1.06 9.72 
 
 Zinc " 3.74 34.2 
 
 Platinum " 6.02 55.1 
 
 Iron " 6.46 59.1 
 
 German silver " 13.91 127.3 
 
 Mercury " 63.24 578.6 
 
 Rel. Resist. 
 
 Nitric acid — commercial @ 15 to 28 C 1,100,000 
 
 Sulphuric acid, 1 to 12 parts water " 2,000,000 
 
 Common salt — saturated sol. " 3,200,000 
 
 Sulphate copper " " 18,000,000 
 
 Distilled water not less than 10,000,000,000 
 
 Glass @ 200° C 15,000,000,000,000 
 
 Gutta percha @ 0° C. . . .5,000,000,000,000,000,000,000 
 
 The resistance of metals increases slowly as the temperature 
 rises ; but that of liquids and the other poor conductors in the 
 second list decreases very rapidly with a rise in temperature. 
 The resistance of ordinary impure metals is often much higher 
 than that given in the table. 
 
 § 179. Formula for internal resistance. — Resistance in 
 a voltaic circuit may be divided, for convenience, into two parts ; 
 viz., internal resistance (r), which the current encounters in 
 
204 ELECTEICITY AKD MAGNETISM. 
 
 passing through the liquid between the two plates in the cell, 
 and external resistance (E), which it suffers in the remain- 
 der of its path. The internal resistance is governed by the 
 same laws as the external resistance. In this case 
 _ T7- distance of the plates apart (/) 
 areas of the plates submerged {d?) 
 
 QUESTIONS AND PROBLEMS. 
 
 1. What length of copper wire will have the same resistance as a 
 mile of iron wire of the same diameter? 
 
 2. How can you reduce the resistance of an Iron wire to that of a 
 copper wire of the same length? 
 
 3. About how much is the conductivity of water affected by adding a 
 little sulphuric acid? 
 
 4. How many times greater is the resistance of dilute sulphuric acid 
 than that of copper? 
 
 6. Upon what does the resistance offered by the liquid part of a 
 circuit depend, and how may it be diminished ? 
 
 6. What is the resistance of 500 ft. of copper wire .014 inch in 
 diameter (No. 30 B.W. gauge)? Ans. 24.7 + ohms. 
 
 7. What length of copper wire -.006 inch in diameter (No. US) will 
 offer a resistance of 1 ohm ? 
 
 8. What is the resistance of 16 yards of German silver wire (No. 30) 
 .014 inch in diameter ? 
 
 9. What is the resistance of 1 mile of iron telegraph wire, the usual 
 size being .175 inch in diameter ? 
 
 10. Express in ohms the resistance of 1 mile of copper wire, 0.06 
 
 inch In diameter? Ans. 9.72 x^^= 14.256 olims. 
 
 § 180. Electro-motive force. — The experiments described 
 in § 151 show that electricity constantly flows in a closed circuit 
 containing a voltaic cell ; hence the cell has the power of setting 
 electricity in motion, or an electro-motive force (usually abbre- 
 viated E.M.F.). Again, Exp. 4, § 176, proves that a Grove 
 cell, in a circuit of a given resistance, sets in motion a greater 
 quantity of electricity than a Smee or gravity cell ; hence we say 
 that the E.M.F. of a Grove cell is greater than that of the other 
 two kinds mentioned. It has been found that E.M.F. depends 
 
ohm's law. 205 
 
 solely upon the nature and condition of tlie substances which form 
 the battery, and is, consequently, quite independent of the size of 
 the plates and their distance apart. The unit employed in the 
 measurement of E.M.F. is called a volt.^ It is about the E.M.F. 
 of a current generated bj' one gravity cell. The following 
 table exhibits the electro-motive force in volts of different 
 cells : — 
 
 TABLE 01' ELEOTRO-MOTIVE FORCES. 
 
 Gravity or Daniell , 0.98 to 1.08 volts. 
 
 Buuseu and Grove 1.75 to 1.95 " 
 
 Leclanch6, at first 1.48 to 1.60 " 
 
 Grenet " 1.80 to 2.3 
 
 Smee 65 .... " 
 
 The E.M.F. of the last three decreases considerably if the circuit Is 
 closed for a few minutes. These numbers signify, for instance, that it 
 will require 195 Smee cells to give the same current in a circuit (of 
 high resistance) as would be given by 65 Grove cells. 
 
 § .181. Ohm's Law. — The law which expresses the strength 
 of the current, and is the basis of most mathematical calculations 
 on currents, is expressed in the formula known as Ohm's Law. 
 Calling the current C, the E.M.F. simply E, and the whole 
 resistance in the circuit R, the formula expressing the law is 
 
 c = |- 
 
 R 
 
 In words, this means that the strength of the current is equal to 
 the electro-motive force of the battery, divided by the resistance of 
 the circuit; i.e., C will be greater or less as E is greater or less, 
 but will be less when R is greater, and greater when R is less. 
 
 F 
 
 The above relation — , when the external resistance is considered 
 
 R 
 separately from the internal, must be converted thus : calling 
 the former R, and the latter r, the expression becomes 
 
 R + r 
 
 ' Volt, from the name Volta. 
 
206 ELECTRICITY AND MAGNETISM. 
 
 For single cells in ordins^ry use the value of r will usuallj' be 
 between .5 and 2 ohms. 
 
 The unit of current strength, called an ampere, is the current 
 flowing in a conductor having a resistance of 1 ohm, between the 
 ends of which a difference of potential of 1 volt is maintained ; 
 or it is a current of 1 coulomb per second. A coulomb is the 
 amount of electricity convej'ed in 1 second by a current of 
 
 1 ampere. 
 
 If a cell has E = 1 volt, and r = 1 ohm, and the connecting 
 wire is short and stout, so that R maj- be disregarded, then the 
 current has a value of 1 ampere. But if the connecting wire 
 has a resistance R, equal to 1 ohm, then 
 
 C = = = -J. = .5 ampere. 
 
 E+r 1+1 2 ' 
 
 § 182. Summary of electrical measurements. — Just as 
 we express an amount of money in the denomination dollars, or 
 a mass of coal in the denomination pounds, we express electrical 
 
 Potential, P (commonly, difference of P) .... in volts. 
 
 Electro-motive force, E " volts. 
 
 Eesistance, E " ohms. 
 
 Strength of current, C " ampBres. 
 
 Quantity of electricity " coulombs. 
 
 The following will give some idea of the magnitude of the 
 denominations. A gravity cell produces a difference of poten- 
 tial or an electro-motive force (for these are only different ways 
 of viewing the same quantity) of nearly 1 volt. To produce a 
 spark 1""" long requires from 3,000 to 4,000 volts. A No. 16 
 ordinary copper wire 250 ft. long (diameter .051 inch, weight 
 
 2 lbs.) has a resistance of about 1 ohm. About 150 ft. of 
 copper wire 1°"" in diameter has & resistance of 1 ohm. An 
 ordinary Grove cell may have an internal resistance of \ ohm ; 
 this cell will send through 125 ft. of No. 16 copper wire a cur- 
 rent whose strjength is 1 ampere. 
 
ABRANGEMEUfT OF BATTERIES. 
 
 207 
 
 PROBLEMS. 
 
 1. What current will be obtained from a gravity cell when E = 1, 
 r = 2 ohms, and R= 10 ohms? 
 
 2. What current may be got from a gravity cell whose internal re- 
 sistance is 3 ohms, and external resistance is 3 ohms? 
 
 3. What current will a Grove cell furnish, having the same internal 
 end external resistances as the last? 
 
 § 183. Arrangement of batteries. — The internal resist- 
 ance may be diminished by placing the plates as near to each 
 other as practicable, and by employing large plates, and thereby 
 increasing the size of the liquid conductor. But it is not always 
 convenient to employ very large plates, or we may have occasion 
 to employ a battery for certain purposes, as we shall see pres- 
 ently, in which large cells would be of little or no advantage. 
 The same result that can be produced by a single pair of large 
 plates, may be obtained by Connecting the similar j,, j^j 
 plates of several pairs in separate cells, thereby 
 practically reducing several pairs to one pair 
 having an area equal to the sum of the areas of 
 the several pairs. Figure 143 illustrates a method 
 of connecting cells for the purpose of reducing 
 the internal resistance. This is called arranging 
 cells parallel, in multiple arc, or abreast. 
 
 This arrangement is very effectual in increasing 
 the current-strength when the internal resistance 
 is the principal one to be overcome. For instance, 
 call the electro-motive force (E) of a single cell 
 1 volt, its internal resistance 5 ohms, and let the 
 plates be connected by a short, thick wire, whose 
 resistance may be regarded as nothing; then 
 
 F 1 
 C = — = — = .2 ampere. Now connect 10 similar 
 
 r 5 
 cells abreast. The size of the liquid conductor 
 being increased tenfold, the internal resistance is one-tenth 
 
 E 
 as large, and we have C = -=l-5-^=2 amperes. So that, 
 
208 BLEOTBIOITY AND MAGNETISM. 
 
 when there is no external resistance, the current increases as 
 the size of the plates is increased. The same is approximately 
 true in case the external resistance is very small in comparison 
 with the internal resistance. 
 
 Again, let E = 1, r = 5 ohms, as above, but the external re- 
 sistance R = 200 ohms : then C = ^— = .0048+ ampere; If 
 
 5 + 200 
 
 10 pairs are connected abreast, C= = .0049+ amp^ra 
 
 '^ ^ + 200 ^ 
 
 In this case, the current is scarcely affected by increasing the 
 
 number of cells abreast. The question then arises, what can be 
 
 done to increase the current when the external resistance is 
 
 necessarily large ; as, for instance, when a long telegraph wire 
 
 is used. In this case R, in Ohm's formula, is unalterable, and 
 
 _. j„ lessening r has little effect; 
 
 so there remains only one 
 
 way, viz., to increase E, the 
 
 electro-motive force. How 
 
 may this be done? If the 
 
 current from a cell, instead 
 
 of passing immediately out of 
 
 the cell on its journey, is made 
 
 to pass through another cell 
 
 first, one might naturally expect that either the two cells would 
 
 counteract one another in the circuit, or that they would double 
 
 the E.M.F. Experiment shows that the latter result is the true 
 
 one, and that the E.M.F. is exactly proportional to the number 
 
 of cells connected in series. Cells so connected as to increase 
 
 the electro-motive force are said to be joined in series or tandem. 
 
 The method of connecting the cells for this purpose. is shown in 
 
 Figure 144. 
 
 It will be seen that in the multiple arc (Fig. 143) all the zinc 
 
 plates are connected with one another, and all the copper plates 
 
 with one another. In the tandem arrangement the zinc of one 
 
 cell is connected with the copper of the next throughout. 
 
 I' i 1^ i I' i I 
 
AERAKGEMENT OF BATTEEIES. 
 
 209 
 
 In the last example given above, let us see what would be the 
 efTect of connecting the 10 cells in series. In this case E is 
 increased tenfold; and, as the current is Kg. 145. 
 
 obliged to pass through the liquid of 10 
 cells instead of one, the internal resistance 
 will also be increased tenfold ; hence, 
 
 C = L><_12 = .0400 ampere, more 
 
 (5x10)4-200 
 than eight times as much as before. Thus 
 it appears that, 'tvhen the external resistance 
 is large in comparison with the internal 
 resistance, the current may be largely in- 
 creased by multiplying the cells in series; 
 in other words, by forming a battery of 
 great electro-motive force. In long tele- 
 graph lines the battery is made up of huu- 
 Fig. 146. d r e d s o f 
 
 cells joined 
 in series. 
 
 Ltirge cells are used simply be- 
 cause the fluids last longer, and 
 so the cells need less attention. 
 
 Sometimes a combination of the 
 two arrangements gives a stronger 
 current than either alone. The 
 cells may be grouped together in 
 pairs (as in Figure 145), or in 
 triplets (as in Figure 146), so as 
 to increase the electro-motive 
 force ; then the several groups 
 may be connected abreast, to reduce the internal resistance. 
 
 
 PROBLEMS. 
 
 1. Suppose that the cells in the last example above be so increased 
 In size that r in each = .fi ohm, what current will be got from the 
 battery? 
 
210 ELECTEICITY AND MAGNETISM. 
 
 2. What current is there on a telegraph wire 100 miles long, when 
 it is in circuit with 40 Grove cells, the internal resistance of each cell 
 being .5 ohm, the resistance of the wire 15 ohms to the mile, and the 
 resistance of the earth connections 100 ohms? 
 
 3. An electric bell, whose resistance is .5 ohm, is found to require a 
 currentof .02amp6re toringit. How many gravity cells will it require, 
 if the circuit consists of an iron wire 1 mUe long, having a diameter 
 of .166 in. (= 4.29""°), disregardiug the resistance of the cells ? 
 
 4. Which is the better arrangement (i.e., abreast or tandem) of 210 
 gravity cells, each of 3 ohms resistance, against an external resistance 
 of 10 ohms, and what will be the current with each ? • 
 
 5. In a battery of 10 cells connected in series, ten times as much 
 zinc and acid are consumed as in 1 cell. Show how about nine- 
 tenths of the chemicals may be wasted. 
 
 6. In a certain circuit a battery of 40 gravity cells, each of 3 ohms 
 resistance, is used. The cells are arranged in two groups of 20 cells 
 each in series, and the two groups are so connected as to diminish 
 the internal resistance. If E= 120 ohms, what current will be obtained? 
 
 7. Devise various arrangements of 30 cells in which r=.8 ohm. 
 Which arrangement is best when K = 10 ohms? when R = 30 ohms? 
 
 § 184. General conclusions. — A perfect battery would 
 have the following qualities : — 
 
 1. It would have a high electro-motive force. 
 
 2 . Its E.M.F. would be constant, whether used to produce strong 
 or weak currents. 
 
 3. It would have a small and constant internal resistance. 
 
 No battery fulfils perfectl_y all these conditions ; so, in practice, . 
 the use to which the battery is to be put, its first cost, and the 
 trouble and expense of keeping it in order, determine which 
 of these qualities shall be given up. The question, What is the 
 best battery ? is discussed in the Appendix, Section F. 
 
 A current from a single cell, traversing a short, thick wire, 
 will produce as large a deflection of a magnetic needle as a cur- 
 rent from 500 cells connected in series. On the other hand, a 
 message has been transmitted through the Atlantic cable, whose 
 resistance is about 7,000 ohms, by a current generated in a 
 
GENERAL CONCLUSIONS. 211 
 
 lady's thimble, and the signals produced were as distinct as 
 those that would be produced by a cell of several square feet. 
 In this case, the quantity of electricity that passed depended 
 chieflj' upon the E.M.F. of the battery, and not upon its inter- 
 nal resistance. (How, in the former case, can the current be 
 increased? How could it have been increased in the latter 
 case ?) 
 
 The same strength of current that would fuse an inch of 
 platinum wire would fuse a mUe of the same wire. But while 
 one cell would fuse the inch of wire, it would require the E.M.F. 
 of many hundred to maintain the same strength of current in. 
 the mile of wire. 
 
 A battery of three cells arranged abreast will fuse a certain 
 length of platinum wire, but will not be felt by a person holding 
 the poles in his hands ; while a battery of 100 cells in series will 
 not fuse the same wire, but will produce quite a shock. 
 
 The power of an electro-magnet depends largely upon the 
 number of times a given current circulates around its core, and 
 upon the nearness of the current to the core ; for compactness, 
 and to keep the current near the core, a fine wire must then be 
 used. But a long, thin wire would offer large resistance, that 
 might so reduce the current as to more than offset the advan- 
 tage that would otherwise be gained. Hence, when there is 
 little other resistance in a circuit, a large wire with few turns 
 will give the strongest electro-magnet. But if an electro-magnet 
 is to be used in a circuit with other large resistance, then the 
 introduction of a helix of many turns of fine wire would add 
 little more resistance comparatively, so the strength of the cur- 
 rent would be reduced but little, while a great gain would be 
 made in the effect on the core. For the same reason, a galva- 
 nometer intended to be used in circuits where there is little 
 resistance, should contain only a few turns of large wire ; but 
 if it is to be used with large resistance, it should contain a 
 long, fine wire. Ulectro-magnets and galvanometers should be 
 adapted to the circuits in which they are used. 
 
212 ELECTRICITY AND MAGNETISM. 
 
 QUESTIONS. 
 
 1. A bell in Washington is to be rung by the action of an electro- 
 magnet. The current used comes from a battery in New York. How 
 should the electro-magnet be constructed? 
 
 2. If you wished to measure the current, by the introduction of a 
 galvanometer into the circuit in Washington, how should it be made? 
 
 3. Would it require a different galvanometer if it were to be intro- 
 duced into the same circuit in New York, ouly a few feet from the 
 battery? 
 
 4. Provided there were no leakages, how would the deflections at 
 the two places compare? 
 
 XXXI. MAGNETS AND MAGNETISM. 
 
 § 185. Permanent and temporary magnets. — One of the 
 most familiar pieces of physical apparatus is a magnet. "Wo 
 know how it can pick up bits of iron and steel. By the aid of 
 a small instrument already studied, we may make a pair of small 
 magnets, and study their actions and laws. 
 
 Experiment. Take the electro-magnet, described on page 196, and 
 a couple of sewing needles or larger steel rods. Apply these needles., 
 ^one at a time, to one end of the electro-magnet, and draw them several 
 times across it from end to end, always in the same direction, and not 
 rubbing back and forth. Repeat the operation with an iron wire of 
 the same size ; both the wire and the steel are attracted by the electro- 
 magnet, but the iron wire more strongly. Observe that both, while in 
 contact with the electro-magnet, possess the power of attracting bits 
 of iron ; but, on removing them, the steel is found to retain the property 
 it had, while the iron does not. 
 
 Both of them exerted that peculiar force called magnetic force, 
 or possessed the property called magnetism; that is, both were 
 magnets ; but, as the steel retains its power, it is called a perma- 
 nent magnet in distinction from a temporary magnet, like the 
 iron wire or the electro-magnet itself. The quality of steel by 
 which it at first resists the power of magnets, and resists the 
 escape of magnetism which it has once acquired, is called coer- 
 
LAW OF MAGNETS. 213 
 
 dve force. The harder steel is, the greater is its coercive force. 
 Hence, highly tempered steel is used for permanent magnets. 
 Hardened iron possesses some coercive force ; hence, the cores 
 of electro-magnets should be made of the softest iron, that thej- 
 may acquire and part with magnetism instantaneouslj-. 
 
 § 186. Law of magnets. — Experiment 1. Suspend the two 
 magnets, each in a horizontal position, by threads that will not untwist, 
 and several feet 
 
 distant from each '^' 
 
 other. When they ^ ^\ \S ^\ ' ^% '^N^ 
 come to rest, no- ' „ ^ » ^=^ ^ -I 
 
 ' Permanent magnet. Induced magnets. 
 
 tice that they have 
 
 taken up a direction nearly north and south. Tie a thread on the end 
 
 of each that points to the north. 
 
 This end, or pole, as it is usually called, we will speak of as 
 the N-end, -f-, or marked end or pole, while the other is the 
 unmarked, — , or S-end or pole. 
 
 Experiment 2. Bring the marked end of one of the magnets near 
 to the unmarked end of the other; they attract one another. Next 
 bring the marked end of one near to the marked end of the other ; they 
 repel one another. Bring the unmarked ends near one another ; they 
 repel one another. 
 
 "We discover the following law of magnets : Like poles repel, 
 unlike poles attract one another. 
 
 § 187. Magnetic transparency and induction. —Experi- 
 ment. Interpose a piece of glass, paper, or wood-shaving between 
 the two magnets. These substances are not themselves perceptibly 
 affected by the magnets, nor do they in the least affect the attraction 
 or repulsion between the two magnets. 
 
 Substances that are not susceptible to magnetism are, like 
 glass, paper, and wood, magnetically transparent. When a 
 magnet causes another body, in contact with it or in its neigh- 
 borhood, to become a magnet, it is said to induce magnetism in 
 that body, i.e., it influences it to be like itself. As attraction, 
 
214 BLBCTEICITY AJSTD MAGNETISM. 
 
 and never repulsion, occurs between a magnet and an unmag- 
 netized piece of iron or steel, it must be that the magnetism 
 induced in the latter is such that opposite poles are adjacent ; 
 that is, a N or +pole induces a S or —pole next itself, as shown 
 in Figure 147. 
 
 § 188. Polarity. — Experiment 1. Strew iron filings on a flat 
 rig. 148. surface, and lay a bar magnet on 
 
 them. On raising the magnet, it 
 is found that large tufts of filings 
 cling to the poles, as in Figure 
 148, especially to the edges ; but the tufts diminish regularly in size 
 from either pole towards the center, where none are found. 
 
 Magnetic attraction is greatest at the poles, and diminislies 
 towards the center, where it is nothing, or the center of the bar is 
 neutral. The dual character of the magnet, as exhibited in its 
 opposite extremities, is called polarity, and magnetism is styled 
 a, polar force. If a magnet is broken at its neutral line, as in 
 Exp. 1, p. 28, it is found that equal and opposite polarities 
 Fig. ii9. exist where there is ordinarily no 
 
 evidence of them. 
 
 Experiment 2. Place a copper wire, 
 through which a very strong current of 
 electricity is passing, in a heap of iron filings, — then raise the wire ; 
 filings cling to the wire somewhat as they do to a magnet, as shown in 
 Figure 149. 
 
 This experiment, and those with the electro-magnet and the 
 deflection of the magnetic needle by an electric current, and a 
 multitude of others that the pupil will meet with, cannot fail to 
 convince him that an intimate relation exists between electricity 
 and magnetism, which, though differing in many of their prop- 
 erties, yet alike in many, and almost invariably accompany- 
 ing one another, and constantly merging one into the other, 
 appear as if they were only different manifestations of one and 
 the same agent. 
 
ATTRACTIOK OF CUEEENTS. 
 
 216 
 
 § 189. Attraction and repulsion between currents. 
 Let us study stiU further ^.^^ ^^ j,,^ j5j 
 
 the properties of the cur- p 
 
 rent. 
 
 Battary 
 
 Experiment 1. Suspend 
 two copper wires (Fig. 
 150), each 50™ long, and 
 aboat 5™™ apart, with their 
 lower extremities dipping 
 about 2"™ into mercury, so 
 as to move with little re- 
 sistance either toward or 
 from each other. In Fig- 
 ure 150 the current divides 
 itself and flows down both 
 wires to the liquid, so that "" 
 
 that part of the circuit presents parallel currents flowing in the same 
 direction. Figure 151 is the same apparatus, with the connections so 
 made that the current flows down one wire and up the other, and we 
 have an example of parallel currents flowing in opposite directions. In 
 the former case the wires mutually 
 attract one another. In the latter 
 there is mutual repulsion. 
 
 Fig. 152. 
 
 Hence, the First Law of Cur- 
 rents : Parallel currents in the same 
 direction attract one another; par- 
 allel currents in opposite directions 
 repel one another. 
 
 An interesting illustration of the 
 former part of this law can be ar- 
 ranged as in Figure 152. A bat- 
 tery wire is bent in the form of a 
 spiral coil. At a the wire is broken, 
 and one end dips just below the surface of mercury in a glass, 
 while the other end is placed in the same liquid at a little dis- 
 tance from the first. "When the circuit is closed the current will 
 be parallel with itself, and will flow in the same direction in 
 
216 
 
 ELECTRICITY AND MAGNETISM. 
 
 all parts of the coil that are adjacent. The attraction that 
 follows will cause the coil to contract and lift one pole out of 
 the mercury and break the circuit. The circuit broken, the 
 attraction ceases, and the coil is drawn down again by the force 
 of gravity, and closes the circuit again ; and thus constant 
 vibratory motion is produced in the coil. 
 
 Experiment 2. 
 
 Fig. 
 
 153, 
 
 Prepare apparatus as represented in Figure 153. 
 Through a cork a, 8™ in diameter 
 ^-f^ and 5™ thick, cut a circular hole 
 r^^,^mk about 4™ in diameter, and insert 
 l^g a glass test-tube 6; about 6™ 
 
 ^^ long, that will just fit in the hole. 
 
 Takean(No. 20) Insulated copper 
 wire about 260™ long, wind the 
 central portion into a coil c, 12™ 
 long and IS""" in diameter, with 
 turns about S""" apart, leaving 
 about 12'="' at both extremities 
 unwound. To these extremities 
 solder strips of copper and amal- 
 gamated zinc about 3™ long, and 
 as wide as the interior of the test- 
 tube will admit, and allow them 
 to be separated about 6°"". In- 
 Fig. 155. sert them in the tube, 
 
 and cover with dilute 
 sulphuric acid. In the 
 center of the coil lay 
 a No. 16 soft iron 
 wire d, and float the 
 whole in a vessel of 
 water. The apparatus 
 constitutes a small 
 floating battery and electro-magnet. Bring one end of a permanent 
 magnet, or a short piece of soft iron wire e, suspended in a paper 
 stirrup n, near to one. of the poles of the core of the electro-magnet, 
 and prove by experiment that the coil and its core behave in every 
 respect like a magnet. 
 
 Experiment 3. Eemove the iron wire from the floating electro- 
 
 Fig. 154. 
 
ATTRACTION OF CUEEENTS. 217 
 
 magnet, and bring a separate battery wire over and parallel with the 
 helix, Js in Figure 154. In this position the two currents flow in 
 planes at right angles to one another. Immediately the coil turns and 
 tends to take a position at right angles to the wire above, so that the 
 two currents may flow in parallel planes and in the same direction, as 
 in Figure 155. 
 
 Hence, the Second Law of Currents : Angular currents tend to 
 become parallel and flow in the same direction. 
 
 Observe that the action of the Fig. ise. 
 
 helix in the last experiment is ( ^TOCT TOg) (TO5W) 
 analogous to the deflection of a 
 magnetic needle by an electric 
 current. 
 
 Experiment 4. Place opposite 
 one end of the floating helix a second 
 helix, Figure 156, in such a manner that the currents in the two helices 
 may have the same direction. The two poles of the helices attract 
 one another in conformity to the First Law of Currents. Reverse the 
 poles of the helix in your hand so that the currents will flow in oppo- 
 site directions, though still parallel; they repel one another. (Why?) 
 
 The two helices appear to be polarized like two magnets, and 
 for many purposes may be considered as magnets. Observe 
 that at one pole of each helix the cui-rent revolves in the direc- 
 tion that the hands of a watch move, and at the opposite pole 
 it revolves in a direction contrary to the movement of the hands 
 of a watch. Bring the north pole of a bar-magnet near that 
 pole of the helix where the motion of the current corresponds to 
 the movement of the hands of a watch. They attract one an- 
 other ; but if the same pole of the helix is approached by the 
 south pole of the magnet, repulsion follows. Hence, that is the 
 south pole of a helix where the current corresponds to the motion 
 of the hands of a watch, (s), and that is the north pole where the 
 current is in the reverse direction, ^. But the important les- 
 son derived from these latter experiments is, that helices through 
 which currents are flowing behave toward one another, or toward 
 a magnet, in many respects as if they were magnets. 
 
218 
 
 BLECTKICITY AND MAGNETISM. 
 
 § 190. Ampfere's theory. — The facts which we have just 
 studied led Ampere about sixty years ago to devise a theory which 
 furnished a connecting link between magnetism and electricity. 
 It assumed that around every molecule of iron, steel, or other 
 magnetizable substance, electric currents circulate continuously, 
 and thus every molecule becomes a magnet. According to the 
 theory, in an unmagnetized bar these currents lie in all possible 
 planes, and, having no unity of direction, they neutralize one 
 another, and so their effect as a system is zero. But if a current 
 of electricity or a magnet is brought near, the effect of the in- 
 duction is to turn the currents into parallel planes, and in the 
 same direction, in conformity to the Second Law of Currents. 
 If the coercive force is strong enough, this parallelism will be 
 attained on the removal of the inducing cause, and a permanent 
 magnet is the result. 
 
 Intensity of magnetization depends on the degree of parallel- 
 ism, and the latter depends on the strength of the influencing 
 magnet. "When these currents have become quite parallel, the 
 body has received all the magnetism that it is capable of receiv- 
 ing, and is said to be saturated. Although the currents really 
 
 circulate around the individual 
 molecules, yet the resultant of 
 these forces is essentially the 
 same as if the currents circu- 
 lated around the body as a 
 whole. Figure 157 represents 
 sections of a cylindrical mag- 
 net, and the included circles 
 the circulation of the several 
 currents around the molecules 
 lying in these sections. It will 
 be seen that the currents at the 
 contiguous sides of any two of these circles move in opposite 
 directions, and therefore must neutralize one another ; while the 
 currents that pass next the circumference of the magnet are not 
 so affected. 
 
AMPERE S THEORY. 
 
 219 
 
 The hypothetical currents that circulate around a magnetic 
 molecule we shall call AmpMan currents, to distinguish them 
 from the known current that traverses the helix. In strict accord- 
 ance with this theory, the poles of the electro-magnet are deter- 
 mined by the direction of the current in the helix. The inductive 
 influence of the electric current causes the Amp^rian currents to 
 take the same direction with itself, as represented in Figure 158. 
 
 Fig. 158. 
 
 However well adapted this theory may be to explain most of the 
 known phenomena of magnetism, it should be borne in mind 
 that physicists of this generation value the theory rather as a 
 help to the imagination and memorj^, than as a true statement 
 of the facts. It is nearer the truth to say that the molecules 
 are polarized as if currents were circulating around them ; of 
 the actual existence of such currents we know nothing. So 
 also of the real nature of polarity we know little or nothing. 
 
 EXERCISES AND QUESTIONS. 
 
 1. Regarding your lead-pencil as a rod of iron, and a string as an 
 electric wire, tie a knot at the end where the current is supposed to 
 enter It, and wind the string spirally around your pencil, so as to make 
 the point of the pencil a south pole. 
 
 2. What would be the effect of reversing the current? 
 
 3. Take two tin mustard-boxes, and paint arrows around them, also 
 on the ends, aU turned in the same direction, to represent Ampgrian 
 currents, as in Figure 159. Imagine each to be a magnet, determine 
 
220 ELECTRICITY AND MAGNETISM. 
 
 which is the north and which is the south pole of each, and mark them 
 accordingly with the letters N and S. 
 
 4. (o) Place the two south poles near one another, and ascertain 
 why they should repel one another. (6) Do the same with the two 
 north poles. 
 
 5. Let a north and a south pole face one another, and show why 
 they should attract one another. 
 
 6. Stretch a string in a northerly and southerly direction,, and sus- 
 pend one of the boxes as a magnetic needle over and parallel with the 
 string, with its north pole pointing north ; then imagine a current to 
 enter the string at its southern extremity, and determine its effects on 
 the needle. 
 
 7. Why is a magnetic needle deflected by an electric current? 
 
 8. Why is the direction of the deflection dependent on the direction 
 of the current? 
 
 § 191. The earth a great magnet. — Experiment l. Mag- 
 netize a cambric needle. Suspend it by a fine thread attached to<ats 
 middle over a magnet, and midway between its poles. The needle, 
 however placed, immediately takes a position parallel with the magnet. 
 The magnet exerts a directive influence on the needle. Remove the 
 magnet, and the needle takes a northerly and southerly direction. 
 
 If you carry the needle all over your town or State, it will still main- 
 tain this direction. Something, like the magnet, exerts a directive 
 influence on the magnetic needle. 
 
 Fig. 160. 
 
 ^ 
 
 1\ 
 
 Experiment 2. Place the needle once more in its original position 
 over the magnet, and gradually move it from the middle towards one 
 pole of the magnet ; the needle ceases to be horizontal. At either side 
 of the center it dips; if it is nearer the N-pole of the bar, the S-pole 
 dips, and conversely, as shown in Figure 160. If the needle is properly 
 supported, the dip increases till at the poles the inclination is 90°. 
 
 If a magnetic needle freely suspended is carried to different 
 parts of the earth's surface, it will dip as it approaches 
 the polar regions, and is onlj' horizontal at or near the earth's 
 
THE EAETH A MAGNET. 
 
 221 
 
 Fig. 162. 
 
 equator. A common compass needle must have the S-end 
 loaded to keep it horizontal. Like effects are commonly at- 
 tributed to like causes. These phenom- pj jgj 
 ena are just what we should expect 
 if (as is very improbable) a huge magnet 
 were thrust through the axis of rotation 
 of the earth, as represented in Figure 
 161, — having its N-pole near the S 
 geographical pole, and its S-pole near 
 the N geographical pole ; or if (as is 
 more probable) the earth itself is a 
 magnet. 
 
 Bxperiment 3. Magnetize a circular steel disk, so that its poles 
 may be at the extremities of one of its diameters. Place it beneath a 
 plate of glass. Sift over 
 the glass fine iron-filings, 
 as in Exp. 2, p. 28. Gently 
 tap the glass a few times, 
 so as to agitate the filings. 
 Once in motion, they ar- 
 range themselves in lines 
 radiating from either pole, 
 forming graceful curves 
 from pole to pole, as rep- 
 resented in Eigure 162. 
 These represent what are 
 called lines of magnetic 
 force. They represent the 
 resultants of the combined 
 action of the two poles. 
 Now carry the little mag- 
 netized cambric needle 
 around the disk. It follows 
 the lines of magnetic force 
 as mapped out by the fil- 
 ings, always assuming a 
 position tangent to the magnetic curve, as shown In Figure 162. 
 
 It is evident that the space around a magnet is the seat of a. 
 
222 ELECTRICITY AND MAGNETISM. 
 
 peculiar influence ; this space, extending as far as the magnet 
 exerts any efltect, is called the magnetic field. The last experi- 
 ment presents a true exhibition, on a snlall scale, of what the 
 earth does on a large one, and thereby presents one of many 
 phenomena which lead to the conclusion that the earth is a 
 magnet. 
 
 § 192. Magnetic poles of the earth. — It will be seen 
 that there are two points where the needle points directly to the 
 center of the disk. A point was found on the western coast of 
 Boothia, by Sir James Eoss, in the year 1831, where the dipping 
 needle lacked only one-sixtieth of a degree of pointing directly 
 to the earth's center. The same voj'ager subsequently reached 
 a point in Victoria Land where the opposite pole of the needle 
 lacked only 1° 20' of pointing to the earth's center. 
 
 It will be seen that, if we call that end of a magnetic needle which 
 points north the N-pole, we must call that magnetic pole of the earth 
 which Is in the northern hemisphere the S-poIe, and vice versa. (See 
 Fig. 162.) Hence, to avoid confusion, many careful writers abstain 
 from the use of the terms north and south poles, and substitute for 
 them the tferms positive and negative, or marked and unmarked poles. 
 
 § 193. Variation of the needle. — Inasmuch as the mag- 
 netic poles of the earth do not coincide with the geographical 
 poles, it follows that the needle does not in most places point due 
 north and south. The angle which the needle makes with the 
 geographical meridian is known as the angle of declination. 
 This angle differs at different places. 
 
 Experiment. As Columbus found, we can easily find, the declina- 
 tion at any place as follows : Set up two sticks so that a string joining 
 them points to the North Star ; the string will lie in the geographical 
 meridian. Place a long magnetic needle over the string; the angle 
 between the needle and the string is the required declination. If great 
 accuracy is required, allowance must be made for the fact that the 
 star is not exactly over the pole, but appears to describe daily around 
 it a circle whose diameter is about 4°. 
 
VARIATION OF THE ITBBDLE. 223 
 
 Let A (Fig. 163) represent a magnetic pole, and B the North 
 Star ; it will be seen that there is a posi- Fig. 163. 
 
 tion in which the needle will point due 
 north. A line passing around the earth 
 through the two magnetic poles, con- 
 necting those places where the needle 
 points due north, is called a line of no 
 variation. On the map, Plate II., it is marked 0. Lines east 
 and west of this line, and approximately parallel with it, repre- 
 sent lines of equal variation. At places in the United States 
 east of this line the needle points west of north, e.g., New 
 England ; but most of the States lie west of this line, so in them 
 the needle points east of north. 
 
 The magnetic poles are not fixed objects that can be located 
 like an island or cape, but are constantly changing. They ap- 
 pear to swing, somewhat like a pendulum, in an easterly and 
 westerly direction, each swing requiring centuries to complete it. 
 The north magnetic pole is now on its westerly swing. The 
 chart given in this book was only true at the time of observation 
 in 1870. To be true for the present time, each of the lines 
 should be moved westward at the rate of about 1° for every 
 twelve years. 
 
 § 194. Natural magnets. — On the assumption that the 
 earth is a magnet, it would not be strange if magnetizable sub- 
 stances should partake of its magnetic properties by induction. 
 An ore of iron called lodestone, composed of a mixture of two 
 oxides of this metal, possesses more or less magnetic power. 
 Such magnets are termed natural magnets, to distinguish them 
 from the artificial magnets of steel. 
 
 § 195. Cause of the earth's magnetism. — The cause of 
 the earth's magnetism is not known. The theory that it is an 
 electro-magnet in virtue of currents flowing around it near its 
 surface, from east to west, explains all the effects that it pro- 
 duces on the magnetic needle. But what sustains these electric 
 
224 
 
 ELECTKICITY AKD MAGNETISM. 
 
 currents? There are many things that point to the sun as the 
 source of the earth's magnetism. Those who adopt this theory 
 generally regard the terrestrial currents as thermo-electric. 
 
 A single instance must suffice to illustrate the intimate relation that 
 certainly exists between the sun's condition and, the earth's mag- 
 netism. In 1859 two observers remote from each other saw simul- 
 taneously a bright spot break out on the face of the sun, whose duration 
 was only five minutes. Exactly at' this time there was a general dis- 
 turbauce of magnetic needles, and telegraph wires all over the world 
 were traversed with so-called earth currents. Telegraphers received 
 shocks, and an apparatus in Norway was set on fire. These phenomena 
 were quickly followed by auroral displays. Sometimes telegraphs are 
 worked by earth currents alone, without any battery in the circuit. 
 
 Fig. 164. 
 
 § 196. General remarks on magnets and magnetism. 
 
 — Artificial magnets, including permanent magnets and electro- 
 magnets, are usually made in the shape eitherof a straight bar 
 or of the letter U, called the horse-shoe, according to the use 
 made of them. If we wish, as in the experiments already de- 
 scribed, to use but a single pole, it is desirable to have the other 
 as far away as possible ; then obviousl}- the bar-magnet is most 
 convenient. But if the magnet is to be used for lifting or hold- 
 ing weights, the horse-shoe form is far better, because the 
 attraction of both poles is conveniently available, 
 and because their combined power is more than 
 twice that of a single pole. This is due to the 
 reflex influence of the poles on one another through 
 the armature. Magnets, when not in use, ought 
 always to be protected by armatures (A, Fig. 164) 
 of soft iron ; for, notwithstanding the coercive 
 power of steel, they slowly part with their magne- 
 tism. But when an armature is used, the opposite 
 poles of the magnet and armature being in contact 
 with one another, i.e., N with S, they serve to bind 
 one another's niagnetism. 
 
 Thin bars of steel can be more thoroughly magnetized than 
 
Phie II. 
 
DIAMAGNETISM. 226 
 
 thick ones. Hence, if several thin bars (Fig. 164) are laid side 
 by side, with their corresponding poles turned in the same 
 direction, and then screwed together, a very powerful magnet 
 is the result. This is called a compound magnet. In any mag- 
 net the outer layers are far more strongly magnetized than the 
 central ones ; so a steel tube makes very nearly as strong a 
 magnet as a rod of the same diameter, and is much lighter than 
 the latter. 
 
 § 197. Diamagnetism. — Besides iron and steel, many 
 other substances, and possibly all substances, both in the liquid 
 and gaseous, as well as in the solid state, are more or less sus- 
 ceptible to magnetic influence. Conspicuous among these are 
 nickel and cobalt. But this influence is not always of the same 
 kind. A small bar of bismuth suspended between the poles of 
 a powerful electro-magnet, instead of being attracted is repelled 
 bj- the poles of the magnet, as shown by its taking a position 
 with its longest axis at right angles to a direct line between the 
 poles. Substances which behave in this manner are called dia- 
 magnetic, and they are said to place themselves equatorially 
 between the poles. Substances that place themselves axially 
 between the poles, as iron and nickel, are called paramagnetic. 
 or simply magnetic. 
 
 Paramagnetic liquids placed in a watch-glass between the 
 poles become heaped up at the poles and depressed in the cen- 
 ter, while the opposite phenomena occur with diamagnetic 
 liquids. The magnetic behavior of gases may be learned by 
 inflating soap-bubbles with them, and noting the direction of 
 their distension. Alcohol, water, nitrogen, and carbonic acid 
 are diamagnetic. Oxygen is paramagnetic. The only sub- 
 stances whose magnetic properties can be shown without extra- 
 ordinary apparatus are iron and its compounds. 
 
 § 198. Magnets not sources of energy. — Perpetual- 
 motion seekers are easily led into the error of supposing that in 
 the magnet they have an inexhaustible supply of energy ; but 
 
226 
 
 ELECTRICITY AND MAGNETISM. 
 
 a very little study will serve to exhibit the character of the 
 error. If, for instance, we bring a piece of iron near a magnet, 
 it is attracted, and, if allowed to move up to the magnet, this 
 force of attraction will do a certain amount of work. Take now 
 another piece of iron similar to the first ; this also wUl be at- 
 tracted, and a certain amount of work will be performed, but a 
 less amount than that done in the first instance. Continue the 
 operation until the magnet no longer attracts ; then the magnet 
 has done a definite amount of work, and lost the power of doing 
 more. To restore it to its original condition, we must remove 
 all the pieces of iron ; this will require an expenditure of exter- 
 nal work exactlj"^ equal to .that originally performed by the 
 magnet. 
 
 XXXII. MAGNETO-ELECTRIC AND CURRENT INDUCTION. 
 
 § 199. Introductory experiments. — Experiment 1. Con- 
 nect a helix with a delicate galvanometer (Fig. 165), and quickly thrust 
 a magnetized steel rod into the coil. A deflection of the needle shows 
 that a current of electricity at that Instant traverses the wire. But 
 _. ... the needle, after a few oscilla/- 
 
 r Ig. 16o. 
 
 tions, assumes its original posi- 
 tion. This shows that the current 
 was only momentary. Quickly 
 remove the magnet; again the wire 
 is traversed by a current, but this 
 time in an opposite direction to 
 the first, as shown by an opposite 
 deflection. Repeat the experiment, 
 and notice that when the magnet 
 approaches the coil the Induced 
 current runs in the opposite direc- 
 tion to the Amp6rian currents, as 
 represented in Figure 166. But 
 when the magnet is withdrawn, 
 the induced current takes the same direction with the Ampferian cm'- 
 rents, as in Figure 167. In the former case, the repulsion due to 
 opposite currents must act as a resistance to the force that brings them 
 
MAGNETO AND DYNAMO MACHINES. 
 
 227 
 
 together. Likewise, in the latter case, the attraction due to currents 
 flowing in the same 
 direction must resist 
 the force that sepa- 
 rates them. Hence, 
 the energy shown by 
 the electric current ha.i 
 been generated at the 
 expense of mechanical 
 energy. 
 
 Bxperiment 2. 
 Place within the coil 
 a core of soft iron. "Wave back and forth, over one extremity of the 
 core, one of the poles of a powerful har-magnet. The needle of the 
 galvanometer is violently agitated, being deflected in one direction at 
 each approach, and in the opposite direction at each departure. Now 
 repeat the experiments with the opposite pole of the magnet. The 
 eflfect is, as we should expect, to reverse 
 all the currents. 
 
 Fis, 
 
 § 200. Magneto and dynamo 
 machines. — If the permanent mag- 
 net is stationary, and the electro- 
 magnet is moved back and forth, 
 the result is the same as when the 
 magnet was moved and the electro- 
 magnet was stationary. Machines 
 constructed for the purpose of gene- 
 rating electric currents in this manner 
 are called magneto-electrical machines. 
 
 Figure 168 will give a general idea of 
 the construction of the simpler kinds of 
 magneto machines. N S is a permanent 
 compound horse-shoe magnet. EE are 
 coils containing cores of soft iron con- 
 nected by the back-armature C C, the 
 whole constituting a sort of an armature 
 to the permanent magnet. The brass axle D D is rigidly connected 
 with the back-armature C C, so that when the axle is rotated by means 
 
228 
 
 ELECTBICITY AND MAGNETISM. 
 
 of the crank A, both helices are carried around with it. Now, suppose 
 the cranio to be turned ; during the first quarter of a revolution a sep- 
 aration of poles occurs, and currents of electricity are established in 
 both helices. The wire that constitutes the helix is wound in opposite 
 directions around the two cores, so that the two currents may not flow 
 in opposite directions through the wire, and thereby neutralize one an- 
 other, but may have a common direction, and thereby produce a current 
 of double the electro-motive force that would be produced in a single 
 helix. During the second quarter-revolution the poles approach one an- 
 other, and the effect would be to reverse the current ; but the polarity of 
 the cores also change as they are now brought under the influence of the 
 poles which they are approaching, and this double change leaves the cur- 
 rent to flow in the same direction as it did before. At the end of a half 
 revolution there is a reversal of current, as the poles do not change at 
 this point. The result would be that during every revolution there 
 would be a current half of the time in one direction, and half of the 
 time in the opposite direction. In order to secure a constant current 
 in one direction, a current-reverser I, or commutator, as it is called, at- 
 tached to the axle, is so arranged that the current is reversed at the 
 end of each half revolution, and is then conducted away by the wires 
 GH. 
 
 Each of the two currents produced in a single revolution has a 
 
 maximum point, or point of 
 ' r J greatest intensity, when the 
 
 cores are nearest the poles of 
 the magnet; and a minimum 
 point, or point of least intensity, 
 when they are farthest from the 
 poles. Between these two 
 points the current is constantly 
 growing or diminishing. It is 
 apparent that such a machine 
 gives not only an intermittent 
 current, but one that resembles 
 a succession of waves or a 
 stream produced by the strokes 
 of a pump, alternately rising 
 and sinking. But for most 
 purposes for which electricity is employed, it is important that the 
 current should be continuous and uniform. Figui-e 169 will serve to 
 illustrate the principle by which this is secured in the widely-known 
 Gramme machine. 
 
MAGNETO AND DYNAMO MACHINES. 229 
 
 The armature ns consists of a ring composed of a bundle of soft 
 iron wires (better shown in Fig. 169 a) surrounded by what is virtually 
 an endless coil of wire. The wire, however, is put on in separate 
 coils, the in-wire of one united to the out- wire of the next, and from 
 each junction a branch wire is led to a copper plate on the axis of 
 rotation mm. A horse-shoe magnet NS (only a portion of which is 
 shown in the cut) is so placed that one-half of the ring is under the 
 influence of the N-pole, and the other half under that of the S-pole. 
 Suppose the ring to rotate in the direction of the arrow ; then every 
 point of the iron core, as it comes opposite a given point of the 
 magnet, will successively become a pole of opposite name, while the 
 points i and i' are the neutral points. If we imagine the core to be 
 divided at the points n and s, we have two semicircular magnets whose 
 north poles and whose south poles respectively face one another. In 
 the two mutually- facing poles on either side, the Amperian currents 
 must be in opposite directions. Now an attentive study of this ideal 
 diagram in the light of what you have previously learned respecting 
 the generation of induced currents will enable you to see that as the 
 ring armature rotates, the corresponding advance of the induced poles 
 of the ring will induce currents in the wire in such a manner that all 
 the coils which at any given moment are in the semicircle next one of 
 the magnet poles — say the North — are traversed by a current of one 
 direction. Similarly, the semicircle formed by the coils immediately 
 approaching, or immediately receding from the South pole are at the 
 same time traversed by a current of the opposite direction. The result 
 is that currents in the lower half tend toward the point m ou the axis, 
 and in the upper half from point m'. So long as the leading out- wires 
 from these points are open, these currents have no outlet, and conse- 
 quently oppose and neutralize one another. But if the points m and 
 m' are connected by a wire L, we shall have a constant and non-alternat- 
 ing current flowing through the wire from m to m'. The contact at 
 these points is made by means of brushes of thick wire provided as 
 springs. These press on the contact pieces and make practically a 
 constant connection with the two halves of the circuit. 
 
 Inasmuch as an electro-magnet may be made a much more powei'ful 
 magnet than a permanent magnet, it is now extensively used as the 
 inducing or the so-called field magnet. Such a machine is called a 
 dynamo-electrical machine, or often more briefly a dynamo. Figure 
 169 6 represents such a machine. EE is the stationary field magnet, 
 A the moving armature, and N and S large pole-pieces brought as 
 near as practicable to the armature and partially encircling it. When 
 
230 
 
 ELECTRICITY AND MAGNETISM. 
 
 the machine is at rest, there are no currents ; but when the armature is 
 in motion, the residual magnetism (a small portion of the magnetism 
 which soft iron always retains after it has been magnetized) induces 
 at first a weak cm-rent in the wire of the armature; but as a portion of 
 this current is carried by means of a shunt wire I through the coil of 
 ' the field magnet, and magnetizes the core more and more strongly, 
 the current in both the shunt I and the main wire L quickly reaches 
 its maximum. 
 
 By the kind permission of the United States Electric Lighting 
 Company we introduce a cut, Fig. 169 c, of the popular American 
 dynamo called the Weston. It will be seen that in this machine two 
 powerful field magnets are placed one on either side of the 
 revolving armature. Power originated in a steam engine is com- 
 municated to the dynamo by means of a belt passing over the circum- 
 ference of the wheel W and causes the armature, which is on the axle 
 of this wheel, to revolve. 
 
 § 201. Current induction. — If, in the original experiment 
 in magneto-electric induction (p. 226), a helix connected with a 
 battery is substituted for the permanent magnet, precisely the 
 same results are obtained as with the magnet. Indeed, we ought 
 to expect the same results. (Why?) The wire A, Figure 170, 
 
 Fig. no. 
 
 through which the battery current circulates, is known in this 
 case as the primary wire, and the battery current, the primary 
 or inducing current. The wire B, through which the induced 
 currents circulate, is called the secondary wire, and the currents 
 that traverse this wire are frequently called secondary currents. 
 
Pig. 169 e. 
 
 
232 ELECTRICITY AND MAGNETISM. 
 
 ductor gives rise to a current. But it is evident that in a single 
 wire every portion must be considered as a neighboring conduc- 
 tor with respect to every other portion ; consequently there can 
 be no change of electrical condition in a wire without accom- 
 panying induction phenomena. If we suddenly close a circuit 
 the current does not abruptly assume its final intensity, because 
 there ie a current induced in the same circuit whose direction is 
 such as to retard the change from zero. So, too, if a closed 
 circuit be suddenly broken, there is a current induced in the 
 direction of the primarj' current which retards the change to 
 zero. These induced currents are often, for the sake of dis- 
 tinction, called extra currents. Of course, if all parts of the con- 
 ductor are kept close together by winding the wire into a helix 
 or a spiral, the effect is much increased. It is evident that the 
 direct extra current must produce a much greater effect than 
 the indirect, because the former is added to the primary, whUe 
 the latter is subtracted. This is the cause of the bright spark 
 on breaking a strong current, and also of physiological effects 
 or shocks experienced on breaking the primary circuit in the 
 experiment illustrated by Figure 170. If a soft iron core is 
 introduced into a helix, the extra currents are vastly increased 
 by the action of the magnetic changes. (Why?) 
 
 § 203. Induction coils. — If a core of iron, or, still better, 
 a bundle of wires (A A, Fig. 171), is inserted in the primary 
 coil, it is evident that it will be magnetized and demagnetized 
 every time the primary is made and broken. The starting and 
 cessation of Ampferian currents in the core in the same direction 
 as the primary- current, and simultaneous with the commence- 
 ment and ending of the primary current, greatly intensifies the 
 secondary current. To save the trouble of making and break- 
 ing b}' hand, as in Figure 171, the core is also utilized in the 
 construction of an automatic make-and-break piece. A soft 
 iron hammer 6 is connected with the steel spring c, which is in 
 turn connected with one of the terminals of the primary wire. 
 
RUHMKORFF S COIL. 
 
 233 
 
 The hammer presses against the point of a screw d, and thus, 
 through the screw, closes the circuit. But when a current 
 passes through the primary wire, the core becomes magnetized, 
 draws the hammer away from the screw, and breaks the circuit. 
 
 rig. 171. 
 
 The circuit broken, the core loses its magnetism, and the hammer 
 springs back and closes the circuit again. Thus the spring and 
 hammer vibrate, and open and close the primary circuit with 
 great rapidity. An instrument made on these principles is 
 called an induction coil. 
 
 § 204. Ruhmkorflf's coil.— This instrument has the impor- 
 tant addition, to the parts alreadj" explained, of a condenser BB. 
 This consists of two sets of layers of tinfoil separated by paraf- 
 fine paper ; the layers are connected alternately with one and 
 the other pole of the battery, as the figure shows, so that they 
 serve as a sort of expansion of the primary wire. When the 
 circuit is broken, the extra current would jump across at 6, and 
 would vaporize the points of contact, and form a bridge with the 
 vapor of metal that would prolong the time of breaking. But, 
 
234 ELECTRICITY AND MAGNETISM. 
 
 when the condenser is attached, the extra current finds an 
 escape into it easier than to jump across at b, so the vaporizing 
 of the contact is avoided, and the time of breaking being much 
 shortened, the secondary is much more intense. 
 
 The primary helices of induction coils consist of comparatively 
 few turns of coarse insulated wire ; but the secondary helices 
 contain man}' turns of very fine wire, insulated with great care. 
 The secondary current is, at breaking, as we ought to expect 
 from the extreme rapidity with which the primary circuit is 
 broken, distinguished from the primary, or galvanic current, by 
 its vastl}- greater tension, or power to overcome resistances. 
 A coil constructed for Mr. Spottiswoode of London has two 
 hundred and eighty miles of wire in its secondary coil. With 
 five Grove cells this coil gives a secondary spark forty-two inches 
 long, and perforates glass three inches thick. Manj' brilliant 
 experiments may be performed with these coils which will be 
 indicated in connection with frictional machines. 
 
 XXXIII. THERMO-ELBCTRICITT. 
 
 § 205. So far in our experiments we have obtained a current 
 of electricity by using the potential energy due to the chemical 
 affinity of zinc and sulphuric acid, or by expending mechanical 
 energj- ; can we not also get a current directly from the molec- 
 ular energy that we know as heat ? 
 
 Experiment. Insert in one screw cup of a sensitive galvanometer 
 an iron wire, and in tlie other cup a copper, or, better, a German silver 
 wire. Twist the other ends of the wire together, and heat them at 
 their junction in a flame ; a deflection of tlie needle shows that a cur- 
 rent of electricity is traversing the wire. Place a piece of ice at their 
 junction. A deflection in the opposite direction shows that a current 
 now traverses the wire in the opposite direction. 
 
 These currents are named, from their origin, tliermo-electric. 
 The appai'atus required for the generation of these currents is 
 very simple, consisting merely of bars of two different metals 
 
THBKMO-ELECTRICITT. 
 
 235 
 
 joined at one extremitj', and some means of raising or lowering 
 tiieir temperature at tiieir junction, or of raising tlie temperature 
 at one extremity of the pair and lowering it at the other ; for the 
 electro-motive force, and consequently the strength of the cur- 
 rent, is nearly proportional to the difference in temperature of 
 the two extremities of the pair. The strength of the current is 
 also dependent, as in the voltaic pair, on the thermo-electro- 
 motive force of the metals employed. The following thermo- 
 electric series is so arranged that if the temperatures of both 
 junctions are near the ordinary temperatures of the air, those 
 metals farthest removed from each other give the strongest cur- 
 rent when combined ; and the current passes, when heated at 
 their junction, from the one first named to that succeeding it. 
 The aiTows indicate the direction of the current at the heated 
 and cold ends respectively. At high temperatures the current 
 maj- be reversed.. 
 
 Cold. 
 
 CO 
 
 3 
 
 C3 
 
 O 
 
 > 
 
 CO 
 
 a 
 
 oi 
 
 g 
 
 <- 
 
 <0 
 
 03 
 
 d 
 
 o. 
 o 
 
 1 
 
 a) 
 > 
 
 .3 
 
 Is 
 
 Hi 
 
 H 
 
 U 
 
 Ph 
 
 02 
 
 N 
 
 
 a 
 
 Heat. 
 
 Fig. 172. 
 HEAT 
 
 § 206. Thermo -electric batteries and thermo-pile. — 
 The electro-motive force of the thermo-electric pair is very 
 small in comparison with that of the voltaic pair ; 
 hence the greater necessity of combining a large 
 number of pairs with one another in series. This 
 is done on the same principle, and in the same 
 manner, that voltaic pairs are united, viz., by join- 
 ing the -|- metal of one pair to the —metal of an- 
 other. Figure 172 represents such an arrange- 
 ment. The light bars are bismuth, and the dark 
 ones antimony. If the source of heat is strong 
 and near, by either conduction or convection one face may be 
 
236 BLECTKICITY AND MAGNETISM. 
 
 heated much hotter than the other, and a current equal to that 
 from an ordinarj- galvanic cell is often obtained. Instruments 
 constructed on these principles, and used as a source of elec- 
 tricity, are very convenient and efficient for many purposes, 
 especially when a steady current is required with small external 
 resistance ; they are called thermo-electric batteries. 
 
 If th^ source of heat is feeble or distant, the feeble current 
 may serve to measure the difference of temperature between the 
 ends of the bars turned toward the heat (as in Figure 172) 
 and the other ends, which are at the temperature of the air. 
 The apparatus, when used for this purpose, is called a thermo- 
 pile, or a thermo-multiplier. A combination of as many as 
 thirty-six pairs of antimony and bismuth bars, connected with 
 a very sensitive galvanometer, constitutes an exceedingly deli- 
 cate thermoscope and thermometer. Quantities of heat, that 
 would not perceptibly expand the mercury in an ordinary ther- 
 mometer, can, by the use of a thermo-electric pile, be made to 
 produce large deflections of the galvanometer needle. Heat 
 radiated from the body of an insect several inches from the pile 
 may cause a sensible deflection. 
 
MECHANICAL ENEKGY. 
 
 237 
 
 XXXIV. FRICTIONAL ELECTRICITY. 
 
 § 207. Mechanical energy transformed into electrifi- 
 cation. — Experiment. Prepare an insulated stool (see § 214) by- 
 placing a square board on four dry and clean glass tumblers, used as 
 legs. Let a person whom we will call John stand on this stool, and 
 let a second person, 
 James, strike John a 
 few times with a cat's 
 fur. Then let James 
 bring a knuckle of a 
 finger near to some part 
 of John's person, for 
 instance a knuckle of 
 his hand, or his chin or 
 nose ; an electric spark 
 will pass between the 
 two, and both will expe- 
 rience a slight shock. 
 The length of the spark 
 shows that the electri- 
 city is urged by a high 
 E.M.E., like the induced 
 currents of the magneto-machine and induction coil. 
 
 As mechanical energy is transformed into a kind of molecular 
 motion, or internal energy, called heat, when one hammers an 
 anvil, so in this case a portion of the motion of the fur at each 
 stroke is transformed into another phase of internal energy known 
 as electrification. Electricity made apparent in this manner is 
 called frictional electricity, because the electrification pig. 174, 
 is developed by friction between two surfaces. 
 
 § 208. Electroscope. — Experiment. Suspend in 
 a loop, tied in a white silk thread, a strip of gold foil 20=' 
 long and 15°™" wide, so that the two vertical portions may 
 be near each other. After John has been struck a few ' 
 times with the fur, let him bring a finger gradually near the upper ex- 
 tremity of the foil ; the two portions of the foil gradually diverge, 
 as in Figure 174, indicating the presence of an imusual force in his body. 
 
238 
 
 ELECTRICITY AND MAGNETISM. 
 
 We have already found that this force is due to clectricitj-. 
 Bodies in this state are said to be charged with electricity, or 
 simply electrified. Such electrification in a person is often 
 manifested by a divergence of hair on his head. Any ar- 
 rangement, like that of the foil just described, intended to 
 detect the presence of electrification, is called an electroscope. 
 One of the most common and useful electroscopes consists 
 of one or two pith-balls, made from the pith of elder or 
 sunflower, suspended by silk thread. If an electroscope is 
 brought near to either pole of a secondary wire of an induction 
 coil, a similar electrification is manifested by the poles. Like- 
 wise, by means of very delicate electroscopes, the poles of a 
 galvanic battery, or of a thermo-battery, are found to be feebly 
 electrified. 
 
 § 209. Attractions and repulsions. — Experiment l. Poise 
 a flat wooden ruler on an inverted bottle or flask, having a round bot- 
 tom, as in Figure 175. Draw a rubber comb two or three times through 
 J,} j^g your hair, or rub it with a woolen cloth, 
 
 and place it near one end of the ruler ; 
 instantly the ruler moves toward the 
 comb. 
 
 Experiment 2. Hold the comb over 
 a handful of bits of tissue paper ; the 
 papers quickly jump to the comb, stick 
 to it for an instant, and then leap ener- 
 getically from the comb. The papers 
 are first attracted to the comb, but in 
 a short time acquire some of its electri- 
 fication, and then are repelled. 
 
 § 210. Two states of electri- 
 city. — It is quite apparent that we are now dealing with a very 
 different class of electrical phenomena from any that we have 
 previously observed. It is also quite as obvious that we are 
 dealing with electricity in a very different state or condition 
 from that in which we have before studied it. Hitherto we 
 have studied only those phenomena produced by electricity 
 
TWO STATES OF ELECTRICITY. 
 
 239 
 
 when in motion ; and, Inasmuch as when in that state its energy 
 is expended in work, or transformed into some other form of 
 energy as rapidly as it is generated, there was no such thing 
 as an accumulation of electricity. In our late experiments 
 there is wanting anything like a current ; but, on the other hand, 
 we find that electricity in this new state may accumulate, be 
 stored up, and remain in a quiescent state for an indefinite 
 time. In the latter state it is incapable of affecting a magnetic 
 needle, magnetizing, generating heat, illuminating, producing 
 decomposition, or giving shocks. But in this state of appar- 
 ent repose it may attract and afterwards repel light bodies in 
 the vicinity of the body in which it resides. These attrac- 
 tions and repulsions are quite distinct from the attractions and 
 repulsions which occur between parallel currents. 
 
 This state of electricity is called static, in distinction from the 
 current state, which is often called dynamic. We have seen 
 that, under certain conditions, electricity may change from one 
 state to the other, as when the electricity which had accumu- 
 lated in the boy on the insulated stool passed to the other boy. 
 
 Fig. 176. 
 
 producing, in its current 
 state, both illuminating and 
 phj'siological effects ; and 
 again, when a current is 
 broken, the current ceases, 
 but electricitj' accumulates 
 in the wire (see § 208) . We 
 have also learned that elec- 
 tricity of high potential, 
 such as is most readily de- 
 veloped by friction, exhib- 
 its the static phenomena, i.e., attractions and repulsions, most 
 strikingly ; but we must be careful to avoid the notion that 
 these are peculiar to electricity so derived. 
 
 §211. Two kinds of electriflcation.— Experiment 1. Bend 
 a small glass tube into the form represented by A, Figure 176, and insert 
 
240 
 
 BLECTEICITY AND MAGNETISM. 
 
 Fig. 177. 
 
 one end in a block of wood B for a base ; and suspend from the tube a 
 pith-ball C by a sUk thread. Rub a glass rod D with a silk handker- 
 chief, and present it to the ball ; attraction at first occurs, followed by 
 repulsion after contact. Now rub a stick of sealing-wax, or a hard- 
 rubber ruler, with flannel, and present it to the ball, which is in a con- 
 dition such that it is repelled by the electrified glass ; it is attracted by 
 the electrified sealing-wax. We are led to suspect that the sealing- 
 wax possesses a difiterent kind of electri- 
 fication from that of the glass. Let u? 
 further test the matter. 
 
 Experiment 2. Suspend two glass 
 
 rods that have each been rubbed with 
 
 siUi in two wire stirrups (Fig. 177) , and 
 
 present them to each other; they repel 
 
 one another. Suspend two sticks of 
 
 sealing-wax that have been rubbed with 
 
 flannel in the same manner; the same 
 
 result follows. Now, in a like manner, present one of the glass rods 
 
 and one of the sticks of sealing-wax to each other ; they attract one 
 
 another. 
 
 Experiment 3. Make a pin 
 hole in each end of a hen's egg, 
 and blow its liquid contents out. 
 Apply, with flour paste, tinfoil 
 smoothly to the surface of the 
 shell, and completely cover it. 
 With a drop of melted sealing-wax 
 attach one end of a silk thread 
 midway between the ends of the 
 shell, so that it may be suspended, 
 as in Figure 178. Repeat the last 
 two experiments with the shell as 
 with the pith-ball ; you obtain simi- 
 lar results. 
 
 It is evident (1) that tliere 
 are two kinds or conditions of 
 electrification; or, for conven- 
 ience, we sometimes say two kinds of electricity; (2) that they 
 are so related to each other that like kinds repel and unlike kinds 
 attract one another. The two kinds are usually distinguished 
 
INDUCTION. 
 
 241 
 
 from one another by the names positive and negative^ or, more 
 briefly, as +e and — e. The former is, by definition, such as 
 is developed on glass when rubbed with silk, and the latter is 
 the kind developed on sealing-wax when rubbed with flannel. 
 There is no reason, except custom, for calling the one positive 
 rather than the other. 
 
 Experiment 4. Once more electrify a stick of sealing-wax with a 
 flannel, and present it to the ball or shell, and after the ball is repelled, 
 bring the surface of the flannel which had electrifled the rod near the 
 ball ; the ball is attracted by it, showing that the rubber is also electri- 
 fied and with the opposite kind to that Avhich the sealing-wax pos- 
 sesses. (Which kind of electrification has the flannel?) 
 
 Fig. 179. 
 
 One kind of electrification is never developed alone ; when two 
 substances are rubbed together, both always become oppositely 
 electrifled, and to an equal amount. In general, whenever any 
 electricity of either sign is developed, an equal quantity of the 
 other is to be found. (Ascertain the kind of electrification de- 
 veloped on a rubber comb when it is passed through the hair ; 
 also the kind developed on a person when whipped with fur, by 
 presenting the bodies whose electrification is to be tested to a 
 body having a known electrification.) 
 
 § 212. Induction.— Experiment. Suspend two egg-shells, pre- 
 pared as above, so as to touch one another, end to end, as in Figure 179. 
 
242 ELECTEICITY AND MAGNETESM. 
 
 Bring near to one end of the shells, but not to touch, a sealing-wax rod 
 excited with flannel, and therefore having —e. While the rod is in this 
 position, carry a thin strip of tissue paper, or a pith-ball suspended by 
 a silk thread, along the eggs. The paper is attracted most strongly at 
 the ends ; but in the middle, where the shells are in contact, there is 
 very little electrification. Separate B from A about 10"", while the rod 
 D is still in position. Then place D midway between A and B ; the rod 
 repels B and attracts A. It appears that when the two shells touched 
 one another, thereby constituting practically one body, that the shells 
 were oppositely electrified, as represented by the signs -|- and — in the 
 diagram ; and when the two bodies were separated, they retained their 
 opposite charges. 
 
 We learn from this experiment that by induction we may 
 charge at the same time two bodies, one with -f-e, and the other 
 with — «. 
 
 § 213. Discharge. — Experiment. Bring the two shells oppo- 
 sitely charged near one another; when near enough they exhibit 
 mutual attraction for one another. On bringing them still nearer, a 
 spark passes between them, their mutual attraction suddenly ceases, 
 and on testing them with an electroscope, it is found that both have 
 lost their electrification, i.e., both have become discharged. 
 
 When two bodies containing equal amounts of opposite electri- 
 cities are brought together, both become discharged. During 
 the process of discharge, the electricity which was previously in 
 a condition of rest, or a static state, assumes a condition of 
 motion, or a dynamic state, as is shown by a sparii passing 
 between the two bodies when brought near one another. One 
 of the bodies — that positively charged — is at a potential higher 
 than that of the earth, the other being lower. When they are 
 brought sufBciently near, the tendency for the electricity to pass 
 from the region of higher potential becomes strong enough to 
 penetrate the insulating air and establish a condition of equili- 
 brium. In this particular case the result is zero potential or 
 no electrification ; but in general both bodies would be left at a 
 like condition of electrification, its sign depending upon the 
 sign of that electricity which was in excess. 
 
 We may now understand how it is that an electrified body 
 
INSULATION. 243 
 
 attracts to itself light bodies in its vicinity. For example, a 
 stick of sealing-wax, excited with — e, brought near a pith ball, 
 induces +e next itself, and repels — e to its farthest side ; then, 
 of course, attraction follows. There is the same attraction be- 
 tween heavy bodies, but usually not suflScient to produce motion. 
 
 § 214. Insillation. — Experiment. Bring again the electrified seal- 
 ing-wax near one end of one of the shells ; the shell becomes polarized, 
 that is, the opposite ends become oppositely electrified. Touch the shell 
 with the finger. Through your body the negative charge is driven to 
 the earth, while the positive charge remains in proximity to the rod. 
 (Explain.) Remove the finger, and afterwards remove the rod; test 
 the shell, and you will find that it is charged with electricity. (Is it 
 — e or -l-e?) Touch this shell with the other shell, then separate them. 
 Test them, and you find that they have the same kind of electrification. 
 It is evident that the first shell became electrified by induction and the 
 last shell by conduction. Touch with the finger one of the shells ; it 
 loses its electrification. 
 
 "When you touch the shell with your finger, the electric charge 
 diffuses itself through your body and the earth. It is evident 
 that the electricity could not traverse the sUk thread, otherwise 
 we could not have charged the shell. Substances which do not 
 allow electricity to pass readily through them are called non- 
 conductors or insulators. A body that is to receive a permanent 
 charge of electricity must be insulated, i.e., have no connection 
 with the earth through a conducting substance. Some of the 
 best insulating substances are dry air, ebonite, shellac, resins, 
 glass (free from lead, e.g., common bottle glass), silks, and 
 furs. In experiments with electricity in the statical state, the 
 E. M. F. is in general so much greater than when a galvanic 
 battery- is the source of electricity, that substances — such as dry 
 wood, for instance — which are practically good insulators in the 
 latter case are not so regarded in the former. Moisture injures 
 the insulation of bodies ; hence experiments succeed best on 
 dry, cold days of winter, when moisture of the air is least liable 
 to be condensed on the surfaces of apparatus, especially if it is 
 kept warm. 
 
244 ELECTKICITY AND MAGNETISM. 
 
 § 215. Eleotrifloation oonflned to the external surface. 
 — Experiment 1. Place a tin fruit-can on a clean, dry glass tumbler 
 (Fig. 180). Fasten a circular disk a of tin 15""" in diameter to one end 
 of a rod of sealing-wax. Charge the can heavily with electricity from 
 an electrical machine (seep. 245). Through an orifice c In thd can 
 _, ,.„ introduce the disk, and touch the Interior surface of the 
 
 can. Withdraw the disk, and present It to an electroscope. 
 
 It shows no electrification. Now touch the exterior sur- 
 face of the can with the disk, and present It to the electro- 
 scope ; it is found to be electrified. 
 
 Experiment 2. Attach to the can a gold foil, or double 
 pith-ball electroscope, and put into the can a few feet of 
 metal chain. Fasten the outer end to a rod of glass, or 
 some other insulator, and charge the can till the leaves of the electro- 
 scope diverge widely. Then draw up the chain by the glass rod ; the 
 leaves come together somewhat. Drop the chain into the can; the 
 leaves separate again, showing that the charge had not been lost. 
 
 These experiments show (1) that no electricity can be found 
 inside of a hollow-charged body ; or, roughly stated, electricity 
 at rest resides on the exterior surfaces of bodies; (2) that 
 when the exterior surface of an electrified body is increased with- 
 out increasing its mass or the charge, the amount of electricity at 
 any point is diminished. 
 
 § 216. Electrical potential. — "We have seen that the 
 passage of electricity from point to point sometimes causes a 
 spark ; so, conversely, the spark indicates the passage of elec- 
 tricity. The passage of a current from one shell to the other 
 (Fig. 179) might be proved, and its direction determined, by 
 connecting the shells by wires joined to a suitable galvanome- 
 ter. The current would flow from A charged with +e, to B 
 charged with — e, thus showing that A had a higher potential 
 than B. A body charged with -|-e is understood to be one that 
 has a higher potential than that of the earth, and a body 
 charged with --e is one that has a lower potential than that 
 of the earth, the potential of the earth being regarded for con- 
 venience as zero. 
 
 .id 
 
PLATE MACHINE. 
 
 245 
 
 With a very sensitive electroscope it can be shown that the 
 wires connected with the plates of a galvanic battery are at 
 different potentials when the circuit is broken. But the differ- 
 ence of potential is so small, compared with the difference pro- 
 duced by friction, that a thousand gravit3- cells in series give 
 a spark only about -j-J-j of an inch long . 
 
 XXXV. ELECTEICAL MACHINES. — CONDENSERS, ETC. 
 
 § 217. If, then, for any purpose we wish electricity of high 
 potential, we must use an enormous number of cells, an induc- 
 tion, coil, or, more cheaplj- and conveniently', an electrical 
 machine depending either on friction or on the induction of a 
 charge of electricity. Brief descriptions of a few machines will 
 now be given, followed by a series of experiments that may be 
 performed with them. 
 
 Fig. 181. 
 
 § 218. Plate machine. — It consists of a positive or prime 
 conductor A, a negative conductor B, a glass plate C, a rubber D, 
 made of two cushions of leather covered with an amalgam, four insu- 
 lating supports E, E, G, and H, a silk insulating bag I, and a brass 
 chain K, used to connect either conductor with the earth. An exten- 
 sion of the prime conductor L consists of two combs, one on either 
 side of the plate ; their pointed teeth are turned toward the plate. M is 
 a, pith-ball electroscope. 
 
246 
 
 EtiECTBICITY AND MAGNETISM. 
 
 Fig. 182. 
 
 "When the plate is turned in the direction indicated by the 
 arrow, it passes between the rubbers, and the frictioil generates 
 +e on the plate and — e on the rubber. The electrified portion 
 of the plate then passing through the silk bag comes opposite 
 the comb, when it polarizes the prime conductor, attracting — e 
 and repelling +e. But the — e escapes from the points of the 
 comb (see § 226) to the plate and neutralizes the +e of the plate, 
 and thereby leaves the conductor charged with +e. If both con- 
 ductors are insulated at the same time, the mutual attraction of 
 the two kinds of electricity would prevent their becoming heavily 
 
 charged, so one of the con- 
 ductors is always connected to 
 earth by a chain. If +e is 
 wanted, A is insulated ; if — e 
 is wanted, B is insulated. 
 
 219. Eleottophorus. — 
 Experiment. On a circular dislk 
 of sheet-iron or tin 26™ in diame- 
 ter cement a circular disk of vul- 
 canite 22=™ in diameter. To the 
 center of another circu- 
 lar disk of tin 18"=" in 
 diameter (Fig. 182) ap- 
 ply with heat one end of 
 a stick of sealing-wax 
 for a handle. Strike the 
 surface of the vulcanite 
 a few times with a cat's 
 fur or a fox-tail ; it will 
 become electrified with 
 — e. Then place the tin 
 disk on the vulcanite; 
 —e of the vulcanite will 
 polarize the disk, induc- 
 ing +e on its lower sur- 
 face and — e on its upper surface. Now place a finger on the disk. The 
 — e will escape through your body to the earth, but the +e will remain 
 
CONTINUOUS ELECTEOPHOEUS. 247 
 
 on the disk, hound by the — e of the vulcanite. Finally, raise the disk 
 by its insulating handle. Eemoved from the influence of the — « on the 
 vulcanite, the +e of the disk is now free, and if a knuckle of one of 
 your hands (Fig. 183) is brought nearlt, a bright spark will pass from 
 it to your hand, and it will become discharged. 
 
 The disk may be charged and discharged in the same manner a great 
 number of times without again whipping the vulcanite with the fur. 
 A Leyden jar (page 250) may be charged with th^p apparatus in a few 
 minutes. (Is the disk charged by conduction or induction ? "What are 
 the proofs?) 
 
 § 220. Continuous eleotrophorus. — Various methods 
 have been adopted for developing electricity continuouslj' from 
 the electrophorus, and more Pig. i84. 
 
 rapidly and with less manipu- 
 lation than can be done with 
 the apparatus above described. 
 Figure 184, from which the 
 supporting parts are omitted 
 for the sake of simplicity, will 
 serve to illustrate the general 
 principle of such machines. 
 
 A is a vulcanite or glass 
 wheel, which can be rotated by means of a system of wheels 
 CC. About 2™ back of A is a vulcanite sector D, which serves 
 as an inducer, or the same purpose as the vulcanite disk of the 
 electrophorus. Opposite D and in front of A is a metallic comb 
 B, which is connected with the conductor N. Let — e be ex- 
 cited on D with a cat-skin. Then the conducting system NB 
 will be polarized by its influence ; — e will be driven to its 
 farthest extremity N, and -f-e drawn to the points of the comb 
 B. Then, since electricity escapes readily from points, the 
 -\-e will leap from B to A, drawn off from the points by the 
 — e of D.- But vulcanite being a non-conductor, only that 
 portion of the surface of A will be charged with +e that is 
 directly opposite the comb B. The conductor BN, being de- 
 prived of its +e, is left charged with free — e. Now, rotate the 
 
248 
 
 ELECTRICITY AND MAGNETISM. 
 
 disk A. When it has accomplished half a revolutiou, that por- 
 tion of it which is charged with +e comes opposite another 
 comb B', which is also connected with a conductor P. The con- 
 ductor B'P becomes polarized. Its — e passes off from the 
 points of B' to the disk A, and discharges the +e on this disk, 
 while the conductor PB' is left charged with free +e. It is 
 evident that a constant rotation of A would cause it to be con- 
 stantly charged with -f e at its lower part by the influence of the 
 sector D, and constantly discharged at its upper part, while the 
 conductor BN is constantly receiving a charge of —e in conse- 
 quence of the loss of its -fe ; and for a similar reason the con- 
 ductor B'P is con- 
 stantly receiving a 
 charge of -J-e. With 
 a rapid rotation of 
 the disk the two con- 
 ductors wiU be so 
 rapidly and highly 
 electrified, the one 
 with — e and the other 
 with +e, that under 
 the influence of their 
 mutual attraction al- 
 most an incessant flow 
 of sparks will pass 
 between them, even 
 when the extremities, 
 P and N, are several 
 inches apart. 
 
 §221. Carre ma- 
 chine. — The sector D is liable to lose its charge suddenly, 
 and loses it very quickly after the operation of the machine 
 ceases ; so that, to begin again, it is necessary to recharge the 
 sector. In the Carr6 machine this diflJculty is avoided. 
 
CONDENSER. 249 
 
 A circular plate of glass A, which serves as the inducer, passes 
 between two leather cushions B, as it is rotated by means of the crank 
 C ; and thus by frictiou, occasioned by rubbing against the cushions, the 
 plate is kept constantly and highly electrified during the operation of 
 the machine. By means of a system of pulleys, motion is communi- 
 cated from the shaft of the plate A to the shaft of an ebonite disk D. 
 The glass plated becomes electrified with 4-e. The method by which the 
 plate D and the conductors F and E become charged is like that of the 
 machine last described. (Explain.) The cylinder E, called the prime 
 conductor, has a large area, and is therefore capable of receiving a 
 large charge. The conductor F is so jointed at N that it may be brought 
 near or carried away from E. During operation the conductor E should 
 be connected by a chain, or other good conductor, with the earth. 
 When in operation, if E is brought within two or three inches of E, 
 sparks will psiss between them so rapidly as to present the appearance 
 of a constant and continuous line of light. If F is removed to quite a 
 distance from E, the charge wiU so accumulate in E that sparks five 
 or six inches in length may be drawn from it with the fist. If a 
 Leyden jar (§ 223) is suspended by its knob from the loop G, and its 
 outside coating connected with F, the discharge will become so intense 
 as to produce a report nearly as loud as that of a pistol. 
 
 § 222. Condenser. — A very important adjunct to an elec- 
 trical machine is a condenser of some kind, by means of which 
 a large quantity can be collected on a small surface. 
 
 Experiment. Let a person stand on an insulated stool (p. 237), and 
 place one hand on the prime conductor of a machine. Let the other 
 open hand press against a plate of glass or disk of vulcanite, held on the 
 open hand of a second person standing on the floor. After a few turns 
 of the machine, let the hand that has been on the prime conductor 
 grasp the free hand of the second person. Quite a shock wiU be felt 
 by both. Or the connection may be made through a group of persons 
 having hold of one another's hands, when the whole company may 
 receive a shock. 
 
 It is evident that by this process an unusual quantity of elec- 
 tricity had collected previous to the discharge. The explanation 
 is simple. The hand of the first person, charged with -fe, acts 
 by induction through the glass upon the second person, attract- 
 ing _e to the surface of the glass with which his hand is in 
 
260 ELECTRICITY AKD MAGNETISM. 
 
 contact, and repelling +e to the earth. Thus, through their 
 mutual attraction, the two kinds of electricity become, as it 
 were, heaped up opposite each other, and yet are prevented, by 
 the insulating glass, from uniting. 
 
 § 223. Leyden jar. — The most convenient form of con- 
 denser is the Leyden jar. Coat a green glass quart 
 fruit-jar (Fig. 186), within and without, for about 
 two-thirds its hight, with tin foil, using flour paste. 
 Close the mouth with a cork saturated with hot 
 parafHne. Through the cork pass a stout brass wire 
 till it touches the inner foil. Cast a lead bullet a on 
 the exposed end of the wire. Clean, warm, and var- 
 nish the exposed glass surface of the jar, and when thoroughly 
 dry it is ready for use. 
 
 The jar may be charged by connecting one of its coatings 
 with the + conductor, and the other with the —conductor of an 
 electrical machine, or by connecting one of the coatings with 
 Kg. 187. one of the conductors, and the other with 
 
 the earth. Or it may be charged by con- 
 necting the outside coating with one of the 
 poles of the secondary coil of an induction 
 coil, and bringing the other pole near to the 
 ball leading from the inner coating. To 
 discharge the jar, connect the outer coating 
 with the knob of the jar. To avoid a shock in so doing, prepare 
 a discharger as follows: Through the cork of a bottle (e.g., a 
 soda-water bottle. Figure 187) pass a stout brass semicircular 
 wire. Cast on each of its ends a lead bullet. Use the bottle 
 as an insulating handle. 
 
 The effects are greater in proportion to the number and size 
 of the jars in electrical connection. Let any number of jars 
 (Fig. 188) be placed on a sheet of tin foil, by which their 
 outer coatings are connected. Confiect also their inner coat- 
 ings with one another by a wire running around their projecting 
 
ELECTRICITY NOT IN THE COATINGS. 
 
 251 
 
 rods. The several jars are by this means practically converted 
 into one large jar. This combination of jars is called a Leyden 
 battery. A strip of gold leaf placed on the glass slip a may 
 be fused, and even volatilized, by a battery discharge passed 
 through it ; cards and slips of glass may be perforated, and 
 gas or ether ignited. 
 
 § 224. Electricity not in the coatings.— If the two per- 
 sons in the experiment (p. 249) both remove their hands from 
 the glass plate, after they have been charged, and grasp one 
 another's hands, they experience little or no shock. But if they 
 
 Fig. 18S. 
 
 replace their hands on the glass, and grasp one another's hands, 
 they receive a shock. This shows that electricity was not on 
 their bodies, but on the surface of the glass. The coatings of a 
 Leyden jar serve the purpose of conductors to spread electricity 
 on the glass at the time of charging, and to allow its escape 
 from all parts of its electrified surface at the time of a discharge. 
 
 QUESTIONS. 
 
 1. An Insulated jar cannot receive a great charge. Why? 
 
 2. If points are attached to the outer coating of an insulated jar, it 
 can receive a much larger charge. AiVTiy? 
 
262 
 
 BLBOTJBICITY AND MAGNETISM. 
 
 Fig. 189. 
 
 3. If the knob of a second- jar be held near the outer coating of an 
 insulated jar, sparks will pass from the coating to the knob, and both 
 jars will be charged. Suppose that the inner coating of the first jar is 
 charged with +e, what kind of electricity will each of the other coat- 
 ings have? 
 
 § 225. Attractions and repulsions. —Experiment 1. Sup- 
 port a plate of window glass (Fig. 189) about 5™ from a table. Rub its 
 upper surface with a silk handkerchief, 
 and place pith-balls, or bits of tissue paper, 
 on the table beneath the glass. They will 
 dance up and down between the plate and 
 table in a lively manner. (Explain.) 
 Experiment 2. Place a handful of bits of tissue paper on a tin disk 
 supported by a prime conductor of an electrical machine. The papers 
 become excited, are repelled into the air, and faU on aU sides, giving 
 the appearance of a miniature snow-storm. 
 
 Experiment 3. Apply one end of a discharger to the conductor of 
 a machine, and the other end to the inner surface of a glass tumbler, 
 and charge the interior with electricity, and then place it over some 
 pith-balls, or images cut from pith; a ludicrous dance will be kept up 
 for several minutes. 
 
 The electric whirl consists of a cap of metal resting upon a 
 pointed wire, which serves as a pivot. The cap has pointed 
 wu-es branching out from it, like the spokes of a 
 wheel, and bent near their ends at right angles, 
 and all turned in the same direction, as shown in 
 Figure 190. When this apparatus is placed upon 
 the conductor of a machine, the air particles 
 around the highly electrified points become ex- 
 cited, and are repelled, producing a current of air 
 issuing from the points. The reaction causes 
 the wheel to revolve in the opposite direction, as indicated by 
 the arrows in the figure. A candle flame placed near the point 
 of a rod attached to a conductor will be extinguished. 
 
 § 226. Effect of points. — We might reasonably expect 
 that a current of excited air-particles issuing from points on 
 an excited conductor would serve to carry away with them elec- 
 
 Kg. 190. 
 
LUMINOUS EFFECTS. 
 
 253 
 
 tricity from the conductor ; in other words, to discharge it. 
 they produce this result ? 
 
 Do 
 
 Fig. 191. 
 
 Experiment. While the electrical machine is in operation, hold 
 your knuckle near the conductor; a succession of sparks will pass 
 from the conductor to your hand. Now place several points on the 
 conductor, and again present your knuckle as before ; either no sparks 
 wUl pass to your knuckle, or, at most, very feeble ones, and in a few 
 seconds after the operation of gener- 
 ating electricity ceases, the conductor 
 wUl be found completely discharged, 
 although it Is thoroughly insulated. It 
 Is apparent that the electricity escaped 
 from the points. 
 
 We conclude, therefore, that the 
 effect of points on an electrified in- 
 sulated body is greatly to facilitate 
 the discharge of its electricity. 
 
 
 SMSSSMS; 
 
 
 Jj "^' ^i* ij t s^~x 
 
 
 § 227. Luminous effects. 
 Figure 191 represents a glass shade 
 having circular bits of tinfoil pasted 
 spirally around it, from top to bot- 
 tom, and about 1°™ apart. If the 
 poles of an induction coil, or the 
 conductors of an electrical machine, are connected, one with 
 each extremity of this spiral line, an intermittent line of light 
 will be produced in the path of the current by the sparks which 
 appear at the intervals between the bits of foil. All experiments 
 illustrating luminous effects should be performed in a dark room. 
 
 Beautiful luminous effects may be produced with apparatus 
 arranged as follows : Apply to one surface of a mica disk (Fig. 
 192), about 15 X 10""', a sheet of silver leaf or tin foil, 8 x 5"". 
 Place two pointed poles of an inductorium, or a Carr6 machine, 
 within V" of the foil, and as far apart as the power of the 
 machine will admit. Sparks will leap from the poles to the foil, 
 and travel in tortuous branching lines between the poles. 
 
264 
 
 BLBCTEICITY AND MAGNETISM. 
 
 If air is partially exhausted from the glass tube used in Ulus- 
 trating the law of falling bodies (Fig. 87, page 106), and the 
 poles of a coil or machine are applied to the opposite extremi- 
 ties of the tube, sparks of electricity passing through the rarefied 
 air spread out in sheets of bluish white light resembling the 
 auroral lights, hence this tube has received the name Aurora 
 tvibe. 
 
 Fig. 192. 
 
 If a circular disk is divided into black and white sectors, as 
 In Figure 193, and rotated very rapidly in ordinary daylight, 
 the colors blend, and the disk appears of a uniform graj' color. 
 jfig 193 But if the disk is illuminated in a 
 
 darkened room by the electric spark, 
 each sector appears separate, and the 
 disk appears to be at rest. A rail- 
 road train in rapid motion, and even 
 its wheels, appear to be at rest when 
 illuminated on a dark night by a flash 
 of lightning. This shows that the 
 duration of an electric spark must be 
 very brief, inasmuch as it fails to 
 illuminate these objects in two successive positions. 
 
 The remarkable beauty and brilliancy of the discharge is 
 perhaps best exhibited by means of the well known Geissler's 
 tubes. These tubes contain highly rarefied vapors and gases of 
 various kinds. Platinum wires are sealed into the glass at each 
 end to conduct the electric current through the glass. The 
 light, instead of appearing, as in the Aurora tube, like a stream 
 
LIGHTNING. 255 
 
 pouring from pole to pole, is often striated or divided trans- 
 versely into luminous sections, with alternating darker sections, 
 as shown in Figure 194. These striae vary in shape and color 
 
 Fig. 194. 
 
 with the degree of the vacuum, and the kind of gas or vapor 
 through which the discharge passes. Experiments with these 
 tubes succeed best when used with the induction coil. 
 
 § 228. Lightning. — Certain clouds which have formed very 
 rapidly are highly charged with electricity, usually positively 
 charged. The surface of the earth and objects thereon imme- 
 diately beneath the cloud are charged inductively with the 
 opposite kind of electricity. The cloud and the earth corre- 
 spond to the coatings, and the intervening air to the glass of a 
 huge Leyden jar. The charge in the earth and that in the cloud 
 hold one another prisoner by their mutual attraction, until, as 
 the charges accumulate, the attraction becomes great enough to 
 overcome the resistance of the intervening air, when a discharge 
 takes place. It is the accumulation of induced electricity on 
 elevated objects, such as buildings and trees, that offers an 
 attraction for the opposite electricity of the cloud, and renders 
 them especially liable to be struck by lightning. 
 
 § 229. Lightning-rods. — The flash will pass along the line 
 of least resistance. A good lightning conductor ofl"ers a peace- 
 ful means of communication between the earth and a cloud ; it 
 leads the electricity of the earth gently up toward the cloud, 
 and allows it to combine with its opposite without disturbance. 
 
256 ELECTEICITX AND MAGNETISM. 
 
 thereby so far discharging the cloud as to prevent a lightning 
 stroke ; or, if the tension is too great to be thus quietly disposed 
 of, the flash strikes downward, and is led harmlessly to the 
 earth by the conductor. An ill-constructed lightning-rod may 
 be worse than none. A good rod should be made of good con- 
 ducting material, so large that it will not be melted, and free 
 from loose joints. The lower end should be buried in earth 
 that is alwaj's moist, and the upper end should terminate iu 
 several shaqj points. 
 
 § 230. General observations. — Although the E. M. F, 
 of the frictional machine is enormous, still, the current which 
 it can produce is always small on account of its very great 
 internal resistance. That this resistance must be almost im- 
 measurably greater than that of any galvanic battery is evident 
 when we consider that a part of the circuit is always through 
 the air, for instance in the plate machine, that part between 
 the plate and the comb. Any source of electricity that cannot 
 yield a strong current is, ordinarily, of little value, inasmuch as 
 the amount of work that can be done by electricity is propor- 
 tional to the square of the strength of the current. The fric- 
 tional machine is, therefore, of little practical value, except as 
 a source of amusement, and a convenient means of investiga- 
 ting a certain class of electrical phenomena. 
 
 By an ingenious application of the principle illustrated by the 
 disk of black and white sectors (Fig. 193) , it has been ascer- 
 tained that the duration of the spark is often times less than 
 the millionth part of a second, and the velocity of the electric 
 discharge from a Leyden jar through a short, thick copper wire 
 is 280,000 miles in a second. 
 
 The phenomena of electricity in a statical state are limited 
 to those of attractions and repulsions. Heating^ luminous, 
 magnetic, physiological, chemical, and mechanical effects can be 
 produced by electricity in the dynamical state only. In the 
 former state it seeks the surface ; in the latter it travels 
 
JKANSFOBMATION OF EISTEKG-Y. 267 
 
 through the body. Statical and dynamical phenomena are 
 rarely coexistent. One must cease before the other begins. 
 
 Much is known of erectricity, its nature, its laws, and its 
 capacity for work ; much remains to be learned. The question, 
 Wliat is electricity f is so far unanswered. But we may reason 
 as follows concerning it, and the conclusion answers all practi- 
 cal purposes. For example, the energy of the chemicq.1 combi- 
 nation of coal and oxygen in the furnace is transformed into 
 heat, heat works an engine, the engine rotates a coil of wire in a 
 magnetic iield, the motion of this coil in the vicinity of a magnet 
 induces currents of electricity in the wire, these currents pro- 
 duce an arc, and thereby heat and light. So the energy of the 
 coal is transformed into heat and light, through the intermediate 
 agency of electricity. Hence, it is certain that this intermediate 
 agency, this so-called electricity, whatever it is, may receive and 
 impart energy. 
 
 § 231. Transformation of energy. — We have found that 
 every contrivance for the development of electric energy is simply 
 a machine for the transformation of some other form of energy 
 into electric energy. In the voltaic battery the chemical poten- 
 tial energy of the combustibles is transformed into the kinetic 
 energy of the electric current. "With the magneto and friction al 
 machines, mechanical energy is transformed into electric energy. 
 In the thermopile, heat is changed directly into electric energy. 
 By means of an induction coil, a strong current of small E.M.F. 
 is transformed into a momentary weak current of great E.M.F. 
 The kinetic or current form of electricity may, under suitable 
 conditions, be converted into the potential or static state, and 
 vice versa. Not only are these various forms of energy trans- 
 formable into electric energy, but electric energy may be changed 
 into any one of these. Thus electric energy may be transformed 
 into heat, magnetism, light, chemical action, and mechanical 
 motion. These forms of energy are all interchangeable ; as in 
 fact, all known forms of energy are mutually convertible. 
 
268 ELECTRICITY AND MAGNETISM. 
 
 EXERCISES. 
 
 1. A spark of fire applied to a mass of^ soap bubbles, filled with a 
 mixture of oxygen and hydrogen gases generated by a galvanic current, 
 produces a powerful explosion. Commencing with the battery, state 
 the transformations of energy, in order, to the final result. 
 
 2. The needle of a galvanometer connected with a thermopUe is 
 deflected. Trace the transformations of energy concerned. 
 
 3. A steam engine and a dynamo machine furnish an electric light. 
 State all the transformations of energy necessary. 
 
 XXXVI. USEFUL APPLICATIONS OF ELECTRICITY. 
 
 § 232. Medical and surgical operations. — Currents from 
 <in induction coil have great E.M.F., like frictional electricity, 
 and so can pass through the poorly conducting tissues of the 
 human body and produce violent muscular contractions. Cur- 
 rents induced by a single voltaic cell, through the mediation of 
 au induction coil, may produce agonizing convulsions. A vol- 
 taic current has a similar effect at the instants of making and 
 breaking the circuit (why ?) ; but by beginning with a mild cur- 
 rent, and slowly and gradually increasing its strength, a current 
 from two hundred cells has been passed through a person with 
 impunity. (Explain.) The physiological effect produced by an 
 Induced current at its negative pole is more violent than at the 
 positive pole. In this way we may readily distinguish one pole 
 from the other by simply holding one in each hand. The grad- 
 ual current produces a benumbing influence, or insensibility to 
 pain. A to-and-fro motion of the current produces a muscular 
 agitation of the part through which it is sent, the tonic and 
 stimulating effects of which are similar to those of muscular 
 exercise. The galvanic current also exerts a powerful elec- 
 trolytic effect on the system. On this principle it has been 
 successfully employed in reducing tumors, etc. 
 
 A platinum wire heated by a galvanic current is used like a 
 knife in surgical operations. The former has tlic advantage 
 
ELBCTEIC LIGHT. 
 
 259 
 
 over the latter in that it sears the extremities of the blood ves- 
 sels and thereby prevents hemorrhage. Enough has been said 
 to show that a medical practitioner who can apply the laws of 
 electricity has at his command a powerful therapeutic agent ; 
 but except in experienced hands it is likely to prove useless, if 
 not positively dangerous. 
 
 § 233. Electric light. — If the terminals of wires from a 
 powerful magneto machine or galvanic battery are brought to- 
 gether, and then separated 1 or 2 millimeters, the current does 
 not cease to flow, but volatilizes a portion of the terminals. 
 The vapor formed becomes a conductor of high resistance, and 
 remaining at a very high temperature produces intense light. 
 The light rivals that of the sun both in intensity and purity. 
 The heat is so great that it fuses the most refractory substances, 
 including even the diamond. Metal terminals quickly melt and 
 drop off like tallow, and thereby become so far separated that 
 the electro-motive force is no longer sufficient for the increased 
 resistance, and the light is extinguished. Hence, pencils of 
 carbon (prepared from 
 coke deposited in the a 
 
 distillation of coal in- 
 side of gas retorts), 
 which are less fusible, 
 are used for terminals. 
 For simple experi- 
 ments, these pencUs may be held in forceps (Fig. 195) at the 
 ends of two brass rods, to which the battery-wires are attached. 
 These rods slide in brass heads A and B, suppoi'ted by insu- 
 lating pillars, so that the distance between the carbon points 
 may be regulated. 
 
 Fig. 195. 
 
 § 234. Voltaic arc. — The light is too intense to admit of 
 examination with the naked eye ; but if an image of the termi- 
 nals is thrown on a screen by means of a lens, or a pin-hole in 
 
260 ELECTKICITY AND MAGNETISM. 
 
 a card (see page 330), au arch-shaped light is seen extending 
 from pole to pole, as shown in Figure 196. This light has 
 received the name of the voltaic arc. The larger portion of the 
 light, however, emanates from the tips of the two 
 carbon terminals, which are heated to an intense 
 whiteness, but some from the arc. The +pole is 
 hotter than the —pole, as is shown by its glowing 
 longer after the current is stopped. The carbon of 
 the +pole becomes volatilized, and the light-giving 
 particles are transported from the -j-pole to the 
 —pole, forming a bridge of luminous vapor between 
 the poles. What we see is not electricity, but luminous matter. 
 Neither light nor a current can exist without matter, as may be 
 shown by trying to pass a current between two metallic poles, a 
 little way apart, in a charcoal vacuum (page 56) ; no spark can 
 be produced. 
 
 § 235. Electric lamp. — It is apparent that the -f-pole is 
 subject to a wasting away, and the —pole to a slight accession 
 of matter. At the point of the former a conical-shaped cavity 
 is formed, while around the point of the latter warty protuber- 
 ances appear. When, in consequence of the wearing away of 
 the +pole, the distance between the two pencils becomes too 
 great for the electric current to span, the light goes out. Nu- 
 merous self-acting regulators for maintaining a uniform distance 
 between the poles have been devised. Such an arrangement is 
 called an electric lamp. In some, the carbons are moved by 
 clock-work, which requires winding up occasionally ; in others, 
 the movement of the carbons is accomplished automatically by 
 the action of the current itself. 
 
 § 236. Electric candle.— The " Jablochkoff Candle" ob- 
 viates all necessity for regulators. In this candle, instead of 
 the carbons pointing toward each other, they are placed side by 
 side, a and 6 (Fig. 197), separated by a thin insulating septum. 
 
ELECTEOTYPING. 261 
 
 c, of kaolin. The current passes up one carbon, across the 
 space between the points, and down the other. In its passage 
 between the points it forms the luminous are. The ^j ^^^ 
 heat of the arc fuses and volatilizes the kaolin, and ^ 
 it wastes slowly awaj' like the wick of a candle ; 
 hence its name. 
 
 The electric light is of the purest white. In it the 
 most delicate colors retain their noonday purity of 
 tint, while a gas light appears of a sickly yellow hue 
 in comparison. 
 
 § 237. Blectrotyping. — This book is printed 
 from electrotype plates. A moulding-case of brass, in the shape 
 of a shallow pan, is filled to the depth of about one centimeter 
 with melted wax. A few pages are set up in common type, and 
 an impression or mould is made by pressing these into the wax. 
 The type are then distributed, and again used to set up other 
 pages. Powdered plumbago is applied by brushes to the sur- 
 face of the wax mould to render it a conductor. The mould is 
 then flowed with alcohol to prevent adhesion of air-bubbles, and 
 afterwards with a solution of copper sulphate, and dusted with 
 iron filings, which form by chemical action a thin film of copper 
 on the plumbago surface. The case is then suspended in a bath 
 of copper sulphate dissolved in dilute sulphuric acid. The 
 —pole (why the —pole?) of a galvanic battery or magneto ma- 
 chine is applied to it ; and from the -f-pole is suspended in the 
 bath a copper plate (why?) opposite and near to the wax face. 
 The salt of copper is decomposed by the electric current, and 
 the copper is deposited on the surface of the mould. The sul- 
 phuric acid appears at the -{-pole, and, combining with the 
 copper of this pole, forms new molecules of copper sulphate. 
 "When the copper film has acquired about the thickness of an 
 ordinary visiting card, it is removed from the mould. This shell 
 shows distinctly every line of the tj^es or engraving. It is 
 then backed with melted type-metal to give firmness to the 
 
262 
 
 ELECTRICITY AND MAGNETISM. 
 
 plate. The plate is then fastened on a block of wood, and thus 
 built up type-high, and is now ready for the printer. 
 
 § 238. Electro-plating'. — The distinction between electro- 
 plating and electrotyping is, that with the former the metallic 
 coat remains permanently on the object on which it is deposited, 
 while,, with the latter, it is intended to be removed. The pro- 
 cesses are, in the main, the same. The articles to be plated are 
 first thoroughly cleaned, and suspended on the —pole of a 
 
 Fig. 198. 
 
 battery, and then a plate of the same kind of metal that is to be 
 deposited on the given articles is suspended from the -f-pole 
 (Fig. 198). The bath used is a solution of a salt of the metal 
 to be deposited. The cyanides of gold and silver are generally 
 used for gilding and silvering. Many of the base metals re- 
 quire to be electro-coppered first in order to secure the adhesion 
 of the gold or silver. The magneto-electric machine has^almost 
 completely replaced the voltaic battery for electrotyping and 
 electro-plating purposes. 
 
 §239. Electro -magnetic engines. — The great power 
 which electro-magnets may exert, even when excited by feeble 
 
THE TELEGRAPH. 263 
 
 currents, might seem to justifj' the expectation that through 
 their instrumentality a motive power may be obtained that 
 would vie with steam. Electro-magnetic engines have, indeed, 
 been constructed of four and five horse-power, and boats and 
 railroad cars have been propelled and fields plowed by them. 
 Their great disadvantage is that they are not economical : the 
 zinc and acids required to produce a given amount of power 
 cost nearly a hundred times as much as the coal that would 
 give the same power. But, on the other hand, the efHciency 
 may be about five times ^reater^thaaife?* of ^ steam engine. But 
 where the absolute amount of power is--Qf less consequence than 
 the facility of producing it- instantaneously and at will, electro- 
 magnetic engines may be used with advantage, as in driving 
 sewing-machines. 
 
 § 240. The telegraph. — The word telegraph, literally, sig- 
 nifies to write far away. In its broadest sense, it embraces all 
 methods of communicating thought with great speed to a dis- 
 tance by means of intelligible characters, sounds, or signs ; but 
 usually it is applied onlj' to electrical methods. 
 
 First, it should be understood that, instead of two lines of 
 wire, one to convey the electric current far away from the bat- 
 tery, and another to return it to the battery, if the distant pole 
 is connected with a large metallic plate buried in moist earth, 
 or, stUl better, with a gas or water pipe that leads to the earth, 
 and the other pole near the battery is connected in a like man- 
 ner with the earth, so that the earth forms about one-half of 
 the circuit, there will be needed only one wire to connect 
 telegraphically two places that are distant from each other. 
 Furthermore, the resistance offered by the earth to the electric 
 current is practically nothing; so that, disregarding the resist- 
 ance of the ground connections, there is a saving of one-half 
 the wire and one-half the resistance, and consequently one-half 
 the battery power. 
 
264 ELECTRICITY AND MAGNETISM. 
 
 Let B, Figure 1, Plate III., represent the message-sender, or oper- 
 ator's key ; Y, the message-receiver. It may be seen that the circuit 
 is broken at B. Let the operator press his finger on the knob of the 
 key. He closes the circuit, and the electric current instantly fiUs the 
 wire from Boston to New York. It magnetizes a ; a draws down the 
 lever 6, and presses the point of a style on a strip of paper c that is 
 drawn over a roller. The operator ceases to press upon the key, the 
 circuit is broken, and instantly 6 is raised from the paper by a spiral 
 spring d. Let the operator press upon the key only for an instant, or 
 long enough to count one, a simple dot or indentation wiU be made in 
 the paper. But if he presses upon the key long enough to count three, 
 the point of the style will remain in contact with the paper the same 
 length of time ; and, as the paper is drawn along beneath the point, a 
 short straight line is produced. This short line is called a dash. These 
 dots and dashes constitute the alphabet of telegraphy. For instance, a 
 part of a message, " man is in," is represented as printed in tele- 
 graphic characters on the strip of paper. The Boman letters above 
 interpret their meaning. 
 
 § 241. Sounder. — If the strip of paper is removed, and 
 the style is allowed to strike the metallic roller, a sharp click is 
 heard. Again, when the lever is drawn up by the spiral spring, 
 it strikes a screw point above (not represented in the figure) , 
 and another click, differing slightly in sound from the first, is 
 heard. A listener is able to distinguish dots from dashes by 
 the length of the intervals of time that elapse between these 
 two sounds. Operators generally read by ear, giving heed to 
 the clicking sounds produced by the strokes of a little hammer. 
 A receiver so used is called a sounder, a common form of which 
 is represented in the lower central part of Plate III. 
 
 § 242. Relay and repeater. —The strength of the current 
 is diminished, of course, as the line is extended and the number 
 of instruments in the circuit is increased. Hence, a current 
 that would move a single sounder audibly, on a short line, 
 would not move many sounders on a long line with sufficient 
 force to render the message audible. Resort is had to relays 
 and repeaters. The principle on which they remove this diffl- 
 
Plate III 
 
RELAY AND EEPBATEE. 265 
 
 culty may, perhaps, be best explained by analogy. In days gone 
 by, posts for couriers were stationed a day's journey apart. 
 At each post were a courier and a horse at all hours ready to 
 start. The courier, bearing a dispatch, rode all day, and at 
 night reached a post where fresh horses were saddled ready for 
 the next stage of the journey ; he himself was exhausted, his 
 force was nearly spent, but he could awaken a courier who 
 was stationed there and deliver the despatches to him, and he 
 with fresh strength instantly took up the journey. In a similar 
 manner we picture to ourselves the electric current arriving at 
 a station so nearly exhausted that it cannot deliver intelligible 
 signals, yet it may still .have strength to Wake up another bat- 
 tery and set in motion a fresh current which shaU receive and 
 announce audibly, or carry forward the message which the 
 exhausted current has just strength to whisper. 
 
 In Figure 2, Plate III., the letter R represents a relay and S a sounder. 
 Suppose a weak current arrives at New York from Boston, and has 
 sufficient strength to attract the armature of the relay at that station. 
 This, as may be seen by examination of the diagram, will close another 
 short circuit, called the local circuit, and send a current from a local 
 battery located in the same office, through the sounder at that station. 
 The sounder, being operated by a battery in a circuit of only a few feet 
 in length, delivers the message audibly. If it is desired that the mes- 
 sage should go beyond New York, — for instance, to Philadelphia, — 
 then we have only to suppose the local line at New York to be length- 
 ened so as to extend to Philadelphia, and a powerful line battery to be 
 substituted for the small local ; then the message that leaves Boston will 
 be shifted from one circuit to the other at New York, and be delivered 
 in Philadelphia without the intervention of any operator on the route. 
 In this case a relay is called a repeater. The electro-magnets in relays 
 are wound with long and thin wire, while those of sounders are wound 
 with short, large wire. (Explain. The main battery consists of many 
 cells ; how should they be connected? It may be located at either ter- 
 minus, but it is generally split in halves, and one half placed at each 
 terminus ; how should the two halves be connected ?) 
 
 In the diagram the circuit is represented as open at both keys. 
 When the line is not in use, the circuit ought always to be left closed, 
 by means of switches connected with the keys (not represented in the 
 
266 ELECTKICITY AND MAGNETISM. 
 
 diagram), so that, when the line is not "at work," an electric current 
 is constantly traversing the wire. Sending a message, consequently, 
 consists in Interrupting this current by means of a iey. Suppose that 
 Boston wishes to communicate with New York. He first removes the 
 switch on his key, which breaks the circuit and enables him to control 
 the circuit with his key. He then manipulates his key so as to produce 
 an understood signal, which will attract New York's attention. Every 
 time that Boston presses on his key, every armature in his own office, 
 and in the New York office, and at way-stations, falls. Of course the 
 message may be read at every station on the route. 
 
 TELEGEAPmC ALPHABET. 
 
 A 
 
 B 
 
 • 
 
 C 
 
 D 
 
 E 
 
 ¥ 
 
 G 
 
 H 
 
 
 I 
 
 J 
 
 K 
 
 L 
 
 M 
 
 N 
 
 
 
 
 P 
 
 Q 
 
 R 
 
 S 
 
 T 
 
 
 u 
 
 V 
 
 W 
 
 X 
 
 T 
 
 Z 
 
 
 & 
 
 _•__ 
 
 ? 
 
 • 
 
 
 
 TELEGRAPHIC 
 
 FIGURES. 
 
 
 
 I 
 
 2 
 
 
 3 
 
 4 
 
 6 
 
 6 
 
 
 r 
 
 
 8 
 
 9 
 
 
 
 
 § 243. Fac-simile telegraph. — This is an autographic ap- 
 paratus by means of which a message may be, practicallj', trans- 
 mitted over a wire and appear at a distant terminus in the exact 
 hand-writing of the sender, and ready at once for delivery. The 
 principle on which it operates may be learned from the diagram 
 in Plate I., in which all details of its mechanism are omitted for 
 simplicity of illustration. X is a sheet of tin-foilf on which the 
 message to be sent is written with an ink prepared by dissolving 
 sealing-wax in alcohol. The alcohol quickly evaporates, leaving 
 the lines of sealing-wax adhering to the foil. Y is a sheet of 
 paper moistened with a solution of prussiate of potash. Each 
 of the pens is simply a small, pointed iron needle. Now suppose 
 that both of the pens are moved at the same time and with the 
 
THE ELECTKIC FIRE-ALARM. 
 
 26T 
 
 same rapidity across their respective sheets. Then the electric 
 current, decomposing the prussiate of potash, will cause the 
 needle in New York to trace a continuous blue line on Y, until 
 the needle in Boston reaches a line of sealing-wax on X, when 
 the circuit is broken as it passes over this line. At the same 
 time there is a bi-eak in the continuity of the line traced on Y. 
 If, further, each needle is moved down a hair's breadth each 
 time it traverses its respective sheet, then we shall have an 
 exact fac-simile of the writing on the tin-foil produced on the 
 chemically-prepared paper, except that whereas the original is 
 written in dark letters on a light ground, the message is received 
 in light letters on a dark ground. Pen-and-ink sketches of pho- 
 tographs and other pictures may be transmitted in the same 
 way. The pens are not, of course, held and guided by human 
 hands, but by complex machiner}^. The rigorous exactness 
 requisite in the movements of the two pens is secured by the 
 absolute synchronism in the vibrations of two pendulums, one 
 at each terminus, controlled by the electric current. 
 
 Kg. 199. 
 
 § 244. The electric fire-alarm. — This is a modification 
 of the electro-magnetic telegraph. Figure 199 will serve to 
 illustrate the general plan of the American system, invented by 
 
268 ELECTRICITY AKD MAGNETISM. 
 
 Prof. M. Gr. Farmer, and by him first introduced into Boston In 
 
 the year 1852. 
 
 From some central station wires radiate to every part of the 
 city. At suitable intervals there are inserted in these circuits 
 small cottage-shaped boxes, usually attached to buildings at the 
 corners of streets. On opening one of these boxes, a person 
 who is to give an alarm finds a crank A, which he is directed to 
 " pull down once and let go." This winds the spring H, which 
 sets in motion a train of wheels, and causes a make-and-break 
 wheel C to revolve. This wheel bears upon its circumference 
 notches corresponding to the number of the box. Two terminals 
 of the line are so connected, one with C and the other with a 
 lever b, that when the lever touches the wheel the circuit is 
 closed. But when the wheel revolves, and a notch passes under 
 the lever, the circuit is broken. The eflfect of breaking the 
 circuit is to demagnetize the electro-magnet F at the central 
 station, and release the armature which is attached to the 
 tongue of a bell. The tongue then being drawn forcibly by 
 the spring G in the opposite direction, produces one stroke on 
 the bell. By pulling the lever down once, the spring is wound 
 up just enough to cause C to revolve three times, and thus the 
 number of the box is struck three times in succession. The 
 watchman at the central station, being thus notified of the 
 existence and localitj' of the fire, at once and in a similar man- 
 ner notifies the several fire-engine companies. 
 
 XXXVII. TELEPHONE AND MICROPHONE. 
 
 § 245. Bell telephone. — Eigure 200 represents a sectional !ind 
 a perspective view of this instrument. It consists of a steel magnet 
 A, encircled at one extremity by a spool B of very fine insulated wire, 
 the ends of which are connected with the binding screws DD. Im- 
 mediately in front of the magnet is a thin circular iron disk EE. The 
 whole is enclosed in a wooden or rubber case F. The conical-shaped 
 cavity G serves the purpose of either a mouth-piece or an ear-trumpet. 
 There is no difference between the transmitting and receiving tele- 
 phone ; consequently either instrument may be employed as a trans- 
 mitter, while the other serves as a receiver. Two magneto telephones 
 
BELL TELEPHONE. 
 
 269 
 
 in a circuit, are virtually in the relation of a magneto-electric generator 
 and a motor. Tlie transmitter being in itself a diminutive magneto 
 machine, of course no battery is required in the circuit. Connect in 
 circuit two such telephones, and the apparatus is ready for use. 
 
 When a persou talks to the disk of the transmitter, he throws it 
 into rapid vibration. The disk, being quite close to the magnet, is 
 magnetized by induction; and, as it vibrates, its magnetic power 
 l3 constantly changing, being strengthened as it approaches the 
 magnet, and enfeebled as it recedes. This fluctuating magnetic force 
 will of course induce currents in alternate directions in the neighboring 
 coil of wire. These currents traverse the whole length of the wire, 
 and so pass through the coil of the distant instrument. When the 
 direction of the arriving current Is such as to reenforce the power of 
 the magnet of the receiver, the magnet attracts the iron disk in front 
 of it more strongly than before. If the current is in the opposite 
 direction, the disk is less attracted, and flies back. Hence, whatever 
 movement is imparted to the disk of the transmitting telephone, the 
 disk of the receiving telephone is forced to repeat. The vibrations of 
 the latter disk become sound in the same manner as the vibrations of 
 a tuning fork or the head of a drum. 
 
 The above is a description of the original and simplest form of the 
 Bell telephone. It is apparent that the original energy, i.e., that of 
 the voice, applied at the transmitter must, during its successive trans- 
 formations and especially during its transmission in the form of 
 gl„„+-!« +1 »- 1 — '-'^ become very much en- 
 
270 
 
 ELECTEICITY AND MAGNBCTISM. 
 
 feebled, so that when it reappears as sound, the sound is quite feeble 
 and frequently inaudible. The first grand improvement on the original 
 consists in introducing a battery into the circuit aud so arranging that 
 the voice instead of being obliged to generate currents should be 
 required to act only as a controlling force of a current already 
 
 Tig. 200 a. 
 
 Fig. 200 6. 
 
 generated by the battery. It is evident that only a fluctuating 
 or undulating current can produce the necessary vibrations in the 
 disk of the receiver. The fluctuations are caused by a varying resist- 
 ance in the circuit. The pupil must have learned by experience ere 
 this that the effect of a loose contact between any two parts of a 
 circuit is to increase the resistance and thereby weaken the current ; 
 but the effect of a slight variation in pressure is especially noticeable 
 when either or both of the parts are carbon. Tigure 200 a illustrates a 
 simple telephonic circuit in which are included a variable resistance 
 transmitter T, a magneto receiver R, and a battery B. One of the 
 electrodes, a platinum point, touches the center of the transmitter 
 disk; the other electrode, a carbon button a, is pressed by a spring 
 gently against the platinum point. Every vibration of the disk, how- 
 ever minute, causes a variation In the pressure between the two 
 electrodes and a corresponding variation in the circuit resistance. 
 As changes the resistance, so changes the current strength, and so 
 consequently changes the foroe with which the magnet in the receiver 
 
MICROPHONE. 
 
 271 
 
 R pulls its disk. The varying tension between magnet and disk 
 causes the latter to vibrate and reproduce sounds. 
 
 The next improvement of considerable importance consists in the 
 adoption of an induction coil, v?hich, we have learned, produces a 
 current of much greater force than is possessed by the original 
 battery current. By its adoption we are able to. converse over 
 much longer distances, and since the battery current traverses only 
 a local circuit, as may be seen by reference to Fig. 200 6, a single 
 Leclanchfi cell is generally sufBcient to operate it. The currents 
 induced by the fluctuating primary current traverse the line wire and 
 generate sonorous vibrations in the disk of the receiver in the same 
 manner as in the original telephone. 
 
 Fig. 201. 
 
 § 246. Microphone. — In Figure 201, A and B are buttons of 
 carbon ; the former is attached to a sounding-board of thin pine wood, 
 the latter to a steel spring C, and both are connected In circuit with a 
 battery and a telephone used as a receiver. The spring presses B 
 against A, and any slight jar will cause a variation in the pressure and 
 corresponding variations in the current strength. 
 
 By means of this Instrument, called the microphone, any little sounds, 
 as its name indicates, such as the ticking of a watch or the footfall of 
 an insect, may be reproduced at a considerable distance, and be as 
 audible as though the original sounds were made close to the oar. 
 
CHAPTER V. 
 SOUND. 
 
 The subjects of Sound and Light, which we have now to 
 study, have two important characteristics in common that dis- 
 tinguish them from the subjects already studied. First, each of 
 them affects its peculiar organ of sense, the ear or eye, and 
 very many of the phenomena to be studied under each subject 
 are of importance only to one or the other of these senses ; 
 while the most common, and many of the most important appli- 
 cations of heat and electricity have no direct relation to anj 
 organ of sense. Second, both sound and light, we shall find 
 originate in vibrating bodies, and reach us only by the inter- 
 vention of some medium capable of being set in vibration. 
 
 Here, as in all other kinds of motion, energy is involved ; the 
 ear or eye absorbs energy whenever a sensation is produced, but 
 the amount absorbed is so minute, and the difHcultj^ of measuring 
 it so great, that usually other points better deserve the student's 
 attention. 
 
 Let us begin with the study of such vibrations as will neither 
 produce sound, nor in a dark room affect the eye. 
 
 XXXVIII. VIBEATION AND WAVES. 
 
 §247. Vibration. —Experiment 1. Repeat the experiment with 
 the pendulum 1™ long, page 111, and note in what respects its motion 
 differs from most other motions. 
 
 Experiment 2. Take a pendulum 50™ long, hold it with the string 
 just touching an edge of a table, having the hand about 38™ above the 
 table, and set it vibrating ; the ball wiU be seen to vibrate faster in the 
 portion of its arc that is under the table than in the other portion, and 
 so more vibrations are made in ten seconds than if the string swing 
 freely without touching the table. 
 
DIRECTION OF VIBBATION. 273 
 
 Experiment 3. Without the pendulum, move the hand quickly from 
 side to side every two seconds, turning instantly at one side, and wait- 
 ing at the other till the two seconds are up. 
 
 These three motions, though very different, have this in com- 
 mon : the motions in each case occur at equal intervals of time. 
 This interval of time is called the period of vibration. In Exp. 1 
 it was two seconds ; in Exp. 2, about one second ; and in Exp. 3, 
 two seconds. The motion from one side to the other and back 
 is called a vibration. If w = the number of vibrations in one 
 
 second, and t = the period, t= — The amplitude of pendulum 
 
 n 
 
 vibrations is assumed to be very small. In Exp. 1 the motion is 
 called a simple (or pendular) vibration; in the other cases the 
 vibration of the ball or the hand is complex. Do not confound 
 period with duration of the vibrating state ; in Exp. 1 the 
 pendulum may have vibrated ten or one hundred seconds, 
 before coming to rest, but the period was two seconds. Con- 
 sidered mathematically, other periodic (and therefore vibratory) 
 motions are, the movements of the hands of a watch, the regu- 
 lar trips of a stage-coach, etc. A vibration is a recurrent change 
 of position. 
 
 § 248. Direction of vibration. — A small rod, like a yard- 
 stick, fixed at one end, may be set in vibration by pulling the 
 other end to one side ; a tree vibrates in the wind ; the strings 
 of a piano swing from side to side when vibrating ; in all these 
 cases the motion is at right angles to the length of the body, 
 and so the body is bent. These are all cases of transversi 
 vibrations. 
 
 Experiment. Hang up a spiral spring, or elastic cord, with a weight 
 attached to the lower end; lift the weight, and, dropping it, notice 
 that the cord vibrates, lengthening and shortening rapidly. 
 
 The motion of the body is in the direction of its length, and 
 so it is not bent ; this is a case of longitudinal vibration. Twist 
 the string, and see that it is possible to set up torsional vibra- 
 
2T4 SOUND. 
 
 tions. Compare these kinds of vibration with the kinds of 
 elasticity studied on page 30. 
 
 § 249. Propagation of vibration. — Waves. — Experi- 
 ment. Take a soft cotton rope, a few meters long, lay it straight ou 
 a floor, set one end in vibration by quick movements of the hand. 
 Notice any point in the rope, and see that it is set in vibration ; that 
 is, it moves up and down, or laterally from side to side through its 
 original position of rest. Make a single movement of the hand, which 
 is better called a pulse than a vibration ; it is easy to see that the 
 pulse does not reach all points of the rope at the same time. Send a 
 quick succession of equal pulses along the rope ; at any instant differ- 
 ent pulses affect different parts of It, and you get more or less perfectly 
 the familiar form that we call a wave-line. Notice that any point of 
 the rope only moves up and down, while the form of the wave moves 
 on. Vibrate the hand in a longer period, and notice that the distance 
 from crest to crest is longer than before. 
 
 § 250. "Wave-length and amplitude. — Imagine an in- 
 stantaneous photograph taken of the rope along which the waves 
 J,. 202 ^^® passing. It would appear 
 
 „ .^_^ much like the curved line CD, 
 
 ^^--^ Figure 202. This curve repre- 
 
 ■u V sents what is known as a simple 
 
 ■<;:::^;;;^~---"^^ wavc-linc. The shortest of the 
 
 ^- ..^ ^ 
 
 similar portions into which a 
 
 wave-line can be cut is called a wave-length, as wx, wo, or en. 
 
 The greatest distance of any point in a wave from the axis, as 
 
 ou, is called the amplitude of the wave. 
 
 § 251. Reflection of waves. — Interference." — Experi- 
 ment 1. Stretch the rope horizontally between two elevated points, 
 and pluck it with the hand or strike it with a stick near one end, and 
 send along it a single pulse, forming a crest on the rope (A, Fig. 
 203). This travels to the other end, and there we see it reflected and 
 inverted (B). 
 
 • See Section G of the Appendix. 
 
STATIONARY VIBEATIONS, ETC. 
 
 275 
 
 Kg. 203. 
 
 Experiment 2. Just at the instant of reflection, .start a second 
 crest; tliese two, the crest and the returning inverted crest or trough 
 (C), are now traveling 
 along the rope in oppo- 
 site directions, and must 
 meet at some point. This 
 point will be urged up- 
 ward by the crest and 
 downward by the trough, 
 and ^ its motion wUl be 
 due to the difference of | 
 the two forces. 
 
 Experiment 3. Send 
 along the rope, first a trough, then a crest; now two crests (D) will 
 meet near the middle of the rope, and the motion here will be due to 
 two forces acting in the same direction, and so the resulting crest will 
 be greater than either of the original ones. 
 
 This action on a single point of two pulses, or two trains of 
 waves, no matter if from different sources, is termed interfer- 
 ence. The resulting motion may be greater or less than that 
 due to either pulse alone, or it may be zero. 
 
 § 252. Stationary vibrations, nodes, etc. — Experiment. 
 
 Hold one end of a rubber tube, about 2"" long, whUe the other is fixed, 
 and send along it a regular succession of equal pulses from the vibrat- 
 ing hand; it will be easy, by varying the tension a little, to obtain a 
 succession of gauzy spindles (Fig. 204) separated by points that are 
 
 Fig. 201. 
 
 nearly or quite at rest. Unlike the earlier experiments, the waves here 
 do not appear to travel along the tube ; yet in reality they do traverse 
 it. The deception Is caused by stationary points being produced by the 
 interference of the advancing and retreating waves. 
 
 This interference of direct and reflected waves gives rise to 
 the important class of so-called stationary vibrations. The 
 
276 SOUND. 
 
 points of least motion, as a and b, are called nodes; the points 
 of greatest motion, c and d, are called antinodes; and the por- 
 tion of the rope between a node and an antinode, as ac, is a 
 semi-ventral segment, and ab is a ventral segment. 
 
 § 253. Water-waves. — If you have a long and rather 
 narrow box or trough, nearly filled with water, you can pro- 
 duce much the same effects as with the rope. A crest is 
 caused by thrusting the hand into the water ; a trough, by sud- 
 denly withdrawing it. Chips floating on the water show that 
 here, as with the rope, it is only a form that advances — not 
 the matter. But more careful observation will show that the 
 chip, when on the crest of the wave, does move forward a little, 
 and when in the trough moves backward a little ; thus it does 
 not merely rise and fall, but goes round in a curve that is 
 approximately a circle. After a little practice, you may be able 
 to produce interference and stationary waves ; or you may pro- 
 duce them by blowing on the surface of water in a basin, or by 
 tapping the basin. Water-waves furnish important illustrations 
 of the fact that energy may be transmitted by vibration as truly 
 as by the actual transfer of the medium, as in the river's current 
 or the wind. 
 
 §254. Longitudinal waves. — Experiment. Procure a brass 
 
 wire wound in the form of a spiral spring,' about 4" long. Attach one 
 
 end to a cigar box, and fasten the box to a table. Hold the other end H 
 
 of the spiral firmly in one hand, and with the other hand insert a Imif e- 
 
 blade between the 
 Fig. 206. . ^ XI. • 
 
 . T, p turns of the wire, 
 
 and quickly rake 
 
 it for a short dis- 
 
 tance along the 
 
 spiral toward the 
 
 box, thereby crowding closer together for a little distance (B, Fig. 
 
 205) the turns of wire in front of the hand, and leaving the turns 
 
 behind pulled wider apart (A) for about an equal distance. The 
 
 1 About 26" of No. 20 brass spring-wire should be wound with care in a lathe on a 
 spindle 1°™ in diameter, as close as possible. 
 
AIR AS A MEDIUM OI" "WAVE-MOTION. 277 
 
 crowded part of the spiral may be caUed a condensation, and the 
 stretched part a rarefaction. The condensation, followed by the rare- 
 faction, runs with great velocity through the spiral, strikes the box, pro- 
 ducing a sharp, loud blow ; is reflected from the box back to the hand, 
 and from the hand again to the box, producing a second blow ; and by 
 skilful manipulation three or four blows may be produced in rapid suc- 
 cession. If a piece of twine be tied to some turn of the wire, it will 
 be seen, as each wave passes it, to receive a slight jerking movement 
 forward and backward in the direction of the length of the spiral. 
 
 How is energy transmitted through these 4" of spring so as 
 to deliver the blow on the box? Certainly not by a bodily 
 movement of the spiral as a whole, as might be the case if it 
 were a rigid rod. The movement of the twine shows that the 
 only motion which the coil undergoes is a vibratory movement 
 of its turns. Here, as in the case of water-waves, energy is 
 transmitted through a medium by the transmission of vibrations. 
 
 There are two important distinctions between this kind of 
 wave and a liquid wave : the former consists of a condensation 
 and a rarefaction ; the latter, of an elevation and a depression ; 
 in the former, the vibration of the parts is in the same line with 
 the path of the wave, and hence these are called longitudinal 
 waves; in the latter, across its path, and_ they are therefore 
 transverse waves. 
 
 A wave cannot be transmitted through an inelastic soft iron 
 spiral. Elasticity is essential in a medium, thai it tnay transmit 
 waves made up of condensations and rarefactions; and the greater 
 the elasticity, the greater the facility and rapidity with which a 
 medium transmits waves. 
 
 § 255. Air as a medium of wave-motion. — May not air 
 and other gases, which are elastic, serve as media for waves ? 
 
 Experiment. Place a candle flame at the oriflce a of the tube,' Figure 
 206, and strike the table a sharp blow with a book near the orifice 6. 
 
 ' 1 This tube, which will serve many important purposes, may be made of tin in three 
 parts, A and B, each 2.5» long, and 10" in diameter, and a conical-shaped cap C about 
 30<™ long, having an oriflce of 3»" diameter. The ends of the three parts should be 
 made slightly tapering, so that they may be put together like a stove-pipe. 
 
278 
 
 SOUND. 
 
 Instantly the candle flame is quenched. The body of air in the tube 
 Serves as a medium for transmission of motion to the candle. 
 
 Was it the motion of a current of air through the tube, as when 
 blown through, or was it the transfer of a vibratory motion? Bum 
 touch-paper ' at the orifice 6, so as to fill this end of the tube with 
 Smoke, and repeat the last experiment. 
 
 Evidently, if the body of air is moved along through the tube, the 
 iSmoke will be carried along with it. The candle is blown out as before, 
 but no smoke issues from the orifice a. It is clear that there Is no 
 
 Fig. 206. 
 
 translation of material particles from one end to the other, — nothing 
 like the flight of a rifle bullet. The candle flame was struck by some- 
 thing like a, pulse of air, and not by a wind. 
 
 § 256. How a wave is propagated through a medium. 
 — The effect of applying force with the hand to the spiral 
 spring is to produce in a certain section (B, Fig. 205) of the 
 spiral a crowding together of the turns of wire, and at A a 
 separation ; but the elasticity of the spiral instantly causes B to 
 expand, the effect of which is to produce a crowding together of 
 the turns of wire in front of it, in the section C, and thus a for- 
 ward movement of the condensation is made. At the same 
 time, the expansion of B causes a filling up of the rarefaction at 
 A, so that this section is restored to its normal state. This is 
 not all : the folds in the section B do not stop in their swing 
 when they have recovered their original position, but, Uke a 
 pendulum, swing beyond the position of rest, thus producing a 
 rarefaction at B, where, immediately before, there was a con- 
 
 1 To prepare touoh-paper, dissolve about a teaspoonfol of saltpeter in a half teacnpftal 
 of hot water, dip unsized paper in the solution, and then allow It to dry. The paper pro- 
 duces much smoke in burning, but no flame. 
 
HOW A WAVE-LINE KEPBESENTS A VIBRATION. 279 
 
 densation. Thus a forward movement of the rarefaction is 
 made, and thus a pulse or wave is transmitted with uniform 
 velocity through a spiral spring, air, or any elastic medium. 
 
 § 257. How a wave-line represents a vibration, — We 
 saw (page 274) that a wave might be caused by a vibration, 
 and readily believe that if the vibration is changed in any way, 
 tlie wave must show some corresponding change. In fact the 
 wave-line shows at once something about the vibration for sev- 
 eral successive periods ; so, if we could attach a cord to a 
 vibrating body, or set up vibrations in water by it, and then 
 take an instantaneous photograph of the rapidly-disappearing 
 waves, we might learn much about the nature of the original 
 vibrations. 
 
 A much more practical arrangement, which gives a permanent 
 wave-line, is the following 
 
 Experiment. Attach, by means of sealing-wax, a bristle or a fine 
 wire to the end of one of the prongs of a tuning-fork, as seen in 
 Figure 207. Set the fork in p. ^^ 
 
 vibration, and quickly draw /^ 
 
 the point of the bristle 
 lightly over a smoked glass 
 (A, Fig. 207). A beautiful wavy line will be traced on the glass, each 
 wave corresponding to a vibration of the prong when vibrating as a 
 whole. 
 
 Next tap the fork, near its stem, on the edge of a table, and trace its 
 vibrations on a smoked glass as before. You will generate the same 
 set of waves that you did before ; but, running over these, is another set 
 of waves, of much shorter period, much like No. 3 of Figure 223, page 
 312, showing that the prong vibrates, not only as a whole, but in parts. 
 The serrated wavy line produced represents the resultant of the com- 
 bined vibrations, and may be called a complex wave-line. 
 
 If we imagine the piece of twine on the spiral (page 277) 
 replaced by a bristle pointing downward, and under it a smoked 
 glass drawn at right angles to the length of the spiral, the 
 vibrating bristle will trace a characteristic curve on the glass. 
 We may even conceive a writing point attached to a particle 
 
280 SOUND. 
 
 of air and tracing these curves, and thus understand how it 
 can illustrate the nature of the vibration of the air. This method 
 is known as the graphical method of studying vibrations. 
 
 XXXIX. SOUND-WAVES. 
 
 § 258. How sound originates. — Listen to yonder sound- 
 ing church-bell. It produces a sensation ; it is heard. If the 
 orifices of the ears be stopped by pressing the palms of the 
 hands against them, the sensation, in a great measure, ceases. 
 The ear is, therefore, the organ of sense through which the 
 sensation of hearing is produced. The bell must be the cause 
 of the impression made on the ear. But the bell is at such a 
 distance that it cannot itself act on the ear ; yet something must 
 act on the ear, and it must be the bell which causes that some- 
 thing to act. 
 
 Commencing at the origin of sound, let the first inquiry be, 
 How does a sounding body differ from a silent body ? 
 
 Experiments. Strike a bell or a glass bell-jar, and touch the edge 
 with a small cork ball suspended by a thread ; you not only hear the 
 sound, but, at the same time, you see a tremulous motion of the ball, 
 caused by a motion of the bell. Touch the bell gently with a finger, 
 and you feel a tremulous motion. Press the hand against the bell ; 
 you stop its vibratory motion, and at that instant the sound ceases. 
 Strike the prongs of a tuning-fork, press the stem against a table, you 
 hear a sound. Touch gently the cheek with the end of one of the 
 prongs ; you feel a tickling sensation produced by its minute vibrations. 
 Thrust the ends of the prongs just beneath the surface of water; the 
 water is thrown off in a fine spray on either side of the vibrating fork. 
 Watch the strings of a piano, guitar, or violin, or the tongue of a jews- 
 harp, when sounding. You can see that they are in motion. 
 
 The difference between a body when sounding and when not 
 sounding is, that when sounding it is in a state of continuous 
 vibration ; when not sounding, this vibration is absent, and the 
 parts of the body are at rest among themselves. We conclude 
 that sound originates in a vibrating body. 
 
HOW SOUND TRAVELS. 281 
 
 Sounds that proceed from the tuning-fork and the viohn 
 string are examples of sound produced by transverse vibrations. 
 
 Experiment 1. With one hand grasp at its center a glass tube 
 about 1" long; lay a damp woolen cloth on the palm of the other hand, 
 and grasp the tube tightly with this hand, and slide it quickly length- 
 vise the tube. The friction between the cloth and the tube wiU throw 
 the latter Into longitudinal vibrations, and a loud, shrill sound will be 
 produced. 
 
 Experiment 2. Take a strip of sheet-iron or brass 16™ long aud 
 Qcm ,vije, make a hole near one end, and suspend by a string 1™ long 
 from the hand, and rotate it rapidly abont the hand after the manner 
 of a sling. The string will rapidly twist and untwist, and a loud sound 
 will result from the torsional vibrations. 
 
 § 259. How sound travels. — How can a bell, sounding 
 at a distance, affect the ear? If the bell while sounding pos- 
 sesses no peculiar property except motion, then it lias nothing 
 to communicate to the ear but motion. But motion can be 
 communicated by one body to another at a distance only through 
 some medium. 
 
 Does sound require a medium for its communication? If so, 
 what is the medium? 
 
 Experiment. Lay a thick tuft of cotton-wool on the plate of an 
 air-pump, and on this, face downward, place a loud-ticking watch, and 
 cover with the receiver. Notice that the receiver, interposed between 
 the watch and your ear, greatly diminishes the sound, or interferes 
 with the passage of something to the ear. Take a few strokes of the 
 pump and listen ; the sound is more feeble, and continues to grow less 
 and less distinct as the exhaustion progresses, until either no sound 
 can be heard when the ear is placed close to the receiver, or an ex- 
 tremely faint one, as if coming from a great distance. The removal 
 of air" from a portion of the space between the watch and your ear 
 destroys the sound, although the watch continues to tick. Let in the 
 air again and the sound is restored. 
 
 Thus it appears that sound cannot travel through a vacuum ; in 
 
 other words, without a medium, and the medium in this case is air. 
 
 By which of the two methods described on page 278 is mo- 
 
282 SOUND. 
 
 tion transmitted from the sounding body through the air? Take 
 an extreme case : A cannon is discharged at a distance of one- 
 fourth of a mile from you. You not only hear the sound, but 
 feel the shock communicated bj' the air; the windows are 
 shaken by it ; at the same time, you easily perceive that it is 
 not the motion of a wind, but the motion of a pulse. It can 
 easily be shown that the pulse travelled at a rate of about 800 
 miles in an hour, or with nearly the velocity of a rifle ball, 
 whereas the wind of a hurricane seldom exceeds 75 miles an 
 hour. What, think you, would be the result if you were to be 
 struck hy a gust of wind of such velocity? Yet the softest 
 whisper travels with very nearly the same speed. 
 
 § 260. Air-waves. — Boys amuse themselves by inflating 
 paper bags, and with a quick blow bursting them, producing 
 with each a single loud report. First the air is suddenly and 
 greatly condensed bj- the blow, the bag is burst ; the air now, as 
 suddenly and with equal force, expands, and by its expansion 
 condenses the air for a certain distance all around it, leaving a 
 rarefaction where just before had been a condensation. If many 
 bags were burst at the same spot in rapid succession, the result 
 would be that alternating shells of condensation and rarefaction 
 would be thrown off, all having a common center, enlarging as 
 they advance, like the waves formed by stones dropped into 
 water ; onlj' that, in this case, the waves are not like rings, but 
 hollow globes ; not circular, but spherical. 
 
 As a wave advances, each individual air-particle concerned in 
 its transmission performs a short excursion fro and to in a 
 straight line radiating from the center of the shells or hollow 
 globes. A particle begins to move when the front of the shell 
 of compression touches it, and completes its motion when the 
 back of the next shell of rarefaction leaves it. Accordingly, an 
 air-wave travels its oion length in the time that a particle occupies 
 in going through one complete vibration so as to be ready to start 
 again. 
 
SOLIDS AND LIQTHDS AS MEDIA OF SOUND. 283 
 
 § 261. What sound is. — The term sound is sometimes 
 used to denote a sensation, sometimes to denote the external 
 cause of the sensation ; it is in this latter sense that the word is 
 used in Physics, and that we have to define it. 
 
 If the ear replace the candle in the experiment (page 278) , the 
 air pulse produces a loud sound. Conversely, air-waves started 
 by the voice may afifect a flame, as shown on page 313. In fact, 
 the relation between the cause of our sensation and a vibration 
 is so uniform, that we may say, Sound is vibration that may he 
 appreciated by the ear. 
 
 § 262. Solids and liquids as media transmitting sound. 
 — Experiment 1. Lay a watch, with its back downward, on and near 
 to one end of a long board (or table), and cover the watch with loose 
 folds of cloth till its ticking cannot be heard through the air in any 
 direction at a distance equal to the length of the board. Now place 
 the ear in contact with the distant end of the board, and you will hear 
 the ticking of the watch very distinctly. 
 
 Experiment 2. Place one end of a long pole on a resonance box 
 (page 296), and apply the stem of a vibrating tuning-fork to the other 
 end ; the sound-vibrations will be transmitted through the pole to the 
 box, and a loud sound will be given out by the box, as though that, 
 and not the tuning-fork, were the origin of the sound. . 
 
 Experiment 3. Place the ear to the earth, and listen to the rambling 
 of a distant carriage ; or put the ear to one end of a long stick of tim- 
 ber, and let some one gently scratch the other end with a pin. 
 
 Experiment 4. The following experiment will be found very in- 
 structive and satisfactory : Let two persons stand about fifteen rods 
 apart, and one of them strike two pebble-stones together, so as to be 
 scarcely audible to the other. Then, when at the same distance apart, 
 let one of them dive to the bottom of a pond of water, or hold one ear 
 for a few seconds beneath the surface of the water, while the other, 
 extending his hands into the water, strikes the stones together as 
 before. The sound is much more audible than when conveyed by air. 
 
 Solids and liquids, as well as gases, transmit sound-vibrations. 
 
284 SOUND. 
 
 XL. VELOCITY OP SOUND. 
 
 § 263. On what velocity of sound depends. — The 
 
 of a gun, however distant, is seen by an observer at the instant 
 it is made. But the report, if the distance is several hundred 
 yards, is heard a little later. If the distance is a mile, an in- 
 terval of nearly five seconds will occur; so that sound must 
 occupy that time in traveling a mile, or it must travel about 
 1100 feet in a second, — a velocity somewhat less than that of 
 a rifle ball. 
 
 It is apparent that sound must travel more slowly in a dense 
 than in a rare medium, inasmuch as in the former there is a 
 greater mass to be moved ; on the other hand (see page 277), 
 it travels faster in the medium that is the most elastic. Density 
 retards and elasticity increases the velocity of sound. The rela- 
 tion of velocity to the density and elasticity of gases, as ascer- 
 tained by careful experiment, is as follows : the velocity of sound 
 in gases is directly proportional to the square root of their elasti- 
 city, and inversely proportional to the square root of their 
 respective densities. 
 
 The velocity of sound in air at 0° C. has been found to be 
 333°" (1093 ft.) per second. Its velocity increases nearly six- 
 tenths of a meter for each degree centigrade. At the temper- 
 ature of 16° C. (60° F.) we may reckon the velocity of sound 
 at about 342" (1125 ft.) per second. 
 
 The greater density of solids and liquids, as compared with 
 gases, tends, of course, to diminish the velocity of sound ; but 
 their greater elasticity'' more than compensates for the decrease 
 of velocity occasioned by the increase of density. As a general 
 ral6, solids are more elastic than liquids ; hence, sound generallj' 
 travels faster in the former than in the latter. For example, 
 sound travels in water about 4 times as fast as in air ; in lead, 
 
 • The queetion will very pertinently arise here, inasmuch as gases are (page 63) per- 
 fectly elastic. How can solids and liquids he regarded as having greater elasticity? It 
 should he understood that while gases completely recover their volume after a compres- 
 ■ing force is removed, they do it more sluggishly than solids and liquids. 
 
EEFLECTION. 285 
 
 4 times ; in gold, 5 times ; in brass, 10 times ; in. copper, 11 
 times ; in iron, 16 times ; in glass, 16 times ; in wood, along 
 the fiber, between 10 and 15 times ; in wood, across the fiber, 
 between 4 and 6 times. 
 
 QUESTIONS. 
 
 1. (a) If a body of gas is compressed, how is its density or volume 
 affected? (See page 156.) (6) How Is its elasticity affected? (c) How 
 is it affected as regards the velocity with which it will transmit sound? 
 
 2. Hydrogen Is sixteen times lighter (or rarer) than oxygen under 
 the same pressure, (a) In which will sound travel faster? (6) Why? 
 (c) How many times faster? 
 
 3. When sound travels in air with a velocity of 331™ per second, it 
 travels in carbonic acid gas at the rate of 262"' per second, (a) Which 
 is the denser gas? (6) How many times denser? 
 
 4. When a confined body of air is heated, it has its elasticity in- 
 creased without any change of density. How will this affect transmis- 
 sion of sound? 
 
 5. If air is heated and allowed to expand freely, as on a warm 
 summer day, its elasticity is unaffected, but its density is diminished ; 
 how wiU this affect the transmission of sound? 
 
 XLI. REFLECTION AND REERACTION OF SOUND. 
 
 § 264. Reflection. — In the experiment with the spiral 
 spring, waves were refiected from the box to the hand, and 
 from the hand to the box. "When a sound-wave meets an 
 obstacle in its course, it is reflected ; and a sound heard after 
 being thus reflected is often called an echo, or reverberation when 
 many times reflected, so that the sound becomes nearly con- 
 tinuous. 
 
 § 265. Sound reflected by concave mirrors. — Experi- 
 ment. Place a watch at the focus (page 286) A, Figure 208, of a con- 
 cave mirror G. At the focus B of another concave mirror H, place the 
 large opening of a small tunnel, and with a rubber connector attach 
 the bent glass tube C to the nose of the tunnel. The extremity D 
 being placed in the ear, the ticking of the watch can be heard very 
 
286 
 
 SOUND. 
 
 Fig. 208; 
 
 distinctly, as though it were somewhere near the mirror H. Though 
 the mirrors be 5"> apart, the sound will be heard much louder at B than 
 at an intertermediate point E. 
 
 How is this explained? Every air-particle in a certain 
 radial line, as Ac, receives and transmits motion in the direc- 
 tion of this line ; the last particle strikes the mirror at c, and 
 being perfectly elastic, bounds oflf in the direction cc' in con- 
 formity to the law of reflection (page 118), communicating its 
 motion to the particles in this line. At c' a similar reflection 
 gives motion to the air-particles in the line c'B. In consequence 
 of these two reflections, all divergent lines of force, as Ad, Ae, 
 
 etc. , that meet the mirror 
 J G, are there rendered 
 \ y parallel, and afterwards 
 rendered convergent at 
 the mirror H. The prac- 
 tical result of the concen- 
 tration of this scattering 
 force is, that a sound of 
 great intensity is heard at B. The points A and B are called 
 the foci of the mirrors. The front of the wave as it leaves A 
 is convex, in passing from G to H it is plane, and from H 
 to B concave. If you fill a large circular tin basin with 
 water, and strike one edge with a knuckle, circular waves with 
 concave fronts will close in on the center, heaping up the 
 water at that point. 
 
 Long "whispering-galleries" have been constructed on this prin- 
 ciple. Persons stationed at the foci of the concave ends of the long 
 gallery can carry on a conversation in a whisper which persons be- 
 tween cannot hear. A most notable instance was that of the " Ear of 
 Dionysius," in the dungeon of Syracuse. The roof of the prison was 
 so constructed as to transmit through a narrow passage cut in the rock, 
 to the ear of the tyrant, even the whispers of the victims there con- 
 fined. 
 
 The external ear is a sound condenser. The hand held concave 
 behind the ear, by its increased surface, adds to its efficiency. An e?,r- 
 
REFRACTION. 
 
 287 
 
 trumpet, by successive reflections, serves to concentrate, at the small 
 orifice opening into the ear, all the sound-waves that enter at the large 
 end. 
 
 § 266. Eefraction. — If you place your ear at the small end 
 of a tunnel C (Fig. 209) , and listen to the ticking of a watch A, 
 
 Fig. 209. 
 
 4" distant, and then introduce a collodion balloon B filled with 
 carbonic acid gas between your ear and the watch, and very 
 near the latter, the sound becomes much louder. 
 
 The cause is obvious ; for, let the curved lines a, b, o, etc., represent 
 sections of sound-waves with convex fronts, and B a spherical body 
 of carbonic acid gas which is denser than air ; then it is clear that, 
 owing to the slower progress of the waves in the denser gas, they 
 would become flattened on entering this gas, and the waves of convex 
 fronts may be changed to waves of plane fronts. Again, points at 
 the extremities of the waves, having less distance to travel in the denser 
 gas than points near the center, would emerge first and get in advance, 
 and thus the wave fronts which are plane while wholly in the dense 
 gas, become concave on leaving it. By these changes in the form of 
 the wave fronts, sound energy which was originally becoming diffused 
 through wider and wider space, and therefore becoming less intense 
 as it progressed, is so changed in direction in passing into and out of 
 a medium of greater density, that the energy is finally concentrated at 
 a distant point, as at C, and thereby Intensified. 
 
 Any change in direction of sound, caused by passing from a 
 medium of a certain density into a medium of different density, 
 is called refraction. 
 
288 soinsTD. 
 
 XLII. LOUDNESS OP SOUND. 
 
 § 267. Loudness depends on amplitude of vibrations. — 
 
 Gently tap the prongs of a tuning-fork and dip them into water, 
 — the water is scarcely moved by them ; increase the force of 
 the blow, ^ — the vibrations become wider, and the water spray is 
 thrown with greater force and to a greater distance. The same 
 thing occurs when the fork vibrates in air ; though we do not 
 see the air-particles as they are batted by the moving fork, 
 yet we feel the effects as a sound sensation, and we judge of 
 their energy by the intensity of the sensation. Loudness of 
 sound is really the measure of a sensation ; but as we have no 
 suitable or constant standard of measurement for a sensation, 
 we are compelled to measure rather the intensity of the sound- 
 wave, knowing at the same time that the loudness is not pro- 
 portional to this intensity ; unfortunately the expressions loud- 
 ness and intensity of sound are often interchanged. The inten- 
 sity of a vibration is measured by the energy of the vibrating 
 particle. It is clear that if the amplitude of vibration of a 
 particle is doubled while its period remains constant, its velocity 
 is doubled (or nearly so) , and its energy becomes therefore four 
 times as much as at first. Hence, (1) Measured mechanically, 
 the loudness or intensity of sound is proportional to the square 
 of the amplitude of the vibrations of the sounding body. 
 
 § 268. Loudness depends upon the density of the me- 
 dium. — In the experiment with the watch under the receiver 
 of the air-pump (page 281), the sound grew feebler as the air 
 became rarer. Aeronauts are obliged to exert themselves 
 more to make their conversation heard when they reach great 
 hights than when in the denser lower air. Fill a glass bell-jar 
 with hydrogen gas, and place in it a small alarm clock ; the 
 sound is exceedingly weak and thin, as compared with the 
 sound when the jar is filled with air. These experiments teach 
 us, (2) that the intensity of sound depends upon the density of 
 
LOUDNESS DEPENDS ON DISTANCE. 289 
 
 tlie medium in which it is produced. In a rare medium a vibrat- 
 ing body during a single vibration sets in motion either fewer 
 particles, as in the case of the partially exhausted receiver, or, 
 as in the case of the hydrogen gas, it sets in motion lighter par- 
 ticles than in a dense medium ; consequently it parts with its 
 energy more slowly, and the sound is consequently weaker. 
 
 (In which ought the vibrations of a body to last longer, — in 
 a dense or in a rare medium ? Why ?) 
 
 § 269. Loudness depends on distance. — It is a matter 
 of every-day observation that the loudness of a sound dimin- 
 ishes very rapidly as the distance from its source to the ear 
 increases. The ear is not, however, able to compare very accu- 
 rately the loudness of two sounds ; for instance, it cannot 
 determine when one sound is just twice as loud as another. 
 This, however, so far as it is affected by distance, can be very 
 accurately determined by calculation. For it is evident that as 
 a sound-wave recedes from its source in an ever-widening sphere, 
 a given amount of energy becomes distributed over an ever- 
 increasing surface ; and as a greater number of particles par- 
 take of the motion, individual particles receive proportionally 
 less energy ; hence it. follows, — as a consequence of the geomet- 
 rical truth, that the surface of a sphere varies as the square of its 
 radius, — that (3) the intensity of sound varies inversely as the 
 square of the distance from its source. For example, if two per- 
 sons, A and B, are respectively 500 and 1000 meters from a gun 
 when it is discharged, the report that reaches A will be four 
 times as loud as the same report when it reaches B. 
 
 § 270. Speaking tubes. — Experiment. Place a watch at one 
 end of the long tin tube (Fig. 206), and the ear at the other end. The 
 ticking is heard very loud, as though the watch were close to the ear. 
 
 Long tin tubes, called speaking tubes, passing through many 
 apartments in a building, enable persons at the distant extremi- 
 ties to carry on conversation in a low tone of voice, while per- 
 
290 SOUND. 
 
 sons in the various rooms through which the tube passes hear 
 nothing. The reason is that the sound-waves which enter the 
 tube are prevented from expanding, consequently the intensity 
 of sound is not affected by distance, except as its energy is 
 wasted by friction of the air against the sides of the tube. 
 
 § 271. Reenforoement of sound. — Observe the difference 
 between the loudness of a sound made in a room, and the same 
 made in the open air. In a room of moderate size the original 
 and reflected sounds are heard simultaneously, one intensifying 
 the other and producing what is called resonance. In large 
 rooms, the blending of the two is not perfect, resulting in a sort 
 of blurred sound, which is loud but indistinct. 
 
 Experiment. Set a tuning-fork in vibration ; you can scarcely hear 
 the sound produced unless it is held near the ear. Press the stem 
 against a table ; the sound rings out loud, but seems to proceed from 
 the table. Again set it vibrating, hold it to the ear, and, watch in 
 hand, note the number of seconds it can be heard ; then note the time 
 that it can be heard when the stem rests on the table. The vibrations 
 continue longer in the former case than in the latter. 
 
 When only the fork vibrates, the prongs presenting little sur- 
 face cut their way through the air, producing very slight conden- 
 sations, and consequently sounds of little intensity. "When the 
 fork rests upon the table, the vibrations are communicated to 
 the table ; the table with its larger surface throws a larger mass 
 of air into vibration, and thus greatly intensifies the sound. 
 But as the sound is rendered more intense, the energy of the 
 vibrating body is sooner exhausted, and the sounds have shorter 
 duration. 
 
 In all stringed instruments, like the piano, violin, etc. , reen- 
 forcement of sound is necessary ; here the sounding board of 
 thin wood fills more perfectly the place of the table. This 
 sounding board must strengthen all notes within the compass of 
 the instrument. The strings of the piano, guitar, and violin 
 owe as much of their loudness of sound to their elastic sounding 
 boards, as does the fork to the table. 
 
EEENTORCEMENT BY MASSES OF AIK. 
 
 291 
 
 Hg. 210. 
 
 § 272. Reenforcement by masses of air. — Resonators. 
 — Experiment. Take a glass tube A, Figure 210, 45™ long and 4°"> 
 in diameter ; thrust one end Into a vessel of water, C, and hold over the 
 other end a vibrating tuning-fork B that makes (say) 256 vibrations in 
 a second. (See page 300.) Gradually lower the tube into the water, 
 and when it reaches a certain depth, i.e., when the column of air oc 
 attains a certain length, the sound 
 of the fork becomes very loud; 
 continuing to lower the tube, the B^ 
 sound rapidly dies away. Try 
 other forks that make different 
 numbers of vibrations in a sec- 
 ond. The sound of each is inten- 
 sified, but each requires a length 
 of air-column suited to its par- 
 ticular vibration number. 
 
 Columns of air are thus 
 found to serve as well as 
 sounding boards to strengthen 
 a sound. When so used they 
 
 ^ 
 
 are called resonators; but unlike the sounding board they can 
 respond loudly to only one tone, or to a few tones of widely 
 different pitch. An important form of resonator is shown on 
 page 309. 
 
 How is this reenforcement effected ? When the prong a moves 
 from one extremity of its arc a' to the other a", it sends a con- 
 densation down the tube ; this condensation striking the surface 
 of the water, is reflected by it up the tube. Now suppose that 
 the front of this reflected condensation should just reach the 
 prong at the instant it is starting on its retreat from a" to a' ; 
 then the reflected condensation will conspire with the condensa- 
 tion formed by the prong in its retreat to make a greater con- 
 densation in the air outside the tube. Again the retreat of the 
 prong from a'' to a' produces in its rear a rarefaction, which also 
 runs down the tube, is reflected, and will reach the prong at the 
 instant it is about to return from a' to a", and to cause a rare- 
 
292 
 
 SOUND. 
 
 faction in its rear ; these two rarefactions moving in the same 
 direction conspire to produce an intensified rarefaction. The 
 original sounds thus combine with their echoes to produce reso- 
 nance ; but this can only happen when the like parts of each 
 wave coincide each with each ; for if the tube were somewhat 
 longer or shorter than it is, it is plain that condensations would 
 meet rarefactions in the tube, and tend to destroj- one another. 
 The loudness of sound of all wind instruments is due to the 
 resonance of the air contained within them. A simple vibra- 
 tory movement at the mouth or orifice of the instrument, 
 scarcely audible in itself, such as the vibration of a reed in reed 
 pipes, or a pulsatory movement of the air produced by the pas- 
 sage of a thin sheet of air over a sharp wooden or metallic edge, 
 jis in organ pipes, flutes, and flageolets, or more simply still 
 by the friction of a gentle stream of breath from the lips sent 
 obliquely across the open end of a closed tube, bottle, or pen- 
 Fig. 211. case, is sufficient to set the large body of enclosed 
 air in the instrument into vibration, and thus reen- 
 forced, the sound becomes audible at long distances. 
 
 Experiment 2. Attach a rose gas-burner A, Figure 
 211, to a metal gas tube about 1" in length, and connect 
 this by a rubber tube with a gas-burner. Light the gas 
 at the rose burner, and you will hear a low rustling 
 noise. Eemove the conical cap from the long tin tube 
 (Fig. 206, page 278), support the tube in a vertical po- 
 sition, and ^adually raise the burner into the tube; 
 when it reaches a certain point not far up, the body of 
 air in the tube will catch up the vibrations, and give out 
 a deafening sound that will shake the walls and furni- 
 ture in the room. 
 
 § 273. Measuring wave-lengths and veloc- 
 ity of sound. — Experiments like that described 
 on page 291 enable us readily to measure the wave-length 
 produced by a fork that makes a given number of vibrations 
 in a second, and also to measure the velocity. of sound. It is 
 
MEASURING VELOCITi^ OF SOTTND. 293 
 
 evident that if a condensation generated by the prong of the 
 fork in its forwpxd movement from a' to a" (Fig. 211) met 
 with no obstacle, its front, meantime, would traverse the dis- 
 tance od, or twice the distance oc ; hence the length of the con- 
 densation is the distance od. But a condensation is only one- 
 half of a wave, and the passage of the prong from a' to a" is 
 onlj' one-half of a vibration ; consequently the distance od is 
 one-half of a wave-length, and the distance oc is one-fourth 
 of a wave-length. The measured distance of oc in this case is 
 about 33™ ; hence the length of wave produced by a C'-fork 
 making 256 vibrations in a second is (33™ x4 = ) 1.32"'- And 
 since a wave from this fork travels 1.32" in -^ of a second, 
 it will travel in an entire second (1.32 X 256 = ) 338". The 
 distance oc is modified by temperature. It is also modified by 
 the diameter of the tube. For accuracy about two-thirds of the 
 diameter should be added to the length of the tube to obtain 
 one-fourth of the wave-length. It is evident that the three 
 quantities expressed in the formula 
 
 , ,, velocity 
 
 wave-length = ; ——fi- — -: — 
 
 number of vibrations 
 
 bear such a relation to one another that if anj- two are known 
 the remaining quantity can be computed. It will further be 
 observed that with a given velocity the ivave-length varies 
 inversely as the number of vibrations, i.e., the greater the num- 
 ber of vibrations per second, the shorter the wave-length. 
 
 QUESTIONS. 
 
 1. (o) Which produces greater wave-lengths, a fork making 256 
 vibrations in a second, or one making 512 vibrations in the same time? 
 (6) How many times? 
 
 2. Disregarding the diameter of the tube, what number of vibrations 
 does a fork make in a second, whose resonance tube is 22.26™ long, 
 when the temperature is 16° C. ? 
 
 3. What Is the wave-length produced by a fork that makes 384 vibra- 
 tions in a second, when the temperature is 16° C. ? 
 
294 
 
 SOUND. 
 
 § 274. Interference of BOund--waves. — Is it possible for 
 two sounds to destroy one another and produce silence ? 
 
 Eig. 212. 
 
 Experiment 1. While the fork 
 B (Fig. 210) is vibrating in the 
 position represented in the figure, 
 slowly roll the fork over in the 
 fingers, through a quarter of a 
 revolution, until the two prongs 
 are in the same horizontal plane, 
 with their edges turned toward 
 the opening of the tube. When 
 *i the fork has accomplished one- 
 
 eighth of a revolution, and is in 
 an oblique position, as in Figure 
 212, the reSnforcement from the 
 ■ «»■ _j»j t! " tube entirely disappears, but re- 
 
 appears when the fork completes 
 Its quarter of a revolution. Return to the position where there is no 
 resonance, and enclose the prong farthest from the tube, without touch- 
 ing the fork, in a loose roll of paper, so as to prevent the sound- 
 waves produced by that prong from passing into the tube; the 
 resonance resulting from the vibrations of the other prong Immediately 
 appears in full force. 
 
 Experiment 2. Carry, while sounding, a tuning-fork mounted on 
 a resonance-box (see Fig. 214), from a distance slowly toward a wall 
 of a room ; the sound will become wavy, rising and sinking at regu- 
 lar intervals. That is, at certain points the condensations and rare- 
 factions of the waves advancing from the fork will coincide each to 
 each with those of the waves refiected from the wall, and when this is 
 the case the sound is louder. At other points the condensations of the 
 waves issuing from the fork occur at the same places where the rare- 
 factions of the reflected waves occur; and in this case they nearly 
 destroy one another, and a fainter sound is the result. 
 
 Thus it appears that two sounds of the same pitch may unite 
 to form a sound louder or weaker than either alone, or even 
 cause silence, according to their difference of phase and their rela- 
 tive intensities. "When like phases of two sets of sound-waves 
 coincide, i.e., condensation with condensation, and rarefaction 
 
FORCED AND SYMPATHETIC VIBKATIONS. 
 
 295 
 
 with rarefaction, the result is, as we might expect, an intensified 
 sound. In this case the air-particles are subject to the action 
 of two joint forces in the same direction, which tends to quicken 
 their motions. On the other hand, when unlike phases of two 
 sets of sound-waves coincide, i.e. , the condensations of one set of 
 waves with the rarefactions of another, as would happen if one 
 set of waves should be half of a wave-length behind the other ; 
 the air-particles will be subject to two forces in opposite direc- 
 tions ; and the evident result of an equal tendency to the two 
 opposing forces is a state of repose. 
 
 § 275. Forced and sympathetic vibrations. — Experi- 
 ment 1. Suspend by a string I" long a stone weighing about 2K 
 Swing the stone, and learn its rate of vibration ; then stop it, and blow 
 gentle puflfs of breath against the stone in the same periods. The first 
 few puflfs produce no visible effect; but, persevering, the stone will 
 soon move visibly, and after a large number 
 of these feeble impulses, the stone will move 
 through a wide arc, and will require consid- 
 erable force to stop it. 
 
 Experiment 2. Suspend from a frame 
 several pendulums, A, B, C, etc. (Fig. 213). 
 A and D are each 1™ long, C a little longer, 
 and B and E shorter. Set A in vibration, and 
 slight impulses will be communicated through 
 the frame to D and cause it to vibrate. The 
 vibration-period of D being the same as that 
 of A, all the impulses tend to accumulate mo- 
 tion in D, so that it soon vibrates through 
 arcs as large as those of A. On the other hand, C, B, and E, having 
 different rates of vibration from that of A, will at first acquire a slight 
 motion, but soon their vibrations will be in opposition to those of A, 
 and then the impulses received from A will tend to destroy the slight 
 motion they had previously acquired. 
 
 Experiment 3. Hang up, a few feet distant from the pendulum of 
 Exp. 1, a bullet or shot by a shorter string, and connect the bullet and 
 stone by a tight thread. Set the stone swinging, and the bullet must 
 vibrate in the same period, although its natural time of vibration is 
 shorter. 
 
 Fig. 
 
 213 
 
 
 
 jgnn 
 
 HiHiii iiiiunr 
 
 gi 
 
 Jll|l|l|jj|l|l| 
 
 
 ""I 
 
 
 < 
 
 E 
 
 1 
 
 < 
 E 
 
 1 
 i 
 
 
 
 ) 
 A 
 
 ( 
 
 ) 
 3 
 
 
 i 
 C 
 
 ? 
 
 
 
296 
 
 SOUND. 
 
 Experiment 4. Press down gently one of the keys of a piano so as 
 to raise the damper without making any sound, and then sing loudly 
 into the instrument the corresponding note. The string correspond- 
 ing to this note will be thrown into vibrations that can be heard for 
 several seconds after the voice ceases. If another note be sung, this 
 string will not respond audibly. 
 
 Eaise the dampers from all the strings of the piano by pressing the 
 foot on the right-hand pedal, and sing strongly some note into the 
 piano. Although all the strings ai-e free to vibrate, only those that 
 correspond to the note you sing (i.e., those that are capable of making 
 the same number of vibrations per second as are produced by your 
 voice), will respond loudly. 
 
 Experiment 5. Take two forks, A and B (Fig. 214), tuned exactly 
 in unison, and mounted on resonance-boxes, and place them from three 
 
 to ten meters apart. Fasten, 
 
 Fig. 214. , u-^ * 1- 
 
 by a bit of sealing-wax, a 
 thread to a thin piece of glass 
 12"™ square (glass used for mi- 
 croscopic mountings is the 
 best, or a piece of photographic 
 tintype plate will answer well), 
 and suspend so as to touch a 
 corner of one of the prongs of 
 the fork B. Set the fork A in 
 vibration by drawing a resined bass-viol bow strongly across the ends 
 of its prongs. In about ten seconds stop the vibrations of A with the 
 fingers, and you will see and hear the piece of glass rattling against 
 the prong of the fork B ; remove the glass, and place the ear near the 
 fork B, or better, the open end of the box, and you may hear a distinct 
 sound, showing that the fork B has been thrown into a state of vibra- 
 tion by the fork A. 
 
 So the pulses that traverse the air between the forks, so 
 gentle that only the sensitive organ of the ear can perceive 
 them, become great enough to move the rigid steel when their 
 blows, dealt at the rate of perhaps 512 in a second, add them- 
 selves together. The large number of blows make up for the 
 feebleness of each by itself. 
 
 These experiments show that a vibrating body tends to make 
 other bodies near it vibrate in its own period. The vibrations 
 
DISTINCTION BETWEEN NOISE AND MUSIC. 297 
 
 thus caused are called forced vibrations. These occur, in Exp. 2, 
 with B, C, and E ; in the vibrations of sounding-boards, and 
 of the membrane and fluids of the ear (page 315), and in the 
 air when transmitting a sound-wave, etc. But as the period of 
 the incident waves coincides more and more nearly with the 
 period of the second body, the amplitude of the vibrations of 
 the latter becomes greater and greater, until finally its vibration 
 is uniform, like D (Fig. 213), not irregular, like B, C, and E. 
 Such are called sympathetic vibrations, as in Exps. 4 and 5. 
 
 § 276. Distinction between noise and musical sound. 
 If the body that strikes the air deals it but a single blow, like the 
 discharge of a fire-cracker, the ear receives but a single shock, 
 and the result is called a noise. If several shocks are slowly 
 received by the ear in succession, the ear distinguishes them 
 as so many separate noises. If, however, the body that strikes 
 the air is in vibration, and deals it a great number of little blows 
 in a second, or if a large number of flre-crackers are discharged 
 one after another very rapidly, so that the ear is unable to dis- 
 tinguish the individual shocks, the effect produced is that of one 
 continuous sound, which may be pleasing to the ear ; and, if so, 
 it is called a musical sound. But continuity of sound does not 
 necessarily render it musical. The sound produced by a hun- 
 dred children beating various articles in a room with clubs 
 might not be lacking in continuity, but it would be an intoler- 
 able noise. There would be wanting those elements that please 
 the ear ; viz., regularity both in periodicity and intensity of the 
 shocks which it receives. The distinction between music and 
 noise is, generally speaking, a distinction between the agreeable 
 and the disagreeable, between regularity and confusion. The 
 characteristics of a musical sound are regularity and simplicity. 
 
298 
 
 SOUND. 
 
 XLIII. PITCH OF SOUNDS. 
 § 277. On what pitch depends. — Draw the finger-nail 
 slowly, and then rapidly, across the teeth of a comb. The two 
 musical sounds produced are commonly described as low or 
 grave, and higJi or acute, and the hight of a musical sound is 
 called pitch. "What is the cause of a difference in hight or 
 pitch of two sounds? 
 
 Experiment. Procure a circular sheet-iron or pasteboard disk A, 
 Figure 215, 30™ in diameter. From the center of the disk describe a 
 circle with a radius of 12<=">. In the circumfer- 
 ence of this circle, with a punch, cut holes 8°"° 
 in diameter, leaving equal intervals of about 2™ 
 between the holes. Insert in a rubber tube a 
 piece of glass tube B, of 1=™ bore, drawn out at 
 one end so that its orifice is about 4™" in diame- 
 ter. Attach the disk to some rotating apparatus, 
 hold the small orifice of the glass tube opposite 
 the holes, and blow steadily through the tube, 
 and rotate the disk at first very slowly and then 
 with gradually increasing rapidity. The breath, 
 as it makes its exit from the tube, cannot escape 
 continuously through the holes, but is cut up by 
 the passing obstructions into a series of puffs, 
 which at first are heard as so many distinct 
 sounds ; as the speed increases, the number of 
 pufls in a second increases, until the ear can no 
 longer separate them, when they blend together 
 in a deep sound of a definite pitch. 
 
 The peculiarity of this instrument is that it does not produce 
 sound by its own vibrations. Every time the air is driven 
 through a hole, it produces a pulse of condensation in the air 
 beyond ; and during the interval between the successive dis- 
 charges, a pulse of rarefaction will be caused by the elasticity of 
 the air, so that the result is the same, so far as the effect on 
 the air medium is concerned, as if a body were vibrating 
 in it. As the velocity increases, the pitch constantly rises. 
 
SIREN". 299 
 
 until, at the greatest speed conveniently attainable, it becomes 
 painfully shrill. Varying the force of the breath affects the 
 loudness of the sound, but does not affect its pitch. 
 
 We learned on page 293 that on the number of vibrations in 
 a second, called the vibration-frequency, depends the wave- 
 length. So we have discovered the important fact that pitch 
 depends upon vibration-frequency or wave-length, i.e., the greater 
 the number of vibrations per second, or the shorter the wave- 
 length, the higher the pitch. 
 
 QUESTIONS AND EXERCISES. 
 
 1. Why does the same bell always give a sound of the same pitch? 
 
 2. (a) What is the effect of striliing a bell with different degrees of 
 force? (6) What change in the vibrations is produced? (c) What 
 property of sound remains the same? 
 
 3. (a) Strike a key of a piano and hold it down ; what is the only 
 change you observe in the sound produced while it remains audible? 
 (6) What is the cause of this change? 
 
 4. Eake the teeth of a comb with a finger-nail, at first slowly, then 
 quickly, and account for the difference in the character of the sounds 
 produced. 
 
 5. (a) On what does pitch depend? (6) On what, loudness? 
 
 § 278. How to find the vibration-frequency of a tone.— 
 Siren. — The perforated wheel described above is a cheap 
 imitation of a portion of an important instrument called a siren. 
 The instrument completed has an attachment called a counter, 
 which shows the number of revolutions the wheel makes in a 
 given time. 
 
 Suppose that it is required to ascertain the number of vibra- 
 tions per second necessary to produce a given pitch. Take 
 some instrument that gives the required pitch, e.g., a tuning- 
 fork, set it in vibration ; also rotate the siren, causing the pitch 
 of its sound gradually to rise until it corresponds with the pitch 
 of the fork ; then, sustaining that pitch, set the counter in oper- 
 ation, and at the end of a given time read off the number of 
 revolutions made by the wheel ; this number, multiplied by the 
 
300 
 
 SOUND. 
 
 number of holes rn the wheel, gives the uumbtiy of sound-waves 
 produced by the wheel during the given time, and the number 
 of vibrations made by the fork in the same time ; and this num- 
 ber, divided by the number of seconds employed, gives the 
 number of vibrations that must be made in a second by any 
 instrument in order to produce a sound of the same pitch. 
 With the siren we may even determine the number of vibrations 
 made by the wing of a fly which buzzes aiound our ears. 
 
 Fig. 216. 
 
 § 279. Musical scale. —Long before arty one had attempted 
 to find the frequency of vibration of a sounding body, men 
 had used a succession of sounds, differing in pitch, that 
 formed the so-called musical scale, or gamut, and were familiar 
 with its intervals. Very different scales have satisfied musi- 
 cians of different ages and nations. We can find a scale that 
 will nearly or exactly satisfy modern musical ears among 
 Europeans and Americans on a well-tuned piano or organ. On 
 such a piano, by the siren or otherwise, it is found that the note 
 called middle C (C) has, on the best American 
 instruments, about 270 double vibrations per 
 second ; on German, 264 ; while the French 
 legal standard is 261. Physical apparatus is 
 usually based on C'= 256 vibrationa, 256 being 
 a power of 2. Assuming C = 264 vibrations, 
 if we extend our measures up and down the 
 scale, or get a violinist or singer to perform 
 near an instrument that counts the vibrations, 
 e.g., the siren, numbers agreeing very closely 
 with those given in Figure 216 are obtained ; 
 no one's ear is accurate enough to play or sing 
 precisely the same on two trials. Since the ear 
 is wholly incajftble of determining the number 
 of vibrations corresponding to a given note, 
 but is capable of determining with wondrous 
 precision the ratio of the vibration numbers of two notes, it is 
 
 1 
 
 11 
 
 g 
 
 c 
 
 132 
 
 1 
 
 E 
 
 U8J 
 165 
 
 : 
 
 F 
 
 176 
 
 
 G 
 
 198 
 
 I 
 
 A 
 
 220 
 
 f 
 
 B 
 
 247^ 
 
 V 
 
 C 
 
 264 
 
 2 
 
 D' 
 
 297 
 
 1 
 
 E' 
 
 330 
 
 5 
 
 F' 
 
 352 
 
 1 
 
 G' 
 
 396 
 
 A' 
 
 440 
 
 ¥ 
 
 B' 
 
 495 
 
 ¥ 
 
 C" 
 
 528 
 
 4 
 
LIMITS OP THE SCALE AND HEARING. 301 
 
 clear that all music must depend upon the recognition of such 
 ratios. For this reason the numbers in the third column are of 
 great importance. The eighth note, above or below a given 
 note, counting the given note as one, is called an eighth, — more 
 commonly, an octave, — above or below. Thus C is the octave 
 above C, and C_i an octave below. In a similar manner D is 
 called the second, and G the JiftJi, etc. , in the scale in which C 
 is the prime or first note. 
 
 PROBLEMS. 
 
 1. Rnd the vibration number for each note of the scale of which 
 C is the first note. 
 
 2. What is the vibration number of C_i, an octave below C ? 
 
 3. Pind the wave-length corresponding to each note of the scale of 
 which C is the first, when the temperature of the air is 16° C. ? 
 
 4. Pind the length of a resonance tube (disregarding its diameter), 
 closed at one end, which will respond to C when the temperature is 
 16° C? 
 
 s 280. Limits of the scale and hearing. — The lowest 
 note of a 7^ octave piano makes about 27^, the highest, 4,224 
 vibrations per second ; but these extreme notes have little musical 
 value, and the lowest notes are only used for their harmonics (see 
 page 305). The range of the human voice lies between 100 and 
 1,000 vibrations per second, or a little more than three octaves ; 
 an ordinary singer has about the compass of two octaves. 
 
 The ear is capable of hearing vibrations far exceeding in num- 
 ber the requirements of music. It can appreciate sounds arising 
 from 32 to 38,000 vibrations' per second, i.e., a range of about 
 eleven octaves, and a corresponding range of wave-length be- 
 tween seventy feet and three or four-tenths of an inch. These 
 numbers vary, however, considerably with the person. Excep- 
 tional ears can hear as many as 50,000 vibrations. Some ears 
 can hear a bat's cry, or the creaking of a cricket ; others cannot. 
 Singing mice are sometimes placed on exhibition. Of those 
 who go to hear them, some can hear nothing, others a little, and 
 
 ^ Preyer places the lowest limit for some ears at 16 Tibrations per second. 
 
302 
 
 SOUND. 
 
 others again can hear much. In the ability to hear sharp 
 sounds, no animal is superior to the cat, which finds her prey 
 in the dark by its. squealing. 
 
 §281. Beats. — Experiment 1. Strike simultaneously the lowest 
 note of a piano and its sharp (black key next above), and listen to the 
 resulting sound. 
 
 Experiment 2. Take two forks which make the same number of 
 vibrations per second (page 296), load one of the prongs of one fork 
 by sticking to it a small ball of wax, and thereby cause it to make a 
 few less vibrations per second than the other. Set both forks in vibra- 
 tion, and note the result. 
 
 In both cases you will hear a peculiar wavy or throbbing 
 sound, caused by an alternate rising and sinking in loudness. 
 These alternations in loudness are called heats. 
 
 Let the continuous curve line AC (Fig. 217) represent a series of 
 waves proceeding from the prongs of the loaded fork, and the dotted 
 line a series of waves proceeding from the other fork. As explained 
 on page 311, the elevations of these waves may represent the distance 
 the air-particle has been moved in the condensed part of the wave ; 
 similarly with the depressions for the rarefied part. Now the waves 
 from both forks may start together at A ; but as the waves from the 
 loaded fork are given less frequently, so are they correspondingly 
 longer and lag behind; and at certain inteiwals, as at B, condensa- 
 tions will correspond with rarefactions, producing by their interference 
 momentary silence, too short, however, to be perceived ; but the sound 
 as received by the ear is correctly represented in its varying loudness 
 by the curved line in the lower part of the figure. This line represents 
 the exact resultant of the two alternately concurring and opposing 
 forces on the particles of the air between the forks and the ear. 
 
SONOMETEK. 
 
 303 
 
 If one of the forks makes 256 vibrations, and the otljer 255 
 vibrations in a second, it is apparent that once during the sec- 
 ond the condensation of one series of waves will coincide with 
 the condensation of the other, producing a sound of maximum 
 intensity ; and once during the same time the condensation of 
 the one will coincide with the rarefaction of the other, producing 
 a sound of minimum intensity ; this will cause just one beat per 
 second. If there is a difference of two vibrations per second 
 between the two forks, then there will be two beats per second. 
 
 In every case the number of heats per second due to two simple 
 tones is equal to the difference of their respective vibration-num- 
 bers. The sensation produced on the ear by such a throbbing 
 sound, when the beats are sufficiently frequent, is unpleasant, 
 for the simUar reason that the sensation produced by flashes of 
 light that enter the eye, when j^ou walk on the shady side of a 
 picket fence, is unpleasant. The unpleasant sensation, called 
 by musicians discord, is found to be due to beats (see page 
 307). 
 
 Fig. 218. 
 
 XLIV. VIBRATION OE STRINGS. 
 § 282. Sonometer. — Experiment. Take a piece of violin-string 
 or piano-wire a little longer than your table. Fasten one end to a 
 nail in one end of the table, 
 and pass the other end over 
 a pulley fastened to the 
 other end of the table, and 
 to this end of the string 
 suspend a pail containing 
 sand, the two weighing just ^ 
 a pound. Place under the n 
 string, near the ends of the 
 table, two wedge-shaped 
 bridges A and B (Fig. 218). An apparatus thus aiTanged is called a so- 
 nometer. Pluck the string with the fingers near the middle, causing it 
 to vibrate, and note the pitch of the sound, and the length of the string 
 between the bridges. Move the bridge A toward B ; the pitch rises 
 as the vibrating portion of the string is shortened. Vary the position 
 of A until a pitch is obtained an octave above the pitch given at first, 
 
304 SOUND. 
 
 and it wjll be found that the string Is just one-half its original length ; 
 i.e., by halving the string its vibration-number is doubled. At two-thirds 
 its original length, it gives a note at an interval of a fifth above that 
 given by its original length ; and genera'.y the reciprocals of the fractions 
 (page 300), representing the relative vibration-numbers of the several notes 
 of a scale, represent the relative lengths of the strings that produce these 
 notes. 
 
 Now, increasing the weight in the pail, the pitch rises, till, when the 
 tension is four pounds, the pitch has risen an octave. Let the ten- 
 sion be the same ; try another string, weighing, for the same length, 
 four times as much ; the pitch is an octave lower than that given by 
 the lighter string. (These experiments wiU not give very accurate 
 results.) 
 
 Those conclusions may be summarized by.saj'ing : The vibra- 
 tion-numbers of strings of the same material vary inversely as 
 their lengths and square roots of their weights, and directly as the 
 square roots of their tension. 
 
 QUESTIONS AND PROBLEMS. 
 
 1. Why does a violinist finger the strings of the violin when 
 playing? 
 
 2. Examine the strings of a piano, and ascertain the different metli- 
 ods by which a wide range of pitch is effected. 
 
 3. How does the length of the string that gives the note F compare 
 with the length of the C-striug below it, other things being equal? 
 
 XLV. OVERTONES AND HARMONICS. 
 
 § 283. Vibration in parts. — Experiment l. Hang up a rubber 
 tube AC (Fig. 219), S" long, filled with sand, fastening both ends. 
 Pluck it near the middle, and it will swing to and fro as a whole (2), at 
 a rate dependent on its length, tension, etc. Hold it fast at B (3), and 
 pluck it at a point half-way between A and B. Both halves are thrown 
 into independent vibrations, and continue so to vibrate for a brief time 
 after the hand is withdrawn from B. Again hold it fast at B, one- 
 third its length above A (4), and pluck it half-way between A and B ; 
 the length BC instantly divides itself at B' into two equal parts, and 
 on withdrawing the hand from B, the whole tube is seen to vibrate 
 in three distinct and equal sections. In a similar manner it may be 
 made to vibrate in four, five, etc., sections. 
 
COMPLEX VIBRATIONS. 
 
 306 
 
 All of the above experiments may be repeated with the same 
 results on the string of the sonometer. By placing paper riders^ 
 along the string, the ventral segments and the nodes can be 
 easily discovered, as those placed near the center of the seg- 
 ments will be thrown off, Kg. 219. 
 while those at the nodes will 
 remain comparatively at rest. 
 
 The sounds coming from 
 a string or other body that 
 vibrates in parts are called 
 overtones. If, as is the case 
 with a string or a column of 
 air in an organ pipe (page 
 321), the vibration-number 
 of the overtone is just two, 
 three, four, etc., times that 
 of the fundamental or lowest 
 tone, the sound is called a 
 harmonic. Many overtones 
 can be produced from a steel 
 bar or a metallic plate, but 
 no harmonics. This distinc- 
 tion is of great importance, 
 for, practically, no musical instruments are of much use unless 
 ,their vibrating parts furnish harmonics. 
 
 § 284. Complex vibrations. — Experiment 1. strike one of 
 the lowest notes of a piano, hold the key down, and immediately 
 apply the tip of the finger to some point of the wire struck, and notice 
 any changes in tone that may occur after applying the finger. Eepeat 
 this at many points along the string. If, after touchiug the string, the 
 fundamental tone continues, it shows that you have touched a node, 
 and consequently have not stopped the vibrations by which this tone 
 is produced ; still you will notice that the sound, though not changed 
 in pitch, is changed somewhat in quality (see page 309). If the fUnda- 
 
 1 Made by folding narrow strips of paper in tb« middle, so that they may be hung on 
 the string. 
 
306 SOUND. 
 
 mental sound disappears, there will most probably be a sound of a 
 higher pitch that will continue, showing that although you have stopped 
 one set of vibrations, there were still other vibrations in the string of 
 a higher vibration-period which you did not stop, and which now be- 
 come audible since the louder fundamental is silenced. 
 
 Experiment 2. Press down the C'-key (middle C) gently, so that 
 it will not sound; and while holding it down, strike the C-wire 
 strongly. In a few seconds release the key, so that its damper will stop 
 the vibrations of the string that was struck, and you will hear a sound 
 which you wUl recognize by its pitch as coming from the C'-wire. 
 Place your finger lightly on the C'-"wire, and you will find that it is 
 indeed vibrating. Press down the right pedal with the foot, ,so as 
 to lift the dampers from all the wires, strike the C-key, and touch 
 with the finger the C'-wire ; it vibrates. Touch the keys next to C, 
 viz., B and D'; they have only a slight forced vibration. Touch G'; 
 it vibrates. 
 
 Now it is evident that the vibrations of the C and G'-wires 
 are sympathetic. But a C-wire vibrating as a whole cannot 
 cause sympathetic vibrations in a C'-wire ; but, if it vibrates in 
 halves, it may. Hence, we conclude that when the C-wire was 
 struck it vibrated, not onlj' as a whole, giving a sound of its 
 own pitch, but also in halves ; and the result of this latter set 
 of vibrations was, that an additional sound was produced by 
 this wire, just an octave higher than the first-mentioned sound. 
 
 Again, the G-'-wire makes 396 vibrations in a second, or 
 three times as many (132) as are made by the C-wire ; hence 
 the latter wire, in addition to its vibrations as a whole and in 
 halves, must have vibrated in thirds, inasmuch as it caused the 
 G'-wire to vibrate. It thus appears that a string may vibrate 
 at the same time as a whole, in halves, thirds, etc., and the 
 result is that a sensation is produced that is compounded of the 
 sensations of several sounds of different pitch. 
 
 Not only do stringed instruments produce compound tones, 
 but no ordinary musical instrument is capable of producing a 
 simple tone, i.e., a sound generated by vibrations of a single 
 period. In other words, when any note of any musical instru- 
 ment is sounded, there is produced, in addition to the primary 
 
CAUSE OP HARMONY AND DISCORD. 307 
 
 tone, a number of other tones in a progressive series, each tone of 
 the series being usuaMy of less intensity than the preceding. The 
 primary or lowest tone of a note is usually sufBciently intense 
 to be the most prominent, and hence is called the fundamental 
 tone. 
 
 § 285. Cause of harmony and discord. — The harmonics 
 in any note are produced successively by two, three, etc., times 
 the number of Adbrations made by its fundamental. Hence, 
 if anj' two notes an octave apart, — for instance, C and C, — 
 are sounded simultaneously, there will result for 
 
 _,! '' ',' '' ■' }■ times the number of vibrations made 
 C, 2, 4, 6, etc., ) 
 
 by the fundamental of C. So that the fundamental of C, and 
 each of its overtones (with the exception of the highest, which 
 are too feeble to affect the general result) coincides with one of 
 the overtones of C. Not only is there perfect agreement among 
 the overtones of two notes an octave apart when sounded to- 
 gether, as when male and female voices unite in singing the 
 same part of a melody, but the richness and vivacity of the 
 sound is much increased thereby. That two notes sounded to- 
 gether may harmonize, it is essential not only that the pitch of 
 their fundamental tones be so widely different that they cannot 
 produce audible beats, but that no beats shall be formed by their 
 overtones, or by an overionS and a fundamental. 
 
 For example, the vibration-numbers of the fundamentals of C and 
 its octave C" are respectively 264 and 628, and the number of beats that 
 they give is 264 in a second. If, instead of C", a note, the vibration- 
 number of whose fundamental is 527, is sounded with C, the number of 
 beats produced by their fundamentals would be 263, and no discord 
 would result therefrom (why?); but there would be one beat per second 
 between the first overtone of C and the fundamental of C", and this 
 would introduce a discord. 
 
 Observe that the relation between the vibration-numbers of 
 the fundamentals of C and C, C and G, C and F, and C, of 
 any diatonic scale and any note in the same scale, can be 
 
308 souKD. 
 
 expressed in terms of small numbers, e.g., 1:2, 2:3, 3:4, etc. 
 (see p. 300). Generally, those notes and only those harmonize 
 whose fundamental tones bear to one another ratios expressed 
 by small numbers; and the smaller the numbers which express 
 the ratios of the rates of vibration, the more perfect is the har- 
 mony of two sounds. 
 
 It follows, from what has been said, that only a limited num- 
 ber of notes can be sounded with any given note assumed as a 
 prime without generating discord. Hence, the musical scale is 
 limited to certain determinate degrees, represented by the eight 
 notes of the so-called musical or diatonic scale. This scale is 
 not the result of any arbitrary or fanciful arrangement, but is 
 determined by the possibility of its notes harmonizing with the 
 prime of the scale, both as regards their fundamental tones and 
 their overtones. 
 
 EXERCISES. 
 
 1. Prepare a table of the series of overtones of C and G respectively, 
 as on page 307, and ascertain what overtones of the two series har- 
 monize. 
 
 2. Arrange the notes of the diatonic scale in a single octave in the 
 order of their rank with reference to their harmonizing with the prime 
 of the scale, on the principle that "the smaller the numbers which 
 express the ratio," etc. 
 
 3. Verify your conclusions as follows : Strike the C-key of a piano, 
 together with each of the seven white keys above it, consecutively, and 
 compare the results of the different pairs with reference to harmony. 
 
ANALYSIS OP SOUNDS. 309 
 
 XLVI. QUALITY OF SOUND. 
 
 Let the same note be sounded with the same intensity, suc- 
 cessively, on a variety of musical instruments, e.g., a violin, 
 comet, clarinet, accordion, jews-harp, etc. ; each instrument 
 will send to your ear the same number of waves, and the waves 
 from each wiU strike the ear with the same force, j'et the ear is 
 able to distinguish a decided difference between the sounds, — 
 a difference that enables us instantly to identify the instruments 
 from which they come. Sounds from instruments of the same 
 kind, but by different makers, usually exhibit decided differences 
 of character. For instance, of two pianos, the sound of one 
 will be described as richer and fuller, or more ringing, or more 
 "wiry," etc., than the other. No two human voices sound 
 exactly aUke. That difference in the character of sounds, not 
 due to pitch or intensity, that enables us to distinguish one 
 from another, is called quality. Two sounds may differ from 
 one another in loudness, pitch, or quality ; they can differ in no 
 other respect. 
 
 Pitch depends on frequency of vibrations, loudness on their 
 amplitude ; on what does quality depend f 
 
 § 286. Analysis of sounds.^ The unaided ear is unable, ex- 
 cept to a very limited extent, to ^ 220 
 distinguish the individual tones 
 that compose a note. Helmholtz 
 arranged a series of resonators 
 consisting of hollow spheres of 
 brass, each having two openings : 
 
 one (A, Pig. 220) large, for the rg^^Hffl^^^^^^^^^^^^^^ 
 receptionof the sound-waves, and B'^^IH^^^B ^^ 
 
 the other (B) small and funnel- 
 shaped, and adapted for insertion 
 into the ear. Each resonator of 
 the series was adapted by its size 
 to resound powerfully to only a 
 single tone of a definite pitch. When any musical sound is produced 
 In front of these resonators, the ear, placed at the orifice of any one, 
 
310 SOUND. 
 
 is able to single out from a collection that overtone, if present, to 
 which alone this resonator is capable of responding. It is found that, 
 when a note is produced on a given instrument, not only is there a great 
 variety of intensity represented by the overtones, but all the possible 
 overtones of the series are by no means present. Which are wanting 
 depends very much, in stringed instruments, upon the point of the 
 string struck. For example, if a string is struck in its middle, no node 
 can be formed at that point ; consequently, the two important overtones 
 produced by 2 and 4 times the number of vibrations of the fundamental 
 will be wanting. Strings of pianos, violins, etc., are generally struck 
 near one of their ends, and thus they are deprived of only some of their 
 higher and feebler overtones. 
 
 § 287. Ssmthesis of sounds. — The sound of a tuning-fork, 
 when its fundamental is regnforced by a suitable resonance-cavity, is 
 very nearly a simple tone. By sounding simultaneously several forks 
 of different but appropriate pitch, and with the requisite relative inten- 
 sities, Helmholtz succeeded in reproducing sounds peculiar to various 
 musical instruments, and even in imitating most of the vowel sounds 
 of the human voice. 
 
 Thus it appears that he has been able to determine, both 
 analytically and sj^nthetically, that the quality of a given sound 
 depends upon what overtones combine with its fundamental, and 
 on their relative intensities; or, we may say more brieflj', upon 
 the form of vibration, since the form must be determined by 
 the character of its components. 
 
METHOD OF BEPKESENTING SOUND VIBRATIONS. 311 
 
 XLVII. COMPOSITION OF SONOROUS VIBRATIONS, AND THE 
 RESULTANT "WAVE-FORMS. 
 
 § 288. Method of representing sound vibrations graph- 
 ically. — It is evident that there must be a particular aerial 
 wave-form corresponding to each compound vibration, other- 
 wise the ear would not be able to appreciate a difference in 
 quality of sounds to which these combination-forms give rise. 
 Every particle of air engaged in transmitting a compound sound 
 is simultaneously acted upon by several sets of vibratory move- 
 ments, and it remains to investigate what its motion will be 
 under their joint influence. 
 
 Fig. 221. 
 
 The light wave-lines AB (Fig. 221) represent typically two 
 series of aerial sound-waves, corresponding respectively to a 
 fundamental and its first overtone. The heavy line represents 
 the form of the joint wave which results from the combination 
 of the two constituents. If we suppose lines perpendicular to the 
 axis, that is, to the dotted line, or line of repose, to be drawn 
 to each point in this line, as ab, cd, eF, etc., they will represent 
 by their varying lengths the displacement of any particle in a 
 vibrating body, or any particle of air traversed by sound-waves, 
 from its normal position. 
 
 The rectangular diagram C D is intended to represent a por- 
 tion of a tranverse section of a body of air traversed by the 
 joint wave represented by the heavy wave-line above. The 
 
312 
 
 SOUND. 
 
 depth of shading in different parts indicates the degree of con- 
 densation at those parts. 
 
 Figure 222 represents wave-lines drawn by an instrument called a 
 vibrograph. The second line represents a sound two octaves above 
 that which the first line represents, and the third line shows the result 
 of the combination of the two sets of vibrations. 
 
 Fi£. 222. 
 
 In an elaborate apparatus called the logograph, a thin membrane of 
 gold-beater's skin carries a marker resembling the point of a stylo- 
 graphic pen. "When a person sings or talks to this membrane, it traces 
 upon paper a graphic representation of the varying air pressure. That 
 is, all the changes in the density of the air, and all the move^ients of a 
 given air-particle during the passage of the sound-waves, are faithfully 
 depicted in a line traced by the marker on a passing paper ; just as the 
 heavy wave-line AB (Fig. 221) may be said to represent the condition 
 of ihe air CI), or of the motion of any particle of it, supposing that 
 a marner were attached to It and a paper drawn beneath it at right 
 angles to the path of its motion. The diagram in Figure 223 shows the 
 result produced by pronouncing the sentence there given at the rate 
 of six syllables in a second. 
 
 § 289. Manometric flames. -^ Apparatus like that shown 
 In Figure 224 may be very easily prepared, and will serve to illustrate in 
 a pleasing manner many facts pertaining to sound. Procure a wooden 
 pill-box or tooth-pick box A, having a capacity of 60 to 100™™. Across 
 the top of the open box stretch tightly a circular piece of gold-beater's 
 
MAKOMETRIC FLAMES. 
 
 313 
 
 skin a, and glue it at its edges so that it may cover the box like the 
 head of a drum. Crowd on the cover, and the box will have two com- 
 partments, 6 and c. Through the bottom of the box, and through the 
 cover, pass glass tubes e and d, opening into the compartments. Also 
 introduce another tube n through the side of the cover. Connaet the 
 last tube by means of a rubber tube with a gas burner. Attach a piece 
 of large-sized rubber tube to the glass tube e, and into the other ex- 
 tremity of the rubber tube introduce the small end of a pasteboard 
 
 Fig. 224. 
 
 cone B. The tube d 
 should be drawn out 
 so as to be able to 
 give a small flame. 
 Place twoithin glass 
 mirrors M, about 
 14™ square, back to 
 back, and secure 
 them by light frames 
 at the top and bot- 
 tom, and in the ccu- 
 ter of each frame 
 insert small rods C 
 and D. 
 
 Light the gasi at 
 the extremity of d, 
 and hold the mirror 
 vertically, and at a 
 short distance from 
 the flame F; an im- 
 age of the flame will 
 appear in the mirror, 
 as represented by A 
 (Kg. 225). , Rotate 
 the mirror, and the 
 flame appears drawn out in a band of light, as shown in B of the same 
 flgure. \^ 
 
 Now sing into the cone B (Fig. 224) , the sound of oo in tool, and 
 waves of air will run down the tube, beat against the membrane a, as 
 against the drum-head of the ear (see § 290), causing it to vibrate, and 
 the membrane in turn acts upon the gas in the compartment c, throwing 
 it into vibration. The result is, that instead of a flame appearing in the 
 rotating mirror as a continuous band of light, it is divided up into a 
 
 1 If gas is not accessible, tlie end of the tribe d may be Inserted in a candle flame, and 
 good results obtained. 
 
314 
 
 SOUND. 
 
 series of tongues of light, as shown in C of Figure 225, each condensa- 
 tion being represented by a tongue, and each rarefaction by a dark 
 interval between the tongues. If a note an octave higher than the last 
 is sung, we obtain, as we should expect, twice as many tongues in the 
 
 Hg. 225. 
 
 
 iiMiMM^hhiMMM 
 
 same space, as shown in D. E represents the result when the two 
 tones are produced simultaneously, and illustrates in a striking manner 
 the effect of interference. (Explain.) F represents the result when 
 the vowel e is sung on the key of C ; and G, when the vowel o is sung 
 on the same key. These are called manometric flames. 
 
THE BAE. 
 
 315 
 
 XLVIII. SOME SOUND-EECEIVING INSTRUMENTS. 
 
 § 290. The ear. — In Figure 226, A represents the external ear- 
 passage; a is a membrane, called the tympanum, a little thicker than 
 gold-beater's skin, stretched across the bottom of the passage, and 
 thus closing the orifice of a cavity 6 in the bones of the skull called the 
 drum; c is a chain of small bones stretching across the drum, and con- 
 necting the tympanum with the thin membranous wall of the vestihule 
 e; ff are a series of semicircular canals opening into the vestibule; 
 
 Fig. 226. 
 
 g Is the opening into another canal in the form of a suail-shell g', 
 hence called the cochlea (this is drawn on a reduced scale) ; d is a tube 
 (the Eustachian tube) connecting the drum with the throat ; and h is 
 the auditory nerve. The vestibule and all the canals opening into it 
 are filled with a transparent liquid which is mainly water. The drum 
 of the ear contains air, and the Eustachian tube forms a means of 
 Ingress and egress of air through the throat. 
 
 Now how does the ear hear? and how is it able to distinguish 
 between the infinite variety of form, rapiditj', and intensity of 
 
316 SOUND. 
 
 aerial sound-waves, so as to interpret correctly the correspond- 
 ing quality, pitch, and loudness of sound ? Sound-waves enter 
 the external ear-passage A as ocean-waves enter the bays of the 
 sea-coast, are reflected inward, and strike the tympanum. The 
 air-particles, beating against this drum-head, impress upon it 
 the precise wave-form that is transmitted to it through the air 
 from the sounding body. The motion received by the drum- 
 head is transmitted^ by the chain of bones to the membranous 
 wall of the vestibule. From the walls of this cavity project 
 into its liquid contents thousands of fine elastic threads or 
 fibres, which we may, for convenience, call bristles. Especially 
 in the spiral passage of the cochlea, as it becomes smaller and 
 smaller, these vibratile bristles become of gradually diminishing 
 length and size (such as the wires of a piano may roughly 
 represent) , and are therefore suited to respond sympathetically 
 to a great variety of vibration-periods. This arrangement is 
 sometimes likened to a harp of three thousand (this being 
 about the number of bristles) strings. The auditory nerve at 
 its extremity is divided into a large number of filaments, like 
 a cord unravelled at its end, and one of these filaments is 
 attached to each bristle. Now, as the sound-waves reach 
 the membranous wall of the vestibule, they set it, and by 
 means of it the liquid contents, into forced vibration, and so 
 through the liquid all the fibres receive an impulse. Those 
 bristles whose vibration-periods correspond with the periods of 
 the constituents forming the compound wave are thrown into 
 sympathetic vibration. The bristles stir the nerve filaments, 
 and the nerve transmits to the brain the impressions received. 
 Just as a piano, when its dampers are raised and a person sings 
 into it, may be said to analyze each sound, and show by the 
 vibrating strings of how many tones it is composed, as well as 
 their respective pitch, and by the amplitude of their vibrations 
 their respective intensities ; so it is thought this wonderful harp of 
 the ear analyzes every complex sound-wave into a series of simple 
 vibrations . Tidings of the disturbances are communicated to the 
 
THE PHONOGRAPH. 
 
 31T 
 
 brain, and there, iu some mysterious manner, these disturbances 
 are interpreted as sound of definite quality, pitch, and intensity. 
 
 § 291. Phonograph. — Figure 227 represents a vertical sec- 
 tion of the Edison phonograph. A metallic cylinder A is rotated bj 
 means of a crank B in the direction indicated by the arrow. On the sur- 
 face of the cylinder is cut a shallow 
 spiral groove running around the 
 cylinder from end to end, like the 
 thread of a screw. A small metallic 
 poiut, or style, projecting from the 
 under side of a thin metallic disk o, 
 which closes one orifice of the mouth- 
 piece C, stands directly over the 
 thread. By a simple device the cyl- 
 inder, when the crank is turned, is 
 made to advance just rapidly enough 
 to allow the groove to keep constantly 
 under the style. The cylinder is cov- 
 ered with tinfoil. The space B represents the space (greatly exag- 
 gerated) between the tinfoil and the bottom of the groove. 
 
 Now, when a person directs his voice toward the mouth-piece, the 
 aerial waves cause the disk o to participate in every motion made by 
 the particles of air as they beat against it, and the motion of the disk 
 is communicated by the style to the tinfoil, pro- 
 ducing thereon impressions or indentations as it 
 passes on the rotating cylinder. The result is that 
 there is left upon the foil an exact representation 
 in relief of every movement made by the style. Some of the indenta- 
 tions are quite perceptible to the naked eye, while others are visible 
 only with the aid of a microscope of high power. Figure 228 repre- 
 sents a piece of the foil as it would appear inverted after the indenta- 
 tions (here greatly exaggerated) have been imprinted upon it. 
 
 The words addressed to the phonograph having been thus impressed 
 upon the foil, the mouth-piece and style are temporarily removed, while 
 the cylinder is brought back to the position it had when the talking 
 began, and then the mouth-piece is replaced. Now, evidently, if the 
 crank is turned in the same direction as before, the style, resting upon 
 the foil beneath, will be made to play up and dowa as it passes over 
 ridges and sinks into depressions ; this will cause the disk to repro- 
 duce the same vibratory movements that caused the ridges and depres- 
 
 mg. 228. 
 
318 SOUND. 
 
 sions In the foil. The vibrations of the disk are communicated to the 
 air, and through the air to the ear ; and thus the words spoken to the 
 apparatus may be, as it were, shaken out into the air again at any 
 subsequent time, even centuries after, accompanied by the exact 
 accents, intonations, and quality of sound of, the original. 
 
 § 292. String telephone. —In the phonograph, the metallic disk 
 serves, as it were, alternately, as an ear and a tongue. If, instead of 
 the same disk being made to do double duty, two disks (or, better, two 
 membranes of gold-beater's skin or bladder) connected by a thread are 
 used, either one of which may serve as a tongue and the other simul- 
 taneously as an ear, conversation may be carried on by means of them 
 J,. 229 B through considerable distances. 
 
 ^^ ^^ Figure 229 represents such an 
 
 '^S ^S arrangement, which constitutes 
 
 the well-known, instructive toy, called the lover's telegraph, though It 
 is more properly a telephone. 
 
 The thread is attached at each extremity to the centers of the mem- 
 branes which cover one orifice of each of the tin speaking-tubes A and 
 B, by passing the thread through the membranes, and tying the knots 
 at the ends. A person speaking into one of the tubes throws its 
 membrane into vibration; these impulses are communicated through 
 the string to the other membrane, which is thus caused to vibrate in 
 unison with the first. If now another person place his ear near the 
 latter membrane, he can hear distinctly the words sj^oken by the first 
 person, though a quarter of a mile distant, while other persons sta- 
 tioned midway between these two hear nothing. 
 
 It seems fair to presume, that if the movements of the hand or 
 of machinery could be rendered sufficiently delicate to imitate these 
 minute movements of the membrane, talking might be accomplished 
 with the hand or machinery ; for talking, after all, is only mechanical 
 motion. 
 
 § 293. Electric telephone. — In this telephone the vibrations 
 of one disk are reproduced in another through the agency of electricity, 
 as explained on page 270. 
 
SOUNDING AIB-COLUMNS. 319 
 
 XLIX. MUSICAL INSTRUMENTS. 
 
 § 294. Musical instruments may be grouped in three classes : 
 (1) Stringed instruments; (2) wind instruments, in which the 
 sound is due to the vibration of columns of air confined in tubes ; 
 (3) instruments in which the vibrator is a membrane or plate. 
 The first class has received its share of attention ; the other two 
 merit a little further consideration. 
 
 §295. Sounding air-columns.— Experiment i. Take four 
 glass tubes, A, B, C, and D, respectively 48, 48, 24, and 12™ long, and 
 about 2.5"™ diameter. Blow gently across one of the ends of each ; C 
 gives a sound an octave higher than A or B, and D an octave higher 
 than C. Close one of the ends of B, C, and D, and repeat the experi- 
 ment, and you wiU find that the notes obtained from these three have 
 still the same relation to one another. Blow across one end of A, 
 which is open at both ends, and across the open end of B ; A gives 
 a note about an octave higher than B. 
 
 These experiments show (1) that the pitch of vibrating air- 
 columns, as well as of strings, varies with the length, and in both 
 stopped^ and open pipes the number of vibrations is inversely pro - 
 portional to the length of the pipe '^ ; (2) that an open pipe gives 
 a note an octave higher than a dosed pipe of the same length. 
 
 Experiment 2. — Blow across the orifice of B as before, gradually 
 increasing the force of the current. It will be found that only the 
 gentle current will give the full musical fundamental tone of the tube, — 
 a little stronger current produces a mere rustling sound ; but when the 
 force of the current reaches a certain limit, an overtone will break 
 forth ; and, on increasing still further the power of the current, a still 
 higher overtone may be reached. 
 
 Figure 230 represents an open organ-pipe provided with a glass 
 window A in one of its sides. A wire hoop B has, stretched over it, a 
 membrane, and the whole is suspended by a thread within the pipe. If 
 the membrane is placed near the upper end, a buzzing sound proceeds 
 
 1 A stopped pipe is one which is closed at one end. 
 
 2 The diameter has the same influence here as in the resonance-jar (p. 293), but we 
 shall neglect it. 
 
320 
 
 SOUND. 
 
 Fig. 230. 
 
 from the membrane when the fundamental of the pipe is sounded ; and 
 sand placed on the membrane will dance up and down in a lively man- 
 ner. On lowering the membrane, the buzzing sound becomes fainter, 
 till, at the middle of the tube, it ceases entirely, and the 
 sand becomes quiet. Lowering the membrane still further, 
 the sound and dancing recommence, and increase as the j 
 lower end is approached. 
 
 It is thus found, that (3) when the fundamental of 
 an open pipe is sounded, its air-column divides itself 
 into two equal vibrating sections, with the antinodes 
 at the extremities of the tube, and a node in the 
 center. 
 
 If the pipe is stopped, there is a node at the 
 stopped end ; if it is open, there is an antinode at the 
 open end ; and in both cases there is an antinode at 
 the end where the wind enters, which is always to a 
 certain extent open. 
 
 lA 
 
 s^^mz^^^i^^^^a^^mi 
 
 mg. 231. A, B, and 
 
 C of Figure 
 231 show 
 respectively 
 the positions 
 of the nodes 
 and anti- ■ 
 
 nodes for the fundamen- 
 tal and first and second 
 overtones of a closed 
 pipe ; and A', B', and C 
 show the positions of 
 the same in an open pipe 
 of the same length. The 
 distance between the 
 dotted lines shows the 
 relative amplitudes of 
 the vibrations of the 
 air-particles at various 
 points along the tube. 
 Now the distance between a node and its nearest antinode is a quarter 
 of a wave-length. Comparing then A and A', it will be seen that the 
 
SOUNDING PLATES. 
 
 321 
 
 wave-length of the fundamental of the closed pipe must be twice the 
 wave-length of the fundamental of the open pipe ; hence the vibration- 
 period of the latter is half that of the former ; consequently the funda- 
 mental of the open pipe must be an octave higher than that of the 
 closed pipe. 
 
 The number of segments into which the length of the air-col- 
 umn is divided, in the three cases of the closed tube, are respec- 
 tively ^, f, and f ; hence the coiTesponding vibration-numbers 
 are as 1:3:5, etc. Hence, (4) in dosed tubes, only those over- 
 tones whose vibration-numbers correspond to the odd multiples of 
 the fundamental are present. 
 
 The.number of segments into which the length of the air-col- 
 umn is divided, in the three cases of the open tube, are respec- 
 tiveij- f , f , and f ; their vibration-numbers are therefore as 
 1:2:3, etc. Hence, (5) in open tubes, the complete series of 
 overtones corresponding to its fundarnental are present. 
 
 Fig. 232. 
 
 § 296. Sounding plates. ^Experiment. Procure at a hard- 
 ware store a perfectly flat piece of sheet brass 2™"! thick and 20™ 
 square. Fasten it at its center to a supporting rod A, Figure 232. 
 Scatter on the plate some fine sand, and draw a resined bow steadily 
 
322 SOUND. 
 
 and firmly over one of its edges near a corner ; and at the same time 
 touch the middle of one of its edges with the tip of the finger; a musi- 
 cal sound will be produced, and the sand will dance up and down, and 
 quickly collect in two rows, extending across the plate at right angles 
 to one another. Draw the bow across the middle of an edge, and touch 
 with a finger one of its corners, and the sand will arrange itself in two 
 diagonal rows (2) across the plate, and the pitch of the note will be a 
 fifth higher. Touch, with the nails of the thumb and forefinger, two 
 points a and & (3) on one edge, and draw the bow across the middle c 
 of the opposite edge, and you will obtain additional rows and a shriller 
 note. 
 
 By varying the position of the points touched and bowed, a 
 great variety of patterns can be obtained, some of them exceed- 
 ingly complicated and beautiful. It will be seen that the effect 
 of touching the plate with a finger is to prevent vibration at that 
 point, and consequently a node is there produced. The whole 
 plate then divides itself up into segments with nodal division 
 Hubs in conformity with the node just formed. The sand rolls 
 away from those parts which are alternately thrown into crests 
 and troughs, to the parts that are at rest. 
 
 § 297. Interference. — Experiment. Provide a tin tube C, 
 rigure 232, 1"> long and S"" in diameter, made in two parts so as to 
 telescope one within the other. The extremity of one of the parts 
 terminates in two slightly smaller branches. Bow the plate, as in the 
 first experiment (1), place the two orifices of the branches over the 
 segments marked with the + signs, and regulate the length of the tube 
 so as to reenforce the note given by the plate, and set the plate in 
 vibration. Now turn the tube around, so that one orifice may be over 
 a 4- segment, and the other over a —segment; the sound due to reso- 
 nance entirely ceases. It thus appears that the two segments marked 
 -I- pass through the same phases together ; likewise the phases of 
 —segments correspond with one another; i.e., when one -|-segment is 
 bent upward, the other is bent upward, and at the same time the two 
 —segments are bent downward ; for, when the two orifices of the tube 
 are placed over two -1-segments or two —segments, two condensa- 
 tions followed by two rarefactions pass up these branches and unite 
 at their junction to produce a loud sound ; but when one of the orifices 
 is over a -|-segment and the other over a -segment, a condensation 
 
VOCAIi ORGANS. 323 
 
 passes up one branch at the same time that a rarefaction passes up the 
 other, and the two destroy one another when they come together; i.e., 
 the two sound-waves combine to produce silence. 
 
 § 298. Bells. — A bell or goblet is subject to the same laws 
 of vibration as a plate. 
 
 Experiment. — Nearly flU a goblet with water, strew upon the sur- 
 face lycopodium powder, and draw a resined bow gently across the edge 
 of the glass. The surface of the water wUl become rippled with wave- 
 lets radiating from four points 90° apart, corresponding to the cen- 
 ters of four ventral segments into which the bell is divided, and the 
 powder will collect in lines proceeding from the nodal points of the 
 bell. By touching the proper points of a bell or glass with a finger- 
 nail, it may be made to divide itself, like a plate, into 6, 8, 10, etc., 
 (always an even number) vibrating parts. 
 
 § 299. Vocal organs. — It is diflacult to say which is more 
 to be admired, — the wonderful capabilities of the human voice 
 or the extreme simplicity of the means by which it is produced. 
 The organ of the A'oice is a reed instrument situated at the top 
 of the windpipe or trachea. A pair of Fig. 233. 
 
 elastic bands a a, Figure 233, called the 
 vocal chords, is stretched across the top 
 of the windpipe. The air-passage 6, 
 between these chords, is open while a 
 person is breathing ; but when he speaks 
 or sings they are brought together so 
 as to form a narrow, slit-like opening, 
 thus forming a sort of double reed, 
 which is made to vibrate, when air is 
 forced from the lungs through the nar- 
 row passage, somewhat like the little 
 tongue of a toy trumpet. The sounds are grave or high accord- 
 ing to the tension of the chords, which is regulated by muscu- 
 lar action. The cavities of the mouth and the nasal passages 
 form a compound resonance-tube. This tube adapts itself, by 
 
324 SOUND. 
 
 its varying width and length, to the pitch of the note produced 
 by the vocal chords. Place a finger on the protuberance of 
 the throat called the Adam's apple, and sing a low note ; then 
 sing a high note, and you will observe that the protuberance rises 
 in the latter case, thus shortening the distance between the vocal 
 chords and the lips. Set a tuning-fork in vibration, open the 
 mouth as if about to sing the corresponding note, place the 
 fork in front of it, and the cavity of the mouth will resound to 
 the note of the fork, but will cease to do so when the mouth 
 adapts itself to the production of some other note. The differ- 
 ent qualities of the different vowel sounds are produced by the 
 varying form of the resonating mouth-cavity, the pitch of the 
 fundamentals given by the vocal chords remaining the same. 
 This constitutes articulation. 
 
CHAPTER VI. 
 
 RADIANT ENERGY. -LIGHT. 
 
 L. INTRODUCTION. 
 
 § 300. Light a form of energy. — Exposed to the sun, the 
 skin is warmed, and thus the sense of touch is affected ; it is 
 illuminated, and thereby the sense of sight is affected; it is 
 tanned, and thereby its chemical condition is changed. It is evi- 
 dent that we receive something which must come to us from the 
 sun. To the sense of touch it appears to be heat ; to the eye 
 it is light ; to certain substances it is a power to produce chemi- 
 cal changes. But what is it that we receive 
 from the sun ? 
 
 Fig. 234. 
 
 Experiment. — Blacken one-half of one side of a 
 slip of glass with candle-smoke. With a convex 
 lens, sometimes called a " burning-glass," converge 
 the sun's light upon the blackened portion so as to 
 produce a small luminous spot on the black surface. 
 This spot quickly becomes very hot, but the lens 
 meantime remains comparatively cold. Move the 
 luminous spot to the unblackened portion of the 
 glass. The spot becomes only slightly heated. 
 Place a piece of paper behind and in contact with 
 the glass, and it quickly burns. 
 
 Whether we receive heat from the sun or 
 not, it is evident that we receive something 
 that can be converted into heat. 
 
 Figure 234 represents an instrument called 
 a radiometer. The moving part is a small vane resting on the 
 point of a needle. It is so nicely poised on this pivot that it 
 
326 BADIANT ENBKGY. — LIGHT. 
 
 rotates with the greatest freedom. To the extremities of each 
 of the four arms of the vane are attached disks of aluminum 
 which are white on one side and black on the other. The whole 
 is enclosed in a glass bulb from which the air is exhausted till 
 less than x^v of t^^ original quantity is left. If the instrument 
 is exposed to the sun's light, or even to the light of a candle, 
 the wheel wiU rotate with the unblackened faces in advance. 
 
 In just what manner it is caused to rotate does not concern 
 us ; but the fact that it does rotate, and that it is caused to 
 rotate directly or indirectly by something that comes from the 
 sun or the candle, is pertinent to the question before us. When- 
 ever a body is caused to move or increase its rate of motion, 
 energy must be imparted to it ; hence energy must be imparted 
 to the radiometer- vane by the sun or candle. 
 
 Bell, the inventor of the telephone, has succeeded in produc- 
 ing musical sounds by the action of sun-light and other intense 
 lights. But sound always originates in motion, and motion 
 springs only from some form of energy. So, then, that which we 
 receive from the sun, whether it affects the sense of touch and is 
 called heat, or the eye and is called light, or produces chemical 
 changes and is called chemism, is in reality some form of energy. 
 
 § 301. Ether the medium of motion. — If light is motion, 
 what moves ? Our atmosphere is but a thin investment of the 
 earth, while the great space that separates us from the sun con- 
 tains no air or other known substance. But empty space can 
 neither receive nor communicate motion. It is assumed — it is 
 necessary to assume — that there is some medium filling the 
 interplanetary space, in fact, filling all otherwise unoccupied 
 space (i.e., where matter is not, ether is), by which motion 
 can be communicated from one point in the otherwise empty 
 space to another. This medium has received the name of ether. 
 Ether is supposed to penetrate even among the molecules of 
 liquid and solid matter, and thus surrounds every molecule of 
 matter in the universe, as the atmosphere surrounds the earth. 
 
TJNDTTLATORY THEORY OP LIGHT. 327 
 
 No vacuum of this medium cau be obtained ; an attempt to 
 pump it out of a space would be like trying to pump water 
 with a sieve for a piston. We cannot see, hear, feel, taste, 
 smell, weigh, nor measure it. "What evidence, then, have we 
 that it exists ? You believe that a horse can see ; you have no 
 absolute knowledge of the fact. But you reason thus : he be- 
 haves as if he could see ; in other words, you are able to account 
 for his actions on the hypothesis that he can see, and on no 
 other. Phenomena occur just as they would occur if all space 
 were filled with an ethereal medium capable of transmitting 
 motion, and we can account for these phenomena on no other 
 hypothesis ; hence our belief in the existence of the medium. 
 
 The transmission of energy through the medium of ether is 
 called radiation; energy so transmitted is called radiant energy, 
 and the body emitting energy in this manner is called a radiator. 
 Sound is another form of radiant energy transmitted through 
 solid, liquid, or gaseous media. 
 
 § 302. Undulatory theory of light. — Is motion commu- 
 nicated by a transfer of a medium or by a transfer of vibrations, 
 i.e., by undulations ? All evidence points to one conclusion: 
 that we receive energy from the sun in the form of vibrations or 
 wave-action ; that these vibrations, inaudible to our ears, cause 
 through the eye the sensation of sight, and through the hand the 
 sensation of warmth. This is known as the undulatory theory of 
 light. To learn what the special evidences of the correctness 
 of this theory are, the pupU must wait for further development 
 of our subject ; but it should be borne in mind that the strongest 
 proof of the correctness of any theory is its exclusive competence 
 to explain phenomena. Light is vibration that may be appre- 
 ciated by the organ of sight. 
 
 § 303. Light itself invisible. -^ Darken a room, and ad- 
 mit a sunbeam through a small naQ- or key-hole. You can 
 trace its path through the room only by particles of dust float- 
 ing in the room. JBut if the air in a certain space is cleansed of 
 
328 
 
 RADIANT ENERGY. — LIGHT. 
 
 Fig. 235. 
 
 dust, the path of a sunbeam through this space Trill -be totally 
 dark. If the eye is placed in its path, or any object upon which 
 it may strike, you become aware of its presence, not by seeing 
 the light, but by seeing the object which sends you the light. 
 
 § 304. Light travels in straight lines. — The path of the 
 light admitted mto a darkened room through a small aperture, 
 
 as indicated by the Uluminated dust, 
 is perfectly straight. An object is 
 seen by means of light it sends to the 
 eye. A small object placed in a straight 
 Ime between the eye and a luminous 
 point may intercept the light in that 
 path, and the point become invisible. 
 Hence, we cannot see around a cor- 
 ner, or through a tube bent so that a 
 straight string cannot be drawn through 
 its bore. 
 
 § 305. Ray, beam, pencil. — Any 
 
 line RR, Figure 235, which pierces the 
 surface of a wave of light ab perpen- 
 dicularly is called a ray of light. It 
 is an expression for the direction in 
 which motion is propagated, and along 
 which the successive effects of light occur. If the wave-surface 
 a'b' is a plane, the rays R R' are parallel, and a collection of 
 such rays is called a beam of light. If the wave-surface a"b" 
 is spherical or concave, the rays R" R" have a common point at 
 the center of curvature, and a collection of such rays is called 
 a pencil of light. 
 
 § 306. Transparent, translucent, and opaque bodies. — 
 Bodies are transparent, translucent, or opaque, according to the 
 manner in which they act upon the luminiferous waves which 
 pass through them. Generally speaking, those objects are 
 
LUMINOUS AND ILLUMINATED OBJECTS. 
 
 329 
 
 transparent that allow other objects to be seen through them 
 distinctly ; e.g., air, glass, and water. Those objects are trans- 
 lucent that allow light to pass, but in such a scattered condition 
 that objects are not seen distinctly through them ; e.g. , fog, 
 ground glass, and oiled paper. Those objects are opaque that 
 apparently cut off aU the light and prevent objects from being 
 seen through them. 
 
 § 307. Luminous and illuminated objects. — Some bodies 
 are seen by means of light, which they generate and emit ; e.g., 
 the sun, a candle flame, and -.i. "live coal"; they are called 
 luminous bodies. Other bodies are seen only by means of light 
 which they receive from luminous ones, and when thus rendered 
 visible, are said to be illuminated; e.g., the moon, a man, a 
 cloud, and a ' ' dead " coal. 
 
 Mg. 236. 
 
 § 308. Every point of a luminous body an independent 
 source of light. — Place a candle flame in the center of a 
 darkened room ; every wall and 
 every point of each wall becomes 
 illuminated. Place your eye in 
 any part of the room, i.e., in any 
 direction from the flame ; it is able 
 to see not only the flame, but 
 every point of the flame ; hence 
 every point of the flame must emit 
 light in every direction. Every 
 point of a luminous body is an in- 
 dependent source of light and emits 
 light in every direction. Such a 
 point is called a luminous point. In Figure 236 there are 
 represented a few of the infinite number of pencils of light 
 emitted by three luminous points of a candle flame. Every point 
 of an illuminated object ab receives light from every luminous 
 point. 
 
330 
 
 KADIANT ENERGY. LIGHT. 
 
 § 309. Images formed through small apertures.— Ex- 
 periment. — Cut a hole about 8=™ square in one side of a box; cover 
 the hole with tin-foil, and prick a hole in the foil with a pin. Place the 
 box in a darkened room, and a candle flame in the box near to the pin- 
 hole. Hold an oiled-paper screen before the hole in the foil; an 
 inverted image of the candle flame will appear upon the translucent 
 paper. An image is a kind of picture of an object. 
 
 If light from objects illuminated by the sun — e.g., trees, 
 houses, clouds, or even an entire landscape — is allowed to pass 
 through a small aperture in a window shutter and strike a 
 white screen, or a white wall in a dark room, rays carrying with 
 them the color of the points from which they issue will imprint 
 their own color on the screen, and inverted images of the objects 
 in their true colors will appear upon it. The cause of these phe- 
 j^ JJ3J nomena is easily understood. 
 
 "When no screen intervenes 
 between the candle and the 
 screen A, Figure 237, every 
 point of the screen receives 
 light from every point of 
 the candle ; consequently, on 
 every point on A, images of 
 the infinite number of points 
 of the candle are formed. 
 The result of the confusion of images is equivalent to no image. 
 But let the screen B, containing a small hole, be interposed ; then, 
 since light travels only in straight lines, the point Y' can only 
 . receive an image of the point Y, the point Z' only of the point 
 Z, and so for intermediate points ; hence a distinct image of the 
 object must be formed on fac screen A. TTiat an image may be 
 distinct, the rays from different points of the object must not mix 
 on the image, but all rays from each point on the object must 
 be carried to its own point on the image. 
 
SHADOWS. 331 
 
 QUESTIONS. 
 
 1. Why are images, formed through apertures, Inverted? 
 
 2. Why Is the size of the image dependent on the distance of the 
 screen from the aperture? 
 
 3. Obtain the dimensions, respectively, of an object and its image, 
 and their respective distances from the intervening screen, and ascer- 
 tain the law that determines in all cases the size of an image. 
 
 4. Why does an image become dimmer as it becomes larger? 
 
 6. Why do we not imprint an image of our person on every object 
 in front of which we stand? 
 
 6. Can rays of light cross one another without interfering? 
 
 7. What fact does a gunner recognize in taking sight? 
 
 § 310. Shadows. — Experiment 1. Procure two pieces of tin 
 or card-board, one 18™ square, the other 3<»" square. Place the first 
 between a white wall and a candle flame in a darkened room. The 
 opaque tin intercepts the light that strikes it, and thereby excludes 
 light from a space behind It. 
 
 This space is called a shadow. That portion of the surface 
 of the wall that is darkened is a section of the shadow, and 
 represents the form of a section of the body that intercepts the 
 light. A section of a shadow is frequenth' for convenience 
 called a shadow. Notice that the shado-w is made up of two 
 distinct parts, — a dark center bordered on all sides by a much 
 lighter fringe. The dark center is called the umbra, and th^ 
 lighter envelope is called the penumbra. 
 
 Experiment 2. Carry the tin nearer the wall, and notice that th^ 
 penumbra gradually disappears and the outline of the umbra becom^^ 
 more distinct. Employ two candle flames, a little distance apart, and 
 notice that two shadows are produced. Move the tin toward the wall, 
 and the two shadows approach one another, then touch, and finally over- 
 lap. Notice that where they overlap the shadow is deepest. This part 
 gets no light from either flame and is the umbra ; while the remaining 
 portion gets light from one or the other and is the penumbra. 
 
 Just so the umbra of every shadow is the part that gets no 
 light from a luminous body, while the p^umbra is the part 
 
332 
 
 BADIANT ENBKGY. 
 
 ■ LIGHT. 
 
 that gets light from some portion of the body, but not from 
 the whole. 
 
 Experiment 3. Repeat the above experiments, employing the 
 smaller piece of tin, and note all differences in phenomena that occur. 
 
 Hold a hair in the sunlight, about a 
 ^s- ^^- centimeter in front of a fly-leaf of this 
 
 n - ^' ' book, and observe the shadow cast by 
 
 the hair. Then gradually increase the 
 distance between the hair and the leaf, 
 and note the change of phenomena. If 
 the source of light were a single luminous point, as A, Figure 238, the 
 shadow of an opaque body B would be of infinite length, and would con- 
 sist only of an umbra. But, if the source of light has a sensible size, 
 the opaque body will intercept just as many separate pencils of light as 
 there are luminous points, and consequently will cast an equal number 
 of independent shadows. 
 
 Kb- 239. 
 
 Let AB, Figure 239, represent a luminous body, and CD an opaque 
 body. The pencil from the luminous point A will be intercepted be- 
 tween the lines C F and D G, and the pencil from B will be intercepted 
 between the lines CE and DF. Hence, the light will be wholly ex- 
 cluded only from the space between the lines CF and DF, which 
 enclose the umbra. The enveloping penumbra, a section of which is 
 included between the lines CE and CP, and between DF and DG, 
 receives light from certain points of the luminous body, but not from all. 
 
LAW OP INVERSE SQUARES. 333 
 
 QUESTIONS. 
 
 1. Explain the umbra and penumbra cast by the opaque body H I, 
 Figure 239. 
 
 2. When will a transverse section of an umbra of an opaque body be 
 larger than the object Itself? 
 
 3. When has an umbra a limited length? 
 
 4. What Is the shape of the umbra cast by the sphere C D, Figure 239 ? 
 
 5. If C D should become the luminous body, and A B a non-luminous 
 opaque body, what changes would occur In the umbra and the shadow 
 cast? 
 
 6. Why Is It difficult to determine the exact point where the umbra 
 of a church-steeple terminates on the ground? 
 
 7. What is the shape of a section of a shadow cast by a circular disk 
 placed obliquely between a luminous body and a screen? What Is Its 
 shape when the disk Is placed edgewise? 
 
 8. The section of the earth's umbra on the moon in an eclipse always 
 has a circular outline. What does this show respecting the shape of 
 the earth? 
 
 LI. PHOTOMETRY. 
 
 § 311. Law of inverse squares. — Experiment l. Arrange 
 apparatus as follows : Lay a silver half-dollar on the center of a circu- 
 lar piece of stiff, white, unglazed paper of 15""" diameter, and rub the 
 entire surface, except the portion covered by the coin, with a sperm or 
 a tallow candle. Hold the paper In a warm oven for a minute. When 
 the paper is placed between two lights in a darkened room, the un- 
 greased spot will appear light on a dark background on the side which 
 receives the more light, and 
 
 dark on a light background *" 
 
 on the side which receives 
 less light ; but the spot be- 
 comes nearly Invisible 
 when both sides are equal- 
 ly Illuminated. Draw a 
 straight chalk line across 
 a table, and place at right 
 angles to this line a row of four lighted candles, and on the same 
 line, at a distance, a single lighted candle. Half-way between this 
 candle and the row of candles place the prepared paper, as In Figure 
 240. It is evident that one side of the paper receives four times the 
 
334 RADIANT ENEKGY, — LIGHT. 
 
 light that the other does. Move the row of lights slowly away from 
 the paper, or move the single light toward the paper, and a point will 
 be found in either case where the spot wiU nearly disappear. When 
 this occurs it will be found that the row of lights is twice as far from 
 the paper as the single light. The paper now receives the same amount 
 of light from the single light as from the four lights. 
 
 Thus, by doubling the distance, the intensity of illumination 
 is diminished four-fold. In a similar manner it may be shown 
 that at three times the distance it takes nine lights to be equiv- 
 alent to one light. Hence, the intensity of light diminishes as 
 the square of the distance increases. This is called the law of 
 inverse squares. 
 
 £xperiineiit 2. Introduce the paper disk, as above, between a 
 candle light and a kerosene light or a gas flame, and so regulate the 
 distance that the central spot will disappear, and calculate the relative 
 intensities of the two lights in accordance with the law of Inverse 
 squares. 
 
 Apparatus arranged for this purpose is called a photometer. 
 "The candle power, which is the unit of light generally em- 
 ploj'ed in photometry, is the amount of light given by a sperm 
 candle weighing one-sixth of a pound, and burning one hundred 
 and twenty grains an hour." The relative brightness of the com- 
 mon sources of light are approximately as follows ' : — 
 
 Sunlight at the sun's surface 190,000 candle power. 
 
 Most powerful electric arc 55,900 " " 
 
 Most powerful calcium light 1,300 " " 
 
 Light of ordinary gas-burner 12 to 16 " " 
 
 Standard candle 1 " " 
 
 " The total quantity of light emitted by the sun is equivalent 
 to the light of 6,300,000,000,000,000,000,000,000,000 (six thou- 
 sand three hundred billions of billions) candles." Of this enor- 
 mous quantity of light the earth intercepts an extremely small 
 fraction. 
 
 » C. A. Young. 
 
VISUAi ANGLE. 335 
 
 QUESTIONS. 
 
 1. Suppose that a lighted candle is placed in the center of each of 
 three cubical rooms respectively 10, 20, and 30 feet on a side ; would a 
 single wall of the first room receive more or less light than a single 
 wall of either of the other rooms? 
 
 3. Would one square foot of a. wall of the third room receive as 
 much light as would be received by one square foot of a wall of the 
 first room? If not, what difference would there be, and why the differ- 
 ence? 
 
 3. If a board 10™ square is placed 25=™ from a candle flame, the area 
 of the shadow of the board cast on a screen 76"=™ distant from the 
 caudle will be how many times the area of the board? Then the light 
 intercepted by the board will illuminate how much of the surface of 
 the screen If the board is withdrawn? 
 
 4. Give a reason for the law of Inverse Squares. 
 
 5. To what besides light has this law been found applicable? 
 
 6. The two sides of a paper disk are illuminated equally by a candle 
 flame 50=™ distant on one side and a gas flame 200=™ distant on the other 
 side ; compare the intensities of the two lights at equal distances from 
 their sources. 
 
 Fig. 241. 
 
 LII. VISUAL ANGLE, ETC. 
 
 §312. Visual angle. — Experiment. Prick a pin-hole in a 
 card, place an eye near the hole, and look at a pin about 20™" distant, 
 Then bring the pin slowly toward the eye, and the dimensions of the 
 pin will appear to increase as the distance diminishes. 
 
 Why is this ? We see an object by means of its image formed 
 on the retina of the eye, and its apparent magnitude is deter- 
 mined by the extent of the retina covered by its image. Eays 
 
336 RADIANT ENERGY. — LIGHT. 
 
 proceeding from opposite extremities of an object, as AB, Fig- 
 ure 241, meet and cross one another in the window of the eye, 
 usually called the pupil. Now, as the distance between the 
 points of the blades of a pair of scissors depends upon the 
 angle that the handles form with one another, so the size of the 
 image formed on the retina depends upon the size of the angle, 
 called the visual angle, formed by these rays as they enter the 
 eye. But the size of the visual angle diminishes as the distance 
 of the object from the eye increases, as shown in the diagram ; 
 e.g., at twice the distance the angle is one-half as great, at 
 three times the distance the angle is one-third as great, and so 
 on. Hence, the apparent size of an object diminishes as its dis- 
 tance from the eye increases. 
 
 QUESTIONS. 
 
 1. Why do the rails of a raih-oad track appear to converge as their 
 distance from the observer increases? 
 
 2. Why, in looking through a long hall or tunnel, do the floor and 
 the ceUing appear to approach one another? 
 
 3. Why do parallel lines, retreating from the eye, appear to converge? 
 
 4. Why can a book, held in front of the face, entirely conceal from 
 view a house? 
 
 § 313. Methods of estimating size. — Let a man stand beside 
 a boy of half his hight, and to an observer, twenty feet distant, the for- 
 mer will subtend a visual angle twice as great as the latter, and will 
 appear twice as tall. Then, let the man move back twenty feet farther 
 from the observer, and he and the boy will then subtend equal angles, 
 but they will not appear to be of equal hight, nor will the man's hight 
 appear diminished in a very perceptible degree. The sun and the moon 
 are about 4,000 miles nearer to us when they are in the zenith than when 
 near the horizon, but in the latter case they appear much larger. 
 It makes a great difference in the variation of the apparent size of a 
 pin, as it moved to and from the eye, whether it is seen through a 
 pin-hole in a card or whether the card is removed ; and, again, whether 
 it is seen with one eye or both eyes. The fact is, that in estimating 
 the size of objects, our judgment is influenced by many other things 
 
VELOCITY or LIGHT. 337 
 
 besides the visual angles which they subtend. Our knowledge of the 
 real size of an object, also of the fact that the tendency of an increase 
 in distance is to diminish the apparent size of a body, and that an ob- 
 ject does not become shorter as it moves away from us, does much 
 toward correcting an estimate based on the size of the visual angle. 
 Our estimate of the size of objects whose size is unknown is influ- 
 enced much by comparison with objects in their vicinity whose size 
 is known, as in the case of the sun and the moon when they are in 
 range with other objects in the horizon, and in the case of the pin, 
 Whether it is seen alone through a hole or in conjunction with other 
 objects. Again, when we look at an object with both eyes we are 
 obliged to turn the eyes inward or outward, according as an object 
 approaches or recedes, ia order that light from the object may continue 
 to enter the eye. The effort necessary to adapt the position of the eyes, 
 so as to see objects at different distances, helps in forming a correct 
 estimate of their size. Hence, the pin seen by both eyes does not 
 appear to undergo so great a change in size, as it moves to and from 
 the observer, as when seen by one eye. We are not at the time con- 
 scious of going through the processes of reasoning indicated above, 
 because it has become a matter of habit with us. If a man born blind 
 suddenly acquires the power of seeing, he at first makes ludicrous 
 mistakes in judging of size and distance of objects, because he has not 
 acquired these methods of reasoning. An infant will reach out its 
 hands to seize a bird that may be flying many yards above. 
 
 § 314. Velocity of Light. — "We must believe that light- 
 waves require time to traverse space, although their speed is 
 so gi-eat that no ordinary means can measure the time, it is 
 so short. But the distances of the heavenly bodies are so great 
 that the time that their light requires to reach us may be easily 
 measured. 
 
 To illustrate one method, let J, in Figure 242, represent a clock 
 striking a single stroke every hour, and the circle E E' a road around 
 which a person W travels ; the length of the straight line B E' is four 
 miles. So long as W remains at E, the strokes come exactly once an 
 hour by his watch ; but, as he moves away, the intervals become slightly 
 longer, so that, however long he is on the road, if the watch and clock 
 run accurately, when he has reached E' the sound of the bell reaches 
 him about twenty seconds after the hour. As he continues back to E, 
 
33& 
 
 RADIANT ENEEGY. — LIGHT. 
 
 Fig. 242. 
 
 the sounds come more and more nearly on time, so that at B they are 
 
 just at the proper time. * Similarly, at regular Intervals in the heavens 
 
 an eclipse of one 
 of Jupiter's moons 
 takes place ; the 
 average interval 
 being known, add 
 it to the time at 
 which an eclipse 
 is observed when 
 the earth is near 
 E , and thus we may 
 predict the times 
 of an eclipse for 
 years ahead. All 
 the eclipses, ex- 
 cept when the 
 earth is at E, are 
 observed to be a 
 little behind the 
 predicted times; at 
 E' as much as 16^ 
 
 minutes. But at E' the light has had to travel 184,000,000 miles 
 
 farther to reach the eye than at E. 
 
 Hence, light must travel at the rate of 184,000,000 -5-(16iX 60) 
 = about 186,000 miles (about 300,000"™) in a second. 
 
 Sound creeps along at the comparatively slow pace of about 
 one-fifth of a mile (or -J"™) per second. The former is the ve- 
 locity with which waves in ether are transmitted ; the latter, the 
 velocity with which waves in air move forward. This great 
 difference can be accounted for only on the supposition that the 
 rarity and elasticity of ether are enormously greater than that of 
 air (see page 284). 
 
LAW OP REFLECTION. 
 
 839 
 
 Fig. 243. 
 
 LIIJ. REFLECTION OF LIGHT. 
 
 § 315. Law of reflection. — Arrange apparatus as follows: 
 A B, Figure 243, is a board 12™ square, having a mirror 8™ square 
 fastened to one of its sides. E is a rod 24""" long inserted in the board 
 close to the middle of one of the edges of the mirror, and perpendicu- 
 lar to the surface of the board. D F is an arc of pasteboard supported 
 by the rod. The outer edge of the arc is described by a radius equal 
 to the length of the rod, and is divided into degrees. Cover the open- 
 ing orifice of the tube C of the porte lumiere ' with a circular tin pierced 
 in its center by a circular hole m, 7°™ in diameter, and admit a slender 
 beam of sunlight mc. 
 
 Experiment. Place the mirror so that the beam of light may strike 
 it obliquely, and just graze the arc so as to illuminate it at one point. 
 A beam of light as it approaches an object is termed an incident beam. 
 The beam, unable to pass through the opaque silvered surface of the 
 mirror, is reflected by this surface obliquely, but on the opposite side 
 of the perpendicular oc. A beam of light after reflection is termed a 
 reflected beam. The, spot of light 
 on the arc produced by the re- 
 flected beam will be found to be 
 the same number of degrees dis- 
 tant from the perpendicular as the 
 spot produced by the incident 
 beam. Hence, the angle nco, called 
 the angle of reflection, is equal to 
 the angle mco, called the angle of 
 incidence. Incline the mirror so 
 that the Incident beam may strike 
 the mirror more or less obliquely, 
 and the reflected beam -will leave 
 it always at an equal angle. Ren- 
 der the path of the incident and 
 reflected beam luminous by introducing a cloud of smoke from touch 
 
 * Some means of Intrpduciiig a beam of stmlight into a darkened room is indispensable 
 In experimenting with ligl^t. The experiments on this subject Tvill be given on the suppo- 
 (lition that the pupil is provided with means of accomplishing this. Directions for con- 
 structing apparatus suited to this purpose, usually called a porte lumiire, may be found 
 In Mayer and Barnard's little book on "Light," published by D. Appleton & Co., New 
 York, and in Dolbear's " Art of Projection," published by Lee & Shepherd, Boston. A 
 description of an inexpensive apparatus devised by the author maybe found in Section H 
 of the Appendix. 
 
340 RADIANT ENBKGY. — LIGHT. 
 
 paper, and the angles formed with the perpendicular will be quite 
 apparent. Light, as well as sound, conforms to the general law of reflec- 
 tion. (See page 118.) 
 
 § 316. Diffused light. — Experiment l. Introduce a small beam 
 of light into a darkened room, by means of a porte lumiere, and place 
 in its path a mirror. The light is reflected in a definite direction. If 
 the eye is placed so as to receive the reflected light, it will see, not the 
 mirror, but the image of the sun, and the light will be painfully intense. 
 Substitute for the mirror a piece of unglazed paper. The light is 
 not reflected by the paper in any definite direction, but is scattered in 
 every direction, illuminating objects in the vicinity and rendering them 
 visible. Looking at the paper, you see, not an image of the sun, but 
 the paper, and you may see it equally well in all directions. 
 
 Fig. 244. 
 
 The duU surface of the paper receives light in a definite direc- 
 tion, but reflects it in every direction ; in other words, it scatters 
 or diffuses the light. The diflerence in the phenomena in the 
 two cases is caused by the difference in the smoothness of the 
 two reflecting surfaces. AB, Figure 244, represents a smooth 
 surface, like that of glass, which reflects nearly all the rays of 
 light in the same direction, because nearly all the points of 
 reflection are in the same .plane. CD represents a surface of 
 paper having the roughness of its surface greatly exaggerated. 
 The various points of reflection are turned in every possible direc- 
 tion ; consequently, light is reflected in every direction. Thus, 
 the dull surfaces of various objects around us reflect light in all 
 directions, and are consequently visible from every side. Objects 
 rendered visible by reflected light are said to be illuminated. 
 
 By means of regularly reflected light we see images of objects in 
 mirrors, but only in definite directions ; by means- of diflFtised light we 
 see the mirror itself in every direction. Whethet we see the image of 
 the source of the light (the eye being situated so as to receive the 
 
REFLBCTIOK PROM PLANE MIEROBS. 341 
 
 regularly reflected light), or the object on -which the light falls, or both 
 at the same time, depends largely upon the degree of smoothness pos- 
 sessed by the object that reflects the light. Smopth surfaces are 
 called mirrors. Polished metals are the best mirrors. Surfaces of 
 liquids at rest are excellent mirrors. It is sometimes difficult to see a 
 smooth surface of a pond surrounded by trees and overhung by clouds, 
 as the eye is occupied by the reflected images of these objects : but a 
 faint breath of wind, slightly rippling the surface, ■will reveal the water. 
 Experiment 2. Place a basin of water on a table, and hold a candle 
 flame so that its rays may form a large angle with the liquid surface, 
 and notice the brightness of its image. Lower the candle and the eye 
 so that the incident and reflected rays, as nearly as possible, graze the 
 surface of the liquid, and notice how much brighter the image be- 
 comes. Notice how much brighter the varnished surfaces of furni- 
 ture appear when viewed very obliquely, than when seen by light 
 reflected less obliquely. Also notice how much more dazzling is the 
 light reflected from the surface of a pond just before the sun sets, 
 than at noon when the sun is overhead. This is due in part to our 
 being at a suitable position to observe it. 
 
 The amount of light reflected from a smooth surface increases 
 rapidly as the angle of incidence increases. Thus, at a perpen- 
 dicular incidence, out of 1,000 parts of light that strike a sur- 
 face of water, only 18 parts are reflected ; at 40°, 22 parts are 
 reflected ; at 80°, 333 parts ; and at 89^°, 721 parts. The above 
 is not even approximately true of metals or substances having 
 metallic reflection, such as galena, etc. 
 
 § 317. Reflection from plane mirrors ; virtual images. — 
 M M (Pig. 245) represents a plane mirror, and A B a pencil of diver- 
 gent rays proceeding from the point A of an object A H. Erecting 
 perpendiculars at the points of incidence, or the points where these 
 rays strike the mirror, and making the angles of reflection equal to 
 the angles of incidence, the paths BC and EC of the reflected rays 
 are found. 
 
 It appears that divergent incident rays remain divergent after 
 reflection from a plane mirror. In like manner construct a 
 diagram, and show that parallel incident rays are parallel after 
 reflection. Construct another diagram, and show that convergent 
 
342 
 
 RADIANT ENERGY. LIGHT. 
 
 Kg. 845. 
 
 incident rays are convergent after reflection. To an eye placed 
 at C, the points from which the rays appear to come are of course 
 in the direction of the rays as they 
 enter the eye. These points may be 
 found by continuing the rays CB and 
 CE behind the mirror, till they meet 
 at the points D and N. Every point 
 of the object AH sends out its pen- 
 cils of rays, and those that strike 
 the mirror at a suitable angle to be 
 reflected to the eye, produce on the 
 retina of the eye an image of that 
 point, and the point from which the 
 light appears to emanate is found, as 
 previously described. Thue, the pencils EC and BC appear to 
 emanate from the points N and D, and the whole body of light 
 received by the eye seems to come from an apparent object ND, 
 behind the mirror. This apparent object is called an image, 
 but as of course there can be no real image formed there, it is 
 called a virtual or an imaginary image. It will be seen, by 
 Construction, that an image in a plane mirror appears as far 
 behind the mirror as the object, is in front of it, and is of the 
 same size and shape as the object. 
 
 If the mirror is vertical, objects appear in their proper relations to 
 the horizon ; but, if the mirror has any other position, objects assume 
 unnatural postures. Thus, turn this book so that the mirror MM 
 (I"ig. 245) may represent a horizontal mirror, and AH a vertical object 
 above It, and it will be seen that the image appears inverted. To 
 verify this, place a mirror in a horizontal position, and set on it a 
 goblet of water. Also show by construction that, in a mirror making 
 an angle of 45° with the horzon, vertical objects appear horizontal and 
 vice versa. Verify this by experiment. Pupils may amuse themselves 
 at their leisure, and at the same time be instructed, by performing the 
 following experiments : — 
 
 Experiment 1. Place a printed page in front of a mirror, and 
 attempt to read the print from the mirror. It wUl be seen that there 
 
MULTIPLE REFLECTION. 343 
 
 is always a latei'al inversion ; for the same reason that when two per- 
 sons stand facing one another, the right hand of one Is opposite the 
 left hand of the other. 
 
 Experiment 2. Place two mirrors facing one another and about 16™ 
 apart. Hold a pencil half-way between the mirrors, and look obliquely 
 into one mirror just over the edge of the other, and you will see a 
 large number of images of the pencil arranged at equal distance^ 
 behind one another. Account for these images. 
 
 Experiment 3. Place two mirrors edge to edge so as to form an 
 angle of 45° with one another. Place the face in the opening, and 
 gradually close the mirrors till they touch the head. 
 
 § 318. Multiple reflection. — Experiment l. Allow thg 
 beam of light in the last experiment to strike a wall of the room. 
 There will be projected upon the wall two, and perhaps more, circular 
 images of the sun overlapping one another. It appears as though thg 
 beam of light is somehow split, by re- -^ 246 
 
 flection from the mirror, into two or 
 more parts, and that these parts travel 
 thereafter in slightly different paths. 
 
 Experiment 2. Hold a candle flame 
 in such a position (Fig. 246) that its 
 light may strike a mirror (one having 
 very thick glass is best) very obliquely, 
 and place the eye so that It may receive 
 the reflected light, and you may sec 
 many images of the flame. 
 
 Experiment 3. Place a pencil per- 
 pendicular to a mirror, with the point 
 touching the glass, and you will see two 
 images of the pencil, — one touching the point of the pencil, and the 
 other at a distance equal to twice the thickness of the glass. 
 
 How are these phenomena produced? As you travel the 
 sidewalk and pass windows, you frequently see your own image 
 and images of other outdoor objects reflected by the glass, 
 showing that even so transparent a substance as glass does not 
 allow all the light that strikes it to pass through it, but reflects 
 a portion. Let a beam of light Aa, Figure 247, strike a mirror 
 B C obliquely ; a portion of the light is reflected from the point 
 
344 
 
 EADIANT ENERGY. — LIGHT. 
 
 of incidence a, and strikes the screen D E at 6. Another por- 
 tion of the light enters the glass, and a portion of it is reflected 
 from the point c, and a portion of this last reflected light strikes 
 the screen at d, while the remainder is reflected from e to /, 
 and again from /, and a portion of it reaches the screen at g, 
 mg. 247. while the remainder 
 
 is reflected from h 
 to », and undergoes 
 further reflections 
 and splittings, until 
 the light, in conse- 
 quence of the loss 
 occasioned by suc- 
 cessive divisions, 
 becomes too feeble 
 to produce distinct 
 I effects. If the eye 
 take the place of the screen, since an object is seen in the direc- 
 tion in which the light comes to the eye, the point A will appear 
 to lie somewhere on the line 6a, extended ; for the same reason 
 it wiU appear to lie on the lines de, gh, etc. ; but as these lines 
 
 have no point in com- 
 mon, it is clear that 
 the effect would be that 
 of multiple images. 
 (Show the application 
 of this explanation in 
 accounting for the phe- 
 nomena obtained in the 
 above experiments.) 
 
 gig. 248. 
 
 § 319. Reflection from concave mirrors. — Let MM', 
 Figure 248, represent a section of a concave mirror, which may 
 be regarded as a small part of a hollow spherical shell having a 
 polished interior surface. The distance MM' is called the aper- 
 
EEFLECTION FROM CONCAVE MIEEOES. 345 
 
 ture of the mirror. C is the center of the sphere, and is called 
 the center of curvature. G is the vertex of the mirror. A 
 straight line DG, drawn through the center of curvature and 
 the vertex is called the principal axis of the mirror. A concave 
 mirror may be considered as made up of an infinite number of 
 small plane surfaces. All radii of the mirror, as CA, CG, and 
 CB, are perpendicular to the small planes which they strike. 
 If C be a luminous point, it is evident that all light emanating 
 from this point, and striking the mirror, will be reflected back to 
 its source at C. 
 
 Let E be any luminous point in front of a concave mirror. To find 
 the direction that rays emanating from this point take after reflection, 
 draw any two lines from this point, as EA and EB, representing two 
 of the infinite number of rays composing the divergent pencil of light 
 that strikes the mirror. Next draw radii to the points of incidence A 
 and B, and draw the lines AE and BE, making the angles of reflection 
 equal to the angles of incidence. Place arrow-heads on the lines rep- 
 resenting rays of light to indicate the direction of the motion. The 
 lines AE and BE represent the direction of the rays after reflection. 
 
 It wiU be seen that the rays after reflection are convergent, 
 and meet at the point F, called the focus. This point is the 
 focus of all reflected rays that emanate from the point E. It 
 is obvious that if F were the luminous point, the lines AE 
 and BE would represent the reflected rays, and E would be 
 the focus of these rays. Since the relation between two such 
 points is such that light emanating from either one is brought 
 by reflection to a focus at the other, they are called conju- 
 gate foci. Conjugate foci are two points so related that the 
 image of one is formed at the other. The rays EA and EB 
 emanating from E are less divergent than raj's FA and FB, 
 emanating from a point F less distant from the mirror, and 
 striking the same points. Rays emanating from D, and striking 
 the same points A and B, wUl be still less divergent ; and if the 
 point D were removed to a distance of many miles, the rays 
 incident at these points-would be very nearly parallel. Hence 
 
346 RADIANT ENERGY. — LIGHT. 
 
 rays may be regarded as practically parallel when their source 
 is at a very great distance, e.g., the sun's rays. If a sunbeam, 
 consisting of a bundle of parallel rays, as E A, D G, and H B 
 (Fig. 249), strike a concave mirror parallel with its principal 
 _, -. axis, they become convergent by reflection, 
 
 and meet at a point (F) in the principal axis. 
 This point, called the principal focus, is just 
 half-way between the center of curoaiure and 
 the vertex of the mirror. 
 
 On the other hand, it is obvious that diver- 
 gent rays emanating from the principal focus 
 of a concave mirror become parallel by reflection. 
 
 If a small piece of paper is placed at the principal focus of a 
 concave mirror, and the mirror is exposed to the parallel rays 
 of the sun, the paper will quickly burn, showing that the focus 
 of light is also a focus of heat; or, in other words, that all forms 
 of radiant energy follow the same laws of reflection as light. 
 
 Construct a diagram, and show that rays of light proceed- 
 ing from a point between the principal focus and the mirror 
 are divergent after reflection, but less divergent than the inci- 
 dent rays. Reversing the direction of the light, the same dia- 
 gram will show that convergent rays of light are rendered more 
 convergent by reflection from concave mirrors. The general 
 effect of a concave mirror is to increase the convergence or to de- 
 crease the divergence of incident rays. 
 
 The statement, that parallel rays after reflection from a concave 
 mirror meet at the principal focus, is only approximately true. The 
 smaller the aperture of the mirror, the more nearly true is the state- 
 ment. It is strictly true only of parabolic mirrors, such as are used 
 with the head-lights of locomotives. Construct a diagram representing 
 a mirror of large aperture, and it wiU be found that those rays that 
 strike the mirror at considerable distance from its center, intersect the 
 principal axis after reflection at points nearer to the mirror than the 
 principal focus. 
 
 § 320. Formation of images. — Experiment l. In a dark room 
 hold the concave side of a bright silver dessert spoon a little distance 
 
FORMATION OF IMAaES. 
 
 347 
 
 In front of the face, and Introduce a candle flame between the spoon 
 and your eyes ; you will see a small inverted image of the flame about 
 a centimeter in front of the spoon. 
 
 Experiment 2. Turn the convex side of the spoon toward you, and 
 you will see a small erect image of the flame a little back of the spoon. 
 
 Experiment 3. Repeat the two preceding experiments, holding the 
 spoon between the flame and the eyes, but not so as to screen the face 
 from the light, and you will see similar images of yourself. 
 
 To determine the position and kind of images formed of objects 
 placed in front of concave mirrors, proceed as follows : Locate the 
 object, as D E, Figure 250. Draw lines, E A and DB, from the extrem- 
 ities of the object through the center Fig. 250. 
 of curvature of the mirror, to meet the 
 mirror. These lines are called the sec- 
 ondary axes. Incident rays along these 
 lines win return by the same paths 
 after reflection. (Why?) Draw another 
 line from D to any point in the mirror, 
 e.g., to F, to represent any other of the 
 infinite number of rays emanating from 
 D. Make the angle of reflection CFiy equal to the angle of in- 
 cidence CFD, and the reflected ray wUl Intersect the secondary axis 
 DB at the point D'. This point is the conjugate focus of all rays 
 proceeding from D. Consequently, an image of the point D is formed 
 at D'. This image is called 
 a real image, because rays 
 actually meet at this point. 
 In a similar manner, find the 
 pointE',the conjugate focus 
 of the point E. The images 
 of intermediate points be- 
 tween D and E lie between 
 the points D' and E' ; and, 
 consequently, the image of 
 the object liesbetweenthose 
 points as extremities. 
 
 If, for the second ray to be drawn from any point, we select 
 that ray which is parallel with the principal axis, as AG, Figure 261, it 
 will not be necessary to measure angles. For this ray, after reflec- 
 tion, must pass through the principal focus F ; and consequently the 
 conjugate focus A' is easUy found, and so for the point B' and inter- 
 
348 
 
 RADIANT ENERGY. — LIGHT. 
 
 Fig. 252. 
 
 mediate points. Both methods of constructing Images should be prao 
 tlsed by the pupil. 
 
 It thus appears that an image of an object placed beyond the 
 center of curvature of a concave mirror is real, inverted, smaller 
 than the object, and located between the center of curvature and the 
 principal focus of the mirror. An eye placed in a suitable posi- 
 tion to receive the light, as at 
 H (Fig. 252), will receive the 
 same impression from the re- 
 flected rays as if the image 
 E' D' were a real object. For 
 a cone of rays originally eman- 
 ates from (say) the point D of 
 the object, but it enters the eye 
 as if emanating from D', and consequently appears to originate 
 from the latter point. A person standing in front of such a 
 mirror, at a distance greater than its radius of curvature, will 
 see an Iniage of himself suspended, as it were, in mid-air. Or, 
 if in a darkened room an illuminated object is placed in front of 
 the mirror, and a small oiled-paper screen is placed where the 
 image is formed, a large audience may see the image projected 
 upon the screen. 
 
 If E' D' (Fig. 250) is taken as the object, then the direction 
 
 of the light in the diagram 
 will be reversed, and ED 
 will represent the image. 
 Hence, the image of an ob- 
 ject placed between the prin- 
 cipal focus and the center of 
 curvature is also real and 
 inverted, but larger than the 
 object, ' and located beyond 
 the center of curvature. The image in this case may be pro- 
 jected upon a screen, but it will not be so bright as in the 
 former case, because the light is spread over a larger surface. 
 
 Fig. 253. 
 
FORMATION OP IMAGES. 349 
 
 Construct the image of an object placed between the principal 
 focus and the mirror, as in Figure 253. It wiU be seen in this 
 case that a pencil of rays proceeding from j.ig_ 254. 
 
 any point of an object, e.g., D, has no 
 actual focus, but appears to proceed from- 
 a virtual focus D', back of the mirror, and 
 so with other points, as E. The image of 
 an object placed between the principal focus 
 and the mirror is virtual, erect, larger than 
 the object, and is back of the mirror. 
 
 QUESTIONS. 
 
 Ascertain the answers to the following questions by constructing 
 suitable diagrams, and afterwards verify your conclusions by experi- 
 ment, if convenient. 
 
 1. When an object is located at a distance from a concave mirror 
 equal to its radius, will any image be formed? Why? 
 
 2. What is the effect of placing the object at the principal focus? 
 Why? 
 
 3. (a) When is the real image formed by a concave mirror smaller 
 than the object? (6) When is it larger? 
 
 4. (a) When is the Image formed by a concave mirror real? (6) 
 When is it virtual? 
 
 5. (a) Is the image of an object formed by a convex mirror real or 
 virtual? (6) Is it larger or smaller than the object? (c) Is it erect or 
 inverted? 
 
 Note. — The diagram in Figure 254 will be found saflSciently sug-. 
 gestive as to the method of finding the disposition of a pencil of rays 
 emanating from any point, e.g., A, after reflection from a convex 
 mirror. 
 
 6. Is the general effect of a convex mirror to collect or to scatter 
 rays? 
 
350 
 
 BADIANT ENEEaT. — LIGHT. 
 
 Fig. 25S. 
 
 LIV. REFRACTION. 
 
 EbEperlment 1. Across the bottom of a rectangular tin basin ABC 
 D, Figure 255, mark a scale of millimeters. Into a darkened room 
 admit a beam of sunlight, so that its rays may fall obliquely on the 
 bottom of the basin, and note the place on the scale where the edge of 
 
 the shadow D E cast by the side of 
 the basin D C meets the bottom at E. 
 Then, without moving the basin, fill 
 it even full with water slightly 
 clouded with milk, or with a few 
 drops of a solution of mastic in alco- 
 hol. It will be found that the edge 
 of the shadow has moved from D E 
 to D F, and meets the bottom at F. 
 Beat a blackboard rubber, and create 
 a cloud of dust in the path of the 
 beam in the air, and you will discover 
 that the rays G D that graze the edge of the disk at D become bent 
 at the point where they enter the water, and now move in the bent 
 line GD F, instead of, as formerly, in the straight line GE. The path 
 of the light in the water is now nearer to the vertical side DC; 
 in other words, this part of the beam is more nearly vertical than before. 
 Experiment 2. Place a coin (A, Fig. 256) on the bottom of an 
 empty basin, so that, as you look through a small hole in a card B C 
 over the edge of the vessel, the coin is just out of sight. Then, with- 
 out moving the card or basin, fill the latter with water. Now, on 
 looking through the aperture in the card, the coin is visible. The 
 beam of light AE, which formerly moved in the straight line AD, is 
 now bent at E, where it leaves the water, and, passing through the 
 aperture in the card, enters the eye. Observe 
 that, as the light passes from the water into 
 the air, it is turned farther from a vertical line 
 EF; in other words, the beam is farther from 
 the vertical than before. 
 
 Experiment 3. From the same position as 
 in the last experiment, direct the eye to the 
 point G in the basin filled with water. Reach 
 your hand around the basin, and place your 
 finger where that point appears to be. On ex- 
 amination, it will be found that your finger is considerably above the 
 
 Kg. 256. 
 
CAUSE OF EEFEACTION. 351 
 
 bottom. Hence, the effect of the bending of rays of light, as they pass 
 ohliquely out of water, is to cause the bottom to appear more elevated than it 
 really is; in other words, to cause the water to appear shallower than it is. 
 
 Experiment 4. Thrust a pencil obliquely into water, and it will 
 appear shortened, bent at the surface of the water, and the j,. „- 
 immersed portion elevated. 
 
 Experiment 5. Place a piece of wire (Fig. 257) verti- 
 cally in front of the eye, and hold a narrow strip of thick 
 plate glass horizontally across the wire, so that the light 
 from the wire may pass obliquely through the glass to the 
 eye. The wire will appear to be broken at the two edges 
 of the glass, and the intervening section will appear to be moved to 
 the right or left according to the inclination of the glass ; but, if the 
 glass is not inclined to the one side or the other, the wire does not 
 appear broken. 
 
 When a beam of light passes from one medium into another of 
 different densitj-, it is bent or refracted at the boundary plane 
 between the two media, unless it falls exactly perpendicularly 
 on this plane. If it passes into a denser medium, it is refracted 
 toward a perpendicular to this plane; if into a rarer medium, it 
 is refraMed from the perpen- pj j^g 
 
 dicular. The angle GDO (Fig. 
 255) is called the angle of inci- 
 dence; FDN, the angle of re- 
 fraction; and EDF, the angle 
 of deviation. 
 
 § 321. Cause of refraction. 
 
 — Careful experiments have 
 proved thai the velocity of light 
 is less in a demise than in a rare 
 medium. Let the series of par- 
 allel lines AB (Fig. 258) repre- 
 sent a series of wave-fronts leaving an object C, and passing 
 through a rectangular piece of glass DE, and constituting a 
 beam of light. Every point in a wave-front moves with equal 
 velocity as long as it traverses the same medium ; but the point 
 
352 
 
 EADIAifT ENERGY. — LIGHT. 
 
 a of a given wave ab enters the glass first, and its velocity is 
 impeded, while the point b retains its original velocity ; so 
 that, while the point a moves to a', 6 moves to 6', and the 
 result is that the wave-front assumes a new direction (very 
 much in the same manner as a line of soldiers execute a wheel) , 
 and a ray or a line drawn perpendicularly through the series of 
 waves is turned out of its original direction on entering the glass. 
 Again, the extremity c of a given wave-front cd first emerges 
 from the glass, when its velocity is immediately quickened ; so 
 that, while d advances to d', c advances to c', and the direction 
 of the ray is again changed. The direction of the ray, after 
 emerging from the glass, is parallel to its direction before enter- 
 ing it, but it has suffered a lateral displacement. Let C repre- 
 sent a section of the wire used in Exp. 5, and the cause of 
 the phenomenon observed will be apparent. If the beam of 
 light strikes the glass perpendicularly, all points of the wave 
 will be checked at the same instant on entering the glass ; con- 
 sequently it will suffer no refriaction. 
 
 § 322. Index of refraction. — The deviation of light, in 
 
 Fig. 259. 
 
 passing from one medium to 
 another, varies with the me- 
 dium and with the angle of 
 incidence. It diminishes as 
 the angle of incidence dimin- 
 ishes, and is zero when the 
 incident ray is normal (i.e., 
 perpendicular to the surface 
 of the medium) . It is highly 
 important, knowing the angle 
 of incidence, to be able to 
 determine the direction 
 which a ray of light will take 
 on entering a new medium. Describe a circle around the point 
 of incidence A (Fig. 259) as a center, with a radius of (say) 
 
INDICES OF BEPRACTION. 
 
 353 
 
 10"™; througli the same point draw IH perpendicular to the 
 surfaces of the two media, and to this hue drop perpendiculars 
 BD and CE from the points where the circle cuts the ray in the 
 two media. Then suppose that the perpendicular B D is ^ of 
 the radius A B ; now this fraction ^ is called (in Trigonom- 
 etry) the sine of the angle DAB. Hence, ^ is the sine of 
 the angle of incidence. Again, if we suppose that the perpen- 
 dicular C E is -j^ of the radius, then the fraction y% is the 
 sine of the angle of refraction. The sines of the two angles 
 are to one another as j^ : -j*^, or as 4 : 3. The quotient (in this 
 case f ) obtained by dividing the sine of the angle of incidence 
 by the sine of the angle of refraction is called the index of refrac- 
 tion. It can be proved to be the ratio of the velocity of the 
 incident to that of the refracted light. It is found that, for the 
 same media the index of refraction is a constant quantity; i.e., 
 the incident ray might be more or less oblique, still the quotient 
 would be the same. 
 
 § 323. Indices of refiraotion. — The index of refraction for 
 light in passing from air into water is approximately ^, and 
 from air into glass f .; and, of course, if the order is reversed, the 
 reciprocal of these fractions must be taken as the indices ; e.g., 
 from water into air the index is f , from glass into air f . "When 
 a ray passes from a vacuum into a medium, the refractive index 
 is greater than unity, and is called the absolute index of refrac- 
 tion. The relative index of refraction, from any medium A into 
 another B, is found by dividing the absolute index of B by the 
 absolute index of A. . . 
 
 The refractive index varies with the color of the light. (See 
 page 365.) The following table is intended to represent mean 
 indices : — 
 
 TABLE OF ABSOLUTE mDICES. 
 
 Air at 0" C. and TeO"" preBBUrs . 1.000294 
 
 Pure water 1.33 
 
 Alcohol .....'..•.. 1.37 
 
 Spirits of turpentine 1.48 
 
 Humors of the eye (about) . . 1.35 
 
 Carbon Waulphlde 1.641 
 
 Crown glass (about) 1.53 
 
 Flint glaBS (about) 1.61 
 
 Diamond (about) 2.6 
 
 Lead chromate 2.97 
 
364 RADIANT BNEKGr. — LIGHT. 
 
 EXERCISES. 
 
 1. Draw a straight line to represent a surface of flint glass, and 
 draw another line meeting this obliquely to represent a ray of light 
 passing from a vacuum into this medium. Find the direction of the 
 ray after it enters the medium, employing the index as given in the 
 above table. 
 
 2. (a) Determine the index of refraction for light in passing from 
 water into diamond. (6) In passing from water into air. 
 
 3. Ascertain the index of refraction for water in Exp. 1, p. 350, in 
 
 "P p 
 which sine I (sine of angle of incidence) = =rp: (Fig. 255), and sine 
 
 R (sine of angle of refraction) = =^. Hence, the index of refraction 
 ^ sine I ^ E C . F C 
 sineR ED ' FD 
 
 Fig. 260. 
 
 §324. Critical angle; total reflection. — Let SS' (Fig. 
 260), represent the boundarj'-surface between two media, and 
 AO and BO incident rays in the more refractive medium (e.g., 
 glass) ; then OD and OE may represent the same rays respec- 
 tively after they enter the less refractive medium (e.g., air). 
 It will be seen that, as the angle of incidence is increased, the 
 refracted ray rapidly approaches the surface.OS. Now, there 
 taunt be an angle of incidence (e.g., COM) such that the angle 
 
REFRACTION AND TOTAL REFLECTION. 356 
 
 of refraction will be 90° ; in this ease the incident ray CO, after 
 refraction, will just graze the surface OS. This is called the 
 critical or limiting angle. Any incident ray, as LO, making a 
 larger angle with the normal than the critical angle, cannot 
 emerge from the medium, and consequently is not refracted. 
 Experiment shows that all such rays undergo internal reflection, 
 e.g.f the ray LO is reflected in the direction ON. Reflection in 
 this case is perfect, and hence is called totoH reflection. Total 
 reflection occurs when rays in the more refraMoe medium are in- 
 cident at an angle greater than the critical angle. Surfaces of 
 transparent media, under these circumstances, constitute the 
 best mirrors possible. The critical angle diminishes as the re- 
 fractive index increases. For water it is about 48^° ; for flint 
 glass, 38° 41'; and for diamond, 23° 41'. Light cannot, there- 
 fore, pass out of water into air with a greater angle of incidence 
 than 48^°. The brilliancy of gems, particularly the diamond, 
 is due in part to their extraordinary power of internal reflection; 
 It is evident that all incident light embraced in the angular 
 space KOS, not reflected at the surface, is condensed by refrac- 
 tion into the angular space COM of 48^°, or that the whole 
 light that passes into the water is condensed into an angular 
 space of 97°. A diver, looking upward, can see external ob- 
 jects, as it were, only through a circular aperture overhead of 
 limited diameter ; while beyond this circle he sees, as the effect 
 of total reflection, the various objects on -the bottom. 
 
 § 325. Illustrations of refraction and total reflection.— 
 
 Experiment 1. Place a bright coin in a tumbler of water, and tilt the 
 
 glass till the light from the coin strikes the surface of the water above 
 
 with sufficient obliquity, so that, looking upward toward that surface, 
 
 you can see there a distinct image of the coin. 
 
 Experiment 2. Thrust the closed end of a glass test-tube into 
 water, and incline the tube. Look down upon the immersed part of 
 the tube, and its upper surface will look like burnished silver, or as if 
 the tube contained mercury. Fill the test-tube with water, and immerse 
 as before ; the total reflection which before occurred at the surface of 
 the air in the submerged tube now disappears. Explain. 
 
S66 
 
 BiADIANT ENERGY. — LIGHT. 
 
 Fig. 261. 
 
 Experiment 3. Place uncolored glass beads, or glass broken into 
 quite small pieces, in a test-tube. They appear not only wMte, due to 
 
 difElised reflection, but quite opaque, 
 due to refraction and internal reflec- 
 tion. Pour some water into the tube, 
 and it becomes somewhat translucent. 
 Substitute spirits of turpentine for 
 the water, and the translucency is 
 increased. By mixing a small quantity 
 of carbon bisulphide with the turpen- 
 t:n6, or olive oil with oil of cassia, 
 a liquid can be obtained whose re- 
 fractive index is about the same as 
 that of glass, when the light wUl 
 pass through the liquid without ob- 
 struction, and the beads become trans- 
 parent and nearly invisible. The last 
 illustration shows that one transparent body within another can be seen 
 only when their refractive powers differ. Place your eye on a level with 
 the surface of a hot stove, and you inay observe a wavy motion in the 
 air, due to the mingling of currents of heated and less refractive air, 
 with cooler and more refractive air. 
 
 A ray of light from a heavenly body A (Pig. 261) undergoes a 
 series of refractions as it reaches successive strata of the atmos- 
 phere of constantly increasing density, and to an eye at the earth's 
 surface appears to come from a point A' in the heavens. The general 
 eflfect of the atmosphere on the path of light that traverses it is such 
 as to increase the apparent altitude of the heavenly bodies. It enables 
 us to see a body (B) which is actually below the horizon, and prolongs 
 the apparent stay of the sun, moon, and other heavenly bodies above 
 the horizon. Twilight is due both to refraction and reflection of light 
 by the atmosphere. 
 
LENSES. 
 
 367 
 
 LV. PRISMS AND LENSES. 
 
 § 326. Optical prisms. — An optical prism is usually a 
 ti-ansparent wedge-shaped body. Figure 262 represents a 
 transverse section of such a Fig. 262. 
 
 prism. Let AB be a ray of 
 light incident upon one of its 
 surfaces. On entering the 
 prism it is refracted toward the 
 normal, and takes the direction 
 BC. On emerging from the 
 prism, it is again refracted, but 
 now from the normal in the direction CD. The object that 
 emits the ray wiU appear to be at F. Observe that the ray AB, 
 at both refractions, is bent toward the thiclcer part, or base, of 
 the prism. 
 
 § 327. Lenses. — Any transparent medium bounded by two 
 curved surfaces, or one plane and the other curved, is a lens. 
 
 Experiment 1. Procure a couple of lenses thicker in the middle 
 than at the edge ; strong spectacle glasses, or the large lenses in an 
 opera glass, will answer. Hold one of the lenses in the sun's rays, and 
 notice the path of the beam in dusty air (made so by striking together 
 two blackboard rubbers) after it passes through the lens ; also, that on 
 a paper screen all the rays may be brought to a small circle, or even a 
 point, not far from Yig. 263. 
 
 the lens. This point 
 is called the focus, 
 and its distance from 
 the lens, the focal 
 length of the lens. 
 
 Find the focal 
 
 length of this lens, and of the second, and then of the two together. 
 You find the focal length of the two combined is less than of either 
 alone, and learn that the more powerful a lens or combination of 
 them is, the shorter the focal length ; that Is, the more quickly are the 
 parallel rays that enter different parts of the lens brought to cross one 
 another. 
 
368 RADIANT BNEEGY. — LIGHT. 
 
 Experiment 2. Procure a lens thinner in the middle than at its 
 edge. One of the small lenses or eye-glasses of an opera glass -will 
 answer. Repeat the above experinient with this lens, and notice that 
 the light emerging from the lens, instead of coming to a point, becomes 
 spread out. 
 
 Lenses are of two classes, converging and diverging, accord- 
 ing as they collect or scatter beams of light. Each class com- 
 prises three kinds (Fig. 263) : — 
 
 Class I. Class n. 
 
 1. Double-convex "J Converging or convex 
 
 2. Plano-convex ] lenses, thicker in 
 
 3. Concavo-convex | the middle than at 
 
 (or meniscus) j the edges. 
 
 , _ ,, fX)ivergmg, or con-. 
 
 4. Double-concave ^ , iv 
 
 „ „, oave lenses, thinner 
 
 5. Plano-concave < . ,. uj, ^i 
 
 „ ^ I in the middle than 
 
 6. Convexo-concave 1 
 
 I. at the edges. 
 
 A straight line, as AB, normal to both surfaces of a lens, 
 and passing through its center of curvature, is called its princi- 
 pal axis. In every lens there is a point in the principal axis 
 called the optiocd center. Every ray of light -that passes through 
 it has parallel directions at incidence and emergence, i.e., can 
 suffer at most only a slight lateral displacement. In lenses 1 
 and 4 it is half-way between their respective curved surfaces. 
 A ray, drawn through the optical center from any point of an 
 object, as A a (Fig. 269, p. 362), is called the secondary axis 
 of this point. 
 
 § 328. Effect of lenses. — We may, for convenience of illus- 
 
 _. -g. tration, regard a convex lens as composed, 
 
 approximately, of two prisms placed base to 
 
 base', as A (Fig. 264), and a concave lens 
 
 as composed of two prisms with their edges 
 
 in contact, as B. Inasmuch as a beam or 
 
 pencil of light ordinarily strikes a lens in 
 
 such a manner that the -rays will be bent 
 
 toward the thicker parts or bases of these 
 
 approximate prisms, it is obvious that the lens A would tend 
 
 to bend the transmitted rays toward one another, while the 
 
 lens B would tend to separate them. The general effect of all 
 
EFFECT OF LENSES. 
 
 369 
 
 convex lenses is to converge transmitted rays; and of concave 
 lenses, to cause them to diverge. Incident rays parallel with the 
 principal axis of a convex lens are brought to a focus F (Fig. 265) 
 at a point in the principal axis. This point is called the prin- 
 cipal focus, i.e., it is the focus of incident rays parallel with the 
 principal axis. It may Kg. 265. 
 
 bo found by holding the 
 Ions so that the rays of 
 the sun may fall perpen- 
 dicularly upon it, and then 
 moving a sheet of paper 
 back and forth behind it 
 until the image of the 
 sun formed on the paper is brightest and smallest. Or in a room 
 it may be found approximately by holding a lens at a considerable 
 distance from a window, and regulating the distance of the paper 
 so that a distinct image of the window will be projected upon it. 
 The focal length is the distanceof the optical center of the lens 
 to the center of the image on the paper. The shorter this 
 distance the greater is the power of the lens. 
 
 If the paper is kept at the principal focus for a short 
 time it will take 
 Are. Hence, this 
 is the focus of 
 heat as well as of 
 light. The reason 
 13 apparent why 
 convex lenses are 
 comctimes called 
 ' 'burning glasses." 
 A pencil of rays 
 emitted from the principal focus F (Fig. 265), as a luminous 
 point, becomes parallel on emerging from a convex lens. If 
 the rays emanate from a point nearer the lens, they diverge after 
 egress, but the divergence is less than before ; if from a point 
 
360 RADIANT ENERGY. — LIGHT. 
 
 beyond the principal focus, the rays are rendered convergent. 
 A concave lens causes parallel incident rays to diverge as if 
 they came from a point, as F (Fig. 266). This point is there- 
 fore its principal focus. It is, of course, a virtual focus. 
 
 § 329. Conjugate foci. — When a luminous pomt S (Fig. 
 Hg.267. 267) sends 
 
 rays to a con- 
 vex lens, the 
 emergent rays 
 converge to 
 another point 
 S'; rays sent 
 from S' to the 
 
 lens would converge to S. Two points thus related are called 
 conjugate foci. The fact, that rays which emanate from one 
 point are caused by convex lenses to collect at one point, 
 gives rise to real images, as in the case of concave mirrors. 
 
 § 330. Images formed, — Fairly distinct images of objects 
 may be formed through very small apertures (page 330) ; but 
 owing to the small amount of light that passes through the 
 aperture, the images are very, deficient in brilliancy. If the 
 aperture is enlarged, brilliancy is increased at the expense of 
 distinctness. (Why?) A convex lens enables us to obtain both 
 brilliancy and distinctness at the same time. 
 
 Experiment 1. By means of a, parte lumiere A (Pig. 268) introduce a 
 horizontal beam of light into a darkened room. In its path place some 
 object, as B, painted in transparent colors or photographed on glass. 
 (Transparent pictures are cheaply prepared by photographers for sunlight ■ 
 and lime-light projections.) Beyond the object place a convex lens L, 
 and beyond the lens a screen S. The object being illuminated by the 
 beam of light, all the rays diverging from any point a are bent by the 
 lens so as to come together at the point of. In like manner, all the rays 
 proceeding from c are brought to the same point c' ; and so also for all 
 Intermediate points. Thus, out of the billions of rays emanating from 
 
IMAGES FOBMED. 361 
 
 each of the millions of points on the object, those that reach the lens 
 are guided by it, each to its own appropriate point in the image. It 
 is evident that there must result am image, both bright and distinct, 
 provided the screen is suitably placed, i.e., at the place where the 
 rays meet. But if the screen is placed at S' or S", it is evident 
 that a blurred image will be formed. Instead of moving the screen 
 back and forth, in order to "focus" the rays properly, it is cus- 
 tomary to move the lens. 
 
 Experiment 2. Fill some globular-shaped glass vessel (e.jr., a flask, 
 decanter, or fish-aquarium) with water, and place it l™ in front of a 
 white wall of a darkened room. A little beyond the vessel place a 
 candle flame, and move it back and forth till a distinct image of the 
 flame is projected upon the wall by the water lens. Move the vessel 
 farther from the wall, and, on again focusing the flame, its image will 
 be larger than before. Bepeat the same with a glass lens. 
 
 mg. 268. 
 
 By properly varjang the distances of the lens and flame from 
 the wall, in the last experiment, you may learn that when the 
 distance of the object is twice that of the principal focus, the 
 object and image are of equal size. When the image is within 
 twice the focal distance it is less, and when beyond this same 
 distance it is greater, than the oliject. In all cases the corre- 
 sponding linear dimensions of an object and its image are to one 
 another directly as their respective distances from the optical center. 
 
 § 331. To construct the image formed by a convex lens. 
 
 — Given the lens L (Fig. 269), whose principal focus is at F (or F', 
 
362 
 
 RADIANT ENEEGY. — LIGHT. 
 
 for rays coming from the other direction), and object AB in front of 
 it ; any two of the many rays ftom A will determine where its image a 
 is formed. The only two that can be traced easily are, the one along 
 the secondary axis AOa, and the one parallel to the principal axis A A' -, 
 
 tie latter will be deviated so as to pass through the principal focus F, 
 and will afterward intersect the principal axis at some point a ; so this 
 is the conjugate focus of A; similarly for B, and all intermediate 
 points along the arrow. Thus, a real, inverted image is formed at 06. 
 
 rig. 270. 
 
 § 332. Virtual images. — Since rays that emanate from a 
 point nearer the lens than the principal focus diverge after 
 egress, it is evident that their focus must be virtual and on the 
 same side of the lens as the object. Hence, the image of an 
 
SPHERICAL ABERRATION. 363 
 
 object placed nearer the lens than the principal focus is virtual, 
 magnified, and erect, as shown in Figure 270. A convex lens 
 used in this manner is called a simple microscope. 
 
 Since the effect of concave lenses is to scatter transmitted 
 rays, pencils of rays emitted from A and B (Fig. 271), after 
 
 Fig. 271. 
 
 refraction, diverge as if they came from A' and B', and the 
 image will appear to be at A'B'. Hence, images formed by 
 concave lenses are virtual, erect, and smaller than the object. 
 
 § 333. Spherical aberration. — In all ordinary convex 
 lenses the curved surfaces are spherical, and the angles which 
 incident rays make with the little plane surfaces, of which we 
 may imagine the spherical surface to be made up, increase 
 
 Fig. 272. 
 
 rapidly toward the edge of the lens. Hence, while those rays 
 from a given point of an object, as A (Fig. 272), which pass 
 through the central portion, meet approximately at the same 
 point F, those which pass through the marginal portion are 
 deviated so much that they cross the axis at nearer points, e.g., 
 
364 
 
 RADIANT ENERGY. — LIGHT. 
 
 at F' ; so a blurred image results. This wandering of the rays 
 from a single focus is called spherical aberration. The evil may 
 be largely corrected by interposing a diaphragm DD' (Fig. 
 272), provided with a central aperture, smaller than the lens, so 
 as to obstruct those rays that pass through the marginal part of 
 the lens. 
 
 Fig. 273. 
 
 LVI. PRISMATIC ANALYSIS OF LIGHT. — SPECTRA. 
 
 §334. Analysis of "white light. — Experiment 1. Paste tin- 
 foil smoothly over one side of a glass plate about 5"™ sqtiare. In the 
 center of the foil cut a slit 3"" long by 1™"" wide, leaving smooth 
 and parallel edges. Place the plate with the slit in the aperture of 
 a,porte lumiere so as to exclude all light from a darkened room except 
 that which passess through the slit. Near the slit interpose a double 
 convex lens of (say) 10-inch focus. A narrow sheet of light will 
 traverse the room and produce an image AB of the slit on a white, 
 screen placed in its path. Now place a glass prism C in the path of 
 
ANALYSIS OF WHITE LIGHT. 365 
 
 the beam with its axis (the straight line connecting the centers of the 
 triangular faces) vertical. (1) The light now is not only turned from 
 its former path, but that which before was a narrow sheet, is, after 
 emerging from the prism, spread out fan-like into a wedge-shaped 
 body, with its thickest part resting on the screen. (2) The image, 
 before only a narrow vertical band, is now drawn out into a long 
 horizontal ribbon of light DE. (3) The image, before white, now 
 contains all the colors of the rainbow, from red at one end to violet 
 at the other ; it passes gradually through all the gradations of orange, 
 yellow, green, blue, and violet. (The difference in deviation between 
 the red and the violet is purposely much exaggerated in the figure.) 
 
 From this experiment we learn (1) that white light is not sim- 
 ple in its composition, but the result of a mixture. (2) The colors 
 of which white light is composed may be separated by refraction. 
 (3) The cause of the separation is due to the different degrees 
 of deviation which they undergo by refraction. Red, which is 
 always least turned aside from a straight path, is the least 
 refrangible color. Then follow orange, j-ellow, green, blue, and 
 violet in the order of their refrangibility. The many-colored 
 ribbon of light pE is called the solar spectrum. This separa- 
 tion of white light into its constituents is called dispersion. The 
 number of colors of which white light is composed is really 
 infinite, but we have names for only seven of them ; viz., red, 
 orange, yellow, green, cyan-blue,^ ultramarine-blue, and violet; 
 and these are called the primary or prismatic colors. The 
 names of the blues are derived from the names of the pigments 
 which most closely resemble them. The rainbow is an illustra- 
 tion of a solar spectrum on a grand scale. It is the result of 
 the dispersion of sunlight 'by rain drops. 
 
 The spectrum may be projected upon a screen, or it may be 
 received directly by the eye, as in the two following experi- 
 ments : — 
 
 Experiment 2. Upon a black card-board A (Fig. 274) paste a 
 strip of white paper 3™ long and 2™™ wide ; and place the prism and 
 the eye as in the figure. Now a beam of white light from the strip Is 
 
 ^ See Rood's Modern Chromatics. 
 
366 
 
 RADIAJifT ENERGY. • 
 
 ■ LIGHT. 
 
 refracted and dispersed by the prism, and, falling upon the retina of 
 
 the eye, you see, not the narrow white strip in its true position, but 
 
 a spectrum in the position A'. This experiment is performed in a 
 
 lighted room. 
 
 Experiment 3. Instead of a continuous white strip, paste short 
 
 strips of red, white, and blue, end to end, on the black card, as repre- 
 sented in Figure 275. The spectrum of each color 
 is given on the right, the light portions repre- 
 senting the illuminated parts. 
 It will be seen that in the 
 spectrum of the red, the green, 
 ^ \\ \\ blue, and violet portions are 
 
 ^1 ^ra^ almost completely dark, but 
 
 ■ti TIhiI there is a faint trace of or- 
 
 ■r r*''«B ange ; in the spectrum of the 
 
 ' "^ !» blue, the red, orange, and yel- 
 
 low are wanting, blue and vio- 
 let are present, and a small 
 quantity of green. (What 
 lessons does this experiment teach?) 
 
 Experiment 4. In place of the white strip of 
 paper used in Exp. 2, admit light into a dark 
 
 room through a narrow slit, and examine its spectrum. 
 
 § 335. Synthesis of white light. — The composition of 
 white light has been ascertained by the process of analysis ; can 
 it be verified by synthesis? — i.e., can the colors after dispersion 
 be reunited? and, if so, will the result of the reunion be white 
 light? 
 
 Experiment 1. Place a second prism (2) in such a position /^ that 
 light which has passed through one prism (1), and been refracted and 
 decomposed, may be refracted back, and the colors will be reblended, 
 and a white image of the slit will be restored on the screen. 
 
 Experiment 2. Place a large convex lens, or a concave mirror, so 
 as to receive the colors after dispersion by a prism, and bring the rays 
 to a focus on a screen. The image produced will be white. 
 
 Experiment 3. Receive the spectrum on a common plane mirror, 
 and rapidly tip the mirror back and forth in small arcs at right angles 
 to the path of the light, and the light reflected by the mirror upon a 
 screen will produce a white image on the screen. 
 
CAUSE OP COLOR AND DISPERSION. 367 
 
 § 336. Cause of color and dispersion. — The color of light 
 is determined solely by the number of waves emitted by a lumi- 
 nous body in a second of time, or by the corresponding wave-length. 
 In a dense medium, the short waves are more retarded than the 
 longer ones; hence they are more refracted. This is the cause 
 of dispersion. The ether waves diminish in length from the 
 red to the violet. As pitch depends on the number of aerial 
 waves which strike the ear in a second, so color depends on the 
 number of ethereal waves which strike the eye in a second. 
 From well-established data, determined by a varietj'^ of methods 
 (see larger works), physicists have calculated the number of 
 waves that succeed one another for each of the several prismatic 
 colors, and the corresponding wave-lengths ; the following table 
 contains the results. The letters A, C, D, etc., refer to Fraun- 
 hofer's lines (see page 370) . 
 
 Length of ■waves No. of waves 
 
 in millimeters. per second. 
 
 Dark red A 000760 396,000,000,000,000 
 
 Orange C 000656 468,000,000,000,000 
 
 TeUow D 000589 510,000,000,000,000 
 
 Green E 000627 570,000,000,000,000 
 
 C. Blue F 000486 618,000,000,000,000 
 
 TJ. Blue G 000431 697,000,000,000,000 
 
 Violet H 000897 760,000,000,000,000 
 
 There is a limit to the sensibility of the eye as well as of the 
 ear. The limit in the number of vibrations appreciable by the 
 eye lies approximately within the range of numbers given in the 
 above table ; i.e., if the succession of waves is much more or less 
 rapid than indicated by these numbers, they do not produce the 
 sensation of sight. It is evident that the frequency of the waves 
 emitted by a luminous body, and consequently the color of the 
 light emitted, must depend on the rapidity of the vibratory mo- 
 tions of the molecules of that body, i.e., upon its temperature. 
 This has been shown in a convincing manner as follows : The 
 temperature of a platinum wire is slowly raised by passing a 
 gradually increasing current of electricity through it. At a 
 
368 RADIANT BKEEGY. — LIGHT. 
 
 temperature of about 640° C. it begins to emit light ; and the 
 light, analyzed by a prism, shows that it emits only red light. 
 As the temperature rises, there wiU be added to the red of the 
 spectrum, first yellow, then green, blue, and violet successively. 
 When it reaches a white heat, it emits all the prismatic colors. 
 It is significant that a white-hot body emits more red light than 
 a red-hot body, and likewise more Ught of every color than at 
 any lower temperature. The conclusion is, that a body which 
 emits white light sends forth simtdtaneously waves of a variety of 
 lengths. 
 
 § 337. Continuous spectra. — The spectrum produced by 
 the platinum is continuous ; that is, the band of light is un- 
 broken. If the spectrum is not complete, as when the tempera- 
 ture is too low, it will begin with red, and be continuous as far 
 as it goes. All luminous solids and liquids give continvious 
 spectra. 
 
 Fig. 276. 
 
 § 338. Spectroscope. — A small instrument called a pocket 
 spectroscope^ will answer for all experiments given in this book. More 
 elaborate experiments require more elaborate apparatus, a description 
 of which must be sought for In larger works on this subject. This 
 instrument contains three or more prisms, A, B, and C (Fig. 276). The 
 prisms are enclosed in a brass tube D, and this tube in another tube E. 
 F is a convex lens, and G is an adjustable slit. By moving the inner 
 tube back and forth, the instrument may be so focused that parallel 
 rays will faU upon prism A. By varying the kind of glass used in the 
 different prisms," as well as their structure, the deviation of light trova. 
 a straight path, in passing through them, is overcome, while the dis- 
 persion is preserved. On account of the directness of the path of light 
 through It, this instrument is called a direct-msion spectroscope. 
 
 1 It is expected tbat the pupil will be provided with a pocket spectroBcope, the coat of 
 which need not exceed ten dollars. 
 
 3 A and C are crown-glass, and B is flint-giasiB. Bee foot-note, p. 395, 
 
BRIGHT-LINE SPECTRA. 369 
 
 § 339. Bright line, absorption, or reversed spectra. — 
 
 Experiment 1. Open the slit a little less than 1""" wide, and look 
 through the spectroscope at the sky (not at the sun, for its light is too 
 intense for the eye) , and you will see a continuous spectrum. 
 
 Experiment 2. Repeat the last experiment with a candle, kerosene, 
 or ordinary gas flame, and you will obtaiu similar results. 
 
 Experiment 3. Take a piece of platinum wire 10=™ long, seal one 
 end of it by fusion to a short glass tube for a handle, and make a loop at 
 the other end about 1"™" in diameter. Wet the loop in clean water, 
 dip it into pulverized common salt, and introduce it into the almost in- 
 visible and colorless flame of a Bunsen burner. Instantly the flame 
 becomes luminous and colored a deep yellow. Examine the light with a 
 spectroscope, and you wiU flnd, instead of a continuous spectrum be- 
 ginning with red, only a bright, narrow line of yeUow in the yellow part 
 of the spectrum, next the orange. Your spectrum consists essentially 
 of a single bright yellow line on a comparatively dark ground (see 
 Sodium, rig. 277). 
 
 Experiment 4. Heat the platinum loop until it ceases to color the 
 flame, then wet it and dip it into chloride of lithium, and repeat the 
 las't experiment. You obtain a carmine-tinted flame, and see through 
 the spectroscope a bright red line and a faint orange line (see Lithium, 
 Fig. 277). 
 
 Experiment 5. Use potassium hydrate, and you obtain a violet- 
 colored flame, and a spectrum consisting of a red line and a violet line 
 (the latter quickly disappears). Use strontium nitrate, and obtain a 
 crimson flame, and a spectrum consisting of several lines in the red 
 and the orange, and a blue line. (See Potass, and Stron., Fig. 277.) 
 
 Experiment 6. Use a mixture of several of the above chemicals, 
 and you wiU obtain a spectrum containing all the lines that characterize 
 the several substances. 
 
 Every chemical compound used in the above experiments 
 contains a different metal, e.g., common salt contains the metal 
 sodium ; the other substances used successively contain respec- 
 tively the metals lithium, potassium, and strontium. These 
 metals, when introduced into the flame, are vaporized, and we 
 get their spectra when in a gaseous state. All gases give dis- 
 continuous, or bright line, spectra, and no two gases give the same 
 spectra. The fact that in the second experiment we obtained 
 continuous and similar spectra, appears to contradict the last 
 
370 
 
 RADIANT ENERGY. — LIGHT. 
 
 two statements. But it should be remembered that all that 
 gives light in those flames is small particles of solid carbon 
 floating in the burning gas. We see, then, that the spectroscope 
 furnishes us with a reliahle means of determining, at any time, 
 whether light proceeds from a luminous solid or a luminous gas. 
 
 o. 
 
 Pig. 277. 
 G. C.B. U.B. 
 
 lU aHJ OU IV uu J~Lu ±au mju j 
 
 ilililiMiliMili ililili I ilili ilililililililililililililili I 
 
 ABC 
 
 Bb 
 
 HH 
 
 § 340. Dark-line spectra. — Experiment l. Close the slit of 
 the spectroscope so that the aperture will be very narrow ; direct it 
 once more to the sky, and slowly move the inner tube back and forth, 
 and you wUl find, with a certain suitable adjustment which may be 
 obtained by patient trial, that the solar spectrum is not in reality con- 
 tinuous, but is crossed by several dark lines (see Tig. 277). 
 
 Experiment 2. The electric light is now in so common use that it 
 may be possible to perform this experiment. Between the electric 
 light and the spectroscope introduce the flame of a Buusen burner, and 
 color it yellow with salt. Examine the electric light transmitted 
 through this yellow flame. 
 
 In the last experiment you will naturally expect to find the 
 yeUow part of the spectrum uncommonly bright, for there would 
 
SPECTBTTM ANALYSIS. 371 
 
 apparently be added to the yellow of the electric light the yellow 
 of the salted flame. But precisely where you would look for the 
 brightest yellow, there you discover that the spectrum is crossed 
 by a dark line. If you use salts of lithium, potassium, and 
 strontium in a similar manner, you will find in every case your 
 spectrum crossed by dark lines where you would expect to find 
 bright lines. Remove the Bunsen flame, and the dark lines 
 disappear. It thus appears that the vapors of different sub- 
 stances absorb or quench the very same rays that they are capable 
 of emitting ; very much, it would seem, as a given tuning-fork 
 selects from various sounds only those of a definite wave-length 
 corresponding to its own vibration-period. The dark places of 
 the spectrum receive light in full force from the salted flame ; 
 but the light is so feeble, in comparison with those places illumi- 
 nated by the electric light, that the former appear dark by con- 
 trast. Light transmitted through certain liquids (as sulphate of 
 quinine and blood) and certain solids (as some colored glasses) 
 produces dark-line spectra. These spectra are obtained only 
 when light passes through media capable of absorbing rays of 
 certain wave-length ; hence, they are commonly called absorp- 
 tion spectra. Since a given vapor causes dark lines precisely 
 where, if it were itself the only radiator of light, it would cause 
 bright lines, dark-line spectra are frequently called revei'sed 
 spectra. There are then three kinds of spectra: continuous 
 spectra, produced by luminous solids, liquids, or, as has been 
 found in a few instances, gases under great pressure ; bright- 
 line spectra, produced by luminous vapors ; and absorption spec- 
 tra, produced by light that has been sifted by certain media. 
 
 § 341. Spectrum analysis. — More elaborate spectroscopes 
 contain inany prisms, by which we greatly increase the purity of 
 the spectrum. (By purity is meant a freedom from the over- 
 lapping of Images of the slit, by which many lines of the 
 spectra are concealed.) They also contain an illuminated scale 
 which may be seen adjacent to the spectrum, by which the exact 
 
372 KADIANT ENERGY. — LIGHT. 
 
 position of the lines, and tlieir relative distances from one another, 
 can be accurately determined, and a telescope by which the spec- 
 trum and scale may be magnified. The positions of some of the 
 prominent lines of the solar spectrum were first determined, 
 mapped, and distinguished from one another by certain letters 
 of the alphabet b^' Fraunhofer ; hence, the dark lines of the 
 solar spectrum are commonly called Fraunhofer' s lines. So 
 far as discovered, no two substances have a spectrum con- 
 sisting of the same combination of lines ; and, in general, 
 different substances but very rarely possess lines appearing to 
 be common to both. Hence, when we have once observed and 
 mapped the spectrum of any substance, we may ever after be 
 able to recognize the presence of that substance, when emit- 
 ting light, whether it is in our laboratory or in a distant 
 heavenly body. The spectroscope, therefore, furnishes us a 
 most efficient means of detecting the presence (or absence) of 
 any elementary substance, even when it is combined or mixed 
 with other substances. It is not necessary that the given sub- 
 stance should exist in large quantities ; for example, the four- 
 teen-millionth part of a milligram of sodium can be detected bj"^ 
 the spectroscope. Substances that are not easily converted into 
 vapors at low temperatures may be placed between the poles 
 of an electric battery or an induction coil. The heat generated 
 by electricity will vaporize all substances. After maps of the 
 spectra of all known substances have been made out, if, on ex- 
 amination of a complex substance, any new lines should at any 
 time appear in the spectrum, it would indicate the presence of 
 a substance hitherto undiscovered. It was thus that the elements, 
 caesium, rubidium, thallium, and indium were discovered. 
 
 § 342. Celestial chemistry and physics. — The spectrum 
 of iron has been mapped to the extent of 460 bright lines. The 
 solar spectrum furnishes dark lines corresponding to nearly all 
 these bright lines. Can there be any doubt of the existence of 
 iron in the sun? By examination of the reversed spectrum of 
 
HEAT AND CHEMICAL SPECTRA. 373 
 
 the sun, we are able to determine with certainty the existence 
 there of sodium, calcium, copper, zinc, magnesium, hydro- 
 gen, and many other known substances. Again, from our 
 knowledge of the way in which a reversed spectrum can be pro- 
 duced, we may conclude that the sun consists of a luminous 
 solid, liquid, or an intensely heated and greatly condensed gas 
 (called a pliotosphere) , and that this nucleus is surrounded by 
 iin atmosphere of cooler vapor, in which exist at least aU the 
 substances just named. The moon and other heavenly bodies 
 that are visible only by reilected sun-light give the same spectra 
 as the sun, while those that are self-luminous give spectra which 
 differ from the solar spectrum. 
 
 § 343. Heat and chemical spectra. — If a sensitive ther- 
 mometer is placed in different parts of the solar spectrum, it 
 will indicate heat in aU parts ; but the heat generally increases 
 from the violet toward the red. It does not cease, however, with 
 the limit of the visible spectrum ; indeed, if the prism is made 
 of flint glass, the greatest heat is just beyond the red. A strip 
 of paper wet with a solution of chloride of silver suffers no 
 change in the dark ; in the light it quickly turns black ; ex- 
 posed to the light of the solar spectrum, it turns dark, but 
 quite unevenly. The change is slowest in the red, and con- 
 stantly increases, till about the region indicated by G (Fig. 277) , 
 when it attains its maximum ; from this point it falls off, and 
 ceases at a point considerably beyond the limit of the violeb. 
 It thus appears that the solar spectrum is not limited to the 
 visible spectrum, but extends beyond at each extremity. Those 
 rays that lie beyond the red are usually called the ultra-red 
 rays, while those that lie beyond the violet are called the ultra- 
 molet rays. The ultra-red rays are of longer vibration-period, 
 and the ultra-violet of shorter period, than the luminous rays. 
 
 § 344. Only one kind of radiation. —The fact that radi- 
 ant energy produces three distinct effects, — viz., luminous, 
 heating, and chemical, — has given rise to a quite prevalent idea 
 
374 EADIANT ENERG-S. — LIGHT. 
 
 that there are three distinct kinds of radiation. There is, how- 
 ever, absolutely no proof that these different effects are produced 
 by different kinds of radiation. The same radiation that produ- 
 ces vision can generate heat and chemical action. The fact that 
 the ultra-red and ultra-violet rays do not affect the eye does 
 not argue that they are of a different nature from those that do, 
 but it does show that there is a limit to the susceptibility of the 
 eye to receive impressions from radiation. Just as there are 
 sound-waves of too long, and others of too short, period to 
 affect the ear, so there are etherial waves, some of too long, and 
 others of too short, period to aff'ect the eye. It is true, how- 
 ever, that waves of long period from the sun are more energetic 
 in producing heating effects than those of short period ; and 
 those of short period are more effective in generating chemical 
 action in certain substances than those of long period ; while 
 only those which lie between the extremes affect the eye. 
 
 LVII. COLOR. 
 
 § 345. Color produced by absorption. — "All objects are 
 black in the dark ; " this is equivalent to saying that without 
 light there is no color. Is color a quality of an object, or is it a 
 quality of the light which illuminates the object? 
 
 Experiment 1. We have found that common salt introduced into 
 a Bunsen flame renders it luminous, and that the light when analyzed 
 with a prism Is found to contain only yellow. Expose papers or 
 fabrics of various colors to this light in a darkened room. No one of 
 {hem exhibits its natural color except yellow. 
 
 Experiment 2. Hold a narrow strip of red paper or ribbon in the 
 red portion of the soiru" sp:ctrum; it appears red. Slowly move it 
 toward the other end of the spectrum ; on leaving the red it becomes 
 darker, and when it reaches the green it is quite black or colorless, and 
 remains so as It passes the other colors of the spectrum. Eepeat the 
 experiment, using other colors, and notice that only in light of its own 
 color does each strip of paper appear of its natural color ; while in all 
 other colors it is dark. 
 
SKY COLORS. 375 
 
 These experiments show that (1) color is a quality of the light 
 which illuminates, and not of the object illuminated; (2) in order 
 that an object may appear of a certain color, it must receive light 
 of that color; and of course if it receives other colors at the same 
 time, it must be capable of absorbing them. The energy of the 
 waves absorbed is converted into heat, and warms the object. 
 When white light strikes an object, it appears white if it reflects 
 all the colors. If red light falls upon the same object, it appears 
 red, for it is capable of reflecting red ; or it appears green, if 
 green light alone falls on it. If white light falls upon an object, 
 and all the colors are absorbed except the blue, the object ap- 
 pears blue. When we paint our houses we do not applj- color 
 to them. We apply substances called pigments, that have a 
 property of absorbing all the colors except those which we would 
 have our houses appear. 
 
 Experiment 3. By means of a porte lumilre introduce a beam of 
 light into a dark room. Cover the orifice with a deep red (copper) glass. 
 The white light, in passing through the glass, appears to be colored 
 red. Does the glass color the light red 9 
 
 Experiment 4. With the slit and prism form a solar spectrum, and 
 between the prism and screen interpose the red glass. All the colors 
 of the spectrum instantly disappear except the red. 
 
 It thus appears that a red transparent bod}' transmits onlj- 
 red, and absorbs all other colors. No bod}' gives color to light 
 that it reflects or transmits. 
 
 § 346. Sky colors. — Experiment 1. Dissolve a little white cas- 
 tile soap in a tumbler of water ; or, better, stir into the water a few drops 
 of an alcoholic solution of mastic, enough to render the water slightly 
 turbid. Place a black screen behind the tumbler, and examine the liquid 
 by reflected sunlight, — the liquid appears to be blue; examine the 
 liquid by transmitted sunshine, — it now appears yellowish red. 
 
 Skylight is reflected light. The particles of atmospheric dust 
 (of water, probably) that pervade the atmosphere, like the fine 
 particles of mastic suspended in the water, reflect blue light; 
 while, beyond the atmosphere, is a black background of darkness. 
 
376 EADIANT ENERGY. — LIGHT. 
 
 But we must not, from this, conclude that the atmosphere is 
 blue ; for, unlike blue glass, but like the turbid liquid, it trans- 
 mits yellow and red rays freely, so that, seen by reflected 
 light it is blue, but seen by transmitted light it is yellowish red. 
 
 Experiment 2. Pour some of the turbid liquid into a small test- 
 tube, and examine it and the tumbler of liquid by transmitted light ; 
 the former appears almost colorless, while the latter is quite deeply 
 colored. 
 
 When the sun is near the horizon, its rays travel a greater 
 distance in the air to reach the earth than when it is in the zenith 
 (see Fig. 261, p. 356) ; consequently, there is a greater loss by 
 absorption and reflection in the former case than in the latter. 
 But the yellow and red rays suffer less destruction, proportionally, 
 than the other colors ; consequently, these colors predominate 
 in the morning and evening. 
 
 § 347. Mixing' colors. — A mixture of all the prismatic 
 colors, in the proportion found in sunlight, produces white. 
 Can white be produced in any other way? 
 
 Elxperiiueut 1. On a black surface A (Tig. 278), about 4"™ apart, 
 lay two small rectangular pieces of paper, one yellow and the other 
 blue. In a vertical position between, and from 4™ to 
 ^g^jis^^^ gem above these papers, hold a slip of plate glass C. 
 Looking obliquely down through the glass you may 
 see the blue paper by transmitted light and the yel- 
 low paper by reflection. That is, you see the object 
 itself in the former case and the image of the object 
 in the latter cai^e. By a little manipulation, the 
 image and the object may be made to overlap one 
 another, when both colors will apparently disappear, 
 and in their place the color which is the result of 
 the mirture will appear. In this case it will be 
 white, or, rather, gray, which is white of a low de- 
 gree of luminosity. If the color is yellowish, 
 lower the glass; if bluish, raise it. 
 Experiment 2. Cut out of stiff drawing-paper two circular disks, 
 each 16"=™ in diameter. Paint one with chrome yellow, and the other 
 with ultramarine blue. Cut a radial slit in each, and pass an edge of 
 
MIXING COLORS. 
 
 377 
 
 one slit through the slit of the other, and so arrange them that one 
 shall partly fconceal the other, leaving rather more blue exposed than of 
 the yellow, as In Figure 279. Attach the disks so combined to some 
 apparatus by which they may be rapidly rotated; for example, to a 
 " color top," such as are sold at toy stores. Rotate the disks, and the 
 colors wiU be so blended in the eye as to appear gray ; or, if either color 
 predominates, arrange the disks so that less of that color will be ex- 
 posed. Mgure 280 represents " Newton's disk," which contains the 
 seven prismatic colors arranged in a proper proportion to produce gray 
 when rotated. 
 
 Fig. 279. 
 
 Kg. 280. 
 
 Hg. 281. 
 
 In a like manner, Fig. 282. 
 
 you may produce white ^ ""^ 
 
 by mixing purple and 
 green ; or, if any color 
 on the circumference 
 of the circle (Fig. 282) 
 is mixed with the color 
 exactly opposite, the 
 resulting color will be 
 white. Again, the three 
 colors, red, green, and 
 violet, arranged as in 
 Figure 281, with rather 
 less surface of the 
 green exposed than of 
 the other colors, will 
 
 give gray. Green mixed with red, in varying proportions, will 
 produce any of the colors between these two colors in the dia- 
 gram (Fig. 282) ; green mixed with violet wUl produce any of 
 
 N33«0 
 
378 KADIANT EUEKGY. LIGHT. 
 
 the colors between them ; and violet mixed with red gives purple ^ 
 but no two colors mixed will produce any of these three colors. 
 Hence, a very widely accepted theory is adopted by many, that 
 red, green, and violet are the three primary color sensations, and 
 that the other colors of the spectrum are simply the products of 
 mixtures, in varying proportions, of these three. 
 
 § 348. Mixing pigments. — Experiment 1. Mix a little of the 
 two pigments, chrome yellow and ultramarine blue, and you obtain a 
 green pigment. 
 
 The last three experiments show that mixing certain colors, 
 and mixing pigments of the same name, may produce very 
 different results. In the first experiments you actuallj^ mixed 
 colors ; in the last experiment j'ou did not mix colors, and we 
 must seek an explanation of the result obtained. If a glass 
 vessel with parallel sides containing a blue solution of sulphate 
 of copper is interposed in the path of light which forms a solar 
 spectrum, it will be found that the red, orange, and yellow rays 
 are cut out of the spectrum, i.e., the liquid absorbs these rays. 
 And if a yellow solution of bichromate of potash is interposed, the 
 blue and violet rays will be absorbed. It is evident that, if both 
 solutions are interposed, all the colors will be destroyed except 
 the green, which alone will be transmitted ; thus : — 
 
 Cancelled by the blue solution, ^ / G B V. 
 Cancelled by the yellow solution, R O Y G ^ J^. 
 Cancelled by both solutions, j^ / O^J^. 
 
 In a similar manner, when white light strikes a mixture of 
 yellow and blue pigments on the palette, it penetrates to some 
 depth into the mixture ; and, during its passage in and out, all the 
 colors are destroyed except the green ; so the mixed pigments 
 necessariljr appear green. But, when a mixture of yellow and 
 blue lights enters the eye, we get, as the result of the combined 
 sensations produced by the two colors, the sensation of white ; 
 hence, a mixture of yellow and blue gives white. 
 
EFFECT OF CONTKAST. 379 
 
 §349. Oomplementary colors.— Experiment. On a piece of 
 white, or better, gray paper, lay a circular piece of blue paper IS""™ iu 
 diameter. Attach one end of a piece of thread to the colored paper, 
 and hold the other end in the hand. Place the eyes within about 15™ 
 of the colored paper, and look steadily at the center of the paper for 
 about fifteen seconds ; then, without moving the eyes, suddenly pull 
 the colored paper away, and instantly there will appear on the gray 
 paper an image of the colored paper, — but the image will appear to be 
 yellow. This is usually called an after-image. If yellow paper is used, 
 the color of the after-image will be blue ; and if any other color given in 
 the diagram. Figure 282, the color of its after-image wiU be the color 
 that stands opposite to it. 
 
 This phenomenon is explained as follows : When we look 
 steadily at blue for a time, the eyes become fatigued by this 
 color, and less susceptible to its influence, while they are fully 
 susceptible to the influence of other colors ; so that when they 
 are suddenly brought to look at white, which is a compound of 
 yellow and blue, they receive a vivid impression from the for- 
 mer, and a feeble impression from the latter ; hence, the pre- 
 dominant sensation is j-eUow. Any two colors which together 
 produce white are said to be complementary to each other. 
 The opposite colors in the diagram. Figure 282, are complement- 
 ary to one another. 
 
 § 350. Effect of contrast. — When any two colors given in 
 the circle. Figure 282, are brought in contrast, as when they 
 are placed next one another, the effect is to move them farther 
 apart. For example, if red and orange are brought in contrast, 
 the orange assumes more of a yellowish hue, and the red more 
 of a purplish hue. Colors that are already as far apart as pos- 
 sible, e.g., yellow and blue, do not change their hue, but merely 
 cause one another to appear more brilliant. 
 
 § 351. Color produced by interference. —Experiment l. 
 
 In a vise or other convenient instrument, press two clean pieces of 
 thick plate glass firmly together. A number of colors will be seen 
 arranged in a certain order, and forming curves more or less regular 
 around the point of pressure. 
 
380 
 
 RADIANT ENERGY. — LIGHT. 
 
 Experiment 2. Paint one side of a piece of window glass with In- 
 dia Ink so as to render it quite opaque ; then, when dry, with the point 
 of a needle rule fifteen to twenty parallel lines in the ink, about 2°™ 
 apart, cutting quite through the ink, so that light may pass through the 
 scratches. Now stand at a distance of ten feet or more from a kerosine 
 or gas flame, and look through the glass with one eye at the flame, 
 edge on ; move the glass to and from the eye slowly, so as to properly 
 focus it, and you will see many spectra of the flame on each side of it, 
 separated by dark intervals. 
 
 Experiment 3. Place the ruled glass in the path of a beam of light 
 thrown into a dark room by a parte lumiere, and project an image of the 
 glass on a screen by means of a convex lens of two to five inches focal 
 length, and you will obtain a series of beautiful spectra. 
 
 Kg. 283. 
 
 If in the path of the beam a red glass is interposed, a large 
 number of alternating red and dark lines may be obtained, though 
 the experiment is a difficult one. Let us study the last result. 
 Let the series of parallel lines AB (Pig. 283) represent the 
 series of waves constituting the beam of light before it strikes 
 the ruled glass CD; and EP, the portions of the same waves 
 that succeed in passing through the scratches, GH and MN. 
 The wave-lengths and the width of the scratches, etc., are 
 
COLOR PEODUOED BY INTEEFEEENCE. 381 
 
 immensely exaggerated in the diagram. Now, if you watch 
 waves of water as they beat against an obstacle rising above its 
 surface, you will see that part of their energy is expended in 
 forming a new set of waves, which we will call secondary waves, 
 radiating from the obstacle and winding around behind it. In a 
 similar manner, secondary waves of light are generated at the 
 edges of obstacles against which light grazes. This apparent 
 bending of the waves of light round the edges of opaque bodies 
 receives the name of diffraction. Sections of such waves are 
 represented in the diagram as crossing the original or primary 
 waves at certain points, and also one another, behind the obsta- 
 cle M. The continuous lines represent one phase of the waves, 
 and the dotted lines the opposite phase, as crest and trough. 
 Now, it will be seen that at certain points (denoted by heavy 
 dots) which lie in the same line as db, the primary and secondary 
 waves meet in similar phases ; and the consequence is, that the 
 point 6 of the screen P is illuminated by the combined action 
 of the two sets of waves. But at other points (denoted by 
 small crosses), as cd, the opposite phases of the two sets of 
 waves coincide with one another, and the result is that they 
 tend to neutralize one another ; and consequently the point d 
 of the screen is deprived of light, and a dark line occurs at 
 this place. In a similar manner the points h, i, j, etc., are 
 illuminated by the joint action of the two sets of waves, while 
 the points e, /, g, etc. , are deprived of light by their mutual 
 destruction. Such will be the result when monochromatic light, 
 or light of one wave-length is used, as is approximately the case 
 when we interpose the red glass. But if white light, or light 
 of various wave-lengths is used, it will happen that those 
 places which are deprived of red light will receive light of 
 other colors ; hence the color effects produced when white light 
 passes through the ruled glass. Of course waves are generated 
 at the points G and N, as well as at the points H and M, but 
 they are omitted for the sake of simplicity. This figure illus- 
 trates only in a very incomplete way the complex phenomena. 
 
382 EABIANT ENERGY. — LIGHT. 
 
 Such experiments as the above furnish a very strong argument 
 for the wave theory of light, since two lights produce darkness 
 apparently in a manner analogous to that in which two sounds 
 produce silence. 
 
 Thin, transparent films of varying thickness, such as the film 
 of a soap bubble, are well suited to show the effects of inter- 
 ference of light. Some of the light which strikes the anterior 
 surface of the film is reflected ; another portion enters the film, 
 and is reflected from the posterior surface ; but, by travelling 
 twice through the film, the wave loses ground, so that, on emer- 
 gence, its phases may or may not correspond with the phases 
 of the former portion : this will depend evidently upon the 
 thickness of the film at a given point, and the length of the 
 waves striking that point. In this manner the phenomena ob- 
 tained in the first experiment are explained ; the film in this 
 case is the layer of air between the two surfaces of glass.* 
 
 Colors are produced by reflection from the surfaces of thin transpar- 
 ent films of all kinds f for example, the colors of the soap bubble, of oil 
 on water, of the thin coating of metallic oxide formed in tempering 
 steel, the changeable colors of the peacock's feathers and of certain 
 insects' wings, the colors seen in cracks in glass and ice, are all colors 
 of thin films. The halos seen around the moon or a street lamp on a 
 misty evening, and the rainbow tints seen bordering the eyelashes 
 when, with eyes partially closed, you look at a strong light, are exam- 
 ples of colors produced by diffraction. 
 
 Waves of light which emanate from the points H and M, 
 Figure 283, travel equal distances to reach the point i oh the 
 screen ; but to reach the point g, the waves from H must travel 
 just one-half of a wave-length farther than the waves from M ; 
 and to reach the point J, thej'' must travel just one wave-length 
 farther. Hence, if we can ascertain the difference between the 
 two distances, B.g and Mg, we obtain the wave-length for that 
 color. In this manner the wave-lengths given in § 336 were 
 ascertained. 
 
DOUBLE EEPKACTION. 
 
 383 
 
 LVIII. DOUBLE 
 
 REFRACTION AUD 
 LIGHT. 
 
 POLARIZATION OF 
 
 § 352. Double refraction. —Experiment. Through a card 
 make a pin-hole, and hold the card so that you may see skylight through 
 the hole. Now bring a crystal of Iceland spar, Figure 284, between 
 the eye and the card, 
 
 Kg. 284. 
 
 Fig. 285. 
 
 c 
 
 
 b 
 
 \\ 
 
 ■. 
 
 . Kb 
 
 \\-''%A\ 
 
 ^\^ 
 
 . V XX 
 
 
 \ 
 
 
 I U 
 
 and look at the hole 
 through two parallel 
 surfaces of the crys- 
 tal. There will appear 
 to be two holes, with 
 light shining through 
 each. Cause the crys- 
 tal to rotate in a plane 
 parallel with the card, 
 and one of the holes 
 will appear to remain nearly at rest, while the other rotates around the 
 first. A ray of light na immediately on entering the crystal is divided 
 into two parts, one of which obeys the regular law of refraction ; the 
 other does not. The former is called the ordinary ray; the latter, the 
 extraordinary ray. The rays issue from the crystal parallel with one 
 another. In all crystals which produce this phenomenon there is one 
 direction, and in some two directions, in which, if an object is looked 
 at through the crystal, it does not appear double. If all the edges 
 of a crystal of Iceland spar are equal, and it is cut by two planes near 
 each extremity of the line AB, which connects the two opposite solid 
 obtuse angles, and at right angles to it, as shown in Figure 285, ob- 
 jects viewed in this line, or in any line parallel with it, do not appear 
 double. 
 
 In every direction in which one looks through the crystal, 
 except parallel to AB, objects seen through it appear double. 
 
 Fig. 286. 
 
 (See Fig. 286.) The line AB is caUed 
 
 the optic axis of the crystal, and is a line 
 
 around which the molecules of the crystal 
 
 appear to be aiTanged symmetrically. A 
 
 crystal is called uniaxial when it has only 
 
 one optic axis, and biaxial when it has two such axes. Crystals 
 
 of many other substances possess the property of causing objects 
 
384 
 
 EADIANT ENERGY. 
 
 • LIGHT. 
 
 seen through them to appear double. This phenomenon is called 
 double refraction. 
 
 mg. 287. 
 
 Fig. 288. 
 
 § 353. Polarization. — Slices of crystals of the mineral 
 tourmaline, cut in planes parallel with their axes, are prepared 
 and sold for optical experiments. If two of these slices simi- 
 larly situated, as in 
 Figure 287, are placed 
 between the eye and a 
 card pierced by a hole, 
 the hole will be plainly 
 visible. But if one of 
 the slices is slowly rotated in a plane at right angles with the 
 mg. 289. beam of light, the hole 
 
 wiU grow dimmer until the 
 slice has psissed through 
 a quarter of a revolution 
 (as represented in Figure 
 288), when it disappears. If the rotation is continued, the hole 
 reappears, faint at first, but at the end of another quarter- 
 revolution it reaches its maximum brightness. Thus, at each 
 quarter-revolution it is alternately extinguished and restored. 
 
 It appears, then, that light which has passed through one 
 transparent slice of tourmaline diflfers so much from common 
 light, that a second similar slice may act like an opaque body, 
 and stop it altogether. The action of the tourmaline may be 
 compared to that of a grating (A, Fig. 289) formed of parallel 
 vertical rods, which will allow all vertical planes (as aa') to pass, 
 but stops the planes (as cc') that are at right angles to these rods. 
 Any plane that has succeeded in passing one grating will readily 
 pass a second similarly placed. But if the second grating B is 
 turned so that its rods are at right angles to the first, the plane 
 that has succeeded in getting through the first grating will be 
 stopped by the second. Light, in this condition, is said to be 
 polarized; polarization is either the act of producing the change 
 
POLABIZATION. 
 
 386 
 
 to the light, or the result of the change, and the instrument used 
 is & polarizer. 
 
 In order to understand this phenomenon, it is necessary to 
 know more of the un- Big. 290. 
 
 dulatory theory of light. 
 "This theory supposes 
 that the undulations in 
 ether which constitute 
 light are much like undulations in a cord when one end is shaken 
 by a hand, as seen in Figure 290. If the hand moves vertically, 
 all the undulations will lie in a vertical plane ; if the movements 
 of the hand are horizontal or oblique, the undulations lie in 
 corresponding planes. So we can produce these waves on the 
 rope in any plane passing through the rope, and can change 
 rapidly from one plane to another. These waves appear differ- 
 ently when viewed from difierent sides. If we could look end- 
 wise at a ray of light for an instant, it is believed that we should 
 see the ether particles vibrating, as in the figure of the rope, in 
 
 Fig. 291. 
 
 one plane ; but in only a thousandth of a second so many million 
 waves reach the eye, that there is time for the vibrating par- 
 ticles, which, like the hand, start the waves, to vibrate in many 
 planes. In an ordinary beam of light, as it reaches the eye, 
 there are therefore undulations in all possible planes, as is par- 
 tially represented by the cross section A, Figure 291. But any 
 motion may be considered as the effect of two forces that would 
 produce motions in directions at right angles to one another. 
 So here, for many practical purposes, the vibrations may be 
 regarded as taking place in only two sets of planes at right 
 
386 EADIANT ENERGY. — LIGHT. 
 
 angles to one another, as represented by B of the same figure. 
 Now, when a ray of light, consisting, according to supposition, of 
 undulations in planes at right angles to one another, strikes a slice 
 of tourmaline, its molecular structure allows those undulations 
 which are in planes parallel with its axis to pass through, but 
 it absorbs those undulations that are in planes at right angles 
 to its axis. By this means the undulations are reduced to those 
 in parallel planes only, as represented in C. The unaided eye 
 cannot usually detect any difference between common and polar- 
 ized light. An instrument which will enable the eye to detect 
 polarized light is called an analyzer ; thus the first slice of tour- 
 maline serves as a polarizer, and the second slice as an analyzer. 
 A complete polarizing apparatus, called a polariscope, used for 
 Pig 292. observing the phenom- 
 ena of polarized light, 
 consists essentially of a 
 polarizer and an ana- 
 ^ — lyzer. 
 
 * The favorite analyzer is 
 
 the Nicol prism, which consists of a crystal of Iceland spar divided 
 diagonally, as AB, Figure 292, and the two surfaces cemented together 
 again with Canada balsam. The extraordinary ray CE, falling upon the 
 transparent balsam, passes through it ; but the ordinary ray CN strikes 
 the balsam at a greater than its critical angle, and is therefore reflected 
 out of the crystal, and thus got rid of. Now, when polarized light 
 enters this prism in one position, it will pass freely through It, but if 
 the prism is turned 90°, none will pass through. In the example given 
 above, light is polarized by absorption. 
 
 § 354. Polarization by double refraction and by reflec- 
 tion. — If light which has undergone double refraction, as in 
 passing through a crystal of Iceland spar, is examined with an 
 analyzer, it is found that both the ordinary and the extraordi- 
 nary rays are completely polarized in planes at right angles to 
 each other. Again, light reflected obliquely from smooth sur- 
 faces, such as water, glass, and polished furniture, etc., is found 
 
DESCRIPTION OF A SIMPLE POLAEISCOPE. 
 
 387 
 
 Fig. 293. 
 
 on examination to be partially polarized. There is a definite 
 angle of incidence at wliieh the maximum polarizing effects are 
 produced. This angle varies with different substances. "With 
 glass it is 55° ; with water, 53°. 
 
 § 355. Description of a simple polarisoope. — D (Fig. 293) 
 is a plate of glass, about 15™ square, used as a polarizer. A is the 
 analyzer, — preferably a Nicol 
 prism, — so placed as to view the 
 center of the glass at the proper 
 polarizing angle (about 55°). The 
 prism may be mounted in a cork, 
 and the whole should be free to 
 rotate in its support. S is a piece 
 of ground glass used to cut off 
 the Images of outside objects. G 
 is a glass shelf, on which objects 
 to be examined are placed. The 
 instrument, covered with a black cloth, is placed on a table with S 
 toward a window. The prism can be obtained of any dealer in optical 
 apparatus. 
 
 § 356. Colors by polarization. —Experiment. Place on the 
 support G a thin film of selenite or mica, and slowly rotate the analyzer. 
 A beautiful display of colors will appear. At a certain point they will 
 appear of maximum brilliancy, then they will gradually fade away and 
 change into their complementaries. 
 
 This is reaUy a phenomenon of interference, brought about 
 through the combined agency of the object examined and the 
 polariscope. If a piece of plate glass, subjected to pressure by 
 means of a screw-clamp, or a piece of unannealed or poorly 
 annealed glass, — a glass stopper, for example, — is examined, 
 it will exhibit analogous phenomena. 
 
RADIANT ENERGY. — LIGHT. 
 
 LIX. THERMAL EFFECTS OF RADIATION. 
 
 § 357. Diathermancy and athermanoy. — What becomes 
 of radiations that strike a body depends largely upon the char- 
 acter of the body. If the nature of the body is such that its 
 molecules can accept the motion of the ether, the undulations 
 of ether a,re said to be absorbed by the body, and the body is 
 thereby heated; that is, the undulations of ether are trans- 
 formed into molecular motion or lieat. A good illustration of 
 this is the experiment with blackened glass, page 325. On the 
 other hand, the unblackened glass allows the radiations to pass 
 freely through it, and very little is transformed into heat. 
 Notice how cold window-glass maj'^ remain, while radiations 
 pour through it and heat objects within the room. It must be 
 constantly borne in mind, that only those radiations that a body 
 absorbs heat it; those that pass through it do not affect its tem- 
 perature. Bodies that transmit radiant heat freely are said to 
 be diathermanous, while those that absorb it largely are called 
 athermanous. The most diathermanous solid is rock salt. 
 Among the most athermanous solids are lamp-black and alum. 
 Carbon bisulphide, among liquids, is exceptionally transparent 
 to all forms of radiation ; while water, transparent to short 
 waves, absorbs the longer waves, and is thus quite athermanous. 
 
 Experiment 1. Bring the bulb of an air thermometer into the 
 focus of a burning-glass exposed to the sun's rays. The radiation 
 concentrated on the enclosed air scarcely afftects this delicate instru- 
 ment. 
 
 Experiment 2. Cover the outside of the bulb of the air thermom- 
 eter with lamx>-black and repeat the last experiment. The lamp-black 
 absorbs the radiant heat, and the heat conducted through the glass to 
 the enclosed air raises its temperature and causes it to expand and 
 rapidly push the liquid out of the stem. 
 
 Dry air is almost perfectly diathermanous. All of the sun's 
 radiations that reach the earth pass through a layer of air, from 
 fifty to two hundred miles in depth, which contains a vast 
 
DIATHERMANCY AND ATHERMANCY. 389 
 
 amount of aqueous vapor. This vapor, like water, is compara- 
 tively opaque to long waves ; hence it modifies very mudh the 
 character of the radiations which r6ach the earth. This fact, 
 together with what we have learned from Exp. 2, enable us 
 to understand the method by which our atmosphere becomes 
 heated. First, a very considerable portion of the radiant energy 
 which comes to us from the sun, in the form of relatively long 
 waves, is stopped by the watery vapor in the air, which is, in 
 consequence, heated. Most of that which escapes this absorp- 
 tion heats the earth by falling upon it. The warmed earth loses 
 its heat, — partly by conduction to the air, still more largely by 
 rsi,diation outward. The form of radiation, however, has been 
 greatly changed ; for now, coming from a body at a low temper- 
 ature, it is chiefly in long waves that the energy is transmitted ; 
 while, as we have seen, it was largely in the form of short waves 
 that the earth received its heat. But it is exactly these long 
 waves which are most readily stopped by the atmosphere ; hence, 
 the atmosphere, or rather the aqueous vapor of the atmosphere, 
 acts as a sort of trap for the energy which comes to us from the 
 sun. Remove the watery vapor (which serves as a " blanket " 
 to the earth) from our atmosphere, and the chill resulting from 
 the rapid escape of heat by radiation would put an end to ail 
 animal and vegetable life. Glass does not screen us from the 
 sun's heat, but it can very effectually screen us from the heat 
 radiated from a stove or any other terrestrial object. Glass is 
 diathermanous to the sun's radiations (simply because they 
 have already lost most of the very long waves by atmospheric 
 absorption) , but quite athermanous to other radiations. This 
 is well illustrated in the case of hot-beds and green-houses. 
 The sun's heat passes through the glass of these enclosures, 
 almost unobstructed, and heats the earth; but the radiations 
 given out in turn by the earth are such as cannot pass out 
 through the glass, hence the heat is retained within the enclo- 
 sures. 
 
390 BADIANT ENERGY. — LIGHT. 
 
 § 358. All bodies radiate heat. — Hot bodies usucUly part 
 with their heat much more rapidly hj radiation than by all other 
 processes combined. But cold bodies, like ice, radiate heat even 
 when surrounded by warm bodies. This must be so from the 
 nature of the case, for the molecules of the coldest bodies 
 possess some motion, and being surrounded by ether, they can- 
 not move without imparting some of their motion to the ether, 
 and to that extent become themselves colder. 
 
 § 359. Theory of Exchanges. — Let us suppose that we 
 have two bodies, A and B, at diflferent temperatures, — A warmer 
 than B. Radiation takes place not only from A to B, but from 
 B to A ; but, in consequence of A's excess of temperature, more 
 heat passes from A to B than from B to A, and this continues 
 until both bodies acquire the same temperature. At this point 
 radiation by no means ceases, but each now gives as much as it 
 receives, and thus equilibrium is kept up. This is known as 
 the " Theory of Exchanges." 
 
 § 360. Good absorbers, good radiators. — Experiment. 
 
 Select two small tin boxes of equal capacity, — one should be bright out- 
 side, while the other should be covered thinly with soot from a candle 
 flsime. Cut a hole in the cover of each box large enough to admit the 
 bulb of a thermometer. Fill both boxes with hot water, and introduce 
 into each a thermometer. They will register the same temperature at 
 first. Set both in a cool place, and in half an hour you will find that 
 the thermometer in the blackened box registers several degrees lower 
 than the other. Then fill both with cold water, and set them in front 
 of a Are or in the sunshine, and it will be found that the temperature 
 in the blackened box rises fastest. 
 
 As bodies differ widely in their absorbing power, so they do 
 in their radiating power, and it is found to be universally true 
 that good absorbers are good radiators, and bad absorbers are 
 bad radiators. Much, in both cases, depends upon the charac- 
 ter of the surface as well as the substance. Bright, polished 
 surfaces are poor absorbers and poor radiators ; while tarnished, 
 dark, and roughened surfaces absorb and radiate heat rapidly. 
 
COMPOUND MICROSCOPE. 391 
 
 Dark clothing absorbs and radiates heat more rapidly than light. 
 (Which is better to wear at all seasons? Why? Why are cer- 
 tain parts of steam engines kept scrupulously bright? ) 
 
 § 361. Dew. — It requires no elaborate experiments to show 
 that some bodies radiate heat more rapidly than others. All 
 nature testifies to this every still, cloudless summer night. Dur- 
 ing the day objects on the earth's surface receive more heat by 
 radiation than they lose, but as soon as the sun has set this 
 is reversed. Then everything begins to cool as its heat is radi- 
 ated into space. Objects becoming cool, the air in contact with 
 them becomes chilled ; its watery vapor condenses, and collects 
 in tiny liquid drops on their surfaces. But these dew-drops 
 collect much more abundantly on certain things, such as grasses 
 and leaves, than on others, such as stones and earth. The 
 reason that it does not collect on the latter so freely, is because 
 of their poor radiating power ; they do not get cool as rapidly. 
 
 Fig. 294. 
 
 LX. SOME OPTICAL INSTRUMENTS. 
 
 §362. Compound mioroscope. — The simple microscope 
 was described on page 362. When it is desired to magnify an 
 object more than can be done conveniently and with distinct- 
 ness by a single lens, two convex lenses are used, — one (O, 
 Fig. 294) called the object-glass, to form a magnified real image 
 
392 BADIANT ENERGY. — LIGHT. 
 
 A'B' of the object AB ; and the other (E) called the eye-glass, 
 to magnify this image so that the image A'B' appears of the size 
 A"B". In the same sense as we look at the object with one 
 lens when we use a simple microscope, here we look at A'B'. 
 
 S 363. Astronomical telescope. — The astronomical re- 
 fracting telescope consists essentially, like the compound micro- 
 scope, of two lenses. The object-glass (0, Fig. 295) forms a 
 real diminished image ab of the object AB ; this image, seen 
 through the eye-glass E, appears magnified and of the size cd. 
 The object-glass is of large diameter, in order to collect as 
 much light as possible from a distant object for a better illumi- 
 nation of the image. Some idea of the power of some of our 
 
 Fig. 296. 
 
 best telescopes may be obtained from the fact that Mr. Clark 
 of Cambridgeport has made a telescope of such magnifying 
 power, and possessing such distinctness of definition, that a ball 
 two inches in diameter, and two hundred and fifty miles distant 
 (about the distance between Boston and New York), would be 
 distinctly visible as a body of perceptible dimensions, if properly 
 illuminated. 
 
 § 364. Photographer's camera. — The photographer's cam- 
 era, or camera obscura, of which AB, Figure 296, represents a 
 vertical section, consists of a dark box painted blaiok on the 
 interior. A screen of ground glass S forms a partition in the 
 
THE HUMAN BYE. 
 
 393 
 
 box. A sliding tube T contains a convex lens L. If an object 
 D is placed some distance in front, and the distance of the lens 
 from the screen is suitably adjusted, a distinct, real, and inverted 
 image can be seen upon the screen by looking through the 
 aperture C. When the image is properly focused, the photo- 
 grapher replaces the ground glass plate by a sensitized plate, 
 and the chemical power of the sun's rays paints a true picture 
 of the object on this plate. 
 
 Kg. 296. 
 
 B 
 
 S 
 
 T 
 
 L 
 
 c 
 
 
 
 / 
 
 A 
 
 
 
 
 Tig. 297. 
 
 § 365. The human eye. — Figure 297 represents a horizontal 
 section of this wonderful organ. Covering the front of the eye, like a 
 watch-crystal, is a transparent coat 1, 
 called the cornea. A tough membrane 
 2, of which the cornea is a continua- 
 tion, forms the outer wall of the eye, 
 and is called the sclerotic coat, or 
 "white of the eye." This coat is 
 lined on the interior with a delicate 
 membrane 3, called the choroid coat; 
 the latter is covered with a black 
 pigment, which prevents internal 
 reflection. The inmost coat i, called 
 the retina, is formed by expansion 
 of the optic nerve 0. The front of 
 the choroid coat ii is called the iris ; 
 its color constitutes the so-called 
 
 "color of the eye." In the center of the iris is a circular opening 5, 
 called the pupil, whose function is to regulate, by involuntary enlarge- 
 ment and contraction, the quantity of light admitted to the interior 
 chamber of the eye. Just back of the iris Is a tough, elastic, and 
 transparent body 6, called the crystalline lens. This lens divides the 
 
394 RADIANT ENERGY. — LIGHT. 
 
 eye into two chambers ; the anterior chamber 7 is filled with a limpid 
 liquid, called the aqueous humor; the posterior chamber 8 is filled with 
 a jelly-like substance, called the vitreous humor. 
 
 The eye is a camera obscura, in which the retina serves as a 
 screen. Images of outside objects are projected by means of 
 the crystalline lens, assisted by the refractive powers of the 
 humors, upon this screen, and the impressions thereby made ou 
 this delicate network of nerve filaments are conveyed by the 
 optic nerve to the brain. If the two outer coatings are removed 
 from the back part of the eye of an ox, recently killed, so as to 
 render it somewhat transparent, true images of whole land- 
 scapes may be seen formed upon the retina of the eye, when it 
 is held in front of your eye. With the ordinary camera, the 
 distance of the lens from the screen must be regulated to adapt 
 itself to the varying distances of outside objects, in order that 
 the' images may be properly focused on the screen. In the eye 
 this is accomplished by changing the convexity of the lens. We 
 can almost instantly and involuntarily change the lens of the 
 eye, so as to form on the retina a distinct image of an object 
 miles away or only a few inches distant. The nearest limit at 
 which an object can be placed, and form a distinct image on the 
 retina, is about five inches. On the other hand, the normal eye 
 in a passive state is adjusted for objects at an infinite distance. 
 Curious enough, the retina on careful examination is found to 
 be covered with little projections which have received, from 
 their appearance, the names of rods and cones. These project 
 from the nerve fibres very much like nap from the threads of 
 velvet. It is thought that these rods and cones receive and 
 respond to the vibrations of light ; in other words, that they 
 CO- vibrate with the undulations of the ether, and thereby we get 
 our sensation of light. 
 
 § 366. Chromatic aberration. — There is a serious defect 
 in ordinary convex lenses, to which we have not before alluded, 
 called chromatic aberration, which has required the highest skill 
 
STEREOPTICON. 
 
 395 
 
 of man to correct. The convex lens both refracts and disperses 
 the light that passes through it. The tendency, of course, is to 
 bring the more refrangible rays, as the violet, to a focus much 
 sooner than the less refrangible rays, such as the red. The 
 result is a disagreeable coloration of the images that are formed 
 by the lens, especially by that portion of the light that passes 
 through the lens near its edges. This evil has been overcome 
 very effectually by combining with the convex lens a plano-con- 
 cave lens. Now, if a crown-glass convex lens is taken, Fig. 298. 
 a flint-glass concave lens may be prepared that will 
 correct the dispersion of the former without neutralizing 
 all its refraction. 1 A compound lens, composed of these 
 two lenses (Fig. 298) cemented together, constitutes what 
 is called an achromatic lens. 
 
 Fig. 299. 
 
 §367. Stereopticon. — This instrument is extensively em- 
 ployed in the lecture-room for producing on a screen magnified 
 images of small transparent pictures on glass, called slides; 
 also for rendering a certain class of experiments visible to a 
 large audience by projecting them on a screen. The light most 
 commonly used is the lime light, though the electric light is pre- 
 ferred for a certain class of projections. The flame of an oxyhy- 
 drogen blow-pipe A, Figure 299, is directed against a stick of 
 lime B, and raises it to a white heat. The light of the lime is 
 converged — by means of a convex lens c, called the condensing 
 lens (usually two plano-convex lenses are used) — upon the slide 
 
 • The refractive and dispersive powers of the two lenses are not proportional. 
 
396 EADIANT ENERGY. — LIGHT. 
 
 D, and strongly illuminates it. In front of it is placed another 
 convex lens E (or a system of lenses) , called the projecting lens. 
 The latter lens produces (or projects) a real, inverted, and 
 magnified image of the picture on the screen S. The mounted 
 lens E may be slid back and forth on the bar F, so as properly 
 to focus the image. (For useful information relating to the 
 operation of projection, see Dolbear's Art of Projection.) 
 
APPENDIX, 
 
;]]] 
 
 The area of this figure Ib a square decimeter. 
 A cuhe of water, one of whose sides is this area^ 
 Js a cubic decimeter or a liter of water, and at the 
 temperature of 4" C. weighs a kilogram. The 
 same volume of air at 0^ C., and under a pressure 
 of one atmosphere, weighs 1.293 grams. The 
 gram is the weight of 1" of pure water at 4" C. 
 
 898 
 
APPENDIX. 
 
 SECTION A. 
 
 Metric system of measures. — The term metric is derived from 
 the word meter, which is the name of the fundamental unit employed 
 in this system for measuring length, and from which aU other units 
 of the system are derived. The meter is, approximately, the ten- 
 millionth part of the distance from the Equator to the North Pole. 
 Defined by law, it is the distance at 0° C. between two lines engraved 
 on a platinum bar kept in the Paris Observatory. The gram is theo- 
 retically the mass of l" of distilled water at 4P C. By law it is -^^ 
 of the muss of a piece of platinum preserved in the same observatory. 
 At Washington are kept exact copies of the meter and other metric 
 measures. 
 
 The following tables contain all the requirements of this book. The 
 pupil will find more complete tables in any good arithmetic. 
 
 TABLE OF LENGTHS. 
 
 10 millimeters ("™) = 1 centimeter (""). 
 10 centimeters = 1 decimeter C*™). 
 
 10 decimeters = 1 meter (">). 
 
 1000 meters = 1 kilometer (^"). 
 
 TABLE OF ABEAS. 
 
 100 square millimeters (9">™) = 1 square centimeter (i™'). 
 100 square centimeters = 1 square decimeter {i^. 
 
 100 square decimeters = 1 square meter («■"). 
 
 1,000,000 square meters = 1 square kilometer (fl"™). 
 
400 APPENDIX. 
 
 TABLE OF VOLTOCES. 
 
 1000 cubic millimeters (cmni) = i cubic centimeter (""" or °°) . 
 1000 cubic centimeters = 1 cubic decimeter («'■>'). 
 
 1000 cubic decimeters «= 1 cubic meter (*"). 
 
 The volumes of liquids and gases are either expressed in the units 
 of the above table or in liters. The liter is l"*-, or 1000«=. 
 
 TABLB OF MASSES OR WEIGHTS. 
 
 10 milligrams (""8) = 1 centigram (<«). 
 10 centigrams = 1 decigram (*e). 
 10 decigrams = 1 gram (e). 
 
 1000 grams = 1 kilogram or kilo (k). 
 
 TABLB OF EQUIVALENTS. 
 
 1 inch = 0.0254 meter, or about 2J centimeters. 
 1 foot = 0.3048 meter, or about 30 centimeters. 
 lyard= 0.9144 meter, or about ^ meter. 
 1 mile = 1609.0000 meters, or about 1^ kilometers. 
 
 1 U.S. ^ ^ quart = i 0.946 liter, _ ^ ,,,,^ ^ l^ss^ ^,^^ ^ ^^^ 
 
 1 U.S. gallon = 3.785 liters, or about S-^ liters. 
 
 ,1 avoirdupois , 0.02835 kilo, „„„„+,,„, j less 
 
 ^^ Troy and apothecaries' o™ce = ^ ^ ^g^jg ^.^^^ or rather -j ^^^^ 
 
 than 30 grams. 
 1 avoirdupois pound = 0.45359 kilo, or about ^ kilo. 
 
 When great accuracy is not required, it will be found convenient to 
 remember that 
 
 centimeters X f = inches (nearly) ; 
 inches X f = centimeters (nearly) ; 
 
 5 meters = 1 rod (nearly) ; 
 
 also, kilos X V- = pounds (nearly) ; 
 
 pounds X^ = ^ilos (nearly). 
 
APPENDIX. 
 
 401 
 
 SECTION B. 
 
 Fig. 300. 
 
 Cutting grlasa. — Bottoms of glass bottles may be cut off, and 
 plate glass may be easily cut in any pattern desirable, by observing the 
 following directions. Procure an iron rod B, Fig. 300, 25°"" long and 
 7mm jjj diameter, and insert one end in a wooden handle C, and let the 
 exposed end be filed to a smooth surface. With a pointed piece of soap, 
 trace a line on the glass where you would cut ; and, if it is a bottle 
 that is to be cut, file a short gash A (to a depth varying with the thick- 
 ness of the glass) 
 in the bottle in the 
 direction of the 
 line drawn. Heat, 
 in a Bunsen flame, 
 the free end of the 
 rod to a bright red •""""'i- *"j*a.^ A limr _?-, 
 
 heat (the hotter 
 the better), and 
 apply the heated 
 end to the glass, as 
 
 in the figure, about l"" from one extremity of the gash for (say) about 
 five seconds (longer if the glass is very thick ; not, however, long enough 
 to crack the glass), and then quickly apply it in the same manner to 
 the other extremity of the gash, as D, and hold it firmly till you see 
 a fine crack creeping toward the rod ; then slowly move the rod along 
 the traced line, and the crack will follow faithfully the movements 
 of the rod. If plate glass is to be cut, file a small gash E in one 
 edge; and, commencing with this gash as before, you may cut in the 
 glass a circle, or any design you desire. To bore holes in glass, make 
 a thick paste by partially dissolving gum camphor in spirits of tur- 
 pentine ; nip off a short piece from the end of a small rat-tail file, 
 and, keeping the ragged end wet with the paste, you can readily bore 
 a hole by employing strong pressure, and by a twisting movement as 
 in boring. 
 
402 
 
 APPENDIX. 
 
 SECTION C. 
 
 TABLES OF SPECIFIC GRAVITIES OF BODIES. 
 [The standard employed iU the tables of solids and liquids is distilled water at 4' C] 
 
 I. Solids. 
 
 Antimony 6.712 
 
 Bismuth 9.822 
 
 Brass 8.380 
 
 Copper, cast 8.790 
 
 Iridium 23.000 
 
 Iron, cast 7.210 
 
 Iron, bar 7.780 
 
 Gold 19.360 
 
 Lead, cast 1 1.350 
 
 Platinum 22.069 
 
 Silver, cast 10.470 
 
 Tin, cast 7.290 
 
 Zinc", cast 6.860 
 
 Anthracite coal 1.800 
 
 Bituminous coal 1.250 
 
 Diamond 3.530 
 
 Glass, flint 3.400 
 
 Human body 0.890 
 
 Ice 0.920 
 
 Quartz 2.650 
 
 Rock salt 2.257 
 
 Saltpetre 1.900 
 
 Sulphur, native 2.033 
 
 Tallow 0.942 
 
 "Wax 0.969 
 
 Cork 0.240 
 
 Pine 0.650 
 
 Oak 0.845 
 
 Beech 0.852 
 
 Ebony 1.187 
 
 II. Liquids. 
 
 Alcohol, absolute 0.800 
 
 Bisulphide of carbon 1.293 
 
 Ether 0.723 
 
 Hydrochloric acid 1.240 
 
 Mercury 13.698 
 
 Milk 1.032 
 
 Naphtha 0.847 
 
 Nitric acid 1.420 
 
 Oil of turpentine 0.870 
 
 Olive oil 0.915 
 
 Sea water 1.026 
 
 Sulphuric acid 1.841 
 
 "Water, 4° C, distilled. .. 1.000 
 
 "Water, 0° C. , distilled ... 0.999 
 
 III. Oases. 
 [Standard : air at 0° C. ; barometer, 76"°.] 
 
 Air 1.0000 
 
 Ammonia 0.5367 
 
 Carbonic acid 1.5290 
 
 Chlorine 3.4400 
 
 Hydrochloric acid 1.2540 
 
 Hydrogen 0.0693 
 
 Nitrogen 0.9714 
 
 Oxygen 1.1057 
 
 Sulphuretted hydrogen.. 1.1912 
 Sulphurous acid 2.2474 
 
APPENDIX. 
 
 403 
 
 SECTION D. 
 
 TABLE OF NATURAL TANGENTS. 
 
 Deg. 
 
 Tangent. 
 
 Deg. 
 
 Tangent. 
 
 Deg. 
 
 Tangent. 
 
 Deg. 
 
 Tangent. 
 
 1 
 
 .017 
 
 24 
 
 .445 
 
 47 
 
 1.07 
 
 70 
 
 2.75 
 
 2 
 
 .035 
 
 25 
 
 .466 
 
 48 
 
 1.11 
 
 71 
 
 2.90 
 
 3 
 
 .052 
 
 26 
 
 .488 
 
 49 
 
 1.15 
 
 •72 
 
 3.08 
 
 4 
 
 .070 
 
 27 
 
 .510 
 
 50 
 
 1.19 
 
 73 
 
 3.27 
 
 5 
 
 .087 
 
 28 
 
 .532 
 
 51 
 
 1.23 
 
 74 
 
 3.49 
 
 6 
 
 .105 
 
 29 
 
 .554 
 
 52 
 
 1.28 
 
 75 
 
 3.73 
 
 7 
 
 .123 
 
 80 
 
 .577 
 
 53 
 
 1.33 
 
 76 
 
 4.01 
 
 8 
 
 .141 
 
 31 
 
 .601 
 
 54 
 
 1.38 
 
 77 
 
 4.33 
 
 9 
 
 .158 
 
 32 
 
 .625 
 
 55 
 
 1.43 
 
 78 
 
 4.70 
 
 10 
 
 .176 
 
 33 
 
 .649 
 
 56 
 
 1.48 
 
 79 
 
 5.14 
 
 11 
 
 .194 
 
 34 
 
 .675 
 
 57 
 
 1.54 
 
 80 
 
 5.67 
 
 12 
 
 .213 
 
 35 
 
 .700 
 
 58 
 
 1.6Q 
 
 81 
 
 6.31 
 
 13 
 
 .231 
 
 36 
 
 .727 
 
 59 
 
 1.66 
 
 82 
 
 7.12 
 
 14 
 
 .249 
 
 37 
 
 .754 
 
 60 
 
 1.73 
 
 83 
 
 8.14 
 
 16 
 
 .268 
 
 38 
 
 .781 
 
 61 
 
 1.80 
 
 84 
 
 9.51 
 
 16 
 
 .287 
 
 39 
 
 .810 
 
 62 
 
 1.88 
 
 85 
 
 11.43 
 
 17 
 
 .306 
 
 40 
 
 .839 
 
 63 
 
 1.96 
 
 86 
 
 14.30 
 
 18 
 
 .325 
 
 41 
 
 .869 
 
 64 
 
 2.05 
 
 87 
 
 19.08 
 
 19 
 
 .344 
 
 42 
 
 .900 
 
 65 
 
 2.14 
 
 88 
 
 28.64 
 
 20 
 
 .364 
 
 43 
 
 .933 
 
 66 
 
 2.25 
 
 89 
 
 57.29 
 
 21 
 
 .384 
 
 44 
 
 .966 
 
 67 
 
 2.36 
 
 90 
 
 Infinite. 
 
 22 
 
 .404 
 
 45 
 
 1.000 
 
 68 
 
 2.48 
 
 
 
 23 
 
 .424 
 
 46 
 
 1.036 
 
 69 
 
 2.61 
 
 
 
404 
 
 APPEKDIX. 
 
 SECTION B. 
 
 Galvanometer. — A galvanometer that will answer sufficiently 
 well all the purposes of this book can be easily and cheaply prepared 
 as follows : Make a wooden frame A (Fig. 301), 10™ square and 
 2.5™ thick, joined by wooden or brass pins in grooves ; on it wind 50 
 to 60 turns (l lb.) insulated No. 16 wire in three layers, leaving I"" 
 space in the center (in the figure this space is exaggerated in order 
 to show the position of the needles), and insert the extremities in the 
 brass screw-cups L and K. In this frame insert a copper or brass 
 wire D, carrying a cork E, which supports a silk fibre F and a strip of 
 
 Big. 301. 
 
 11 
 
 paper G. Magnetize a large sewing-needle H, and insert in the paper, 
 as in the figure ; also insert a small copper wire I in the paper for a 
 pointer, and suspend the whole so that the needle will swing freely 
 between the upper and lower windings of wire, and the pointer will be 
 just above the coils. Prepare a graduated circle on a card M, having 
 a hole in the center through which to pass the needle, and lay it on the 
 coU. To prevent disturbance from currents of air, cover the whole 
 with a frame N, having a glass plate laid over its top. Connect the 
 battery wires with the screw-oups L and K. The cost of material need 
 not exceed 75 cents. 
 
AtPENDIX. 
 
 405 
 
 SECTION F. 
 
 Kind of battery to use. — Several things must be considered 
 in the selection of a battery for a particular use. Among the most 
 important of these are the intensity of current required, and the 
 service required; i.e., whether continuous, temporary, or occasional 
 currents are wanted. The cost is of consequence, but that must be 
 governed mainly by the preceding considerations. In the following- 
 arrangement, preferences are given to the several batteries by nimi- 
 bers, in the order in which they occur against the several uses 
 specified : — 
 
 ITAMES OF BATTERIES, ETC. 
 
 1. Smee. 4. Daniell. 
 
 2. Leclanche. 5. Grenet. 
 
 3. Gravity. 6. Bunsen or Grove. 
 
 7. Magneto or dy- 
 namo machines. 
 
 8. Thermo-batteries. 
 
 USES CELLS ARE SUITED FOR. 
 
 Strong, Continuous Currents. 
 
 Electrotyplng or Electro-plating 7, 4, 1, 3. 
 
 Electro-magnets 3, 4, 1. 
 
 Electric light 7, 6. 
 
 Telegraph (closed circuit) 3,4. 
 
 Temporary. 
 
 Induction coils 6, 6, 4, 3. 
 
 Medical coils 5> !• 
 
 Occasional. 
 
 Annunciators, domestic bells 2,1,3,4. 
 
 Exploding fuses 2,4. 
 
 Electrical measurements (constant current) 8, 4, 3. 
 
406 
 
 APPENDIX. 
 
 SECTION G. 
 
 Apparatus to illustrate wave-motion. — The most efficient 
 apparatus for this purpose that we have seen may be constructed as 
 f oUows. Procure forty wooden return-balls (sold at toy stores) ; sus- 
 pend them by strings (better, fine wires) about 1™ long, as in Figure 
 302, and about 7™ apart. Connect all the balls horizontally by small 
 
 Fig. S02. 
 
 elastic cord (better, small spiral wire coil), and connect the ball at one 
 extremity of the series with a suspended weight B (weighing about 
 I'') , and from the ball at the other extremity suspend a small weight 
 A, which may be easUy removed when desirable. By a sunple vibrar 
 tion given with the hand to A, a wave, as CD, wiU be projected 
 through the series, and on reaching B will be reflected ; though when 
 reflection is wanted, B.had better be replaced by a hook attached to a 
 wall. 
 
APPENDIX. 
 
 407 
 
 SECTION H. 
 
 Porfce Lumifere. — Two half -sections of a tube A and B (Fig. 303) 
 may easily be sawn from a block of pine wood. These glued together 
 at their edges make the tube C. 
 This tube is 20™ long and 15™" in 
 diameter, with a bore of II™ diam- 
 eter. Raise a window-sash about 
 50™", and fit a board D just to fill 
 the opening. In the middle of this 
 board cut a hole just large enough 
 to receive the tube, and allow it to 
 turn in the hole freely. Attach a 
 bolt E to the board D, and about 
 12™ from one end of the tube bore 
 a row of holes around the tube, 
 1™ in depth and about 1™ apart, 
 to receive the bolt. By means of a 
 hinge, attach to the outer edge of the tube a board G, 30™ long, 14:<"» wide, 
 and 1.5™ thick. A mirror F, 26™ long and 12™ wide, is fastened by 
 tacks with large heads to the upper surface of this board. A stout 
 string attached to one of the long edges of the board is carried through 
 the tube and fastened to a binding screw H. When the mirror is to 
 be adjusted so as to receive the sun's rays and reflect them through the 
 tube, rotate the tube, and raise or depress the mirror by means of the 
 string, so as to adapt it to the position and elevation of the sun in the 
 heavens, and then fasten by means of the bolt and string. A win- 
 dow on the south side of a building should be selected for experiments 
 with this apparatus. The portion of the window not occupied with 
 the board D, as well as other windows not in use, may be darkened 
 with curtains of black enamelled cloth. The whole cost of the above 
 apparatus need not exceed fl.OO. 
 
SYLLABUS. 
 
 CHAPTER I. 
 MATTER AND ITS PROPERTIES. 
 
 I. INTRODUCTION. 
 
 An experiment is a question put to Nature. 
 
 By experiment we learn that invisible air, like matter, and 
 like nothing else with which we are acquainted, can displace 
 matter {e.g., a bubble), exert pressure, and has weight ; hence, 
 we conclude that air is matter, and that matter can exist in an 
 invisible state. 
 
 No visible body of matter, however compact it may appear, 
 ever fills the space enclosed by its surface ; but every visible 
 body is a collection of countless smaller bodies called molecules, 
 separated by invisible spaces called pores. Every molecule is 
 in motion, and this motion is such as to prevent permanent 
 contact between one another. 
 
 By the mass of a body we understand the quantity of matter 
 in it ; and by its density, the mass in a unit volume. 
 
 Substances whose molecules can be separated into molecules 
 differing in substance from the original molecules are called 
 compound. Substances whose molecules have never been so 
 separated are called simple. There are known only about 71 
 of the latter, and an innumerable number of the former. 
 
 Any change in a body that does not cause a change of sub- 
 stance is a physical change. A change of substance is a chemi- 
 cal change 
 
410 SYLLABUS, 
 
 Matter is nowhere created, nowhere annihilated. The mass 
 of the universe is constant. 
 
 The tendency which matter possesses to push and to pull is 
 called force. Whatever tends to produce or alter motion is 
 force. It is manifested only in pushes and pulls. 
 
 Forces are classified as molecular or molar., according as they 
 act between molecules or larger bodies ; attractive or repellent, 
 according as they are manifested in pulls or pushes. 
 
 When, bj' external force, the molecules of a body are brought 
 nearer together, it is said to be compressed or condensed; if they 
 are brought together by internal forces, the body is said to con- 
 tract, and if they are separated by internal forces, it is said to 
 expand. 
 
 II. THREE STATES OF MATTER. 
 
 Any substance may exist in any one of three states, — solid, 
 liquid, or gaseous. 
 
 General characteristics of matter in the solid state : Immobil- 
 ity of the molecules, and permanence of shape. 
 
 Liquid state : Greater mobility of the molecules, easily poured, 
 and shaped by the containing vessels. 
 
 Gaseous state : Almost perfect freedom of motion of the mole- 
 cules ; unlimited tendency to expand ; great compressibility. 
 
 Owing to their tendencj' to flow, both liquids and gases are 
 called ^MJds. 
 
 The state which a body assumes depends on temperature and 
 pressure. 
 
 III. PHENOMENA OF ATTRACTION. 
 
 The force of attraction which exists between all bodies at 
 distances however great is called the force of gravity, and the 
 phenomenon is called gravitation. Weight is a term applied 
 to the measure of this force as exerted between the earth and 
 terrestrial objects. Weight varies as the mass, and with the 
 distance from the centre of the earth. At the same place, 
 weight is proportional to the mass. 
 
MATTER AND ITS PEOPERTIES. 411 
 
 When attraction is molecular, and between like molecules, it 
 is called cohesion; when between unlike molecules, it is called 
 adhesion. 
 
 When a body of matter in a solid state exhibits method in 
 the arrangement of its molecules, it is said to be crystalline; 
 otherwise, amorphous. Matter crystallizes, usually, while pass- 
 ing from the liquid to the solid state. 
 
 A theory, suggested as a possible explanation of the cause of 
 crystallization, is based upon the hypothesis that the molecules 
 of crystalline matter possess something akin to polarity, in which 
 case the molecules would tend to arrange themselves somewhat 
 as u'on filings do when they possess polarity. 
 
 Hardness is due to some peculiar action (not well understood) 
 of cohesion, that enables a body to resist another body tending 
 to scratch it. 
 
 When molecular forces tend to restore a body to its original 
 shape and volume after having yielded to some force, they are 
 called elastic forces, and the body is said to possess the property 
 of elasticity. 
 
 Substances which tend to break rather than suffer a permanent 
 alteration in form are said to be brittle. 
 
 Substances which, though brittle when a force is applied sud- 
 denly, will suffer a permanent change in form if subjected to a 
 gradual and long-continued stress, are called -viscous. 
 
 All substances in the solid state possess, to some extent, the 
 property of fluidity, and hence are more or less flexible, malle- 
 able, and ductile. This implies, also, that they possess a power 
 of preventing rupture when subjected to a pulling force. This 
 power, due to cohesion, is called tenacity. 
 
 Liquids ascend or are depressed in capillary tubes according 
 as the adhesion between the liquid and the tubes is greater or 
 less than the cohesion in the liquids. For the four laws of 
 capillary action, see page 36. 
 
 A liquid will dissolve a solid when the adhesion is greater 
 than the cohesion. 
 
412 SYLLABUS. 
 
 Absorption of gases by solids is caused chiefly by molecular 
 attraction, and is said to be superficial when the gases are 
 taken into the cavities of solids, and intermolecular when taken 
 into the pores. 
 
 Absorption of gases by liquids is inteimolecular, and is 
 caused both by attraction of the molecules and their incessant 
 motion. 
 
 DifRision of liquids is caused mainly by the motion of their 
 molecules. 
 
 Osmose, or the diffusion of liquids through porous septa, is 
 imperfectly understood, though it is supposed that adhesion be- 
 tween the liquids and the septa is the chief agent. 
 
 Diffusion of gases depends almost wholly on molecular motion. 
 All gases diffuse regardless of the force of gravity. 
 
 Osmose depends on the size of molecules, size of pores, and 
 on molecular motion ; very complex. 
 
CHAPTER II. 
 
 DYNAMICS. 
 
 IV. DYNAMICS OF FLUIDS. 
 
 Dynamics treats of force and motion. When several forces 
 so act on a body as to neutralize one another's effect, both the 
 forces and the body are said to be in equilibrium, A body in 
 a state of rest or uniform motion is in equilibrium. 
 
 (Can absolute rest or uniform motion exist except there 
 is absolute equilibrium? Is there any body known to be in 
 a state of absolute equilibrium, i.e., in equilibrium with refer- 
 ence to all extei'nal forces ?) 
 
 When a pushing force is resisted, i.e., when any portion of 
 the force is not effective in producing motion, there results a 
 pressure. Under similar conditions a pulling force causes 
 tension. (The word tension is also applied to the expansive 
 power of gases.) 
 
 At every point in a body of fluid, gravity causes pressure to 
 be exerted equally in all directions. In gases the pressure 
 increases with the depth ; in liquids, as the depth. 
 
 The average sea-level atmospheric pressure (and consequently 
 the tension of the air at this level) is 1033.3^ (about 1'') per 
 square centimeter, or 14.7 lbs. (about 15 lbs.) per square inch. 
 An atmosphere (when the term is used to denote pressure) is 
 the pressure of 1'' per square centimeter. Any instrument 
 which will measure atmospheric pressure is a barometer. 
 
 Makiotte's or Boyle's Law : At the same temperature the 
 volume of a body of gas varies inversely as the pressui'e, 
 density, or elastic force. 
 
 In consequence of the mobility and perfect elasticity of fluids. 
 
414 SYLLABUS. 
 
 any pressure exerted on a given area of a fluid enclosed in a 
 vessel is transmitted undiminished to every equal area of the 
 interior of the vessel. In the hydrostatic (or hydraulic) press 
 we have a practical application of this principle. 
 
 The pressure on the bottom or sides of a vessel, due to the 
 gravity of the liquid which it holds, depends on the depth and 
 area of the surface pressed upon, and the density of the liquid, 
 and is independent of the shape of the vessel and the quantity 
 of liquid. 
 
 The pressure upon any portion of a vessel is the weight of a 
 column of that liquid whose base is the area of the portion 
 pressed upon, and whose hight is the average depth of that 
 portion. 
 
 The free surface of a body of liquid, at rest, partakes of the 
 sphericity of the earth, but for most practical purposes may be 
 regai-ded as level. 
 
 V. BUOYANT FORCE OF LIQUIDS. 
 
 A solid immersed in a fluid is buoj-ed up by it in consequence 
 of the unequal pressures upon the top and bottom at their dif- 
 ferent depths, and the amount of buoyancy (or the apparent 
 loss of weight of the solid) is the weight of a body of that fluid 
 wliose volume is equal to the volume of the solid. A floating 
 solid displaces its own weight of fluid. The absolute weight of 
 a body is its weight in a vacuum. 
 
 VI. DENSITY AND SPECIFIC GRAVITY. 
 
 The speciflc gravity of a substance is the ratio of the density 
 of that substance to the density of another substance taken as 
 a standard. It is found by dividing the weight of a given 
 volume of the substance by the weight of an equal volume of 
 the standard. (In finding the specific gravity of solids and 
 liquids, state various methods of ascertaining the weight of an 
 equal volume of the standard.) 
 
DYNAMICS. 415 
 
 VII. MOTION. 
 
 Motion and rest are wholly relative terms, i.e., they are 
 applicable to an object only when considered in connection with 
 some other object. There is no such thing as absolute rest in 
 the universe. 
 
 Velocity is given in units of space and time. 
 
 Motion is uniform or varied. Varied motion is accelerated 
 or retarded. We may conceive of uniform motion though it 
 nowhere exists. 
 
 Vni. FIRST LAW OF MOTION. — INERTIA. 
 
 Motion always arises from mutual action between at least 
 two bodies, and cannot originate in an object isolated from all 
 others. 
 
 Motion in a body is caused only by another body's parting 
 with some of its power of producing motion. 
 
 Bodies receive motion gradually and part with it gradually'. 
 
 No body possesses any innate power to change its condition 
 with reference to motion or rest. It is sometimes convenient to 
 speak of this complete absence of power as a property of matter, 
 under the name of inertia. 
 
 First Law of Motion. — A body at rest remains at rest 
 (why?), and a bodj' in motion moves with uniform velocity 
 (why?) in a straight line (why?), unless acted upon by some 
 external force to change its condition. 
 
 IX. SECOND LAW OF MOTION, AND APPLICATIONS. 
 
 Second Law of Motion. — A given force has the same effect 
 in producing motion, whether the body on which it acts is in 
 motion or at rest ; whether it is acted upon by that force alone, 
 or by others at the same time. 
 
 It is usually possible to substitute for two or more forces a 
 
416 SYLLABUS. 
 
 single force which will produce the same result as the combined 
 forces. Such a force is called a resultant. 
 
 The resultant of two forces acting at an angle to each other 
 may be represented by a diagonal of a parallelogram, of which 
 the components form two adjacent sides. 
 
 Any single force may be resolved into two or more compo- 
 nents. 
 
 The resultant of parallel forces having the same direction is 
 their sum ; the resultant of two parallel forces acting in opposite 
 directions is motion in the direction of the greater force propor- 
 tionate to their difference. 
 
 When two parallel forces having the same direction act upon 
 a body at different points, the distances of their points of 
 application from the points of application of their resultant are 
 inversely as their intensities. 
 
 A pair of forces, equal, parallel, opposite, and applied at 
 opposite extremities of an object, produces only rotation, and is 
 called a couple. A couple has no resultant and no equilibrant. 
 
 X. CENTER OF GRAVITY. 
 
 The center of gravity of a body is the point of application of 
 the resultant of the forces of gravity acting on its molecules. 
 To support any body, it is only necessary to provide an equi- 
 librant for this resultant, and to applj' it at some point in the 
 line of direction. Whether a body will stand or fall depends 
 upon whether its line of direction falls within its base, i.e., 
 whether its support is applied in the line of direction. 
 
 A body tends to assume a position such that its e.g. will be 
 as low as possible, and when in such position it is said to be in 
 stable eqidlibrium. When a disturbance would lower its e.g., it 
 is said to be in unstable equilibrium; and when disturbance 
 would not lower or raise its e.g., it is in neutral equilibrium. 
 A broad base and low e.g. give stability to a body. 
 
DYNAMICS. 417 
 
 Xi; CURVILINEAR MOTION. 
 
 A curved Hue is one whose direction changes at every point. 
 To produce curvilinear motion, a continuous (why continuous?) 
 force must be applied at an angle (why?) to its otherwise 
 straight path. (See First Law of Motion.) Centrifugal force 
 is the result of the tendency of a body to move in a straight 
 line ; centripetal force is the force which compels it to depart 
 from a straight line. 
 
 Centrifugal force increases as the mass and the square of the 
 velocity ; hence, to produce circular motion, the centripetal 
 force must increase as the mass and the square of the velocity. 
 
 Xn. ACCELERATED AND RETARDED MOTION. 
 
 A body impelled by a single constant force, and encounter- 
 ing no resistance, always has a uniformly accelerated motion. 
 A moving body, encountering constant resistances, has uni- 
 formly retarded motion. The acceleration or retardation per 
 unit of time is represented by Jc (or g, when the force is gravity). 
 
 Formulas for uniformly accelerated motion : — 
 
 (1) V = (iA;x2T) = fcT 
 
 (2) s = i&(2T-l) 
 
 (3) ^ = \hT^ 
 
 Hence, velocity varies as the time, and the entire distance trav- 
 ersed as the square of the time. 
 
 The acceleration due to gravity in the Northern States, near 
 the sea level, when there are no resistances, is (g) 9.8°'(or 32.2 
 ft.) per second. This is the measure of the force of gravity at 
 these places. 
 
 All bodies, of whatever mass, density, or substance, fall with 
 equal velocities in a vacuum. (Why?) 
 
 The horizontal distance attained by a projectile is its range or 
 random. The greatest range is obtained at an angle a little 
 less than 40°. 
 
418 SYLLABTTS. 
 
 A body projected ho rizontally, with any velocity, will reach 
 the ground in precisely the same time that it would if dropped 
 vertically. (Why ?) 
 
 XIII. THE PENDULUM. 
 
 The time of vibration of a pendulum varies inversely as the 
 number of vibrations. 
 
 The time of vibration and the number of vibrations are inde- 
 pendent of both the mass and the length of arc. 
 
 The time of vibration and the number of vibrations depend 
 upon both the length of the pendulum and the force of gravity. 
 
 The time of vibration varies as the square root of the length 
 of the pendulum. 
 
 The number of vibrations varies inversely as the square root 
 of the length of the pendulum. 
 
 The time of vibration varies inversely as the square root of 
 the force of gravity. 
 
 The number of vibrations varies as the square root of the 
 force of gravity. 
 
 The length of a pendulum is the distance from the point 
 of suspension to its center of oscillation. These two points are 
 interchangeable. 
 
 The center of percussion is coincident with the center of 
 oscillation. 
 
 XIV. MOMENTUM.— THIRD LAW OF MOTION. 
 
 Momentum is the product of mass, multiplied by velocity ; or, 
 it is the product of force, multiplied by the time during which it 
 acts. 
 
 Third Law of Motion. To every action there is an equal and 
 opposite reaction. 
 
 The momentum of the reaction is equal to the momentum of 
 the action. 
 
 Law of Bejl^ction. — When the striking body and the body 
 struck are perfectly elastic, the angle of reflection is equal to 
 the angle of incidence. 
 
DYNAMICS. 418 
 
 XV. WORK.— ENERGY. 
 
 Work is done whenever force acts through space. It is 
 estimated by multiplying resistance by the space, or force by the 
 space through which it acts. It is commonly expressed in kilo- 
 grammeters or foot pounds. 
 
 In estimating the rate of doing work, or the power of an 
 agent to do work, time is taken into consideration. The unit 
 employed is a horse-power, which is a power capable of doing 
 33,000 ft. lbs. = 4,570"=s" per minute. 
 
 Power to do work is called energy. Every moving body 
 possesses energy due to its motion ; energy due to motion is 
 called kinetic energy. A body may possess energy due to an 
 advantage of position given it by work done upon it. Energy 
 due to position is called potential. Potential energy becomes 
 kinetic on the return of bodies to their original positions. 
 
 Formvlasfor energy: 
 
 (1) Energy = :i|l-; 
 
 or, ,a\ V MV^ 
 
 (2) Energy = ^— 
 
 But, since W=Mg', 
 
 9 
 hence, in using the second formula, the value of M must be found 
 by dividing W by g. 
 
 Force may be measured by the change of momentum it pro- 
 duces in a second. 
 
 In the C.G.S. system, the centimeter., gram, and second are 
 taken as the units of distance, mass, and time respectively, and 
 in it the dyne is the unit of force. A dyne is a force which, 
 acting for a second, will give to a gram of matter a velocity of 
 one centimeter per second. 
 
420 SYLLABUS. 
 
 In the gravitation system the term gram (or pound, etc.) is 
 applied to both mass and force. 
 
 In the C.G-.S. system the unit of work is the erg. The erg 
 and kilogrammeter measure both work and energy, or power to 
 do work. An erg is the work done, or the energy imparted, by 
 a force of one dyne working through a distance of one centi- 
 meter. 
 
 Energy may be transformed from one condition to another, as 
 from kinetic to potential ; or, from one variety to another, as 
 from heat to mechanical or molar motion. 
 
 Physics treats of transferences and transformations of energy. 
 
 XVL MACHINES. 
 
 Advantages of machines: (1) They enable us to exchange 
 power for velocity, or velocity for power. (2) Thej^ enable us 
 to employ a force in a direction which is more convenient than 
 the direction in which the resistance is to be moved. (3) They 
 enable us to employ other forces than our own in doing work. 
 
 Law of Machines : The work applied to a machine is equal 
 to the effective work plus the internal work done by the machine. 
 The useful work done by a machine is less than the work done 
 upon the machine. In a perfect machine they would be equal. 
 None exists. 
 
 In every machine P : W :: W :p ; i.e., The power and resist- 
 ance vary inversely as the distances they respectively travel- 
 
CHAPTER III. 
 MOLECULAR ENERGY. -HEAT. 
 
 XVII. WHAT HEAT IS. — SOME SOURCES OF HEAT. 
 
 Two theories of heat have successively prevailed, viz. : (1) 
 that heat is matter ; (2) that it is motion. Molar motion is 
 convertible into heat, and heat Is convertible into molar motion. 
 It is scarcely conceivable that motion can be converted into 
 matter, or matter into motion. But it is a matter of everyda}' 
 observatioh, that when motion of one kind (or thing) ceases, 
 motion of another kind (or thing) takes its place. Conclusion : 
 heat is motion, i.e., molecular motion ; this implies the existence 
 of kinetic energy. 
 
 Molecules may possess potential energy, which becomes kinetic 
 during chemical action, i.e., the clashing together of molecules 
 in consequence of affinity, thereby generating heat, as in com- 
 bustion. This is the origin of animal heat and muscular motion. 
 The sun is the ultimate source of nearly all the energy at man's 
 command. 
 
 Temperature is determined by the average kinetic energy of 
 the individual molecule ; quantity of heat, by the average 
 kinetic energy of the individual molecule multiplied by the 
 number of molecules. 
 
 XIX. DIFFUSION OF HEAT. 
 
 Heat is diffused by conduction, convection, and radiation. 
 (Explain the first two. How is ventilation usually accomplished ? 
 By which method do we receive heat from the sun? Why not 
 by either one of the other two methods ?) 
 

 422 SYLLABUS. 
 
 XX. EFFECTS OF HEAT. — EXPANSION. 
 
 Effects of heat : Expansion, liquefaction, vaporization, change 
 of temperature, and specific heat in part. 
 
 (In what state is matter least expansive ? Wliy ? In what 
 state is the coefficient of expansion the same for all substances ? 
 What is the coefficient ? State an exception to the general rule 
 that matter expands with a rise of temperature.) 
 
 XXI. THERMOMBTEY. 
 
 Change of temperature is measured by expansion. A ther- 
 mometer measures expansion, hence it measures temperature. 
 
 (State the method of construction and graduation of a mercury 
 thermometer. What kind of thermometer is more sensitive 
 than a mercurj' thermometer? Why?) 
 
 Formulas for conversion of thermometer readings : 
 
 I (F - 32) = C ; f C + 32 = F. 
 
 Absolute temperature is reckoned from an absolute zero, or 
 state of no heat. It may be found by adding 273 to the C. 
 reading, or 460 to the F. reading. 
 
 Law of Charles : The volume of a given body of gas at a 
 constant pressure varies as its absolute temperature. 
 
 Conversely, the tension of a given body of gas, whose volume 
 is constant, varies as its absolute temperature. 
 
 Maeiotte's Law : At a constant temperature, the volume of a 
 given body of gas varies inversely as the external pressure. At 
 a constant temperature, the product of the volume and tension 
 of a given body of gas is constant. The product of the volume 
 and tension of a body of gas varies as its absolute temperature. 
 
 The tension of a body of gas is due to the kinetic energy of 
 its molecuies. 
 
MOLECULAR ENERGY. — HEAT. 423 
 
 XXII. LIQUEFACTION AND VAPORIZATION. 
 
 See laws of fusion and boiling, page 161. 
 
 Distillation, or the separation of mixed liquids by vaporiza- 
 tion, is conducted on the principle that the temperature of the 
 boiling points of different substances differs. 
 
 The rapidity of evaporation varies with the temperature 
 (why?), amount of surface exposed, and drj'ness of the atmos- 
 phere, and inversely with the pressure upon the liquid. Dew- 
 point is the temperature of the atmosphere when saturated with 
 watery vapor. The atmosphere is dry when the difference 
 between its temperature and dewpoint is great. The term dry- 
 ness, when applied to the atmosphere, signifies capacity for 
 receiving more moisture, and does not necessarily imply defi- 
 ciency of moisture. 
 
 [The molecules of every body of liquid are in motion. The 
 distances traversed by the molecules in the interior of a 
 body are limited by the proximity of neighboring molecules on 
 all sides. When they reach the free surface of the bodj-, they 
 are not subject to this restraint, and more or less of them 
 depending upon the temperature (i.e., the energy of their move- 
 ments) , become released from the force of cohesion and pass 
 off as a vapor. Tliis is evaporation. On the other hand, mole- 
 cules of the vapor, resting upon the liquid surface, beat against 
 it, and, it is supposed, become entangled in it and thus return 
 to the liquid state. When the number of molecules which thus 
 return to the liquid state equals those which escape, the space 
 above the liquid is said to be saturated.'] 
 
 XXIII. HEAT CONVETlTIBT^Ti; INTO POTENTIAL ENERGY, 
 AND VICE VERSA. 
 
 Heat is measured in calories ; temperature, in degrees. A 
 calorie is the quantity of heat required to raise the temperature 
 of 1* of water from 0° to 1° C. 
 
424 SYLLABUS. 
 
 Eighty calories are consumed in converting one kilogram of 
 ice into water. Five hundred and thirtj'-seven calories are con- 
 sumed in converting 1'' of water at 100° C. into steam. In the 
 first case, the heat is consumed in doing interior work, such as 
 neutralizing, in part, the force of cohesion. In the second 
 case, the larger portion (about -ff ) of the heat is consumed in 
 the interior work of completely overcoming cohesion, and the 
 remaining portion {■^) in the exterior work of overcoming 
 atmospheric pressure. 
 
 The temperature of a body is reduced, either by imparting 
 heat to a colder body, or by the consumption of its heat in doing 
 work. By the latter method artificial cold is produced. The 
 work done is usually that of melting or dissolving some solid, 
 vaporizing a solid or liquid, or producing expansion in a gas 
 against resistance. (Give illustrations of each.) 
 
 Heat which is consumed in melting, dissolving, and vaporiz- 
 ing, is restored when the opposite changes occur. (Explain.) 
 
 XXIV. SPECIFIC HEAT. 
 
 Equal quantities of heat applied to equal weights of different 
 substances raise their temperatures unequally. In the case of 
 solids and liquids, this is explained by the fact that a portion of 
 the heat applied is always consumed in doing internal work ; and 
 since in different substances the amount consumed in doing 
 work varies, consequently the amount of heat left to raise the 
 temperature of different substances must vary. 
 
 The number of heat units required to raise a body 1° C. is 
 called its capacity for heat. 
 
 The specific heat of a body is the ratio of its capacity for heat 
 to that of an equal weight of water. 
 
 Hydrogen gas has the greatest capacity for heat. Water ranks 
 next. 
 
MOLECtJLAE ENBBGY. — HEAT. 425 
 
 XXV. THERMO-DYNAMICS. 
 
 A definite quantity of mechanical work can produce a defi- 
 nite quantity of heat ; and conversely, this heat can perform 
 the original amount of work. One calorie is equivalent to 
 424''s™ of work. The quantity, 424''^, is called the mechanical 
 equivalent of heat. 
 
 Doctrine of coiYelation of energy : Any kind of energy can be 
 converted into any other kind. 
 
 Doctrine of conservation of energy : When one form or kind 
 of energy disappears, an exact equivalent of another form or 
 kind always takes its place, so that the sum total of energy in 
 the universe is constant. 
 
 XXVI. STEAM ENGINE. 
 
 A steam engine is a machine by means of which a portion of 
 the motion of the molecules of steam (i.e., its heat) is trans- 
 formed into molar or mechanical motion. 
 
 In a non-condensing engine, a large amount of energy is 
 wasted in producing motion against the resistance of atmos- 
 pheric pressui-e. 
 
CHAPTER IV. 
 BLBCTRIOITY. 
 
 XXVII. CURRENT ELECTRICITY. 
 
 Just as a difference of level Is necessary to produce a current 
 of water, and a difference of temperature to cause a flow of heat, 
 so a difference of electrical condition, called a difference of 
 potential, is necessary to cause a flow of electricity. To estab- 
 lish the necessary conditions in each case (i.e., difference of 
 level, etc.) energy must be expended. On the other hand, the 
 return of each to its normal condition or state of equilibrium is 
 attended with the development of energy. The constant expen- 
 diture of chemical potential energy- in a voltaic cell causes a 
 constant inequality of potential, and this in turn causes a con- 
 stant tendency to equalization of potential throughout the circuit; 
 in other words, a continuous current. 
 
 As the stress (called foj-ce of gravity) between an elevated 
 body of water and the earth is the cause of the so-called water- 
 power, .so it is probable that a stress between two parts of a 
 body having diffierent potential is the cause of a power usually 
 called electro-motive force. 
 
 The greater the disparity between the two solid elements of 
 a voltaic cell with reference to the action of the liquid on them, 
 the greater the diflference of potential or electro-motive force 
 of the cell ; hence, the stronger the current. 
 
 The office, of a voltaic battery is to create inequality of poten- 
 tial, i.e., to ge^ierate electro-motive force. 
 
 The zinc element generally needs to be amalgamated to pre- 
 vent local action and consequentlj' a waste of energy. 
 
 Hydrogen ought not to be allowed to collect on the electro- 
 negative plate, as it offers a resistance to the current, but 
 chiefly because it tends to reduce the difference of potential 
 
ELECTRICITY. 427 
 
 between the two plates, and thereby reduce the current. This 
 may be prevented b^^ either mechanical or chemical action. 
 
 The effects of electricity are heating, luminous, electrolytic, 
 physiological, and magnetic. 
 
 XXX. ELECTRICAL MEASUREMENTS. 
 
 Upon the strength of the cun-ent depends the magnitude of 
 these effects. By the strength of the current is meant the 
 quantity of electricity which flows through a circuit in a unit of 
 time. The voltameter and galvanometer measure the strength 
 of the current. In the tangent galvanometer the strength of 
 current is proportional to the tangent of the angle of deflection. 
 
 Ohm's Law : The strength of the current varies as the electro- 
 motive force, and inversely as the resistance in the entire circuit; 
 i.e., an effect is directly proportional to that which tends to pro- 
 duce it, and inversely proportional to that which tends to oppose it. 
 
 Resistance varies as the length, and inversely as the squares 
 of the diameters of cylindrical conductors. 
 
 When the external resistance is much greater than the 
 internal, it is best to connect cells "tandem" in order to 
 increase the electro-motive force. When the internal resistance 
 is greater than the external, the cells should be connected 
 " abreast" in order to diminish the internal resistance. When 
 the external and internal resistances are nearly equal, it may be 
 best to connect them in both ways. 
 
 In a circuit having a given external resistance the greatest 
 possible efficiency is obtained from a given battery when the ex- 
 ternal and internal resistances are about equal. 
 
 XXXI. MAGNETS AND MAGNETISM. 
 
 Law op Magnets : Like poles repel, unlike poles attract one 
 another. 
 
 The laws of currents on which Ampere's theory of magnets 
 is based are as follows : Parallel currents in the same direction 
 
428 SYLLABUS. 
 
 attract one another; parallel currents in opposite directions 
 repel one another. Angular currents tend to become parallel 
 and flow in the same direction. 
 
 Ampere's theory assumes that there are constant currents 
 circulating around the molecules of every magnetizable sub- 
 stance, and that the resultant of these forces in a magnet is the 
 same as though " a sheet of currents" circulated around the 
 magnet as a whole. The deflection of the magnetic needle is 
 due to the tendency of angular currents to become parallel. 
 
 The attractions or repulsions of the poles of magnets are due 
 to the attractions or repulsions of parallel currents according as 
 they flow in the same or opposite directions. 
 
 The earth's magnetism is probably due to the circulation of 
 currents around the earth, from east to west, in planes at right 
 angles to its axis. Substances which are attracted by a magnet 
 are called paramagnetic; those which are repelled are called 
 diamagnetic. . 
 
 XXXII. MAGNETO- ELECTRIC AND CURRENT INDUCTION. 
 
 When Amp^rian currents (i.e., a magnet) or a battery cur- 
 rent approaches a neighboring closed circuit, a momentary 
 current is induced in this circuit opposite in direction to the 
 inducing current ; when carried away, a current is induced in 
 the same direction- as the primary or inducing curi-ent. The 
 same happens whenever in one of two neighboring circuits a 
 current is started or stopped by making or breaking the circuit. 
 At these instants not only are secondary or induced currents 
 sent through the neighboring circuit, but, likewise, corresponding 
 currents are induced in its own circuit. The latter are called 
 extra currents. 
 
 Briefly, any magnetic or electrical disturbance in the neighbor- 
 hood of a circuit will induce currents in that circuit. 
 
 The currents established by magneto and dynamo machines 
 are induced currents. Induced currents have high tension, i.e., 
 great power of overcoming resistances. 
 
ELECTRICITY. 429 
 
 XXXIII. THERMO-ELECTRICITY. 
 
 When two diflferent metals so connected as to form a circuit 
 are brought in contact, and heated or cooled at the junction, a 
 thermo-electric current is established. 
 
 The electro-motive force, and consequently the strength of the 
 current, depends upon the elevation or depression of tempera- 
 ture at their junction, and upon the metals employed. 
 
 XXXIV. ERICTIONAL ELECTRICITY. 
 
 Friction between two bodies, especially if they are composed 
 of unlike substances, tends to produce a diffei-ence of potential 
 in the bodies. As long as the bodies remain in this condition 
 they are said to be electrified or charged with electricity ; one 
 with positive, the other with negative electricity. Electricity in 
 this condition is said to be static. On the return of either to 
 its normal potential a discharge is said to occur, a current is 
 established, and the electricity for the time being is said to be 
 dynamic. As commonly understood, an electrified body is one 
 that has a different potential from that of the earth, and is said 
 to be positively electrified when its potential is higher than that 
 of the earth, and negatively electrified when lower than that of 
 the earth. Similarly-electrified bodies repel one another ; dis- 
 similarly-electrified bodies attract one another. [Phenomena 
 of electric attraction and repulsion are thought by many to be 
 phenomena of ether-stress, or of "action at a distance" through 
 the medium of ether. J 
 
 An electrified body brought near a body whose potential is 
 zero tends to electrify it by induction, causing the part of the 
 body nearest itself to be of a different potential from itself, 
 while the remote part of the body, if it is insulated, becomes of 
 like potential. The electricity in the former case is said to be 
 bound, while the latter is free, since, if the insulated body is 
 connected with the earth, a discharge of the latter occurs ; in 
 
430 SYLLABUS. 
 
 other words, the location of this potential is transferred to the 
 earth. 
 Electrification is confined to the surface of a body. 
 
 XXXV. ELECTRICAL MACHINES. 
 
 By means of the so-called electrical machines mechanical 
 energy is transformed into electric energy. These machines 
 are capable of producing a great change in potential, con- 
 sequently their electro-motive force is great, but their internal 
 resistance is so great that the strength of current they are 
 capable of yielding is extremely small, and consequently they 
 are of little practical value. 
 
 The phenomena of electricity in a statical state are limited to 
 those of attraction and repulsion. All other effects are produced 
 by electricity in the dynamical state, and the magnitude of the 
 effects generally varies as the square of the current. 
 
 No one knows what electricity is. [It is not "a form of 
 energy."] For practical purposes, it suffices to regard it as a 
 medium for communication of energy, and to know the laws to 
 which it is subject. 
 
 XXXVI. USEFUL APPLICATIONS OF ELECTRICITY. 
 
 These are well-nigh innumerable. Some of the more impor- 
 tant are those pertaining to medical and surgical operations, 
 electric lighting, electrotyping, electroplating, telegraphy, tele- 
 phony, and the production of mechanical motion through the 
 instrumentality of electro-motors in great variety. [One of the 
 most recent applications is that of storing energy, as in the so- 
 called storage-batteries. Energy of any kind, e.g. water-power 
 of any of the great water-falls, may be transformed into electric 
 energy, and the latter may be transformed into potential energy 
 and stored in these batteries. These batteries may be trans- 
 ported to distant places, and the potential energy restored to 
 electric energy, and made to do any species of work.] 
 
CHAPTER V. 
 SOUND. 
 
 XXXVIII. VIBRATION AND WAVES. 
 
 A vibration is a recurrent change of position. The propaga- 
 tion of a vibration through a series of particles produces wave 
 motion. A succession of such propagations produces a wave- 
 line. Only the wave-form advances. The distance between 
 any point on one wave and a similarly situated point on its 
 successor or predecessor is a wave-length. The greatest dis- 
 tance which a particle reaches from its median position is the 
 amplitude of the vibration or wave. The distance traversed 
 by a given wave in one second is the velocity of propagation. 
 If V be the velocity, I the wave-length, and n the number of 
 waves per second, 
 
 v = nl, n = -, and I = -. 
 I n 
 
 When a given particle is subjected simultaneously to two or 
 more impulses, due to two or more trains of waves, the motion 
 of the particle is the resultant of the several impulses, and the 
 phenomenon is called interference. Interference may intensify 
 or nullify motion. In cords, membranes, etc., it may result in 
 vibration in segments, or stationary vibrations, the points of 
 least vibration being called nodes, the points of greatest motion, 
 antinodes, and the portion between two nodes, a ventral seg- 
 ment or loop. 
 
 Waves are longitudinal or transverse, according as the par- 
 ticles vibrate in the same plane with the path of the wave, or 
 across it. 
 
 Wave motion is one of the most common and most important 
 
432 SYLLABUS. 
 
 methods of transmission of energy. Elasticity is essential in a 
 medium, that it may transmit waves made up of condensations 
 and rarefactions ; and the greater the elasticity, the greater the 
 facility and the rapidity with which a medium transmits waves, 
 
 XXXIX. SOUND-WAVES. 
 
 Sound is vibration that may be appreciated by the ear, and 
 originates in a vibrating body. It is transmitted by wave 
 motion, and therefore cannot travel in a vacuum. 
 
 XL. VELOCITY OF SOUND. 
 
 The velocity of sound in gases varies as the square root 
 of their elasticity, and inversely as the square root of tBSr" 
 densities. 
 
 XLI. REFLECTION AND REFRACTION OF SOUND. 
 
 Sound-waves are reflected in accordance with the general law 
 of reflection. Echoes are the result of reflected sound-waves. 
 
 When the form or direction of a wave is altered in consequence 
 of changing media of difl'erent densities the phenomenon is called 
 refraction. 
 
 XLII. LOUDNESS OF SOUND. 
 
 Loudness, which is a measure of the intensity of a sensation, 
 varies with the intensity of sound, but there are many reasons 
 why they are not exactly proportional. 
 
 The intensity of sound varies as the square of the ampli- 
 tude of the vibrations of the sounding body. It is also affected 
 by the density of the medium in which it is produced, being 
 weaker when originating in a rare medium. The intensity of 
 sound varies inversely as the square of the distance from the 
 source. "When sound is re-enforced or intensified by interfer- 
 ence the phenomenon is called resonance. Re-enforcement is 
 produced by means of sounding-boards, columns of air, etc. 
 
SOUND. 433 
 
 When one vibrating body causes another body having the 
 same vibration period to vibrate, the vibrations of the latter are 
 called sympathetic vibrations. They represent the accumulated 
 effect of a series of impulses transmitted from the sounding body 
 through the sound medium to the body thus caused to vibrate. 
 
 When a vibratile body is compelled to surrender its own 
 vibration period and to vibrate in an arbitrary manner imposed 
 upon it by another, the phenomenon is known as forced vibra- 
 tions. 
 
 The sensation of noise is caused by irregularity in the im- 
 pulses received by the ear and by its inability to distinguish 
 pitch. Regularity and simplicity are characteristics of musical 
 sound. 
 
 XLIII. PITCH OF SOUND. 
 
 Pitch depends upon vibration-frequency or wave-length ; the 
 greater the number of vibrations per second, or the shorter the 
 wave-length, the higher the pitch. The siren is one of many 
 instruments used to determine vibration-frequency. 
 
 A wavy sound caused by interference of sound waves is 
 known by the name of beats. The number of beats per second 
 due to two simple tones is equal to the difference of their 
 respective vibration-numbers. Beats are one of the chief causes 
 of discord. 
 
 XLIV. VIBRATION OF STRINGS. 
 
 The vibration-frequency of strings of the same material varies 
 inversely as their lengths and the square roots of their weights, 
 and directly as the square roots of their tension. 
 
 XLV. OVERTONES AND HARMONICS. 
 
 Sounds proceeding from instruments vibrating in parts are 
 called overtones. If the vibration-number of the overtone 
 bears some simple ratio to the vibration-number of the funda- 
 mental, the overtone is called a harmonic. 
 
434 SYLLABUS. 
 
 Generally, only those notes harmonize whose fundamental 
 tones bear to one another ratios expressed by small numbers ; 
 and the smaller the numbers which express the ratios of the 
 rates of vibration, the more perfect is the harmony. 
 
 XL VI. QUALITY IN SOUND. 
 
 Quality, or that property of sound which enables us to dis- 
 tinguish different sounds having the same pitch and intensity, is 
 shown both by analysis and synthesis to depend upon what 
 overtones combine with its fundamental, and on their relative 
 intensities ; or, brieflj', upon the form of vibration. Sounds 
 differ only in intensity, pitch, and quality. The manometric 
 flame apparatus is well suited to illustrate these three properties. 
 
 XLVIII. SOME SOUND-EECEIVING INSTRUMENTS. 
 
 The ear is a mechanical contrivance for the transmission of 
 vibration to the organs of sensation. For example, the aerial 
 waves cause forced vibrations in the outer membrane or tym- 
 panum ; these are communicated by a chain of bones to the 
 membranous walls of the vestibule, and thereby to the liquid 
 contained in the cavity. The bristles suspended in this liquid 
 take up and analyze the vibrations, much as when we sing into 
 a piano with the dampers down, only those strings respond 
 which are in unison with the sound produced by the voice. 
 The bristles stir the nerve filaments connected with them,' and 
 the nerve transmits to the brain the impressions received. 
 
 XLIX. MUSICAL INSTRUMENTS. 
 
 In pipes the vibration-frequency varies inversely as its 
 length. When the fundamental of an open pipe is sounded its 
 air-column divides itself into two equal vibrating sections with 
 a node in the center, hence an open pipe should be twice as 
 long as a closed pipe to produce the same pitch. 
 
CHAPTER VI. 
 * RADIANT ENERGY. -LIGHT. 
 L. INTRODUCTION. 
 
 That we receive energy from the sun, and that nearly all the 
 energy employed by man came from the sun, is certain. The 
 average amount of energy received by the earth is estimated to 
 be 83 fl.-lbs. per square foot of surface per second of time 
 (Daniell). This energy appears to be transmitted in the fonn 
 of wave-motion. This method of transmission, or indeed any 
 method, would seem to require a medium for its transmission. 
 The hypothetical medium has received the name of ether, and 
 this method of transmission is called radiation. Radiant 
 energy manifests itself as heat, light, or chemism according to 
 the object upon which it acts. Light is the vibration of ether 
 that may be appreciated by the organ of sight. 
 
 Luminous bodies are seen by the light which they emit; 
 Illuminated bodies, by the light which they reflect. Every point 
 of a luminous body emits light in every direction. 
 
 The intensity of light diminishes as the square of the dis- 
 tance from the source iftcreases. (Why?) 
 
 The apparent size of an object diminishes as its distance 
 from the eye increases. (Why?) 
 
 The velocity with which light traverses interplanetary space 
 is about 186,000 miles per second. 
 
 ini. REFLECTION OF LIGHT. 
 
 Light is so reflected that the angle of reflection is equal to 
 the angle of incidence. Owing to the greater or less roughness 
 of the surfaces of all objects light becomes by reflection more or 
 less scattered or diffused. 
 
436 SYLLABUS. 
 
 The amount of light reflected from a smooth surface in- 
 creases rapidly with the angle of incidence. 
 
 Concave mirrors tend to produce a convergence of rays; 
 convex mirrors cause divergence; plane mirrors do not alter 
 the relation of rays. 
 
 Images formed by plane and convex mirrors are virtual 
 images. Images formed of objects situated between a concave 
 mirror and its principal focus are virtual ; in all other situations 
 the images are real. 
 
 (Describe the variety of images that may be formed by a con- 
 cave mirror. Describe an image formed by a convex mirror ; 
 also one formed by a plane mirror.) 
 
 LIV. REFRACTION. 
 
 When light passes obliquely from a rarer into a denser 
 medium it is refracted toward a perpendicular to the boundary 
 plane ; if from a denser into a rarer medium, it is refracted 
 from the perpendicular. 
 
 The ratio of the sine of the angle of incidence to the sine of 
 the angle of refraction is called the index of refraction, and is 
 the same as the ratio of the velocity of the incident to that 
 of the refracted light. 
 
 When a ray passes obliquely from a vacuum into a medium, 
 the index of refraction is greater than unity, and is called the 
 absolute index of refraction. The relative index of refraction, 
 from any medium A, into another B, is found by dividing the 
 absolute index of B by the absolute index of A. 
 
 When the angle of mcidence is such that the angle of refrac- 
 tion is 90°, i.e., the reflected ray moves in the plane of the 
 refracting surface, the angle is called the critical angle. Total 
 reflection occurs when rays in the more refractive medium are 
 Incident at an angle greater than the critical angle. 
 
RADIANT KNERGY. — LIGHT. 437 
 
 LV. LENSES. 
 
 £he general effect of convex lenses is to converge trans- 
 mitted rays ; and of concave lenses, to cause them to diverge. 
 
 The corresponding linear dimensions of an object and its 
 image formed by a convex lens are to one another as the re- 
 spective distances from the optical center of the lens. 
 
 (Describe the variety of images that may be formed by convex 
 and concave lenses.) 
 
 LVI. PRISMATIC ANALYSIS OF LIGHT. — SPECTRA. 
 
 When a beam of white light passes through an optical prism, 
 tLa colors of which it is composed are separated by refraction. 
 Owning to their different degrees of refrangibility. If the dif- 
 ferent colors are again brought together, white light is repro- 
 duced. 
 
 Difference of color is a difference of vibration-rate or wave- 
 length. In a dense medium the shorter waves are more 
 retarded than the longer ones ; hence, they are more refracted. 
 A body which emits white light sends forth simultaneously 
 waves of a variety of lengths. 
 
 Luminous solids and liquids give continuous spectra, while 
 gases usually give discontinuous or bright-line spectra. Hence, 
 the spectrum reveals the state of the substance emitting light. 
 
 A vapor of any substance is opaque to those rays which it 
 would itself emit if luminous. Hence, when white light 
 traverses vapors capable of absorbing certain rays, the spectrum 
 formed by the transmitted light will be crossed by dark lines. 
 These dark lines occur where bright lines would be formed if 
 the same vapors were rendered luminous, hence the former are 
 sometimes called reversed spectra. 
 
 No two substances give spectra consisting of the same com- 
 bination of lines. Spectrum analysis consists in determining 
 the presence or absence of given substances in a luminous 
 
438 SYLLABtrS. 
 
 vapor by the presence or absence of their characteristic lines in 
 the spectrum. Likewise the substances which are present in 
 the solar atmosphere and the photosphere can be determined by 
 the reversed lines of the solar spectrum. 
 
 The solar spectrum is not limited in either direction by the 
 visible spectrum. Although the eye is not susceptible to impres- 
 sions from the ultra-red and ultra-violet rays, yet the former 
 are quite energetic in producing heat, and the latter in generat- 
 ing chemical action. 
 
 LVII. COLOR. 
 
 Color is a quality of the light which illuminates, and not of 
 the object illuminated. No body gives color to light which it 
 reflects or transmits. 
 
 The tendency of atmospheric dust is to absorb the colors at 
 the violet end of the spectrum, and to transmit the colors at the 
 red end. On the other hand, it tends to reflect the colors of the 
 violet end, and absorb those of the red. Hence the redness of 
 the light at sunrise and sunset, when the light passes long dis- 
 tances through this dust ; also, the blueness of skj^-light, whicli 
 is reflected light. 
 
 Red, green, and violet are thought to be the three primary 
 color-sensations, and all other colors are supposed to be the 
 product of mixed sensations of these three in varying propor- 
 tions. 
 
 A color resulting from a mixture of pigments is the color 
 that is left after the two pigments have absorbed all the other 
 colors, and is not the result of a combination of colors. 
 
 When any two colors combined will produce white, they are 
 said to be complementary to each other. 
 
 Waves of light, like sound-waves, may interfere so as to pro- 
 duce mutual destruction. If the light is monochromatic, dark- 
 ness is tlie result. If the light is white, and only waves of 
 certain length interfere, then a color is produced which is the 
 
RADIANT ENERGY. — LIGHT. 439 
 
 •^sult of the subtraction of the auaihilated color from ■white 
 light. Interference may be caused by reflection from thin 
 films, and by the bending of rays of light around the edges of 
 opaque objects. 
 
 LVm. DOUBLE REFRACTION AND POLARIZATION 
 OF LIGHT. 
 
 Light transmitted through the crystals of certain substances, 
 notably Iceland spar, suffers a double refraction, i.e., it becomes 
 divided, and pursues two different paths. 
 
 Ordinary light is supposed to consist of vibrations in ether, in 
 every possible plane at right angles to the path of the light. 
 When, by reflection or transmission through certain substances, 
 it is reduced to vibrations of one plane, it is said to be polarized. 
 
 TAX. THERMAL EFFECTS OF RADIATION. 
 
 When a body absorbs largely the radiations which strike it, 
 i.e., when the undulations of the ether are largely transformed 
 into molecular motion, the body becomes heated thereby, and is 
 said to be other manous. But if the nature of the molecules of 
 a body is such that their motions are not readily quickened by 
 the undulations, but the body allows a large portion of the 
 undulations to pass through it unabsorbed, then is it slightly 
 heated thereby, and is said to be diather manous. 
 
 All bodies emit radiations, and, in common parlance, are said 
 to radiate heat. Good absorbers are good radiators ; bad 
 absorbers are bad radiators. The absorbing and radiating 
 power of a body of the same substance depends largely upon 
 the character of its surface, i.e., whether it be bright and 
 smooth, or tarnished and rough. Dew, which is the result of 
 condensation of the watery vapor of the air, collects most abun- 
 dantly on good radiators, inasmuch as they part with their heat 
 rapidly, and, consequently, become cooler than poor radiators. 
 
II^DEX. 
 
 [I^UMBEBS Refer to Pases.] 
 
 Aberration, Chromatic, 394. 
 
 Spherical, 363. 
 Absorption, 38, 39. 
 Acceleration, Unit of, 128, 
 Acbromatic lens, 395. 
 Action and reaction, 116. 
 Adhesion, 33. 
 Air, a medium of wave-motion, 277. 
 
 Weight of, 3. 
 Air-pump, 54. 
 Air-TraTes, 282. 
 Alpliabet, Telegraphic, 266. 
 Amalgamating zinc, 187. 
 Ampdre, a unit of current, 206. 
 Ampere's rule, 183 ; theory, 218. 
 Analysis of light, 364. 
 Angles of incidence and reflection, 118. 
 Antinodes, 276. 
 Armature, 197. 
 Artesian wells, 70. 
 Atliermancy, 388. 
 Atmosphere, a unit of pressure, 49. 
 Attraction, Phenomena of, 20. 
 
 mutual, 13, 20, 21. 
 
 Ballistic curve, 109. 
 
 Barometer, 50. 
 
 Battery, Bunsen or Grove, 189. 
 
 Gravity, 191. 
 
 Grenet or tottle, 189. 
 
 Smee, 188. 
 
 Kind of to use, 405. 
 
 Qualities of good, 210. 
 Batteries, Arrangemsnt of, 207. 
 
 Thermo, 235. 
 
 Various, 188. 
 Beam of light, 328. 
 Beats, 302. 
 
 BeUs, 323. 
 
 Blake transmitter, 271. 
 Boiling, Laws of, 161. 
 Brlttleness, 31. 
 Buoyant force of iluids, 76. 
 
 Camera Ohscura, 392, 
 Photographer's, 392. 
 Candle-power, 334. 
 Capillarity, 34. 
 
 Celestial chemistry and physics, 372, 
 Center of gravity, 96. 
 Centrifugal force, 102. 
 Centripetal force, 102. 
 C.G.S. system, 125. 
 Chemical changes, 9. 
 Cohesion, 23. 
 Coil, Rhumkorff's, 233. 
 Coils, Induction, 232. 
 Cold, Methods of producing, 167, 
 Color hy absorption, 374. 
 by interference, 379. 
 by polarization, 387. 
 Cause of, 367. 
 Effect of contrast of, 379. 
 Colors, Complementary, 379. 
 Mixing, 376. 
 Prunary, 365. 
 Sky, 375. 
 Compound substances, 8. 
 Compressibility of gases, 52. 
 Condenser, 249. 
 Conservation of energy, 174. 
 Constitution of matter, 6. 
 Correlation of energy, 174. 
 Couple, Mechanical, 95. 
 Critical angle, 354. 
 Current attraction, 216. 
 Kztra, 231. 
 
INDEX. 
 
 Cnrrent Induction, 230. 
 
 Strength of, 197, 201. 
 Currents, Earth, 224. 
 
 Laws of, 215, 217. 
 Curvilinear motion, 101. 
 Cutting glass, 401. 
 
 D. 
 
 Density, 7, 79. 
 Dew, 391. 
 
 point, 164. 
 Dialysis, 40. 
 Diamagnetism, 225. 
 Diathermancy, 388. 
 Diffraction, 381. 
 Diffusion, 39. 
 Discharge, Electrical, 242. 
 Discord, Cause of, 307. 
 Dispersion of light, 365. 
 Distillation, 162. 
 Ductility, 32. 
 Dynamics defined, 44. 
 
 of fluids, 44. 
 Dynamo machines, 227. 
 Dyne, 125, 128. 
 
 Ear, 315. 
 
 Earth, a magnet, 220, 223. 
 Elasticity, 29. 
 Electric candle, 260. 
 
 lamp, 260. 
 
 light, 259. 
 Electrical attractions, etc., 238, 252. 
 
 machines, 245. 
 
 measurements, 197. 
 Electricity, Chemical effect of, 192. 
 
 Cun'ent, 179. 
 
 Frictional, 237. 
 
 Heating effect of, 191. 
 
 how it originates, 184. 
 
 Luminous effect of, 192, 253. 
 
 Magnetic effect of, 196. 
 
 Physiological effect of, 195. 
 
 Thermo, 234. 
 
 Two states of, 238. 
 
 Useful applications of, 258, 
 
 What is, 257. 
 Electrification, 237. 
 
 on surface, 244. 
 
 Two kinds of, 239. 
 
 Electro-chemical series, 186. 
 Electrodes, 183. 
 Electrolysis, 193. 
 Electro-magnet, 196. 
 Electro-magnetic machines, 262. 
 Electro-motiTe force, 204, 
 ElectrophoruB, 246. 
 Electroplating, 262. 
 Electroscope, 237. 
 Electrotyping, 261. 
 Energy, Conservation of, 174. 
 
 contrasted with momentum, 123. 
 
 Correlation of, 174. 
 
 defined, 121. 
 
 Formula for, 124. 
 
 Potential and kinetic, 121. 
 
 Eadiant, 327. 
 
 Transformation of, 128, 129, 257. 
 
 Unit of, 128. 
 Engine, Steam, 175. 
 Engines, Kinds of steam, 177. 
 Equilibrant force, 95. 
 Equilibrium, 44. 
 
 Three states of, 98. 
 Erg, 126, 128. 
 
 Ether, a medium of motion, 326. 
 Evaporation, 163. 
 Expansibility of gases, 52. 
 Expansion, Abnormal, 150. 
 
 by heat, 148. 
 
 Coefficients of, 149. 
 
 Power of, 150. 
 Experiment defined, 1. 
 Eye, Human, 393. 
 
 P. 
 
 Falling bodies, 104. 
 Fire-alarm, Electric, 267. 
 Flexibility, 29. 
 Foci, Conjugate, 360. 
 Focus, Principal, 346, 359. 
 
 Virtual, 360. 
 Foot-pound, 120. 
 Force, Absolute unit of, 126, 
 
 Centrifugal, 102. 
 
 Centripetal, 102. 
 
 defined, 12, 13. 
 
 Equilibrant, 95. 
 
 Gravity unit of, 126. 
 
 Measure of a, 124. 
 
INDEX. 
 
 Force, Measure of the effect of, 126. 
 
 Resultant, 01. 
 Forces, Composition of, 91, 94, 93. 
 
 Graphic representation of, 90. 
 
 Molar, 13. 
 
 Molecular, 13. 
 
 Resolution of, 92. 
 Fraunliofer's lines, 872. 
 Fusion, Laws of, 161. 
 
 O. 
 
 Galvanometer. 198, 404. 
 
 Tangent, 199. 
 Gal-ranoscope, 184. 
 Gaseous bodies, Laws of, 156. 
 Gases, Kinetic theory of, 157. 
 Gravitation, 14, 20. 
 Gravity, Acceleration of, 106. 
 
 Center of, 96. 
 
 Force of, 14, 21. 
 
 H. 
 
 Hardness, 28. 
 Harmonics, 305. 
 Harmony, Cause of, 307. 
 Hearing, Limits of, 301. 
 Heat, Capacity for, 171. 
 
 Conduction of, 142. 
 
 Convection of, 143. 
 
 convertible, 138, 165. 
 
 defined, 139. 
 
 Diffusion of, 142. 
 
 Expansion by, 148. 
 
 from chemical action, 140. 
 
 Mechanical equivalent of, 175. 
 
 Origin of animal, 140. 
 
 Reference tables for specific, 172. 
 
 Bome sources of, 138. 
 
 Specific, 170. 
 
 units, 165. 
 Helix, 196. 
 Horse-power, 121. 
 Hydrogen at the copper plate, 185. 
 Hydrometers, 83. 
 Hydrostatic bellows, 64. 
 
 press, 64. 
 
 I. 
 
 Imagres, After, 379. 
 Formation of, 346, 360. 
 
 Imagoes, Real, 347. 
 
 through apertures, 330. 
 
 To construct, 347, 361. 
 
 Virtual, 342, 362. 
 Impenetrability, 1, 6. 
 Induction, 241. 
 
 coils, 232. 
 Inertia, 90. 
 Interference of light, 379. 
 
 of sound-waves, 274, 322. 
 Insulation, 243. 
 
 J. 
 
 Joule's equivalent, 175. 
 
 Kilogrammeter, 120. 
 Kinetic energy, 121. 
 theory of g;aBes, 157. 
 
 liaw, Mariotte's, 156. 
 
 of Charles, 156. 
 Laws of fusion and boiling, 161. 
 
 of gaseous bodies, 156. 
 Ijenses, 357. 
 
 Efi'ects of, 338. 
 liCyden jar, 260. 
 Ijight, a form of energy, 325. 
 
 Analysis of, 364. 
 
 Difitised, 340. 
 
 Electric, 259. 
 
 invisible, 327. 
 
 Reflection of, 339. 
 
 Synthesis of, 366. 
 Ughtnlngr, 235. 
 
 rods, 255. 
 I^iquid surface level, 69. 
 Iiuminous and illuminated bodies, 
 
 machines, 131. 
 
 Law of, 133. 
 
 Uses of, 132. 
 Mag^nets and magnetism, 212, 224. 
 
 Law of, 213. 
 
 Natural, 223. 
 
 not sources of energy, 225. 
 Magnetic transparency, 213. 
 
INDEX. 
 
 magnetism, Cause of the earth's, 223. 
 Magneto machines, 227. 
 
 electric induction, 226. 
 MaUeabiUty, 32. 
 Manometric flames, 312. 
 Mariotte'B law, 57, 166. 
 Mass, 7, 20. 
 Matter a constant quantity, 10, 11. 
 
 Conditions of, 24. 
 
 Crystalline and amorphous, 24. 
 
 Three states of, 15. 
 Metric system, 399. 
 Microphone, 270. 
 Microscope, Simple, 362. 
 
 Compound, 391. 
 Minuteness of particles of matter, 3. 
 Mirrors, Reflection from, 341. 
 Molecule, 4. 
 Momentunx, 115. 
 Motion, Accelerated, 104. 
 
 Curvilinear, 101. 
 
 First law of, 89. 
 
 Formulas for uniformly accelerated, 
 106. 
 
 Kinds of, 87. 
 
 Retarded, 107. 
 
 Second law of, 91. 
 
 Third law of, 117. 
 
 versus rest, 86, 87. 
 Multiple reflection, 343. 
 Musical instruments, 319. 
 
 Scale, 300. 
 
 Nodes, 275. 
 Noise, 297. 
 
 N. 
 
 O. 
 
 Olim, 202. 
 Ohm's law, 205. 
 Opacity, 328. 
 
 Oscillation, Center of. 111. 
 Osmose, 40. 
 Overtones, 305. 
 
 P. 
 
 Parabolic curve, 109. 
 Paramagnetism, 225. 
 Pencil of light, 328. 
 Pendulum, 110. 
 
 Pendulum, Center of oscillation of. 111, 
 
 Center of percussion of, 113. 
 Phenomenon, 1. 
 Phonograph, 317. 
 Photometry, 333. 
 Physical changes, 9. 
 Physics defined, 129. 
 Pigments, 375. 
 
 Mixing, 378. 
 Pitch, 298. 
 
 Points, Effects of, 252. 
 Polarity, 28, 214. 
 Folariscope, 387. 
 Polarization, 334. 
 
 of plates, 188. 
 Poles of battery, 183. 
 Porosity, 7. 
 Potential, Electric, 183, 244. 
 
 energy, 121, 168. 
 Porte lumiere, 339, 407. 
 Press, Hydrostatic, 64. 
 Pressure in fluids, 44-79. 
 Primary colors, 365. 
 Prisms, Optical, 357. 
 Projectiles, 108. 
 Pump, Air, 64-57. 
 
 Force, 75. 
 
 Lifting, 74, 75. 
 
 Quality of sound. 309. 
 Qualities of perfect battery, 21fl 
 
 B. 
 
 Radiation, 327. 
 
 Thermal effects of, 388. 
 Kadiator, 327. 
 Radiometer, 325. 
 Random of projectiles, 108. 
 Ray, 328. 
 Reaction, 116. 
 Reflection, Angle of, US. 
 
 Law of, 118. 
 
 Multiple, 343. 
 
 Total, 355. 
 Refraction, 350. 
 
 Cause of, 351. 
 
 Double, 383. 
 
 Index of, 362. 
 
INDEX. 
 
 Kelay and repeater, 264. 
 Kepulslon mutual, 13. 
 Resonance, 290. 
 Resonators, 291. 
 Resistance, Formula for, 202. 
 
 lutenial, 203. 
 
 External, 204. ' 
 Rest, 86, 87. 
 Resnitant force, 91. 
 
 S. 
 Shadows, 331. 
 Simple subfitanceB, 8. 
 Siphon, 72. 
 Siren, 299. 
 
 Solution of solldB, 37. 
 Sonometer, 303. 
 Sowid, Analysis of, 309. 
 
 bow it originates, 280.' 
 
 how it travels, 281. 
 
 Loudness of, 288. 
 
 media, 283. 
 
 Musical, 297. 
 
 Pitch of, 298. 
 
 Quality of, 309. 
 
 Keenforcement of, 290. 
 
 Befiection of, 285. 
 
 Refraction of, 287. 
 
 Synthesis of, 310. 
 
 Velocity of, 284. 
 
 what it is, 283. 
 Sounder, 264. 
 Sounding air-columns, 319. 
 
 plates, 321. 
 Sound-waves, 272, 274, 280. 
 Speaking tubes, 289. 
 Specific gravity, 80. 
 Spectra, Bright-line, 369. 
 
 Continuous, 368. 
 
 Dark-line, 370. 
 
 Heat and chemical, 373. 
 Spectrum analysis, 371. 
 
 Solar, 366. 
 Spectroscope, 368. 
 Stability of bodies, 99. 
 Steam engine, 175. 
 Stereopticon, 395. 
 Summary of elec. measurements, 206. 
 
 of mechanical tmlts and formulas, 127. 
 gun as a source of energy, 141. 
 
 Table of boiling points, 161. 
 
 of E.M.F., 205. 
 
 of indices of refraction. 353. 
 
 of melting points, 161. 
 
 of metric system, 399. 
 
 of natural tangents, 403. 
 
 of specific gravities, 402. 
 
 of specific heat, 172. 
 Telegraph, 263. 
 
 Fac-simile, 266. 
 Telegraphic alphabet, 266. 
 Telephone, Bell, 269, 318. 
 Telephone, Dolbear, 271. 
 
 Strhig, 318. 
 Telescope, Astronomical, 392. 
 Temperature, Absolute, 155. 
 
 defined, 141. 
 
 measured by expansion, 151. 
 Tenacity, 32. 
 Tension, 44. 
 
 Theory of exchanges, 390. 
 Thermo batteries, 235. 
 Thermopile, 236. 
 Thermo-dynamlcs, 174. 
 Thermometer, Air, 154. 
 
 Construction of, 151. 
 
 Oraduation of, 152. 
 Thermometry, 151. 
 Transformation of energy, 128, 129, 
 
 257. 
 Translucency, 328. 
 Transparency, 328. 
 Tubes, Speaking, 289. 
 
 V. 
 Undnlatory theory, 327. 
 
 Tacuum, Absolute, 56. 
 Variation of needle, 222. 
 Velocity, Accelerated, 104. 
 
 defined, 87. 
 
 of electric discharge, 258. 
 
 of light, 837. 
 
 of sound, 284, 292. 
 
 Unit of, 128. 
 Ventilation, 146. 
 
INDEX. 
 
 Ventral negment, 276. 
 Vibration, Direction of, 273. 
 
 of strings, 303. 
 
 Propagation of, 274. 
 
 Sound, 272. 
 Vibrations, Complex, 273, 806. 
 
 Composition of, 311. 
 
 forced, 295. 
 
 Stationary, 275. 
 
 Sympatlietic, 295. 
 Viscosity, 31. 
 Visual angle, 335. 
 Vocal organs, 323. 
 Volt, 205. 
 Voltaic arc, 259. 
 Voltameter, 198. 
 
 W. 
 
 Waves, Air, 282. 
 
 Interference of, 274, 294. 
 
 Longitudinal, 276. 
 
 Reflection of, 274. 
 
 Sound, 272, 274, 260. 
 
 Water, 276. 
 Wave-length, 274, 292. 
 
 Keasuring, 292. 
 Wave-lengths of light, 367. 
 Wave-Une, 274, 279. 
 Wave -motion, Apparatus to illus- 
 trate, 406. 
 Wave-propagation, 278. 
 Weber, 206. 
 
APPARATUS ADAPTED TO GAGE'S PHYSICS. 
 
 Immediately following the first appearance of the book, in Novem- 
 ber, 1882, the Publishers received many calls for apparatus especially 
 adapted to the carrying out of the plan of the book. It appearing 
 almost a necessity, Mr. Gage reluctantly consented to give some atten- 
 tion to the furnishing of schools with cheap and efficient apparatus, 
 thereby rendering it possible for every school in the land, however 
 limited its means, to teach this branch in a rational manner. In 
 future, he will devote a portion of his time to the study of (1) new 
 forms of apparatus, and (2) methods of making the same pieces, with 
 slight modifications, answer a variety of purposes. His popular 
 "little marvels," the New Porte-Lumifere, Seven in One Apparatus, 
 Eight in One Apparatus, improved Pascal's Vases, Bunsen Batteries, 
 Apparatus for making electrical measurements, etc., are a sufficient 
 testimony to his success thus far. 
 
 Only a minimum profit is charged on this apparatus, so that no 
 discounts are possible, and the school which has but a dollar to expend 
 can purchase on terms which will compare favorably with the lowest 
 net prices ever offered. A set of this apparatus will be kept on con- 
 stant exhibition at our office, 13 Tremont Place, Boston. 
 
 For price lists, and other information respecting the apparatus, 
 address 
 
 A. P. GAGE, English High School, Boston, Mass. 
 
 Unsolicited testimonial from L. B. Char'boimieT, Professor of Physics in the 
 University of Georgia. 
 
 The apparatus ordered from you has heen received to-day. Like all previ- 
 ously bought from you, it gives entire satisfaction. You are really doing an 
 excellent work for our schools in furnishing such apparatus as you do, and at 
 the most reasonable cost. I have had excellent opportunity to judge of the 
 . quality of your work, as I have under my charge an extensive collection of 
 apparatus bought from different makers here and in Europe. The apparatus 
 bought of you is used by the students of the lower class in the laboratory; 
 and hence I have been able to compare your work with that of other makers. 
 I feel it due you to testify to the excellence of your work. There is no reason 
 why physical science should not be now fully illustrated in our schools, when 
 the inexpensiveness of your apparatus brings it within the reach of the most 
 moderate means. 
 Athens, Ga., October 13, 1887. 
 
 GINN & COMPANY, Publishers, Boston, New York, and Ohioago. 
 
SCIENCE AND HISTORY. 
 
 NATURAL SCIENCE. 
 
 INTROD. PRICE 
 
 Everett : Vibratory Motion and Sound $ 2.00 
 
 Gage : Elements of Physics 1.12 
 
 Introduction to Physical Science 1.00 
 
 Hale : Little Flower-People .40 
 
 Hill : Questions on Stewart's Physics 35 
 
 Journal of Morphology (per vol.) 6.00 
 
 Knight : Primer of Botany 30 
 
 WilliamB : Introduction to Chemical Science 80 
 
 PHILOSOPHICAL SCIENCE. 
 
 Davidson : Rosmini's Philosophical System 2.50 
 
 Eickok- Philosophical Works 00 
 
 Ladd : Lotze's Outlines of Metaphysic 80 
 
 Lotze's Outlines of Philosophy of Religion . . .80 
 Lotze's Outlines of Practical Philosophy ... .80 
 
 Lotze's Outlines of Psychology 80 
 
 Lotze's Outlines of Esthetics 80 
 
 Lotze's Outlines of Logic 80 
 
 Seelye : Hickok's Mental Science (Empirical Psychology) . 1.12 
 Hickok's Moral Science 1.12 
 
 POLITICAL SCIENCE. 
 
 Clark: Philosophy of Wealth 1.00 
 
 Clark Sc Giddiugs : The Modern Distributive Process . (retail) .75 
 
 Maoy : Our Government . 70 
 
 Political Science Quarterly . . . . . (per vol.) 3.00 
 Seligman ; Railway Tariffs and the Interstate Law . (retail) .75 
 
 HISTORY. 
 
 Allen : Readers' Guide to English History .... .25 
 
 Andrade : Historia do Brazil 75 
 
 Fiske-Irviug : Washington and His Country 1.00 
 
 Halsey : Genealogical and Chronological Chart ... .25 
 
 Journal of Arohseology ..... (per vol.) 5.00 
 
 Judson : Caesar's Ajmy ' '. 1.00 
 
 Montgomery: Leading Facts of English History .... 1.00 
 
 English History Reader 60 
 
 Moore : Pilgrims and Puritans .60 
 
 Myers : Mediaeval and Modern History 1.60 
 
 Ancient History 1.40 
 
 Copies sent to Teachers for Examination, with a view to Introduction, 
 on receipt of Introduction Price. 
 
 GINN & COMPANY, PubUshers. 
 
 8T0N. NEW YORK. CHIC 
 
Mathematics.' 
 
 Intred, 
 Prices. 
 
 Byerly Differential Calculus $2.00 
 
 Integral Calculus 2.00 
 
 Glnn Addition Manual 1^ 
 
 HaUted Mensuration 1.09 
 
 Hardy Quaternions 2.00 
 
 Hill Geometry for Beginners 1.00 
 
 Spragne Bapid Addition .10 
 
 Taylor Elements of the Calculus 1.80 
 
 WentTTOrth Grammar School Arithmetic 75 
 
 Shorter Course in Algebra 1.00 
 
 Elements of Algebra 1.12 
 
 Complete Algebra l.*0 
 
 Plane Geometry 75 
 
 Plane and Solid Geometry 1.25 
 
 Plane and Solid Geometry, and Trigonometry 1.40 
 Plane Trigonometry and Tables. Paper. . .60 
 PI. and Sph. Trig., Surv., and Navigation . 1.12 
 
 PI. and Sph. Trig., Surv., and Tables 1.25 
 
 Trigonometric Formulas 1.00 
 
 iV^entworth & HtU : Practical Arithmetic 1.00 
 
 Abridged Practical Arithmetic 75 
 
 Exercises In Arithmetic 
 
 Part I. Exercise Manual 
 
 Part II. Examination Manual 35 
 
 Answers (to both Parts) 25 
 
 Exercises in Algebra 70 
 
 Part I. Exercise Manual •. . . .36 
 
 Part II. Examination Manual. . .' 35 
 
 Answers (to both Parts) 25 
 
 Exercises in Geometry 70 
 
 Five-place Log. and Trig. Tables (7 Tables') .50 
 
 Five-place Log. and Trig. Tables ( Comp. Ed. ) 1.00 
 
 Wentworth & Beed : First Steps in Number, Pupils' Edition .30 
 
 Teachers' Edition, complete .90 
 Parts I., II., and III. (separate), each .30 
 
 Wheeler Plane and Spherical Trig, and Tables 1.00 
 
 Copies sent to Teachers for examination, with a view to Introductier. 
 on receipt of Introduction Price. 
 
 GINN & COMPANY, Publishers. 
 
 BOSTON. NKW YORK. CHICAGO. 
 
BOOKS ON ENGLISH LITERATURE. 
 
 Allan. . 
 Arnold . . 
 Bancroft . 
 Bro-wne . 
 Fulton & 
 
 Oenung , 
 Qilmore . 
 Oinn . . . 
 
 Oummere 
 Hudson , 
 
 Johnson . 
 Lee .... 
 Martineau 
 Minto . . 
 
 Rolfe . . , 
 Scott . 
 
 Sprague 
 
 Swift. 
 Thorn. 
 
 . Reader's Guide to English History $ -2$ 
 
 . English Literature i.jo 
 
 , A Method of English Composition 50 
 
 . Shakespere Versification 25 
 
 Trueblood: Choice Readings ....... 1.50 
 
 Chart Illustrating Principles of Vocal Expression, 2.00 
 
 . Practical Elements of Rhetoric 1.25 
 
 . Outlines of the Art of Expression 60 
 
 , Scott's Lady of the Lake . . . Bds., .33 ; aotk, .50 
 Scott's Tales of a Grandfather . Btis., .40 ; Cloth, .50 
 
 . Handbook of Poetics i-oo 
 
 . Harvard Edition of Shakespeare : — 
 
 20 Vol. Edition. CloiA, retail 25.00 
 
 10 Vol. Edition. Cloth, retail 20.00 
 
 Life, Art, and Character of Shakespeare. 2 vols. 
 
 Cloth, retail 4.00 
 
 New School Shakespeare. Cloth. Each Play . .45 
 
 Old School Shakespeare, per play 20 
 
 Expurgated Family Shakespeare 10.00 
 
 Essays on Education, English Studies, etc. . . .25 
 
 Three Volume Shakespeare, per vol 1.25 
 
 Text-Book of Poetry 1.25 
 
 Text-Book of Prose 1.25 
 
 Pamphlet Selections, Prose and Poetry ... .15 
 
 Classical English Reader i.oo 
 
 . Rasselas » Bds., .30 ; Cloth, .40 
 
 . Graphic Chart of English Literature 25 
 
 , The Peasant and the Prince . . Bds., .35 ; Cloth, .50 
 . Manual of English Prose Literature . . . .1.50 
 
 Characteristics of English Poets 2.00 
 
 . Craik's English of Shakespeare 90 
 
 . Guy Mannering Bds., .60 ; Cloth, .75 
 
 Ivanhoe Bds., .60 ; Cloth, .75 
 
 Talisman Bds., .50 ; Cloth, .60 
 
 Rob Roy Bds., .60 ; Cloth, .75 
 
 . Milton's Paradise Lost, and Lycidas 45 
 
 Six Selections from Irving's Sketch-Book 
 
 Bds., .25 ; Cloth, .35 
 
 Gulliver's Travels Bds., .30 ; Chth, .40 
 
 . Shakespeare and Chaucer Examinations ... .00 
 
 Copies Bent to Teachers for Examination, frith a Tlew to Introdnctlon, 
 on receipt of the Introduction Price given abore. 
 
 CINN & COMPANY, Publishers, 
 
 Boston, New York, and Chicago.